Devalle, FedericoRoxin, AlexMontbrió, Ernest, 1974-2021-07-062021-07-062017Devalle 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.10058811553-734Xhttp://hdl.handle.net/10230/48086Recurrently 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.application/pdfeng© 2017 Devalle et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/articlehttp://dx.doi.org/10.1371/journal.pcbi.1005881NeuronsNeural networksAction potentialsSynapsesMembrane potentialBehaviourPhase diagramsNetwork analysisinfo:eu-repo/semantics/openAccess