Correlations and Population Dynamics in Cortical Networks

Abstract

The function of cortical networks depends on the collective interplay between neurons and neuronal populations, which is reflected in the correlation of signals that can be recorded at different levels. To correctly interpret these observations it is important to understand the origin of neuronal correlations. Here we study how cells in large recurrent networks of excitatory and inhibitory neurons interact and how the associated correlations affect stationary states of idle network activity. We demonstrate that the structure of the connectivity matrix of such networks induces considerable correlations between synaptic currents as well as between subthreshold membrane potentials, provided Dale's principle is respected. If, in contrast, synaptic weights are randomly distributed, input correlations can vanish, even for densely connected networks. Although correlations are strongly attenuated when proceeding from membrane potentials to action potentials (spikes), the resulting weak correlations in the spike output can cause substantial fluctuations in the population activity, even in highly diluted networks. We show that simple mean-field models that take the structure of the coupling matrix into account can adequately describe the power spectra of the population activity. The consequences of Dale's principle on correlations and rate fluctuations are discussed in the light of recent experimental findings.

Large-scale neural dynamics: Simple and complex

“…In other situations equations going beyond the mean-field approach have been proposed that govern second-order correlations [100,101,102,103]. Indeed there has been a recent upsurge of interest in this area adapting methods from non-equilibrium statistical physics to determine corrections to mean-field theory involving equations for two-point and higher-order cumulants [104,105].…”

Functional and Effective Connectivity: A Review

“…We discuss examples of both. In terms of emergent behaviors, we will consider dynamics on structure (Bressler and Tognoli, 2006;Buice and Cowan, 2009;Coombes and Doole, 1996;Freeman, 1994Freeman, , 2005Kriener et al, 2008;Robinson et al, 1997;Rubinov et al, 2009;Tsuda, 2001) and how this behavior has been applied to characterizing autonomous or endogenous fluctuations in fMRI (e.g., Deco et al, 2009Deco et al, , 2011Ghosh et al, 2008;Honey et al, 2007Honey et al, , 2009). We will then consider causal models that are used to explain empirical observations.…”

Interpreting neurodynamics: concepts and facts

“…This implies time constants in the range of tens of milliseconds. Interestingly, on the level of neuronal populations, the same cells can operate on time scales in the rage of milliseconds, if they are part of a recurrent network (Kriener et al 2008). Population activity is one order of magnitude faster, although it occurs on a higher level of organization.…”

“…An additional twist on this argument refers to the fact that the network models considered in most studies of cortical dynamics have actually a ''random'' structure (Brunel 2000;Voges et al 2007;Kriener et al 2008). This means that they have a fixed complex wiring diagram which reflects the cortical wiring in a statistical sense (Braitenberg and Schüz 1998).…”