title: Irregular activity arises as a natural consequence of synaptic inhibition.
abstract: Irregular neuronal activity is observed in a variety of brain regions and states. This work illustrates a novel mechanism by which irregular activity naturally emerges in two-cell neuronal networks featuring coupling by synaptic inhibition. We introduce a one-dimensional map that captures the irregular activity occurring in our simulations of conductance-based differential equations and mathematically analyze the instability of fixed points corresponding to synchronous and antiphase spiking for this map. We find that the irregular solutions that arise exhibit expansion, contraction, and folding in phase space, as expected in chaotic dynamics. Our analysis shows that these features are produced from the interplay of synaptic inhibition with sodium, potassium, and leak currents in a conductance-based framework and provides precise conditions on parameters that ensure that irregular activity will occur. In particular, the temporal details of spiking dynamics must be present for a model to exhibit this irregularity mechanism and must be considered analytically to capture these effects.
authors.affiliation: Department of Mathematics, The Ohio State University, Columbus, Ohio 43210, USA.
authors.forename: D
authors.initials: D
authors.lastname: Terman
authors.affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA.
authors.forename: J E
authors.initials: JE
authors.lastname: Rubin
authors.affiliation: Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey 07102, USA.
authors.forename: C O
authors.initials: CO
authors.lastname: Diekman
mesh_terms: D006801:Humans; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D011188:Potassium / Q000378:metabolism; D012964:Sodium / Q000378:metabolism; D009435:Synaptic Transmission / Q000502:physiology*
chemical_list: D012964:Sodium; D011188:Potassium