Structured chaos shapes spike-response noise entropy in balanced neural networks.

Guillaume Lajoie,Jean-Philippe Thivierge,Eric Shea-Brown

doi:10.3389/fncom.2014.00123

Abstract

Large networks of sparsely coupled, excitatory and inhibitory cells occur throughout the brain. For many models of these networks, a striking feature is that their dynamics are chaotic and thus, are sensitive to small perturbations. How does this chaos manifest in the neural code? Specifically, how variable are the spike patterns that such a network produces in response to an input signal? To answer this, we derive a bound for a general measure of variability—spike-train entropy. This leads to important insights on the variability of multi-cell spike pattern distributions in large recurrent networks of spiking neurons responding to fluctuating inputs. The analysis is based on results from random dynamical systems theory and is complemented by detailed numerical simulations. We find that the spike pattern entropy is an order of magnitude lower than what would be extrapolated from single cells. This holds despite the fact that network coupling becomes vanishingly sparse as network size grows—a phenomenon that depends on “extensive chaos,” as previously discovered for balanced networks without stimulus drive. Moreover, we show how spike pattern entropy is controlled by temporal features of the inputs. Our findings provide insight into how neural networks may encode stimuli in the presence of inherently chaotic dynamics.

Highlights

IntroductionWe study population level spiking responses in a neural network model with sparse, random connectivity and balanced excitation and inhibition
If a time-dependent signal is presented to a network whose dynamics are chaotic and whose initial conditions cannot be perfectly controlled, how much variability can one expect in its responses? Such a scenario is central to questions of stimulus encoding in the brain.In this article, we study population level spiking responses in a neural network model with sparse, random connectivity and balanced excitation and inhibition
Biological neural networks may operate in a chaotic regime, with irregular activity driven by a balance of fluctuating excitatory and inhibitory interactions

Summary

Introduction

We study population level spiking responses in a neural network model with sparse, random connectivity and balanced excitation and inhibition. Such models are ubiquitous in neuroscience, and reproduce the irregular firing that typifies cortical activity. Their autonomous activity is known to be chaotic, with extremely strong sensitivity of spike outputs to tiny changes in a network’s initial conditions (van Vreeswijk and Sompolinsky, 1998; London et al, 2010; Sun et al, 2010). Our goal is to add a stimulus drive, and understand the implications for the network spike patterns that result—a task made challenging by the fact that spikes are related to phase space dynamics in a highly non-linear way

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