CANCELLED - Synchronization, waves and stochasticity in spatially structured neuronal networks

Synchronization between distant brain regions, in the 20-30 Hz frequency range, has been observed in areas such as V1 or in the motor cortex during movement preparation. In order to shed light on these data, we have revisited the synchronization properties of distinct oscillating local Excitatory-Inhibitory (E-I) modules induced by distance-dependent long-range excitation. First, focusing on the sparsely synchronized oscillation regime which prevails in vivo, we have developed a rate model that accurately describes the stochastic oscillations of a single spiking E-I module. Second, we have considered the case of a chain of E-I modules with long-range excitation that decreases with distance. For modules of large sizes, complex dynamical regimes are observed in a sufficiently long chain, when long-range excitation mainly targets excitatory neurons. Synchronization of the module oscillations is otherwise observed. For modules with a moderate and biologically realistic size, stochasticity plays an important role in the observed dynamics. We show that its effect can be quantitatively described by modifications of the well-known Edwards-Wilkinson or KPZ equations. We analyse the resulting stochastic dynamics and discuss their relations to observed experimental observations.