When do Correlations Increase with Firing Rate?

TL;DR

This study investigates how pairwise neural correlations relate to firing rates in recurrent excitatory-inhibitory networks, revealing that stronger excitatory coupling induces a positive correlation-firing rate relationship explained by network motifs and low-rank correlation structures.

Contribution

The paper demonstrates that increased excitatory coupling in recurrent networks leads to correlations that grow with firing rate, using linear response theory and motif analysis to explain this phenomenon.

Findings

Stronger excitatory coupling induces positive correlation-firing rate relationships.

Correlation matrices exhibit low-rank structure when correlations covary with firing rate.

Motif decomposition explains the emergence of correlation-firing rate relationships in recurrent networks.

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 study 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 emerges 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.