Impact of network structure and cellular response on spike time correlations

TL;DR

This paper develops a theoretical framework to understand how network architecture and cellular dynamics influence spike time correlations in neural populations, with explicit formulas for correlations in various network configurations.

Contribution

It extends linear response theory to general integrate-and-fire networks, providing explicit correlation expressions and analyzing the effects of network balance and architecture.

Findings

Correlations depend strongly on neuronal operating points.

Explicit formulas for correlations in large networks.

Balance of excitation and inhibition affects correlation structure.

Abstract

Novel experimental techniques reveal the simultaneous activity of larger and larger numbers of neurons. As a result there is increasing interest in the structure of cooperative -- or correlated -- activity in neural populations, and in the possible impact of such correlations on the neural code. A fundamental theoretical challenge is to understand how the architecture of network connectivity along with the dynamical properties of single cells shape the magnitude and timescale of correlations. We provide a general approach to this problem by extending prior techniques based on linear response theory. We consider networks of general integrate-and-fire cells with arbitrary architecture, and provide explicit expressions for the approximate cross-correlation between constituent cells. These correlations depend strongly on the operating point (input mean and variance) of the neurons, even when connectivity is fixed. Moreover, the approximations admit an expansion in powers of the matrices that describe the network architecture. This expansion can be readily interpreted in terms of paths between different cells. We apply our results to large excitatory-inhibitory networks, and demonstrate first how precise balance --- or lack thereof --- between the strengths and timescales of excitatory and inhibitory synapses is reflected in the overall correlation structure of the network. We then derive explicit expressions for the average correlation structure in randomly connected networks. These expressions help to identify the important factors that shape coordinated neural activity in such networks.