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.
Highlights
New multielectrode and imaging techniques are revealing the simultaneous activity of neural ensembles and, in some cases, entire neural populations [1,2,3,4]
We show how correlations between spike trains of cells can be approximated using response characteristics of individual cells along with information about synaptic dynamics, and the structure of the network
We start by briefly reviewing linear response theory of neuronal responses [28,34,35], and use it to approximate the correlation structure of a network
Summary
New multielectrode and imaging techniques are revealing the simultaneous activity of neural ensembles and, in some cases, entire neural populations [1,2,3,4] This has thrust upon the computational biology community the challenge of characterizing a potentially complex set of interactions – or correlations – among pairs and groups of neurons. Theoretical [9,10,11,14,15,16], and empirical studies [17,18,19] do not provide a consistent set of general principles about the impact of correlated activity This is largely because the presence of correlations can either strongly increase or decrease the fidelity of encoded information depending on both the structure of correlations across a population and how their impact is assessed
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