Recurrent networks of dynamic elements frequently exhibit emergent collective oscillations, which can show 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 behaviour 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 high regularity observed experimentally in the brain as an instance of collective stochastic coherence.
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We thank A. Compte for useful comments, and our colleagues from CSIC-CNM in Barcelona (X. Villa, R. Villa, G. Gabriel) for providing the recording arrays used in Fig. 5. This work was supported by the Ministerio de Economia y Competividad and FEDER (Spain, projects FIS2012-37655-C02-01, to J.G.-O., and BFU2014-52467-R, to M.V.S.-V.) and EU project CORTICONIC (contract number 600806, to M.V.S.-V.). B.R. was supported by the FPI programme associated to BFU2011-27094 (Spain, Ministerio de Economia y Competividad). J.G.-O. acknowledges support from the ICREA Academia programme and from the Generalitat de Catalunya (project 2014SGR0974).
The authors declare no competing financial interests.
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Sancristóbal, B., Rebollo, B., Boada, P. et al. Collective stochastic coherence in recurrent neuronal networks. Nature Phys 12, 881–887 (2016). https://doi.org/10.1038/nphys3739
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