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Relating spontaneous dynamics and stimulus coding in competitive networks

Banff International Research Station for Mathematical Innovation and Discovery

Understanding the relation between spontaneously active and stimulus evoked cortical dynamics is a recent challenge in systems neuroscience. Recordings across several cortices show highly variable spike trains during spontaneous conditions, and that this variability is promptly reduced when a stimulus drives an evoked response. Networks of spiking neuron models with clustered excitatory architecture capture this key feature of cortical dynamics. In particular, clusters show stochastic transitions between periods of low and high firing rates, providing a mechanism for slow cortical variability that is operative in spontaneous states. We explore a simple Markov neural model with clustered architecture, where spontaneous and evoked stochastic dynamics can be examined more carefully. We model the activity of each cluster in the network as a birth-death Markov process, with positive self feedback and inhibitory cluster-cluster competition. Our Markov model allows a calculation of the expected transition times between low and high activity states, yielding an estimate of the invariant density of cluster activity. Using our theory, we explore how the strength of inhibitory connections between the clusters sets the maximum likelihood for the number of active clusters in the network during spontaneous conditions. We show that when the number of stimulated clusters matches the most-likely number of spontaneously active clusters then the mutual information between stimulus and response is maximized. This then gives a direct connection between the statistics of spontaneous activity and the coding capacity of evoked responses. Further, our work relates two disparate aspects of cortical computation lateral inhibition and stimulus coding.

Mathematics; Biology and other natural sciences; Probability theory and stochastic processes; Mathematical biology

video/mp4

Author affiliation: University of Pittsburgh

2016-06-07

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/58251

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/