Global organization of neuronal activity only requires unstructured local connectivity

Abstract

Cortical connectivity mostly stems from local axonal arborizations, suggesting coordination is strongest between nearby neurons in the range of a few hundred micrometers. Yet multi-electrode recordings of resting-state activity in macaque motor cortex show strong positive and negative spike-count covariances between neurons that are millimeters apart. Here we show that such covariance patterns naturally arise in balanced network models operating close to an instability where neurons interact via indirect connections, giving rise to long-range correlations despite short-range connections. A quantitative theory explains the observed shallow exponential decay of the width of the covariance distribution at long distances. Long-range cooperation via this mechanism is not imprinted in specific connectivity structures but rather results dynamically from the network state. As a consequence, neuronal coordination patterns are not static but can change in a state-dependent manner, which we demonstrate by comparing different behavioral epochs of a reach-to-grasp experiment.

An estimation of the absolute number of axons indicates that human cortical areas are sparsely connected

“…These constraints encourage consideration of models of cortical function where connections are dense but mainly local. Neural models with multiple paths between cortical neurons due to numerous short connections can show long-range covariance and even synchrony [16][17][18][19] , and these have been observed experimentally in humans 20 . Lastly, it is useful to note that these quantitative considerations are radically different in other species, where the smaller number of cortical neurons and inter-areal distances allow greater connectivity between cortical areas, as well as a larger proportion of subcortical connectivity.…”

Strong and localized recurrence controls dimensionality of neural activity across brain areas

“…We show that a single number measuring the effective network connectivity at a given activity level, the spectral radius, is determined by local synaptic motifs and regulates not only the degree of criticality of network dynamics (32), but also the most basic aspect of their statistics: their dimensionality. Previous theoretical contributions linked average connectivity (33)(34)(35)(36)(37), the block and spatial structure of connectivity (38)(39)(40)(41)(42) or connectivity motifs (10,11,(43)(44)(45)(46)(47)(48)(49) to activity correlations, linked connectivity length and timescales (50) or low-rank structures (51) to low-dimensional activity patterns or linked general motifs and other network structures (5) to the spectral density of neural activity, emphasizing the consequence of reciprocal motifs for the dimension of network activity (52) (cf. Suppl.…”

A mean-field toolbox for spiking neuronal network model analysis

“…They allow studying pair-wise correlations of neuronal activity (Sejnowski, 1976;Ginzburg and Sompolinsky, 1994;Trousdale et al, 2012) and were able to reveal why pairs of neurons in random networks, despite receiving a high proportion of common input, can show low output correlations (Hertz, 2010;Renart et al, 2010;Tetzlaff et al, 2012;Helias et al, 2014), which for example has important implication for information processing. They describe pair-wise correlations in network with spatial organization (Rosenbaum and Doiron, 2014;Rosenbaum et al, 2017;Dahmen et al, 2021) and can be generalized to correlations of higher orders (Buice and Chow, 2013). Mean-field theories were utilized to show that neuronal networks can exhibit chaotic dynamics (Sompolinsky et al, 1988;van Vreeswijk and Sompolinsky, 1996;van Vreeswijk and Sompolinsky, 1998), in which two slightly different initial states can lead to totally different network responses, which has been linked to the network's memory capacity (Toyoizumi and Abbott, 2011;Schuecker et al, 2018).…”