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Finite size effects and rare events in balanced cortical networks with plastic synapses

Banff International Research Station for Mathematical Innovation and Discovery

Cortical neuron spiking activity is broadly classified as temporally irregular and asynchronous. Model networks with a balance between large recurrent excitation and inhibition capture these two key features, and are a popular framework relating circuit structure and network dynamics. Balanced networks stabilize the asynchronous state through reciprocal tracking by the inhibitory and excitatory population activity, leading to a cancellation of total current correlations driving cells within the network. While asynchronous network dynamics are often a good approximation of neural activity, in many cortical datasets there are nevertheless brief epochs wherein the network dynamics are transiently synchronized (Buzs?aki and Mizuseki, 2014,Tan et al., 2014). We analyze paired whole cell voltage-clamp recordings from spontaneously active neurons in mouse auditory cortex slices (Graupner and Reyes, 2013) showing a network where correlated excitation and inhibition effectively cancel, except for intermittent periods when the network shows a macroscopic synchronous event. These data suggest that while the core mechanics of balanced activity are important, we require new theories capturing these brief but powerful periods when balance fails. Traditional balanced networks with linear firing rate dynamics have a single attractor, and fail to exhibit macroscopic synchronous events. Mongillo et. al. (2012) showed that balanced networks with short-term synaptic plasticity can depart from strict linear dynamics through the emergence of multiple attractors. We extend this model by incorporating finite network size, introducing strong nonlinearities in the firing rate dynamics and allowing finite size induced noise to elicit large scale, yet infrequent, synchronous events. We carry out a principled finite size expansion of an associated Markovian birth-death process and identify core requirements for system size and network plasticity to capture the transient synchronous activity observed in our experimental data set. Our model properly mediates between the asynchrony of balanced activity and the tendency for strong recurrence to promote macroscopic population dynamics.

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

video/mp4

Author affiliation: University of Pittsburgh

2016-06-09

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/58273

Unreviewed

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