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

Devalle, Federico; Roxin, Alex; Montbrió, Ernest, 1974-

doi:http://dx.doi.org/10.1371/journal.pcbi.1005881

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

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Citació

Devalle F, Roxin A, Montbrió E. Firing rate equations require a spike synchrony mechanism to correctly describe fast oscillations in inhibitory networks. PLoS Comput Biol. 2017;13(12):e1005881. DOI: 10.1371/journal.pcbi.1005881

Resum

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 Class 1 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.