| Precise timing of spikes and synchronization in the millisecond range have been experimentally observed in different neuronal systems. Their occurrence correlates with external stimuli and might thus be a key feature of neural computation. The dynamical origin of precise and coordinated spike timing, however, is not well understood. Here we show in a modelling study that synchronous spiking activity of neuron subpopulations can persist and propagate in purely random networks if we take into account the non-additive nature of dendritic input integration that was recently uncovered experimentally. We find a transition from unstable to stable propagation of synchronized spiking: For additive coupling and at low strength of non-additivity synchronous spiking dies out; above a critical strength stable propagation of a group of synchronized spikes becomes possible. We derive a map yielding the average future size of a synchronous group in terms of the current group size. For networks with homogeneous parameters the map can be obtained analytically in Poissonian approximation and reveals that the discontinuous transition found is due to a tangent bifurcation at a critical strength of non-additivity. We discuss the mechanism underlying this transition and its consequences for networks with inhomogeneous parameters and additional external noise. Prominent standard models for the stable propagation of synchronous activity in cortical networks, 'synfire-chains', require embedded strong excitatory feed-forward structures. It is unclear, however, whether these structures actually exist in biological neural networks. Our study suggests that additional structural features of the network connectivity may not be required for the propagation of synchronous spiking activity in the presence of synaptic interactions with non-additive dendritic integration. |
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