Dynamic flux tubes form reservoirs of stability in neuronal circuits

Abstract

Neurons in cerebral cortical circuits interact by sending and receiving electrical impulses called spikes. The ongoing spiking activity of cortical circuits is fundamental to many cognitive functions including sensory processing, working memory, and decision making. London et al. [Sensitivity to Perturbations In Vivo Implies High Noise and Suggests Rate Coding in Cortex, Nature (London) 466, 123 (2010).] recently argued that even a single additional spike can cause a cascade of extra spikes that rapidly decorrelate the microstate of the network. Here, we show theoretically in a minimal model of cortical neuronal circuits that single-spike perturbations trigger only a very weak rate response. Nevertheless, single-spike perturbations are found to rapidly decorrelate the microstate of the network, although the dynamics is stable with respect to small perturbations. The coexistence of stable and unstable dynamics results from a system of exponentially separating dynamic flux tubes around stable trajectories in the network's phase space. The radius of these flux tubes appears to decrease algebraically with neuron number N and connectivity K, which implies that the entropy of the circuit's repertoire of state sequences scales as N ln(KN).