You may notice some images loading slow across the Open Collections website. Thank you for your patience as we rebuild the cache to make images load faster.

UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Characterizing patches of primary visual cortex with minimal bias Spacek, Martin A. 2015

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Notice for Google Chrome users:
If you are having trouble viewing or searching the PDF with Google Chrome, please download it here instead.

Item Metadata


24-ubc_2015_september_spacek_martin.pdf [ 21.86MB ]
JSON: 24-1.0166333.json
JSON-LD: 24-1.0166333-ld.json
RDF/XML (Pretty): 24-1.0166333-rdf.xml
RDF/JSON: 24-1.0166333-rdf.json
Turtle: 24-1.0166333-turtle.txt
N-Triples: 24-1.0166333-rdf-ntriples.txt
Original Record: 24-1.0166333-source.json
Full Text

Full Text

Characterizing patches of primary visual cortex with minimal biasbyMartin A. SpacekBSc Engineering Physics, University of Alberta, 2001a thesis submitted in partial fulfillmentof the requirements for the degree ofDoctor of Philosophyinthe faculty of graduate and postdoctoral studies(Neuroscience)The University of British Columbia(Vancouver)June 2015c© Martin A. Spacek, 2015AbstractThe brain is highly complex, and studying it requires simplifying experiments, analyses, and the-ories. New techniques can capture more of the brain’s complexity while reducing biases in ourunderstanding of how it works.This thesis describes experiments in primary visual cortex of anesthetized cat, using high-densitysilicon multisite electrodes to simultaneously record from as many neurons as possible across allcortical layers, thereby characterizing local cortical populations with minimal bias. Recordings weremaintained for many hours at a time, and included both spontaneous and stimulus-evoked periods,with a wide variety of naturalistic and artificial visual stimuli. A new “divide-and-conquer” spikesorting method translated correlated multisite voltages into action potentials of spatially localized,isolated neurons. This method tracked neurons over periods of many hours despite drift, anddistinguished neurons with firing rates < 0.05 Hz.Neuron physiology was reasonably normal and mostly agreed with accepted principles of visualcortex, but there were exceptions. Surprisingly, firing rates across the population followed a lognor-mal distribution, and 82% of neurons had mean firing rates < 1 Hz. Also surprisingly, orientationtuning strength across the population was inversely correlated with log firing rate. Finally, therewas evidence for neural shift work: over long durations, as some neurons became silent, othersbecame active. To break down analyses by cell type, neurons were classified by their temporalspike shape and receptive field.Responses to repeated natural scene movie clips consisted of unique patterns of remarkablysparse, temporally precise (20 ms wide), reliable events. Mean pairwise correlations between neu-rons, as measured between trial-averaged responses to natural scene movies, were weakly positive.Correlations between simple and complex cells were lower — and between complex cells were higher— than expected, challenging the hierarchical model of complex cells. Cortical state was classi-fied according to the local field potential, revealing greater natural scene movie response precision,sparseness, and reliability during the synchronized than desynchronized cortical state, contrary toreports in rodents.The open-ended, inclusive, high-dimensional experiments and analyses described here make fewassumptions, potentially leading to more insightful theories of brain function than hypothesis-drivenresearch alone.iiPrefaceSome of the methods described in Sections 2.1–2.3 and Appendix C were published in Blanche etal. (2005) and Spacek et al. (2009), respectively. The clustering technique described in Section 3.9.1and the overlap index described in Section 3.10.2 were devised by Nicholas Swindale and publishedin Swindale and Spacek (2014). Experiments on one animal (ptc15, Table 2.1) were done jointlywith Tim Blanche, while the rest were done jointly with Nicholas Swindale. Experimental workwas covered by UBC Ethics Certificates A04-0098 and A11-0280. The author declares no conflictsof interest.iiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xNote to Reader . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.1 General setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2 Polytrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.3 Data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.4 Visual stimulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.5 Histology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213 Spike Sorting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.1.1 Existing methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.1.2 Clustering methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.2 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.2.1 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.3 Preprocessing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293.4 Spike detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.5 Spatial localization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.6 Initial channel split . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36iv3.7 Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.8 Dimension reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.9 Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.9.1 Gradient ascent clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.10 Cluster verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.10.1 Undersplitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.10.2 Oversplitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513.10.3 Misassignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.10.4 Duplicate spikes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543.11 Autocorrelograms & refractory periods . . . . . . . . . . . . . . . . . . . . . . . . . . 543.12 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553.13 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.13.1 Spike detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 573.13.2 Dimension reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593.13.3 Clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603.13.4 Autocorrelograms & refractory periods . . . . . . . . . . . . . . . . . . . . . . 623.13.5 Drift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624 Basic Physiology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634.2 Neuron yields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634.3 Firing rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654.4 Templates & positions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694.5 Orientation tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 784.6.1 Neuron yields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 784.6.2 Firing rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 814.6.3 Templates & positions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 844.6.4 Orientation tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 875 Cell Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 895.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 895.2 Spike shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 915.3 Spatial extent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 955.4 Receptive field type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 955.5 Cell type comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1015.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1035.6.1 Spike shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1035.6.2 Spatial extent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106v5.6.3 Receptive field type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1065.6.4 Cell type comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1096 Natural scenes & cortical states . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1106.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1106.2 Natural scene movie responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1116.3 Natural scene movie response correlations . . . . . . . . . . . . . . . . . . . . . . . . 1156.4 Cortical states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1216.5 UP/DOWN phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1266.6 Natural scene movie responses vs. cortical state . . . . . . . . . . . . . . . . . . . . . 1296.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1376.7.1 Natural scene movie responses . . . . . . . . . . . . . . . . . . . . . . . . . . 1376.7.2 Natural scene movie response correlations . . . . . . . . . . . . . . . . . . . . 1416.7.3 Cortical states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1446.7.4 UP/DOWN phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1466.7.5 Natural scene movie responses vs. cortical state . . . . . . . . . . . . . . . . . 1486.7.6 Clustering cortical states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1507 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156Appendix A Receptive field stability . . . . . . . . . . . . . . . . . . . . . . . . . . . 177Appendix B Spike correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178Appendix C Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179C.1 dimstim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179C.2 spyke . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181C.3 neuropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184Appendix D Impedance meter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186Appendix E ACSF recipe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188viList of TablesTable 2.1 Cats used in this study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10Table 2.2 Tracks recorded in this study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Table 2.3 54-channel polytrode designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14Table 2.4 Stimulus sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20Table 4.1 Neuron yield. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64Table 5.1 Spike & receptive field type counts . . . . . . . . . . . . . . . . . . . . . . . . . . 95Table 6.1 Counts of cells responsive to natural scene movies . . . . . . . . . . . . . . . . . . 113Table E.1 ACSF ingredients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188viiList of FiguresFigure 2.1 General experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11Figure 2.2 Silicon polytrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15Figure 2.3 50 ms of high-pass voltage waveform data . . . . . . . . . . . . . . . . . . . . . . 16Figure 2.4 Phase locking of V1 to a low refresh CRT monitor . . . . . . . . . . . . . . . . . 18Figure 2.5 Example frames from natural scene movie sets . . . . . . . . . . . . . . . . . . . 20Figure 3.1 Motivation for careful spike sorting . . . . . . . . . . . . . . . . . . . . . . . . . . 23Figure 3.2 Multichannel template matching . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Figure 3.3 Example spikes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31Figure 3.4 Spike detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33Figure 3.5 Spike propagation in space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35Figure 3.6 Spatial locations & Vpp of spikes . . . . . . . . . . . . . . . . . . . . . . . . . . . 37Figure 3.7 Spike misalignment can result in artifactual clusters . . . . . . . . . . . . . . . . 39Figure 3.8 Spike misalignment can result in non-Gaussian clusters . . . . . . . . . . . . . . 40Figure 3.9 Channel selection affects clusterability . . . . . . . . . . . . . . . . . . . . . . . . 42Figure 3.10 ICA separates clusters with large size ratios better than PCA . . . . . . . . . . . 44Figure 3.11 GAC dependence on σc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47Figure 3.12 Plotting clusters in time is necessary to check for drift. . . . . . . . . . . . . . . . 51Figure 3.13 Examining autocorrelograms for refractory period violations . . . . . . . . . . . . 56Figure 4.1 Mean firing rates had a lognormal distribution . . . . . . . . . . . . . . . . . . . 66Figure 4.2 Coarse firing rates vs. time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68Figure 4.3 Single channel & multichannel templates . . . . . . . . . . . . . . . . . . . . . . . 70Figure 4.4 Cell positions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71Figure 4.5 Spike parameters vs. time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73Figure 4.6 Smoothed spike parameters vs. time . . . . . . . . . . . . . . . . . . . . . . . . . 74Figure 4.7 Distributions of changes in y position over time for all cells . . . . . . . . . . . . 75Figure 4.8 Orientation tuning curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77Figure 4.9 Orientation tuning strength vs. mean firing rate . . . . . . . . . . . . . . . . . . 78Figure 4.10 Orientation preference, tuning strength & normalized depth . . . . . . . . . . . . 80Figure 5.1 A demonstration of the potential dangers of threshold-based metrics . . . . . . . 93Figure 5.2 Temporal spike shape measures & classification . . . . . . . . . . . . . . . . . . . 94Figure 5.3 Distributions of spatial extent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96viiiFigure 5.4 Example drifting bar & grating raster plots of simple & complex cells . . . . . . 97Figure 5.5 Spike triggered average to m-sequence . . . . . . . . . . . . . . . . . . . . . . . . 98Figure 5.6 Spatiotemporal receptive fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100Figure 5.7 Spatial distribution of cell types . . . . . . . . . . . . . . . . . . . . . . . . . . . 102Figure 5.8 Comparison of receptive field type vs. spike type . . . . . . . . . . . . . . . . . . 103Figure 5.9 Mean firing rate & activity duration distributions vs. cell type . . . . . . . . . . 104Figure 6.1 Natural scene movie responses (1) . . . . . . . . . . . . . . . . . . . . . . . . . . 113Figure 6.2 Venn diagram of active & responsive cells . . . . . . . . . . . . . . . . . . . . . . 113Figure 6.3 Responsive cell counts vs. cell type . . . . . . . . . . . . . . . . . . . . . . . . . . 114Figure 6.4 Natural scene movie responses (2) . . . . . . . . . . . . . . . . . . . . . . . . . . 117Figure 6.5 Temporally precise response events can be shared by disparate neurons . . . . . 118Figure 6.6 Natural scene movie PSTH correlations . . . . . . . . . . . . . . . . . . . . . . . 119Figure 6.7 Matrices of natural scene movie mean PSTH correlations vs. cell type . . . . . . 120Figure 6.8 Power spectral density and amplitude of deep layer LFP . . . . . . . . . . . . . . 122Figure 6.9 Cortical state (1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124Figure 6.10 Cortical state (2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126Figure 6.11 Synchrony index distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127Figure 6.12 Scatter plots of multiunit activity vs. synchrony index . . . . . . . . . . . . . . . 128Figure 6.13 Up & down phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130Figure 6.14 Natural scene movie responses vs. cortical state (1) . . . . . . . . . . . . . . . . . 131Figure 6.15 Natural scene movie responses vs. cortical state (2) . . . . . . . . . . . . . . . . . 132Figure 6.16 Responsive inactive cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134Figure 6.17 Response precision, sparseness & reliability vs. cortical state . . . . . . . . . . . 135Figure 6.18 PSTH correlations vs. cortical state . . . . . . . . . . . . . . . . . . . . . . . . . 138Figure 6.19 PSTH correlation differences between cortical states . . . . . . . . . . . . . . . . 139Figure 6.20 Complex cell models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144Figure A.1 Long duration receptive field stability . . . . . . . . . . . . . . . . . . . . . . . . 177Figure B.1 Spike train binary code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178Figure C.1 Example dimstim script . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180Figure C.2 Visualizing time series voltage waveforms with spyke . . . . . . . . . . . . . . . . 182Figure C.3 Sorting detected spikes with spyke . . . . . . . . . . . . . . . . . . . . . . . . . . 183Figure C.4 GAC run time vs. σc & N . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184Figure C.5 Neuropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185Figure D.1 Impedance meter circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186ixList of Abbreviations1Dsep one-dimensional separation metricA1 primary auditory cortexα-BTX α-bungarotoxinACSF artificial cerebrospinal fluidAC area centralisADC analog-to-digital converterAHP afterhyperpolarizationCRF classical receptive fieldCRI constant rate infusionCRT cathode ray tubeCSF cerebrospinal fluidCSD current source densitydH2O deionized waterDJS Jensen-Shannon divergenceDKL Kullback-Leibler divergenceEEG electroencephalogramEM expectation-maximizationFFT fast Fourier transformfMRI functional magnetic resonance imagingfps frames per secondFWHM full width half maximumGAC gradient ascent clusteringGMM Gaussian mixture modelxGUI graphical user interfaceHEPES 4-(2-hydroxyethyl)piperazine-1-ethanesulfonic acid (C8H18N2O4S)HC hierarchical clusteringIC independent componentICA independent component analysisIM intramuscularISI inter-spike intervalIP intraperitonealIV intravenousLGN lateral geniculate nucleusLFP local field potentialLM Levenberg-MarquardtM1 primary motor cortexM2 secondary motor cortexMEA multichannel electrode arrayMT middle temporal cortexMUA multiunit activityNDsep N-dimensional separation metricPC principal componentPCA principal component analysisPFC prefrontal cortexPPT pedunculopontine tegmentaPSTH peristimulus time histogramPSD power spectral densityPSP postsynaptic potentialxiRAM random-access memoryREM rapid eye movementRF receptive fieldRGC retinal ganglion cellRGP rigid gas permeableRMS root mean squareRPV refractory period violationS1 primary somatosensory cortexSI synchrony indexSPC superparamagnetic clusteringSTA spike-triggered averageSTC spike-triggered covarianceSTRF spatiotemporal receptive fieldV1 primary visual cortexxiiNote to ReaderGiven the inherent limitations of extracellular electrophysiology, the terms “cell” and “neuron”should be considered synonymous with “unit” throughout this thesis.For Chapters 4–6, methods and results are combined within each main section, followed by a singlediscussion at the end of each chapter.Chapter, section, appendix, figure, table, and equation references in this document are activehyperlinks, as are citations and abbreviations. The page numbers in the table of contents, lists offigures and tables, and bibliography are also hyperlinked. Chapters, sections, and appendices arebookmarked in the PDF.A digital version of this document will be made available at parents, for their constant support over all the years.My supervisor, Nicholas Swindale, whose door has always been open, and for generously supportingme for so many years. Nick provided extensive training, as well as critical support during animalexperiments. Most of the ideas, methods, and results in this thesis are a direct result of interactingwith Nick.Tim Blanche for introducing me to the use of polytrodes, and for setting up the recording systemand writing the acquisition software “Surf”.Catalin Mitelut for his work on spike shape clustering, showing that the width of the second peakis more informative than that of the first peak, and for preliminary spike sorting of data brieflymentioned in Section 6.7.5.My girlfriend, Annay, for putting up with me during thesis writing.This thesis depended heavily on free, open source software including Linux, Python, Geany, Git,LATEX, BibTEX, Inkscape, GIMP, and qpdfview. It also benefited from a steady stream of electronicmusic.This work was supported by funding from the Canadian Institutes of Health Research (CIHR) andthe Natural Sciences and Engineering Research Council of Canada (NSERC).xiv1 Introduction“Brain cells fire in patterns.” — How the brain works, in 5 words or less.Steven Pinker, The Colbert Report (2007)From insects to humans, brains are incredibly complicated computational machines. They maybe the most complex systems in the known universe, and studying such systems is an exercise inmanaging complexity. For most of neurophysiological history, much of this complexity has beendealt with by, in essence, ignoring it. The technology to simultaneously monitor the activity ofmultiple neurons is relatively new, so by necessity, the interactions between neurons — perhapsthe brain’s most powerful feature — were long unexamined. Low density short duration extracel-lular recordings cannot distinguish between missing neurons and silent neurons, so again, partlyby necessity, low firing rate neurons have mostly been ignored. High dimensional naturalistic stim-uli are more complicated than low dimensional artificial stimuli, so the latter were, until recently,overwhelmingly used, and the responses to the former remain underappreciated. And finally, evenwhen asleep or lightly anesthetized, the brain is likely performing a multitude of different simulta-neous tasks. Yet when characterizing neural activity in a supposedly controlled way, over seeminglyidentical trials with identical stimuli or tasks, neural activity can vary substantially from one trialto the next. This variability is often labelled “noise”, and is dealt with by averaging across trials.Although convenient for the neurophysiologist, doing so ignores the reality that the brain functionson a continuous basis. A brain’s life is one continuous single trial, and this thesis is an attempt totreat it that way.1.1 BackgroundAction potentials (spikes) are the currency of the brain. A spike allows one neuron to communicatevia its axon to thousands of downstream neurons the precise moment at which its membranepotential threshold has been exceeded. Spikes are significant and energetically costly events (Attwelland Laughlin, 2001; Lennie, 2003). They can be recorded intracellularly with an electrode placeddirectly on or within the neuron’s cell membrane, or extracellularly with an electrode placed outsidebut very near the membrane. Perhaps the first to isolate single spikes from single neurons (units)were Adrian and Bronk (1928), who dissected away the phrenic nerve in anesthetized rabbit untilonly one axon within the nerve remained intact. Removing all other possible transmitting axonswithin the nerve allowed for unambiguous extracellular recordings from single motoneuron axonsusing simple, relatively large brush electrodes placed on the nerve at either end of the dissection.This revealed that single-unit firing rates of motoneurons in the spinal cord control the force ofdiaphragm contraction critical to breathing. Hodgkin and Huxley (1939) later performed the first1in vitro intracellular recordings (which guarantee single-unit isolation) using a blunt 100 µm widewire electrode inserted longitudinally into 500 µm diameter squid giant axon. This led to theirwidely-used mathematical model of spike initiation and propagation (Hodgkin and Huxley, 1952).However, if the goal is to record isolated spikes from neurons within the intact brain, removingall other units to gain single-unit resolution or limiting oneself to squid giant axon is not viable.Recording extracellularly but very close to the neuron’s soma or axon hillock, where its spikes aregenerated, minimizes contamination by spikes from other nearby cells or axons. To further improvesingle-unit resolution, extracellular recordings can be filtered into high- and low-pass frequencybands. High-pass frequencies (> 300 Hz) capture most of a spike’s signal. Low-pass frequencies(< 100 Hz), referred to as the local field potential (LFP), are the sum of synaptic (Linde´n et al.,2011) or spiking (Buzsa´ki et al., 2012; Reimann et al., 2013) activity of the wider neural population.While not useful for single-unit isolation, the LFP can be used to monitor the overall activity of aregion of cortex (Katzner et al., 2009; Kelly et al., 2010; Harris and Thiele, 2011).Recording either intracellularly or extracellularly directly from intact neurons requires veryfine micron-scale electrodes with high input impedance, such that they do minimal damage anddo not perturb the very currents and potentials they measure. For extracellular electrodes, highimpedance also rejects the noisy extracellular signal from the multitude of neurons located furtheraway from the electrode. The first such microelectrodes were fine (25 µm tip) glass micropipettes,used by Renshaw et al. (1940) to extracellularly isolate single units in intact, anesthetized cathippocampus. Ling and Gerard (1949) used even finer tapered (< 1 µm tip) glass micropipettesintracellularly. These were fine enough for the cell membrane to seal around them after insertion,minimizing damage.Glass micropipettes have the advantage of being easily shaped under heat and tension (pulling)to form very fine tips, but they are brittle and delicate. Wire electrodes are more durable, butwere difficult to sharpen. Hubel (1957) developed a way of electrolytically sharpening the tips ofinsulated tungsten wire down to < 0.5 µm, and Green (1958) did the same with stainless steel wire.Sharp wire electrodes allowed for larger scale single-unit investigations, revealing retinotopicallyorganized, localized, oriented, direction selective receptive fields (RFs) of single units in cat andmonkey primary visual cortex (V1), as well as the existence of visual stimulus feature maps acrossthe surface of V1 (Hubel and Wiesel, 1959, 1962, 1968).Hubel and Wiesel also found that single-unit RFs in V1 could be categorized into two types:simple and complex (Hubel and Wiesel, 1962). Simple cells have oriented RFs with alternating,spatially distinct on and off subregions. This gives them spatial phase preference for light and darkoriented stimuli. Complex cells have spatially overlapping subregions, and are therefore invariantto spatial phase, but they still maintain orientation preference, making them slightly more generalthan simple cells. To explain this, Hubel and Wiesel proposed a hierarchical model in which complexcells pool from many different simple cells with similar orientation preference but different spatialphase preferences, resulting in spatial phase invariance (Figure 6.20A). This has been the dominant2model of complex cells ever since.The next major advances in recording technology were stereotrodes and tetrodes, which consistof twisted pairs or tetrads of insulated sharp wire electrodes, respectively, with tips spaced about25 µm apart (McNaughton et al., 1983; O’Keefe and Recce, 1993; Wilson and McNaughton, 1993).Increasing the number of closely spaced electrodes improves single-unit isolation by sampling theextracellular potential at multiple points in space, thereby increasing the chance that spike-inducedextracellular potentials from even the most closely spaced neurons will appear sufficiently differenton at least one electrode channel to separate their (multichannel) spike waveforms (Gray et al.,1995; Harris et al., 2000). However, this benefit comes at the cost of added complexity. Detectingextracellular spikes above noise and separating spikes from multiple neurons (spike sorting) ischallenging enough. Doing so for many closely spaced electrode sites with correlated voltages iseven more difficult.Contemporary use of tetrodes often combines many of them into a circular or conical array,such that they all point toward the same region of neural tissue (Wilson and McNaughton, 1993;Jog et al., 2002; Battaglia et al., 2009; Voigts et al., 2013). The depth of each tetrode is individuallycontrolled via independent screw drives, each of which is adjusted to maximize its single-unit yield.Tetrode arrays increase yield by simultaneously recording from many more neurons than a singletetrode. However, tetrodes in an array rarely, if ever, come close enough to one another to isolatespikes from the same or immediately neighbouring neurons, and their relative positions are difficultto infer. Therefore, tetrode arrays cannot fully sample a contiguous volume of brain. Moreover,because neurons that fire at a high rate are easier to isolate than those that fire at a low rate,and due to the desire to maximize neuron yield, arrays of individually adjustable tetrodes may bebiased towards high rate neurons, and may neglect the majority of neurons which fire at very lowaverage rates (Lennie, 2003; Olshausen and Field, 2005; Shoham et al., 2006).A more recent advance in extracellular single-unit electrophysiology is high-density silicon mul-tisite electrodes (polytrodes) (Drake et al., 1988; Henze et al., 2000; Harris et al., 2000; Csicsvariet al., 2003; Blanche et al., 2005; Bere´nyi et al., 2014). These are arrays of ∼ 15 µm diametermetal (iridium, platinum or gold) electrode sites on silicon shanks, manufactured using micron-scale deposition and etching technology adapted from the integrated circuits industry. The siliconshanks are often thin (∼ 15 µm) to minimize damage, but their widths and lengths can rangewidely (20–200 µm & 500–6000 µm respectively). Sites are arranged in a 1D, 2D, or even 3D (Duet al., 2009) array in almost any conceivable spatial pattern. Site spacing can be < 20 µm, but ismore commonly > 30 µm. Both single- and multi-shank designs exist with 1–64 electrode sites pershank, and the potential for many more.One major benefit of polytrodes over tetrode arrays is that, like tetrodes, the electrode sitedensity is high, but unlike tetrode arrays, polytrodes can maintain consistently high site densityover many hundreds of microns, even millimeters. Another related benefit of polytrodes is thatthe precise relative location of each electrode site is fixed and known. As a result, correlated spike3signals from neighbouring electrode sites can be used to help localize the isolated neuron, and therelative locations of all neurons isolated by the polytrode can therefore be inferred (Henze et al.,2000; Csicsvari et al., 2003; Blanche et al., 2005; Blanche, 2005; Du et al., 2009). The cost of havinga fixed array of electrode sites is that neuron yield cannot be maximized by individually positioningeach site, or group of sites, as it can with tetrode arrays. Only the entire array can be moved upor down. However, this cost can be considered a benefit because it may reduce bias towards highfiring rate neurons.All of the above recording methods involve inserting a device into the brain, thereby causing atleast some micro-scale tissue damage. The most recent advance in large-scale recording of neuralpopulations, two-photon calcium imaging (Denk et al., 1990; Svoboda et al., 1997; Helmchen andDenk, 2005; Kerr et al., 2005; Ohki et al., 2005, 2006), provides an alternative in which the brainremains untouched and therefore undamaged. Neurons are either loaded with a photosensitive cal-cium indicator, or are genetically engineered to express it endogenously (Wallace et al., 2008; Lu¨tckeet al., 2010). When stimulated with two-photon laser scanning, the calcium indicator fluorescesas a function of intracellular calcium concentration, which itself is a function of spiking activity,allowing for large-scale 3D optical readout of spiking activity of a complete neural population. Thelaser scanning used for readout can image a volume of superficial cortex ∼ 300 µm on a side (Ohkiet al., 2006), and several hundred microns deep. Imaging depth has steadily improved over time,and has now reached as much as 800 µm (Mank et al., 2008; Mittmann et al., 2011). Due to dif-ferences in cortical thickness and transparency, two-photon calcium imaging works best in rodentsor immature cats, and is perhaps not as well suited for adult cats whose primary visual cortex is∼ 1500 µm thick (Beaulieu and Colonnier, 1985; Jones and Peters, 1987; Payne and Peters, 2001).More importantly, intracellular calcium signals are slow, with decay time constants on the order ofdozens or hundreds of milliseconds (Koester and Sakmann, 2000; Stosiek et al., 2003; Kerr et al.,2005; Wallace et al., 2008; Sasaki et al., 2008), making detection of precise spike times in arbitraryspike patterns (including bursts) difficult, if not impossible. Finally, the equipment required fortwo-photon calcium imaging (laser, scanning mechanism, optics, detectors) is currently much moreexpensive than the equipment required for polytrode recordings.Why is recording precise spike times so important? A long-standing hypothesis in neuroscienceis Hebb’s cell assembly hypothesis (Hebb, 1949). A cell assembly is a spatially distributed set ofneurons whose transient, temporal pattern of activation might serve as the neural substrate forstimuli, memories, concepts, decision making, and motor actions. The appeal of cell assemblies liesin two main attributes. First, their spatial distribution means that they degrade gracefully upondamage to a specific location in the brain. Second, since a neuron can participate in one of manydifferent cell assemblies, the combinatorics allow for nearly unlimited representational capacity,despite a limited number of neurons. Definitively proving the cell assembly hypothesis will requiresimultaneously recording precise spike times of many more neurons than is currently possible.The appeal of cell assemblies is closely related to the appeal of spike timing as a coding mech-4anism. Precise spatiotemporal spike patterns in neuronal recordings could be signatures of cellassemblies at work (Hopfield, 1995; Engel et al., 2001; Harris, 2005). Furthermore, the psychophys-ically measured speed of object categorization in primates and the conduction velocity of spikesfrom one cortical area to the next put a hard upper limit on the number of spikes (∼ 1–2) thatneurons in each area have time to send to the next area (Thorpe et al., 1996; Kirchner and Thorpe,2006). VanRullen and Thorpe (2002) go on to argue that this is insufficient for downstream areasto calculate the firing rates of their inputs, and that instead coding must be based on spike arrivaltime. In addition, sparse coding theory (Olshausen and Field, 1996, 2004) suggests that for variousreasons including energy efficiency and representational capacity, only a small fraction of neuronsare active at any time, and that mean firing rates are very low. Sparse coding therefore implicitlyfavours spike time coding over spike rate coding.Experimental evidence in support of precise spike timing is accumulating (Burr and Ross, 1979;Gray et al., 1989; Mainen and Sejnowski, 1995; Vaadia et al., 1995; Bair and Koch, 1996; Harriset al., 2002, 2003; Salami et al., 2003; Wehr and Zador, 2003; Ikegaya et al., 2004; Johansson andBirznieks, 2004; Luczak et al., 2007; Gollisch and Meister, 2008; Havenith et al., 2011; Mackeviciuset al., 2012; Luczak et al., 2013; Garcia-Lazaro et al., 2013), but the debate over spike rate codingvs. spike time coding is far from settled (Softky, 1995; Shadlen and Newsome, 1998; Oram et al.,1999; Baker and Lemon, 2000; Latham et al., 2006; London et al., 2010), making this a fertile areaof study. Both types of coding are likely used for different purposes, and there is no hard lineseparating the two. The debate is mostly about just how fine a temporal scale of integration thebrain might use for coding.Why focus on extracellular and not intracellular electrophysiology for large scale recordings?The benefit of intracellular recording is that it directly measures cell membrane potential, and allowsnot only detection of spikes with high signal to noise ratio and no risk of spike contamination fromneighbouring cells, but also detection of excitatory and inhibitory postsynaptic potentials (PSPs).But since intracellular electrodes touch or pierce the cell membrane and are very sensitive to motion,successfully recording (“holding”) one cell intracellularly in vivo for hours at a time is challenging.Holding multiple cells simultaneously is that many times more difficult. Ko et al. (2011) recordedintracellularly from 4 cells and Perin et al. (2011) from 12 cells simultaneously, yet these impressivenumbers are much lower than for large-scale extracellular recordings, which currently record fromdozens or hundreds of neurons at once (Csicsvari et al., 2003; Segev et al., 2004; Buzsa´ki, 2004;Blanche et al., 2005; Bere´nyi et al., 2014). Moreover, breaching the cell membrane can alterthe cell’s electrophysiology, and ultimately reduce its lifespan. Therefore, large scale single-unitmultielectrode recordings have been mostly limited to extracellular recordings.Why perform acute recordings in anesthetized animals instead of chronic recordings in awakeanimals? Acute recordings are generally simpler and require fewer resources than chronic recordings.The same holds for anesthetized vs. awake animals. Acute experiments face no ethical concernsabout subject pain upon waking, and have less need for stringent sterile techniques during surgery.5In acute recordings, anesthesia is required for two reasons: ethical, to eliminate pain and stress;and practical, to keep the animal still during recordings. The downside of anesthesia is that brainactivity may not be as naturalistic as in an awake head-restrained or freely behaving animal, andmay therefore lead to biased data and conclusions. Although it is possible that precise neuronalspike timing may be disrupted during anesthesia (Swindale, 2003), V1 is an early cortical area andmay not be as affected by anesthesia as higher level areas. A study by Vincent et al. (2007) foundthat, at least at the spatial and temporal resolution of functional magnetic resonance imaging(fMRI), patterns of spontaneous activity in monkey cortex, including V1, were independent ofdepth of anesthesia. Furthermore, there is strong evidence that cortical state (typically measuredby LFP frequency content) can vary considerably during both anesthesia and wakefulness (Arieliet al., 1996; Petersen et al., 2003; Fiser et al., 2004; Harris and Thiele, 2011; Marguet and Harris,2011; Sakata and Harris, 2012; Xu et al., 2012). Considering cortical state may therefore be evenmore important than considering whether the animal is awake or anesthetized.There are at least two types of cortical state (Berger, 1929; Harris and Thiele, 2011). The first isthe synchronized state, in which large groups of neurons tend to fire in synchrony, resulting in largelow-frequency extracellular fluctuations as measured by the electroencephalogram (EEG) or LFP.The second is the desynchronized state, in which neurons fire more independently, and the resultingextracellular fluctuations are lower in amplitude and higher in frequency. The synchronized stateoccurs during deep anesthesia, slow-wave sleep, and quiet wakefulness, while the desynchronizedstate occurs during light anesthesia, rapid eye movement (REM) sleep, and alert wakefulness.Because both cortical states can occur during both wakefulness and anesthesia, controlling forcortical state may allow results from anesthetized animals to be directly applicable to those fromawake animals (Arieli et al., 1996; Petersen et al., 2003; Fiser et al., 2004; Harris and Thiele, 2011).Why study V1, and why use cats? Early sensory areas are the information gateways to the brain.This may make them easier to study and understand than higher-level multimodal and cognitiveareas. Vision is the richest and most complex sensory modality, with over 100 million photoreceptorsalone in human retina dedicated to detecting incident rays of light (Kandel et al., 2012). Despitedecades of work, vision research is full of unsolved computational problems. Replicating the brain’snatural visual capabilities in machines has proven to be very difficult, although progress is beingmade (Lowe, 2004; Krizhevsky et al., 2012). Cats have a long history of study in vision. They havegood acuity, and as predators have forward facing eyes like humans. Cats are also widely available.However, long-duration large scale recordings combined with a rich set of visual stimuli can bothhelp to reduce the number of animals needed.V1 has mostly been investigated using simple artificial stimuli, such as drifting and flashedspots, bars and gratings, as well as spatiotemporal white noise, all of which help to characterizethe RFs of neurons in V1. Each neuron has its own combination of stimulus preferences forretinotopic position, orientation, spatial and temporal frequency, and even direction of motion.These preferences are quantified using tuning curves, which plot trial-averaged firing rate as a6function of stimulus parameter. Although convenient for characterizing such preferences, theseartificial stimuli are not behaviourally relevant. The brain did not evolve in an environment ofbars and gratings. It evolved in a 3D environment full of physical objects with texture, occlusion,perspective, lighting, shadow, motion, and parallax. The statistics of natural scene movies are verydifferent from those of artificial stimuli (Olshausen and Field, 1996, 2000). Furthermore, naturalvision involves full field stimulation, and is not restricted to a small portion of visual space as isoften the case with artificial stimuli.It should therefore not come as a great surprise that the spiking responses of neurons in V1 tofull field naturalistic stimuli are very different from responses to spatially localized artificial stimuli(Vinje and Gallant, 2000, 2002; Yen et al., 2007; Haider et al., 2010; Herikstad et al., 2011), orthat response models based on artificial stimuli do a poor job of predicting responses to naturalisticstimuli (Olshausen and Field, 2005; Carandini et al., 2005). Specifically, responses to naturalisticstimuli are sparser and more temporally precise and reliable than responses to artificial stimuli.These are still recent revelations that remain underappreciated.1.2 SummaryThis thesis characterizes local neuronal populations in anesthetized cat V1 in a wider manner thanusual. Extensive efforts were made to minimize bias at every step of the way, from stimulation,recording and spike sorting, to response characterization, cell typing, and cortical states.Chapter 2 describes the experimental methodology. Various strategies were used to help min-imize bias during recording. Extracellular waveform data were recorded using single shank poly-trodes spanning most or all layers of cat visual cortex. Compared to wire or tetrode arrays withindividually positionable recording elements, the fixed relative electrode site positions of polytrodesmay reduce potential biases towards specific cell types, including high firing rate cells. Recordingdurations were many hours long in a given position (track). For each track, a host of both artificialand naturalistic stimuli were used, in addition to spontaneous recordings. For artificial stimuli withtunable parameters, a full range of stimulus parameters (such as orientation) were used to minimizebias. Both artificial and natural scene movie stimuli spanned as much of the visual field as possible,well outside the classical RFs of all recorded neurons.Chapter 3 tackles the methodological challenge of high-density multichannel spike sorting. Be-fore performing any further analysis, spikes must be detected and sorted from the raw extracellularvoltage waveform data acquired during the experiment. Spike sorting can lead to a range of bi-ases, such as exclusion of low firing rate cells, or incorrect grouping together of low and high firingrate cells. Most critically, like tetrodes, polytrodes with closely spaced electrode sites present achallenge for spike sorting in that spikes tend to appear on several channels at a time. Yet, un-like tetrodes, polytrodes sample a long and potentially contiguous volume of brain. Existing spikesorting methods cannot deal with all of these challenges, so a novel spike sorting technique was7developed. Inspired by existing methods, this “divide-and-conquer” spike sorting method addressesthese challenges (Swindale and Spacek, 2014), and is implemented in freely available software. Thismethod sorted millions of spikes from up to 93 simultaneously isolated units. Units were trackedover many hours despite some of them exhibiting significant drift and very low mean firing rates(< 0.05 Hz).Data were acquired from a total of 15 tracks in 10 hemispheres in 6 cats. Due to time and spaceconstraints, only 3 tracks were fully spike sorted (Section 4.2), resulting in 245 single units whichwere analyzed in Chapters 4–6.Chapter 4 describes the basic physiology of these units. Across all spontaneous and stimulus-evoked recording periods, mean firing rates were surprisingly low. Mean firing rates were notnormally distributed, but rather lognormally, with a geometric mean of 0.11 Hz. 82% of neuronshad mean firing rates below 1 Hz. These results support the theory of sparse coding (Olshausenand Field, 1996, 2004). Evidence is also presented that neuronal populations in V1 perform a kindof shift work. Over the course of minutes and hours, as some cells stopped firing, others startedfiring, keeping the geometric mean firing rate reasonably constant over time. Shift work could be auseful mechanism for maintaining cell physiology, or even network stability. Neurons were localizedrelative to the polytrode by their multichannel waveforms. Overall, they were well distributed alongits length, but at a finer scale their positions were biased towards the positions of the electrodesites, suggesting that the 65 µm hexagonal electrode site spacing of the polytrodes used here isnot dense enough to fully capture the local neural population. Orientation tuning curves werecalculated for each cell, and 61% of all cells were significantly tuned, but 87% were tuned if onlyactive neurons (firing rates ≥ 0.05 Hz) were considered. Surprisingly, orientation tuning strengthwas significantly but inversely correlated with log firing rate. This is incongruent with the notionthat higher firing rates result in better stimulus encoding, and further strengthens the relevanceof low firing rate cells. The issue of polytrode tissue damage is discussed, and the use of narrowerpolytrodes is suggested to reduce damage.Chapter 5 examines the classification of cells according to temporal spike shape, multichannelspatial extent, and RF. As many as 4 different types of spike shapes, and 4 different types of RFswere found. Cells were not found to cluster according to the 2D spatial extent of their multichanneltemplates. Spike shape and RF types were compared by spatial location and mean firing rate. Theseclassifications were used later in Chapter 6.Chapter 6 examines responses to natural scene movies, and the dependence of those responseson cortical state as measured from the LFP. Short (5 s) natural scene movie clips were presentedhundreds of times each. Trial-aligned spike raster plots had short, temporally precise and reliableresponse events consisting of as little as one spike each. These resulted in peristimulus time his-togram (PSTH) peaks as little as 20 ms wide, showing that responses in V1 are more temporallyprecise and reliable than widely assumed. Moreover, very low stimulus-evoked firing rates did notpreclude cells from having temporally precise and reliable response events. Response event preci-8sion and reliability varied from one cell to the next, and there was great diversity in the patternof response events between cells and across movies. Response correlations between all cell pairswere measured at a fine (20 ms) time scale, and were mostly very weak, even between simple andcomplex cells. However, between complex cells, response correlations were stronger than expected,challenging the hierarchical model of complex cells and providing evidence for an alternative re-current model. Cortical state switched spontaneously between synchronized and desynchronized.Stimulus-evoked superficial cell firing rates were higher in the desynchronized than synchronizedstate, while the reverse was true for spontaneous activity. Deep layer cells showed a more heteroge-nous relationship. Contrary to other reports, response event precision, sparseness, and reliabilityfor almost all neurons was higher during the synchronized than desynchronized state. Finally,cortical state had a greater influence on response correlations than did the particular movie clippresented, demonstrating the importance of taking cortical state into account.By minimizing bias during stimulation, recording, spike sorting, and analysis of multiple simul-taneously recorded single units from patches of V1, the conclusions from many different studies,each of which may focus on only a subset of layers or cell or stimulus types, can be replicated orchallenged. This manner of experimentation is less hypothesis-driven than most neurophysiologyexperiments, which might be a weakness in the short term. But in the long term, collecting datain such a hypothesis- and analysis-agnostic way is a strength. It allows analyses to be done in aricher, higher dimensional space, and enables examination of neural responses and properties invarious combinations (subspaces) that more hypothesis-driven experiments might not be capableof. Besides adding flexibility, such an approach may also help explain apparent neural responseand property variability as an artifact of inappropriate pooling of results over many of these di-mensions. This approach therefore has the potential to reveal greater reliability of neural responsesand properties, and to show that the brain is less noisy than widely believed.92 Experimental Methods2.1 General setupExtracellular recordings were made from cortical areas 17 and 18 of anesthetized domestic cat.The general experimental setup is shown in Figure 2.1. Animal experiments followed the guidelinesof the Canadian Council for Animal Care and the Animal Care Committee of the University ofBritish Columbia. Six cats were used in total: four were normal domestic cats, while two wereheterozygous lipoprotein lipase deficient, left over from an unrelated study (Table 2.1). Initialstages of each animal experiment were performed with the aid of a veterinarian. For 3 of the 6 cats(ptc20–22), initial sedation was by intramuscular (IM) injection of dexmedetomidine (25 µg/kg)and initial analgesia by IM injection of butorphanol (0.3 mg/kg). The other 3 cats may have beensedated using different drugs as seen fit by the veterinarian. An intravenous (IV) catheter wasinserted, and initial anesthesia was induced by IV injection of sodium thiopental or propofol. Anendotracheal tube was then inserted and a catheter placed in the urethra. The animal was placedin a stereotaxic frame and its head fixed in place with ear bars coated in topical anesthetic (5%lidocaine). The stereotaxic frame was mounted on an air table which was floated prior to polytrodeinsertion to minimize vibrations.For 4 cats, anesthesia was maintained by inhalation of 0.5–1.5% isoflurane with 70% N2O inO2. During surgical procedures and euthanization, up to 3% isoflurane was used. For the 2 othercats, constant rate infusion (CRI) of propofol (5–10 mg/kg/h) and fentanyl (5–7 µg/kg/h) was usedinstead of isoflurane and N2O. In two cats, the opioid buprenorphine (0.01 mg/kg) was injectedsubcutaneously every 12 hours as an analgesic. In one cat (ptc18), xylazine (2 mg/kg) was injectedAnimal Sex Age Weight Source Stimulus DrugsID (y) (kg) set Anesthestic Paralytic Otherptc15 F 2 2.5 UV A iso + N2O PBptc17 M 7 7.0 HLLD B iso + N2O α-BTX buprptc18 M 5 5.1 HLLD B iso + N2O α-BTX bupr, atrop, xylaptc20 F 1 3.4 UCD C prop + fent PB bupivicaineptc21 F 1 3.5 UCD C prop + fent PBptc22 F 1 3.2 UCD C iso + N2O PB bupr, dobutTable 2.1: Cats used in this study. Stimulus sets are summarized in Table 2.4. Drugs mentionedin the text but not listed here were administered to all cats. UV: Unique Ventures, Balmoral,MB. HLLD: heterozygous lipoprotein lipase deficient cats, UC Davis. UCD: UC Davis. iso:isoflurane. prop: propofol. fent: fentanyl. PB: pancuronium bromide. α-BTX: α-bungarotoxin.bupr: buprenorphine. atrop: atropine. xyla: xylazine. dobut: dobutamine.10videosignalstimulus information & video rasterstimuluscomputerheadstage& amplifieracquisitioncomputeranesthetizedcatpolytrodestimulusmonitorFigure 2.1: General experimental setup. The stimulus computer was the master and the acquisi-tion computer was the slave. To begin recording, the user first armed the acquisition computer tosave both spike and stimulus data to disk. Then the user ran the desired stimulus on the stimuluscomputer, which subsequently triggered the acquisition computer to begin saving to disk. Stimulusinformation, represented by a 16 bit integer, was acquired on every (5 ms) raster of the stimulusmonitor. Adapted from Spacek et al. (2009).IM as a preanesthetic, and atropine (0.02 mg/kg) was injected IM as needed to decrease salivationand increase heart rate.Dobutamine (0.25 mg initial bolus, then CRI of 0.15–0.3 mg/kg/h) was administered IV in onecat (ptc22) to increase blood pressure. The antibiotic bupivicaine was injected subcutaneously (0.6mL) around the scalp wound in one cat (ptc20). Table 2.1 summarizes the drugs administereduniquely for each cat.Animals were mechanically ventilated (Harvard Apparatus, Holliston, MA) at ∼ 20 breaths/minto maintain end-tidal CO2 of 30–40 mmHg. This was especially necessary during systemic paralysis(see below). Blink and pinna (ear) reflexes and toe pinch were used to ensure sufficient anestheticdepth. Dexamethasone (1 mg/kg) was injected IM to reduce swelling and salivation. The catwas kept hydrated on a mixture of lactated Ringer’s salt solution (10–20 mL/h), sometimes withadded potassium chloride (20 mEq/L) and dextrose (2.5%). Heart rate and blood oxygenationwere monitored with a pulse-oximeter (Nonin 8600V), with the sensor placed on the tongue or ashaved part of the tail. Mean arterial blood pressure was monitored with a doppler blood pressuremonitor (Parks Medical 811-B) on a shaved section of hind leg. End-tidal CO2 and respirationrate was monitored with a capnographer (Hewlett-Packard HP47210A) on the gas exhaust close tothe endotracheal tube. Body temperature was monitored with a rectal probe and maintained viaclosed-loop control with a homeothermic blanket (Harvard Apparatus). All vital signs were loggedduring the course of each experiment.Local anesthetic (bupivacaine) was injected subcutaneously around the top of the skull andinto the ear muscles before cutting the skin to expose the skull. A roughly 4 × 6 mm craniotomy(1–5 mm lateral and 3–9 mm posterior relative to the centerline and earbar zero, respectively)11Track ID Duration Position Angle Area Polytrode Agar(hours) L P D ML AP Designptc15.tr7c 17.6 3 5 700 0 20 17 2a 4% in salineptc17.tr1 17.1 -3 6 0 10 10 17 1a 4% LTAptc17.tr2b 12 2 4 300 10 10 17 1a 4% LTAptc18.tr1 14.9 -3 6 0 10 10 17 2b 3% LTAptc18.tr2c 13.9 3 5 600 15 15 17 2b 3% LTAptc20.tr1 15.7 -3 4 0 10 10 17 2b 2.5% LTAptc20.tr2 14.2 3 3 0 10 10 18 2b 2.5% LTAptc20.tr3 5.1 3 4 0 10 10 17 2a 2.5% LTAptc21.tr2 7.5 -3.5 6 0 5 10 17 2a 2.5% LTAptc21.tr5c 9.5 -4 5.5 400 5 10 18 2a 2.5% LTAptc21.tr6b 6.8 -3 3.5 150 2 10 18 2a 2.5% LTAptc22.tr1 9.5 -3.5 5.5 0 0 20 17 1a 2.5% LTAptc22.tr2 7.3 3 4 0 0 20 17 1a 2.5% LTAptc22.tr4b 8.5 -2.5 4.5 150 0 20 17 1a 2.5% LTAptc22.tr5b 6.2 -2 3.5 150 0 16 17 1a 2.5% LTATable 2.2: Tracks recorded in this study. Tracks fully sorted and analyzed are highlighted ingrey. The first part of each track ID is the associated animal ID from Table 2.1. The second partis the track number within that animal, with a letter suffix to distinguish different depths withinthe same insertion. Duration: track duration, i.e., the total amount of time spent in each track,including any gaps in recording. L: lateral distance (mm) from midline. Negative values denote lefthemisphere, positive values denote right hemisphere. P: posterior distance (mm) from ear bar zero.D: depth (µm), a rough estimate of how far, along the path of the track, the topmost sites of thepolytrode were beneath the cortical surface. ML: mediolateral angle (◦): lateral tilt of polytrodefrom vertical. AP: anteroposterior angle (◦): posterior tilt of polytrode from stereotaxic vertical.Area: Brodmann’s area (not definitive) as defined solely by stereotaxic coordinates. Polytrodedesigns are described in Table 2.3. LTA: low-temperature high purity agarose in ACSF.was drilled with a dental drill (Midwest Stylus, DENTSPLY Professional, Des Plaines, IL) overBrodmann’s area 17 and 18. A stereo surgical microscope was used during drilling, removal ofmeninges, and polytrode insertion. Artificial cerebrospinal fluid (ACSF) (Appendix E) was usedto flush away blood and other detritus from the meninges, and to keep them moist. Ophthalmicsurgical sponges (Ultracell Eye Spears, Aspen Surgical, Caledonia, MI) were used to wick blood andexcess fluid away. Care was taken to not apply pressure to the brain. Sometimes the dura materwas completely reflected to expose the underlying pia mater, but more often only a small area ofdura was dissected away one layer at a time with an ophthalmic slit knife (Beaver Optimum 15◦,BD Medical, Le Pont-de-Claix, France; or ClearCut 3.2 mm, Alcon, Mississauga, ON). A small nickin the pia was then made with the ophthalmic slit knife to allow for polytrode insertion. Prior toinsertion, cerebrospinal fluid (CSF) was wicked away from the point of insertion using an ophthalmicsurgical sponge. This seemed to improve unit isolation, perhaps because the CSF acts as a lowimpedance path to ground. Immediately before or after insertion, high purity low temperature12agarose (Type III-A, Sigma-Aldrich, St. Louis, MO) dissolved in ACSF at a concentration of 2.5–4% was applied in liquid form at 38–40◦C to the craniotomy. This quickly set and greatly reducedor eliminated brain motion due to respiration and heart beats. Sometimes, if the dura and pia wereinsufficiently dissected away, the polytrode would cause the brain to dimple during insertion beforefinally breaking through. Applying agar first helped reduce dimpling, and thereby increased thechance of a successful insertion. The polytrode was advanced through the tissue using a manualmicromanipulator (Model 1460 Electrode Manipulator, David Kopf Instruments, Tujunga, CA)under visual control until the topmost electrode sites disappeared below the surface of the cortex.Any subsequent advancement through the tissue was made with a hydraulic micromanipulator(Narishige MHW-4, East Meadow, NY), typically 150–300 µm at a time.Nictitating membranes were retracted with phenylephrine (10%, 1–2 drops/eye), and pupilswere dilated with tropicamide (0.5%, 1–2 drops/eye). Custom-made rigid gas permeable (RGP)contact lenses (14 mm diameter, 7.8–8.7 mm base curvature, +2.00 to +4.00 diopter, HarbourCity Contact Lens Service, Nanaimo, BC) protected the eyes and refracted the cat’s vision tothe distance of the stimulus display monitor. To improve focus, 3 mm diameter artificial pupilswere placed directly in front of the lenses. To prevent eye drift, the cat was given an initial IVbolus of the systemic paralytic pancuronium bromide (1 mg/kg), and paralysis was maintained byCRI (0.2 mg/kg/h). For some animals, pancuronium bromide was not used (Table 2.1). Instead,α-bungarotoxin (α-BTX) was injected retrobulbarly (125 µM, 0.5 mL per eye), acting as a localparalytic to prevent eye drift. Especially for α-BTX animals, eye position was closely monitoredby reverse ophthalmoscopy (Section 2.4) to ensure stability, using fine blood vessels as landmarks.α-BTX injections were found to be effective at preventing the eyes from drifting.Experiments lasted up to 3 days. At the end of the experiment, the anesthetic level was increasedand the cat was killed with an IV injection of euthanyl. The animal was then perfused with salinefollowed by 10% paraformaldehyde, and the brain was removed for subsequent histology. Giventhe long duration of recordings from each insertion in each animal, and the hypothesis-agnosticexperimental design, only 6 cats were required. A ‘track’ was defined as a single polytrode insertionat a single fixed depth. Data were acquired from 15 tracks from 10 hemispheres, for a total trackduration of 166 hours (total amount of time in each track, including gaps in recording). However,only 3 of these tracks were fully spike sorted (Section 4.2), with a total track duration of 34.4 hours.Table 2.2 provides details about each of the tracks recorded from in this study.A separate set of recordings were also performed in V1 of 13 anesthetized rats. These weremostly pilot experiments to test the recording and stimulus systems and to practice experimen-tal techniques. Procedures were similar to those described above for cats, with a few differences.230–570 g male and female Long Evans rats were anesthetized by intraperitoneal (IP) injectionof urethane (1300–1500 mg/kg), followed by maintenance injections as needed (50–100 mg each).Rats were held in place with ear bars in a stereotaxic frame and were not paralyzed or mechan-ically respirated, but supplementary oxygen was often provided. As above, heart rate and blood13Design Columns Layout Spacing (µm) Width (µm) Length (µm)1a 3 hexagonal 65 207 11381b 3 collinear 43 × 50 210 8501c 3 hexagonal 75 208 13132a 2 hexagonal 65 200 17232b 2 hexagonal 50 207 1325Table 2.3: 54-channel polytrode designs. Width is the shank width, and length is the distancebetween the most vertically distant sites. Collinear design 1b had tighter horizontal than verticalspacing.oxygenation were continuously monitored and logged, and blink and pinna reflexes and toe pinchwere used to ensure sufficient anesthetic depth. A heat pad was used to maintain constant bodytemperature. Experiments lasted up to 16 hours each. Unfortunately, very few units were isolatedduring these recordings, and they are therefore only briefly discussed in Section PolytrodesExtracellular voltage data (Figure 2.3) were recorded using multichannel silicon polytrodes (Blancheet al., 2005) manufactured by the University of Michigan’s Center for Neural CommunicationTechnology, and NeuroNexus (Ann Arbor, MI). The polytrodes used here had a single shank, 15 µmthick and ∼ 200 µm wide, with an array of platinum-iridium electrode sites, each 15 µm in diameter(Figure 2.2, middle). Designs had 54 channels in two or three column collinear or hexagonalconfigurations (Table 2.3). Electrode sites were closely-spaced (43–75 µm), such that a spike froma given neuron would usually generate signal on several neighbouring channels (Figure 2.2, right).This provided more information for spike sorting, and also allowed for 2D triangulation of neuronalposition with respect to the plane of the polytrode. By using a model of extracellular signal decayin the neuropil, it may also be possible to estimate the distance between each neuron and thepolytrode, and hence each neuron’s 3D position relative to the polytrode (Section 4.6.3; Blanche,2005).Before use, electrode site impedances were tested using a custom-made low current impedancemeter (Appendix D). If a polytrode had more than 5 faulty sites, it was rejected. A faulty sitecould be the result of a poor wire bond between the polytrode shank and its electrode interfaceboard, or poor etching of the electrode site itself. Faulty sites were often noisy and were groundedout so that they would not induce unnecessary noise onto neighbouring sites or their conductors.2.3 Data acquisitionExtracellular waveforms from all 54 electrode sites were unity-gain buffered by a pair of 27-channelheadstages (HS-27, Neuralynx, Tucson, AZ), and then amplified by a 64-channel 5000× amplifierwith fixed analog filters (FA-I-64, Multichannel Systems, Reutlingen, Germany). The first 5414A C200 μm65 μmB1723 μm1343 μm12/34A4B56A6Blayer56 μmFigure 2.2: Silicon polytrodes. A: A cartoonof a small patch of area 17 of cat primary vi-sual cortex, depicting cells in different layers.Polytrodes are designed to record from all cor-tical layers. White cell bodies represent pyra-midal cells, shaded cell bodies represent non-pyramidal cells. Horizontal and vertical dimen-sions are not to scale, but A and B share thesame vertical scale. B : A polytrode (‘2a’ de-sign) with 54 equally-spaced recording sites ar-ranged in a hexagonal two column layout. Poly-trode designs are listed in Table 2.3. C : A spikefrom a neuron close to the polytrode (red dotin B shows its estimated 2D position) will typi-cally generate signals on several channels (high-lighted in red). A adapted from Payne and Pe-ters (2001), B adapted from Blanche (2005).channels of the amplifier were high-pass filtered (0.5–6 kHz) for use as spike channels (Figure 2.3).Data from a subset of 10 of the 54 electrode sites, evenly distributed along the length of thepolytrode, were also separately low-pass filtered (0.1–150 Hz) for use as LFP channels. All 64channels were then digitally sampled (25 kHz for the high-pass channels, 1 kHz for the low-passchannels) by a pair of 12-bit 32-channel acquisition boards with an internal gain of 1–8× (DT3010,Data Translations, Marlboro, MA). To reduce costs, each acquisition board had only a single analog-to-digital converter (ADC), and could only sample one channel at a time. To closely approximatesimultaneous sampling of all channels, each ADC used a sample-and-hold technique, in which itschannels were sampled very quickly in succession at 1 MHz, followed by a pause until it was timefor the next acquisition timepoint (every 40 µs for high-pass channels, every millisecond for thelow-pass channels).Acquisition was controlled by a custom program “Surf” written in the Delphi programminglanguage (Blanche et al., 2005; Blanche, 2005). A channel of interest could be selected for viewingon-screen (1 ms of data displayed every 100 ms) or directly on an analog oscilloscope. The selectedsignal was played concurrently through an audio monitor. Data were saved to .srf files at a rateof ∼ 2.7 MB/s. A single continuous recording consisted of one type of visual stimulus (Section 2.4)and usually lasted no more than 45 minutes, resulting in individual files up to ∼ 7 GB in size. Other15Figure 2.3: 50 ms of high-pass (0.5–6 kHz) voltage waveform data, Nyquist interpolated to 50 kHz(Section 3.3), for all 54 channels of a polytrode recording of spontaneous activity in track ptc15.tr7c(Table 2.2). The channels of this 2 column hexagonal polytrode are arranged here in vertical spatialorder, from superficial (top) to deep (bottom). Colours cycle to distinguish neighbouring channels.Two faulty channels (green and violet) were grounded out. Spikes are visible at various times andcortical depths, and most spike waveforms span multiple neighbouring channels. This segment isfrom a longer sample of spontaneous data available online (Section C.2). Dashed box denotes asegment shown in greater detail in Figure 3.4. Scale bar: 1 ms, 100 µV. Channel spacing: 65 µm.information was also saved to the .srf file, such as polytrode layout, stimulus information (with amicrosecond precision time stamp for screen refresh), and the absolute start time of the recording.Saving the absolute start time allowed for later determination of the intervals between recordings,which was important for dealing with drift while spike sorting multiple recordings from the sametrack all at once (Section 3.2). Online current source density (CSD) analysis (Section 4.6.3) wasused as a rough indicator of polytrode depth, and was saved to a separate file. A short period ofextracellular multichannel waveform data is shown in Figure Visual stimulationStimuli were displayed on a flat 19” (36 × 27 cm) CRT monitor (Iiyama HM903DTB) at 800×600resolution and 200 Hz refresh rate. A high refresh rate was required to prevent artifactual phaselocking of neurons in V1 to the screen raster (Figure 2.4; Williams et al., 2004). The monitorwas placed 57 cm in front of the cat’s eyes. At this distance, the monitor subtended horizontaland vertical angles of ∼ 36◦ and 27◦ respectively, and 1 cm on the screen subtended 1◦ of visualangle. The monitor was gamma corrected, with a maximum luminance of 116 cd/m2. This ensureda linear relationship between input pixel values and output luminance. Mouse-controlled stimuli,such as an oriented bar, were displayed simultaneously on two monitors: one for the cat, the otherfor the experimenter. Both manual and automated stimuli were generated using “dimstim”, a freelyavailable custom software package written in Python (Section C.1, Spacek et al., 2009), based onthe Vision Egg stimulus library (; Straw et al., 2006; Straw, 2008) whichitself depends on OpenGL ( Graphics were double-buffered to minimize latency(< 1 ms) and ensure that no frames (5 ms each at 200 Hz refresh rate) were ever dropped. Everyscreen raster was detected by the acquisition computer directly from the analog video signal cable,and its microsecond precision time stamp was saved concurrently with the spike waveforms. Foreach type of stimulus, a table of stimulus parameters was generated. On each raster, the stimuluscomputer sent a stimulus table index value to the acquisition computer which was stored alongwith the raster time stamp. Thus, there was a record of exactly what was displayed on every screenraster, allowing for precise temporal analysis of the relationship between stimulus and response.Three different sets of stimuli (designated by letter in Table 2.4) were used depending on theanimal (Table 2.1). For all sets (A–C), a mouse-controlled oriented bar was used to map out theaverage RF position of the population of cells, on which all subsequent stimuli were then centered.Artificial stimuli were used to characterize RF properties of each of the cells in the population, allof which had similar retinotopic positions. Together, the artificial stimuli allowed for mapping ofsimple and complex cell RFs, as well as orientation, spatial frequency, temporal frequency, phase,and contrast tuning curves. Natural scene movie stimuli were used to examine how responses mightdiffer from artificial stimuli.Running a full stimulus set took several hours, and each type of stimulus (see below) was usuallypresented at least once per track. Each stimulus resulted in a single continuous recording of up to1 h in duration, and an entire track’s recordings spanned 5–18 h, including brief gaps in recording(Table 2.2).Artificial stimuli included: drifting bars at various orientations; flashed gratings at variousorientations, spatial frequencies, and phases; drifting gratings at various orientations, spatial andtemporal frequencies, phases, and contrasts; and m-sequence white noise movies. Additionally,single raster (5 ms) uniform full-screen white flashes were presented at 1.3 Hz to generate strongsynchronous feedforward stimulation of V1 for calculating CSDs (Section 4.6.3). Although not17Figure 2.4: Phase locking of V1 to a low re-fresh CRT monitor. A: When stimulated with auniform display at 60 Hz refresh rate (top), thespike trains of a neuron in macaque V1 phaselocked to the display raster (middle). A strong60 Hz component (and its 120 Hz harmonic) isapparent in the power spectrum of its responses(bottom). B : Presenting the same uniform dis-play to the same neuron at 135 Hz eliminatedphase locking to the display raster. Taken fromWilliams et al. (2004).analyzed in this study, sets A and B also included flashed bars at various locations, orientations,and contrasts, and set C included a full-screen sinusoidal grating that progressed over a range oftemporal frequencies (‘freqsweep’ column in Table 2.4). For drifting and flashed bars and gratings,all stimulus conditions were presented an equal number of times, and in pseudorandom order tominimize response adaptation (Maffei et al., 1973).Drifting bars consisted of white and/or black bars on either a grey background or a backgroundof opposite luminance. Bars were 10 or 6◦ long and 0.5 or 0.3◦ wide, and drifted at 2.5 or 5◦/s for4 s, for a total of 10 or 20◦. Each condition was followed by a 1 or 0.5 s blank period. Steps inorientation were 20 or 30◦. Each stimulus condition was presented 8 or 12 times.Flashed grating stimuli consisted of a rapid succession of stationary, spatially sinusoidal grat-ings, each displayed for only 40 ms. Flashed gratings can be used to rapidly characterize the RFproperties of an entire population of cells (Ringach et al., 1997a,b). Flashed gratings were eitherpresented within a circular aperture 10◦ in diameter on a mid-grey (50% luminance, 58 cd/m2)background, or they were presented full screen. Steps in orientation were 10 or 15◦. Spatial fre-quencies ranged roughly logarithmically from 0.05 to 1.6 cycles/◦. Steps in spatial phase were 90or 60◦. A Michelson contrast (the luminance difference between bright and dark extremes of thegrating, divided by the sum) of 1 was used (100% of the screen’s maximum capability). Mean18grating luminance was mid-grey. There was no blank period following each trial, although a blankscreen was presented for 40 ms or 2 s every 721 or 6000 trials (29 s or 4 min) as a control to allowestimation of baseline responses. Each stimulus condition was presented 40 or 100 times.Drifting gratings had a sinusoidal brightness profile in both space and time, and were presentedeither in a circular aperture 8◦ in diameter on a mid-grey background, or full screen. Steps inorientation were 45 or 30◦. Spatial frequency ranged a roughly logarithmic scale from 0.05 to5 cycles/◦, but was usually kept below 2 cycles/◦. Temporal frequency also ranged a roughlylogarithmic scale from 0.5 to 20 Hz, but was usually kept below 5 Hz. Trial duration was eitheradjusted according to temporal frequency, such that each trial consisted of exactly 6 full temporalcycles of the grating, or trial duration was fixed at 6 s. Like the flashed gratings, there was noblank period following each trial, although a blanks screen was presented for 5 or 2s every 24 or 20trials (120 or 40 s). Contrast ranged roughly logarithmically from 0.016 to 1, but was usually keptat 0.5 or 1. Mean grating luminance was mid-grey. Each stimulus condition was presented 8 times,or only once.Drifting gratings generally had coarser steps in orientation because more non-orientation stim-ulus dimensions were included than either drifting bars or flashed gratings (spatial frequency, tem-poral frequency, and/or contrast). To keep the run time of each stimulus type roughly the same,the number of steps in orientation was therefore decreased.An m-sequence (Shapley et al., 1991; Reid et al., 1997) was used to generate a white noisemovie. The movie had 65535 frames, each 32×32 pixels and 5–12.7◦ on a side, with an aspect ratioof 1. Each frame was presented for 20 or 40 ms. Every pixel in the m-sequence movie was white andblack for an equal amount of time, and each frame had an equal number of white and black pixels.Hence, the first order statistics of the movie were uniform, and summing all the frames from them-sequence movie resulted in a mid-grey image. The second-order spatial statistics were similarlyuniform: all pairwise correlations between pixels were zero when calculated across all movie frames.Natural scene movies came from two different sources: ‘old’ and ‘new’ (Figure 2.5 & Table 2.4).The ‘old’ set of movies were courtesy of the Peter Ko¨nig lab. They were filmed by attaching a camerato a cat’s head and allowing it to wander through natural environments (Kayser et al., 2003). 64×64pixel subsets from these movies were displayed on the stimulus monitor at a subtended visual angleof 12.7◦. However, these movies had some practical problems, including VHS tape transfer artifacts,low resolution, and a low frame rate necessitating interpolation between frames (courtesy of NickLesica). The ‘new’ set of natural scene movies were filmed by the author with a digital camera(Canon PowerShot SD200) at 320×240 pixel resolution and 60 frames per second (fps), low to theground, with movements approximating that of a cat exploring its environment, as well as suddensaccade-like movements. A total of 52 min were filmed outdoors over 3 days in a variety of woodedor grassy locations in Vancouver, BC. Footage consisted mostly of dense grass and foliage witha wide variety of oriented edges. Focus was kept within 2 m and exposure settings were set toautomatic. The horizontal angle subtended by the camera lens (51.6◦) was measured for proper19BA10°Figure 2.5: Example frames from ‘old’ (A)and ‘new’ (B) natural scene movie sets. Framesare shown at the same relative size as when theywere displayed on-screen during experiments.Both sets exceeded the classical receptive fieldsizes of cells in this study. Individual moviepixels were roughly the same size in both sets(0.2 and 0.16◦, respectively). Scale bar appliesto both panels. 10◦ is approximately the widthof a closed fist at arm’s length.Set Movies Repeats Blank screen Refresh rate Flashed bars FreqsweepA old 25 no no yes noB new 200–400 yes yes yes noC new 400 yes yes no yesTable 2.4: Stimulus sets. The set used for each animal is shown in Table 2.1. See text for details.scaling to match the visual angle subtended by the movie on the stimulus monitor. These moviesare available upon request. An example movie is available at movie sources resulted in clips of 1–5 min in duration, presented up to 8 times in succession.Shorter clips (4.5–5 s in duration) were also presented, but much more repeatedly. Short clips fromthe ‘old’ movies in stimulus set A were repeated 25 times, while short clips in the ‘new’ moviesin sets B and C were repeated 200–400 times (‘repeats’ column in Table 2.4). These were used tostudy the reliability of neuronal responses to repeated naturalistic stimuli. They were also intendedfor studying how responses might change over time as a result of plasticity (Yao et al., 2007).In stimulus set A, except for the occasional brief periods in between artificial stimulus trials(see above), spontaneous activity was acquired without the screen. In sets B and C, spontaneousactivity was acquired while presenting a blank grey screen. Finally, sets B and C included naturalscene movies and blank screen stimuli which were run at a 66 Hz refresh rate in addition to theusual 200 Hz. These may be used to investigate in greater detail how a low refresh rate screenmight affect responses.Other than the full-screen flashes and some of the blank screen stimuli, stimuli were presentedmonocularly to the eye that was dominant for the majority of the recorded neural population. Thiswas judged by listening to visually evoked responses on the audio monitor. Monocular stimulationavoided the difficulty of keeping the eyes accurately converged in an anesthetized animal. Althoughnatural scene movies were more naturalistic than the artificial stimuli, they excluded colour, andbecause they were presented monocularly they also lacked depth. At least once per track, the areacentralis (AC) of the open eye was mapped by reverse ophthalmoscopy onto a sheet of paper onthe stimulus monitor, and the center position of the stimuli was marked as well. This confirmedthat the neural population had RFs at low eccentricity, within a few degrees of the AC. Classical20RF sizes were usually < 5◦ at the low eccentricities in this study.2.5 HistologyAt the end of the experiment, all cats except ptc15 were perfused with saline followed by 10%formalin to fix the tissue. The visual cortex was blocked and sectioned coronally into ∼ 50 µmthick slices on a freezing microtome. The polytrode track could sometimes be localized to lessthan a handful of slices. This potentially allowed determination of track depth, and thereforeroughly which cortical layers the polytrode spanned. Histology also had the potential to roughlydetermine the angle between the polytrode track and the vector normal to the cortical surface,and therefore how inter- or intra-columnar the track may have been. However, the histology workremains incomplete and is not presented here. Future efforts may yet recover useful histologicalinformation from the stored samples.213 Spike SortingBefore any spike analysis can be performed, single unit spikes must be extracted from the extra-cellular multichannel waveform data. Spike sorting has a long history, and can be a very difficultprocess (see Lewicki (1998) for a review). Not only must spikes be separated from noise, but theymust also be separated from each other. A further complication is that the number of neuronscaptured by a given recording and their specific extracellular multichannel waveform shapes areunknown a priori. Accurate spike sorting is essential for later analyses, especially those that dependon precise timing relationships such as spike correlations (Ventura and Gerkin, 2012; Figure 3.1;Appendix B). Spike sorting therefore deserves considerable attention.3.1 BackgroundThere are a wide variety of problems that may be encountered during spike sorting. During spikedetection, noise events may be mistaken for spikes (false positives), or spikes may be mistakenfor noise (false negatives). Once spikes have been detected, they need to be clustered. A clustermay be mistakenly divided into two or more clusters (oversplitting), or it may mistakenly com-bine spikes from multiple neurons (undersplitting) resulting in a multiunit cluster of single unitspikes. Conversely, instead of being discarded, non-isolatable multiunit spikes may be mistaken forisolated single unit spikes. Spike shape variability is another complication. During longer record-ings, electrode and tissue drift can result in non-stationary spike waveforms, and during bursts,spike amplitudes can diminish (Buzsa´ki, 2004). Neurons can also exhibit great variability in theirresponsivity, sometimes resulting in complete silence for long periods of time (Henze et al., 2000;Lennie, 2003; Buzsa´ki, 2004; Shoham et al., 2006; Mizuseki and Buzsa´ki, 2013). All these problemsare a potential source of bias.Electrode arrays with many closely spaced recording sites have the potential to improve spikesorting quality. Traditionally, most electrophysiology has been done using single channel electrodes(either tungsten in glass or single wire), stereotrodes (McNaughton et al., 1983), or tetrodes (Grayet al., 1995). More recently, multichannel electrodes have come into use (Section 1.1). As thenumber of recording sites increases, so can the complexity of spike sorting. As long as the spacingbetween each site (or each tetrode) is great enough such that a single spike shows up on no morethan one channel (or tetrode), single channel spike sorting methods can easily scale up to anynumber of channels. However, for electrodes with sufficiently low site spacing (< 100 µm and ∼1 MΩ site impedances), a single spike may be picked up by multiple electrode sites (Figure 2.2).This has the benefit of potentially increasing the spike signal to background noise ratio, trackingneurons over time despite drift, improving the ability to sort spikes from neurons very close to eachother, and providing a better estimate of the locations of recorded neurons relative to the electrode22spontaneous natural scene movie white noise movienormalized pair countspike correlation coefficientdrifting barold sortingnew sorting0.1 0.0 0.1 0.2 0.1 0.0 0.1 0.2 0.1 0.0 0.1 0.2 0.1 0.0 0.1 0.2mean=0.067 mean=0.049 mean=0.031 mean=0.035mean=0.020 mean=0.024 mean=0.015 mean=0.015Figure 3.1: Motivation for careful spike sorting. Each plot is a distribution of spike correlations(Appendix B) between all active neuron pairs in a given recording. Four different types of recordingsfrom track ptc15.tr7c are shown, one in each column (3, 15, 22 and 12 min in duration, left toright). The top row used spikes sorted by the previous multichannel template matching method(Section 3.1.1) while the bottom row used spikes sorted by the method presented here. Mean spikecorrelations between the (fewer) neurons measured from spikes sorted with the previous methodwere artifactually higher than those measured from spikes sorted with the method presented here(0.031–0.067 vs. 0.015–0.024). One reason for this may have been an implementation problem withthe old method: it was possible for a single spike to be assigned to more than one cluster.and to each other (Drake et al., 1988; Harris et al., 2000; Csicsvari et al., 2003; Blanche et al., 2005;Du et al., 2009; Figures 3.6, 3.12 & 4.3).However, these potential benefits come at the cost of further complications. One of these isin spike detection. A single spike that generates signal on more than one channel can triggermultiple threshold crossing events. Deciding which threshold crossing events are close enoughtogether in space and time to be considered part of the same spike is not straightforward. It maybe that multiple adjacent events belong to the same single spike, or they may belong to multiplespatiotemporally adjacent, yet distinct, spikes. Spike detection therefore becomes a problem notjust of detecting threshold crossing events, but of clustering them into distinct spikes (Swindaleand Spacek, 2015). Only then can these spikes be clustered into different single units.Once spikes have been detected, another complication is consistently aligning spikes in spaceand time. If a neuron’s physical location falls in between two or more electrode sites, the channelon which its spike waveforms have their maximum amplitude may vary as a result of multichannel23waveform shape variation, whether systematically due to drift or randomly due to noise. This cancause the channels that are selected for inclusion for spike sorting for one spike to differ from thoseof other spikes from the same neuron. A method is therefore required for choosing a common set ofchannels and timepoints for all spikes that might conceivably be from the same neuron. A commonset of channels and timepoints is necessary for the dimension reduction and clustering steps thatfollow spike alignment.Perhaps the greatest difficulty is the current lack of sufficiently realistic ground truth data,whether simulated or experimental, of many simultaneously spiking neurons recorded by closelyspaced cortical electrode arrays. Unfortunately, until this situation changes, objective performancecomparisons of different spike sorting methods will remain very difficult to make (Section 3.12;Einevoll et al., 2012).Efforts were made here to deal with all of the above spike sorting challenges, but one furtherdifficulty was not dealt with: spatially adjacent spikes overlapping in time. The solution to this isspike overlap decomposition, in which each spike overlap event is treated as a linear superposition ofspikes from different neurons at different temporal shifts (Lewicki, 1994; Segev et al., 2004; Frankeet al., 2010; Prentice et al., 2011; Ja¨ckel et al., 2012; Marre et al., 2012; Pillow et al., 2013). Spikeoverlap decomposition was considered too difficult here in the context of long duration recordingswith non-stationary waveforms. Fortunately, given the low mean firing rates of neurons in catV1 (Section 4.3), spike overlap is much less of a concern here than in retinal ganglion cell (RGC)recordings (Segev et al., 2004; Prentice et al., 2011; Ja¨ckel et al., 2012; Marre et al., 2012; Pillowet al., 2013).3.1.1 Existing methodsThere are a wide variety of spike sorting methods (Lewicki, 1998), but no single existing methodaddresses all of the problems associated with spike sorting of long duration cortical polytroderecordings. Most methods divide the process into separate spike detection, dimension reduction,and clustering steps. Some methods extract simple spike features, such as spike height or width,as a form of dimension reduction, but may miss other subtle but important differences in spikeshape (Gray et al., 1995; Nguyen et al., 2003). Some only handle single channel or independentchannel recordings (Lewicki, 1994; Zouridakis and Tam, 1997, 2000; Quian Quiroga et al., 2004;Wood and Black, 2008; Wolf and Burdick, 2009) while others are tailored to stereotrode or tetrodedata, but may not scale well to higher numbers of non-independent channels (Gray et al., 1995; Feeet al., 1996; Harris et al., 2000; Nguyen et al., 2003; Gasthaus et al., 2009; Calabrese and Paninski,2011). Some methods require Gaussian-shaped clusters, and therefore assume stationarity of spikewaveforms over time (Harris et al., 2000; Litke et al., 2004; Hazan et al., 2006). Others explicitlydeal with non-stationarity (Bar-Hillel et al., 2006; Wolf and Burdick, 2009; Calabrese and Paninski,2011) but may not scale well to large numbers of spikes and clusters (Hulata et al., 2002; Shohamet al., 2003; Pouzat et al., 2004; Gasthaus et al., 2009).24Figure 3.2: Multichannel template matching. Left : A multichannel template with member spikes(grey) and mean waveform (black). Right : The distribution of difference values between the multi-channel template and all points in the recording. Ideally, this was a bimodal distribution, allowinga threshold to be set to separate spikes (green) from noise (red). In practice, this distribution wasoften unimodal, with no obvious place to set the threshold. Adapted from Blanche et al. (2008).Many of the problems associated with polytrode spike sorting were described by Blanche (2005),but some of that method was never fully implemented in software. More fundamentally, the methodof Blanche (2005) had a number of problems, most of which were a result of using multichanneltemplate matching for both spike detection and clustering. Briefly, initial spike detection wasperformed on short random sections of data, resulting in a few thousand spikes. These spikes werethen clustered using a binary split algorithm, followed by k-means clustering. The intent was tosample enough data that all neurons would be represented by a cluster of at least a few spikeseach. The multichannel mean waveform, or template, was calculated for each cluster and comparedto the data at every timepoint. Temporally local minima in root mean square (RMS) differencevalues between each template and every timepoint in the data were found, and their distributionplotted (Figure 3.2). Ideally, the distribution of difference values would be bimodal, the lowermode being true matches of the template to its spikes in the data, and the upper mode beingcoincidental matches to noise. This would give the user a clear indication of where to set the RMSdifference threshold between matches to spikes and to noise. However, in practice the distributionwas often unimodal, with no clear distinction between matches to spikes and to noise, and thereforeno principled way for the user to set a difference threshold.Another problem was that template matching cannot typically handle large systematic wave-form variability, such as that due to drift (Section 4.4). The method of Blanche (2005) assumedthat templates derived from just a portion of a track’s recordings were accurate across all of itsrecordings. These could be separated by several hours, and therefore could be subject to substan-tial amounts of drift or other systematic sources of waveform variability. As a result, templatespartly derived from earlier sections of data could generate substantial false positive or false negative25matches to later sections of data, and vice versa. A related problem with template matching wasthat the initial random sampling meant that a rarely firing neuron might never result in a template,and therefore might be missed altogether. This is a significant issue, given that most neurons in catV1 have very low firing rates (Section 4.3). Finally, an implementation issue allowed some spikes tomatch multiple templates and therefore belong to multiple neurons at the same time. This likelyresulted in artifactually strong spike correlations between neurons (Figure 3.1).The above arguments against template matching for long duration cortical polytrode recordingsalso hold for many other spike sorting methods that are based on template matching (Segev et al.,2004; Franke et al., 2010; Prentice et al., 2011; Ja¨ckel et al., 2012; Marre et al., 2012). However,template matching may be more suitable for other kinds of data, such as shorter in vitro multi-channel electrode array (MEA) recordings of RGCs (Segev et al., 2004; Prentice et al., 2011; Ja¨ckelet al., 2012; Marre et al., 2012). Such recordings may be less vulnerable to drift than the longerin vivo cortical polytrode recordings reported here. RGCs also have higher firing rates, therebymitigating the above mentioned sampling problem. Higher firing rates come with greater severity ofspike overlap from spatially adjacent neurons. Fortunately for RGC recordings, template matchingis well-suited for spike overlap decomposition of recordings with stationary waveforms.3.1.2 Clustering methodsCompared to template matching, the use of separate spike detection, dimension reduction, andclustering steps is the more common approach to spike sorting. For the clustering step, a variety ofdifferent clustering methods have been used, including manual cluster cutting (Gray et al., 1995), k-means, hierarchical clustering (HC), expectation-maximization (EM) of a Gaussian mixture model(GMM), and superparamagnetic clustering (SPC). All were considered for use here, but all wererejected.K-means (Forgy, 1965; MacKay, 2003) is a simple, commonly used, two step iterative algorithm.Before iteration begins, a set of cluster centers (or means) is initialized in some manner, usuallyrandomly. First, each data point is assigned to the nearest cluster. Second, the position of eachcluster is updated by taking the mean of the positions of all its member points. Given enoughiterations, k-means is guaranteed to converge (MacKay, 2003). However, it has two major problems.First, because it uses Dirichilet domains, which assign each point to a cluster based solely on whichcluster’s centre is nearest, highly elongated and non-convex clusters are often poorly separated.Second, the number of clusters k must be known a priori, which it is not during spike sorting. Thiscan be dealt with by running k-means multiple times, each with a different value of k, but then thebest solution must be evaluated somehow. Doing so is complicated by the fact that k-means is notdeterministic, due to its random initialization which is important to test robustness.Hierarchichal clustering organizes data points into a hierarchy, with individual points at thebottom, and groups of increasing size further up the hierarchy, culminating in a single group forall the points at the very top. There are two types of HC: agglomerative, which combines points26into increasingly larger and fewer clusters; and divisive, which iteratively divides the data intoincreasingly smaller and more numerous clusters. Both require a pairwise similarity matrix (e.g.,distance matrix) of all points. Murtagh and Contreras (2012) provide a recent overview of the fieldof HC, while Fee et al. (1996) apply it to the problem of spike sorting. An interesting feature ofHC is that each level in the hierarchy can be considered a valid clustering. Moving up or downthe hierarchy allows one to track how different points are related to each other at different spatialscales. One challenge then is deciding at what level to “slice” the hierarchy. There are manydifferent distance metrics and group linkage criteria available for HC, and deciding which to use isanother challenge. In general, for agglomerative clustering, at each level in the hierarchy the twopoints closest to each other are merged, and for divisive clustering the two points furthest fromeach other in a group are split. This may make traditional HC vulnerable to the same problem ask-means: if each cluster’s position is based solely on its centre, or its edge, or some other singlefeature that does not fully describe cluster shape and point density, clusters can become poorlyseparated.EM is a method of fitting a model to data, in this case, models of clusters to points in clusterspace. EM searches for a set of model parameters that maximize the likelihood that the datawere generated from the model (Bilmes, 1998). A GMM is one such model, where the number ofGaussians itself is also a parameter. Like k-means, EM is a two step iterative process. First, inthe expectation step, it guesses a set of parameter values, and calculates the expectation that themodel fits the data. Then, in the maximization step, it chooses parameter values that maximizethe expectation. On each iteration, the likelihood of the chosen parameter values is guaranteed toincrease and eventually reach a local maximum. KlustaKwik (Harris et al., 2000; Hazan et al., 2006)is a widely used clustering program tailored for spike sorting, which implements EM of a GMM(EM+GMM). However, use of a GMM assumes that clusters are Gaussian in shape, which is notalways the case. For example, neurons drifting over time can result in highly non-Gaussian clusters(Figure 3.12). Bar-Hillel et al. (2006) clustered spikes using EM+GMM but allowed for drift bysplitting the data into time chunks, and then linking the clusters in consecutive chunks. Wolf andBurdick (2009) and Calabrese and Paninski (2011) both employed similar strategies. However, EMcan be computationally expensive, and is non-deterministic, again due to random initialization.SPC (Blatt et al., 1996, 1997; Quian Quiroga et al., 2004) represents each point as a magneticdomain that can have one of a number of possible spin values. Interactions between points aremodelled as an exponential function of squared distance between points. Points are assigned randomspins, and a Monte-Carlo algorithm is run at different simulated temperatures, allowing the pointsto affect each other’s spins in a pairwise manner. At each temperature, a point’s spin is perturbed,and neighbouring points correspondingly change their spin with some probability. Those thatdo so with a high enough probability are classified as belonging to the same cluster. This isrepeated for all points and many different temperatures. The ideal temperature is picked from a(superparamagnetic) range of temperatures that exhibits cluster stability. The benefit of SPC is27that it makes no assumptions about cluster shape, does not require prior knowledge of the numberof clusters, and does not necessarily assign points to the nearest cluster mean. However, SPC canbe slow if many temperature steps are used, and choosing an ideal temperature can be difficult.3.2 OverviewThe spike sorting procedure used here was similar to that described in Swindale and Spacek (2014).First, raw spike data (0.5–6 kHz) were preprocessed (Section 3.3) by Nyquist interpolation toincrease the effective sampling rate, and to correct for sample-and-hold delays in the acquisitionhardware. Next, spike detection (Section 3.4) designated plausible neuronal spikes in the raw data.These were then initially partitioned (Section 3.6) into up to one cluster per channel, according tothe channel with the sharpest voltage peaks for each spike. The multichannel spikes in each of theseinitial clusters were then aligned in time (Section 3.7). Next, dimension reduction (Section 3.8) wasperformed on each cluster using principal component analysis (PCA) or independent componentanalysis (ICA) of channels with significant signal. The 3 most significant components were plottedin 3D. To check for drift, spike time could be chosen as one of the 3 dimensions. Spikes werethen clustered (Section 3.9) in the chosen 3D space using the gradient ascent clustering (GAC)algorithm (Swindale and Spacek, 2014). These more refined clusters were cleaned (usually by furtherclustering in ICA space) and compared and realigned to similar clusters to check for significantseparation (Section 3.10). Sufficiently similar clusters were merged, and sufficiently multimodalclusters were split. Every merge or split required reverification of nearby clusters. All remainingunclustered spikes that had been discarded could be compared to existing clusters for potentialincorporation. Finally, each cluster’s autocorrelogram could be checked for a satisfactory refractoryperiod, although this was found to be of dubious utility (Section 3.11).Within a given track, sorting each recording independently would result in a correspondenceproblem: how to determine cluster correspondence across recordings adjacent in time? Track-widesorting was done to avoid this correspondence problem. It had the added benefit of potentiallyincreasing the size of clusters that would otherwise be too small to consider on a single recordingbasis (i.e., when considering a shorter stretch of data), and would therefore be erroneously discarded.While this made small clusters bigger and denser, it also made big clusters even bigger. This wasa disadvantage because in PCA space these could then encroach on each other, and on smallerclusters. However, ICA helped get around this problem (Section 3.8). Because it was desirable toconserve time gaps between recordings to keep track of drifting units over time, null data of theappropriate length was inserted between recordings to represent the time gaps. This also made itclear to the user where and how long the gaps were when scrolling through the continuous data.Time gaps would then also show up in the 3D cluster plots of detected spikes when plotted againsttime (Figure 3.12, right column).283.2.1 SoftwareTo implement the methods described here, new spike sorting software, called “spyke” (, was written in the Python programming language (; Spacek etal., 2009; Spacek and Swindale, 2009). For spike sorting large data sets such as an entire track,spyke requires a 64-bit computer with at least 4 GB of random-access memory (RAM) and a 64-bitoperating system. In principle, spyke can run on Linux, Windows, or Mac OS X, but most recentlyhas only been tested in Linux (Xubuntu 14.04). Spyke can deal with millions of spikes at a time(∼ 1 million spikes per GB of RAM). The longest sorted track (ptc15.tr7c) was 11.8 hours long,excluding recording time gaps. There was no limitation in the recording duration that could besorted, only the memory limitation as a function of the number of detected spikes. A spike sortingsession could be saved and resumed at any time. For a track-wide sorting session, the saved data,including waveforms of detected spikes, took ∼ 1 GB of disk space per million spikes (7 GB forptc15.tr7c). This data could be further sorted even in the absence of the original .srf raw datafiles (107 GB for ptc15.tr7c) saved by the acquisition software “Surf” (Blanche et al., 2005). Allspike sorting methods described here were implemented in spyke. Most of the methods here werealso independently implemented in Fortran (Swindale and Spacek, 2014, 2015), which allowed forcross-validation of methods. Track-wide sorting with spyke was used to sort all spike data foranalysis in subsequent chapters. Further details about spyke are in Section C.2.3.3 PreprocessingThe data acquisition boards acquired raw spike data at 25 kHz using a sample-and-hold techniquein which each ADC cycled between its channels at a rate of 1 MHz, taking one sample at a time(Section 2.3). This resulted in an artifactual delay of 1 µs between consecutive channels, and upto 31 µs between channels at opposite ends of a single 32 channel ADC board. Furthermore, spikedetection and alignment at 25 kHz is inferior to that at 50 kHz or 100 kHz, because positive andnegative peaks in spikes happen quickly, and insufficiently fast sampling can cause these peaks toartifactually fall below spike detection threshold (Blanche and Swindale, 2006). Nyquist interpo-lation was used to correct for both of these artifacts. Nyquist interpolation to 50 kHz was chosenbecause there was no appreciable improvement in going any higher (Blanche and Swindale, 2006).Sample-and-hold correction and interpolation were performed in a single step on the fly everytime raw data were called for, such as when scrolling through the data or during spike detection.Data were Nyquist interpolated by convolution (numpy.convolve) with a bandpass sinc function.The sinc function used for each channel was offset by the appropriate amount to correct for itssample-and-hold delay.Because the frequency content of extracellular spikes spanned most of the recorded bandwidth(0.5–6 kHz), any further digital filtering to reduce noise would have also reduced signal, and thesignal to noise ratio would have remained unchanged (Swindale and Spacek, 2014). Therefore, no29filtering was performed on the raw data.3.4 Spike detectionNext, spike detection was performed on the preprocessed data. Data were divided into slightlyoverlapping blocks (10 s long, 2 ms overlap), and preprocessing and detection were performed oneach block independently. This allowed time dependent voltage thresholds to be calculated andapplied, with a time resolution of one block. It also allowed detection to be split up into parallelindependent tasks, which made for faster execution on a multicore CPU. Working on blocks wasalso much more memory efficient than trying to preprocess an entire track’s raw data (107 GB forptc15.tr7c) at once. Blocks overlapped slightly to accommodate spikes that straddled block borders.Channel and time dependent voltage thresholds were calculated by estimating the noise on eachchannel within each block. Noise levels can be estimated by taking the standard deviation of eachchannel’s voltage data, but estimation by standard deviation is biased by the presence of spikes inthe data. Higher spike rates and higher amplitude spikes lead to higher standard deviation, evenwhen background noise levels remain the same. The median is a better method for estimating noisein the presence of spikes (Quian Quiroga et al., 2004), and was used instead. Voltage thresholdswere calculated according toVt(i, j) = max{Amedian(|V (i, j)|)0.6745, Vmin}(3.1)(Quian Quiroga et al., 2004), where A is a noise multiplier, V is the preprocessed voltage data, iand j are channel and time block indices respectively, and Vmin is a minimum threshold. A = 6was applied, and gave good discrimination between noise and spike-like peaks. Vmin = 40 µV wasalso applied: events below that were deemed too difficult to reliably discern from noise events, evenon channels and during periods of very low noise.A peak was defined as the largest extremum between each pair of zero crossings on a givenchannel. A subset of these peaks had amplitudes exceeding Vt, referred to here as trigger peaks.Trigger peaks were examined one at a time in temporal order. Each was tested to decide if itwas part of a spike, and also if it was the primary peak of that spike, i.e., the best peak to alignto in space and time. Positive and negative peaks were given equal consideration. Because aspike can generate signal on several channels, and because spikes generally have two or more peaksof opposite sign (Figure 3.3), a local spatiotemporal search was performed around each triggerpeak, constrained to channels within a radius of rlockout = 150 µm and to timepoints within ±dtmax = 0.4 ms. All peaks within the search window were compared to the trigger peak. Peakswere characterized by their “sharpness”, defined asSp =Vp2dtz(3.2)30Figure 3.3: Examples of 4 types of spikes, shown clustered, with 20 randomly chosen spikesplotted in each cluster. Mean and standard deviations of waveforms (thick lines and translucentbands, respectively) are mostly obscured by the spikes. Upper panels show larger slower spikes,while lower panels show smaller faster ones. A: Spikes with most of their signal on one channeland much less on surrounding channels. These had a prominent negative and positive peak. B : Acluster with similar spike shape, but with a broader distribution in space. The neuron generatingthese spikes likely fell in between the two channels with the largest amplitude. C : Rarer, mostlypositive-going spikes, with a very slow, low amplitude negative peak. D : Spikes with 3 peaks, inthis case 2 smaller positive peaks flanking a larger negative peak. Scale bar: 0.5 ms, 100 µV. Sitespacing: 65 µm.where Vp is the amplitude of the peak and dtz is the time between zero crossings on either side ofthe peak. As a result of the squaring, for large and small peaks that were proportionally shaped,larger peaks were defined as sharper.On each channel within the search window, the sharpest peak was found and paired with itssharpest temporally adjacent peak, either the one immediately to its left or its right, if any. Peak-to-peak sharpness Spp was defined as the sum of the sharpness measures of the adjacent pair.The channel within the search window with maximum Spp was labelled the primary channel ofthe putative spike. This channel sometimes differed from the channel of the original trigger peakaround which the search window was centered. In other words, sometimes the trigger channeland the putative spike’s primary channel were not the same. When this was the case, the current31trigger peak was rejected, and eventually the sharpest peak on the primary channel would beencountered as a threshold crossing trigger peak in its own right. This heuristic helped preventexcessive shifting around in space from trigger channel to primary channel, which qualitativelyhelped reduce migration to the spatial edge of the search window, and the associated edge effects.It also prevented low amplitude spikes from locking out (see below) neighbouring larger amplitudespikes that immediately followed.A second heuristic was also applied in time: if the trigger peak came before the sharpest peak,the trigger peak and its associated search window was again rejected. This prevented prematurelysetting the temporal detection lockout (see below) on the primary channel, which was importantbecause sometimes the early peak on the primary channel was part of a different yet to be detectedspike on a nearby channel. Both the spatial and temporal heuristics were used to prevent anincorrectly centered detection lockout in space and time. In this way, the search window was usedto check if the trigger peak and the sharpest peak were identical.Next, the adjacent peak pair with maximal Spp was tested to ensure that its peak-to-peakvoltage Vpp exceeded Vppt = 1.5Vt. If so, the adjacent peak pair was considered to be the centerof a plausible spike. Together, the Vt and Vppt absolute value voltage thresholds, and the dtmaxtemporal threshold constituted a very general expectation of what a spike should look like. Thisallowed for detection of both fast and slow spikes with two or more peaks of alternating sign, and norestriction on the relative amplitudes of the peaks, nor their absolute sign. However, monophasicspikes were excluded (see Section 3.13.1).Unfortunately, there was no parametric measure that could be used to align a spike to one ofits peaks. A small change in spike shape due to noise could cause a sudden shift in the sharpnessrank of peaks belonging to the spike. Therefore, a new inclusion window was formed aligned intime to the negative peak of the pair (Figure 3.4), and centered in space on the primary channel, asbefore. The negative peak was chosen because extracellular spikes are mostly negative-going, andprior to clustering with many other similar spikes, there was no way to otherwise determine whichof the two sharpest peaks, positive or negative, was more appropriate for alignment. Subjectivelyevaluated alignment errors occurred mostly on rarer, positive-going spikes (Figure 3.3C). Afterinitial clustering (Section 3.6), such errors were later corrected by best fit realignment, or byforcing realignment to the biggest positive peak (Section 3.7).The new spatiotemporal window was constrained to an inclusion radius rinclude which, likerlockout, was also set to 150 µm (but could be set differently if desired). For a 3 column polytrodewith 65 µm hexagonal spacing, rinclude = 150 µm resulted in about 12 included channels per spike.One millisecond of data was saved: 0.4 ms before the earlier of the two adjacent peaks, and 0.6 msafter (although figures in this chapter show ± 0.5 ms, this was later changed to capture more ofthe slower afterhyperpolarization (AHP) of each spike). At a sampling rate of 50 kHz, this gave 50timepoints per channel, for a total of ∼ 600 voltage values per spike. These were saved to disk alongwith various other parameters characterizing each spike. Saved waveforms remained interpolated32Figure 3.4: Spike detection of data in the dashed box in Figure 2.3. Detected spikes are indi-cated with a vertical raster line at the negative peak of their primary channel, spanning all thechannels that fell within a 150 µm radius — in this case, 4 channels above and below each primarychannel. Raster lines are coloured according to the primary channel of each spike. Low amplitudesingle channel (grey arrows) and multichannel (white arrows) spike-like events were not detectedbecause they were subthreshold. Each channel had a different threshold based on its noise level(Equation 3.1). Grounded channels were disabled for spike detection. Scale bar: 1 ms, 100 µV.Site spacing: 65 µm.33and sample-and-hold corrected. Saved data were approximately 20× smaller than the original .srfdata acquisition files, and could be relied on almost exclusively for subsequent spike sorting (.srffiles were still required for substantial spike realignment, see Section 3.7). This allowed the rest ofthe spike sorting process to be much more portable.During all of the preceding spike detection steps, a channel dependent temporal lockout wasconstantly enforced and updated. This lockout prevented multiple registrations of the same spike.For example, when testing a putative spike against the lockout, if a previously detected spike ona proximal channel extended up until or past the primary peak of the putative spike, the putativespike was locked out and hence rejected. Most likely, this putative spike consisted of one or morepeaks belonging to the previously detected spike. However, keeping the lockout highly localized inspace and time was also desirable to prevent the unintended lockout of distinct spikes. Therefore,a balance was struck in the spatiotemporal extent of the lockout, between minimizing multipleregistrations of the same spike, and minimizing the loss of distinct spikes.The lockout was updated after each detection of a spike. The channels included in the lockoutwere those that fell within rlockout of the spike’s primary channel. The lockout time for each spikewas different on each locked out channel. On the primary channel, the lockout was set to the timeof the later of the spike’s two adjacent peaks. The same held for the corresponding peaks on otherchannels within rlockout. However, peaks on nearby channels were not always simultaneous in time(Figure 3.5). To find the corresponding peaks on nearby channels, each channel within rlockout wassearched ± dt/2 around the time of each peak on the primary channel, where dt ≤ dtmax is the timebetween the spike’s adjacent peaks on its primary channel. If more than one peak was found on agiven nearby channel within the given time range, the peak closest in time to that on the primarychannel was chosen as the corresponding peak. If no peak was found on a given nearby channelwithin the required time range, the corresponding peak was declared to be at the same timepointas that on the primary channel. When searching for corresponding peaks, sign was ignored. Thisallowed for polarity inversion across channels, which could occasional occur (e.g., green unit inFigure 3.10B).Since sufficiently realistic simulations of extracellular cortical spike data are currently lacking(Section 3.12), manual inspection of hundreds of detected spikes and minutes worth of data was usedto evaluate spike detection performance. No obvious spike detection errors were found, whetherfalse positive or negative (but see arrows in Figure 3.4 for less obvious false negative candidates).Errors were generally only found during clustering (Section 3.9), in which many thousands of spikeswere considered at a time. By nature, only false positives could be found during clustering. Falsepositive spike detection error rates were ∼ 1% of detected spikes. Many other apparent detectionerrors were simply spike alignment errors that were easily corrected (Section 3.7).34Figure 3.5: Spike propogation in spacecan have noticeable delays, resulting in non-simultaneous peaks on nearby channels. 20spikes are shown from a cluster in ptc22.tr1.The top left channel is the primary channel(with maximum Spp), and is also the top leftsite of the polytrode. Yellow markers de-note the primary peak on each channel, andred markers denote the later secondary peak.Markers were aligned to the mean, but eachspike deviated slightly. All channels within 150µm of the primary channel are shown. Thepeaks of channels without markers were toosmall and inconsistent to mark in this display.Scale bar: 0.5 ms, 100 µV. Site spacing: 65 µm.3.5 Spatial localizationOnce detected, each spike was localized to a 2D position along the plane of the polytrode. A2D Gaussian distribution was fitted to the spatial voltage distribution of each spike, namely Vppcalculated from the adjacent peak pair on each of the spike’s included channels (Section 3.4). TheGaussian model’s position was initialized to the Vpp-weighted mean position of the spike’s channels.Although some cells’ voltage distributions were clearly elliptical (e.g., Figure 3.13B, magenta anddarker blue units), a circularly symmetric Gaussian distribution with a spatial extent of σ (withσ ≡ σx ≡ σy) was used to reduce the number of free parameters. Circular symmetry was imposedfor model stability given the limited amount of spatial data provided by each spike, especially inthe x direction which had at most only 3 values for a 3 column polytrode. σ was initialized to 50µm, approximately the average spatial extent across all spikes (Figure 5.3). Vpp at any point (x, y)along the plane of the polytrode was modelled byVˆpp(x, y) = Ae− (x−x0)2+(y−y0)22σ2 (3.3)where (x0, y0) is the distribution’s spatial origin. The amplitude A was fixed to Vpp of the primarychannel, which was usually also the maximum Vpp of all the included channels. Keeping A fixedreduced the number of free parameters to 3.The Levenberg-Marquardt (LM) least squares algorithm (scipy.optimize.leastsq) was usedto fit the model to each spike. The algorithm was given Vpp for each of the spike’s channels, alongwith the (x, y) coordinates of each channel. On every iteration, the free parameters x0, y0, and σwere modified to minimize the squared error between the model (Vˆpp(x, y)) and the data (Vpp(x, y)).The final values of x0, y0, and σ were saved with the rest of the spike’s information.Spike location and amplitude is one way to reduce a ∼ 600 dimensional voltage space (Sec-35tion 3.4) down to only three dimensions (x, y, Vpp), and initial attempts were made to clusterspikes in this space. However, this space on its own ignores all temporal information about spikeshape. Spikes with very distinct shapes could share the same position in this space, and conversely,due to spatial drift over time, spikes with very different positions in this space could still belongto the same cluster (Figures 3.6 & 3.12). Therefore, the (x, y, Vpp) space was poorly suited forunit clustering. Nevertheless, spatial localization was useful for visualizing the spatial positionand amplitude of spikes along the polytrode (Figure 3.6). It was also useful for estimating thespatial position of clusters based on the median of the spatial positions of their constituent spikes(Section 4.4), allowing clusters to be arranged in vertical spatial order.3.6 Initial channel splitTo create an initial set of clusters, the set of detected spikes was split according to each spike’sprimary channel. This resulted in up to 54 initial clusters, one per polytrode channel, numberedin order from top to bottom of the polytrode. This “divide-and-conquer” approach (Swindale andSpacek, 2014) to splitting the full set of spikes into a few dozen smaller ones was desirable fortwo reasons. First, a common set of channels within a given set of spikes was required before anydimension reduction (Section 3.8) could be applied to them. Second, clustering with the GACalgorithm (Section 3.9) takes up to O(N2) computational time, where N is the number of spikes.Splitting up the large initial group of unclustered spikes to reduce N within each group was thereforevery computationally advantageous for clustering.Splitting spikes by their primary channel resulted in only a very preliminary set of clusters.These were then further split into single unit, multiunit, and noise clusters, some of which werelater merged (Section 3.10.2). For example, some units fell half-way between two channels, resultingin spikes whose primary channel alternated between two channels (Figure 3.3B). Also, clustersbelonging to neurons drifting in time (Figure 3.12) were often initially oversplit, and were mergedlater on.The alignment, dimension reduction, clustering, and verification steps that follow were per-formed iteratively on clusters ordered vertically in space, from top to bottom of the polytrode.Once a cluster at a given position on the polytrode was judged sufficiently clean and well clustered(Section 3.10), it was marked as “good”, which highlighted it in green in the cluster list (Fig-ure C.3). Attention was then shifted to the next cluster down the polytrode. This way, progresswas made visually obvious to the user. Occasionally, after a few rounds of merging and splitting,clusters were renumbered to keep them spatially ordered from top to bottom.3.7 AlignmentBefore applying any dimension reduction to a group of spikes, spikes had to be properly aligned,otherwise subsequent clustering steps could split groups of spikes based on spike misalignment36A BCFigure 3.6: Spatial locations and Vpp of ∼ 1.9M spikes from track ptc22.tr1 after clustering(Section 3.9) and verification (Section 3.10). Spikes are plotted as points in a 3D (x, y, Vpp) space,represented by red, green and blue axes respectively. Each dimension is normalized by its standarddeviation, except for y, which was normalized by the standard deviation of x to maintain aspectratio. Positive y points down the polytrode, and Vpp of each spike is that of its primary channel.Points are plotted with perspective, from different views: A: above the plane of the polytrode;B : obliquely; and C : from the side. Colours represent distinct clusters, with 10 colours cyclingalong the y axis. In this space, what appears to be a single cluster can sometimes be multipleclusters when plotted in a more discriminating space, such as PCA (Section 3.8). Alternately,distinct clusters in this space (e.g., the high amplitude bimodal green cluster) can in fact be asingle cluster that has drifted in position (Figure 3.12A). Gaps of points are due to faulty sites oran excess of noise events or multiunit spikes. Axes bars represent σc = 0.43 in each dimension (seeSection 3.9.1).37instead of genuine differences in spike shape (Figure 3.7). Since all spikes were aligned to theirnegative peak during detection, and since most spikes consist of a sharp negative peak followed bya wider positive peak, most spikes within a given cluster were already reasonably well aligned to oneanother. However, some cells had spikes whose primary channel alternated between two or morechannels, due to noise or drift. Some spikes had two similarly sharp negative peaks, while otherspikes were predominantly positive-going. Any of these cases could lead to alignment errors. Evenmodest misalignment could result in artifactual clusters (Figure 3.7). Larger misalignments coulddistort cluster distributions (Figure 3.8), which could further complicate downstream clusteringsteps.With spikes split into an initial set of clusters (Section 3.6), they could now be aligned to oneanother by best fit, instead of by the (often noisy) features of individual spikes. To realign spikes bybest fit, the desired cluster was selected, as were the channels and time range on which to calculatewaveform differences. Usually, only the top one or two largest amplitude channels were selected.On the selected channels, the mean waveform of all of the cluster’s spikes was calculated. Then,for each spike, the sum of squared differences was calculated between the spike’s waveform and themean waveform. The sum of squared differences was used instead of the RMS difference in orderto decrease calculation time. Each spike was then shifted up to 2 interpolated timepoints in eitherdirection (± 40 µs), for a total of 5 possible positions (including no shift). The sum of squareddifferences was calculated at each position, and the spike was shifted to the position that gave riseto the smallest sum of squared differences. The user typically executed this process 2 or 3 times,the mean waveform updating each time. After a few best fit realignments, the number of realignedspikes per realignment approached zero, and the standard deviation of the spike waveforms settledat a minimum value.Note that the above best fit realignment process could be performed on any desired selectionof spikes, whether selected individually or by selecting one or more clusters. The only requirementwas that all selected spikes shared at least one common channel. However, realignment was mostoften performed on one single cluster at a time.When shifting spike waveforms, missing end points were replaced automatically, such that thelast real value at a given edge was repeated the appropriate number of times to pad the waveformto the proper width (50 timepoints for the usual case of 1 ms waveforms interpolated to 50 kHz).Though not often necessary, this edge data could be replaced by reloading the actual data fromdisk. For the occasional spikes that were realigned many times and were shifted by a large amount,this was an important feature. Padding with edge data and only occasionally reloading made formuch faster realignment and decreased the need for access to the continuous waveform data ondisk.After spike detection was complete, the spatiotemporal lockout for each spike (which only madesense in continuous time) could no longer be applied. Yet, given enough best fit realignments,it was possible to violate previously observed lockouts and shift a detected spike far enough that38NDsep = 0.950 NDsep = 0.007pre-aligned post-aligned mergedFigure 3.7: Spike misalignment can result in artifactual clusters. Left : Two clusters are plotted,with mean waveforms above and cluster plot below. Cluster plots are based on the first 3 principalcomponents (PCs) (Section 3.8) calculated from the 5 selected green channels. The first clusterplot is rotated to show maximum cluster separation, and the rest maintain the same orientation. Incluster space, the pair are distinct as indicated by their high NDsep value (Equation 3.9), but thesimilarity of their mean waveforms suggests that they may instead be a single cluster split into twoclusters of slightly different alignments. Middle : The two clusters realigned to each other, usingthe sum of squares best fit of each spike’s waveform to the mean waveform of all the spikes fromboth clusters, measured on only the 5 selected channels (highlighted in green). Realignment wasperformed 3 times, with fewer spikes shifted each time. Separation in cluster space disappeared,suggesting the pair were indeed oversplit. Right : The two realigned clusters merged into a singlecluster. Scale bar: 0.5 ms, 100 µ erroneously merged with another one nearby in space and time. This could happen due tohigh initial misalignment resulting in the lack of a local minimum in the sum of squared differences.During best fit realignment, spikes were shifted by no more than 40 µs at a time to help prevent suchspike mergers. Given enough realignments, even this did not provide complete protection. However,it was generally obvious from the plotted waveforms and the displayed realignment statistics whenspikes were shifting too far or in the wrong direction. In such a case, the user would stop any furtherrealignment, and upon clustering, the now grossly misaligned spikes would split off as a cluster,which could be dealt with separately (Figure 3.8, middle). It was also possible to realign spikes to39pre-aligned post-aligned mergedFigure 3.8: Spike misalignment can result in non-Gaussian clusters. Left : Above, 20 randomlyselected spikes from a cluster are plotted over top of the cluster’s mean waveform (thicker redline). Despite all being aligned to their negative peak by default, many of the cluster’s spikes weremisaligned due to being predominantly positive-going (Figure 3.3C). Below, the resulting non-Gaussian distribution of the cluster’s points, based on the top 3 PCs (Section 3.8) of the selectedchannel. Middle : After best fit realignment of waveforms on the single selected channel (green),the mean waveform increased in amplitude and the main cluster became much more Gaussian.A second sparser cluster below the main one was the result of spikes that began so far out ofalignment that best fit realignment failed to properly realign them. This sparser cluster was splitoff and realigned with some manual intervention (alignment of each spike to its positive peak, thenbest fit of spikes within the cluster, then best fit with the main cluster). Right : The sparser clusterwas then merged back into the main cluster. The final cluster distribution is much more Gaussianthan the original.either of their two original peaks (positive or negative), or to manually shift a selection of spikesleft or right by a desired amount. Once spikes were manually shifted closer to their (subjectively)proper alignment, best fit realignment could once again be used.3.8 Dimension reductionGiven that each spike inhabited an impractically large ∼ 600 dimensional space (Section 3.4), thenumber of dimensions had to be greatly reduced before clustering. Most spike sorting methodsthat rely on clustering in a dimension reduced space use only 2 dimensions (Lewicki, 1998). Since 3dimensions are the most that can be easily visualized, and since any more than the top 3 dimensionsfrom either of the reduction methods below (PCA or ICA) are unlikely to improve clusterability,40spikes were reduced to a 3D space before clustering.One way to reduce dimensionality is with PCA (Shlens, 2009). Neighbouring waveform datavalues are significantly correlated in space and time. PCA can take such a correlated data set andrepresent it in terms of orthogonal (principal) components that are uncorrelated. These orthogonalcomponents can then be ranked according to the amount of variance of the original data thatthey explain. For Gaussian distributed data, typically only the top few components are needed toaccurately reconstruct the data (Shlens, 2009). This allows for a great reduction in dimensionality.Note however that the goal here is not to reconstruct the data in a low dimensional space withmaximal accuracy, but rather to reduce the data to a space that maximally reveals clusters.First, for a given selection of spikes, such as those belonging to the initial channel-based clusters(Section 3.6), the relevant channels were selected either automatically or manually. For automaticchannel selection, the median of the modelled spatial positions of the selected spikes (Section 3.5)was calculated. Then, a radius r was calculated around this median position such that r encom-passed 95% of the modelled spatial σ values of the selected spikes. All channels that fell within rof the median spatial position were then automatically selected. Channels could also be manuallytoggled by simply clicking on them.The relevant time range on the selected channels could be left at the full 1 ms width, ormanually reduced in 0.1 ms increments to include only the higher amplitude parts of the spikewaveforms, around the peaks. In either case, the chosen time range was always centered on thespike waveforms (i.e., at t = 0.5 ms of each spike’s saved waveform data). Generally, the mostrelevant channels and time ranges were those with the greatest signal and/or the greatest signalvariance (Figure 3.9). Discriminative channels and time ranges could also be revealed by plottingrandom subsets (e.g., 20) of the selected spikes at a time, and watching which channels and timeranges had signals that varied the most between subsequent random samplings. Selected channelsand time ranges were highlighted in green (Figures 3.7, 3.8 & 3.9, all showing full 1 ms width timerange selection). Ideally, channel and time range selection excluded waveform data that were notuseful for distinguishing spikes, such as channels and times during which spike waveforms had littleor no signal. Restricted channel and time range selection also reduced the dimensionality of theinputs to PCA and ICA, allowing them to run faster.Next, for each spike, the waveforms on the selected channels in the selected time range wereconcatenated into a single ndim long row vector, where ndim is the product of the number ofselected channels and timepoints. Row vectors from all selected spikes were combined to form annspikes × ndim input data matrix. PCA was performed on this matrix, and the scores of the top 3PCs were used to characterize each spike.Another way to reduce data dimensionality is with ICA (Comon, 1994; Bell and Sejnowski,1995; Hyva¨rinen et al., 2001). Unlike PCA, ICA considers higher-order statistics instead of justsecond order statistics. ICA does a better job of separating out components of non-Gaussiandistributed data by searching for components of maximum independence. These components are41A BNDsep = 0.727 CNDsep = 0.983 NDsep = 0.957Figure 3.9: Channel selection affects clusterability in a dimension reduced space. This is shownhere by comparing two existing clusters (red and yellow), but applies equally well to unclusteredspikes. Top: Mean cluster waveforms. Channels and time ranges selected for dimension reductionare highlighted in green. In this example, the full 1 ms time range was selected on each channel,represented by the full length of each green line. Shorter selected time ranges, symmetric aboutt = 0.5 ms (vertical lines), were represented by proportionally shorter green lines. Bottom :3D PCA cluster plots. PC0, PC1 and PC2 are along the red, green and blue axes respectively.Each cluster plot is rotated to show maximum cluster separation. The optimal manual channelselection in B resulted in a much more clusterable space than in A, as denoted by the NDsepvalues (Equation 3.9). The optimal channels were usually those that showed the greatest signalvariance. C : Automatic channel selection resulted in separation nearly as good as the optimalmanual channel selection in B . Note that even though the channels selected in C are the unionof those in A and B , separation in B is better. This shows that, at least in a dimension reducedcluster space, some channels can worsen clusterability. Scale bar: 0.5 ms, 100 µV.42not necessarily orthogonal to each other, as they are in PCA. Whereas PCA can only rotate itsentire set of components together, ICA can also change the angles between its components. Variousflavours of ICA exist. The method used here was FastICA (Hyva¨rinen, 1999; Hyva¨rinen and Oja,2000), implemented in the MDP Python library (mdp.fastica).Prior to performing ICA, the nspikes × ndim input data matrix was prepared the same way asdescribed above. But because ICA is much more computationally expensive than PCA, PCA wasfirst applied to partially reduce the dimensionality (Scholz et al., 2004). The top 7 × nchans PCs,where nchans was the number of channels selected, were kept to create a reduced input data matrix.ICA was then performed on this reduced matrix. A factor of 7 was chosen as a good trade-offbetween speed and cluster separability. Unlike PCs, independent components (ICs) do not comewith associated scores. However, components can be scored post-hoc by various means. In this case,they were scored by their kurtosis (scipy.stats.kurtosis), a 4th order statistical measure of the“peakiness” of a distribution. Kurtosis is one way of measuring how non-Gaussian a distribution is.By sorting by kurtosis, the components were sorted by how non-Gaussian they were, and thereforeby their statistical independence from each other (Scholz et al., 2004).ICA was especially useful for separating clusters of vastly different numbers of points (sizeratios > 50, Figure 3.10A & B). The small clusters in such pairs could consist of spikes, oftenbelonging to some other existing larger cluster, or noise events, which were discarded. Conversely,and surprisingly, ICA was dramatically worse than PCA at separating similarly sized clusters (sizeratios < 10, Figure 3.10C, see Section 3.13.2 for discussion). Therefore, PCA was generally usedfirst to reveal large clusters within a selection of spikes, and ICA was run later on each of thoseclusters to check for contamination (Section 3.10.1).In addition to the top ranked PCs or ICs, other parameters could also be chosen as one ormore dimensions to plot in 3D: spike spatial parameters x0, y0 and σ; peak-to-peak voltage Vpp;the time dt between the peaks of a spike; and spike time t. Of these, only t was found to be usefulfor clustering. The rest were all encapsulated by PCA and ICA of spike waveforms. Though noteasily visualized, clustering in more than 3 dimensions was explored but did not show any practicalbenefit. Wavelet decomposition (Quian Quiroga et al., 2004) and wavelet packet decomposition(Hulata et al., 2002), extensions of Fourier decomposition which consider both signal frequencyand time, were also explored (using the PyWavelets library, did not prove very useful (not shown). Although any 3 parameters could be plotted in anycombination, all clustering was done either in pure PCA or ICA space, or the top two PCs or ICswere plotted vs. t to handle drift. In practice, all clusters were examined in four different 3D spaces:pure PCA, pure ICA, the top two PCs vs. t, and the top two ICs vs. t. Each plotted dimensionwas rescaled such that it had zero mean and unit variance. Spatial parameters x and y were bothnormalized by the variance of x to maintain a constant spatial aspect ratio.43NDsep = 0.558NDsep = 1.000A BNDsep = 0.668NDsep = 1.000CNDsep = 0.015NDsep = 0.999PCAICAFigure 3.10: ICA separates clusters with large size ratios better than PCA. Top: Mean clusterwaveforms, with channels selected for dimension reduction highlighted in green. Clusters are plottedin PCA space (middle) and ICA space (bottom). Each plot is rotated to show maximum clusterseparation. NDsep values (Equation 3.9) quantify the separation of each cluster pair. A: A pair ofclusters with 6970 (red) and 190 (white) spikes each. Because there were so few points in the whitecluster, the mean waveform of the red cluster was essentially identical to that of all the spikes fromboth clusters. In PCA space, the smaller white cluster is encompassed by the tail of the larger redone. Their distinctness is revealed only in ICA space. B : Another example cluster pair with a largesize ratio (orange: 6772 spikes, green: 101 spikes). C : A cluster pair (same as in Figure 3.12D)with similar numbers of spikes (yellow: 41376; cyan: 36633). In this case, because the clusters werenot drastically different in size, PCA did a much better job of separating them than ICA (but seeSection 3.13.2). Scale bar: 0.5 ms, 100 µV.443.9 ClusteringWith an appropriately chosen low dimensional space, spikes were ready to be partitioned intoclusters representing putative neurons. Initial attempts at manual clustering involved drawing 3Dellipsoids. This generally allowed the user to visually cluster the data as desired, but it incorrectlyimposed ellipsoidal shapes with hard boundaries. Just as critically, it proved far too laborious andslow, and was subject to more user bias than an automated algorithm. However, occasional manual“painting” of points in 3D with the mouse was used to quickly examine and potentially split offsmall numbers of outlier points from a large cluster.All of the clustering algorithms described in Section 3.1.2 were attempted, but with limitedsuccess. HC was tested using the scipy.cluster.hierarchy and hcluster Python libraries,but was eventually rejected due to poor results. EM+GMM was tested using the method andMATLAB code of Bar-Hillel et al. (2006), but was found to be very slow, especially for morethan a few thousand spikes and a few clusters. Also, splitting the data into time chunks resultedin the loss of neurons that fired very sparsely. SPC was tested using software from Blatt et al.(1996) and Quian Quiroga et al. (2004), but often an ideal temperature could not be found tosatisfactorily cluster the data presented here (e.g., Figure 3.11). Clusters were either oversplit orundersplit. Also, SPC was sensitive to narrow, low density bridges of points between clusters, andwould incorrectly combine such clusters (Swindale and Spacek, 2014). SPC is somewhat insensitiveto density variation, and this was found to be a drawback rather than a benefit.With all existing methods, it was often difficult or impossible to cluster the points in the waythe user desired. In 3 dimensions or less, obvious (and often non-Gaussian) clusters were oftenvisible in the data that none of the algorithms could easily find.3.9.1 Gradient ascent clusteringInstead, a new clustering algorithm, GAC, was developed to mimic the clustering a human user doesby eye. Visually we look for local peaks in the density of points, at the appropriate spatial scale.GAC iteratively clusters data according to local density peaks, at the chosen spatial scale. Beforeiteration began, all points were first duplicated into a set of “scout” points. During iteration, theoriginal data points remained motionless, while the scout points were allowed to move and mergewith one other.In the first step of each iteration, the local density gradient of data points around each scoutpoint was calculated, and each scout point was moved up its gradient by an amount relative to thegradient’s magnitude. The update step vector ∆s of scout point i’s ndim-dimensional position si45was∆si =αn∑j=1dijfijn∑j=1fij(3.4)where α is the gain of the step vector (α = 2.0 was used), dij is the distance vector between scoutpoint i and data point j, f is the spatial kernel used to define locality, and n is the number ofdata points in the neighbourhood of the scout point. The summation in the numerator representsthe local density gradient, normalized by the summation in the denominator. Although n couldpotentially include all N data points in the cluster space, in practice given a kernel characteristicscale σc, there was no benefit in setting n = N . Instead, for computational efficiency n was limitedto data points that fell within a radius rneigh = 4σc of the scout point. The chosen spatial kernelwas an ndim-dimensional Gaussian distribution,fij = e−d2ij2σ2c (3.5)where dij is the Euclidean distance between scout point i and data point j. As mentioned previously(Section 3.8), ndim = 3 was used.The second step of each iteration was the merge step, during which the actual clustering oc-curred. During the merge step, a search was performed around each scout point for other nearbyscout points, merging those that were sufficiently close to one another. The threshold for this de-cision was a merge radius set to a fraction of σc, rmerge = 0.25σc. For ease of bookkeeping, for anypair of scout points to be merged, the scout point with the higher index was always merged intothe scout point with the lower index. On each merge, the original index of each scout point andthe new scout point it had been merged into were both kept track of, such that when the algorithmexited, each original data point (from which all scout points originated) had an index that assignedit to one of the remaining scout points.The completion of both steps, gradient ascent and merge, constituted a single iteration of thealgorithm. On each iteration, the number of scout points generally decreased, while each remainingscout point neared its local density peak. There were two convergence criteria, either of which wassufficient to signify convergence and cause the algorithm to exit. The first kept track of how manyiterations in a row had occurred without a single merger of any scout points. If this reached 1000,the algorithm would exit. The second convergence criterion kept track of how far each scout pointmoved during the update step. Scout points that moved less than 10−5σc on any iteration weredeemed to have stopped moving, and were marked as so. Scout points marked as stationary couldbe skipped during the update step, and pairs of stationary scout points could be skipped during themerge step, reducing computational time. If at any point all of the scout points stopped moving,46σc = 0.09 σc = 0.22 σc = 0.52 σc = 0.69A B C DFigure 3.11: GAC dependence on σc. In this example 50,000 points are plotted in 3D PCA space,rotated to show maximum separation. Five distinct clusters are visible to the eye. Clusteringresults from left to right ranged from oversplit to undersplit, depending on the user-set value ofσc. Of the four values, σc = 0.22 (B) gave the best result in this example. Results were consistentwithin about ± 25% of that value. Two axes are visible in each panel. The size of the central axescorresponded to σc, allowing the user to better gauge its optimal value according to the separationof visible clusters.the algorithm would exit. Upon convergence, each remaining scout point represented the center ofa cluster. All scout points that had been merged into a particular remaining scout point shared thesame index and belonged to the same cluster. Any clusters with less than 5 points were marked asunclustered outliers by assigning them a cluster index of 0.The only parameter adjusted by the user on a regular basis was σc, which defined the spatial scaleof cluster separation judged to be relevant to the data. Low σc values yielded many local densitypeaks, corresponding to many small clusters. High σc values yielded fewer local density peaks,corresponding to only a few large clusters (Figure 3.11). A single σc value was used uniformlyin all dimensions. This was feasible because the data were normalized in all dimensions duringdimension reduction (Section 3.8). Importantly, this limited the number of parameters requiringuser adjustment to only one.The normal range of values for σc was 0.1 < σc < 0.9, and the most common value was σc ≈ 0.4.The value of σc chosen by the user was visually guided by the spatial structure of the data plottedin the 3D cluster space. A set of axes whose size represented σc was scaled until it was roughly thesize of the minimum separation between clusters. Using the mouse or keyboard, the cluster spacecould be zoomed, translated, and rotated at will, and the axes could be independently positionedand sized relative to the data (Figure C.3). The desired clustering, as evaluated by eye, was usuallyaccomplished on the first attempt, but if need be σc adjustment and execution of GAC could bedone iteratively until the desired clustering result was obtained (Figure 3.11B). Undersplitting wascorrected by decreasing σc, and oversplitting by increasing it. The user could undo or redo anynumber of clustering operations, including cluster splitting, merging and deletion. This allowed foreasy before and after comparison of GAC results. GAC performed fast enough (Figure C.4) forinteractive manipulation of σc.Clustering results were usually consistent within a range of σc values. For example, the clustering47result in Figure 3.11B was tolerant to within about ± 25% of its optimum value. This meant thatfor a given set of points in a given cluster space, there was rarely a need to finely optimize σc.An automated method of choosing σc, which searches for a range of values over which the numberand size of found clusters remain invariant, is described in Swindale and Spacek (2014). However,because spyke is heavily focused on user interactivity, this automated σc selection method was notimplemented here.The α parameter controlled the rate of gradient ascent. If set too high, scout points couldovershoot and then oscillate around the local density peak. If set too low, the algorithm would takeexcessively long to converge and might even exit prematurely. A good compromise was found bysetting α = 2.0.Although devised independently, it was later found that GAC is a modification of the mean-shiftclustering algorithm (Fukunaga and Hostetler, 1975). The chief difference between the two is thatin GAC, scout points are merged on each iteration, greatly speeding up the algorithm by rapidlydecreasing the number of scout points to iterate over.3.10 Cluster verificationPerforming dimension reduction on a channel-based cluster and running GAC on the resultingset of points was only the first step. Despite appearances, there was no guarantee that the newlyfound clusters were indeed unimodal, distinct, and free of noise events and misassignments. Clusterverification proved to be the most lengthy and laborious step.There were three major issues to deal with during cluster verification: undersplitting, oversplit-ting, and misassignment. The outcome of cluster verification was the classification of each clusteras either single unit or multiunit. This classification was made by the user, and was based on bothsubjective and objective measures. Classification of each cluster depended on its unimodality, itsdistinctness from other clusters in 3D cluster space, and the consistency of its plotted spike wave-forms. If a cluster was mostly composed of what were obviously noise events, or was an unsplittablecollection of noise and spike-like events, a third option was also available: deletion. However, nodetected spikes (whether genuine or noise events) were ever truly deleted. Instead, events werediscarded by assigning them to a special cluster with index 0. Single unit and multiunit clusterswere assigned positive and negative cluster indices, respectively. Given sufficient user confidencein the isolation quality of a single unit cluster, it would also be marked as “good” for export forsubsequent spike train analysis (Chapters 4–6). Any time such a cluster’s list of member spikeschanged due to splitting or merging, its “good” flag was cleared to indicate that it needed to bere-verified. In practice only a subset of single unit clusters were judged to be adequately isolatedand were exported. All other clusters, both single unit and multiunit, were kept for potential fu-ture refinement but were not exported. Only about half of all threshold crossing events acceptedas plausible spikes during spike detection (Section 3.4) were exported (Table 4.1).483.10.1 UndersplittingEach cluster was tested for undersplitting to ensure that it was unimodal and consisted of spikesof uniform shape, with as few noise events as possible. Upon choosing the most relevant channelsand time range (Section 3.8), each cluster was examined for multimodalities in all four of thecritical 3D cluster spaces: pure PCA, pure ICA, and the top two PCs and ICs vs. spike time t.Multimodality in any one of these spaces suggested that the cluster was undersplit, but was notnecessarily definitive. For example, a rapid but smooth and continuous shift in waveform shapecould result in a multimodal cluster in pure PCA space, but when plotted against time, was revealedto much more likely be the same unit undergoing rapid drift (Figure 3.12A–B). Unfortunately, suchsituations required user judgement, precluding automation.Besides visually searching for multimodalities and running GAC to see if it could split off clustersin the chosen 3D space, cluster quality could be further subjectively evaluated by plotting subsetsof a cluster’s spikes (e.g., 20 at a time), and progressing from one overlapping subset to the next(or previous), in temporal order. This sliding spike selection window allowed the user to observehow the waveform shapes changed (or did not) over time, and whether those changes were gradualenough to suggest that they were due to long-term spike shape variability, such as from drift, andnot due to the erroneous merger of separate units.In a given 3D cluster space, if multiple clusters were visible, it was not necessary to separatethem all in a single run of GAC (although this is shown in Figure 3.11B). Splitting off only onecluster at a time was a more effective strategy, and was often (but not always) possible by choosingan appropriate value for σc. Each time a cluster was split off, dimension reduction was separatelyreapplied to not only the remaining points, but also to the cluster that had been split off. This wasrepeated until only unimodal clusters remained. Splitting off only one cluster at a time allowedPCA and ICA to maximally separate the remaining points, making it easier to subsequently splitoff further clusters.Because ICA was better than PCA at separating clusters of greatly differing population sizes(Section 3.8), and because within a given cluster, noise events were typically much fewer in numberthan actual spikes, ICA was better than PCA at separating noise events from spikes. Therefore,most cleaning (i.e., removal of noise events) was done in ICA space. After splitting off a suspectednoise cluster, like any other cluster it was examined in 3D cluster space, and its mean waveform andrandom samples of its spike waveforms were plotted. If the noise cluster was clearly unimodal, andwas composed of inconsistent and clearly not spike-like events, it was deleted. If it was unimodalwith inconsistent waveforms, but had at least some spike-like events, it was labelled multiunit.Sometimes what seemed like a noise cluster was instead clearly a set of spikes that had simply beenmisaligned (Figure 3.8, middle). Instead of discarding them as noise events, these spikes could berealigned to one another (Section 3.7) and then potentially merged back into an existing cluster(Section 3.10.2).When splitting off cluster outliers, instead of always having to run GAC and find an appropriate49NDsep = 0.996NDsep = 1.000BANDsep = 0.253 NDsep = 0.981CENDsep = 1.000 NDsep = 1.000DNDsep = 1.000NDsep = 0.999PC0, PC1, PC2 PC0, PC1, t50Figure 3.12: (Previous page.) Plotting clusters in time is necessary to check for drift. Sometimeswhat appeared to be two distinct clusters (A–B) were only a single cluster that had a relativelysudden drift event. Conversely, sometimes what looked like a single cluster in pure PCA space wasin fact two neighbouring clusters drifting together in time (C ). The channels selected for PCA arehighlighted in green (left). For each example, cluster plots are shown in pure PCA space (middle :PC0, PC1, PC2) and PCA vs. time (right : PC0, PC1, t). Red, green and blue axes point alongthe first, second and third cluster dimensions respectively. Stratification in time (vertical blueaxis, right) was visible because of periods of higher or lower activity or brief periods in betweenrecordings making up the track. A: This cluster corresponds to the large amplitude green double-peaked cluster in Figure 3.6. High amplitude variability on the two selected channels was apparentin the large transparent ± 2 standard deviation limits. In pure PCA space, the cluster appearedundersplit, but plotting in time strongly suggested that it was indeed a single cluster, with highvariability superimposed on slow drift. B : An erroneously split pair of clusters. In pure PCA space,they were completely distinct, but when plotted against time, the two were obviously a single clusterthat had drifted abruptly over a relatively short period of time. The two were later merged. C : Twosimultaneously drifting clusters that could only be distinguished when plotted against time. Theiraverage waveforms looked nearly identical. NDsep values (Equation 3.9) quantified the differencein separability. D : A drifting pair (same as in Figure 3.10C) of completely distinct neighbouringclusters. E : A non-drifting pair of completely distinct neighbouring clusters.value for σc, sometimes it was quicker and simpler to manually select points in the 3D cluster spaceby “painting” them with the mouse. The waveforms of all selected spikes were automaticallyplotted, and could be inspected before being split off from the parent cluster. If split off, theycould then be further inspected, realigned, and cleaned. Points at the fringes of a cluster wereroutinely selected by painting them, and their waveforms were examined to ensure that they werenot notably different from the cluster’s mean waveform.3.10.2 OversplittingEvery cluster was also tested to ensure that it was measurably distinct from all other clusters, andwas therefore not oversplit. The user could quickly compare a cluster to all others near enough inspace to share at least one channel with the cluster, in order of increasing mean waveform RMSdifference. The mean waveforms of each pair were overplotted, and if a pair looked suspiciouslysimilar, or their RMS difference on the selected channels was < 10 µV, or they scored poorly on oneof the cluster pair separation metrics (see below), the pair were potentially oversplit. To investigatefurther, the relevant channels and time range were selected, either manually or automatically (Sec-tion 3.8), for realignment and dimension reduction. If after realignment, no combination of channeland time range selection and dimension reduction clearly separated the two clusters, they weremerged. This new cluster in turn also had to be compared to all other nearby clusters. Checkingfor cluster distinctness could therefore be a laborious task.In addition to mean waveform RMS difference, cluster pair separation was quantified in four51ways: Jensen-Shannon divergence (DJS), 1D overlap area ratio, one-dimensional separation metric(1Dsep) and N-dimensional separation metric (NDsep). The first three required projecting thecluster pair onto a line. The line onto which their points were projected was formed by connectingthe centers of the two clusters, as calculated by the median positions of their member spikes in thechosen cluster space. Another 1D measure of separation is Fisher’s linear discriminant (Hill et al.,2011). It measures cluster separation by taking the ratio of the intercluster variance to the sum ofthe intracluster variances, along a projection line that considers both the means and the covariancematrices of the two clusters. However, this measure assumes Gaussian clusters, and was thereforenot used.DJS (Schneidman et al., 2006) is an information theoretic measure (in bits) of the separation oftwo 1D distributions, Q and P , defined byDJS(P,Q) =DKL(P,M) +DKL(Q,M)2(3.6)whereM =P +Q2. (3.7)DJS is a symmetric (DJS(P,Q) ≡ DJS(Q,P )) version of the Kullback-Leibler divergence (DKL),also measured in bits, defined byDKL(P,Q) =∑xP (x) log2(P (x)Q(x)). (3.8)DKL is the extra number of bits required to encode distribution P based on Q versus if it werebased on P . The closer DJS is to 1, the better the separation of the two distributions. The closer itis to 0, the more similar the two distributions. Though there was no hard threshold, cluster pairswere generally judged to have good separation when DJS ≥ 0.95.The 1D overlap area ratio is a simpler measure which calculates the fraction of area over whichthe two distributions overlapped. At each bin in the common histogram of the two distributions,the lesser of the two values was taken. These lesser values were summed up for all bins, and thendivided by the sum of the histogram values of the smaller distribution to get a (worst case) ratio.Again, there was no hard threshold, but values < 0.05 generally signified good separation.The 1Dsep measure is calculated by normalizing the distance between the medians of the two1D distributions by 3 times the standard deviation, σ, of the distribution with the greater σ.Generally, a value > 1 was required for clusters to be considered well separated. Like Fisher’slinear discriminant, this measure was less meaningful for non-Gaussian distributions, for which σpoorly captures the true spread of the distribution.NDsep was the preferred measure of cluster separation because it does not suffer from the lossof information inherent in projecting 3D clusters onto a single dimension. Like DJS and the 1Doverlap area ratio, it also does not assume Gaussian distributions. It was therefore relied on much52more heavily than the other 3 measures. For a pair of clusters i and j, where the number of pointsin each is Ni < Nj ,NDsep(i, j) = 1−1−Nnni/Ni1−Ni/(Ni +Nj), Ni < Nj (3.9)where Nnni is the number of points in cluster i whose nearest neighbour is also in cluster i. This isexactly 1 minus the overlap index described in Swindale and Spacek (2014). The value ranges from1 for completely separate clusters, to 0 for completely mixed clusters. The numerator is 1 minusthe fraction of points in cluster i whose nearest neighbour is in cluster i. The denominator is 1minus the probability that the nearest neighbour of any point in cluster i was also from cluster i, ifthe two clusters i and j were completely mixed. Like GAC, NDsep has O(N2) computational costbecause distances between pairs of points must be calculated. Also like GAC, it was implementedin fast Cython code with multithreading (Section C.2). However, unlike the merge step in GAC,the input could be subsampled to limit the computational cost. For each cluster with N > 20,000points, 20,000 points were randomly sampled from the cluster before calculating NDsep. As aresult, the calculation took only a fraction of a second per cluster pair, no matter their size.Because channel and time range selections (Figure 3.9) and dimension reduction methods (Fig-ure 3.10) could greatly affect the separation of clusters, multiple combinations of channels, timeranges, and dimension reduction methods were tested for every pair of plausibly oversplit clusters.Clusters that remained poorly separated (as measured by the separation metrics and visualized bythe user) no matter the cluster space were merged. Plotting against time in cluster space allowedthe user to check if one cluster was “drifting into” another. If a pair of clusters showed an unin-terrupted transition over time from one to the other, they were likely oversplit and were thereforemerged (Figure 3.12B). Another way of checking for oversplitting in time was to use the slidingspike selection window (Section 3.10.1) on both clusters simultaneously. This allowed the user tosee exactly how the spike waveforms were changing with time, and whether or not one cluster’sspike waveforms gradually morphed into those of the other.3.10.3 MisassignmentSometimes when comparing pairs of clusters in cluster space, even if a pair remained distinct, somepoints would be obviously misassigned. Most often, this was only a small fraction of points, and thatfraction might depend on which specific cluster space the points were plotted in. If points remainedmisassigned regardless of the cluster space, they were easily corrected by simply running GAC onthe cluster pair with an appropriate σc, or by manually painting the points to be reassigned.Discarded (unclustered) spikes were tested for potential incorporation into existing clusters.The waveforms of all discarded spikes were exhaustively compared to the mean waveforms of allclusters by calculating the RMS difference between each possible pair (the calculation was skippedfor cluster-discarded spike pairs that had no channels in common). The user then selected one targetcluster at a time, and the distribution of RMS differences was plotted for all discarded spikes that53fit the target cluster better than any other. As in multichannel template matching (Section 3.1.1),an RMS difference threshold was set. Discarded spikes that fell below the difference threshold wereautomatically selected, and were then examined in the usual ways. If deemed similar enough to thetarget cluster, they could be merged into it, or GAC could be run on the selected discarded spikesand the target cluster’s spikes, potentially merging some of the discarded spikes into the targetcluster. Once complete, the user would select the next target cluster and repeat the process.However, testing discarded spikes by template matching in this way was risky. Discarded spikescould not be optimally aligned to all clusters simultaneously, and therefore the exhaustive RMSdifference calculation in the very first step suffered from some inaccuracy. Also, as with templatematching, there was often no clear bimodality in the RMS difference distribution, and thereforeno guide for where to place the threshold. Finally, merging formerly discarded spikes into existingclusters altered those clusters, and required re-testing them against all other nearby clusters toensure they remained distinct, a laborious task (Section 3.10.2). This test for discarded spikes wastherefore used only rarely and conservatively. Erroneously discarding some spikes was consideredbetter than potentially contaminating existing clusters.3.10.4 Duplicate spikesFor each cluster, duplicate spikes, i.e., spikes with identical spike times belonging to the samecluster, were searched for and removed. Duplicate spikes were very rare, occurring at a rate of <0.02% of spikes. For tracks ptc15.tr7c, ptc22.tr1, and ptc22.tr2 respectively, 1154/7.3M, 277/2.05M,and 48/1.4M duplicate spikes were found. This was an overestimate because most clustered unitswere not considered “good” for export, yet their duplicate spikes were included in the counts.These duplicate spikes may have been due to temporally broad spikes with spike-like peaks justoutside their spatial lockout, which were then shifted towards the true spike’s primary peak due toexcessive realignment, i.e., excessive realignment may have undone the effects of the spatial lockout(Section 3.7).3.11 Autocorrelograms & refractory periodsAutocorrelograms could be plotted for any cluster and cross-correlograms could be plotted for anypair of clusters. Cluster pairs with very similar autocorrelograms, and whose cross-correlogramswere similar to their autocorrelograms, were considered potential candidates for merging (Hazan etal., 2006), but such evidence alone was not considered enough to warrant a merge. Autocorrelogramswere also inspected for a minimum refractory period gap in spike intervals of ∆t = ±0.75 ms(Figure 3.13A). Although the temporal lockout during spike detection prevented some refractoryperiod violations (RPVs), its duration varied from one spike to the next, and was never greaterthan 0.4 ms (Section 3.4). Moreover, the temporal lockout was not enforced during later spikerealignment (Section 3.7), allowing for further potential RPVs. RPVs were therefore quantified54from the autocorrelogram using a fractional measure f , defined for cluster i asfi =RiNi(3.10)where Ri is the total number of spike intervals within the designated refractory period (0.75 ms)and Ni is the number of consecutive spike intervals (number of spikes minus 1) for cluster i. A valueof 0 indicates that no spike intervals fell within the refractory period, and a value of 1 indicatesthat all of them did (very rare non-consecutive spike interval RPVs may have caused a negligibleoverestimate of this fraction). As expected for well-sorted clusters (those marked as “good” forexport), all had a very small value of f (Figure 3.13A, top two rows). Out of all 3 sorted tracks,the cluster with the highest value had f = 0.004.To show how effective or ineffective autocorrelograms are at revealing cluster contamination,pairs of well-sorted clusters were merged, and the autocorrelograms of the resulting merged spiketrains were plotted (Figure 3.13A, bottom row). The RPVs of the merged cluster m were comparedto those of the original clusters i and j, and the change in fractional RPVs as a result of the mergewas calculated asdfij =Rm − (Ri +Rj)Ni +Nj. (3.11)Because Rm ≥ Ri + Rj , df also ranged from 0 to 1, with 0 indicating no change in RPVs and 1indicating the largest possible change (from no spike intervals to all spike intervals falling withinthe refractory period). This was measured for all possible pairs of neurons in each track. For thevast majority of pairs, df was very small at less than 0.001 (Figure 3.13C). Results were similarfor longer designated refractory periods of 1 or 2 ms (not shown). This demonstrates that mostof the time it was virtually impossible to detect even blatant cluster contamination by examiningautocorrelograms for RPVs.3.12 SimulationSpike sorting methodologies may be tested against data with a ground truth of known spike times.Such data either come from simultaneous intracellular and extracellular recordings (Harris et al.,2000), or from simulated extracellular data. Relatively short simulated polytrode recordings weregenerated by taking templates from real recordings, and adding them at random times to artifi-cial noise generated independently per channel. The autocorrelation of the generated noise wasmatched to that of spikeless segments of real recordings (Swindale and Spacek, 2015). However,such simulated recordings were trivial to sort compared to real data, and could be sorted almostflawlessly even in a single big (x, y, Vpp) cluster space. Few of the methods described here werenecessary for sorting such simulated data. A more realistic simulation with the same spike sortingchallenges of a multi-hour track of real data would be much more complicated to generate. It wouldrequire noise events correlated over multiple channels, variable noise levels, and above all templates55020004000 155094 spikesf = 0.000074 2 0 2 4spike interval (ms)020004000 mergeddf = 0.020A B0200400 34836 spikesf = 0.000170200400 43306 spikesf = 0.00007020004000 165721 spikesf = 0.00018worst typicaldf4 2 0 2 4spike interval (ms)0200400 mergeddf = 0.00032worst typicalpair rank0 1000 2000 3000 4000010-510-410-310-210-1ptc15.tr7cptc22.tr1ptc22.tr2Cworst typicalFigure 3.13: Examining autocorrelograms for RPVs is not useful for diagnosing cluster contam-ination. A: When two distinct clusters (first two rows) were merged, there was typically littleincrease in the number of spike intervals that fell within the refractory period of the merged clus-ter, as shown by its autocorrelogram. The worst case scenario is shown in the left column, and themore typical scenario in the right column. Shaded grey regions represent the designated refractoryperiod (≤ 0.75 ms). B : Colour coded 3D cluster plots (first two PCs vs. time along the verticalaxis) and mean waveforms of the neurons in A, showing that for each of the two example neuronpairs, the cells were simultaneously active and in distinct spatial locations. White scale bars: 0.5ms, 100 µV. C : Simultaneously recorded pairs in each of the 3 tracks were sorted by decreasing df(Equation 3.11). Note the vertical log scale. The vast majority of merged pairs had very small df .About half had df = 0. The positions of the worst case and typical examples from A and B areshown. Results were similar for longer designated refractory periods of 1 or 2 ms.56drifting independently of each other and at non-constant rates. Finally, metrics would be requiredto verify that any simulated data were comparable in complexity to real data. Simulated data weretherefore not extensively used to test the spike sorting method presented here, but would be ofgreat utility in evaluating and improving the performance of all spike sorting techniques (Einevollet al., 2012).3.13 DiscussionThe spike sorting method described here used a divide-and-conquer approach by splitting polytrodedata into multiple smaller overlapping spatial domains (Swindale and Spacek, 2014). As a result,computational complexity and overall spike sorting time (including user time) varied roughly lin-early with the number of electrode sites and the number of isolatable units. This is a desirableproperty, especially if future recording technologies with thousands of sites and neurons are to bemade practical (Einevoll et al., 2012; Kording, 2011; Stevenson and Kording, 2011).Other than during spike detection, there was little automation in the spike sorting proceduredescribed here. This was intentional. There were too many variables, including alignment, channeland time range selection, dimension reduction, and cluster comparison and verification, for anautomated procedure to fully explore and safely make decisions about. Instead, the focus wasplaced on making the software fast to use, in both the time taken to perform each step, as well asin its graphical user interface (GUI) (Section C.2) and keyboard shortcuts. Unfortunately, whenspike sorting long duration cortical recordings with many adjacent cells and significant drift, userintervention and experience remain key. Presenting the user with all relevant options with which toquickly examine and compare clusters in a variety of different spaces allowed for greater confidencein the final result.3.13.1 Spike detectionPutative monophasic spikes (i.e., spikes consisting of only a single peak on the primary channel,with no adjacent peaks within ± dtmax = 0.4 ms) were ignored during spike detection (Section 3.4),and therefore excluded from all subsequent analysis in this study. The spike detection algorithmwas later modified to allow for monophasic spikes, with the requirement that the single peak exceedthe peak-to-peak threshold Vppt and that it be bounded by zero-crossings no more than dtz = dtmaxfrom each other (effectively setting a minimum sharpness threshold). Examination of the specificdifferences in spike detection resulting from these changes revealed that most trigger single peakswere very broad, slow and negative, and were generally part of the AHP of a larger precedingspike. In a recording in ptc15.tr7c (Figure 2.3), only 3/283 (∼ 1%) of trigger single peaks passedall of the above criteria and were detected as monophasic spikes (out of a total of 4491 detectedspikes, i.e., 0.07%). By visual inspection, all 3 of these were indeed plausible spikes, but weremonophasic only due to distortion from partial spike overlap with a preceding spike that was larger57in amplitude (not shown). Moreover, since intracellular spikes must always have at least two phases(depolarization and repolarization), and since extracellular spikes are approximately the negativeof the first derivative of intracellular spikes (McCormick et al., 1985; Henze et al., 2000), non-overlapping extracellular somatic spikes should by necessity have at least two peaks of alternatingsign. Therefore, excluding monophasic spikes during extracellular spike sorting does not introducea bias against them, simply because they do not (and should not) exist.The temporal lockout was different for each detected spike, but the spatial lockout was the samefor all spikes. The 150 µm lockout radius was set for the spatially broadest of spikes. Therefore,spikes that were more spatially focal resulted in an unnecessarily broad spatial lockout, which mayhave resulted in more missed spikes than necessary. A spatially adaptive lockout for each spikebased on the modelled spatial position and extent (Section 3.5) would fix this oversight, while stillminimizing multiple registrations of the same spike. GAC-based spike detection (Swindale andSpacek, 2015) (see below) avoids this problem altogether by not using a lockout.The spike detection method described in Section 3.4 is a way of combining large numbers ofcandidate events into a smaller number of true spikes. It was later found that detecting spikeson many closely spaced channels is fundamentally a clustering problem (Swindale and Spacek,2015), which was solved here by rectangular spatiotemporal search and lockout windows. Thoughsomewhat crude as a clustering method, subjectively it was good at detecting events that wereclearly spikes, rejecting most noise events, and preventing multiple registrations of the same spike.A more sophisticated method now exists that fully treats spike detection as a threshold eventclustering problem (Swindale and Spacek, 2015). It uses a modified version of the GAC algorithm(Section 3.9), in which each threshold crossing event is a point in space and time to be clustered,with scout points moving up a spatiotemporal voltage-weighted gradient to find the highest localpeak, corresponding to the likely origin of a spike in space and time. This method eliminatesthe need for search and lockout windows. Besides being more elegant and principled, GAC-basedspike detection can resolve spikes slightly closer in space and time than the spatiotemporal lockoutmethod described in Section 3.4, with little or no extra computational cost (Swindale and Spacek,2015), and should therefore be implemented in spyke in the future.Spike detection was based on independent single channel thresholds. Visual inspection of thevoltage data revealed instances when several neighbouring channels had similar, simultaneous, butsubthreshold spike-like events (Figure 3.4, white arrows). These were reasonably distinct from theindependent noise on each channel, suggesting a spike. However, because each channel was testedindependently for threshold crossings, and because the events were subthreshold on all channels,the spike was not detected. One solution to this problem is to simply lower the threshold onall channels (e.g., by setting A = 5 instead of 6, Equation 3.1), but doing so would also greatlyincrease the number of false positive spike detections, making later clustering more difficult. Abetter strategy would be to weigh the evidence for a spike by looking across multiple neighbouringchannels at similar timepoints to see if several of them show signs of a spike, even if they are all58low amplitude. One might consider a low amplitude multichannel event to be as likely a spikeas a large amplitude but purely single channel event. A modification of the GAC-based spikedetection method (see above) might be a solution. The event detection threshold could be setlower (perhaps to A = 4) to detect even the smallest plausible multichannel events using a singlechannel threshold. Then, GAC-based spike detection would be run on all of these low amplitudeevents to cluster redundant events close in space and time into putative spikes. Each putative spikecould then be tested using a different kind of threshold, based on the height of the “hill” climbedby GAC, i.e., the density of events around the location and time of the putative spike, each eventweighted by its voltage amplitude. This way, a large number of small-amplitude events from severalnearby channels and timepoints would be about as likely to cross threshold and be accepted as aspike as a large amplitude single channel event.3.13.2 Dimension reductionICA was most useful for separating clusters of vastly different numbers of spikes (size ratios >50, Figure 3.10A & B). This was initially surprising, but can be explained as follows: PCA seeksto explain variance. The variance of the combination of a very small cluster and a large onewill be dominated by the variance of the large cluster (Pedreira et al., 2012). ICA on the otherhand considers higher order correlations than just variance, and seeks dimensions of maximumindependence instead of just orthogonality. If two clusters are truly statistically independent fromeach other, ICA can reveal them regardless of their size ratio. These small clusters could be truespikes (often found to belong to some other existing larger cluster) or noise events, which werediscarded.Conversely, ICA was worse than PCA at separating similarly sized clusters (size ratios < 10,Figure 3.10C), sometimes dramatically so. This was also surprising, and its cause remains unclear.One possible reason is that ICs were sorted by signed kurtosis (decreasing from positive to negative)instead of the absolute value of kurtosis (A. Hyva¨rinen, personal communication). Another possiblereason may be that kurtosis is poorly suited to sorting the ICs from similarly sized clusters, andthat negative entropy (negentropy) (Hyva¨rinen, 1998) is a better choice (A. Hyva¨rinen, personalcommunication). Both of these possibilities were briefly explored, but only after spike sorting hadbeen completed. Sorting ICs by decreasing absolute value of kurtosis did improve the ability ofICA to separate similarly sized clusters, but only occasionally. Sorting ICs by negentropy separatedsimilarly sized clusters even better, but there were still cases where it performed worse than PCA.Neither modification appeared to degrade the ability of ICA to sort very differently sized clusters.Further work in this regard is required. It may be that sometimes the sources of extracellularsignals are not independent, and that therefore ICA is inappropriate to use in such cases (Ja¨ckelet al., 2012).A method was devised to automatically select channels for dimension reduction and clustering,based on the median spatial extent of the selected spikes (Section 3.8). However, this automated59method was often less effective at separating clusters than was manual channel selection (Fig-ure 3.9), hindering downstream clustering. Moreover, time range selection was completely manual,and was identical for all selected channels. An automated method of selecting both channels andtime ranges that is at least as effective at separating clusters as manual channel and time rangeselection could accelerate the entire spike sorting procedure, and would also make it more objective.One such method might choose channels and time ranges (or individual timepoints) based on themean signal amplitude or variance of the selected spikes. More fundamentally, quantitative compar-ison of any method of dimension reduction requires a robust way of measuring the clusterability ofthe resulting distribution of points, i.e., multimodality: the number of modes and their separation.There are many potential ways of measuring multimodality (Hartigan and Hartigan, 1985; Nasonand Sibson, 1992), but a method that considers a specific spatial scale of interest might be simplestand most effective in this context. Finding and/or developing such a measure of multimodalityrequires further work.3.13.3 ClusteringAs a variant of the mean-shift algorithm (Fukunaga and Hostetler, 1975), GAC has several benefits.First, it does not assume clusters are of any particular distribution, such as Gaussian. This isespecially beneficial for dealing with clusters with distorted shapes, due to drift or otherwise.Second, GAC clusters points in a way that matches human visual intuition. Third, GAC makesno assumptions about the number of clusters in the data. Fourth, GAC requires the manipulationof only a single parameter, σc, describing the spatial scale of features of interest. The choice of σcwas greatly aided by onscreen user measurement of such features.A moderate disadvantage of GAC is that it is of O(N2) computational complexity, where Nis the number of points. The O(N2) complexity comes from the need to measure the distancebetween all pairs of points at least once. Although the gradient calculation step can subsample thedata that fall within rneigh to reduce dependence on N , the merge step cannot. With extensiveoptimizations in the implementation of GAC (Section C.2), clustering N = 25,000 data points withσc = 0.4 took ∼ 0.5 s on a first generation quad-core i7 laptop. Smaller values of σc slowed thealgorithm down (Figure C.4), mostly because the merge radius was proportionally smaller.In practice, Manhattan distance (i.e., city block or rectilinear distance) was used instead ofEuclidean distance (Swindale and Spacek, 2014; Equations 3.4 & 3.5) to calculate density gradi-ents for GAC. This was unintentional and went unnoticed until after all spike sorting had beencompleted. Euclidean distance is more principled and has no computational penalty, and shouldtherefore have been used instead. The clustering performance of the two distance metrics wascompared for both real clusters and simulated Gaussian clusters by examining animations of scoutpoint movement, as well as the final cluster counts and positions (not shown). Fortunately, theclustering performance of the two metrics was very similar, and any differences could be attributedto slightly different sensitivities to σc, which was manually set to effect by the user anyway. The60similarity in clustering performance may be due to the small step sizes used during the gradientascent step. The Manhattan distance somewhat favoured clustering points that were distributedparallel to any one of the axes of the cluster space over those that were not, such as diagonallydistributed points. The Euclidean distance had no such directional bias. Since clusters were mostoften aligned with one or more of the clustering axes (such as PC and IC axes), it is possible thatthis directional bias may have even been beneficial for clustering, but this was not explored. Thespike sorting results presented in the following chapters used Manhattan instead of Euclidean dis-tance to calculate density gradients, but there is no reason to believe that this made any practicaldifference.GAC has some similarity to HC in that during the course of the algorithm, each data point hasa history of membership of increasingly populated clusters that could be represented in a hierarchy.However, unlike HC, GAC exits automatically at the appropriate level in the hierarchy. GAC isalso similar to gravitational clustering methods (Wright, 1977) which allow points to attract oneanother and form clusters. The difference is that the density landscape for gravitational algorithmsis constantly changing, while for GAC it remains constant.Several other density-based clustering algorithms exist (Kowalewski, 1995; Ester et al., 1996;Klusch et al., 2003; Wang et al., 2004). All differ from GAC in subtle ways, and like the mean-shiftalgorithm, were found in the literature only after development of GAC. None were investigatedto any great extent here. Ester et al. (1996) suggest an interesting way to quickly determine theoptimal value of σc. For each point, the distance of its kth nearest neighbour (say, k = 4) is found.This is called the “k-dist” of each point. All points are then sorted by their k-dist, in decreasingorder, and plotted. Plateaus in such a plot, where many points have the same k-dist value, signifysignificant structure in the data at that spatial scale. Such plateaus are apparently robust to thechoice of k, and points to the left of the first significant plateau are likely outlying noise points.Such a pre-clustering step could run much faster than even a single run of GAC, especially for largeN , and may be implemented in the future.A new density-based clustering algorithm by Rodriguez and Laio (2014) may represent a sig-nificant improvement over the mean-shift algorithm and GAC. It preserves the ability to handlenon-Gaussian clusters and to automatically discover their number. For the purposes of spike sorting,the algorithm’s major advantages are that a) it is a fast, simple process, requiring no computation-ally expensive iteration, and b) it has essentially no user-set parameters. In the first step, the localdensity ρ around each point is calculated, potentially using a computationally cheap step functionkernel that simply counts the number of points within a critical distance dc, to which the algorithmis highly insensitive. In the second step, the distance δ from each point to the nearest point withhigher ρ is found for each point. Finally, the product γ = ρδ is calculated for each point, and thepoints are ranked in decreasing order. As determined by being above the knee of the γ rank orderplot, points with high values of both ρ and δ represent cluster centers. In practice, when splittingoff only one cluster at a time (Section 3.10.1), only the point with the highest γ need be found.61Other points are assigned to a cluster by following the linked list of nearest neighbours of higherlocal density, generated while calculating δ. Although still of O(N2) computational complexity dueto its need to calculate distances between all pairs of points once, the single-shot nature of thealgorithm of Rodriguez and Laio (2014) likely makes the gain of the O(N2) dependence very low.Incorporation of this clustering method into spyke and other existing spike sorting software maytherefore help speed up the clustering step.3.13.4 Autocorrelograms & refractory periodsAs an experiment, distinct, simultaneously active clusters were intentionally merged to createblatant spike contamination (Section 3.11). Tests on these merged clusters showed that RPVs,typically visualized with autocorrelograms, were a poor indicator of cluster contamination (Fig-ure 3.13). This is perhaps unsurprising in retrospect. Given the low firing rates (Section 4.3)and weak spike correlations (Section 6.3 & Appendix B) reported here in anesthetized cat V1, theprobability that a given pair of cells will both fire a spike within one millisecond of each other isvery low. When merging completely independent spike trains each with a mean firing rate of 0.1 Hz(Figure 4.1), one would expect a 1 ms RPV only once every 100,000 s. For mean firing rates of 1 Hz,RPVs would still arrive at a rate of only one every 1000 s. This conclusion, that autocorrelogramRPVs are a potentially unreliable indicator of spike sorting quality, has been briefly mentioned inthe literature (Gray et al., 1995; Harris et al., 2000). Yet this is an underappreciated finding, asautocorrelograms and RPVs are widely perceived to be a key tool for testing spike sorting quality(Fee et al., 1996; Alonso et al., 1996; Nirenberg et al., 2001; Litke et al., 2004; Segev et al., 2004;Hill et al., 2011; Prentice et al., 2011; Marre et al., 2012; Pillow et al., 2013). At best, they arenecessary but insufficient for the task. At worst, they may provide a false sense of security.3.13.5 DriftThe greatest difficulty in spike sorting multi-hour polytrode recordings was drift (Figure 3.12).Strangely, not all units drifted by the same amount, although generally drift was in the upwarddirection. Certainly, polytrode drift must play some role in this, but on its own cannot accountfor the variability of drift across units. Whether this extra variability is due to a physical propertyof cortical layers, of glial activity, or of some other source, is unknown. Some tracks had moredrift than others (see Figures 4.5 & 4.6 in the next chapter). Efforts to minimize drift should be apriority during future long duration recordings, in order to ease subsequent spike sorting.624 Basic PhysiologyWith spike sorting completed, the next step was to examine the basic neurophysiology of the sortedsingle units, again with the aim of minimizing bias as much as possible. Neurophysiological traitsexamined in this chapter include neuron yields, firing rates, cell templates and spatial positions,and orientation tuning.4.1 SummarySpike sorting of 3 tracks in 3 hemispheres in 2 cats resulted in 245 single units (Section 4.2).Surprisingly, mean firing rates followed a lognormal distribution instead of a normal one, andranged 5 orders of magnitude, from ∼ 0.0001 Hz to ∼ 10 Hz (Section 4.3). The geometric meanwas 0.11 Hz, and 82% of cells had mean rates below 1 Hz. Many studies exclude such low rate cellsfrom analysis, potentially biasing their results towards the properties of high rate cells. All cellswere included for most of the analyses in this study, regardless of firing rates. Surprisingly, initialresults suggest that local neural populations perform a kind of shift work: as some cells stop firing,others start firing, keeping the overall geometric mean firing rate relatively constant despite ordersof magnitude fluctuations in individual firing rates over time.Multiple neighbouring channels were crucial for distinguishing neighbouring cells with verysimilar spike shapes on their primary channel (Section 4.4). Neurons were well distributed acrossthe length of their polytrode, but their spatial positions were biased toward the electrode sitelocations, suggesting that 65 µm site spacing is not fine enough to fully sample the local population.Spatial positions varied as a function of time, suggesting polytrode-tissue drift, yet this drift wasnot consistent across the length of the polytrode, across time, or even across neighbouring neurons,and its source is unknown.Orientation tuning curves were calculated for all neurons. Regardless of firing rate, 61% ofcells were significantly tuned, but when restricted to active neurons (trial-averaged rates ≥ 0.05Hz), 87% of cell were significantly tuned (Section 4.5). As expected for generally vertical polytrodeinsertions, certain orientations were preferred within each track, but some tracks had a wider rangeof orientation preferences than others, indicative of a more transcolumnar insertion. Surprisingly,orientation tuning strength was inversely correlated with log firing rate. Cells with trial-averagedrates < 0.01 Hz had the strongest orientation tuning.4.2 Neuron yieldsInitially, rough spike sorting was performed on small subsets of data from all tracks. Tuning curves(Section 4.5) and RFs (Section 5.4) of the most easily sortable units in each track were examined,63track units sorted spikes detected events % duration spike rateptc15.tr7c 81 2,661,710 7,287,225 36.5 11.8 h 62.6 Hzptc22.tr1 93 1,664,985 2,054,825 81.0 8.3 h 55.5 Hzptc22.tr2 71 797,641 1,399,230 57.0 6.2 h 35.6 Hztotal 245 5,124,336 10,741,280 47.7 26.4 h 54.0 HzTable 4.1: Neuron yield. For each track and in total, columns show single unit yield, sorted spikeand detected event count, percentage of events that were classified as single unit spikes, recordingduration, and mean population sorted spike rate. Recording duration excludes recording time gapswithin each track (Figure 4.2).which allowed for a qualitative estimate of the physiological normality of each track. Subjectively,the best 3 tracks (ptc15.tr7c, ptc22.tr1, and ptc22.tr2, highlighted in Table 2.2) were picked for fullsorting and subsequent analysis. These 3 tracks were 11.8, 8.3, and 6.2 hours in recording duration(track duration minus any recording time gaps), respectively, for a total of 26.4 hours of recordingfrom two different cats. The two tracks that came from the same cat (ptc22) were from oppositehemispheres. Once the spike sorting method was fully developed, sorting a track took about amonth of concerted user effort.Recording conditions for the first few minutes after polytrode insertion were very different frommore stable conditions starting ∼ 30 min later (not shown). Fast, purely single channel spikes wereprevalent, while larger, slower multichannel spikes were mostly absent. The fast single channelspikes persisted for only a few minutes after insertion, followed by a generally quiet period, andthen a slow onset of more typical multichannel spikes. Some of these initial periods were saved todisk, but most recordings saved to disk did not begin until at least 30 min after insertion.Single unit yields, spike counts, and mean population spike rates are shown in Table 4.1. Singleunit yields per track were 81, 93, and 71 respectively, for a total of 245, and a mean of 82 per track.Across all tracks, over 10 million spike-like events were detected (Section 3.4), and about half ofthese were classified as single unit spikes (i.e., belonging to clusters marked as “good” for export,Section 3.10). The rest were classified as either noise events or multiunit spikes. Single unit spikesarrived at a grand average rate of 54 Hz.Single unit yields were greater across a track than for any single recording from that track. Forexample, the first drifting bar recording in ptc22.tr1 lasted 22 minutes. During that time, only 66cells fired at least one spike, out of a total of 93 cells sorted in that track. Relative to that onerecording, track-wide sorting resulted in a 48% increase in yield. If restricted to cells with a meanfiring rate of at least 0.05 Hz, the numbers were 30 and 58 cells respectively, a near doubling ofyield. Therefore, in addition to likely improving detection of very low firing rate cells (Section 3.2),track-wide sorting increased overall neuron yield.644.3 Firing ratesTo examine the mean firing rates of the neural population, the mean firing rate of each neuronwas calculated over the duration of its track. Neurons were plotted in decreasing order of meanfiring rate on a log-linear scale (Figure 4.1A). The plots of all 3 tracks (red, green and blue lines)resembled a rotated sigmoid function, as did their mean (black). The same data were also presentedas a distribution of mean firing rates on a linear-log plot (Figure 4.1B) of all 245 neurons from all3 tracks. The log-average (the mean of the base-10 log, i.e., the geometric mean) of the firingrate across all sorted units was -0.97 log units, or 0.11 Hz (black arrow). The log-average of themean firing rates was calculated instead of the arithmetic mean because on a linear scale the meanfiring rates had a very non-normal distribution. Instead, the distribution of mean rates resembled alognormal distribution, which was fit to the data using the least-squares LM algorithm (Figure 4.1B,magenta curve). The fitted lognormal curve had a mean of -0.82 log units, or 0.15 Hz (magentaarrow), and a standard deviation of 1.05 log units, or roughly an order of magnitude on either sideof 0.15 Hz. Mean firing rates of all cells from all tracks ranged 5 orders of magnitude, from ∼0.0001 Hz to ∼ 10 Hz.The mean trace in black and the lognormal fitted trace in magenta in Figure 4.1A were approx-imately linear over 2 orders of magnitude of mean firing rates, from ∼ 0.01 Hz to ∼ 1 Hz. A linearrange in the rank-order plot would be equivalent to a decreasing exponential firing rate distribution,which would result in a decreasing sigmoid over the same range of firing rates in Figure 4.1B. Sucha sigmoid was not apparent in Figure 4.1B, and the firing rate distribution was therefore unlikelyto be exponential instead of lognormal.Mean firing rates were < 1 Hz for 82% of neurons (74%, 83%, and 89% per respective track), and< 0.05 Hz (dashed grey lines in Figure 4.1) for 35% of neurons (24%, 38%, and 44% per respectivetrack). A 0.05 Hz mean firing rate threshold was used to classify cells as active or inactive. Thischoice of threshold was somewhat arbitrary, but very low, corresponding to one spike every 20 s onaverage. Mean firing rates differed for different analyses, depending on the time span encompassedby the analysis. Therefore, even though the mean firing rate threshold was kept constant, the setof active and inactive neurons for an analysis depended on whether that analysis was specific toone or more recordings, or to an entire track.In addition to track-wide means, firing rates were was also examined over time. To estimateeven very low rate time series, coarse 5 min wide overlapping time bins at 1 min resolution wereused for all neurons. To prevent time gaps in between recordings from causing underestimationof firing rates, gaps were ignored and time bins were aligned to the start of each recording. Ratetime series were plotted on a vertical log scale for the first 5 hours of each track (Figure 4.2A).Some cells had rates that ranged over 2 orders of magnitude. For example, the cyan trace for onecell during a blank screen recording in ptc22.tr2 (arrow, bottom panel, Figure 4.2A) began at 0.02Hz at t = 1.6 h, increased to 6 Hz 18 min later at t = 1.9 h, and then decreased again to 0.026510-4 10-3 10-2 10-1 100 101 102mean firing rate (Hz)051015202530neuron countlog( ) = -0.97= 0.11 Hzlog( ) = -0.82= 0.15 Hzlog( ) = 1.050 20 40 60 80 100neuron rank10-410-310-210-1100101102mean firing rate (Hz)ptc15.tr7cptc22.tr1ptc22.tr2meanlognormalA BFigure 4.1: Mean firing rates had a lognormal distribution. A: Mean firing rates of all 245 cellsof all 3 tracks, ranked in descending order within each track. Note the vertical log scale. The blackdashed line (“mean”) ranks all 245 cells but is compressed horizontally by a factor of 3 for displaypurposes. On this scale, a straight line with negative slope corresponds to a decaying exponentialfiring rate distribution, while a rotated sigmoid corresponds to a lognormal distribution. The solidmagenta line corresponds to the lognormal fit in B . B : Mean firing rate distribution of all cellscorresponding to the black dashed line in A. Note the horizontal log scale. The magenta line is theLM least-squares best fit lognormal distribution, with fit parameters shown in the top right. Blackand magenta arrows denote geometric means of the distribution and fit, respectively. Both A andB show that the majority of cells had mean firing rates below 1 Hz. The grey dashed horizontal andvertical lines at 0.05 Hz in both plots denote the minimum firing rate threshold for cell inclusionfor some subsequent analyses. 35% of cells fell below this threshold.Hz another 15 min later at t = 2.15 h. Visual inspection showed that deep and middle layer cellsgenerally had higher firing rates than superficial cells, and that some cells covaried in their rates,at least at this coarse time resolution. The firing rates of some cells covaried positively (especiallyevident for high rate cells in ptc15.tr7c), and others covaried negatively.How might the firing rate of the entire population fluctuate over time? Since the mean rates ofall neurons over all time were lognormally distributed (Figure 4.1B), instead of the arithmetic meanrate, the log-average (geometric mean) rate was calculated for all neurons as a function of time(thick grey transparent line in Figure 4.2A). Compared to the wide range of rates for each neuronacross time and across neurons at any given point in time, the log-average remained relativelyconstant over the duration of each track, even during some periods of positive covariation in highrate neurons. The distributions of log-average rates are shown for the entire duration of each trackin Figure 4.2B. Each distribution spanned no more than about 1 order of magnitude, and all werewell below 1 Hz. Log-average distribution means for the three tracks were ∼ 0.3 Hz, 0.09 Hz, and0.15 Hz respectively, in line with the 0.11 Hz geometric mean rate shown in Figure 4.1B.6610-210-1100101firing rate (Hz)ptc15.tr7c10-210-1100101firing rate (Hz)firing rate (Hz)ptc22.tr10 1 2 3 4 5time (hours)10-210-1100101 ptc22.tr2ABsuperficial deep log-averageptc22.tr110-2 10-1 100log-average firing rate (Hz)0100 ptc22.tr210-2 10-1 100log-average firing rate (Hz)06710-2 10-1 100log-average firing rate (Hz)0146time bin countptc15.tr7c C all neuronsfractional active duration0 0.5 10102neuron count67Figure 4.2: (Previous page.) A: Coarse firing rates plotted as a function of time for each neuronin each track. Each neuron’s trace is coloured according to its depth rank along the length of thepolytrode. Overlapping time bins were 5 min wide at 1 min resolution. Because of the vertical logscale, 0 Hz bins were excluded. For greater visibility, only the first 5 hours of each track are shown.Each contiguous block of traces represents one recording, separated by gaps from neighbouringrecordings in that track. The stimulus varied from one recording to the next. Middle and deeplayer neurons generally had the highest overall rates. Some neurons had rates that ranged > 2orders of magnitude (arrow denotes an example). Some rates covaried positively (especially inptc15.tr7c), some negatively, and others not at all. The thick grey transparent line is the log-average. Although individual rates varied widely, the log-average remained relatively constant. B :Distributions of log-average rates for each track, collected over the entire duration of each track(not just the first 5 hours). Log-averages ranged no more than about an order of magnitude aroundtheir mean, but this was an overestimate (see text). C : The distribution of activity duration (timebetween first and last spike of each neuron) as a fraction of track duration, for all neurons. Otherthan the ∼ 40% of neurons that were active for their entire track (peak at 1), the distribution wasreasonably uniform.Note that the variance in log-averages (thick grey traces in Figure 4.2A) was overestimatedbecause of the necessary exclusion of many cells during those particular time bins in which theyfired zero spikes. As the number of such excluded cells at any point in time was a substantialfraction of the total number of cells, and as it varied substantially over time, this inflated thevariance in the calculated log-average distributions. The true log-averages were therefore likely tobe even more constant over time than shown here. Wider time bins (20 min instead of 5 min, bothat 1 min resolution) somewhat reduced this tendency by reducing the number of 0 Hz bins, therebydecreasing log-average means and variances (not shown).To further characterize how neural activity fluctuates over broad time scales, the duration ofactivity of each neuron was calculated as the time between its first and last spike. This was thennormalized by total track duration to give the fractional duration that each neuron was active for.The distribution of fractional active durations of all neurons is shown in Figure 4.2C. About 40% ofneurons had active durations close to 1, i.e., they were active for their entire track. The other 60%of neurons were active for some shorter fraction of their track, and the distribution of these fractionswas surprisingly uniform. There was no characteristic activity duration timescale for these 60% ofneurons. Note that some of the 40% of neurons making up the peak at 1 in Figure 4.2C mightbe there only due to the experimentally limited duration of each track. Had they been recordedfrom for longer, there would have been greater opportunity for them to stop firing, and they mighttherefore have moved out of the peak at 1 and into the uniform part of the distribution below1. Analogous plots of first and last spike times as a fraction of track duration (not shown) wereconsistent with the above result. First spike times peaked close to 0 but were otherwise uniform,and last spike times peaked close to 1 but were also otherwise uniform.684.4 Templates & positionsAll spikes from a sorted unit were used to calculate its average multichannel waveform, or “tem-plate”. Templates of all 245 sorted cells from all 3 tracks are shown in Figure 4.3. Many channelshad multiple cells centered on them (left panels). Furthermore, many cells had similar, even iden-tical, templates on their primary channel, and could only be distinguished from each other byconsidering their template differences on neighbouring channels with lower amplitude signal (rightpanels). For example, one primary channel in ptc15.tr7c was shared by three cells (yellow, red,brown) with very similar primary channel templates (Figure 4.3, inset, left panel, white arrow).However, all three neurons were distinct from one another on 2 of the 4 neighbouring channels(right panel, grey arrows). This demonstrates the necessity of having many closely spaced sites tohelp distinguish neighbouring cells (Blanche et al., 2005).The spatial position of each neuron, shown in Figure 4.4A, was taken as the median spatialposition of all of its member spikes (see Section 3.5 for spatial localization of spikes). Cells werereasonably well distributed across the length of their respective polytrode, with no particular biastowards any one part of the polytrode. However, x coordinates of cells were strongly biased towardthe x coordinates of the electrode sites (Figure 4.4A, top). There was a similar but weaker bias ofcell y coordinates to electrode site y coordinates (Figure 4.4A, left). For the y position histogram,bins were placed such that there were equal numbers of bins aligned with and in between electrodesite y coordinates. There were 26 local peaks in the y position histogram that aligned with electrodesites, and only 3 local peaks in between electrode sites (90% and 10%, respectively). 154 cells fellin site-aligned bins, while only 91 fell in inter-site bins (63% and 37%, respectively). The bias in xand y cell coordinates to x and y electrode site coordinates suggests that cell positions were biasedtowards their nearest electrode site.To further examine this, the distribution of 2D distances between each neuron and its nearestelectrode site was measured (Figure 4.4B). Cells were most likely to be found close to electrodesites, with decreasing probability at greater distances. The expected distribution for randomlypositioned cells was analytically estimated by approximating the hexagonal domain surroundingeach electrode site as a circle. The number of points N at a distance r from the site is the areaof an infinitesimally thin concentric ring, times the average areal cell density ρ measured from thedata:N = 2pirρ dr (4.1)This analytical estimate is shown as the dashed blue line in Figure 4.4B, and ignores the edgeeffects of a finite polytrode. A uniform random distribution of 100,000 points was also numericallysimulated for the 3 column probe (1a design), resulting in the dashed red line in Figure 4.4B. Bothexpected distributions for randomly positioned neurons increased linearly as a function of nearestelectrode site distance, while the measured data showed the opposite. This again suggests thatcell positions were not random, but rather were biased to the nearest electrode site. Moreover,69Figure 4.3: Single (primary) channel templates (left in each pair) and primary channel plusnearest neighbour multichannel templates (right in each pair) of all sorted cells from all threetracks. Surrounding channels helped distinguish cells when two or more shared primary channelswith very similar signal. Each template was aligned to its primary channel. For nearest neighbourmultichannel templates, included surrounding channels did not necessarily align the same way.Blank channels either had no cells for which they were best positioned, or were disabled duringrecording. A limited set of 10 colours was cycled through in vertical spatial order to help distinguishcells. The white arrow highlights a channel on which three cells (yellow, red, brown; enlargedin inset) had nearly identical primary channel templates, and were only distinguishable on twoneighbouring channels (grey arrows). Scale bars: 0.5 ms, 100 µV.70Figure 4.4: A: Cell positions for all 3 tracks, coloured by whetherthey were active (mean firing rate > 0.05 Hz, red) or inactive (blue).Black points are electrode site positions, all with 65 µm hexagonalspacing. Light grey backgrounds represent shank widths and approx-imate lengths of the two polytrode designs used for these tracks (1a& 2a, Table 2.3). For the horizontal (top) and vertical (left) cell po-sition histograms, dashed lines denote alignment with electrode sites.All axes are positions in µm unless otherwise labelled. B : Distributionof cell distances to the nearest electrode site. Black bars are measureddata. The dashed blue and red lines are the analytically and numeri-cally simulated distributions, respectively (see text). Both lines showeda trend opposite that of the data. C : Plotting each cell’s spatial ex-tent vs. distance to the nearest electrode site showed a correlation,suggesting that cells with small closed fields were missed in betweensites.activeinactive 28 2804556 0 5604556 0 56045ptc15.tr7c ptc22.tr1 ptc22.tr2count020040060080010001200012 count 28 2802004006008001000120014001600180056 0 56 56 0 56A0 10 20 300. density (1/m) B0 10 20 30nearest site distance ( m)255075100 Cspatial extent (m)71the spatial extent of cell templates (each the median spatial extent of its spikes, Section 3.5) waspositively correlated with the distance to the nearest electrode site (Figure 4.4C), suggesting thatthe positional bias was due to cells with small closed extracellular fields that were too distant froman electrode site to be detected.There was no strong spatial segregation of active cells (mean rates > 0.05 Hz, Figure 4.4, reddots) and inactive cells (mean rates < 0.05 Hz, blue dots) as a function of position along thepolytrode. However, there was a weak tendency for inactive cells to be more superficial.Cell position was also examined as a function of time, as were other spike parameters. The x andy coordinates, spatial extent (σ), and peak to peak amplitude (Vpp) of all 5.1 million spikes from all3 tracks are shown in Figure 4.5. For better visibility, Figure 4.6 shows the same data, with spikeparameters averaged over 10 min wide non-overlapping time bins, resulting in lines representingone cell each. Track ptc15.tr7c showed the most stability, especially in y position. Tracks ptc22.tr1and ptc22.tr2 were both less stable in y. Many cells in those two tracks appeared to drift upward,in tandem, over a span of hours, suggesting polytrode drift relative to the tissue. A few cells driftedupward by as much as ∼ 150 µm. However, many other cells in those two tracks had no upwarddrift, or had periods of downward drift, and some of these were positioned in between cells thatdid have upward drift. This cannot be explained by global, or even local, polytrode-tissue drift. Incomparison to y position, x position, σ and Vpp were all reasonably stable across all tracks.To further investigate stability in y, dy/dt was calculated from the binned values in Figure 4.6.The distribution of dy/dt values across all time bins and cells within each track are shown inFigure 4.7A. Contrary to the visual impressions from Figures 4.5 & 4.6 of consistent upward driftfor many cells in ptc22.tr1 and ptc22.tr2, the distributions of dy/dt for all 3 tracks were nearlysymmetric around dy/dt = 0, suggesting that at least at the timescale of 10 min wide bins, therewas little systematic upward drift. Mean dy/dt was positive (upward) but very low for all threetracks, ranging 0.7–3.4 µm/h. However, dy/dt distributions were broader for the latter two tracks(σ = 64–78 µm/h), indicating greater vertical positional variability than for ptc15.tr7c (σ = 31µm/h). Net rates of change in y position between the first and last spike of each cell (∆y/t) werealso calculated, and their distributions are shown in Figure 4.7B. Results were similar to dy/dt: themeans were positive but very low for all three tracks, ranging 2–2.9 µm/h, and the distributionsfor ptc22.tr1 and ptc22.tr2 were broader than for ptc15.tr7c.4.5 Orientation tuningOriented responses are a characteristic feature of neurons in V1 (Hubel and Wiesel, 1959), andmeasuring orientation tuning is a standard procedure. Three different types of artificial stimuliwere used to measure orientation tuning of neurons: drifting bars, flashed gratings, and driftinggratings (see Section 2.4 for stimulus details).Depending on the stimulus type, steps in orientation ranged from as fine as 10◦ to as coarse72Figure 4.5: Spike parameters as a function of time for all 5.1M spikes from all cells of each track.Each point represents a spike, coloured by cell, with colours corresponding to those in Figure 4.3.From top, plotted spike parameters are vertical (y) and horizontal (x) position, spatial spread (σ),and primary channel peak-to-peak voltage (Vpp). Positions are relative to the polytrode used foreach respective track. Vertical black lines represent recording time gaps. Many spikes are obscured,especially those of low firing rate cells. To maximize spike visibility, different scales were used forx and y, and a different y scale was used for ptc15.tr7c. y roughly corresponded to cortical depth,but less so in ptc15.tr7c due to its angled insertion (Figures 5.6 & 4.10C). Depending on the track,dy/dt was moderate to high, but dx/dt was relatively low. Temporal variation in σ remained fairlylow, while Vpp varied moderately.730 2 4 6 8 10 12 14 16time (hours)0300600V pp (V)50100150 (m)50050x (m)020040060080010001200140016001800y (m)ptc15.tr7c0 2 4 6 8time (hours)03006005010015050050020040060080010001200ptc22.tr10 2 4 6time (hours)ptc22.tr2Figure 4.6: Smoothed spike parameters vs. time. Same as Figure 4.5, but with points averagedby binning into 10 min wide non-overlapping bins and plotting the mean value within each bin.Consecutive bin values of each neuron are represented by connected lines. This results in a smoothersignal with better visibility of all cells, at the cost of a loss of representation of parameter varianceand cell firing rate. Disconnected lines are either due to gaps in recordings or time bins in whichthe cell did not fire at all.7450 25 0 25 50net y/t ( m/h)013neuron count= 2.3= 15.850 25 0 25 50net y/t ( m/h)041neuron count= 2.9= 9.350 25 0 25 50net y/t ( m/h)054neuron count= 2.0= 3.4ptc15.tr7c ptc22.tr1 ptc22.tr2200 100 0 100 200dy/dt ( m/h)01219bin count= 0.7= 30.9200 100 0 100 200dy/dt ( m/h)0463bin count= 3.4= 64.3200 100 0 100 200dy/dt ( m/h)0144bin count= 1.8= 77.8ABFigure 4.7: Distributions of changes in y position over time for all cells in each track. A:Distributions calculated from the uppermost 3 panels in Figure 4.6, using the same 10 min widenon-overlapping time bins. Positive dy/dt corresponds here to movement up the polytrode, soin this case, y represents distance from the bottom of the polytrode instead of the top. Meansand standard deviations are shown for each track. Although many cells in ptc22.tr1 and ptc22.tr2appeared to drift upwards in Figure 4.6, surprisingly their slope distributions were highly symmetricabout dy/dt = 0, with little positive skew. While some cells moved up the polytrode at times, theywere mostly balanced out by other cells moving down the polytrode. B : Distributions of net ratesof change in y position between the first and last time bin of each cell. Note the finer scale on thex axis. Although standard deviations were lower than in A, the means were similar and the sameconclusions 45◦. When calculating orientation tuning curves (Figure 4.8, bottom), spikes were countedacross all stimulus conditions, but the stimulus values of non-orientation stimulus dimensions wereignored. This means that tuning curves were composed of responses collapsed across all otherstimulus dimensions including brightness, contrast, spatial and temporal frequencies, and phase.Tuning curves for flashed gratings were calculated by forward correlating each 40 ms durationflashed grating with the spikes that occurred 40 to 80 ms after stimulus onset. Although differentcells may have different response delays to stimulus onset (Figure 5.6), 40 ms was a good compro-mise across the population, and was therefore chosen as both the flash duration and the reversecorrelation delay. Flashed gratings allow for rapid simultaneous characterization of many stimulusdimensions for each cell, much faster than drifting gratings (Ringach et al., 1997a,b). However,temporal frequency preferences cannot be calculated because the stimulus contains no temporal75frequencies (apart from the 25 Hz frame frequency from the 40 ms frame time).Orientation preference was calculated from the tuning curve of each cell to each stimulus typeby taking the vector mean of spike counts at each evenly spaced stimulus orientation (Swindale,1998). Specifically, this required doubling all the stimulus orientation angles, performing the vectorsum, and then dividing the resulting length by the total number of spikes, and dividing the resultingangle by 2. Finally, modulus 180 of the angle was taken to constrain it to between 0◦ and 180◦ formotion stimuli that go around the clock (drifting bars and drifting gratings). The resulting vectorlength, r, represented tuning strength, and ranged from 0 (low tuning) to 1 (high tuning). Cellswere tested for orientation tuning significance using Rayleigh’s test for circular uniformity (Wilkie,1983; Fisher, 1995). For each significantly tuned cell, the stimulus that resulted in the sharpesttuning curve was used to characterize the orientation tuning of that cell. The stimulus type thatresulted in the strongest orientation tuning varied from cell to cell, with no apparent regularity.Overall, 61% (150/245) of cells were significantly tuned to orientation (p < 0.01). The numbersper track were 62% (50/81), 57% (53/93), and 66% (47/71) for ptc15.tr7c, ptc22.tr1, and ptc22.tr2respectively. However, when restricted only to cells that were active (with mean firing rates ≥0.05 Hz) during at least one oriented stimulus, 87% (131/150) of cells were significantly tuned toorientation (p < 0.01), with 98% (46/47), 77% (48/62), and 90% (37/41) per respective track.Spiking responses to drifting gratings and the associated tuning curves of 3 example neuronsare shown in Figure 4.8. Some cells exhibited strong and significant orientation tuning despiteextremely low firing rates, with orientation preferences in line with those of their higher firingrate neighbours. The example neuron in Figure 4.8C fired only 8 spikes during the entire 22 mindrifting bar recording, with a mean firing rate of 0.006 Hz, yet it was significantly orientationtuned (p = 0.0057) with a tuning strength of r = 0.76. All 8 spikes occurred near the middle of therelevant trials when the bar was at the same position, presumably over the cell’s RF. Like otherwell tuned moderately direction selective cells, it had two peaks in its tuning curve 180◦ apart.Finally, this cell’s preferred orientation of 30.6◦ was similar to that of its neighbours (Figure 4.10C,middle), providing further evidence of significant tuning (not considered in p value calculation).There were other similarly low firing rate neurons that were significantly tuned, with orientationpreferences similar to their neighbours. Figure 4.9A shows how tuning strength varied with meanfiring rate, which was calculated for each of the 150 significantly tuned cells over the duration ofthe stimulus that resulted in that cell’s strongest orientation tuning. Surprisingly, on a linear-logplot of tuning strength vs. mean firing rate, the relationship was inverse: low mean firing rate cellsgenerally had the highest tuning strength, and vice versa. This inverse and approximately linearrelationship (r = −0.5) held regardless of the significance threshold. For significance thresholdsof 0.05, 0.01, 0.001 and 0.0001, the number of significantly tuned cells was 164, 150, 142 and 134,respectively, with r values of −0.56, −0.50, −0.51 and −0.53.Figure 4.9B shows that the distribution of mean firing rates of the 150 significantly tuned cellswas roughly a lognormal distribution, similar to that of the full population shown in Figure 4.1B,76trial indexA B Cspike count0 180 3600350700 pref=32.1°r=0.27p=0.000drift bar orientation (°) drift bar orientation (°)pref=169.2° 0 180 360024 pref=30.6°r=0.76p=0.0057drift bar orientation (°)Figure 4.8: Orientation tuning curves calculated from the responses of 3 simultaneously recordedexample neurons in track ptc22.tr1 to 288 trials of drifting bar stimulus. Top: Raster plots of alltrials, in order of stimulus parameter combination (not temporal order). Responses to white andblack drifting bars are represented by white and black ticks respectively, where each tick representsone spike. Trial 1 started at 198◦ and orientation incremented by 30◦ every 24 trial indices.Horizontal dashed lines denote orientation increments. On and off subfields (Section 5.4) werediscernable in A and B as bar brightness alternated every 12th trial. Bottom : Orientation tuningcurves with orientation preferences (arrows) calculated using the vector mean of trial spike counts.Tuning strength, represented by normalized vector length r, and p values (Rayleigh test for circularuniformity) are shown. A was moderately tuned with high significance and B was very weaklytuned with very low significance. Despite firing only 8 spikes, C was well tuned and significant(p < 0.01). Like A, C ’s orientation preference of ∼ 30◦ was similar to that of its neighbours.7710-3 10-2 10-1 100 101 102mean firing rate (Hz)05101520tuned neuron count=0.26 Hz10-3 10-2 10-1 100 101 102mean firing rate (Hz) strengthr=-0.50p=5e-11A B Figure 4.9: A: Orientationtuning strength vs. mean firingrate for the 150 significantlytuned cells. The red dashedline is the least-squares linearregression (r and p values areshown). Surprisingly, tuningstrength was inversely corre-lated with log mean firing rate.B : The mean firing rate distri-bution for the same set of cellsshowed weak bimodality. Thearrow is the geometric mean.though with a slightly higher geometric mean of 0.26 Hz vs. 0.11 Hz for the full population. Also,restricting the mean firing rate distribution to only tuned cells revealed a weak bimodality, sug-gesting two different orientation tuned cell types. This weak bimodality persisted for significancethresholds of 0.05, 0.01 and 0.0001, but not 0.001 (not shown).The orientation preferences of all 150 significantly tuned cells are shown in Figure 4.10. The fullrange of possible orientation preferences and tuning strengths was represented across the popula-tion of significantly oriented cells, with no particular favoured orientation (Figure 4.10A). To allowfor a very rough comparison of cell depths along polytrodes of different lengths, normalized depthwas calculated for each cell as the fractional distance down the length of the polytrode. Normal-ized depth is represented by point darkness in Figure 4.10A, while Figure 4.10B shows normalizeddepth as a function of orientation preference, with points coloured according to tuning strength. Asexpected, when pooled across all 3 tracks, there was no relationship between normalized depth andorientation preference. However, when taken individually, each track showed relationships betweenorientation preference, tuning strength, and normalized depth (Figure 4.10C). For ptc15.tr7c orien-tation preference varied strongly with normalized depth, at a rate of 104◦/mm (counterclockwise),suggesting (as in Figure 5.6) that this was a transcolumnar track. For track ptc22.tr2, orientationpreference also varied with depth, at a rate of 79◦/mm (clockwise), but this relationship was weaker(statistical significance not calculated).4.6 Discussion4.6.1 Neuron yieldsTrack-wide sorting increased overall neuron yield (Section 4.2). This is unsurprising, given thatlow firing rate cells (Section 4.3) take a long time to accumulate enough spikes to be detected asclusters. However, further analysis is required to determine if most of the additional units gleaned78A0306090120150180orientation preference0 0.25 0.50 0.75 1.00tuning strengthCptc15.tr7c ptc22.tr1 ptc22.tr20 901.00.500 90 0 90 180B10normalized depth0 90 1801.00.50normalized depth tuning strength01orientation preference ( )°79Figure 4.10: (Previous page.) A: Orientation preference, tuning strength, and normalized depthof the 150 cells with significant tuning (p < 0.01, Rayleigh test) to at least one drifting bar,flashed grating, or drifting grating experiment. Point darkness represents normalized cell depthalong the length of the polytrode. B : Orientation preference as a function of depth along thepolytrode. In this case, point brightness represents tuning strength. In both A and B , there wereno obvious relationships between orientation preference, tuning strength, and cell depth, and allwere reasonably uniform across the population. C : Same as A and B , but broken down accordingto track. ptc15.tr7c and ptc22.tr2 showed a linear relationship between orientation preferenceand depth (highlighted by manually positioned dashed lines), with strong and weak relationships,respectively, suggesting that these tracks were strongly and weakly transcolumnar, respectively.from track-wide sorting are low rate cells, cells that respond only to certain stimuli, or cells thatare only active at certain times for other reasons, such as a change in cortical state (Chapter 6).Although not investigated in any detail, perhaps the fast single channel spikes found during thefirst few minutes after polytrode insertion were inhibitory interneurons (Section 5.1) whose activitywas inhibiting that of pyramidal cells. Or perhaps more likely, the fast single channel spikes wereaxonal spikes from cut axons whose cross-section happened to fall near an electrode site.Given known cortical neuronal densities and estimates of recording volumes of extracellularelectrodes, only about 10% of the population of cells that must be physically present and withinrecording range of extracellular electrodes are typically detected (Henze et al., 2000; Shoham et al.,2006). This fraction must depend to some extent on spike sorting quality. Shoham et al. (2006)cited Blanche et al. (2005) as having found 60 neurons out of potentially 700, i.e., 8.6%, estimatedfrom the polytrode recording volume and neocortical neuron density. With 82 units reported herefor that same track (ptc15.tr7c), that percentage increased, but is still only 11.7% of the cells thatshould be there. This “dark neuron” problem might be due to most neurons remaining silent, andtherefore undetectable in extracellular recordings, for long periods of time (Thompson and Best,1989; Henze et al., 2000; Hahnloser et al., 2002; Kerr et al., 2005). Stable continuous recording foreven longer periods of time (days) and under as wide a variety of stimulus and animal conditionsas possible (awake, asleep, anesthetized, behaving, learning) may help resolve this problem.In addition to cats, polytrode recordings were also made in V1 of 13 urethane-anesthetized rats(Section 2.1). However, very few units were isolated, and even fewer were visually responsive (notshown). Given that many other groups successfully record from rat brain using polytrodes withnarrower shanks (< 100 µm) (Harris et al., 2003; Csicsvari et al., 2003; Buzsa´ki, 2004; Sirota et al.,2008; Goard and Dan, 2009; Schjetnan and Luczak, 2011; Luczak et al., 2013; Bere´nyi et al., 2014),this suggests the interesting possibility that the wide (∼ 200 µm) polytrodes used here do moredamage in smaller brains. Further investigation of this hypothesis would require modelling thenumber of dendrites and axons that might be cut by polytrodes with different numbers of shanks ofdifferent widths and spacing, taking into account the density of cells and the size and shape of theirdendritic and axonal fields in different species. This also suggests that using narrower polytrodes80(Section 4.6.3), with either narrower or layered conductors, would further decrease damage andincrease neuron yield in cat cortex.4.6.2 Firing ratesMean firing rates in anesthetized cat V1 were lognormally distributed with a log-average firing rateof ∼ 0.11 Hz and a standard deviation of about one order of magnitude (Figure 4.1B). Althoughmuch lower than reported in most studies (see Olshausen and Field (2005) & Carandini et al.(2005) for reviews), this value and the lognormal distribution around it is nevertheless in line witha handful of reports in other species and cortical areas. Using energy analysis, Lennie (2003)estimated that the average firing rate of human cortical cells is 0.16 Hz. Brecht et al. (2003)found that average spontaneous firing rates were 0.068 Hz in superficial layer pyramidal cells inurethane-anesthetized rat barrel cortex. That study used whole-cell recordings whose electrodeimpedance changes upon contact with a neuron, providing confirmation of neuron isolation evenin the absence of spiking activity. This reduces the probable bias of individually maneuverableextracellular single-wire electrodes or tetrodes towards high rate neurons. Kerr et al. (2005) founda mean spontaneous firing rate of 0.05 Hz in superficial layers in urethane-anesthetized rat primarysomatosensory cortex (S1) and primary motor cortex (M1). That study used both two-photoncalcium imaging and cell-attached recordings, with bias reduction benefits similar to those of whole-cell recordings. Hroma´dka et al. (2008) found a lognormal distribution of firing rates in primaryauditory cortex (A1) of awake rat, using cell-attached recordings. That study used a wide rangeof auditory stimuli, including naturalistic sounds. Their log-average was higher (∼ 3 Hz) thanreported here, but that should be expected given that firing rates are higher in auditory cortex.Sakata and Harris (2009) also reported a lognormal distribution of mean spontaneous firing ratesacross superficial and deep layers of awake and urethane-anesthetized rat A1 (their Figure S14B).Using silicon polytrodes, they found log-averages of 0.5–3 Hz. Finally, Mizuseki and Buzsa´ki (2013)reported lognormal firing rate distributions in awake and asleep rat hippocampus and entorhinalcortex, with log-averages of 0.5–1 Hz. In that study, rate distributions were best fit by a lognormalcurve during slow wave sleep, but were somewhat skewed during REM sleep and awake states.Given the increasing evidence for lognormal (as opposed to normal) distributions of mean firingrates across species and cortical areas, the geometric mean may be more appropriate than thearithmetic mean for describing the central firing rate tendency of populations of cortical neurons.Furthermore, lognormal rate distributions are consistent with the concept of sparse coding, in whichonly a small fraction of the population need be active at any given time to encode a stimulus, mem-ory, or action (Olshausen and Field, 1996). The benefits of sparse coding include computationallyefficient memory storage, efficient extraction and representation of structure within natural stimuli,and energy efficiency (Olshausen and Field, 2004; Attwell and Laughlin, 2001).Wohrer et al. (2013) extensively reviewed population distributions of firing rates in variousspecies and neocortical regions. That study made conclusions about publicly available sorted data81from cat ptc15, which was sorted using the previous spike sorting technique based on multichanneltemplate matching (Section 3.1.1). They concluded that population mean rates from those data arebest fit by a decaying exponential distribution. In linear-log space, such a distribution would havethe shape of a decreasing sigmoid, which clearly does not fit the distribution shown in Figure 4.1B.In contrast, the LM least-squares best fit lognormal distribution shown in that figure does providea reasonable approximation. This is consistent with lognormal distributions described by Wohreret al. (2013) in other species (rat and primate) and cortical areas (A1, prefrontal cortex (PFC), M1and secondary motor cortex (M2)). Spike sorting quality may therefore affect conclusions aboutfiring rate distributions.The majority of cells, 82%, had mean firing rates below 1 Hz (Figure 4.1). This is significantbecause for many studies, ∼ 1 Hz is considered the minimum mean firing rate for unit inclusionfor analysis (Olshausen and Field, 2005). Depending on the area of recording, such studies maybe inadvertently biased towards the properties of high firing rate cells. Perhaps the biggest reasonfor setting such a threshold is that sorting very low firing rate units from those that fire at higherrates is difficult (Section 3.8). The task was made easier in this case by the use of ICA instead ofPCA, when appropriate.Some of the lowest mean firing rates might be from cells that were active for only a short periodof time. Several such cells are apparent in Figure 4.6. While it is possible that these were cells whosesingle unit isolation was gained or lost part way through a track, this seems less likely than suchcells simply starting or stopping their firing, whether due to a change in stimulus, cortical state(Section 6.4), or some other unknown cell-specific reason. Barring sudden electrode movement,loss of cell isolation is usually a gradual process due to gliosis or tissue swelling (Liu et al., 1999;Szarowski et al., 2003; Biran et al., 2005), accompanied by a gradual decrease in spike amplitude(see reviews by Polikov et al. (2005) & Leach et al. (2010)). No such gradual spike attenuation wasencountered during spike sorting, and none was apparent in any of the sorted units (Figure 4.6,bottom row). Since the polytrode is a single rigid structure with fixed electrode site locations, if itwere to shift suddenly, simultaneous isolation loss of many cells would be expected. This was notobserved in any of the 3 sorted tracks.At a time scale of 10–20 min, firing rates of individual cells could fluctuate by orders of magni-tude, while the population geometric mean rate remained fairly stable (Figure 4.2). This suggeststhe possibility that neuronal populations are engaged in a kind of shift work, where some cellsare active for a period of time, while others are silent, with group membership turning over asa function of time, and network functionality remaining intact throughout. This could perhapsallow for offline physiological cell maintenance, independent of sleep. It may also have implicationsfor network stability, such as preventing synaptic weights from growing out of control and givingtoo much weight to too few cells (Markram and Tsodyks, 1996). Kerr et al. (2005) provide simi-lar evidence for shift work using two-photon calcium imaging in urethane-anesthetized rat cortex.However, further work is required to demonstrate neural shift work more definitively. One way82would be to measure the (log-scale) variance in multiunit activity (MUA) of spike trains randomlyshifted in time by different amounts for each neuron, and compare that to the MUA variance ofthe original spike trains. If temporal shifting increases MUA variance, that would strengthen theevidence for neural shift work.It is possible that the wide fluctuations in firing rates of individual neurons was due to rapidgain or loss of single unit isolation due to drift. Cells with small closed extracellular fields (singlechannel cells) might be especially prone to sudden changes in unit isolation. However, while thetraces in Figure 4.2 show that individual firing rates fluctuated greatly at different depths andtimes, these fluctuations did not seem to coincide with sudden changes in y position in Figure 4.6.Further analysis is required to explicitly show this, such as plotting each cell’s firing rate as afunction of Vpp amplitude or y position, to confirm that firing rate is independent of both of thesevariables. However, simultaneous gain and loss of single unit isolation of many different cells acrossthe polytrode seems an unlikely explanation for the wide fluctuations in firing rate of individualcells shown in Figure 4.2.Anecdotally, conventional single-wire extracellular electrophysiology can suffer problems “hold-ing” cells for no more than a few hours, followed by their sudden isolation loss. This is generallyattributed to the electrode suddenly shifting its position relative to the neuron, even if only by asmall amount. However, when slowly approaching or retreating from a neuron using a microdrive, aneuron may remain isolatable over the span of 100 µm or more, contradicting the assumption thatisolation loss is due to fine sensitivity to electrode position relative to the neuron. An alternativeexplanation that resolves this apparent contradiction is that this sudden apparent isolation lossinstead reflects dramatic changes in firing rate (Swindale and Spacek, 2012).Extremely low firing rates could plausibly be an artifact of high drift, causing a single unit’sspikes to be split over time into two (or more) clusters, with insufficient evidence to combine themduring spike sorting. For example, if the spike counts in the two resulting clusters were equal, thiswould create two units with exactly half the mean firing rate of the original unit (half the spikesdivided by the same full track duration). This would increment that particular half mean firingrate bin in Figure 4.1B twice instead of once at the original mean rate. Since low firing rate cellshave fewer spikes (and therefore less evidence for merging) to begin with, perhaps such splittingoccurs more often for low firing rate cells, thereby overestimating their numbers. Although onemight suspect a few such candidate oversplit pairs while examining changes in unit position as afunction of time (Figures 4.5 & 4.6), those plots represent only one narrow view of the sorted units.Many other dimensions were inspected during spike sorting before a decision was made to merge orsplit (Section 3.8). Even if some clusters were oversplit, it seems safer to oversplit cells and therebyunderestimate their mean firing rates than to undersplit them and mistake multiunits for singleunits in later analyses. Nevertheless, the approximate symmetry in log space of both the high andlow end of the mean firing rate distribution in Figure 4.1B suggests that oversplitting was not acommon occurrence.83Time gaps between some recordings were up to 30 min long, and should be minimized in thefuture, both to improve tracking of physiological properties such as firing rate, cell position, andspike shape, as well as to increase confidence in spike sorting of cells that span these time gaps.4.6.3 Templates & positionsEven when the waveforms of spikes from different cells were indistinguishable on their primary chan-nel, high-density polytrodes allowed cells to be distinguished on neighbouring channels (Figure 4.3).Arguably, the greater the number of electrode sites and the higher their density, the higher theprobability that at least some channels will separate cells that would otherwise be indistinguishablewith a single wire electrode or tetrode.At a broad scale, the 2D spatial localization of cells showed a reasonably uniform spatial dis-tribution for each of the 3 tracks (Figure 4.4A). Given that the greatest amount of damage shouldbe expected in superficial layers, past which the greatest fraction of polytrode length must slide toaccess deeper layers, there was no obvious lack of superficial cells. This suggests that there was nogross anatomical damage from polytrode insertion (Blanche et al., 2005).However, at a finer scale, estimated cell positions were biased toward electrode sites (Figure 4.4A& B), and cells with small closed extracellular fields were more biased toward electrode site positionsthan cells with large open fields (Figure 4.4C). This could be due to spatial undersampling of theneuronal population, with electrode sites spaced further apart than optimal. 65 µm hexagonalelectrode site spacing may be insufficiently dense to fully capture the local neural population. Thisis consistent with Du et al. (2011) who reported that about half of all cells recorded using theircustom polytrodes (∼ 40 µm site spacing) were detectable no further than 60 µm away from theirapparent origin. Although most of the sorted cells here had templates spanning several channels,those may have been prevalent only because at 65 µm spacing, cells with small closed fields weremore likely to fall undetected between electrode sites, and were therefore underrepresented.One way to further test this hypothesis would be to divide all the cells into two or moregroups according to spatial extent (σ, Section 3.5). The distribution of cell distances to the nearestsite (Figure 4.4B) could be plotted separately for each group. If the hypothesis is correct, thedistribution of nearest site distances should fall off more quickly for cells with small fields, andmore slowly (or not at all) for cells with large fields. Another way to test this hypothesis would beto sort spikes from other existing data from polytrodes with site spacing less than 65 µm, such as2b polytrodes (50 µm hexagonal spacing) or 1b polytrodes (collinear, with 43 µm horizontal and 50µm vertical spacing, from older tracks omitted from Table 2.2). The hypothesis would predict thatthe distribution of cells to the nearest site should be closer to analytical and numerical simulations(Figure 4.4B) for polytrodes with lower site spacing.Resolving this issue may require polytrodes with greater site density. At least one suitable single-shank high-density design is already commercially available, with < 38 µm hexagonal spacing oftwo columns of electrode sites, and a narrower shank width ranging 30–115 µm (A1x64-Poly2-6mm-8423s-160, Anton Sirota lab, manufactured by NeuroNexus, Ann Arbor, MI). Even at this higher sitedensity, with 64 electrode sites the single shank still spans ∼ 1.5 mm, roughly the thickness of catprimary visual cortex.Another cause for this spatial bias could be the spatial localization method itself (Section 3.5).As an alternative to taking the average localized position of each member spike, spatial localizationcould be performed on the neuronal template, which is smoother and might therefore allow fora better spatial Gaussian fit. However, templates may be subject to distortion due to drift (seebelow), whereas individual spikes are not. Such distortion could introduce errors in template-basedspatial localization. Another possibility is that there may be insufficient unique x values (columns)to properly constrain localization along the x axis. This might require a polytrode with more thanonly 2 or 3 columns. A computational workaround to this physical limitation could be rotatingthe coordinate system during localization so that each site has a unique x and y value in the newrotated space. This could trade off the effective number of rows for an increased effective numberof columns.Blanche (2005) reported that neuron distance from the polytrode (z position) could be inferred,in addition to x and y position along the surface of the polytrode, thereby allowing for 3D local-ization within the tissue instead of only 2D. This was done by modelling the spatial distributionof each neuron’s multichannel peak spike amplitude as a mixed monopole/dipole current source,with voltage decay in extracellular space. The extracellular space was treated as a medium withuniform conductivity in the cortical laminar plane, but differing conductivity orthogonal to thelaminar plane. Parameter convergence of this model was reported for smooth mean templates, butwas not possible for individual spike waveforms due to excess noise. This meant that 3D localizationof spikes from drifting neurons was not possible, although it would be possible to generate multipletemplates per neuron as a function of time, and then fit the 3D model to each such template. Thelow number of electrode site columns in current polytrodes (2 or 3, though see above) also mademodel parameter estimation especially difficult. Although promising, no attempt to use that modelor otherwise perform 3D localization was made here.The spike sorting method described in Chapter 3 (see especially Figure 3.12) tracked verticalchanges in cell position (“drift”) up to a net total of ∼ 150 µm (Figure 4.6). Continuous changes inlocalized spike position were accompanied by continuous changes in spike shape, such as Vpp and σ,but also other spike shape features captured by PCA and ICA. Drift rates varied greatly, ranging0–200 µm/h (Figure 4.7) depending on time, cell, track, and method of calculation. Despitethe appearance of predominantly upward drift in the vertical position plots of cell populations(Figure 4.6, upper panels), there was nearly as much downward drift as upward, with a meanupward drift rate across cells and tracks of ∼ 2 µm/h. There was less drift in ptc15.tr7c than inthe other tracks, though it remains unknown why. One possibility is that longer polytrodes (2avs. 1a designs) exhibit less drift. Another is that transcolumnar tracks exhibit less drift. Trackptc15.tr7c also had more consistent drift across cells and time, suggesting that lower drift rate85might correspond to lower variance in drift rate.Why some cells drifted much more than others is a mystery, and cannot be easily explained bysystematic polytrode-tissue movement. Even more perplexing is that cells that drifted at high ratesoften did so in unison (Figure 4.6, top right panels), even when at opposite ends of the polytrode,while others in between drifted little, not at all, or in the opposite direction. Perhaps some cellsadhered to the polytrode, thereby appearing stationary, while others did not and therefore appearedto drift. Another explanation may be the use of 2D instead of 3D localization. With 2D localization,cells closer to the polytrode might appear to drift more than more distant cells. Although this doesnot explain why some some cells didn’t drift at all, or drifted in opposite directions, using a 3Dinstead of a 2D localization model might help explain some of the strange drift observed here.Buzsa´ki (2004) argued that the apparent location of a neuron may be confounded by differentpossible spike generating mechanisms outside of the usual somatic or axon hillock locations. Per-haps some of what appear to be conventional neuronal spikes are instead spikes from the axons(Section 5.6.1) or dendrites of more distant neurons, whose apparent origination point may bemore greatly disturbed by the polytrode, and which may move in different ways from conventionalsomatic or axon hillock spikes.Remarkably, a recent study by Xie et al. (2013) showed that the extracellular space in mousebrain during both sleep and anesthesia increases by 60% compared to the awake state. This largechange in volume may affect relative neuronal distances and extracellular spike propagation, andcould plausibly fluctuate with depth of anesthesia. Extracellular volume fluctuations could be asignificant source of the apparent drift found here. If so, long-duration recordings in awake animalsmight paradoxically exhibit less drift than in anesthetized animals, whose anesthetic depth andcortical state can vary over time (Sections 6.4 & 6.7.3).After several hours of recording, sometimes the agar surrounding the craniotomy and the poly-trode (Section 2.1) would begin to dry up. This may have led to changes in the polytrode-tissueinterface, and potentially contributed to some of the drift described here. Future experiments mayadd a layer of silicone oil on top of the agar to prevent drying.To address potential template distortion due to drift, future work could calculate templatesover shorter periods of time, perhaps every 30 min of recording, or every certain number of spikes.This would also remove the influence of drift on conclusions about whether the discretized neuronalpositions are due to the localization method, or due to polytrode geometry.A strobe stimulus such as a bright full screen flash generates transient synchronized inputinto cortical layer 4. By calculating the second spatial derivative of the LFP time-locked to thisstrobe stimulus, a characteristic laminar pattern of current sources and sinks can be revealed. Thispattern is called the CSD, and may be used to determine the position of a vertical array of electrodesites with respect to cortical layers (Mitzdorf, 1985; Sakata and Harris, 2009). The CSD thereforeallows estimated neuron positions to be approximately localized by cortical layer. After polytrodeinsertion, the CSD pattern was used here only as a rough indicator of how deep the polytrode86was positioned relative to the cortical layers, and therefore how much further to drive it down foroptimal coverage of all layers. CSD analysis was not used to accurately determine the laminarposition of each localized neuron. Future work should do so, and may not even require a strobestimulus (Section 6.7.4), which might therefore allow continuous tracking of polytrode-tissue driftover time.4.6.4 Orientation tuningOrientation tuning curves were calculated for all isolated cells from responses to orientation stimuli.61% of all cells, including those that were inactive (firing rates < 0.05 Hz) during all orientationstimuli, were significantly tuned, while 87% of cells that were active during at least one orientationstimulus were significantly tuned (Section 4.5). Most extracellular electrophysiology studies reporta high fraction (70–90%) of orientation tuned cells in primary visual cortex. Schiller et al. (1976b)found that 87% (572/654) of cells in rhesus monkey V1 were well tuned, with the disclaimer thatthe reported proportion of tuned cells depends on recording methods. Hammond and Andrews(1978) found 70% (68/97) of cells in cat areas 17 and 18 were tuned to orientation. De Valoiset al. (1982) and Ringach et al. (2002b) reported that 86% (190/222) and ∼ 89% (∼ 274/308)respectively of cells in macaque V1 were well tuned (bandwidth < 90◦).All of these reports likely excluded very low firing rate cells, cells that responded poorly toartificial stimuli, and/or cells whose activity may have only been detectable over long recordingperiods. The proportion of tuned cells in these studies may therefore be most directly comparableto the 87% of active cells reported here. In contrast, an extensive in-vivo two-photon calciumimaging (Section 1.1) study in isoflurane-anesthetized young (P19–40) cat primary visual cortex(area 18) by Ohki et al. (2005) found 61% (97% of the 63% that were responsive) of 6734 cells inlayers 2/3 were significantly tuned to orientation. This corresponds well to the 61% of all isolatedcells reported here.Damage from the wide shank polytrodes used here may be responsible for some of the 39% ofall isolated cells that were not significantly orientation tuned to even a single orientation stimulus.Switching to narrower shank polytrodes might increase the fraction of significantly tuned cells. Be-sides damage, there may be other reasons for non-oriented cells. Perhaps some cells respond onlyto stimuli more naturalistic stimuli than bars or grating. Although technically challenging, per-haps their orientation tuning could be characterized from responses to naturalistic movies instead.Monocular stimulation instead of binocular stimulation may be insufficient to adequately stimulatesome cells. The shift work hypothesis (Section 4.6.2) or changes in cortical state (Chapter 6) mightexplain the inactivity of cells at certain times, which for some cells might by chance have beenduring the relatively brief periods of presentation of artificial orientation stimuli. And finally, theremay very well be a wide range of degrees of orientation selectivity in visual cortex (De Valois etal., 1982), with some cells lacking significant orientation tuning altogether.Cells with very sparse firing were still highly selective for stimulus orientation (Figures 4.8C &874.9). Though often discarded in studies, such low firing rate cells (< 0.1 Hz) may nevertheless beuseful for perception. Surprisingly, orientation tuning strength was inversely and linearly correlatedwith geometric mean firing rate (Figure 4.9A). The author is unaware of any other such report. Thiscontradicts the notion that higher firing rates generally lead to better stimulus encoding (Gershonet al., 1998), and bolsters the importance of low firing rate cells.Across the population of tuned cells from all 3 tracks, there were no obvious relationshipsbetween orientation preference, tuning strength, and normalized cell depth (Figure 4.10A), norwas there any reason to expect otherwise. However, individual tracks exhibited varying degreesof dependence between cell orientation preference and depth, likely due to their vertical angle ofinsertion (Figure 4.10B). Track ptc15.tr7c had orientation preferences that varied strongly withdepth, suggesting that it was a highly transcolumnar track. Direction of motion preferences werenot examined here, but future work should show that, like orientation preference, over multipletracks there was no bias towards any particular preferred direction of motion.885 Cell Type5.1 IntroductionFunctional variation among neurons may be caused by a variety of factors, including differences incellular morphology, physiology, and connectivity. Some of the functional variation in extracellularlyrecorded populations may be explainable by classifying neurons into different types. There areseveral possible ways to do so, five of which are described here, and the first three of which areused.One method is to classify neurons according to their temporal waveform shapes, of which thereare at least two types: longer waveform duration excitatory pyramidal cells and shorter waveformduration inhibitory interneurons (Csicsvari et al., 1998; Bartho´ et al., 2004; Blanche, 2005; Luczaket al., 2007; Sirota et al., 2008; Niell and Stryker, 2008; Mizuseki et al., 2009; Sakata and Harris,2009; Benchenane et al., 2010; Wilson et al., 1994; Gur et al., 1999; Mitchell et al., 2007). Bothtypes are usually labelled as “putative” due to the inability of most extracellular experimentalsetups (including that used here) to directly visualize and measure the intracellular currents ofeach extracellularly recorded neuron.Another way to classify cells may be according to the spatial extent of their waveforms, asmeasured across multiple channels. Like temporal waveform shape, the spatial extent of the extra-cellular field might cluster into two groups: pyramidal cells with large open dipolar extracellularfields, and interneurons with small closed monopolar fields (Blanche, 2005). However, there iscurrently no evidence in the literature for such a bimodality in spatial extent.Third, in primary visual cortex, neurons can be classified into simple and complex cells accordingto the spatial separation of the oriented on and off subfields of their RFs (Hubel and Wiesel, 1962).Simple cells have well separated on and off subfields, while complex cells have overlapping subfields(Section 1.1). A third possibility are afferent axons from the lateral geniculate nucleus (LGN), whichlike simple cells have non-overlapping on and off subfields, but with a centre-surround spatialorganization which makes them untuned to orientation. Classifying cells by RF type is a standardprocedure (Schiller et al., 1976a; Gilbert, 1977; DeAngelis et al., 1993; Kagan et al., 2002), but theease with which it can be done depends on the stimulus used. Classification is straightforward withwhite and black drifting bars or gratings, both of which have large, oriented, spatially separated lightand dark regions for independently stimulating potentially separated subfields. Reverse correlationto an m-sequence white noise movie (Section 2.4) to calculate the spike-triggered average (STA)can also be used to extract non-overlapping subfields, and to therefore check if the RF is simple(Ringach and Shapley, 2004). However, the lack of a discernable RF from the m-sequence doesnot necessarily mean the cell is complex, and may merely mean that the cell was not sufficiently89stimulated by the white noise stimulus. Spike-triggered covariance (STC) of m-sequence responsescan be used to calculate overlapping subfields, and hence detect complex cells (Schwartz et al.,2006), but calculating the requisite covariance matrix for the STC requires many more spikes thanthe STA, and was considered impractical here. In comparison, naturalistic stimuli are desirablefor evoking greater and more realistic responses, but mapping RFs (and especially complex cellRFs) with naturalistic movies is more complicated than reverse correlation to a linear stimuluswith only first order statistics, such as the m-sequence (Ringach et al., 2002a; Smyth et al., 2003;Willmore and Smyth, 2003; Sharpee et al., 2004; Touryan et al., 2005). Also, due to the high spatialcorrelations in naturalistic movies, very long duration recordings and/or high firing rates may berequired to extract reasonable estimates of RFs from naturalistic movie responses. However, themulti-hour recordings described here span both artificial and naturalistic stimuli, with single unitidentification across these different stimuli, potentially allowing for the best of both worlds. Notethat the true discreteness of simple and complex cell classes has been the subject of debate (Deanand Tolhurst, 1983; Chance et al., 1999; Mechler and Ringach, 2002; Abbott and Chance, 2002;Kagan et al., 2002; Priebe et al., 2004; Mata and Ringach, 2005).Fourth, neurons may also be classified by their firing patterns as regular spiking (RS), fastspiking (FS), chattering (CH) or intrinsically bursting (IB) (Gray and McCormick, 1996; Nowaket al., 2003; Bartho´ et al., 2004; Blanche, 2005; Herikstad et al., 2011). This is done by examiningeach cell’s autocorrelogram or inter-spike interval (ISI) histogram. However, cells with very lowfiring rates, such as those reported here (Section 4.3), have mostly empty autocorrelograms and ISIhistograms at the timescales of interest (ISIs < 50 ms), precluding such classification. Note thatHerikstad et al. (2011) showed that it may nevertheless be possible to classify the firing patternsof very low rate cells by plotting their ISI histograms on a log timescale instead of a linear one.Fifth, neurons may be explicitly classified as excitatory or inhibitory by examining their cross-correlograms for evidence of monosynaptic connections. Given enough spikes, excitatory monosy-naptic connections result in peaks in the cross-correlogram, and inhibitory connections result introughs (Perkel et al., 1967). However, monosynaptic connections are very rare, even within alocal population. Bartho´ et al. (2004) found that only 0.2% of local cell pairs recorded in layer 5of rat somatosenory and prefrontal cortex had cross-correlogram peaks or troughs that suggestedmonosynaptic connectivity. Furthermore, less than 8% of neurons induced such peaks or troughs inthe cross-correlograms of other neurons (Bartho´ et al. (2004), Table 1, (72 + 5 + 28)/1414 = 7.4%)and could therefore be classified as excitatory or inhibitory. Qualitative examination of cross-correlograms in the data presented here showed similarly low percentages. Therefore, only a smallfraction of recorded neurons can be classified in this manner, making it a seemingly impracticalmethod for classifying an entire population. Fortunately, the same study showed that spike wave-form duration correlated with whether a cell was excitatory (long duration) or inhibitory (shortduration), allowing waveform duration to be used as a reasonable proxy for the excitatory/inhibitoryclassification.90In this study, cells were classified into types according to their spike shape (Section 5.2) andRFs (Section 5.4). The width of the secondary spike peak, and the amplitude asymmetry of the twopeaks were used to cluster cells into 4 spike types: fast, slow, fast asymmetric and slow asymmetric.Surprisingly, the width of the primary spike peak was not useful for cell typing. The spatial extentof spikes was also unimodal and not useful for cell typing (Section 5.3), although this may havebeen an artifact of using 2D instead of 3D spatial localization. A variety of methods were used tocharacterize RFs, and their consensus was used to classify each cell as simple, complex, putativeLGN afferent, or unknown RF type. There were roughly equal numbers of cells classified as simple,complex, and unknown RF type, with only 5% classified as putative LGN afferents. Cells classifiedas unknown RF type may have been mostly complex cells damaged by polytrode insertion.5.2 Spike shapeSix different measures were used to characterize the shape of the mean waveform of the primarychannel (template) of each neuron: maximum slope, slope-based spike duration, interpeak interval,peak temporal asymmetry, full width half maximum (FWHM) of primary and secondary peaks,and peak amplitude asymmetry. To prevent quantization of temporal measures, templates werespline interpolated to 1 µs resolution.The first measure, maximum slope, was simply the maximum absolute value slope of eachcell’s template (in µV/µs). The second measure, slope-based spike duration, was defined as theinterval between the first and last timepoint in the template which exceeded an absolute valueslope threshold of 0.4 µV/µs. All cells had a maximum absolute value slope of at least 0.49(Figure 5.1A), so picking a threshold of 0.4 did not exclude any cells. Rather, this threshold valueseemed to correspond to qualitative judgements of when each template first departed significantlyfrom zero, and when it last returned to zero.The third measure, interpeak interval, was defined as the time between the primary and sec-ondary peaks in the template. Peaks were defined as the extrema between template zero-crossingsand edges. The primary peak was considered to be the extremum closest in time to the t = 400ms general alignment point used during spike detection (Section 3.4). The secondary peak wasconsidered to be the extremum immediately following the primary peak, and by definition, of op-posite sign. If however the primary peak was the last extremum in the template, it was labelledthe secondary peak, and the one to its immediate left became the primary peak. Only 2 cells outof the 245 required such a swap of peak labels.The fourth measure, peak temporal asymmetry, was an estimate of the temporal skew of eachpeak around its mode. It was calculated by finding the time between the mode and the medianof each peak, normalized by the width of the peak. Peak limits were determined using the fifthmeasure, FWHM, i.e., the width of the peak at one half its maximum amplitude with respect to0 volts. FWHM of the primary and secondary peak was designated as FWHM1 and FWHM2,91respectively.The sixth and final measure was peak amplitude asymmetry, inspired by the asymmetry indexof Sirota et al. (2008) and Sakata and Harris (2009), and by the slope ratio of the depolarizationand repolarization phases of intracellular spikes (McCormick et al., 1985). Sirota et al. (2008)and Sakata and Harris (2009) compared the amplitudes of the first and third peaks of tri-phasicwaveforms. Given that most of the waveforms collected here were only biphasic (Figure 4.3),the index was modified to compare the primary and secondary peaks instead. Peak amplitudeasymmetry was thus defined as (V1 − V2)/(V1 + V2) where V1 and V2 are the absolute values ofamplitudes of the primary and secondary peaks, respectively. Its value ranged from -1 to 1, with 0representing equal peak amplitudes.For the purposes of measuring spike shape, template amplitudes were normalized because am-plitude as measured at a given electrode site is mostly not an inherent property of the cell. Rather,it is mostly a function of distance between cell and electrode site (Henze et al., 2000).Distributions of the first three measures are shown in Figure 5.1A–C. Maximum slope wasunimodal, while slope-based duration showed a clear bimodality and interpeak interval showed ahint of multimodality. Two clear clusters emerged when slope-based duration was plotted againstinterpeak interval (Figure 5.1D). Points were divided by a manually placed line separating fast(red) and slow (blue) spike types. Overplotted templates of the two clusters (Figure 5.1E–F)looked convincingly different. However, the bimodality of the slope-based duration metric wasmerely an artifact of thresholding template slope. For a given slope threshold (0.4 µV/µs in thiscase), either only one peak or both peaks of a given template would exceed threshold, resulting inspike duration values that were artifactually bimodal. Changing the slope threshold made pointsjump from one cluster to another, and cluster sizes were very sensitive to the precise threshold used.Slope-based duration was therefore abandoned as a measure of spike shape, but is left here as ademonstration of the dangers of threshold-based metrics. Thresholding can be dangerous becauseit imposes a nonlinearity, something best avoided before clustering.The fourth measure, peak temporal asymmetry, was unimodal for both primary and secondarypeaks, and its use did not improve clusterability (not shown).Ultimately, only the fifth and sixth measures, FWHM and amplitude asymmetry, were foundto be useful in classifying cells according to spike shape. Their distributions are shown in Fig-ure 5.2A–C. FWHM1 was unimodal, but FWHM2 was bimodal, while amplitude asymmetry wassomewhat multimodal. Therefore, FWHM2 vs. amplitude asymmetry was chosen as the space ofspike shape measures in which to cluster cells into different spike types (Figure 5.2D). This decisionwas further supported by examining 2D and 3D scatter plots of all combinations of the spike shapemeasures described here (excluding slope-based duration). Of all the possible spaces, the FWHM2vs. amplitude asymmetry space revealed the clearest and greatest number of clusters. For example,interpeak interval was highly correlated with FWHM2, and therefore provided no additional clus-tering benefit. A second measure of spike duration based on FWHM (measured from the start of92BE FC0 1 2 3 4 5maximum slope ( V/ s)01020304050neuron countAD0 200 400 600 800time ( s)2001000100200voltage (V)0 200 400 600 800time ( s)2001000100200voltage (V)0 200 400 600 800slope-based duration ( s)0102030405060neuron count0 100 200 300 400interpeak interval ( s)051015202530neuron count0 100 200 300 400interpeak interval ( s)0200400600800slope-based duration (s)Figure 5.1: A demonstration of the potential dangers of threshold-based metrics. A–C : Dis-tributions of three different temporal waveform measures for all cells (see text for details). Ofthe three, only slope-based duration (the interval between the first and last timepoints which ex-ceeded an absolute value slope threshold of 0.4 µV/µs) showed clear bimodality. D : Scatter plot ofspike duration vs. inter-peak interval showing two well-separated clusters, divided manually via thedashed line into fast (red) and slow (blue) spike types. The clusters were an artifact of thresholdingtemplate slope to calculate spike duration. E–F : Overplotted templates, coloured according to theartifactual clustering in D . Slow templates are shown on their own in E , and fast templates areplotted over top of slow in F . Despite being artifactual clusters, their differences in template shapelooked convincing.the primary peak to the end of the secondary peak) was also highly correlated with FWHM2, andprovided no extra clustering information. Finally, full width at different fractions of peak maximum(from 0.125 to 0.9) were also tested, but were all less clusterable than FWHM.Points in FWHM2 vs amplitude asymmetry cluster space were split into 4 clusters using manu-ally placed straight lines (Figure 5.2D). No points were excluded. Clusters were labelled fast (red),slow (blue), fast asymmetric (green), and slow asymmetric (grey). The first 2 clusters were veryclear, the third somewhat less so, and the fourth even less. Overplotted unnormalized templatesare shown separately for each cluster (Figure 5.2E–H), and simultaneously (Figure 5.2I).Cell counts according to spike type and track are shown in Table 5.1. Across all tracks, 52%(128) of cells were fast, 30% (73) were slow, 13% (32) were fast asymmetric, and 5% (12) were93BE FCAD0.4 0.0 0.4 0.8amplitude asymmetry0200400600FWHM2 (s)0 50 100 150 200FWHM1 ( s)05101520253035neuron count0 200 400 600FWHM2 ( s)0102030405060neuron count0.4 0.0 0.4 0.8amplitude asymmetry051015202530neuron count0 200 400 600 800time ( s)2001000100200voltage (V)0 200 400 600 800time ( s)2001000100200voltage (V)0 200 400 600 800time ( s)2001000100200voltage (V)0 200 400 600 800time ( s)2001000100200voltage (V)0 200 400 600 800time ( s)2001000100200voltage (V)H IGfast slowfast asymmetric slow asymmetric allFigure 5.2: Temporal spike shape measures of primary channel templates were used to classifyneurons into two clear clusters (fast and slow), plus another two potential clusters (fast asymmetricand slow asymmetric) that were less clear. A–C : Distributions of three different temporal waveformmeasures (see text for details). FWHM1 showed no mulitmodality (A), but FWHM2 and amplitudeasymmetry did (B–C ). D : Scatter plot of FWHM2 vs. amplitude asymmetry. Points were manuallyclustered according to the dashed lines. To maximize cluster visibility, the y axis limit was set suchthat 3 grey points were excluded. E–H : Overplotted templates of each cluster, coloured accordingto D . Although templates were roughly aligned at 400 µs, they were not explicitly aligned withone another due to the many realignment operations performed during spike sorting. Overplottedtemplates of all four clusters are shown in I for comparison.94track fast slow fast asym slow asym simple complex LGN aff unknownptc15.tr7c 61(75) 12(15) 7(9) 1(1) 53(65) 12(15) 0(0) 16(20)ptc22.tr1 32(34) 36(39) 19(20) 6(6) 18(19) 31(33) 9(10) 35(38)ptc22.tr2 35(49) 25(35) 6(8) 5(7) 14(20) 32(45) 3(4) 22(31)total 128(52) 73(30) 32(13) 12(5) 85(35) 75(31) 12(5) 73(30)Table 5.1: Spike and RF type counts (with percentages in parentheses), for each track and intotal. Compared to the other two tracks, ptc15.tr7c had an excess of fast and simple cells, and alack of slow, slow asymmetric, complex, and putative LGN afferent cells. asym: asymmetric. aff :afferent.slow asymmetric. Compared to the other two tracks, ptc15.tr7c was an outlier, with an excessof fast cells, and fewer slow and slow asymmetric cells. Fast cells had the largest peak-to-peakamplitudes, and asymmetric cells had the smallest (Figure 5.2I). The mostly positive values inamplitude asymmetry (Figure 5.2C & D) indicate that the primary peak (the one at ∼ 400 µs)was generally greater in amplitude than the secondary peak (the one that followed). The disparityin amplitude between the primary and secondary peaks was greatest for the cell types labelledasymmetric.5.3 Spatial extentFor each neuron, the median of the spatial extent (σ) of its member spikes (Section 3.5) wastaken as the spatial extent of the neuron (analogous to how per-neuron x and y positions wereobtained in Section 4.4.) Figure 5.3A shows the distribution of σ for cells in each track, as wellas for all cells across all tracks. The distribution across all tracks peaked at 50 µm and showedno multimodality. Save for perhaps a hint of bimodality in ptc15.tr7c, the individual tracks alsoshowed no multimodality. Also, σ did not correlate with any temporal measures (the best two,FWHM2 and amplitude asymmetry are shown in Figure 5.3B), and did not improve clusterabilityof cells into different types. Spatial extent from 2D spatial localization was therefore not useful forcell typing.5.4 Receptive field typeClassification of cells into simple, complex and putative LGN afferent RF types was performedusing three different types of stimuli: white and black drifting bars at various orientations, driftinggratings at various spatial frequencies and orientations, and m-sequence noise stimuli. Given exper-imental time constraints and the history of stimulus development associated with each track, onlytwo of the three stimulus types were available for each track. All 3 tracks had m-sequence stimuli,but only ptc15.tr7c had drifting gratings with a sufficient number of presentations of each stimuluscondition to allow determination of RF type, and only ptc22.tr1 and ptc22.tr2 had white and blackdrifting bar stimuli. Results from all relevant recordings were considered when classifying a cell’s950 25 50 75 10001020neuron count0 25 50 75 10001020ptc15.tr7c ptc22.tr1ptc22.tr2 all tracksA BFWHM2 ( s)0 200 400 6000255075100(m)0.4 0.0 0.4 0.8amplitude asymmetry0255075100(m)0 25 50 75 100( m)01020neuron count0 25 50 75 100( m)02040Figure 5.3: A: Distributions of spatial extent (σ) of neurons in individual tracks, as well as acrossall tracks. Overall, σ had a unimodal distribution. B : σ plotted against the two best temporalwaveform measures (FWHM2 and amplitude asymmetry) from Section 5.2, showing that σ hadlittle to no correlation with either of them, and did not improve clusterability.RF type.Drifting bar raster plots (Figure 5.4A) were visually inspected for spatial overlap of responses towhite and black bars at the preferred orientation. If white and black bar responses were obviouslynon-overlapping, the cell was classified as simple for that recording. Classifying it as simple didnot rule out later classification as a putative LGN afferent based on the characteristics of its STA(see below). Poor orientation tuning in conjunction with non-overlapping on and off responses(Figure 4.8B) was suggestive of an LGN afferent, but was not considered definitive. If the responseswere obviously overlapping, the cell was classified as complex for that recording. If the degree ofon and off subfield overlap was too difficult to discern by visual inspection of the raster plot, theRF type was classified as “unknown” for that recording.Drifting grating raster plots (Figure 5.4B) were also visually inspected, this time for modulationat the temporal frequency of the grating (2 Hz), at the preferred orientation and spatial frequency.If there was obvious temporal modulation above the baseline firing rate at the expected temporalfrequency, the cell was considered simple. If the rate was elevated (i.e., the cell was tuned) butshowed little to no temporal modulation, the cell was considered complex. Otherwise, for that96complexcomplexsimpleA B simpleFigure 5.4: Example trial raster plots of drifting bar (A) and grating (B) responses of simpleand complex cells. For all panels, visible rows of responses (8–12 trials each) are in order ofstimulus parameter combination (not temporal order). Horizontal dashed lines denote orientationincrements. A: Drifting bar raster plots. Responses to white and black drifting bars are representedby white and black ticks respectively, where each tick represents one spike. Stimulus parameterswere bar brightness (white or black) and orientation (12 steps of 30◦). All possible parametercombinations were presented in pseudorandom order, with 12 presentations per combination. Trialindex increased first by presentation number, then bar brightness, and then orientation. Spatialoverlap of responses to white and black drifting bars distinguished simple cells from complex.Variation in response timing over the range of orientations was due to slight misalignment of thecenter of the stimulus and the RF centers of some cells. B : Drifting grating raster plots. Stimulusparameters were spatial frequency (10 values from 0.15–5 cycles/◦) and orientation (8 steps of 45◦).All possible parameter combinations were presented in pseudorandom order, with 8 presentationsper combination. Trial index increased first by presentation number, then spatial frequency, andthen orientation. Response modulation at the 2 Hz temporal frequency of the grating relative tobaseline firing was obvious for the simple cell, but absent for the complex cell. The raster plots ofall four cells showed strong orientation tuning.recording, the cell was classified as “unknown”.Reverse correlation of spikes to the m-sequence movie to construct the STA is illustrated inFigure 5.5. For a fixed reverse correlation time range of say, 40 ms, each spike’s contribution tothe STA is found by looking backwards 40 ms from the time of each spike to determine whichframe of the movie was on display. That frame’s pixels are added to the running total. Onceall spikes are reverse correlated in such a manner, the sum of the frames is normalized by thenumber of spikes to get the STA, representing the average movie frame that triggered a spike. This97spike times: t1 t2 t3t1 − 40 ms t2 − 40 ms t3 − 40 ms+ + + ... = Figure 5.5: An illustration of the spike triggered average, calculated by reverse correlating thespike train of a cell in response to an m-sequence noise movie to estimate the cell’s RF 0 to 40ms following the presentation of each m-sequence frame. A simple cell is illustrated here. Redare on subregions (stimulated by light pixels, inhibited by dark pixels), blue are off subregions(stimulated by dark pixels, inhibited by light pixels).can be repeated for different time ranges (each typically a multiple of the frame display time) tocalculate the spatiotemporal STA, estimating the cell’s spatially non-overlapping spatiotemporalreceptive field (STRF) (Figure 5.6). Cells with a non-zero (non uniform) STA were considered tobe simple cells or putative LGN afferents, with the STA approximating the cell’s spatially non-overlapping STRF. Oriented STRFs were considered to be simple cells, while small, unoriented,quickly emerging STRFs were considered to be putative LGN afferents. An absence of an STA atall reverse correlation time ranges suggests that the cell is complex, but due to spatially overlappingon and off subfields, the STA cannot reveal the cell’s STRF. A different method, the STC, maybe used to reveal spatially overlapping subfields. However, the STC requires roughly an order ofmagnitude more spikes than the STA to accurately calculate the required covariance matrix, andwas not used here to detect complex cells.Note that reverse correlating the spikes to the movie is equivalent to forward correlating themovie to the spikes. The latter was used here because if was more computationally efficient. Alsonote that reverse correlation timepoints (e.g., 40 ms, 80 ms, 120 ms, etc.) are referred to here astime ranges (0–40 ms, 40–80 ms, 80–120 ms, etc., see time labels in Figure 5.6), because whenreverse correlating from a given spike to a movie frame t ms ago, that frame will have been on-screen for anywhere from 0 to dt ms, where dt is the duration each frame is displayed. Similarly,when forward correlating from a movie frame, a time range of t ms after the start of the frame tot ms after the end of the frame is used to determine which spikes should accumulate that frame’scontents.Cells with non-zero STAs are shown in Figure 5.6, organized vertically according to depthalong the length of the polytrode. Non-zero STAs are shown for 63 cells, from one representativem-sequence recording per track. For all m-sequence recordings from all 3 tracks, there were 9398cells with non-zero STAs. In agreement with DeAngelis et al. (1993), most responses lasted over100 ms, and RF subfields generally reversed polarity 40–80 ms after their initial appearance, itself20–40 ms after stimulus onset. RFs appeared normal, most having one or more elongated subfieldsof alternating sign. There were few obvious holes in RF subfields that might indicate extensivedamage to afferents. RFs calculated from multiple m-sequence recordings hours apart were eitherquite similar (e.g., Figure A.1), or were missing altogether, possibly due to either a gain or lossof responsivity. The first track, ptc15.tr7c, had many more cells with non-zero STAs than did theother two tracks, and their subfield orientation varied systematically as a function of depth alongthe polytrode, suggesting a transcolumnar insertion. Though difficult to see (due to a conservativelylarge choice of m-sequence frame size), the subfield orientations of the other two tracks were moreconstant as a function of depth. Results from the calculation of orientation tuning from orientedstimuli (Section 4.5) agree with the conclusion that track ptc15.tr7c was strongly transcolumnar.Subjective classification of a unit as a putative LGN afferent was mostly based on the m-sequence STA, but also on responses to oriented stimuli. Small, circular fields that emerged early(within 40 ms of stimulation) suggested an LGN afferent, as did poor orientation tuning and highfiring rates in response to drifting bars (Figure 4.8B) or gratings.All relevant recordings (4 or 5, depending on the track) were used to classify each cell as simple,complex, putative LGN afferent, or unknown. Usually the two stimulus types (either white andblack drifting bars and m-sequence, or drifting gratings and m-sequence) agreed on the classification.Since the responsivity of cells could vary substantially over hours of recording (Section 4.3, Swindaleand Spacek (2012)), using as many recordings as possible to classify RF type increased the chanceof a successful classification (something other than “unknown”). It also helped increase confidencewhen responses from multiple recordings of different stimulus types gave the same classification.For 11% (26/245) of cells, the responses from two or more recordings conflicted over whether thecell was simple or complex. In these cases, a voting system was used to resolve the conflict, with onevote per recording. There were no recordings that conflicted over the distinction between simplecells and LGN afferents. Appendix A demonstrates simple cell RF stability over a 14 hour period.Cell counts and percentages according to RF type and track are shown in Table 5.1. Across all3 tracks, there were roughly equal numbers of simple, complex, and unknown cells (about one thirdeach), with only 5% of cells classified as putative LGN afferents. Of the 12 units classified as LGNafferents, only 3 were significantly (p < 0.01) tuned to orientation (Section 4.5), and only weakly so(r¯ = 0.13). Of the 93 cells with non-zero m-sequence STAs, 73% (68/93) were classified as simplecells, 12% (11/93) as complex cells, 13% (12/93) as LGN afferents, and 2% (2/93) as unknown.As was the case for spike type, ptc15.tr7c was an outlier in terms of its RF type distribution(Table 5.1), with an excess of simple cells and a lack of complex cells and LGN afferents comparedto the other two tracks.99ptc15.tr7c. . .ptc22.tr10 40 80 120 ms ptc22.tr20 40 80 120 msLLLCSSSSUSSSSSSSCLLLLSSSCSSSSSCS0 20 40 60 80 100 ms. . .12.7° 5° 7°Figure 5.6: Spatiotemporal RFs from STAs to multiple reverse correlation time ranges of an m-sequence noise movie. Each row represents a unit, and each column a reverse correlation time range.Within a row, the same normalization is used for all time ranges, but each row is independentlynormalized to maximize visibility of RF structure. Units were sorted top to bottom by depth alongthe polytrode and grouped according to track (ptc15.tr7c split vertically), with one representativem-sequence recording chosen for each track. Only units with non-zero STAs are shown. Other m-sequence recordings in each track revealed other units with non-zero STAs. For ptc15.tr7c (left),m-sequence frames were presented for 20 ms each. Orientation tuning changed in a regular clockwisefashion, strongly suggesting the track was transcolumnar. All cells were classified as simple. Forptc22.tr1 and ptc22.tr2 (middle, right), far fewer units with non-zero STAs were present. Lettersdenote RF type: S: simple, C: complex, L: putative LGN afferent, U: unknown. Each classificationtook all relevant recordings into consideration. M-sequence frames were presented for 40 ms each.RFs appear smaller because the absolute movie size in degrees of visual angle was set higher thannecessary, conservatively ensuring capture of the full RFs of the entire population of cells.1005.5 Cell type comparisonThe spatial distributions of cells by both spike type and RF type are shown in Figure 5.7. Forall tracks, slow, complex and unknown cells were fairly evenly distributed along the length of thepolytrodes. For track ptc15.tr7c, both fast and simple cells were also evenly distributed across thelength of the polytrode, but this result may have been because that track was likely transcolumnar(Sections 4.5 & 5.4). In contrast, for the other two tracks, both fast and simple cells were somewhatmore likely to be found higher up the polytrode, presumably in more superficial layers. There weretoo few fast asymmetric, slow asymmetric, and LGN afferent units to make conclusions about theirspatial distributions.The relationship between cell position and spatial extent was also examined, with points repre-senting cell position (as in Figures 4.4A & 5.7) coloured by each cell’s spatial extent (not shown).There was no obvious relationship between cell position and spatial extent for any of the 3 tracks.To see if there was a relationship between spike type and RF type, various comparisons weremade. Figure 5.8A–E shows overplotted templates of cells grouped according to RF type. Exami-nation suggested that simple cells had the highest peak-to-peak amplitude of the four RF types, andwere perhaps slightly faster than complex cells (width of secondary peaks at t ≈ 550 µs of red andblue traces in Figure 5.8E). Putative LGN afferents had the smallest amplitude. Distributions ofpeak-to-peak amplitudes in Figure 5.8F confirmed that RF type amplitudes from largest to smallestwere simple, complex, and LGN afferent. Unknown cells had roughly the same mean amplitude ascomplex cells, suggesting that unknown cells might nominally be mostly complex cells.Plotting cells in the spike type classification space (FWHM2 vs amplitude asymmetry) butcolouring them according to RF type (Figure 5.8G) did not reveal any obvious relationship, savefor perhaps an excess of simple cells (red points) in the fast cell cluster (bottom left). A matrixof cell counts of RF type vs spike type (Figure 5.8H) confirmed the above, showing that simplecells were about 4 times more likely to be fast cells than slow cells, even though overall there wereonly about 1.75 times as many fast cells as slow cells (Table 5.1, statistical tests for significancewere not performed). Furthermore, both complex and unknown cells were classified as fast andslow spike types in roughly equal numbers, suggesting again that unknown cells may nominally bemostly complex cells.How might cell types differ in their mean track-wide firing rates and fractional activity dura-tions? Both measures were calculated as previously described (Section 4.3), and the distributionsfor all four spike types and all four RF types are shown in Figure 5.9. Fast cells had somewhathigher mean rates than slow, fast asymmetric, and slow asymmetric cells (Figure 5.9A), with geo-metric means of 0.17 Hz, 0.078 Hz, 0.053 Hz and 0.054 Hz, respectively. This was despite fast cellshaving the same mean fractional activity duration as slow cells (Figure 5.9B). Cells with unknownRFs had lower mean firing rates and were active for shorter periods of time than simple, complex,and LGN afferent cells, all of which were very similar in both respects (Figure 5.9C & D). Geomet-101ptc15.tr7c ptc22.tr1 ptc22.tr2unknownLGN afferentcomplexsimple28 2802004006008001000120014001600180056 0 56 56 0 56ptc15.tr7c ptc22.tr1 ptc22.tr228 28020040060080010001200140016001800fastslowfast asymmetricslow asymmetric56 0 56 56 0 56Figure 5.7: Spatial distribution of cell types, per track. Left : Temporal spike shape classification.Right : RF classification. Same layout as in Figure 4.4A. Units are in µm.1020 200 400Vpp ( V)05101520253035neuron countF0.4 0.0 0.4 0.8amplitude asymmetry0200400600FWHM2 (s)G065neuron countfast slowfast asymslow asymsimplecomplexunknownH0 200 400 600 800time ( s)2001000100200Asimple B0 200 400 600 800time ( s)complex C0 200 400 600 800time ( s)LGN afferent D0 200 400 600 800time ( s)unknown E0 200 400 600 800time ( s)allvoltage (V)LGN affFigure 5.8: Comparison of RF type vs. spike type. A–D : Overplotted templates of simple,complex, putative LGN afferent, and unknown RF cell types. E : All RF cell types overplottedfor comparison. F : Overlapping distributions of primary channel peak-to-peak voltages of all fourRF cell types. Coloured arrows indicate means of their respective distributions. G: Same spiketype cluster space as in Figure 5.2D, but with points coloured according to RF type instead ofspike type. H : Cell count matrix of RF type (rows) vs. spike type (columns) for all 245 cells. aff :afferent. asym: asymmetric.ric means of simple, complex, LGN afferent and unknown cells were 0.33 Hz, 0.26 Hz, 0.23 Hz and0.011 Hz, respectively. Given that mean rates were calculated track-wide (Section 4.3), the lowermean rates of cells with unknown RFs may have simply been a result of their shorter durations ofactivity.5.6 Discussion5.6.1 Spike shapeAlthough cell typing by intracellular spike shape has been previously reported in cat visual cortex(McCormick et al., 1985; Nowak et al., 2003; Haider et al., 2010), most published cell typing byextracellular spike shape has been done in rodent cortex and hippocampus, and macaque cortex10310-4 10-3 10-2 10-1 100 101 102051015202530neuron count10-4 10-3 10-2 10-1 100 101 102mean firing rate (Hz)0510152025neuron countfastslowfast asymslow asymunknownLGN affcomplexsimpleA0.0 0.5 1.00102030405060 BC0.0 0.5 1.0fractional active duration01020304050 DFigure 5.9: Mean firing ratedistributions (left) and ac-tivity duration distributions(right) broken down by spiketype (top) and RF type(bottom). Arrows indicategeometric (left) and arith-metic (right) means sepa-rately for each cell type. Plotsin A and C are as in Fig-ure 4.1B. Plots in B and Dare as in Figure 4.2C, withbars left unfilled to better dis-tinguish overlapping distribu-tions. aff : afferent. asym:asymmetric.(Csicsvari et al., 1998; Bartho´ et al., 2004; Luczak et al., 2007; Sirota et al., 2008; Niell and Stryker,2008; Mizuseki et al., 2009; Sakata and Harris, 2009; Benchenane et al., 2010; Wilson et al., 1994;Gur et al., 1999; Mitchell et al., 2007). Showing that extracellular spike shape also clusters intotwo or more classes in cat visual cortex (Figure 5.2D) helps generalize extracellular spike shape (inthis case, FWHM2 and amplitude asymmetry) as a useful cell typing property.Given that waveform duration has been shown to be a reasonable proxy for physiological celltype (Bartho´ et al., 2004), slow cells may be considered putative excitatory pyramidal cells, andfast cells putative inhibitory interneurons. However, Robbins et al. (2013) discuss the caveat thataxonal spikes (such as LGN afferents in primary visual cortex) are of short duration, and can beeasily mistaken for interneuron spikes. A small fraction of units here (5%) were classified as putativeLGN afferents (Table 5.1), based on their very small circular RFs as well as their lack of orientationtuning and spatially segregated on and off responses, all of which were indicative of LGN cells.These units also tended to have short duration spikes (Figure 5.8C & green points in G), enforcingthe point of Robbins et al. (2013) of the dangers of assuming that fast spiking units are necessarilyinhibitory interneurons. Vigneswaran et al. (2011) showed that large pyramidal tract neurons (Betzcells) in macaque layer 5 M1 have extracellular spikes as short in duration as fast-spiking inhibitoryinterneurons, providing a further caveat to classifying cell type by extracellular spike shape alone.Unfortunately, despite extensive efforts to minimize sampling bias in these experiments, thegreater proportion of fast cells relative to slow cells (52% vs. 30%, see Table 5.1) is consistentwith the observation of Henze et al. (2000) that slow, low firing rate pyramidal cells tend to beunderrepresented in extracellular recordings. However, if track ptc15.tr7c is excluded due to it104being so transcolumnar, the proportion of fast and slow cells from the remaining two tracks isroughly equal, at about 40% each.Surprisingly, FWHM1, the width of the primary peak, was unimodal and did not cluster, whileFWHM2, the width of the secondary peak, was bimodal and did cluster (Figure 5.2A–B). Thisagrees with observations by McCormick et al. (1985) that the slope of the repolarization phase ofan intracellular spike clusters into high and low values, corresponding to narrow and wide secondarypeaks in the extracellular spike. In comparison, other groups have found FWHM1 to be multimodaland useful for cell typing in rat prefrontal, motor, somatosensory, auditory, and secondary visualcortices, as well as hippocampus (Bartho´ et al., 2004; Luczak et al., 2007; Sirota et al., 2008;Sakata and Harris, 2009; Benchenane et al., 2010). None report on the clustering of FWHM2.Those studies also reported bimodality in interpeak interval (or trough to peak time), which wasabsent here (Figure 5.1C). Furthermore, the fast cells shown here were larger in amplitude thanslow cells (Figure 5.2E–F). This is the opposite of the findings of the above studies, which find fastcells (i.e., narrow spiking cells, attributed to interneurons) to be of lower amplitude than slow cells(i.e., wide spiking cells, attributed to pyramidal cells). These differences may be due to differencesin species and cortical area. They may also be due to extra damage from the relatively wide (∼ 200µm) polytrodes used here, compared to those used by the above studies (∼ 100 µm). Differences inanalog and/or digital filter settings can also affect spike shape, sometimes dramatically (Wiltschkoet al., 2008). Finally, averaging waveforms across periods of recording with drift may distorttemplates, thereby affecting temporal or spatial waveform measures.These differences in spike shape may be explored in the future by using narrower polytrodedesigns (Section 4.6.3), a new recording system with greater ADC dynamic range (16 bits insteadof 12) allowing for open analog filters, and careful digital filtering of LFP from spike waveforms(Wiltschko et al., 2008). As described in Section 4.6.3, the spike shapes reported here may besomewhat distorted due to drift, which could be corrected for by splitting up each cell’s spike trainin time and averaging the spike waveforms within each time period. Finally, many more than the245 neurons shown here should be examined to increase confidence in conclusions about spike shape.If differences in spike shape clustering remain, recordings in other species and cortical areas withthe same recording system would help clarify whether or not those differences are indeed intrinsicto species and cortical area.Interestingly, Sirota et al. (2008) recorded 767 cells from a wide variety of cortical areas in rat.They classified their plot of amplitude asymmetry vs. interpeak interval into two clusters: wide(excitatory) and narrow (inhibitory). However, that plot (their Figure 1C) also suggested anothertwo or three clusters. Though not mentioned in the paper, perhaps these were truly distinct clustersas a result of combining recordings from such a wide range of cortical areas (6 in total, from V2to M1), and therefore perhaps different cortical areas do indeed consist of cells of differing spikeshape, even within the same species.1055.6.2 Spatial extentIn cat primary visual cortex, spatial extent (σ) of multichannel neuron waveforms was not a usefulmetric for cell typing (Section 5.3). Cells did not cluster according to spatial extent (Figure 5.3),spatial extent was not correlated with either spike shape measure, and spatial extent did notshow any particular spatial distribution along the polytrode (Section 5.5). However, these nullresults may have been partly an artifact of calculating each cell’s σ as the average σ of all of itsmember spikes. Since individual spikes are noisier than their cell’s template, calculating σ fromeach spike and then averaging them may have obscured multimodalities in template spatial extent.Future work should also measure spatial extent directly from templates by fitting a 2D Gaussian(Section 3.5) to the template (or multiple templates over time, to account for drift), instead of tothe individual spikes.Another potential artifact is that cell distance from the polytrode affects signal amplitude: thegreater the distance, the smaller the signal. This in turn may have an effect on the apparent spatialextent of the cell, as measured by fitting a 2D Gaussian to its spatial amplitude distribution.Since isolatable cell distances likely form a continuous distribution, their influence may smearout any multimodalities in the true 3D spatial extents of the population of cells. As described inSection 4.6.3, a 3D monopole/dipole current source model of extracellular spike potentials (Blanche,2005) may reveal multimodalities in spatial extent, such as a monopole/dipole distinction, that maybe useful for cell classification.5.6.3 Receptive field typeOn and off response overlap to drifting bar stimuli, temporal phase locking to sinusoidal gratingstimuli, and STAs from m-sequence movies were all used to classify each cell’s RF type as simple,complex, putative LGN afferent, or unknown (Figures 5.4 & 5.6). Each drifting bar and gratingraster plot, and each m-sequence STA was visually inspected to subjectively classify each cell’s RFtype. Future work should employ a more quantitative method of determining on and off subfieldoverlap (Dean and Tolhurst, 1983; Kagan et al., 2002; Mata and Ringach, 2005), temporal phase-locking (Skottun et al., 1991), and the number, size, and shape of non-overlapping on and offsubfields in the m-sequence STA. Though such quantification might not change the classification ofmany cells, automated methods would be faster and would increase confidence in RF classification.Although on and off subfield overlap was Hubel and Wiesel’s original method of distinguishingsimple cells from complex cells (Hubel and Wiesel, 1959, 1962, 1968), a more recent and commonmethod is to measure response phase locking to the temporal frequency of a drifting sinusoidalgrating. This involves creating a PSTH of the repeated trials of the stimulus parameter combinationwith the greatest response, and then taking its Fourier transform to find the power at the grating’stemporal frequency (F1). This is then compared to the DC power (the average firing rate), F0. Ifthe F1/F0 ratio (i.e., modulation ratio) is greater than 1, the cell is considered simple, and if it is106less than 1, the cell is considered complex (Skottun et al., 1991). However, generating the PSTHcan be complicated by the fact that the eyes may slowly drift over the course of a long durationstimulus. This might be corrected for in an automated way, but visually inspecting the spike rastersfor noticeable amounts of the correct temporal modulation was deemed here to be simpler. Further,Kagan et al. (2002) found that F1/F0 correlated poorly with the degree of RF subfield overlap inawake monkey V1, with some cells classified as complex according to their subfield overlap, yetclassified as simple according to their F1/F0 ratio (but see Dean and Tolhurst (1983) and Mataand Ringach (2005)). Chance et al. (1999) & Kagan et al. (2002) argue that the key distinction isthe degree of spatial phase invariance: complex cells have high phase invariance, while simple cellshave low phase invariance. On and off subfield overlap may relate more directly to spatial phaseinvariance than does the F1/F0 ratio, and subfield overlap may therefore be the preferred metric.Therefore, although F1/F0 has been a standard way to distinguish simple cells from complex,its true effectiveness in doing so is unclear, and relying instead on the subfield overlap may bea better strategy. Note that a combination of the two methods (subfield overlap estimated fromdrifting light and dark bars and m-sequence STA, and F1/F0 from drifting gratings) was used here.Simple, complex and unknown RF types each made up about one third of all cells reported here,with only 5% of cells classified as putative LGN afferents. In comparison, Gilbert (1977) reportedthat most cells were complex (24% (44) simple, 68% (125) complex, and 9% (16) unclassified cellsout of 185 cells from all layers of area 17 in 21 cats). Those recordings were performed with single-channel tungsten-in-glass electrodes, with multiple cells characterized within each penetration.However, a more recent review by Carandini et al. (2005) argues that the general consensus isthat there are equal numbers of simple and complex cells in V1. Tracks ptc22.tr1 and ptc22.tr2were somewhat consistent with Gilbert (1977) in that about twice as many cells were complex assimple (Table 5.1). Yet compared to that study, all 3 tracks had a higher fraction of cells withunknown RF type. This could be because wide polytrodes may cause more damage than narrowtungsten-in-glass electrodes.Similar to Gilbert (1977), Kagan et al. (2002) reported 14% simple, 78% complex, and 8%unclassified cells out of 228 cells in V1 of 5 awake macaques, using single channel platinum-tungstenin glass or quartz electrodes. Kagan et al. (2002) also used spatial overlap instead of F1/F0 todistinguish simple cells from complex, and argued that use of F1/F0 overestimates the fraction ofsimple cells.The precise distinction between simple and complex cells is somewhat controversial, as is themethodology used to distinguish them (Dean and Tolhurst, 1983; Carandini and Ferster, 2000;Kagan et al., 2002; Priebe et al., 2004; Mata and Ringach, 2005). Methodology and species mayaccount for some of the variability in these relative proportions across studies. Ideally, naturalscene movies should be used to calculate the RFs of both simple and complex cells, but doing sois, at least for now, complicated (Ringach et al., 2002a; Smyth et al., 2003; Willmore and Smyth,2003; Sharpee et al., 2004; Touryan et al., 2005). What may be simpler is to use natural scene107movie responses purely to distinguish simple and complex cells (see Section 6.7.2).How might polytrode damage affect the relative numbers of simple and complex cells? Damagemight make complex cells look more like simple cells, but not vice versa. If complex cells poolfrom many spatially overlapping simple cells (Hubel and Wiesel, 1962; Alonso and Martinez, 1998;Figure 6.20A), they should become increasingly simple the fewer simple cells they pool from dueto cut afferents. If instead like simple cells they receive direct LGN input, but gain their spatialphase invariance from horizontal connectivity from other cells with different spatial phase LGNinputs (Chance et al., 1999; Tao et al., 2004; Figure 6.20B), then damage to their afferents mightalso make them more simple than complex. Either way, polytrode damage may bias the populationtoward more simple-like cells and fewer complex cells than would normally be the case.Unknown RF cells had lower mean firing rates than all other RF types (Figure 5.9C), suggestingthat they may have been damaged cells that had lost some of their afferents. There are severalweak but independent lines of evidence that unknown RF type cells may have been composedmostly of damaged complex cells in particular. First, unknown RF cells and complex cells sharedsimilar spatially uniform distributions across all three tracks (Figure 5.7). Second, they had similarpeak-to-peak spike amplitudes (Figure 5.8F). Third, they were composed of a similar mix of slowand fast cells (Figure 5.8H). Finally, given reports that complex cells outnumber simple cells 3:1 ormore (Gilbert, 1977; Kagan et al., 2002), all else being equal, unknown RF cells are more likely tobe damaged complex cells than damaged simple cells.Why might the cells labelled as LGN afferents show up as a distinct RF type? Are these trulyLGN afferents, with an axon passing close to the polytrode, or are they instead a distinct corticalcell type that has not been categorized before? The characteristics of the putative LGN afferentRF type described here are similar to what Schiller et al. (1976a) label as T cells, or what Kaganet al. (2002) label as “monocontrast” cells, which they suggest are a third class of RF. With only12 cells labelled as LGN afferent in the present data set, these questions remain open for the timebeing.In retrospect, the use of 40 ms m-sequence frame times and reverse correlation timepoints fortracks ptc22.tr1 and ptc22.tr2 may have been a poor choice. Examination of the finer 20 ms frametimes in ptc15.tr7c (Figure 5.6) reveals that averaging the 0–20 ms and 20–40 ms STAs wouldresult in weaker RFs for nearly every cell, since the 20–40 ms STA would be washed out by noisein the 0–20 ms STA. The 0–40 ms STAs do exactly such averaging. Worse yet, there is a subfieldsign inversion at around 60 ms, and therefore the STA calculated over 40–80 ms might result innear perfect cancellation of the fields. Receptive field dynamics studied by reverse correlation inmacaque and cat V1 also suggest that 20 ms frame times are more suitable than 40 ms (Ringachet al., 1997a,b, 2003).The switch to 40 ms m-sequence frame times was originally made to increase the duration of them-sequence recordings, increase the number of spikes, and therefore improve the STA signal-to-noiseratio. Although more spikes were undoubtedly acquired, the STAs may have been inadvertently108degraded by averaging over exactly the least complementary response time periods. For futureexperiments, m-sequence frame times should be restored to 20 ms, and to maintain the desiredrecording duration and number spikes, the entire m-sequence movie should be presented twiceinstead of just once.5.6.4 Cell type comparisonGiven the relative proportions of fast and slow cells, simple cells were more likely than expected tobe fast cells than slow cells (Figure 5.8H). However, more cells are needed from more tracks and catsto make stronger conclusions about the relationships between spike type and RF type, as well as thespatial distributions of different cell types. Given the uncertainties in the relative laminar positionof each track, it was difficult to align spatial distributions of different cell types across tracks,and therefore difficult to make conclusions about the true spatial distribution of cell types acrosscortical layers. Histology and CSD analysis should greatly reduce these uncertainties in futureexperiments. Future work could also examine how orientation tuning strength and significance(Section 4.5) might relate to spike and RF type.1096 Natural scenes & cortical states6.1 IntroductionVisual neuroscience has traditionally relied on artificial stimuli such as drifting bars and gratingsto characterize neuron response properties. However, more naturalistic stimuli elicit responses thatare poorly predicted from responses to artificial stimuli (David et al., 2004; Olshausen and Field,2005). Although artificial stimuli are easier to characterize and are of much lower dimensionalitythan naturalistic stimuli, relying too heavily on artificial stimuli may obscure insights into how thebrain processes visual information. For a minimally biased characterization of a neural populationin visual cortex, it is therefore important to consider responses to naturalistic stimuli in additionto artificial stimuli. Although sequences of natural images are spatially naturalistic, the goldstandard is natural scene movies (Carandini et al., 2005), which are both spatially and temporallynaturalistic.As a complex dynamic system, the brain is never in exactly the same state twice. Yet exper-iments involving repeated stimulus presentation implicitly assume that it is, or at least that anyresulting variability will average out over enough trials. There is increasing evidence that this maynot always be the case, and that perhaps some of the response variability due to brain state canbe controlled for (Arieli et al., 1996; Petersen et al., 2003; Fiser et al., 2004). There are manynon-perceptual tasks that even primary sensory cortices might be engaged in during stimulus pre-sentation. Such tasks might include attention (Roelfsema et al., 1998; Harris and Thiele, 2011),memory formation and recall (Ji and Wilson, 2007), reward encoding (Shuler and Bear, 2006;Chubykin et al., 2013), locomotion (Saleem et al., 2013), visualization, synaptic normalization,and low level cellular maintenance (Vyazovskiy and Harris, 2013; Xie et al., 2013). None of thesetasks have much to do with encoding the currently presented stimulus. To deal with this multitudeof tasks, cortex may need to engage in some kind of task switching, which could be reflected incortical state changes. There are two broad categorizations of cortical state: synchronized anddesynchronized (Berger, 1929; Destexhe et al., 1999; Harris and Thiele, 2011). The synchronizedstate is characterized by large amplitude low frequency fluctuations, and occurs during deep anes-thesia, slow-wave sleep, and awake quiescent periods (quiet wakefulness). The synchronized statecan be further subdivided into up and down phases (Destexhe et al., 1999; Harris and Thiele,2011), corresponding to periods of higher and lower resting membrane potentials (Steriade et al.,1993a; Anderson et al., 2000; Sanchez-Vives and McCormick, 2000). The desynchronized state ischaracterized by low amplitude high frequency fluctuations, and occurs during light anesthesia,REM sleep, and awake attending behaviour. To minimize bias in the characterization of cortex,taking cortical state into account is a necessity.110Natural scene movie responses and the effects of cortical state are both examined in this chapter.Responses to natural scene movies in anesthetized cat V1 consisted of temporally precise and reliableevents, with some cells responding to one movie clip but not at all to another similar one. Responsecorrelations were very weak for most cell pairs but were significantly stronger between fast cells andbetween complex cells. The weakness of simple-complex and the strength of complex-complex pairschallenges the hierarchical model of complex cells. Synchronized and desynchronized cortical stateswere distinguished using the frequency content of deep-layer LFP, and switched spontaneously.Regardless of cell type, stimulus-evoked superficial (upper layer) cell firing rates were higher inthe desynchronized than synchronized state, while the reverse was true for spontaneous activity.Deep layer cells showed a more heterogenous relationship. Contrary to other reports (Goard andDan, 2009; Marguet and Harris, 2011; Zagha et al., 2013; Pachitariu et al., 2015) natural scenemovie responses were more precise, sparse, and reliable during the synchronized state than thedesynchronized state. Finally, response correlations between cell pairs were more influenced bycortical state than by the particular movie clip presented.6.2 Natural scene movie responsesTwo different sets of natural scene movies were used, as described in Section 2.4. Each set consistedof both long (several minutes) and short (4.5–5 s) clips, repeated anywhere from 5 to 400 times,usually inversely proportional to their length. Except where otherwise stated, this chapter focuseson the responses to short clips (with many repeats). Trial raster plots of responses to short clipsare shown for a few example cells in Figures 6.1, 6.4 & 6.5. A given neuron’s responses wereoften composed of short bursts of spikes that occurred reliably across trials at specific times duringeach trial, with high temporal precision. These temporally precise features are referred to here asresponse “events”, and show up as vertical lines in the trial raster plots. Responses to repeatednatural scene movies were thus very different from responses to repeated artificial stimuli, whichelicited responses with much less temporal precision across trials (Figures 4.8 & 5.4).Though temporally precise, natural scene movie response events were not always reliable, withevents missing on some trials, sometimes for many consecutive trials. This is most noticeable inFigures 6.1 & 6.4, panels A–C, as well as Figure 6.5B. One explanation for this variability is changesin cortical state, examined in Section 6.6.Each cell’s natural scene movie raster plots were visually inspected for signs of response events.If a cell showed a reasonable degree of temporal precision and reliability across trials during atleast one natural scene movie recording, it was considered “responsive”. If its mean firing ratewas ≥ 0.05 Hz, it was considered “active”. Not all responsive cells were active, and not all activecells were responsive, although the two mostly overlapped (Figure 6.2). Table 6.1 shows the countsand percentages of responsive cells for each track and overall. The percentage of responsive cellswas fairly consistent across all three tracks: 47% of all sorted cells and 87% of active cells were11140 20 0 20 4040 20 0 20 4040 20 0 20 40spike interval (ms)coincidence rate (AU)redbluetime (sec)0 20 40 60 80 100 120 msABCDE F G HIJ spike interval (ms) spike interval (ms)0 1 2 3 401firing rate (AU)01trial numbertrial numbertrial number112Figure 6.1: (Previous page.) Natural scene movie responses of a pair of cells (red and blue) inptc15.tr7c to 96 presentations of a 5 s clip from stimulus set A (Section 2.4). A–B : Raster plotsof both cells. Responses consisted of distinct temporally precise events visible as vertical lines inthe raster plots. Horizontal dashed lines demarcate 4 different versions of the same movie, eachat increasing contrast, separated by time gaps of 0–10 min and interleaved with unrelated moviestimuli. C : Overlaid raster plots show that the responses for this pair were very distinct, withno major temporally precise events shared between them. D : Normalized PSTH of both cells,calculated using 20 ms overlapping bins at 5 ms resolution, again showing the distinctness in theirresponses. E–F : Normalized autocorrelograms of the two cells were noticeably different. G: Thecross-correlogram of the cell pair had a trough at t = 0, indicating that the cells tended to avoidfiring together. Autocorrelograms and cross-correlograms were calculated using 0.5 ms wide bins.H : Template waveforms of the cell pair, with channels and timepoints for PCA highlighted in green.Cells were only 16 µm apart, yet their template waveforms were noticeably different. Scale bar: 0.5ms, 100 µV. I : Cluster plot of the cell pair. The red horizontal axis is PC1, the green depth axisis PC2, and the blue vertical axis is spike time. The clusters remained distinct over time. Notethat the autocorrelograms, cross-correlograms, templates and cluster plots were calculated from allrecordings in the track, not only from the natural scene movie recording. J : M-sequence STAs (seeFigure 5.6) of the cell pair showed marked differences. STAs are 6.4◦ across. AU: arbitrary units.track all activeptc15.tr7c 47/81 (58%) 47/53 (87%)ptc22.tr1 39/93 (42%) 34/41 (83%)ptc22.tr2 29/71 (41%) 29/33 (88%)total 115/245 (47%) 110/127 (87%)Table 6.1: Counts of cells responsive (withtemporally precise, reliable events in their rasterplots) to natural scene movies, for each track andin total, listed in the numerators (percentages inparentheses). Counts in the ‘all’ column includeall cells, regardless of their firing rate. Counts inthe ‘active’ column include only those cells whosemean firing rate was ≥ 0.05 Hz during at leastone natural scene movie responsiveallFigure 6.2: Venn diagram of active and respon-sive cells. Cells could be active (with mean fir-ing rates ≥ 0.05 Hz), and/or responsive (withtemporally precise, reliable events in their natu-ral scene movie raster plots). Not all active cellswere responsive, and not all responsive cells wereactive, although the two mostly overlapped. Setmembership could change from one movie to thenext (Figure 6.15).responsive to natural scenes. Note that ptc22.tr1 had 5 cells that did not qualify as active (39 inthe “all” column vs. 34 in the “active” column), but were nevertheless responsive to natural scenemovies (3 of these 5 are shown in Figure 6.16).To see if specific cell types (Chapter 5) were more or less likely to respond to natural scenemovies, a matrix of responsivity vs. cell type was constructed (Figure 6.3). Pooling over all cells inall tracks, the only cell type that was significantly more likely than not to respond to natural scenemovies was simple cells. In contrast, both fast asymmetric and unknown cell types were significantlymore likely to not respond than to respond. However, distributions varied substantially from one113fast slow fastasym slowasym274neuron countAsimple complex LGNaff unknown457neuron countBresponsivenotresponsive* * *responsivenotresponsiveFigure 6.3: Responsive cell counts vs. cell type. For each cell type, matrices show the number ofcells that were classified as responsive (top rows) or not responsive (bottom rows) with a qualitativedegree of temporal precision and reliability to short natural scene movie clips. Asterisks indicatecell types with significantly unequal numbers of responsive and non-responsive cell counts (χ2 testapplied independently to each column, p < 0.01). A: Natural scene movie responsiveness vs. spiketype. B : Natural scene movie responsiveness vs. RF type. Simple cells were the only cell type thatwas significantly more likely than not to respond reliably to natural scene movies. All 245 cellsfrom all 3 tracks are included.track to the next (not shown), so the overall distributions shown in Figure 6.3 may not be veryconclusive.To quantify natural scene movie response precision, PSTHs were constructed by binning spikesin the trial-triggered raster plots into 20 ms wide overlapping time bins at 5 ms resolution (Figures6.1D, 6.4D & 6.5) or 0.1 ms resolution (6.17A). This bin width was chosen because 20 ms isroughly the membrane time constant of neocortical layer 5 (Mainen and Sejnowski, 1995) andhippocampal CA1 (Spruston and Johnston, 1992) pyramidal neurons. This is also the timescale atwhich hippocampal pyramidal cell spike times are best predicted by the activity of peer neurons,and therefore may be the timescale most relevant for cell assemblies (Harris et al., 2003). The widthsof peaks in the PSTHs were measured by their FWHM. For those cells classified as responsive tonatural scene movies, responses were remarkably sparse, with peaks in the PSTHs ranging 20–100ms in width, separated by periods of silence (Figures 6.1D, 6.4D, 6.5 & 6.17A).Each cell’s pattern of response events was usually distinct. The cells in the pair shown inFigure 6.1 were separated (Section 4.4) by only 16 µm, yet their response patterns were verydistinct. Their cross-correlogram (Figure 6.1G) had a trough at t = 0, indicating that they rarelyfired together. Both cells were fast and simple with RFs that were close to 180◦ out of phase(Figure 6.1J). As measured by a drifting bar stimulus, their orientation preference (Section 4.5)differed by 60◦ and their tuning strength differed by 0.64 (not shown). The marked difference ofthese cells’ responses to natural scene movies despite their physical proximity is further evidenceof valid spike sorting.The cell pair in Figure 6.4 are a counterexample. Though separated by a greater distance (31µm), the pair’s response patterns were remarkably similar. All significant response events were114shared by the pair. However, PSTH peak amplitudes (Figure 6.4D) differed between the two ina nonlinear way. Furthermore, a cluster plot of the two cells in Figure 6.4I shows that they werewell separated during spike sorting, suggesting that their similarity in event timing was not anartifact of spike sorting errors. Again, both cells were fast and simple. Although the cells’ RFs hadonly minor differences (Figure 6.4J), their orientation preference differed by 10◦ and their tuningstrength differed by 0.48 (not shown).Temporally precise response events could be shared by more than just two cells. Figure 6.5 showstwo groups of cells from a recording in ptc22.tr2. One group was a triplet of cells (Figure 6.5A) andthe other a quintuplet (Figure 6.5B). All cells in each group shared at least one obvious responseevent (black arrows), despite the maximum cell separation of 204 and 277 µm in each group,respectively. Additionally, two events seemed to be shared across the two groups (grey arrows).The separation of the mean positions of the two groups was 509 µm, while the most separated pairof cells across the two groups was 715 µm apart. The triplet of cells was in the more superficialcortical layers, and the quintuplet in deeper layers. Note that in contrast with the cells shown inthe transcolumnar ptc15.tr7c recording in Figure 6.4, this recording was from a mostly columnartrack (Figure 4.10C, right panel, Figure 5.6, right panel), suggesting that sharing of response eventsbetween cells is possible for both columnar and transcolumnar groups of cells. The two groups ofcells in Figure 6.5 comprised 18% and 29% of only 17 active cells in this particular natural scenemovie recording, and 4% and 7% of the 71 total cells in this track, respectively.Figure 6.16 shows another example of shared response events. Examination of responses acrossall natural scene movie recordings suggested that events shared across many cells tended to bebroader in time. Those shared by few cells seemed to be more temporally precise. However, thisobservation was not quantified.6.3 Natural scene movie response correlationsTo visualize and quantify the similarity of natural scene movie responses across an entire populationof cells, correlations of PSTHs were calculated for all active cell pairs within a given movie recording,or segment of a recording. Pearson’s correlation (ρ) was calculated from the PSTHs of each pairof active cells byρ =xy − x¯y¯σxσy, (6.1)where x and y are the PSTHs of each cell, σx and σy are their standard deviations, and the overlineindicates the mean. Calculating ρ for all cell pairs resulted in a matrix, which was ordered top tobottom and left to right by active cell depth along the length of the polytrode.PSTH correlation matrices from two recordings from the transcolumnar track ptc15.tr7c areshown in Figure 6.6A & B (left panels). For each cell pair, colour represents ρ, and blank rows andcolumns represent inactive cells. In both recordings, a small minority of cell pairs had ρ values ashigh as 0.9. For comparison, the example cell pairs in Figures 6.1 and Figure 6.4 from the same11540 20 0 20 4040 20 0 20 4040 20 0 20 40spike interval (ms)01coincidence rate (AU)redblue0 1 2 3 4time (sec)0 20 40 60 80 100 120 msABCDE F G HIJ spike interval (ms) spike interval (ms)firing rate (AU)01trial numbertrial numbertrial number116Figure 6.4: (Previous page.) Same as Figure 6.1 but with a different cell pair from the samerecording, located 31 µm apart. A–D : Natural scene movie responses for this pair were very similar,with all major temporally precise events shared between them. E–F : Normalized autocorrelogramsof the two cells had only slight differences. G: The cross-correlogram of the cell pair was peakedaround t = 0 and reasonably symmetric, indicating that the cells tended to fire together, but not inany consistent order. H : Template waveforms of the cell pair, though similar, had different spatialdistributions. Scale bar: 0.5 ms, 100 µV. I : Cluster plot of the cell pair. The red horizontal axis ishorizontal position on the polytrode, the green depth axis is vertical position on the polytrode, andthe blue vertical axis is spike time. The clusters remained distinct over time. Clusters were alsodistinct in PCA space (not shown). J : M-sequence STAs of the cell pair showed minor differences.recording as in Figure 6.6A had ρ = −0.12 and ρ = 0.83, respectively. The small minority ofstrongly correlated pairs tended to be close to the diagonal, i.e., the cells in such pairs tended tobe physically close to one another. However, the vast majority of cell pairs, some of which werealso close to the diagonal, had ρ close to 0. This was also visible in the overall distributions ofρ values (middle panels), which were peaked very close to 0. Mean ρ (red vertical dashed line)was slightly but significantly positive for both recordings, at 0.032–0.05 (two-sided Student’s t-test,p < 5 × 10−14). Both recordings had a U-shaped dependence of ρ on cell pair separation (rightpanels). This was consistent with a transcolumnar track in which the cells near the top of thepolytrode had the same orientation preference as those near the bottom, turning through 180◦ oforientation preference along the way (Figure 4.10C, left).Despite stimulation by different movie clips and despite being separated by 12 hours, the cor-relation matrices in Figure 6.6A and B were similar for the set of active cells common to bothrecordings. Their difference is shown in Figure 6.6C. The difference (∆ρ’s) had even fewer stronglyvalued pairs (left panel), indicating that most of the correlations were similar in the two recordings.The overall ∆ρ distribution was symmetric with a mean of 0.01 (middle panel) that was not signif-icantly different from 0 (two-sided Student’s t-test, p = 0.076). There was no apparent dependenceof ∆ρ on pair separation (right panel).To examine how PSTH correlations might relate to cell types, ρ values were calculated for activecells during natural scene movie recordings (both short movies with many repeats and long movieswith few repeats) in all 3 tracks, and binned according to the spike and RF cell type combination ofeach pair. For this analysis, to simultaneously maximize the total duration of recordings examinedwhile also allowing for at least a rough estimate of PSTHs during long movie clips with few trials, allnatural scene movie recordings with at least 5 trials per movie clip were included. This resulted in16, 104 and 53 min of total movie presentation time for tracks ptc15.tr7c, ptc22.tr1 and ptc22.tr2,respectively. If a cell pair was active in more than one natural scene movie recording, only itsmaximum ρ was kept. Results were divided up into transcolumnar (ptc15.tr7c) and columnar(ptc22.tr1 & ptc22.tr2) tracks. The mean correlation (ρ) of each cell type pair was representedby colour in symmetric matrices (Figure 6.7). Those cell pair types whose ρ¯ was not significantly117time (sec)0 1 2 3 4 5BAfiring rate (AU)1trial number0firing rate (AU)1trial number0Figure 6.5: Temporally precise response events can be shared by larger more disparate groupsof neurons. Raster plots and normalized PSTHs (20 ms overlapping bins at 5 ms resolution) ofa superficial layer triplet (A) and a deep layer quintuplet (B) of cells from ptc22.tr2, respondingsimultaneously to 400 presentations of a 4.5 s natural scene movie clip from the ‘new’ movie set(Figure 2.5). Cells are distinguished by colour within each group separately. Trials were separatedby 1 s blank periods (black dashed line). Each group exhibited a prominent event shared by allcells within the group (black arrows). Weaker events were shared between groups (grey arrows).Maximum separation of cells within A and B was 204 and 277 µm respectively, and across bothgroups was 715 µm. Polytrode depths of all 3 cells in A were < 400 µm, while 4/5 cells in B haddepths > 700 µm (one was at 587 µm).118pair countneuron IDρBCpair countneuron IDApair separation (μm)ρρ, Δρ-1 0 1Δρ pair separation (μm)neuron IDneuron IDpair countΔρρ01020304050010203040500 10 20 30 40 5001020304050137 =0.050.2 0.0 0.2 0.4 0.6 0.8 1.0147 =0.0320.6 0.4 0.2 0.0 0.2 0.4 0.681 =0.0099p >0.07p <7e-21p <5e-14Figure 6.6: Natural scene movie PSTH correlation matrices (left), distributions (middle), andseparation dependency (right) for all active cell pairs, for two recordings (A & B) in ptc15.tr7cwith two different 5 s movie clips, separated by 12 hours. Correlation matrices were ordered top tobottom and left to right by active cell depth along the length of the polytrode. A corresponds to therecording in Figures 6.1 & 6.4. Left : White gaps in the matrices represent cells that were active inone recording but not the other. Colour scale bar applies to all 3 matrices. Middle : Red verticaldashed line denotes the mean of each distribution. Right : Red markers are the mean ±1 standarddeviation of each pair separation bin. PSTH correlations had a weak U-shaped dependency oncell separation, as might be expected for this transcolumnar track. C : The difference betweencorrelation matrices in A and B , along with the distributions of the difference values and theirseparation dependency. PSTH correlations were consistent across the two recordings, for specificcell pairs (left), in their distributions (middle), and in their dependence on cell separation (right).119fastslowfast asymslow asymsimplecomplexLGN affunknownfast slowfast asymslow asymfastslowfast asymslow asymsimplecomplexLGN affunknownsimplecomplexLGN affunknownABspike type RF type00.13**ρFigure 6.7: Matrices of natural scene movie mean PSTH correlation (ρ¯) of active cells, indexedby spike type (left) and RF type (right). Blank entries had ρ¯ that was not significantly differentfrom 0 (two-sided Student’s t-test, p < 0.0005). A: ρ¯ matrices for transcolumnar track ptc15.tr7c(1238 cell pairs). ρ¯ was very low and was significant for only 4 cell type combinations: fast-fast,fast-slow, simple-simple, and simple-complex. None were significantly different from one another(p > 0.35). B : ρ¯ matrices for the two columnar tracks in ptc22 (1976 cell pairs). ρ¯ was significantfor 13 cell type combinations, and 3 of them were noticeably higher than the rest: fast-fast, simple-LGN afferent, and complex-complex. Fast-fast was significantly different from all other spike typecombinations (white asterisk, p < 0.01, 268 pairs), and complex-complex was significantly differentfrom all other RF type combinations, save for simple-LGN afferent (black asterisk, p < 0.005, 549pairs). Simple-LGN afferent was not significantly different from any other RF type combinations,likely because of low N (37 pairs). Colour bar applies to all panels.different from 0 (two-sided Student’s t-test, p < 0.0005) were shown as blank.Consistent with Figure 6.6, the transcolumnar track (Figure 6.7A) had very low ρ¯ values forall pairwise combinations of cell types. Only 4 out of a total possible 20 spike and RF cell typecombinations were significantly different from 0. However, cell pairs from the two columnar tracksresulted in higher ρ¯ values, with a total of 13 significant cell type combinations (Figure 6.7B).Pooling was justified across the two tracks in ptc22 not only because both were columnar, but alsobecause their separate ρ¯ matrices were similar (not shown). Fast-fast, simple-LGN afferent, andcomplex-complex cell type pairs had visibly higher ρ¯ than the rest. Comparing the distributionof each cell type combination to all others revealed that in the columnar tracks only fast-fast wassignificantly greater than all other spike type combinations (two-sided Student’s t-test, p < 0.01),120while only complex-complex was significantly greater than all other RF type combinations, savefor simple-LGN afferent (p < 0.005). Likely due to low N (37 cell pairs), simple-LGN afferent itselfwas not significantly different from any other RF type combinations. In the transcolumnar track(Figure 6.7A), none of the 4 cell type combinations had significantly different ρ¯ from one another(p > 0.35).6.4 Cortical statesCortical state, as classified by the degree of synchronization or desynchronization of a region ofcortex, can be measured in a variety of ways. Measures can be based on the EEG, LFP, MUA,or even membrane potential (Poulet and Petersen, 2008; Li et al., 2009; Sakata and Harris, 2009;Renart et al., 2010; Saleem et al., 2010; Harris and Thiele, 2011; Okun et al., 2012; Poulet et al.,2012). The measure used here was the deep layer LFP L/(L+H) ratio (Saleem et al., 2010), avariant of the L/H ratio (Li et al., 2009), and is referred to here as the synchrony index (SI). Deeplayer LFP is considered a better indicator of cortical state than superficial layer LFP (Saleem etal., 2010). L and H represent lowpass and highpass LFP bands, taken here to be 0.5–7 Hz and15–100 Hz respectively (Figure 6.8A). To calculate the L/(L+H) ratio, first an LFP spectrogramwas constructed by taking the fast Fourier transform (FFT) of the LFP within overlapping timebins (30 s wide at 5 s resolution) to find the power spectrum within each time bin. Next, the powerof the L and H bands was summed within each time bin, and the L/(L+H) ratio was calculated,resulting in a series of SI values representing cortical state as a function of time.SI ranges from 0 to 1. Periods dominated by low frequency LFP have high SI, and periodsdominated by high frequency LFP have low SI. High SI also corresponded to high LFP amplitude,and low SI to low LFP amplitude (Figure 6.8B & C). Synchronized and desynchronized states aretwo extremes of a continuous spectrum, with no sharp division between them, and cortical statesmay even be multidimensional (Harris and Thiele, 2011). Nevertheless, recording segments wereclassified here as either synchronized or desynchronized by applying a pair of SI thresholds: SI <0.8 was considered desynchronized, and SI > 0.9 was considered synchronized. Periods that fell inbetween the two thresholds were left undefined.Figure 6.9 shows a spontaneous change in cortical state during a 39 min recording in trackptc22.tr1, consisting of 400 presentations of a 4.5 s natural scene movie clip. Superficial anddeep layer LFP, the deep layer LFP spectrogram, SI, and the population spike raster plot are allshown on the same timescale. At 2/3 of the way through the recording, the LFP spontaneouslyswitched from low amplitude high frequency activity to high amplitude low frequency activity. As aresult, SI switched from low to high, representing a switch in cortical state from desynchronized tosynchronized. In this example, firing rates of most cells were higher during the synchronized period.Note that even while stimulus and cortical state remained constant, near the end of the recording,superficial cells spontaneously became silent (grey dashed line). Figure 6.10 shows the opposite:121100 101 102frequency (Hz)60555045403530power (dB)A CL HBFigure 6.8: Power spectral density (PSD) and amplitude of deep layer LFP. A: PSD of all 15tracks in Table 2.2. Power is in decibels relative to 1 mV2. Red and blue vertical dashed lines markthe limits of the low (L) and high (H) bands, respectively, used to calculate the synchrony index,SI. On this log-log scale, the low band is roughly centered on the broad peak at ∼ 2 Hz. Some ofthe attenuation below 1 Hz is due to analog filtering of the LFP during acquisition. The narrowpositive peaks at 25, 50 and 66 Hz are stimulus induced. The narrow negative peak at 60 Hz isfrom filtering out mains interference using a 0.5 Hz wide elliptic notch filter. B : SI vs. peak-to-peakLFP amplitude (Vpp), measured from 30 s wide overlapping bins at 5 s resolution. C : SI vs. LFPstandard deviation (σ). Red markers are the median ±1 standard deviation. Data from cat ptc21caused a small dip in B & C at SI > 0.8 (not shown). Excluding ptc21, SI was a monotonicallyincreasing function of LFP amplitude, as measured by both Vpp and σ.cortical state spontaneously switched from synchronized back to desynchronized. Although thetwo states were distinct, the spectrograms and SI plots during the desynchronized periods in bothrecordings were far from homogeneous, suggesting other potential categorizations within that state.These were left unexplored.Consistent with the literature, cortical state in cat primary visual cortex spanned a continuumfrom large amplitude low frequency fluctuations (synchronized state) to small amplitude high fre-quency fluctuations (desynchronized state). Also consistent, state changes were more noticeable indeep layer LFP than in superficial layer LFP (not shown, although Figures 6.9A & 6.10A give anindication).Figure 6.11 shows the distribution of SI for each acquired track (including those that were notspike sorted, see Table 2.2), and overall. The distributions varied widely across tracks. Some wereunimodal, others bi- and even trimodal. Some were dominated by low SI, but most were dominatedby high SI. Unfortunately, the desynchronized state was therefore poorly represented, especially inthose tracks that were spike sorted (labelled in red), resulting in fewer opportunities to comparethe effects of cortical state on spiking. Experiment logs were examined for the cause of these wildlydifferent distributions in cortical state. Tracks with greater amounts of synchronization were as-sociated with application of various drugs, most especially atropine (to reduce secretions and/orincrease heart rate). Other implicated drugs were tropicamide (to dilate pupils), dobutamine (to122ABCDneuron depth ranktime (s)synchronizeddesynchronizedSI (L/(L+H))123Figure 6.9: (Previous page.) Cortical state during 400 identical presentations of a 4.5 s naturalscene movie clip in track ptc22.tr1. Over the course of the recording, cortical state spontaneouslychanged from desynchronized to synchronized. A: LFP signal of the most superficial and deepestchannels. B : Spectrogram (frequency histogram) of the deepest channel. Red and blue representhigh and low power, respectively. For display, this spectrogram was constructed using 2 s wideoverlapping time bins at 0.5 s resolution. C : Synchrony index (SI) calculated from the L/(L+H)ratio of the spectrogram (which itself was constructed using wider time bins than in B , see text).D : Population raster plot, showing all 93 cells in this track, including those that fired 0 spikesduring this movie. Rasters are vertically ordered by cell depth. Transparency is used to increasedetail. The blue vertical dashed line marks the end of the desynchronized state, and the red verticaldashed line marks the beginning of the synchronized state. Up and down phases (Section 6.5) arevisible in the synchronized state as broadband vertical lines in B . The vertical grey line marks asudden drop in superficial layer firing, with no apparent change in deep layer (or superficial layer,not shown) LFP frequency content.increase blood pressure), and buprenorphine (analgesia). Atropine and tropicamide are both anti-cholinergics, and buprenorphine is known to have anticholinergic-like effects (Wood and Rackham,1981; Sakuraba et al., 2009). Transitions to greater amounts of synchronization were also foundin individual recordings within some tracks soon after application of a suspect drug (not shown).Subsequent recordings tended to remain more synchronized. Cats ptc17 and ptc18 had no pan-curonium bromide (local retrobulbar injection of α-BTX was used instead of systemic paralysis, seeTable 2.1), and their four tracks had the greatest amount of desynchronization (Figure 6.11). Notethat pancuronium bromide is also an anticholinergic drug (Garland et al., 1998). Finally, higherdoses of isoflurane and resulting greater depth of anesthesia were also associated with more syn-chronized cortical states. Slight changes in isoflurane dosage (±0.25%) sometimes resulted in a shiftin cortical state (not shown). The two animals that used propofol & fentanyl instead of isoflurane& N2O, ptc20 and ptc21, spent almost all of their time in the synchronized state (Figure 6.11).To investigate if a relationship existed between overall firing rates and cortical state, MUA wascalculated by combining the spike trains of specific subsets of active cells, and then binning themat the same time resolution as the SI (again 30 s wide bins, but now at 10 s resolution instead of5 s). MUA was normalized by the number of included active cells. This was done separately forall spontaneous, natural scene movie, and artificial stimulus recordings (m-sequence white noise,drifting bars and gratings, and flashed gratings), as well as for fast, slow, simple, and complex celltypes. Additionally, in view of a report that superficial and deep layer cells respond differentlyto changes in cortical state (Sakata and Harris, 2012), cells were roughly divided into superficial,middle, and deep layers according to their position along the length of the polytrode. Adjustmentswere made according to how transcolumnar each track was estimated to be. The upper/middleand middle/lower boundaries used for tracks ptc15.tr7c, ptc22.tr1, and ptc22.tr2 were 900 & 1100µm, 500 & 700 µm, and 550 & 700 µm respectively. To reduce errors as a result of this rough124ABDSI (L/(L+H))neuron depth ranktime (s)C synchronizeddesynchronized125Figure 6.10: (Previous page.) Same as Figure 6.9, but for a different 4.5 s natural scene movieclip, separated from the previous one by ∼ 20 min of blank grey screen stimulus. During thisrecording, the opposite spontaneous change in cortical state occurred: from synchronized back todesynchronized. Neurons in the rows in D correspond to those in Figure 6.9.delineation, the middle layer cells were excluded from further analysis.Scatter plots and least-squares linear regressions of MUA vs. SI are shown in Figure 6.12. Eachpoint represents 30 s of recording time at 10 s resolution. Insignificant relationships are shown fadedout. The relationship between SI and MUA was complex, and varied depending on stimulus type,cell type, and layer. Correlation coefficients were low (|r| < 0.5), and conclusions were complicatedby a shortage of desynchronized periods (low SI) and seemingly nonlinear relationships betweenMUA and SI. However, for most combinations of stimulus and cell type, MUA and SI had noticeablydifferent relationships for superficial and deep layer cells.Across stimulus type, layer type, and cortical state, fast cells had higher firing rates than slowcells (Figure 6.12, regression lines in 2 leftmost columns). Given that fast-spiking interneurons areknown to have higher firing rates than pyramidal cells, this result adds confidence to the hypothesisthat fast and slow cells, as defined here by their spike shape, correspond to fast-spiking interneuronsand pyramidal cells, respectively.Overall, regardless of cortical state or cell type, superficial layer firing rates were lower duringspontaneous activity (Figure 6.12, red lines, top row) than during stimulus-evoked activity (mid-dle rows). This was not the case for deep layers (blue lines), which sometimes had higher firingrates during spontaneous activity than during stimulus-evoked activity, especially during the syn-chronized state (high SI). Across cell types, spontaneously active superficial and deep layer cellshad r > 0, i.e., on average, spontaneously active cells were more active in the synchronized thandesynchronized state (red & blue lines, top row). For superficial layer cells, this relationship wasreversed for both natural scene movies and artificial stimuli, which both had r < 0 across almostall cell types (red lines, middle rows, 5/6 significant combinations). Superficial layer slow cellsduring natural scene movies were the exception. Complementary to superficial layers, among thesignificant deep layer regressions (blue lines), there was greater variety across cell type, and lessvariety across stimulus type. Across stimulus type, deep layer simple cells had r < 0, while deeplayer complex cells had r > 0. Also across stimulus type, deep layer fast and slow cells both hadr > 0.6.5 UP/DOWN phasesUp and down phases are short alternating periods (< 1 Hz) of membrane potential depolarizationand hyperpolarization in cortex (Steriade et al., 1993a; Anderson et al., 2000; Sanchez-Vives andMcCormick, 2000), and are present during the synchronized cortical state, but absent during the126ptc20.tr2ptc21.tr6bptc17.tr2b0 0.2 0.4 0.6 0.8ptc22.tr5bSI (L/(L+H))ptc20.tr3ptc22.tr1ptc18.tr10 0.2 0.4 0.6 0.8 1all tracks111 SI (L/(L+H))ptc20.tr1ptc21.tr5cptc17.tr10 0.2 0.4 0.6 0.8ptc22.tr4bSI (L/(L+H))ptc18.tr2cptc21.tr2ptc15.tr7c0 0.2 0.4 0.6 0.8ptc22.tr2SI (L/(L+H))Figure 6.11: SI distributions of all 15 tracks in Table 2.2 (only 3 of which were spike sorted,labelled in red). The bottom right panel shows the distribution over all tracks, representing 137hours of recording. Cortical state distributions varied widely across tracks, even within the sameanimal. However, for the sorted tracks, cortical state was mostly synchronized.127fast slow simple complex0 10 1 0 1 0 1 0 1SI (L/(L+H))SI (L/(L+H)) SI (L/(L+H)) SI (L/(L+H)) SI (L/(L+H))all neurons050505MUA (Hz/neuron)nat scene moviesartificial stimulispontaneousMUA (Hz/neuron)MUA (Hz/neuron)all stimuli 05MUA (Hz/neuron)Figure 6.12: Scatter plots of MUA vs. SI for active neurons (activity determined separately foreach relevant recording), classified by stimulus type (rows), cell type (columns), and layer type(red : superficial; blue : deep). Artificial stimuli included m-sequence white noise movies, driftingbars and gratings, and flashed gratings. MUA and SI were both calculated using the same 30 swide overlapping time bins at 10 s resolution. Each point represents one time bin. MUA wascalculated separately by layer, while SI was calculated only from deep layer LFP. Least-squareslinear regression was performed for each of the 24 classifications (3 stimulus types × 4 cell types ×2 layers) plus 16 more in the ‘all’ row and column. Regression r and p values are shown. N is themean number of active cells per point from which MUA was calculated (note that this is less thanthe total number of unique cells that contributed to the respective regression). Lines, points, andstatistics were shown faded if r was not significantly different from 0 (two-sided Student’s t-test,p < 0.001). SI was mostly dominated by high values (see also Figure 6.11). Correlation coefficientswere low (|r| < 0.5), but for most combinations of stimulus and cell type, significant regressionlines differed noticeably between superficial and deep layer cells. Across cell types, superficial cellsduring spontaneous periods had low MUA and r > 0 (top row), and during stimulus-evoked periodshad higher MUA and r < 0 (middle rows). Deep layer cells were more heterogenous across stimulusand cell type, and generally had higher rates than superficial cells.128desynchronized cortical state (Saleem et al., 2010; Harris and Thiele, 2011; Sakata and Harris,2012). In fact, synchronized and desynchronized states are sometimes defined by the presence orabsence of up and down phases, as measured by the coefficient of variation (standard deviationdivided by the mean) of the LFP broadband power (Okun et al., 2012) or of MUA (Renart et al.,2010) as a function of time.To better resolve up and down phases, the LFP spectrogram was constructed using fineroverlapping time bins (1 s wide at 0.25 s resolution) than those used to calculate SI (Section 6.4).Periods of higher SI showed regular increases and decreases in broadband LFP power, consistentwith up/down phases (Figure 6.13A, see also synchronized periods in Figures 6.9B & 6.10B).Population bursts of spiking activity (Figure 6.13C) resulted in peaks in the MUA (Figure 6.13D)which coincided with peaks in broadband LFP power. During spontaneous activity, a full cycleof one up and one down phase typically took ∼ 2.5 s (Figure 6.13). Up phases had MUA peaks(Figure 6.13D) ranging 0.25–1 s in width, as measured by FWHM. Down phases lasted somewhatlonger, at 0.5–2.5 s each. Up/down phases were also present during stimulus-evoked activity, butwere difficult to distinguish from responses to frequencies intrinsic to the stimuli, and were thereforeleft unexplored.6.6 Natural scene movie responses vs. cortical stateHow might cortical state influence natural scene movie responses? Figure 6.14 shows trial rasterplots from 3 example cells to 2 different natural scene movie clips, during which two cortical statetransitions occurred: from desynchronized to synchronized (Figure 6.14A–D), and from synchro-nized to desynchronized (Figure 6.14E–H). Examination of the trial raster plots showed that therewas greater temporal precision and reliability in all 3 cells during the synchronized state thanduring the desynchronized state. Trial raster plots of all responsive cells were visually inspectedduring both of the natural scene movie clips in Figure 6.14. For the first movie (panel A), of the27 responsive cells, the temporal precision and reliability of response events increased for 22 cells(82%), decreased for 3 cells (11%), and remained unchanged for 2 cells (7%). For the second movie(panel E), the temporal precision and reliability of response events decreased for all 31 responsivecells. Overall, for these two natural scene movie recordings (totalling 78 min of recording and sepa-rated by 20 min of blank grey screen), the vast majority of responsive cell firing pattern transitions(53/58, 91%) were consistent with greater temporal precision and reliability of response eventsduring the synchronized state than during the desynchronized state. Only 5% (3/58) of responsivecell firing pattern transitions showed the opposite, while 3% (2/58) showed no change as a functionof cortical state.Although the 3 example cells shown in Figure 6.14 were responsive to both natural scene movieclips, some cells were responsive to only one movie and not the other. Figures 6.15 & 6.16 show6 such example cells. Across the two natural scene movie recordings shown in Figures 6.14 &129depth (μm)C370 380 390 400 410 420 430time (sec)01234MUA (Hz/neuron) D1020304050frequency (Hz) A0. BSI (L/(L+H))Figure 6.13: Up & down phases are visible in spiking activity when cortical state is sufficientlysynchronized. 60 s of example spontaneous activity (blank grey screen at 200 Hz refresh rate) isshown from ptc22.tr1. The deep channel LFP spectrogram (A) and resulting synchrony index (B)show that the local population became increasingly desynchronized over the time period shown.C : Spatial population raster plot. Vertical axis is cell depth along the length of the polytrode, andspike rasters of cells at very similar depths necessarily overlap. 31 out of 93 neurons were active(with mean firing rates ≥ 0.05 Hz) during this recording. 63 cells fired at least one spike and weretherefore used to normalize MUA in D . Superficial layer cells were mostly silent. D : NormalizedMUA calculated from C using 200 ms overlapping time bins at 50 ms resolution. Vertical dashedlines denote the beginning of up phases, as seen in peaks in the MUA, synchronized spiking in thespatial population raster plot, and broadband power peaks in the LFP spectrogram.1300500100015002000time (sec)SI (L/(L+H))0.0 0.2 0.4 0.6 0.80500100015002000time (sec)A B C DE F G HsynchronizeddesynchronizeddesynchronizedsynchronizedFigure 6.14: Cortical state affects precision and reliability of natural scene movie response events.During repeated presentation of two different 4.5 s natural scene movie clips in ptc22.tr1, twospontaneous cortical state transitions occurred: from desynchronized to synchronized (A, samerecording as in Figure 6.9), and from synchronized back to desynchronized (E , same recording asin Figure 6.10). Horizontal dashed lines indicate transitions. SI is the L/(L+H) power ratio fromthe deep channel LFP. B–D, F–H : Trial raster plots of natural scene movie responses of threeexample cells, left to right in order of increasing depth along the polytrode (161, 186 and 820 µm).Cell RF types (Section 5.4) were classified as simple, simple, and LGN afferent, and spike types(Section 5.2) were all fast. Each raster plot consisted of 400 presentations of a 4.5 s movie clip, eachpresentation separated by 1 s of blank screen. For both recordings, responses were more preciseand reliable during the synchronized state than the desynchronized state. There was a gap of ∼20 minutes of blank grey screen separating the end of the first recording (A) from the start of thesecond (E). Responses were distinct for each cell, even for the first two whose physical separationwas only ∼ 25 µm.1310500100015002000time (sec)SI (L/(L+H))0.0 0.2 0.4 0.6 0.80500100015002000time (sec)A B C DE F G Hsynchronizeddesynchronizeddesynchronized synchronizedFigure 6.15: Same as Figure 6.14 but with 3 more example neurons, each of which had temporallyprecise and reliable response events during one movie but not the other. Panels C & F had exactlyone spike each. Left to right, cells were in order of increasing depth along the polytrode (77, 974 and1197 µm). Cell RF types were classified as unknown, unknown and LGN afferent, and spike typeswere fast, fast and slow. Although difficult to see in this layout, the last two cells shared severalresponse events in the second recording. Note that the most superficial cell was most stronglymodulated by cortical state, at least during the movie to which it responded (B). This was part ofa trend (see text), in which responsive superficial layer cells were more likely than responsive deeplayer cells to have a complete absence of response events in the desynchronized state, distinguishingthem from the types of cells in Figure 6.14, which had response events in both states.1326.15, there were 20 cells that responded to only one movie, out of a total of 39 responsive cells:8 responded only to the first movie, and 12 responded only to the second. However, as shown inTable 6.1, most cells isolated in that track (54/93) did not respond to either movie.Another set of cells were those that were responsive in one cortical state but nonresponsive inthe other (Figures 6.15B & 6.16). All such cells were responsive during the synchronized state in atleast one movie, and nonresponsive during the desynchronized state in both movies. In addition,these cells were more likely to be superficial than deep layer cells, as suggested by the examples inFigures 6.15B & 6.16, which ranged 77–262 µm in depth along the polytrode. The layer boundariesdescribed in Section 6.4 were again applied, and only those cells that were responsive at some pointwere included. Of such cells, for the first movie 7/12 (58%) superficial and 5/11 (45%) deep layercells switched from nonresponsive to responsive. During the second movie, 7/9 (78%) superficialand 5/17 (29%) deep layer cells switched from responsive to nonresponsive. There were no cellsduring either movie whose responsivity switched in the opposite direction. The cells missing fromthe above fractions were those that still had discernable response events in the desynchronizedstate.To quantify the change in temporal precision of response events between cortical states in thetwo movies shown in Figures 6.14 & 6.15, a peak detection algorithm was applied to the PSTHof every cell, and peak widths and heights were measured separately for all 4 recording periods(2 synchronized and 2 desynchronized). PSTHs were normalized by the number of trials in eachrecording period, and by the 20 ms bin width, yielding a signal in units of average instantaneousfiring rate. For each PSTH, twice the median signal was designated the baseline level, and the peakdetection threshold was set to 3 Hz above the baseline. Candidate peaks were those where the localmaximum of the PSTH exceeded threshold and then fell below baseline on both sides. For eachpeak, a search was performed for the left and right FWHM timepoints on either side of the peak,from the baseline crossing on either side of the peak inward towards the peak. If the measuredFWHM was greater than 200 ms, the peak was discarded. A range of peak detection parameterswere tested, and results were generally insensitive to the particular parameters chosen. PSTHswere spot-checked to ensure that peaks were adequately detected and measured. Automated peakdetection is demonstrated for 3 cells in Figure 6.16.Out of a total possible 372 PSTHs (4 recording periods × 93 neurons in track ptc22.tr1), 283PSTHs had at least one spike, 120 were active, and 79 were responsive (i.e., had at least onedetected peak). There were significantly more PSTH peaks detected in the synchronized statethan in the desynchronized state: 386 and 143, respectively (χ2 test, p < 5× 10−26). Logarithmicdistributions of peak widths are shown in Figure 6.17A, coloured red for the synchronized stateand blue for the desynchronized state. Peaks in the synchronized state were significantly narrowerthan in the desynchronized state, with FWHM geometric means of 36 and 51 ms, respectively(one-sided Mann-Whitney U test, p < 7× 10−13). Peak amplitudes were also significantly greaterin the synchronized state than in the desynchronized state (Figure 6.17B), with geometric means1330500100015002000time (sec)0.0 0.2 0.4 0.6 0.8SI (L/(L+H))A B Csynchronizeddesynchronized0 1 2 3 4 5036firing rate (Hz) time (sec) 0 1 2 3 4 5 0 1 2 3 4 5time (sec) time (sec)Figure 6.16: Responsive inactive cells. Top: Same as the upper panels in Figures 6.14 & 6.15but with 3 more example neurons, each of which was responsive during the synchronized state, butinactive overall. Cells A–C were in order of increasing depth along the polytrode (82, 249 and 262µm). Mean firing rates during this recording were 0.02, 0.047, and 0.01 Hz, respectively. Cell RFtypes were all classified as simple, and spike types were all classified as fast. None of the 3 cells wereresponsive or active in the subsequent natural scene movie recording. Bottom : All 3 PSTHs hada 0 Hz baseline firing rate, and therefore all had the same peak detection threshold of 3 Hz (greyhorizontal dashed line). Red dots denote detected peaks. The last cell (C ) had no PSTH peaksthat exceeded the automated detection threshold, but for the purposes of Table 6.1 and Figure 6.3was still classified by visual inspection as responsive.of 11.2 and 7.5 Hz, respectively (p < 2× 10−5).To quantify changes in the sparseness of responses, the sparseness measure of Vinje and Gallant(2000) was applied to each responsive PSTH in each of the 4 recording periods. Sparseness wasdefined byS =1−(n∑i=1ri/n)2n∑i=1r2i /n(11− 1/n)(6.2)where ri is the PSTH value in the ith time bin, and n is the number of time bins. Sparseness rangesfrom 0 to 1, with 0 corresponding to a uniform signal, and 1 corresponding to a signal with all of134AB DC101 102peak FWHM (ms)010203040506070PSTH peak count= 35.5 ms= 50.6 msp < 7e-13F10-5 10-4 10-3 10-2 10-1 1reliability05101520cell count= 3.4e-03= 9.7e-04p < 0.003E10-5 10-4 10-3 10-2 10-1 1synchronized reliability10-510-410-310-210-11desynchronized reliability0 0.2 0.4 0.6 0.8 1sparseness05101520cell count= 0.75= 0.56p < 4e-050 0.2 0.4 0.6 0.8 1synchronized sparseness00. sparseness100 101 102peak amplitude (Hz)01020304050PSTH peak count= 11.2 Hz= 7.5 Hzp < 2e-05Figure 6.17: Response precision, sparseness & reliability vs. cortical state. A: Distributions ofresponse event widths, measured by FWHM of PSTH peaks, during the synchronized (red) anddesynchronized (blue) periods of the two recordings shown in Figures 6.14 & 6.15. B : Distributionsof peak amplitudes relative to baseline. C : Scatter plot of response sparseness in the two corticalstates for cells with at least one detected PSTH peak. Cells with no peaks in one of the twostates were assigned a sparseness of 0 in that state. 86% of cells fell below the dashed y = x line.D : Sparseness distributions for cells with at least one detected peak. E : Scatter plot of responsereliability in the two cortical states for all cells. Cells with no spikes during a cortical state wereassigned a reliability of 10-5 in that state. 89% of cells fell below the dashed y = x line. F : Responsereliability distributions for all cells. Geometric means are shown in A, B & F , and arithmetic meansin D . PSTH peaks were significantly narrower and higher, PSTHs were significantly sparser, andresponses were significantly more reliable in the synchronized than desynchronized state (one-sidedMann-Whitney U test, p values shown in each panel).its energy in a single time bin.There were significantly more responsive PSTHs in the synchronized state than in the desyn-chronized state, 49 and 30 respectively (χ2 test, p = 0.033). Figure 6.17C shows a scatter plot ofPSTH sparseness values for all responsive cells in the two states. Cells that were responsive in onlyone state in each synchronized/desynchronized pair of states were assigned a sparseness value of0 in the nonresponsive state. 86% of cells fell below the y = x line, showing that most cells hadsparser responses in the synchronized than desynchronized state. The corresponding distributionsof sparseness values are shown in Figure 6.17D. Responses were significantly sparser in the syn-135chronized state than in the desynchronized state, with mean sparseness values of 0.75 and 0.56,respectively (one-sided Mann-Whitney U test, p < 4× 10−5).To quantify the reliability of responses across trials, the mean pairwise correlations betweenall trials were calculated for each cell during each state (Goard and Dan, 2009). Single trial spiketrains were divided into 20 ms wide overlapping time bins at 0.1 ms resolution, and the number ofspikes in each bin was counted, resulting in a matrix of integer values as a function of time, withone row per trial (this is a modification of the method shown in Figure B.1). Pearson’s correlation(Equation 6.1) was calculated between all possible pairs of trials. For trial pairs in which one orboth trials had no spikes, their correlation was set to 0. The reliability of each cell during eachcortical state was defined as the mean of all of the pairwise correlations of the trials during thatstate. Alternative methods were tested, including taking the median instead of the mean, or themean weighted by the number of spikes in each trial pair, but the results were similar to the simplemean. Response reliability could range from −1 to 1, but was mostly positive. For logarithmicplotting, values that fell below 10−5 were assigned a value of 10−5.Figure 6.17E shows a logarithmic scatter plot of response reliability for all cells in the twocortical states. Cells that fired no spikes in one state in each synchronized/desynchronized pair ofstates were assigned a reliability value of 10−5 in that state. 89% of cells fell below the y = x line,showing that most cells responded more reliably in the synchronized than desynchronized state.The corresponding logarithmic reliability distributions are shown in Figure 6.17F. Responses weresignificantly more reliable in the synchronized than desynchronized state, with mean reliabilityvalues of 3.4× 10−3 and 9.7× 10−4 respectively (one-sided Mann-Whitney U test, p < 0.003).For the recording shown in Figure 6.5, which came from a different track (ptc22.tr2), corticalstate was synchronized the entire time as measured by SI (Figure 6.11, bottom left panel). Consis-tent with the pair of recordings shown in Figures 6.14 & 6.15, responsive cells generally remainedresponsive for the duration of the recording, with generally consistent precision and reliability.There were some exceptions however. Inspection of the LFP spectrogram showed changes in low-frequency power that SI was not able to resolve (not shown). These changes were complex, butcorresponded in time with changes in the response events of some cells.Although cortical state was examined in the transcolumnar track (ptc15.tr7c), there was again alack of desynchronized periods during natural scene movie presentation. However, there was no ev-idence from that track to contradict the findings from ptc22.tr1 in Figures 6.14–6.17. Furthermore,using LFP at a specific depth to calculate SI in a transcolumnar track may create complications,due to the potential for differences in cortical state between columns (Katzner et al., 2009). There-fore little could be concluded about the relationship between measured cortical state and naturalscene movie responses in track ptc15.tr7c.Given that the temporal precision and reliability of response events was higher in the synchro-nized state than in the desynchronized state, how might cortical state affect PSTH correlationsbetween cell pairs? To answer this question, the two natural scene recordings in Figures 6.14 &1366.15 were split, as before, into synchronized and desynchronized periods, and PSTHs were calcu-lated separately for active cells in each of the four resulting periods. PSTH correlations were thencalculated for all active pairs in each recording period. The results are shown in Figure 6.18, in thesame format as Figure 6.6.Qualitatively, PSTH correlation matrices appeared more similar within cortical state and acrossmovies (Figure 6.18B vs. C, left column) than across cortical state and within movies (panels Avs. B, C vs. D). Mean PSTH correlations (ρ¯, red vertical lines, middle column) were higher in thetwo synchronized periods (ρ¯ = 0.13) than in the two desynchronized periods (ρ¯ = 0.075–0.1). Asshown for the natural scene movie in Figure 6.6, ρ was independent of cell pair separation, evenwhen considering cortical states individually (Figure 6.18, right column).To more directly compare the changes in PSTH correlations from one period to the next, ∆ρmatrices were calculated for neighbouring periods in Figures 6.14 & 6.15. The results are shownin Figure 6.19. Although little was concluded from the spatial patterns of the ∆ρ values, theirmeans corresponded with the conclusions from Figure 6.18: mean changes in ρ were significantlygreater than 0 during the transition from the desynchronized to synchronized state (B-A, p =0.0052), not significantly different within the synchronized state across movies (C-B, p = 0.63), andsignificantly less than 0 during the transition from the synchronized to desynchronized state (D-C,p = 4.8× 10−8). ∆ρ values showed no apparent dependence on cell pair separation.6.7 Discussion6.7.1 Natural scene movie responsesThe majority of active cells (87%) showed temporally precise and reliable response events to naturalscene movie stimulation. Response events were as little as 20 ms wide (FWHM). There was greatdiversity in event patterns, even among cells very close to one another (Figure 6.1). Although onlyabout half of all cells responded to natural scene movies, many of those that did not respond mayhave simply been inactive at the time, regardless of stimulus. One way to resolve this might be totightly interleave trials of different stimulus types (including blank screen for spontaneous activity)to determine if some cells expressly do not respond to naturalistic stimuli.There are a handful of reports of such sparse, temporally precise, and reliable responses tonatural scene movies in V1: in awake behaving macaque (Vinje and Gallant, 2000, 2002), and inanesthetized cat, both extracellularly (Yen et al., 2007; Herikstad et al., 2011) and intracellularly(Haider et al., 2010). Yen et al. (2007) also showed that precisely timed events can be sharedbetween nearby cells, as in Figures 6.4–6.5. Bair and Koch (1996) found similar precision andreliability in awake behaving macaque middle temporal cortex (MT) during random dot stimulationwith low motion coherence. There have been more reports of even sparser, more temporally precise(as little as ∼ 1 ms wide) and more reliable response events to high-entropy (though not necessarily137neuron IDA 26pair count ρdesynchronized010203040Bneuron ID55pair count ρsynchronized010203040pair count51ρCneuron IDsynchronized010203040neuron ID ρ87Dneuron ID ρpair countdesynchronized0 10 20 30 40010203040pair separation (μm)=0.1=0.13=0.13Figure 6.18: PSTH correlations vary as a function of cortical state. Same style of plots andsame colour scale bar as in Figure 6.6A–B, but this time for the desynchronized (A & D) andsynchronized (B & C ) periods of the two recordings in Figure 6.14. A & B correspond to therecording in Figure 6.14A–D, while C & D correspond to the recording in Figure 6.14E–H. Left :PSTH correlation matrices appeared more similar within state and across recordings (and movies)than within recordings and across state. Middle : Synchronized periods had slightly higher meanPSTH correlations than desynchronized periods. Right : PSTH correlations were independent ofcell pair separation.138neuron ID19pair countneuron ID35pair countpair count51neuron IDB-AC-BD-C0102030400102030400 10 20 30 40010203040neuron ID Δρ pair separation (μm)ΔρΔρΔρΔρ-1 0 1=-0.00440.6 0.4 0.2 0.0 0.2 0.4 0.6=-0.04=0.035p <0.006p >0.6p <5e-08Figure 6.19: Cortical state has a greater influence on natural scene movie PSTH correlations thandoes the specific natural scene movie being presented. The three rows of panels here correspond tothe differences in ρ values between the four recording periods labelled in Figure 6.18. For example,the panel labelled B-A represents the ∆ρ values between Figure 6.18B & A. Red and blue panellabels represent synchronized and desynchronized periods, respectively. Only cells active in bothrecordings were considered. C-B : The mean ∆ρ for the two synchronized recording periods wasnot significantly different from zero (middle panel, vertical red dotted line, two-sided Student’st-test), despite being from different movies. For B-A and D-C , mean ∆ρ values were significantlypositive and negative respectively, congruent with synchronized periods having greater mean ρ thandesynchronized periods (Figure 6.18). Right : ∆ρ was independent of cell pair separation.139naturalistic) stimuli in RGCs in salamander, rabbit, and cat (Berry et al., 1997; Reich et al., 1997;Gollisch and Meister, 2008), and in LGN in anesthetized cat (Dan et al., 1996; Alonso et al., 1996;Reich et al., 1997; Reinagel and Reid, 2000, 2002).It seems that as visual information propagates from RGCs to LGN to V1, response eventprecision and reliability decrease (Kara et al., 2000). It is interesting to consider that this precision isretained at all. LGN inputs constitute only a small fraction of synapses onto (mostly layer 4) corticalcells, yet these inputs are very effective at driving the cortex (Ahmed et al., 1994; Binzegger et al.,2004). In addition to the high effectiveness of LGN-V1 synapses, convergent event-like input fromLGN cells in response to naturalistic stimuli may be one reason for this strong drive (Alonso et al.,1996; Wang et al., 2010). Clearly, there must be some evolutionary benefit in maintaining, to someextent, these temporally precise response events in V1. Sparse coding, and the energy efficiencythat comes with it (Olshausen and Field, 1996; Attwell and Laughlin, 2001; Lennie, 2003) may beone such reason. Another reason, given by Hopfield (1995), is that precise relatively-timed spikesallow for simple scale-invariant representations of stimuli, and are potentially a common themeused throughout cortex. The delay line coding theory presented in that paper is strengthened byevidence, here and elsewhere, that at least for naturalistic stimuli, cortical cells can have responsesthat are both temporally precise and reliable relative to the stimulus, and therefore also temporallyprecise and reliable relative to each other.The natural scene movies used here spanned visual angles of 12.7◦ for the ‘old’ set of moviesand 51.6◦ for the ‘new’ set (Figure 2.5). Even the smaller of these was several times the size ofthe largest classical RFs shown here. Extra-classical RF stimulation has been found to increaseresponse sparseness, for both artificial and naturalistic stimuli (Vinje and Gallant, 2000, 2002; Yenet al., 2007; Haider et al., 2010; Herikstad et al., 2011). Haider et al. (2010) showed that for regularspiking cells, this is due to more extensive inhibitory barrages by spatially unselective fast-spikinginterneurons. The firing of the excitatory cells is thereby sculpted into temporally precise andreliable events. The temporal precision and reliability of responses reported here almost certainlyrequired such wide field stimulation.An in-vitro study by Mainen and Sejnowski (1995) in pyramidal layer 5 cells found sub-millisecond spike precision and high (∼ 95%) reliability across trials in response to naturalistic,yet identical, input current traces. This is much better than the finest ∼ 20 ms precision foundhere. The main difference is that cells in-vivo have much greater feedforward, feedback, and hor-izontal connectivity than do in-vitro slices. Cell types are also more heterogenous in-vivo than inselective in-vitro recordings. Mainen and Sejnowski (1995) also found that a more artificial stepinput current resulted in much poorer temporal precision. An analogous result may be argued forin-vivo responses to artificial visual stimuli (Figures 4.8 & 5.4).Precise, reliable, and unique responses to natural scene movie clips of 47% of all sorted cellssuggests a high quality of spike sorting for those cells, both from noise and from each other. Ofcourse, this says nothing about the spike sorting of the other 53% of cells that, for whatever reason,140did not respond to natural scene movies, or for cells that were responsive to some movies but notothers. Also, since SI derives from the low-pass LFP data which is methodologically independentof the spike sorted high-pass data, the correspondence in time of sudden changes in both SI andcell firing patterns also increases confidence in the quality of the spike sorting.Five cells in track ptc22.tr1 were responsive to natural scene movies despite having mean firingrates < 0.05 Hz (Table 6.1, three shown in Figure 6.16). At an average of less than one spikeevery 20 s, these cells demonstrate that, as for artificial oriented stimuli (Figures 4.8C & 4.9),cells with extremely low firing rates in V1 can still meaningfully represent naturalistic stimuli viasparse responses. These cells also serve as an example of what can be lost when applying firingrate thresholds for unit inclusion and exclusion, even if those thresholds are set very low. Firingrate thresholds are certainly necessary for many analyses, but they should be used as sparingly aspossible.Half of the responsive cells in Figures 6.14 & 6.15 (20/39, 51%) were responsive to one naturalscene movie but not the other, even though both recordings occurred closely in time, and evenduring periods when cortical state was apparently the same. Although loss of unit isolation isalways a possibility and is difficult to explicitly distinguish from a natural change in responsivity,the results presented here suggest the possibility that some cells in V1 are extremely selectiveto specific naturalistic stimuli, with nearly all or nothing responses (Figure 6.15), even when thelow level stimulus statistics do not change (not shown). Such extreme selectivity challenges thestandard model of simple and complex cells in V1 as fairly simple oriented spatiotemporal filters(Hubel and Wiesel, 1962; Carandini et al., 1997), and may partially explain why such modelsdo so poorly at predicting responses to natural scene movies (David et al., 2004; Olshausen andField, 2005; Carandini et al., 2005). Another possibility is that individual V1 cells, or perhapseven cell assemblies, are engaged in a kind of shift work (Figures 4.2C, 5.9B & D), and alternatebetween various computational and biophysical tasks besides encoding stimulus. Such tasks mightinclude visualization, memory formation and recall, reward encoding, synaptic renormalization,network stability, low level cellular maintenance, and energy conservation. Assuming that most ofthese other tasks take longer than stimulus encoding of a short movie clip, it may be possible todisentangle their potential effects on spiking activity by presenting several different natural scenemovie clips with their trials randomly interleaved. Reconstruction of raster plots for each moviewould reveal if similar fractions of neurons as reported here are found to respond to only somespecific clips but not others, despite their tight interleaving during presentation. Or it may insteadshow that cells simply become responsive or nonresponsive and then stay that way for an extendedperiod of time, regardless of stimulus. Either result would be interesting.6.7.2 Natural scene movie response correlationsOn average, natural scene PSTH correlations in cat V1 were positive, but very weak (ρ¯ < 0.15,Figures 6.6, 6.7 & 6.18). This is congruent with experimental and theoretical findings of near-141zero spike count correlations in macaque and rat cortex (Ecker et al., 2010; Renart et al., 2010).For the transcolumnar track, PSTH correlations decreased with cell pair separation, and thenslightly increased again, as might be expected with orientation preference changing through 180◦as a function of position along the length of the polytrode (Figure 6.6). Surprisingly, for the twocolumnar tracks, PSTH correlations were not dependent on cell separation along the length ofthe polytrode (Figure 6.18). Considering only cell pairs with strongly correlated responses (sayρ > 0.4), such pairs were mostly closely spaced in the transcolumnar track (Figure 6.6), but had awide range of spacing in the columnar tracks (e.g., Figure 6.18). This distance independence withina functional cortical column suggests that cells that respond similarly to natural scene movies arefairly well distributed across layers within a cortical column, and seems incongruent with functionalspecialization of cortical layers. A stronger conclusion regarding this will certainly require more cellpairs in more columnar tracks in more animals, with histological verification of polytrode positionand orientation.A recent report found that the more similar the responses of pyramidal cell pairs in layer 2/3mouse V1 to natural scene movies, the greater the probability of direct synaptic connectivity be-tween the two cells (Ko et al., 2011). That study also concluded that most connected pyramidalcell pairs had bidirectional synaptic connectivity. That study used 2-photon calcium imaging torecord responses in vivo followed by aligned in vitro multiple (up to 4) cell patch-clamp recordingswith electrical stimulation to directly gauge synaptic connectivity. Natural scene movie responsecorrelation may therefore be useful as an indirect measure of direct synaptic connectivity betweenpyramidal cells, and the natural scene movie PSTH correlation matrices presented in this chap-ter (Figures 6.6 & 6.18) may be reasonable approximations of the synaptic connectivity betweenpyramidal cells.When broken down by cell type, the mean natural scene movie PSTH correlations of three celltype combinations were notably higher than all other combinations, but only for columnar record-ings: fast-fast, simple-LGN afferent, and complex-complex (Figure 6.7). Assuming that fast cellsare indeed fast-spiking inhibitory interneurons (Section 5.6.1), strong fast-fast PSTH correlations(significantly stronger than all other spike type combinations) within a column are consistent witha calcium imaging study in layer 2/3 mouse V1 that found neighbouring parvalbumin-expressingfast-spiking interneurons had more strongly correlated responses to naturalistic movies than didpyramidal cells (Hofer et al., 2011). Strong fast-fast PSTH correlations are also consistent withstudies showing that neighbouring fast-spiking inhibitory interneurons are closely coupled via elec-trical gap junctions (Galarreta and Hestrin, 1999; Gibson et al., 1999), and that natural scenemovie responses are sculpted by fast-spiking interneurons (Haider et al. (2010), see previous sec-tion). Simple-LGN afferent correlations were higher (though not significantly) than most other RFtype combinations. This is consistent with the Hubel and Wiesel hierarchical model of simple cellRFs, and the findings of Reid and Alonso (1995). More interestingly, simple-complex correlationswere weak, and complex-complex correlations were significantly stronger than all other RF type142combinations (except simple-LGN afferent). This conflicts with the Hubel and Wiesel hierarchicalmodel of complex cell RFs (Figure 6.20A), i.e., that they are the result of monosynaptic input frommultiple simple cells.Perhaps the best evidence for the hierarchical complex cell RF model is a study by Alonso andMartinez (1998). That study found that extracellular spike train cross-correlograms between layer 4simple cells and layer 2/3 complex cells in anesthetized cat V1 showed monosynaptic simple-complexconnectivity, but not vice versa. However, that study may have been biased in its use of a handfulof electrodes that were independently positioned to maximize cell isolation, and which recorded nomore than a pair of cells at a time. Those results conflict with earlier studies (Toyama et al., 1981a,b;Ghose et al., 1994) which showed, using similar methodology, a lack of simple-complex monosynapticcross-correlogram peaks, but did show some “antihierarchical” complex-simple monosynaptic cross-correlogram peaks. A more recent intracellular study in anesthetized cat V1 by Yu and Ferster(2013) found that although complex cell membrane potentials triggered off of simple cell spikesdid indeed show a significant peak during visual stimulation, that peak disappeared when visualstimulation was replaced with electrical stimulation, suggesting that coordinated activity is whatdrives complex cell responses, not direct monosynaptic connectivity from simple cells.These conflicting results suggest that the hierarchical complex cell model may need refinement,as might the distinction between the two cell types (including that made in Section 5.4). Theseare two independent issues, and there is more support for the first than the second (Toyama etal., 1981a,b; Ghose et al., 1994; Mechler and Ringach, 2002; Abbott and Chance, 2002; Priebeet al., 2004; Mata and Ringach, 2005; Yu and Ferster, 2013). Alternative models (Chance et al.,1999; Tao et al., 2004) suggest that recurrent connectivity between cells in V1 could determinehow simple or complex a cell is (Figure 6.20B). In these models, more complex-like cells have morerecurrent (bidirectional) connectivity with other nearby cells with similar orientation and spatialfrequency preferences, but different spatial phase preferences. These models predict a spectrumof recurrent connectivity from simple to complex, with strong coupling between highly complexcells and weak coupling between highly simple cells. The results shown in Figure 6.7 supportthese recurrent connectivity models of complex cells. Note that these models do not invalidate thebimodal distribution of spiking responses that have long distinguished simple and complex cells.Although membrane potential responses are unimodal across the population, the spike thresholdnonlinearity transforms this unimodal distribution into a bimodal one which distinguishes simpleand complex cells (Mechler and Ringach, 2002; Priebe et al., 2004). Therefore, although recurrentsynaptic connectivity may vary gradually from simple to complex cells, spiking responses, whichare what downstream targets receive, are indeed bimodal.Unfortunately, traditional methods of distinguishing simple and complex cells rely on artificialstimuli: drifting bars and gratings, light and dark flashed bars and spots, flashed gratings, andcounterphase gratings. Ideally, responses from natural scene movies alone should be enough todetermine which cells are simple, which are complex, and which (if any) are somewhere in between.143Figure 6.20: Complex cell models. A: Hierarchical model. Acomplex cell (circle) pools inputs from simple cells (boxes) withsimilar orientation and spatial frequency preferences, but differentspatial phase preferences, making it invariant to spatial phase. B :Recurrent model. Each cortical cell (circles) could be either simpleor complex, depending on the strengths of its recurrent connectionswith others. Each cell receives a weak set of feedforward inputs fromLGN (boxes), which determines its orientation, spatial frequency,and spatial phase preference (θ, k, and φ respectively). In theabsence of strong recurrent connections, a cell retains these pref-erences and behaves like a simple cell. With increasing recurrentconnectivity with other cells of similar orientation and spatial fre-quency preference, but differing spatial phase preference, the cellbecomes more invariant to spatial phase, and hence more like acomplex cell. Taken from Chance et al. (1999).As of yet, no method for doing so exists. Until such a method is devised and applied, the physio-logical relevance of the artificial stimulus-derived simple/complex cell distinction to natural visionshould be considered an open question.Given the ubiquity of temporally precise and reliable response events during natural scenemovie stimulation (at least during the synchronized state), response events could be used as atool to distinguish simple from complex cells. One method might be to present two versions ofthe same natural scene movie: the original, and the contrast inverted version. Since simple cellsare sensitive to spatial phase, their response events should shift in time between the two movies,or rearrange completely. However, the response events of complex cells should not shift, becauseideally complex cells are phase invariant. Increasing degrees of temporal shift of response eventscould signify increasing simple cell-like properties. It would be interesting to see if these temporalshifts clustered into two groups, or if instead they formed a continuous distribution.6.7.3 Cortical statesDeep layer LFP spectrograms revealed spontaneous changes in frequency content (Figures 6.9 &6.10), which roughly clustered into two states: synchronized (slow, large amplitude fluctuations)and desynchronized (fast, low amplitude fluctuations). LFP frequency content was quantified ina more graded way using an index (SI) which describes the degree of synchronization of the localpopulation as a function of time. This index was then correlated with mean population firing rates(MUA) for a variety of cell, layer and stimulus types (Figure 6.12).Across cell type, population firing rates during spontaneous activity in superficial cells were144higher in the synchronized state and lower in the desynchronized state, while the reverse was truefor stimulus-evoked activity (Figure 6.12). Deep layer cells showed a more heterogenous relationshipacross stimulus and cell type. These results agree with those of Sakata and Harris (2012). Thatstudy focused on spontaneous activity in awake and urethane-anesthetized rat A1, and foundthat for both awake and anesthetized animals, superficial layer cells had higher firing rates in thesynchronized state than in the desynchronized state. That study also found that the relationship fordeep layer cells was more heterogenous and depended on cell type: some pyramidal cell types hadhigher rates during desynchronization, but fast-spiking interneurons did not. Assuming that theslow and fast cell types described here correspond to pyramidal cells and fast-spiking interneuronsrespectively (Section 5.6.1), the cell type-specific results presented here for deep layer cells duringspontaneous activity are consistent with that study (Figure 6.12, top row, first two columns, bluelines).Although the laminar and cell type analysis performed here was less reliable than that of Sakataand Harris (2012), which used juxtacellular recording combined with histology and spike shapeanalysis, the results presented here expand on that study by including stimulus-evoked activitywith both natural scene movies and artificial stimuli, in addition to spontaneous activity. Therelative differences in stimulus-evoked firing rates of slow and fast cells in both superficial anddeep layers in Figure 6.12 (rows 2–4, columns 1–2, red & blue lines, high SI) generally agree withthose of an earlier study by the same group (Sakata and Harris (2009), their Figure 2A) whichexamined laminar and cell type dependence of spontaneous and stimulus-evoked activity duringthe synchronized state.This correspondence with other studies in different species and modalities with different anes-thetics suggests that the results in Figure 6.12 are not species, modality, or anesthesia specific.Rather, they may be general properties of primary cortical areas and perhaps other areas. Whatis their functional relevance? Sakata and Harris (2012) suggest that lower superficial firing ratesin the desynchronized state during spontaneous activity may be a way of lowering neural noise,perhaps via attention at a specific retinotopic or tonotopic location, to allow detection of stimuliat lower threshold. Although attention is presumably absent during anesthesia, the broad mecha-nism of global synchronization and desynchronization remains, suggesting that aspects related toattention can be studied in an anesthetized animal (Harris and Thiele, 2011).For the 3 spike sorted tracks, cortical state was mostly synchronized, and the desynchronizedstate was infrequent (Figure 6.11). This limited confidence in conclusions about how V1 differsbetween the two extremes of cortical state. Several steps could be taken to better balance, andeven control, the time spent in both states. Since anticholinergic and anticholinergic-like drugs havea synchronizing effect on cortex (Herrero et al., 2008; Harris and Thiele, 2011), they should be usedwith greater care. Atropine, tropicamide, dobutamine, buprenorphine, and pancuronium bromidewere all implicated here in promoting synchronization and preventing desynchronization. Someare essential, but reduced dosage or complete elimination of others may be possible. Although not145shown here, sometimes a loud noise, such as a hand clap, was enough to desynchronize V1.It may also be wise to avoid propofol & fentanyl anesthesia in the future and use isoflurane (andpotentially N2O) instead. The greater synchronization under propofol & fentanyl (ptc20 and ptc21,Figure 6.11) may have been due to the greater difficulty in regulating its intravenous infusion andits longer half life compared to inhaled isoflurane.Slight changes in isoflurane dosage (±0.25%) sometimes affected cortical state (not shown).Long after completion of surgery and after many consecutive hours of isoflurane administration, itmay be possible to temporarily reduce isoflurane dosage to very low levels while still maintainingsufficient anesthesia (Eger II and Johnson, 1987; Pascoe et al., 2006). Doing so should result inmore desynchronized periods. Given the long recovery times from long duration anesthesia, it mayeven be possible to completely turn off isoflurane for short periods, perhaps 10 s at a time, to inducea shift from the synchronized to desynchronized state. Even greater control is possible by directstimulation of the nucleus basalis (Goard and Dan, 2009) or the pedunculopontine tegmenta (PPT)nucleus (Curto et al., 2009; Sakata and Harris, 2012), at least for V1 and A1 respectively, inurethane-anesthetized rat. However, such stimulation involves greater complexity and risk, andrequires further surgery. A combination of some of the above methods should be sufficient to ensurea balance between synchronized and desynchronized cortical states. Until then, spike sorting ofexisting data that already show greater desynchronization (ptc17 & ptc18, Figure 6.11) is a toppriority.A study by Wo¨rgo¨tter et al. (1998) found that RF size in ketamine- and halothane-anesthetizedcat V1 is greater in the synchronized than desynchronized state. A similar report by Castro-Alamancos (2002) found that whisker fields in urethane-anesthetized rat barrel cortex are larger inthe synchronized than desynchronized state. Both studies relied primarily on single channel elec-trodes, and their results could be tested using the data already collected here. The STAs of simplecells from m-sequence noise movies (Figure 5.5) could be separately calculated during synchronizedand desynchronized states, and their sizes measured. Alternatively, RF size of both simple andcomplex cells during the two cortical states could be measured using light and dark drifting bars(Figure 5.4A). Dependence of RF size on cortical state could then be examined according to spiketype, RF type, and layer.6.7.4 UP/DOWN phasesUp and down phases are present only in the synchronized cortical state and are thought to representtwo alternating modes of cortical function (Harris and Thiele, 2011). Up phases are brief periodsof depolarized membrane potential and desynchronization during which information can flow moreeasily from one brain area to another (Luczak et al., 2007; Hoffman et al., 2007), akin to thetemporary opening of a gate (Luczak et al., 2013), and reminiscent of the data packets and timedomain multiplexing used in digital communication systems. Down phases are somewhat longerperiods between up phases, with hyperpolarized membrane potential and high synchronization146during which information flows more poorly.As in many other species and cortical regions, in this study up and down phases were found inthe synchronized cortical state but were absent in the desynchronized state (Figure 6.13). Duringspontaneous activity, one full up/down cycle lasted ∼ 2.5 s on average, corresponding well to the∼ 0.3–0.4 Hz frequency of up/down phase cycling originally reported intracellularly in vivo inurethane-anesthetized cat cortex (Steriade et al., 1993a). Up phases lasted 0.25–1 s, and downphases lasted somewhat longer at 0.5–2.5 s, similar to findings during slow wave sleep in cat cortex(Destexhe et al., 1999). Up phase duration in cat V1 was similar to that in urethane-anesthetizedrat barrel and somatosensory cortices (Petersen et al., 2003; Hasenstaub et al., 2007; Luczak et al.,2007), but was longer than in awake rat (Petersen et al., 2003; Luczak et al., 2007; Sakata andHarris, 2009; Luczak et al., 2013), and down phase duration was longer than in both anesthetizedand awake rat, as well as ketamine/xylazine anesthetized ferret PFC (Haider et al., 2006).Interestingly, Anderson et al. (2000) found that complex cells in anesthetized cat V1 had biggeramplitude up and down phases than did simple cells. Contrary to the overall finding here, theyalso reported that up phases lasted longer than down phases, especially during visual stimulation.That study recorded intracellularly from one cell at a time. Characterization of up and downphases according to RF, spike, or layer type was not attempted here, and has yet to be reportedusing extracellular polytrode recordings. Even though single unit spike trains on their own donot provide the same up/down phase detection fidelity as single cell intracellular recordings, withenough simultaneously recorded cells of each type, MUA pooled from those cells should revealup/down phases specific to that type. Simultaneous recording might also reveal how up/downphases interact between different RF, spike, or layer types.Luczak et al. (2007) found that spike latencies relative to up phase onset were constant, andwere different for each neuron. This allowed neurons to be ranked according to their up phase spikelatency during spontaneous activity, without the need for any external manipulation of trial startand end. Using an internal trigger for designating trials may be a more natural and less biased wayof denoting trial start than an external trigger. It seems that up phase spike latency has not yetbeen investigated in cat V1. Although methodologically difficult, future experiments might alsoattempt to time the start of stimulus presentation trials to up phase onset, which might increaseresponse precision and reliability.Up phase onset may also serve as a valuable tool for determining polytrode laminar position.Sakata and Harris (2009) used up phase onset as a trigger for CSD (Section 4.6.3) analysis, withoutthe need for an external stimulus trigger. This means that experimental time need not be spentpresenting a transiently synchronizing stimulus, such as a full screen flash or direct electrical thala-mic stimulation, solely for the purpose of constructing the CSD. It would also provide many moretriggers for calculating the CSD with greater fidelity, and allow for continuous tracking of laminarposition. Again, using an internal trigger rather than an external one is arguably more naturalistic.1476.7.5 Natural scene movie responses vs. cortical stateNatural scene movie responses were more temporally precise and reliable during the synchronizedstate than the desynchronized state (Section 6.6). For the two natural scene movie recordingsduring which a spontaneous state change occurred (Figures 6.14 & 6.15) this conclusion held for91% of responsive cells. Only 5% of responsive cells showed the opposite, while 3% showed nochange. These qualitative differences in precision and reliability between the two states were sup-ported by quantitative measures of response precision, sparseness, and reliability, all of which weresignificantly greater in the synchronized state than in the desynchronized state (Figure 6.17).Although other studies have reported temporally precise and reliable responses to naturalisticstimuli in V1 (Vinje and Gallant, 2000, 2002; Yen et al., 2007; Haider et al., 2010; Herikstad etal., 2011), perhaps only one has considered the influence of cortical state on temporal precisionand reliability in V1. Contrary to the results shown in Section 6.6, Goard and Dan (2009) re-ported that responses to natural scene movies in urethane-anesthetized rat V1 were more reliablein the desynchronized state than in the synchronized state. Desynchronization was triggered byelectrical stimulation of the nucleus basalis in the basal forebrain. Another study by Marguet andHarris (2011) came to the same conclusion, using an amplitude-modulated frozen noise stimulusin urethane-anesthetized rat A1. In that study, desynchronization was induced via tail pinch. Athird study by Zagha et al. (2013) reported that tactile stimulus encoding in urethane-anesthetizedmouse barrel cortex was also more reliable in the desynchronized state, which was induced bystimulation of M1. In the above three studies, comparisons of trial raster plots or MUA PSTHsbetween the two cortical states suggest modest changes in temporal precision and reliability com-pared to the more dramatic and opposite changes shown here in Figures 6.14 & 6.15. A fourthstudy by Pachitariu et al. (2015) in variously anesthetized gerbil A1 also found greater precisionand reliability of responses in the desynchronized state than in the synchronized state, this timeto frequency-modulated tones and speech stimuli. Trial raster plot differences between states weremore dramatic in that study than in the other three.There are many experimental differences that might explain the opposing results presented here,including differences in species (cat vs. rodent), anesthetic (isoflurane vs. urethane, ketamine/xy-lazine, and fentanyl/medetomidine/midazolam), desynchronization method (spontaneous vs. evoked),cortical area (V1 vs. A1 and barrel cortex), stimulus modality (visual vs. auditory and tactile), andstimulus type (naturalistic vs. artificial). Since cortical state is likely multidimensional and SI mea-sures only one such dimension (Harris and Thiele, 2011), it is also possible that there were otherundetected changes in cortical state in the two recordings in Figures 6.14–6.15 but not in thosereported in the literature (or vice versa). Such undetected changes might account for some of theseopposing results.The species difference may be the most important. Cats have greater columnar organizationof stimulus features in V1 than do rodents: cats have ocular dominance and orientation columnsthat rodents lack (Horton and Adams, 2005). Up phases in the synchronized state can manifest as148waves of activity travelling across the cortical surface (Petersen et al., 2003; Massimini et al., 2004;Benucci et al., 2007; Xu et al., 2007; Luczak et al., 2007; Mohajerani et al., 2010), while orientedvisual stimuli can evoke standing waves of activity aligned to orientation columns (Benucci et al.,2007). Presumably, stimulus-evoked standing waves are absent in species that lack orientationcolumns, including rodents. Perhaps an interaction between these travelling and standing waves ofactivity in the synchronized state increases the temporal precision and reliability of stimulus-evokedresponses in cat V1 relative to rat V1. This hypothesis predicts that responses in the synchronizedstate of anesthetized ferret and primate V1, which also have orientation columns, should also bemore precise and reliable than in the desynchronized state.These opposing results are surprising because neural responses in awake animals are known tobe stronger and more synchronized in alert than in quiescent animals, and to attended than tounattended stimuli (Roelfsema et al., 1998; Fries et al., 2001; Cohen and Maunsell, 2009; Mitchellet al., 2009; Chalk et al., 2010). The result presented here therefore conflicts with the hypothesisthat the synchronized and desynchronized cortical states in anesthetized animals are respectivelyanalogous to quiescent and attending periods in awake animals (Harris and Thiele, 2011). Perhapsthe relationship is more complex than previously thought.The present finding that responses are less precise and reliable during the desynchronized stateis consistent with Fiser et al. (2004). In awake freely viewing (supposedly highly desynchronized)ferret V1, that study concluded that superficial layer multiunit firing patterns were dominated bycortical state rather than stimulus. In other words, stimulus did little to affect multiunit responsesin the desynchronized state. However, during anesthesia in the same animals (supposedly in amore synchronized state), stimulus had much more of an effect on multiunit responses. This onlyindirectly agrees with Figures 6.14–6.15, because Fiser et al. (2004) did not show any trial rasterplots from which direct conclusions about precision and reliability might be made.Marguet and Harris (2011) also found trial-averaged LFP to be more reliable in the desynchro-nized state than the synchronized state. Although trial-averaged LFP was not calculated here,doing so would be simple, and given the conclusions here on spike train reliability, it is likely thatfor anesthetized cat V1, the trial-averaged LFP will also be more reliable in the synchronized state.Almost by definition, PSTH correlations between cell pairs were higher on average in the syn-chronized than desynchronized state, but only modestly (Figure 6.18). There is wide agreement onthis in the literature (Poulet and Petersen, 2008; Goard and Dan, 2009; Curto et al., 2009; Renart etal., 2010; Marguet and Harris, 2011; Scho¨lvinck et al., 2015; Pachitariu et al., 2015). Even thoughPSTH correlations were only modestly influenced by cortical state, that influence was greater thanthe particular choice of natural scene movie clip that was presented (Figure 6.19). Though perhapssomewhat controversial, this conclusion agrees with a number of other studies (Arieli et al., 1996;Fiser et al., 2004; Marguet and Harris, 2011; Okun et al., 2012). (Okun et al. (2012) is in a some-what different context of spike correlations and multineuron words over the course of ferret visualcortex development, but is still relevant. See Appendix B.)149The conclusions made here are based on only 78 min of data from two recordings from the sametrack. This was due to the paucity of desynchronized periods in the three tracks chosen for carefulspike sorting and detailed analysis (ptc15.tr7c, ptc22.tr1, ptc22.tr2). Other movie recordings fromthese tracks had less dramatic cortical state changes, as exhibited by their LFP. They also seemedto exhibit the same relationship between level of synchronization and temporal precision of responseevents (not shown), but that relationship was less obvious. The surprising conclusion that responsesare more precise and reliable in the synchronized state should be strengthened by spike sortingmore tracks with greater periods of desynchronization (Figure 6.11), and therefore a greater chanceof spontaneously switching between synchronized and desynchronized states. Indeed, another 4natural scene movie recordings showed sudden switches in cortical state (not shown), similar tothose shown in Figures 6.9 & 6.10. These totalled an additional 130 min of recording, from 4 moretracks from 2 more cats (ptc17.tr2b, ptc18.tr1, ptc18.tr2c, ptc22.tr4b). Preliminary spike sortingof these additional recordings (courtesy of Catalin Mitelut) showed the same relationship betweencortical state and spiking response precision and reliability as in Section 6.6 (not shown), therebystrengthening the above conclusion.The third cell in Figure 6.14 (rightmost column) was classified as an LGN afferent, yet it wasclearly modulated by cortical state. Two other such cells were found. As part of the thalamus, theLGN can drive cortical state changes (Steriade et al., 1991, 1993c; Hirata and Castro-Alamancos,2010), but cortical state changes are not thought to directly affect the LGN, although indirectinfluence via the thalamic reticular nucleus is possible (Steriade et al., 1993c). The cells classifiedhere as LGN afferents may therefore reflect state changes in LGN which subsequently drive changesin cortical state.The influence of cortical state on precision and reliability during presentation of artificial stimuliwas not examined here, partly because artificial stimuli such as m-sequence white noise movies,drifting bars, and drifting gratings do not induce very precise or reliable responses compared tonatural scene movies. Nevertheless, this is something that could be examined in the future.6.7.6 Clustering cortical statesLabelling cortical state as synchronized and desynchronized is a start, but is almost certainly overlysimplistic (Harris and Thiele, 2011). Future work should also partition especially the desynchro-nized cortical state into further categories, given the large, sudden changes in LFP spectrogramsduring desynchronized periods (Figures 6.9B & 6.10B), and the trimodality of the SI plots in sometracks (Figure 6.11). Instead of using a simple power ratio of somewhat arbitrarily chosen highand low frequency bands, the full distribution of power across frequencies, i.e., the PSD (Fig-ure 6.8A), at each point in time could be characterized in a more sophisticated way. For example,a high dimensional data set could be generated by collecting LFP PSDs at all points in time inall recordings in all tracks (or perhaps separately for each track). If 1 Hz wide frequency bandswere used from 0 to 100 Hz, this would create a 100 dimensional space varying over time. PCA150or ICA or some other dimension reduction method could be applied to this space to extract thetop 2 or 3 most interesting or descriptive components. Upon mapping each point in time into thislow dimensional space, multiple clusters might emerge. Upon clustering of this dimension reduceddata (perhaps using GAC, Section 3.9.1), dimension reduction could be redone separately for eachcluster, creating a new space with perhaps further subclusters (akin to checking for undersplit clus-ters in Section 3.10.1). One such expected subclustering is the distinction between up and downphases within the synchronized state, but there may be many more. Differences in PSDs acrosschannels could also be exploited to characterize cortical state as a function of depth. All of thiscould allow for a (potentially nested) multidimensional metric of cortical state as a function of time,and a simultaneous increase in the number of labelled states, each potentially having a differentcomputational role.1517 ConclusionThis thesis examined the use of silicon polytrodes for large-scale extracellular recordings of localpopulations of neurons in anesthetized cat V1. A wide variety of both artificial and naturalisticvisual stimuli were used (Section 2.4), and a new divide-and-conquer spike sorting method wasdevised to translate correlated multisite extracellular potential waveforms into sorted spikes fromisolated single units (Chapter 3). From stimulus and recording, to spike sorting and analysis, manysteps were taken to minimize bias in the characterization of patches of V1. Many results concurredwith previous studies, but some results were surprising.Mean firing rates were surprisingly low and lognormally distributed, supporting the theory ofsparse coding (Section 4.3). There was also evidence for neural shift work, which could be a usefulstrategy for physiological maintenance or network stability (Section 4.6.2). 65 µm site spacing wasfound to be too great to fully capture the local neuronal population (Section 4.4), suggesting thatfuture polytrodes should use a higher density of electrode sites to decrease the chance of missedcells. Surprisingly, orientation tuning strength was inversely correlated with stimulus-evoked logfiring rates (Section 4.5), demonstrating the utility of low-rate cells.Cells could be classified into at least 2 and possibly up to 4 different types based on theirspike shape (fast, slow, fast asymmetric, slow asymmetric; Section 5.2), and into 4 types basedon their spatiotemporal receptive fields (simple, complex, LGN afferent, unknown; Section 5.4).Spatial extent of 2D spatially localized multichannel spike waveforms was not useful for classifyingcells (Section 5.3). Approximately equal numbers of cells were classified as simple, complex, andunknown RF type, with only 5% classified as LGN afferents. Cells classified as unknown RF typemay have been mostly complex cells damaged by polytrode insertion.Natural scene movies evoked sparse and reliable spike patterns in most cells that were active,with temporal precision measured in milliseconds (Section 6.2), lending support to the importanceof spike timing in cortical neural coding. Spontaneous changes in cortical state (Section 6.4) played amajor role in these responses. Consistent with other reports, up/down phases were present duringthe synchronized state, and absent during the desynchronized state (Section 6.5). Contrary toreports in other preparations, responses were more precise, sparse, and reliable in the synchronizedstate than in the desynchronized state (Section 6.6). Pairwise correlations of natural scene movieresponses between most cells were close to zero, but mean correlations across the population wereslightly positive. Correlations were lower than expected between simple and complex cells, andhigher than expected between complex cells (Section 6.3), challenging the hierarchical model ofcomplex cells and supporting a recurrent model instead (Section 6.7.2). Response correlations wereinfluenced more by cortical state than by the specific natural scene movie presented (Section 6.6),providing further evidence of the importance of cortical state.152Although bias was minimized in as many ways as practically possible, some bias inevitablyremained. For example, due to time and space limitations, this study focused on only 3 tracksfrom 3 hemispheres in 2 cats, resulting in 245 isolated cells. Increasing the number of cells, tracks,and cats requires further spike sorting, but is a top priority as it would strengthen many of theconclusions in Chapters 4–6.Despite long-duration recordings at fixed positions and substantial effort dedicated to detectinglow-rate cells, neuronal yields were still < 15% of the known anatomical number of neurons withinisolatable recording range (Section 4.6.1). One possible source of remaining bias was that 65 µmelectrode site spacing selected for cells with large open extracellular potential fields, and againstthose with small closed fields. Fortunately, the solution to this is relatively simple: use a polytrodedesign with lower electrode site spacing. Balancing this against the desire to simultaneously recordfrom all cortical layers will require more electrode sites in future experiments. Since polytrodes(e.g., Buzsaki256 probe, NeuroNexus, Ann Arbor, MI) and neurophysiological recording systems(e.g., RHD2000 system, Intan Technologies, Los Angeles, CA) with up to 256 sites and channelsare now easily and relatively cheaply available, this should not be a major obstacle. Higher channelcounts may increase the overall amount of time required for spike sorting, but greater channeldensities may make it easier to distinguish neighbouring neurons and may therefore decrease theamount of spike sorting time required per neuron.Polytrode tissue damage was likely another big source of remaining bias, one that is moredifficult to overcome. Damage could be mitigated in a variety of ways. One way is to insertthe polytrode at a much slower rate, on the order of 10 µm/min or less (Schjetnan and Luczak,2011; Bere´nyi et al., 2014), which may reduce damage associated with dimpling. Another is touse narrower polytrodes. The ∼ 200 µm shank width of the polytrodes used here is at least twicethat of most other designs, and failed to isolate cells in several attempted experiments in urethane-anesthetized rat V1. In comparison, many other groups have had success with narrower polytrodesin rat cortex (Section 4.6.1). If the 200 µm shank width is responsible for such a radical differencein neuron yield in rat cortex, it could also easily affect yield in cat V1, but perhaps less radically.At least one sufficiently long high-density polytrode design of narrower width is available (A1x64-Poly2-6mm-23s-160, Anton Sirota lab, manufactured by NeuroNexus, Ann Arbor, MI) which tapersto a maximum width of 115 µm.Most of the width of a polytrode is to provide space for non-overlapping conductors from eachof the electrode sites up to the headstage connector. Ideally, conductor requirements should notdictate shank width, and polytrode shanks should be no wider than the desired site spacing (<38 µm in the above design). This would require either much narrower conductors, or a multilayerdesign, or some combination of the two. Given that these are passive low current conductors,such changes could lead to undesired coupling between neighbouring conductors (but see Du etal. (2011)). The ultimate solution to this problem might require active electronics, perhaps acurrent buffer stage located immediately adjacent to each electrode site. Unfortunately, given the153specialized nature of polytrodes and their low manufacturing volumes, this would likely result ingreater costs per polytrode, which are fragile and easily broken during handling.Given the dramatic influence of cortical states on spiking responses (Section 6.6), further workshould carefully control for cortical states, manipulate them experimentally, and classify them withgreater fidelity than simply synchronized vs. desynchronized (Section 6.7.6). Spike correlations(Appendix B) are widely used to infer functional connectivity (Bartho´ et al., 2004; Du et al., 2011)and to explain population spike patterns (Schneidman et al., 2006; Shlens et al., 2006; Yu et al.,2008; Ohiorhenuan et al., 2010; Berkes et al., 2011), yet they are very sensitive to changes incortical state (Goard and Dan, 2009; Harris and Thiele, 2011; Okun et al., 2012). Cortical stateshould therefore be considered during spike correlation analysis. Great care should also be taken inthe application of anticholinergics, which induce extended periods of synchronization (Section 6.4).During long duration anesthesia, short-term reduction of isoflurane levels may allow for controlledperiods of desynchronization without risk of loss of anesthesia (Section 6.7.3). More sophisticatedchronic recordings in unanesthetized animals in various waking and sleep states (awake behaving,quiet resting, REM sleep, slow-wave sleep) might allow for a broader characterization of corticalstates, and more direct comparisons to cortical states from the same cells in the same animal underanesthesia. This would help strengthen the argument that cortical state in anesthetized animals isclosely related to that in awake behaving animals, and that, for example, the desynchronized stateis closely related to attention (Harris and Thiele, 2011). Unfortunately, precisely controlling theprojection of visual stimuli onto the retina of awake or sleeping animals is very difficult, yet doing sois necessary to gauge the temporal precision and reliability of spiking responses to repeated naturalscene movies in such animals.Moore’s law describes the exponential growth of the number of transistors that can be packedinto a single integrated circuit, with a doubling time of about 2 years. Although the growthrate of neuronal recording technology, as measured by the maximum number of simultaneouslyrecordable neurons, is slower than Moore’s law, it too is exponential, with a doubling periodof roughly 7 years (Stevenson and Kording, 2011). Within just a few years, polytrodes couldconsist of hundreds of electrode sites and dozens of shanks, perhaps multisided or circular, allowingsimultaneous monitoring of thousands of neurons (Einevoll et al., 2012) from ever larger but mostlycontiguous volumes of grey matter.Like most technologies, the silicon polytrodes used here for large-scale neuronal recording willeventually be supplanted by a superior technology. Two-photon calcium imaging is currently limitedby both its recording depth and its reliance on the slow calcium signal which prevents detection oftemporally precise spike patterns (Section 1.1). While the former limitation is improving, the latterremains a greater challenge. Temporal resolution might be improved by developing a geneticallyengineered fluorophore whose change in fluorescence directly corresponds to change in membranepotential, analogous to voltage-sensitive dye recordings used at coarser spatial scales (Arieli etal., 1995, 1996; Mohajerani et al., 2010). Such a fluorophore would not only allow detection of154arbitrarily fine spike patterns, but might also provide optical access to the subthreshold membranepotential, combining the best of both intracellular and extracellular electrophysiology. Such anadvance, combined with its lack of tissue damage, would allow two-photon imaging to leapfrogpolytrodes for large-scale monitoring of neuronal populations.A more exotic proposal for large-scale recording might involve molecular “ticker tape”, in whicha constant rate of copying of DNA by polymerase in a neuron is interrupted by copying anomalieson every occurrence of a spike (Kording, 2011). This nucleotide signal could then be read outoffline by independently sequencing the DNA of each neuron to obtain its temporal pattern ofspikes. Another exotic possibility is nano-scale magnetic resonance imaging (McGuinness et al.,2011; Hemmer, 2013), in which tiny ultra-pure diamonds with engineered defects can be used ashighly sensitive room temperature magnetometers, capable of detecting changes in the magneticspin of small numbers of nearby electrons or protons using pulsed optical and radio frequencystimulation and readout. These nanodiamonds might be embedded in cell membranes to providehigh-speed non-invasive readout of membrane potential from many neurons at a time.While ever-improving recording technology will help reduce bias in our understanding of thebrain, care must also be taken with all experimental and analytical methods to do the same. As thenumber of simultaneously recorded cells increases, the number of pairwise interactions to analyzeincreases with its square. The combinatorial explosion involved in the analysis of such data couldprove to be more challenging than the technological developments or the experiments themselves.However these problems are tackled, the study of a system as complex as the brain demands theutmost care and attention towards minimizing bias wherever possible.155BibliographyAbbott LF, Chance FS (2002) Rethinking the taxonomy of visual neurons. NatNeurosci 5:391–392. → page 90, 143Adrian ED, Bronk DW (1928) The discharge of impulses in motor nerve fibres: Part I. Impulsesin single fibres of the phrenic nerve. J Physiol 66:81–101. → page 1Ahmed B, Anderson JC, Douglas RJ, Martin KAC, Nelson JC (1994) Polyneuronal innervationof spiny stellate neurons in cat visual cortex. J Comp Neurol 341:39–49. → page 140Alonso JM, Martinez LM (1998) Functional connectivity between simple cells and complex cellsin cat striate cortex. Nat Neurosci 1:395–403. → page 108, 143Alonso JM, Usrey WM, Reid RC (1996) Precisely correlated firing in cells of the lateralgeniculate nucleus. Nature 383:815–819. → page 62, 140Anderson J, Lampl I, Reichova I, Carandini M, Ferster D (2000) Stimulus dependence oftwo-state fluctuations of membrane potential in cat visual cortex. Nat Neurosci 3:617–621. →page 110, 126, 147Arieli A, Shoham D, Hildesheim R, Grinvald A (1995) Coherent spatiotemporal patterns ofongoing activity revealed by real-time optical imaging coupled with single-unit recording in thecat visual cortex. J Neurophysiol 73:2072–2093. → page 154Arieli A, Sterkin A, Grinvald A, Aertsen A (1996) Dynamics of ongoing activity: explanation ofthe large variability in evoked cortical responses. Science 273:1868–1871. → page 6, 110, 149,154Attwell D, Laughlin SB (2001) An energy budget for signaling in the grey matter of the brain. JCereb Blood Flow Metab 21:1133–1145. → page 1, 81, 140Bair W, Koch C (1996) Temporal precision of spike trains in extrastriate cortex of the behavingmacaque monkey. Neural Comput 8:1185–1202. → page 5, 137Baker SN, Lemon RN (2000) Precise spatiotemporal repeating patterns in monkey primary andsupplementary motor areas occur at chance levels. J Neurophysiol 84:1770–1780. → page 5Bar-Hillel A, Spiro A, Stark E (2006) Spike sorting: Bayesian clustering of non-stationary data. JNeurosci Meth 157:303–316. → page 24, 27, 45Bartho´ P, Hirase H, Monconduit L, Zugaro M, Harris KD, Buzsa´ki G (2004) Characterization ofneocortical principal cells and interneurons by network interactions and extracellular features.J Neurophysiol 92:600–608. → page 89, 90, 104, 105, 154Battaglia FP, Kalenscher T, Cabral H, Winkel J, Bos J, Manuputy R, van Lieshout T, Pinkse F,Beukers H, Pennartz C (2009) The lantern: an ultra-light micro-drive for multi-tetroderecordings in mice and other small animals. J Neurosci Meth 178:291–300. → page 3156Beaulieu C, Colonnier M (1985) A comparison of the number of neurons in individual laminae ofcortical areas 17, 18 and posteromedial suprasylvian (PMLS) area in the cat. BrainRes 339:166–170. → page 4Behnel S, Bradshaw R, Citro C, Dalcin L, Seljebotn DS, Smith K (2011) Cython: The best ofboth worlds. IEEE Comput Sci Eng Mag 13:31–39. → page 181Bell AJ, Sejnowski TJ (1995) An information-maximization approach to blind separation andblind deconvolution. Neural Comput 7:1129–1159. → page 41Benchenane K, Peyrache A, Khamassi M, Tierney PL, Gioanni Y, Battaglia FP, Wiener SI (2010)Coherent theta oscillations and reorganization of spike timing in the hippocampal-prefrontalnetwork upon learning. Neuron 66:921–936. → page 89, 104, 105Benucci A, Frazor RA, Carandini M (2007) Standing waves and traveling waves distinguish twocircuits in visual cortex. Neuron 55:103–117. → page 149Bere´nyi A, Somogyva´ri Z, Nagy AJ, Roux L, Long JD, Fujisawa S, Stark E, Leonardo A, HarrisTD, Buzsa´ki G (2014) Large-scale, high-density (up to 512 channels) recording of local circuitsin behaving animals. J Neurophysiol 111:1132–1149. → page 3, 5, 80, 153Berger H (1929) U¨ber das elektrenkephalogramm des Menschen. Arch PsychiatrNervenkr 87:527–570. → page 6, 110Berkes P, Orba´n G, Lengyel M, Fiser J (2011) Spontaneous cortical activity reveals hallmarks ofan optimal internal model of the environment. Science 331:83–87. → page 154Berry MJ, Warland DK, Meister M (1997) The structure and precision of retinal spike trains.PNAS 94:5411–5416. → page 140Bilmes JA (1998) A gentle tutorial of the EM algorithm and its application to parameterestimation for Gaussian mixture and hidden Markov models . → page 27Binzegger T, Douglas RJ, Martin KAC (2004) A quantitative map of the circuit of cat primaryvisual cortex. J Neurosci 24:8441–8453. → page 140Biran R, Martin DC, Tresco PA (2005) Neuronal cell loss accompanies the brain tissue responseto chronically implanted silicon microelectrode arrays. Exp Neurol 195:115–126. → page 82Blanche TJ (2005) Large scale neuronal recording. Ph.D. diss., University of British Columbia,Vancouver, British Columbia, Canada. → page 4, 14, 15, 25, 85, 89, 90, 106, 179Blanche TJ, Godfrey K, Douglas RM, Swindale NV (2008) Spike detection and sortingalgorithms for polytrodes. (unpublished) . → page 25Blanche TJ, Spacek MA, Hetke JF, Swindale NV (2005) Polytrodes: high-density siliconelectrode arrays for large-scale multiunit recording. J Neurophysiol 93:2987–3000. → page iii, 3,4, 5, 14, 15, 23, 29, 69, 80, 84, 186Blanche TJ, Swindale NV (2006) Nyquist interpolation improves neuron yield in multiunitrecordings. J Neurosci Meth 155:81–91. → page 29157Blatt M, Wiseman S, Domany E (1996) Superparamagnetic clustering of data. Phys RevLett 76:3251–3254. → page 27, 45Blatt M, Wiseman S, Domany E (1997) Data clustering using a model granular magnet. NeuralComput 9:1805–1842. → page 27Brecht M, Roth A, Sakmann B (2003) Dynamic receptive fields of reconstructed pyramidal cellsin layers 3 and 2 of rat somatosensory barrel cortex. J Physiol 553:243–265. → page 81Burr DC, Ross J (1979) How does binocular delay give information about depth? VisionRes 19:523–532. → page 5Buzsa´ki G (2004) Large-scale recording of neuronal ensembles. Nat Neurosci 7:446–451. → page5, 22, 80, 86Buzsa´ki G, Anastassiou CA, Koch C (2012) The origin of extracellular fields and currents —EEG, ECoG, LFP and spikes. Nat Rev Neurosci 13:407–420. → page 2Calabrese A, Paninski L (2011) Kalman filter mixture model for spike sorting of non-stationarydata. J Neurosci Meth 196:159–169. → page 24, 27Carandini M, Demb JB, Mante V, Tolhurst DJ, Dan Y, Olshausen BA, Gallant J, Rust NC(2005) Do we know what the early visual system does? J Neurosci 25:10577–10597. → page 7,81, 107, 110, 141Carandini M, Ferster D (2000) Membrane potential and firing rate in cat primary visual cortex. JNeurosci 20:470–484. → page 107Carandini M, Heeger DJ, Movshon JA (1997) Linearity and normalization in simple cells of themacaque primary visual cortex. J Neurosci 17:8621–8644. → page 141Castro-Alamancos MA (2002) Role of thalamocortical sensory suppression during arousal:focusing sensory inputs in neocortex. J Neurosci 22:9651–9655. → page 146Chalk M, Herrero JL, Gieselmann MA, Delicato LS, Gotthardt S, Thiele A (2010) Attentionreduces stimulus-driven gamma frequency oscillations and spike field coherence in V1.Neuron 66:114–125. → page 149Chance FS, Nelson SB, Abbott LF (1999) Complex cells as cortically amplified simple cells. NatNeurosci 2:277–282. → page 90, 107, 108, 143, 144Chubykin AA, Roach EB, Bear MF, Shuler MGH (2013) A cholinergic mechanism for rewardtiming within primary visual cortex. Neuron 77:723–735. → page 110Cohen MR, Maunsell JHR (2009) Attention improves performance primarily by reducinginterneuronal correlations. Nat Neurosci 12:1594–1600. → page 149Comon P (1994) Independent component analysis, a new concept? Signal Processing 36:287–314.→ page 41Csicsvari J, Henze DA, Jamieson B, Harris KD, Sirota A, Bartho´ P, Wise KD, Buzsa´ki G (2003)Massively parallel recording of unit and local field potentials with silicon-based electrodes. JNeurophysiol 90:1314–1323. → page 3, 4, 5, 23, 80158Csicsvari J, Hirase H, Czurko A, Buzsa´ki G (1998) Reliability and state dependence of pyramidalcell–interneuron synapses in the hippocampus: an ensemble approach in the behaving rat.Neuron 21:179–189. → page 89, 104Curto C, Sakata S, Marguet S, Itskov V, Harris KD (2009) A simple model of cortical dynamicsexplains variability and state dependence of sensory responses in urethane-anesthetizedauditory cortex. J Neurosci 29:10600–10612. → page 146, 149Dagum L, Menon R (1998) OpenMP: an industry standard API for shared-memoryprogramming. IEEE Comput Sci Eng Mag 5:46–55. → page 181Dan Y, Atick JJ, Reid RC (1996) Efficient coding of natural scenes in the lateral geniculatenucleus: experimental test of a computational theory. J Neurosci 16:3351–3362. → page 140David SV, Vinje WE, Gallant JL (2004) Natural stimulus statistics alter the receptive fieldstructure of V1 neurons. J Neurosci 24:6991–7006. → page 110, 141De Valois RL, Yund EW, Hepler N (1982) The orientation and direction selectivity of cells inmacaque visual cortex. Vision Res 22:531–544. → page 87Dean AF, Tolhurst DJ (1983) On the distinctness of simple and complex cells in the visual cortexof the cat. J Physiol 344:305–325. → page 90, 106, 107DeAngelis GC, Ohzawa I, Freeman RD (1993) Spatiotemporal organization of simple-cellreceptive fields in the cat’s striate cortex. I. General characteristics and postnatal development.J Neurophysiol 69:1091–1117. → page 89, 99Denk W, Strickler JH, Webb WW (1990) Two-photon laser scanning fluorescence microscopy.Science 248:73–76. → page 4Destexhe A, Contreras D, Steriade M (1999) Spatiotemporal analysis of local field potentials andunit discharges in cat cerebral cortex during natural wake and sleep states. JNeurosci 19:4595–4608. → page 110, 147Drake KL, Wise KD, Farraye J, Anderson DJ, BeMent SL (1988) Performance of planar multisitemicroprobes in recording extracellular single-unit intracortical activity. IEEE Trans BiomedEng 35:719–732. → page 3, 23Du J, Blanche TJ, Harrison RR, Lester HA, Masmanidis SC (2011) Multiplexed, high densityelectrophysiology with nanofabricated neural probes. PLoS ONE 6:e26204. → page 84, 153, 154Du J, Riedel-Kruse IH, Nawroth JC, Roukes ML, Laurent G, Masmanidis SC (2009)High-resolution three-dimensional extracellular recording of neuronal activity withmicrofabricated electrode arrays. J Neurophysiol 101:1671–1678. → page 3, 4, 23Ecker AS, Berens P, Keliris GA, Bethge M, Logothetis NK, Tolias AS (2010) Decorrelatedneuronal firing in cortical microcircuits. Science 327:584–587. → page 142Eger II EI, Johnson BH (1987) Rates of awakening from anesthesia with I-653, halothane,isoflurane, and sevoflurane: a test of the effect of anesthetic concentration and duration in rats.Anesth Analg 66:977–982. → page 146159Einevoll GT, Franke F, Hagen E, Pouzat C, Harris KD (2012) Towards reliable spike-trainrecordings from thousands of neurons with multielectrodes. Curr Opin Neurobiol 22:11–17. →page 24, 57, 154Engel AK, Fries P, Singer W (2001) Dynamic predictions: oscillations and synchrony in top–downprocessing. Nature Rev Neurosci 2:704–716. → page 5Ester M, Kriegel HP, Sander J, Xu X (1996) A density-based algorithm for discovering clusters inlarge spatial databases with noise In Proceedings of the Second International Conference onKnowledge Discovery and Data Mining, pp. 226–231, Portland, OR. AAAI Press. → page 61Fee MS, Mitra PP, Kleinfeld D (1996) Automatic sorting of multiple unit neuronal signals in thepresence of anisotropic and non-gaussian variability. J Neurosci Meth 69:175–188. → page 24,27, 62Fiser J, Chiu C, Weliky M (2004) Small modulation of ongoing cortical dynamics by sensoryinput during natural vision. Nature 431:573–578. → page 6, 110, 149Fisher NI (1995) Statistical analysis of circular data. Cambridge University Press. → page 76Forgy EW (1965) Cluster analysis of multivariate data: efficiency versus interpretability ofclassifications. Biometrics 21:768–769. → page 26Franke F, Natora M, Boucsein C, Munk MHJ, Obermayer K (2010) An online spike detectionand spike classification algorithm capable of instantaneous resolution of overlapping spikes. JComput Neurosci 29:127–148. → page 24, 26Fries P, Reynolds JH, Rorie AE, Desimone R (2001) Modulation of oscillatory neuronalsynchronization by selective visual attention. Science 291:1560–1563. → page 149Fukunaga K, Hostetler L (1975) The estimation of the gradient of a density function, withapplications in pattern recognition. IEEE Trans Inf Theory 21:32–40. → page 48, 60Galarreta M, Hestrin S (1999) A network of fast-spiking cells in the neocortex connected byelectrical synapses. Nature 402:72–75. → page 142Garcia-Lazaro JA, Belliveau LA, Lesica NA (2013) Independent population coding of speech withsub-millisecond precision. J Neurosci 33:19362–19372. → page 5Garland CM, Foreman RC, Chad JE, Holden-Dye L, Walker RJ (1998) The actions of musclerelaxants at nicotinic acetylcholine receptor isoforms. Eur J Pharmacol 357:83–92. → page 124Gasthaus J, Wood F, Go¨ru¨r D, Teh YW (2009) Dependent Dirichlet process spike sorting In AdvNeural Inf Process Syst, Vol. 21, pp. 497–504. Curran Associates, Inc. → page 24Gershon ED, Wiener MC, Latham PE, Richmond BJ (1998) Coding strategies in monkey V1 andinferior temporal cortices. J Neurophysiol 79:1135–1144. → page 88Ghose GM, Freeman RD, Ohzawa I (1994) Local intracortical connections in the cat’s visualcortex: postnatal development and plasticity. J Neurophysiol 72:1290–1303. → page 143160Gibson JR, Beierlein M, Connors BW (1999) Two networks of electrically coupled inhibitoryneurons in neocortex. Nature 402:75–79. → page 142Gilbert CD (1977) Laminar differences in receptive field properties of cells in cat primary visualcortex. J Physiol 268:391–421. → page 89, 107, 108Goard M, Dan Y (2009) Basal forebrain activation enhances cortical coding of natural scenes.Nat Neurosci 12:1444–1449. → page 80, 111, 136, 146, 148, 149, 154Gollisch T, Meister M (2008) Rapid neural coding in the retina with relative spike latencies.Science 319:1108–1111. → page 5, 140Gray CM, Ko¨nig P, Engel AK, Singer W (1989) Oscillatory responses in cat visual cortex exhibitinter-columnar synchronization which reflects global stimulus properties. Nature 338:334–337.→ page 5Gray CM, Maldonado PE, Wilson M, McNaughton B (1995) Tetrodes markedly improve thereliability and yield of multiple single-unit isolation from multi-unit recordings in cat striatecortex. J Neurosci Meth 63:43–54. → page 3, 22, 24, 26, 62Gray CM, McCormick DA (1996) Chattering cells: superficial pyramidal neurons contributing tothe generation of synchronous oscillations in the visual cortex. Science 274:109–113. → page 90Green J (1958) A simple microelectrode for recording from the central nervous system.Nature 182:962. → page 2Gur M, Beylin A, Snodderly DM (1999) Physiological properties of macaque V1 neurons arecorrelated with extracellular spike amplitude, duration, and polarity. JNeurophysiol 82:1451–1464. → page 89, 104Hahnloser RHR, Kozhevnikov AA, Fee MS (2002) An ultra-sparse code underlies the generationof neural sequences in a songbird. Nature 419:65–70. → page 80Haider B, Duque A, Hasenstaub AR, McCormick DA (2006) Neocortical network activity in vivois generated through a dynamic balance of excitation and inhibition. J Neurosci 26:4535–4545.→ page 147Haider B, Krause MR, Duque A, Yu Y, Touryan J, Mazer JA, McCormick DA (2010) Synapticand network mechanisms of sparse and reliable visual cortical activity during nonclassicalreceptive field stimulation. Neuron 65:107–121. → page 7, 103, 137, 140, 142, 148Hammond P, Andrews DP (1978) Orientation tuning of cells in areas 17 and 18 of the cat’s visualcortex. Exp Brain Res 31:341–351. → page 87Harris KD (2005) Neural signatures of cell assembly organization. Nature RevNeurosci 6:399–407. → page 5Harris KD, Csicsvari J, Hirase H, Dragoi G, Buzsa´ki G (2003) Organization of cell assemblies inthe hippocampus. Nature 424:552–6. → page 5, 80, 114161Harris KD, Henze DA, Csicsvari J, Hirase H, Buzsa´ki G (2000) Accuracy of tetrode spikeseparation as determined by simultaneous intracellular and extracellular measurements. JNeurophysiol 84:401–414. → page 3, 23, 24, 27, 55, 62Harris KD, Henze DA, Hirase H, Leinekugel X, Dragoi G, Czurko´ A, Buzsa´ki G (2002) Spiketrain dynamics predicts theta-related phase precession in hippocampal pyramidal cells.Nature 417:738–741. → page 5Harris KD, Thiele A (2011) Cortical state and attention. Nat Rev Neurosci 12:509–523. → page2, 6, 110, 121, 129, 145, 146, 148, 149, 150, 154, 178Hartigan JA, Hartigan PM (1985) The dip test of unimodality. Ann Stat 13:70–84. → page 60Hasenstaub A, Sachdev RNS, McCormick DA (2007) State changes rapidly modulate corticalneuronal responsiveness. J Neurosci 27:9607–9622. → page 147Havenith MN, Yu S, Biederlack J, Chen NH, Singer W, Nikolic´ D (2011) Synchrony makesneurons fire in sequence, and stimulus properties determine who is ahead. JNeurosci 31:8570–8584. → page 5Hazan L, Zugaro M, Buzsa´ki G (2006) Klusters, NeuroScope, NDManager: a free software suitefor neurophysiological data processing and visualization. J Neurosci Meth 155:207–216. → page24, 27, 54, 181Hebb DO (1949) The Organization of Behavior: A Neuropsychological Theory. John Wiley &Sons, New York. → page 4Helmchen F, Denk W (2005) Deep tissue two-photon microscopy. Nat Methods 2:932–940. →page 4Hemmer P (2013) Toward molecular-scale MRI. Science 339:529–530. → page 155Henze DA, Borhegyi Z, Csicsvari J, Mamiya A, Harris KD, Buzsa´ki G (2000) Intracellularfeatures predicted by extracellular recordings in the hippocampus in vivo. JNeurophysiol 84:390–400. → page 3, 4, 22, 58, 80, 92, 104Herikstad R, Baker J, Lachaux JP, Gray CM, Yen SC (2011) Natural movies evoke spike trainswith low spike time variability in cat primary visual cortex. J Neurosci 31:15844–15860. →page 7, 90, 137, 140, 148Herrero JL, Roberts MJ, Delicato LS, Gieselmann MA, Dayan P, Thiele A (2008) Acetylcholinecontributes through muscarinic receptors to attentional modulation in V1.Nature 454:1110–1114. → page 145Hill DN, Mehta SB, Kleinfeld D (2011) Quality metrics to accompany spike sorting ofextracellular signals. J Neurosci 31:8699–8705. → page 52, 62Hirata A, Castro-Alamancos MA (2010) Neocortex network activation and deactivation statescontrolled by the thalamus. J Neurophysiol 103:1147–1157. → page 150Hodgkin AL, Huxley AF (1939) Action potentials recorded from inside a nerve fibre.Nature 144:710–711. → page 1162Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and itsapplication to conduction and excitation in nerve. J Physiol 117:500–544. → page 2Hofer SB, Ko H, Pichler B, Vogelstein J, Ros H, Zeng H, Lein E, Lesica NA, Mrsic-Flogel TD(2011) Differential connectivity and response dynamics of excitatory and inhibitory neurons invisual cortex. Nature Neurosci 14:1045–1052. → page 142Hoffman KL, Battaglia FP, Harris K, MacLean JN, Marshall L, Mehta MR (2007) The upshot ofup states in the neocortex: from slow oscillations to memory formation. JNeurosci 27:11838–11841. → page 146Hopfield JJ (1995) Pattern recognition computation using action potential timing for stimulusrepresentation. Nature 376:33–36. → page 5, 140Horton JC, Adams DL (2005) The cortical column: a structure without a function. Phil Trans RSoc B 360:837–862. → page 148Hroma´dka T, DeWeese MR, Zador AM (2008) Sparse representation of sounds in theunanesthetized auditory cortex. PLoS Biol 6:e16. → page 81Hubel DH (1957) Tungsten microelectrode for recording from single units. Science 125:549–550.→ page 2Hubel DH, Wiesel TN (1959) Receptive fields of single neurones in the cat’s striate cortex. JPhysiol 148:574–591. → page 2, 72, 106Hubel DH, Wiesel TN (1962) Receptive fields, binocular interaction and functional architecturein the cat’s visual cortex. J Physiol 160:106–154. → page 2, 89, 106, 108, 141Hubel DH, Wiesel TN (1968) Receptive fields and functional architecture of monkey striatecortex. J Physiol 195:215–243. → page 2, 106Hulata E, Segev R, Ben-Jacob E (2002) A method for spike sorting and detection based onwavelet packets and Shannon’s mutual information. J Neurosci Meth 117:1–12. → page 24, 43Hunter JD (2007) Matplotlib: A 2D graphics environment. IEEE Comput Sci Eng Mag 9:90–95.→ page 181Hyva¨rinen A (1998) New approximations of differential entropy for independent componentanalysis and projection pursuit In Adv Neural Inf Process Syst, Vol. 10, pp. 273–279,Cambridge, MA. MIT Press. → page 59Hyva¨rinen A (1999) Fast and robust fixed-point algorithms for independent component analysis.IEEE Trans Neural Networks 10:626–634. → page 43Hyva¨rinen A, Karhunen J, Oja E (2001) Independent Component Analysis. Wiley-Interscience.→ page 41Hyva¨rinen A, Oja E (2000) Independent component analysis: algorithms and applications. NeuralNetworks 13:411–430. → page 43163Ikegaya Y, Aaron G, Cossart R, Aronov D, Lampl I, Ferster D, Yuste R (2004) Synfire chains andcortical songs: Temporal modules of cortical activity. Science 304:559–564. → page 5Ja¨ckel D, Frey U, Fiscella M, Franke F, Hierlemann A (2012) Applicability of independentcomponent analysis on high-density microelectrode array recordings. JNeurophysiol 108:334–348. → page 24, 26, 59Ji D, Wilson MA (2007) Coordinated memory replay in the visual cortex and hippocampusduring sleep. Nat Neurosci 10:100–107. → page 110Jog MS, Connolly CI, Kubota Y, Iyengar DR, Garrido L, Harlan R, Graybiel AM (2002) Tetrodetechnology: advances in implantable hardware, neuroimaging, and data analysis techniques. JNeurosci Meth 117:141–152. → page 3Johansson RS, Birznieks I (2004) First spikes in ensembles of human tactile afferents codecomplex spatial fingertip events. Nat Neurosci 7:170–177. → page 5Jones E, Oliphant T, Peterson P et al. (2001) SciPy: Open source scientific tools for Python. →page 181Jones EG, Peters A (1987) Cerebral Cortex – Further Aspects of Cortical Function, IncludingHippocampus, Vol. 6, chapter 7: Number of neurons and synapses in primary visual cortex,pp. 267–294. Plenum Press, New York. → page 4Kagan I, Gur M, Snodderly DM (2002) Spatial organization of receptive fields of V1 neurons ofalert monkeys: comparison with responses to gratings. J Neurophysiol 88:2557–2574. → page89, 90, 106, 107, 108Kandel ER, Schwartz JH, Jessell TM, Siegelbaum SA, Hudspeth AJ (2012) Principles of NeuralScience, Vol. 5. McGraw-Hill, New York. → page 6Kara P, Reinagel P, Reid RC (2000) Low response variability in simultaneously recorded retinal,thalamic, and cortical neurons. Neuron 27:635–646. → page 140Katzner S, Nauhaus I, Benucci A, Bonin V, Ringach DL, Carandini M (2009) Local origin of fieldpotentials in visual cortex. Neuron 61:35–41. → page 2, 136Kayser C, Einha¨user W, Ko¨nig P (2003) Temporal correlations of orientations in natural scenes.Neurocomputing 52:117–123. → page 19Kelly RC, Smith MA, Kass RE, Lee TS (2010) Local field potentials indicate network state andaccount for neuronal response variability. J Comput Neurosci 29:567–579. → page 2Kerr JND, Greenberg D, Helmchen F (2005) Imaging input and output of neocortical networks invivo. PNAS 102:14063–14068. → page 4, 80, 81, 82Kirchner H, Thorpe SJ (2006) Ultra-rapid object detection with saccadic eye movements: Visualprocessing speed revisited. Vision Res 46:1762–1776. → page 5Klusch M, Lodi S, Moro G (2003) Distributed clustering based on sampling local densityestimates In International Joint Conference on Artificial Intelligence, Vol. 18, pp. 485–490.Lawrence Erlbaum Associates Ltd. → page 61164Ko H, Hofer SB, Pichler B, Buchanan KA, Sjo¨stro¨m PJ, Mrsic-Flogel TD (2011) Functionalspecificity of local synaptic connections in neocortical networks. Nature 473:87–91. → page 5,142Koester HJ, Sakmann B (2000) Calcium dynamics associated with action potentials in singlenerve terminals of pyramidal cells in layer 2/3 of the young rat neocortex. JPhysiol 529:625–646. → page 4Kording KP (2011) Of toasters and molecular ticker tapes. PLoS Comput Biol 7:e1002291. →page 57, 155Kowalewski F (1995) A gradient procedure for determining clusters of relatively high pointdensity. Pattern Recognition 28:1973–1984. → page 61Krizhevsky A, Sutskever I, Hinton GE (2012) ImageNet classification with deep convolutionalneural networks In Adv Neural Inf Process Syst, Vol. 25, pp. 1097–1105. Curran Associates,Inc. → page 6Latham PE, Roth A, Hausser M, London M (2006) Requiem for the spike? Soc NeurosciAbstr 36:432.12. → page 5Leach JB, Achyuta AKH, Murthy SK (2010) Bridging the divide between neuroprosthetic design,tissue engineering and neurobiology. Front Neuroeng 2:18. → page 82Lennie P (2003) The cost of cortical computation. Curr Biol 13:493–497. → page 1, 3, 22, 81, 140Lewicki MS (1994) Bayesian modeling and classification of neural signals. NeuralComput 6:1005–1030. → page 24Lewicki MS (1998) A review of methods for spike sorting: the detection and classification ofneural action potentials. Network 9:R53–R78. → page 22, 24, 40Li CY, Poo MM, Dan Y (2009) Burst spiking of a single cortical neuron modifies global brainstate. Science 324:643–646. → page 121Linde´n H, Tetzlaff T, Potjans TC, Pettersen KH, Gru¨n S, Diesmann M, Einevoll GT (2011)Modeling the spatial reach of the LFP. Neuron 72:859–872. → page 2Ling G, Gerard RW (1949) The normal membrane potential of frog sartorius fibers. J CellCompar Physl 34:383–396. → page 2Litke AM, Bezayiff N, Chichilnisky EJ, Cunningham W, Dabrowski W, Grillo AA, Grivich M,Grybos P, Hottowy P, Kachiguine S, Kalmar RS, Mathieson K, Petrusca D, Rahman M, SherA (2004) What does the eye tell the brain?: Development of a system for the large-scalerecording of retinal output activity. IEEE Trans Nucl Sci 51:1434–1440. → page 24, 62Liu X, McCreery DB, Carter RR, Bullara LA, Yuen TGH, Agnew WF (1999) Stability of theinterface between neural tissue and chronically implanted intracortical microelectrodes. IEEETrans Rehabil Eng 7:315–326. → page 82London M, Roth A, Beeren L, Ha¨usser M, Latham PE (2010) Sensitivity to perturbations in vivoimplies high noise and suggests rate coding in cortex. Nature 466:123–127. → page 5165Lowe DG (2004) Distinctive image features from scale-invariant keypoints. Int J ComputVision 60:91–110. → page 6Luczak A, Bartho P, Harris KD (2013) Gating of sensory input by spontaneous cortical activity.J Neurosci 33:1684–1695. → page 5, 80, 146, 147Luczak A, Bartho´ P, Marguet SL, Buzsa´ki G, Harris KD (2007) Sequential structure ofneocortical spontaneous activity in vivo. PNAS 104:347. → page 5, 89, 104, 105, 146, 147, 149Lu¨tcke H, Murayama M, Hahn T, Margolis DJ, Astori S, zum Alten Borgloh SM, Go¨bel W, YangY, Tang W, Ku¨gler S, Sprengel R, Takeharu N, Miyawaki A, Larkum ME, Hlemchen F, HasanMT (2010) Optical recording of neuronal activity with a genetically-encoded calcium indicatorin anesthetized and freely moving mice. Front Neural Circuits 4:9. → page 4MacKay DJC (2003) Information Theory, Inference, and Learning Algorithms, chapter 20: AnExample Inference Task: Clustering, pp. 284–292. Cambridge Univ Pr. → page 26Mackevicius EL, Best MD, Saal HP, Bensmaia SJ (2012) Millisecond precision spike timingshapes tactile perception. J Neurosci 32:15309–15317. → page 5Maffei L, Fiorentini A, Bisti S (1973) Neural correlate of perceptual adaptation to gratings.Science 182:1036–1038. → page 18, 179Mainen ZF, Sejnowski TJ (1995) Reliability of spike timing in neocortical neurons.Science 268:1503–1506. → page 5, 114, 140Mank M, Santos AF, Direnberger S, Mrsic-Flogel TD, Hofer SB, Stein V, Hendel T, Reiff DF,Levelt C, Borst A, Bonhoeffer T, Hu¨bener M, Griesbeck O (2008) A genetically encodedcalcium indicator for chronic in vivo two-photon imaging. Nat Methods 5:805–811. → page 4Marguet SL, Harris KD (2011) State-dependent representation of amplitude-modulated noisestimuli in rat auditory cortex. J Neurosci 31:6414–6420. → page 6, 111, 148, 149Markram H, Tsodyks M (1996) Redistribution of synaptic efficacy between neocortical pyramidalneurons. Nature 382:807–810. → page 82Marre O, Amodei D, Deshmukh N, Sadeghi K, Soo F, Holy TE, Berry II MJ (2012) Mapping acomplete neural population in the retina. J Neurosci 32:14859–14873. → page 24, 26, 62Massimini M, Huber R, Ferrarelli F, Hill S, Tononi G (2004) The sleep slow oscillation as atraveling wave. J Neurosci 24:6862–6870. → page 149Mata ML, Ringach DL (2005) Spatial overlap of on and off subregions and its relation toresponse modulation ratio in macaque primary visual cortex. J Neurophysiol 93:919–928. →page 90, 106, 107, 143McCormick DA, Connors BW, Lighthall JW, Prince DA (1985) Comparative electrophysiology ofpyramidal and sparsely spiny stellate neurons of the neocortex. J Neurophysiol 54:782–806. →page 58, 92, 103, 105166McGuinness LP, Yan Y, Stacey A, Simpson DA, Hall LT, Maclaurin D, Prawer S, Mulvaney P,Wrachtrup J, Caruso F, Scholten RE, Hollenberg LCL (2011) Quantum measurement andorientation tracking of fluorescent nanodiamonds inside living cells. NatureNanotechnol 6:358–363. → page 155McNaughton BL, O’Keefe J, Barnes CA (1983) The stereotrode: a new technique forsimultaneous isolation of several single units in the central nervous system from multiple unitrecords. J Neurosci Meth 8:391–397. → page 3, 22Mechler F, Ringach DL (2002) On the classification of simple and complex cells. VisionRes 42:1017–1033. → page 90, 143Mitchell JF, Sundberg KA, Reynolds JH (2007) Differential attention-dependent responsemodulation across cell classes in macaque visual area V4. Neuron 55:131–141. → page 89, 104Mitchell JF, Sundberg KA, Reynolds JH (2009) Spatial attention decorrelates intrinsic activityfluctuations in macaque area V4. Neuron 63:879–888. → page 149Mittmann W, Wallace DJ, Czubayko U, Herb JT, Schaefer AT, Looger LL, Denk W, Kerr JND(2011) Two-photon calcium imaging of evoked activity from l5 somatosensory neurons in vivo.Nat Neurosci 14:1089–1093. → page 4Mitzdorf U (1985) Current source-density method and application in cat cerebral cortex:investigation of evoked potentials and EEG phenomena. Physiol Rev 65:37–100. → page 86Mizuseki KS A, Pastalkova E, Buzsa´ki G (2009) Theta oscillations provide temporal windows forlocal circuit computation in the entorhinal-hippocampal loop. Neuron 64:267–280. → page 89,104Mizuseki K, Buzsa´ki G (2013) Preconfigured, skewed distribution of firing rates in thehippocampus and entorhinal cortex. Cell Reports 4:1010–1021. → page 22, 81Mohajerani MH, McVea DA, Fingas M, Murphy TH (2010) Mirrored bilateral slow-wave corticalactivity within local circuits revealed by fast bihemispheric voltage-sensitive dye imaging inanesthetized and awake mice. J Neurosci 30:3745–3751. → page 149, 154Murtagh F, Contreras P (2012) Algorithms for hierarchical clustering: an overview. WIREs DataMining Knowl Discov 2:86–97. → page 27Nason GP, Sibson R (1992) Measuring multimodality. Stat Comput 2:153–160. → page 60Nguyen DP, Frank LM, Brown EN (2003) An application of reversible-jump markov chain montecarlo to spike classification of multi-unit extracellular recordings. Network 14:61–82. → page 24Niell CM, Stryker MP (2008) Highly selective receptive fields in mouse visual cortex. JNeurosci 28:7520–7536. → page 89, 104Nirenberg S, Carcieri SM, Jacobs AL, Latham PE (2001) Retinal ganglion cells act largely asindependent encoders. Nature 411:698–701. → page 62167Nowak LG, Azouz R, Sanchez-Vives MV, Gray CM, McCormick DA (2003) Electrophysiologicalclasses of cat primary visual cortical neurons in vivo as revealed by quantitative analyses. JNeurophysiol 89:1541–1566. → page 90, 103Ohiorhenuan IE, Mechler F, Purpura KP, Schmid AM, Hu Q, Victor JD (2010) Sparse coding andhigh-order correlations in fine-scale cortical networks. Nature 466:617–621. → page 154, 178Ohki K, Chung S, Ch’ng YH, Kara P, Reid RC (2005) Functional imaging with cellular resolutionreveals precise micro-architecture in visual cortex. Nature 433:597–603. → page 4, 87Ohki K, Chung S, Kara P, Hu¨bener M, Bonhoeffer T, Reid RC (2006) Highly orderedarrangement of single neurons in orientation pinwheels. Nature 442:925–928. → page 4O’Keefe J, Recce ML (1993) Phase relationship between hippocampal place units and the EEGtheta rhythm. Hippocampus 3:317–330. → page 3Okun M, Yger P, Marguet SL, Gerard-Mercier F, Benucci A, Katzner S, Busse L, Carandini M,Harris KD (2012) Population rate dynamics and multineuron firing patterns in sensory cortex.J Neurosci 32:17108–17119. → page 121, 129, 149, 154Oliphant TE (2006) Guide to NumPy Provo, UT. → page 181Olshausen BA, Field DJ (1996) Emergence of simple-cell receptive field properties by learning asparse code for natural images. Nature 381:607–609. → page 5, 7, 8, 81, 140Olshausen BA, Field DJ (2000) Vision and the coding of natural images. Am Sci 88:238–245. →page 7Olshausen BA, Field DJ (2004) Sparse coding of sensory inputs. Curr OpinNeurobiol 14:481–487. → page 5, 8, 81Olshausen BA, Field DJ (2005) How close are we to understanding V1? NeuralComput 17:1665–1699. → page 3, 7, 81, 82, 110, 141Oram MW, Wiener MC, Lestienne R, Richmond BJ (1999) Stochastic nature of precisely timedspike patterns in visual system neuronal responses. J Neurophysiol 81:3021–3033. → page 5Pachitariu M, Lyamzin DR, Sahani M, Lesica NA (2015) State-dependent population coding inprimary auditory cortex. J Neurosci 35:2058–2073. → page 111, 148, 149Pascoe PJ, Ilkiw JE, Frischmeyer KJ (2006) The effect of the duration of propofol administrationon recovery from anesthesia in cats. Vet Anaesth Analg 33:2–7. → page 146Payne B, Peters A (2001) The Cat Primary Visual Cortex. Academic Press, San Diego, CA. →page 4, 15Pedreira C, Martinez J, Ison MJ, Quian Quiroga R (2012) How many neurons can we see withcurrent spike sorting algorithms? J Neurosci Meth 211:58–65. → page 59Pe´rez F, Granger BE (2007) IPython: a System for Interactive Scientific Computing. IEEEComput Sci Eng Mag 9:21–29. → page 181168Perin R, Berger TK, Markram H (2011) A synaptic organizing principle for cortical neuronalgroups. PNAS 108:5419–5424. → page 5Perkel DH, Gerstein GL, Moore GP (1967) Neuronal spike trains and stochastic point processes:II. Simultaneous spike trains. Biophys J 7:419–440. → page 90Petersen CCH, Hahn TTG, Mehta M, Grinvald A, Sakmann B (2003) Interaction of sensoryresponses with spontaneous depolarization in layer 2/3 barrel cortex. PNAS 100:13638–13643.→ page 6, 110, 147, 149Pillow JW, Shlens J, Chichilnisky EJ, Simoncelli EP (2013) A model-based spike sortingalgorithm for removing correlation artifacts in multi-neuron recordings. PLoS ONE 8:e62123.→ page 24, 62Polikov VS, Tresco PA, Reichert WM (2005) Response of brain tissue to chronically implantedneural electrodes. J Neurosci Meth 148:1–18. → page 82Poulet JFA, Frenandez LMJ, Crochet S, Petersen CCH (2012) Thalamic control of cortical states.Nat Neurosci 15:370–372. → page 121Poulet JFA, Petersen CCH (2008) Internal brain state regulates membrane potential synchrony inbarrel cortex of behaving mice. Nature 454:881–885. → page 121, 149Pouzat C, Delescluse M, Viot P, Diebolt J (2004) Improved spike-sorting by modeling firingstatistics and burst-dependent spike amplitude attenuation: a markov chain monte carloapproach. J Neurophysiol 91:2910–2928. → page 24Prentice JS, Homann J, Simmons KD, Tkacˇik G, Balasubramanian V, Nelson PC (2011) Fast,scalable, Bayesian spike identification for multi-electrode arrays. PLoS ONE 6:e19884. → page24, 26, 62Priebe NJ, Mechler F, Carandini M, Ferster D (2004) The contribution of spike threshold to thedichotomy of cortical simple and complex cells. Nat Neurosci 7:1113–1122. → page 90, 107, 143Quian Quiroga R, Nadasdy Z, Ben-Shaul Y (2004) Unsupervised spike detection and sorting withwavelets and superparamagnetic clustering. Neural Comput 16:1661–1687. → page 24, 27, 30,43, 45Reich DS, Victor JD, Knight BW, Ozaki T, Kaplan E (1997) Response variability and timingprecision of neuronal spike trains in vivo. J Neurophysiol 77:2836–2841. → page 140Reid RC, Alonso JM (1995) Specificity of monosynaptic connections from thalamus to visualcortex. Nature 378:281–283. → page 142Reid RC, Victor JD, Shapley RM (1997) The use of m-sequences in the analysis of visualneurons: Linear receptive field properties. Visual Neurosci 14:1015–1027. → page 19Reimann MW, Anastassiou CA, Perin R, Hill SL, Markram H, Koch C (2013) A biophysicallydetailed model of neocortical local field potentials predicts the critical role of active membranecurrents. Neuron 79:375–390. → page 2169Reinagel P, Reid RC (2000) Temporal coding of visual information in the thalamus. JNeurosci 20:5392–400. → page 140Reinagel P, Reid RC (2002) Precise firing events are conserved across neurons. JNeurosci 22:6837–6841. → page 140Renart A, de la Rocha J, Bartho P, Hollender L, Parga N, Reyes A, Harris KD (2010) Theasynchronous state in cortical circuits. Science 327:587–590. → page 121, 129, 142, 149, 178Renshaw B, Forbes A, Morison BR (1940) Activity of isocortex and hippocampus: electricalstudies with microelectrodes. J Neurophysiol 3:74–105. → page 2Ringach D, Shapley R (2004) Reverse correlation in neurophysiology. Cognitive Sci 28:147–166.→ page 89Ringach DL, Hawken MJ, Shapley R (1997a) Dynamics of orientation tuning in macaque primaryvisual cortex. Nature 387:281–284. → page 18, 75, 108Ringach DL, Hawken MJ, Shapley R (2002a) Receptive field structure of neurons in monkeyprimary visual cortex revealed by stimulation with natural image sequences. J Vision 2:12–24.→ page 90, 107Ringach DL, Hawken MJ, Shapley R (2003) Dynamics of orientation tuning in macaque V1: therole of global and tuned suppression. J Neurophysiol 90:342–352. → page 108Ringach DL, Sapiro G, Shapley R (1997b) A subspace reverse-correlation technique for the studyof visual neurons. Vision Res 37:2455–2464. → page 18, 75, 108Ringach DL, Shapley RM, Hawken MJ (2002b) Orientation selectivity in macaque V1: diversityand laminar dependence. J Neurosci 22:5639–5651. → page 87Robbins AA, Fox SE, Holmes GL, Scott RC, Barry JM (2013) Short duration waveformsrecorded extracellularly from freely moving rats are representative of axonal activity. FrontNeural Circuits 7:181. → page 104Rodriguez A, Laio A (2014) Clustering by fast search and find of density peaks.Science 344:1492–1496. → page 61, 62Roelfsema PR, Lamme VAF, Spekreijse H (1998) Object-based attention in the primary visualcortex of the macaque monkey. Nature 395:376–381. → page 110, 149Sakata S, Harris KD (2009) Laminar structure of spontaneous and sensory-evoked populationactivity in auditory cortex. Neuron 64:404–418. → page 81, 86, 89, 92, 104, 105, 121, 145, 147Sakata S, Harris KD (2012) Laminar-dependent effects of cortical state on auditory corticalspontaneous activity. Front Neural Circuits 6:109. → page 6, 124, 129, 145, 146Sakuraba S, Tsujita M, Arisaka H, Takeda J, Yoshida K, Kuwana SI (2009) Donepezil reversesbuprenorphine-induced central respiratory depression in anesthetized rabbits. BiolRes 42:469–475. → page 124170Salami M, Itami C, Tsumoto T, Kimura F (2003) Change of conduction velocity by regionalmyelination yields constant latency irrespective of distance between thalamus and cortex.PNAS 100:6174–6179. → page 5Saleem AB, Ayaz A, Jeffery KJ, Harris KD, Carandini M (2013) Integration of visual motion andlocomotion in mouse visual cortex. Nat Neurosci 16:1864–1869. → page 110Saleem AB, Chadderton P, Apergis-Schoute J, Harris KD, Schultz SR (2010) Methods forpredicting cortical UP and DOWN states from the phase of deep layer local field potentials. JComput Neurosci 29:49–62. → page 121, 129Sanchez-Vives MV, McCormick DA (2000) Cellular and network mechanisms of rhythmicrecurrent activity in neocortex. Nat Neurosci 3:1027–1034. → page 110, 126Sasaki T, Takahashi N, Matsuki N, Ikegaya Y (2008) Fast and accurate detection of actionpotentials from somatic calcium fluctuations. J Neurophysiol 100:1668–1676. → page 4Schiller PH, Finlay BL, Volman SF (1976a) Quantitative studies of single-cell properties inmonkey striate cortex. I. Spatiotemporal organization of receptive fields. JNeurophysiol 39:1288–1319. → page 89, 108Schiller PH, Finlay BL, Volman SF (1976b) Quantitative studies of single-cell properties inmonkey striate cortex. II. Orientation specificity and ocular dominance. JNeurophysiol 39:1320–1333. → page 87Schjetnan AGP, Luczak A (2011) Recording large-scale neuronal ensembles with silicon probes inthe anesthetized rat. J Vis Exp 56:e3282. → page 80, 153Schneidman E, Berry II MJ, Segev R, Bialek W (2006) Weak pairwise correlations imply stronglycorrelated network states in a neural population. Nature 440:1007–1012. → page 52, 154, 178Scho¨lvinck ML, Saleem AB, Benucci A, Harris KD, Carandini M (2015) Cortical state determinesglobal variability and correlations in visual cortex. J Neurosci 35:170–178. → page 149, 178Scholz M, Gibon Y, Stitt M, Selbig J (2004) Independent component analysis of starch deficientpgm mutants In Proceedings of the German Conference on Bioinformatics, pp. 95–104.Gesellschaft fu¨r Informatik, Bielefeld, Germany. → page 43Schwartz O, Pillow JW, Rust NC, Simoncelli EP (2006) Spike-triggered neural characterization.J Vision 6:484–507. → page 90Segev R, Goodhouse J, Puchalla J, Berry II MJ (2004) Recording spikes from a large fraction ofthe ganglion cells in a retinal patch. Nat Neurosci 7:1155–1162. → page 5, 24, 26, 62Shadlen MN, Newsome WT (1998) The variable discharge of cortical neurons: Implications forconnectivity, computation, and information coding. J Neurosci 18:3870–3896. → page 5Shapley R, Reid RC, Soodak R (1991) Spatiotemporal receptive fields and direction selectivity InLandy MS, Movshon JA, editors, Computational Models of Visual Processing, pp. 109–118.MIT Press, Cambridge, MA. → page 19171Sharpee T, Rust NC, Bialek W (2004) Analyzing neural responses to natural signals: maximallyinformative dimensions. Neural Comput 16:223–250. → page 90, 107Shlens J (2009) A tutorial on principal component analysis. Salk Insitute for Bio