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arXiv · 1705.09205

Firing rate equations require a spike synchrony mechanism to correctly describe fast oscillations in inhibitory networks

Federico Devalle·Alex Roxin·Ernest Montbrió
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Abstract

Recurrently coupled networks of inhibitory neurons robustly generate oscillations in the gamma band. Nonetheless, the corresponding Wilson-Cowan type firing rate equation for such an inhibitory population does not generate such oscillations without an explicit time delay. We show that this discrepancy is due to a voltage-dependent spike-synchronization mechanism inherent in networks of spiking neurons which is not captured by standard firing rate equations. Here we investigate an exact low-dimensional description for a network of heterogeneous canonical type-I inhibitory neurons which includes the sub-threshold dynamics crucial for generating synchronous states. In the limit of slow synaptic kinetics the spike-synchrony mechanism is suppressed and the standard Wilson-Cowan equations are formally recovered as long as external inputs are also slow. However, even in this limit synchronous spiking can be elicited by inputs which fluctuate on a time-scale of the membrane time-constant of the neurons. Our meanfield equations therefore represent an extension of the standard Wilson-Cowan equations in which spike synchrony is also correctly described.

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Federico Devalle, Alex Roxin, Ernest Montbrió. 2017-05-25. Firing rate equations require a spike synchrony mechanism to correctly describe fast oscillations in inhibitory networks. https://doi.org/10.1371/journal.pcbi.1005881

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