Abstract
A central question in neuroscience is to understand how noisy firing patterns are used to transmit information. Because neural spiking is noisy, spiking patterns are often quantified via pairwise correlations, or the probability that two cells will spike coincidentally, above and beyond their baseline firing rate. One observation frequently made in experiments, is that correlations can increase systematically with firing rate. Theoretical studies have determined that stimulus-dependent correlations that increase with firing rate can have beneficial effects on information coding; however, we still have an incomplete understanding of what circuit mechanisms do, or do not, produce this correlation-firing rate relationship. Here, we studied the relationship between pairwise correlations and firing rates in recurrently coupled excitatory-inhibitory spiking networks with conductance-based synapses. We found that with stronger excitatory coupling, a positive relationship emerged between pairwise correlations and firing rates. To explain these findings, we used linear response theory to predict the full correlation matrix and to decompose correlations in terms of graph motifs. We then used this decomposition to explain why covariation of correlations with firing rate—a relationship previously explained in feedforward networks driven by correlated input—emerges in some recurrent networks but not in others. Furthermore, when correlations covary with firing rate, this relationship is reflected in low-rank structure in the correlation matrix.
Highlights
One prominent goal of modern theoretical neuroscience is to understand how the features of cortical neural networks lead to modulation of spiking statistics [1,2,3]
One observation frequently made in experiments is that correlations can increase systematically with firing rate
We demonstrate in our networks that when correlation co-varies with firing rate, the (E-E) correlation matrix could be accurately modeled with a low-rank approximation, and the low-rank projection in this approximation was strongly associated with firing rate
Summary
One prominent goal of modern theoretical neuroscience is to understand how the features of cortical neural networks lead to modulation of spiking statistics [1,2,3] This understanding is essential to the larger question of how sensory information is encoded and transmitted, because such statistics are known to impact population coding [4,5,6,7,8]. Since a population of sensory neurons might change their firing rates in different ways to stimuli, uncovering the general mechanisms for when spiking correlations increases with firing rate (or when they do not) is important in the context of neural coding We study this question in a general recurrent neural network model
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