Abstract
The structure of spiking activity in cortical networks has important implications for how the brain ultimately codes sensory signals. However, our understanding of how network and intrinsic cellular mechanisms affect spiking is still incomplete. In particular, whether cell pairs in a neural network show a positive (or no) relationship between pairwise spike count correlation and average firing rate is generally unknown. This relationship is important because it has been observed experimentally in some sensory systems, and it can enhance information in a common population code. Here we extend our prior work in developing mathematical tools to succinctly characterize the correlation and firing rate relationship in heterogeneous coupled networks. We find that very modest changes in how heterogeneous networks occupy parameter space can dramatically alter the correlation–firing rate relationship.
Highlights
One prominent goal of theoretical neuroscience is to understand how spiking statistics of cortical networks are modulated by network attributes [9, 28, 42]
We showed that using a single-cell firing rate function to examine the relationship between correlations and firing rates is feasible for a wide range of heterogeneous, recurrent networks
We focused on three factors that can modulate the correlation–firing rate relationship: how the network occupies effective parameter space, strength of recurrent excitation, and strength of background noise
Summary
One prominent goal of theoretical neuroscience is to understand how spiking statistics of cortical networks are modulated by network attributes [9, 28, 42] This understanding is essential to the larger question of how sensory information is encoded and transmitted, because the statistics of neural activity impact population coding [7, 15,16,17, 37]. An important relationship observed in many experimental studies is that pairwise correlations on average increase with firing rates. The retinal studies involved cells with a clearly identified function, and allowed investigation of the coding consequences of the observed correlation–firing rate relationship. These studies found that the stimulusdependent correlation structure observed compared favorably to a structure in which stimulus-independent correlations were matched to their (stimulus-)averaged levels. The shape of susceptibility-firing curves did not appear to vary much with the strength of recurrent excitation (i.e., curves within each panel are similar)
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