Impact of Network Structure and Cellular Response on Spike Time Correlations
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. Is neural activity more than the sum of its individual parts? What is the impact of cooperative, or correlated, spiking among multiple cells? We can start addressing these questions, as rapid advances in experimental techniques allow simultaneous recordings from ever-increasing populations. However, we still lack a general understanding of the origin and consequences of the joint activity that is revealed. The challenge is compounded by the fact that both the intrinsic dynamics of single cells and the correlations among then vary depending on the overall state of the network. Here, we develop a toolbox that addresses this issue. Specifically, we show how linear response theory allows for the expression of correlations explicitly in terms of the underlying network connectivity and known single-cell properties – and that the predictions of this theory accurately match simulations of a touchstone, nonlinear model in computational neuroscience, the general integrate-and-fire cell. Thus, our theory should help unlock the relationship between network architecture, single-cell dynamics, and correlated activity in diverse neural circuits.