Collective Stochastic Coherence in Recurrent Neuronal Networks

Belén Sancristóbal, ∗ Beatriz Rebollo, Pol Boada, Maria V. Sanchez-Vives, 3, † and Jordi Garcia-Ojalvo † Departament of Experimental and Health Sciences, Universitat Pompeu Fabra, Barcelona Biomedical Research Park, 08003 Barcelona, Spain Institut de Investigacions Biomèdiques August Pi i Sunyer, 08036 Barcelona, Spain Institució Catalana de Recerca i Estudis Avançats (ICREA), 08010 Barcelona, Spain Abstract Recurrent networks of dynamic elements frequently exhibit emergent collective oscillations, which can display substantial regularity even when the individual elements are considerably noisy. How noise-induced dynamics at the local level coexists with regular oscillations at the global level is still unclear. Here we show that a combination of stochastic recurrence-based initiation with deterministic refractoriness in an excitable network can reconcile these two features, leading to maximum collective coherence for an intermediate noise level. We report this behavior in the slow oscillation regime exhibited by a cerebral cortex network under dynamical conditions resembling slow-wave sleep and anaesthesia. Computational analysis of a biologically realistic network model reveals that an intermediate level of background noise leads to quasi-regular dynamics. We verify this prediction experimentally in cortical slices subject to varying amounts of extracellular potassium, which modulates neuronal excitability and thus synaptic noise. The model also predicts that this effectively regular state should exhibit noise-induced memory of the spatial propagation profile of the collective oscillations, which is also verified experimentally. Taken together, these results allow us to construe the enhanced regularity observed experimentally in the brain as an instance of collective stochastic coherence.