Long-Range Neuronal Coordination Near the Breakdown of Linear Stability

Experimental findings suggest that cortical networks operate in a balanced state [1] in which strong recurrent inhibition suppresses single cell input correlations [2,3]. The balanced state, however, only restricts the average correlations in the network, the distribution of correlations between individual neurons is not constrained. We here investigate this distribution and establish a functional relation between the dynamical state of the system and the variance of correlations as a function of cortical distance. The former is characterized by the spectral radius, a measure for how strong a signal is damped while traversing the network. To this end, we develop a theory that captures the heterogeneity of correlations across neurons. Technically, we derive a mean-field theory that assumes the distribution of correlations to be self-averaging; i.e. the same in any realization of the random network. This is possible by taking advantage of the symmetry of the disorder-averaged [4] effective connectivity matrix. We here demonstrate that spatially organized, balanced network models predict rich pairwise correlation structures with spatial extent far beyond the range of direct connections [5]. Massively parallel spike recordings of macaque motor cortex quantitatively confirm this prediction. We show that the range of these correlations depends on the spectral radius, which offers a potential dynamical mechanism to control the spatial range on which neurons cooperatively perform computations