Oscillatory Mechanisms in Pairs of Neurons Connected with Fast Inhibitory Synapses

We study dynamical mechanisms underlying oscillatory behavior in reciprocal inhibitory pairs of neurons, using a two-dimensionalcell model. We introduce one-and-two dimensional phase portraits to illustratethe behaviors, thus reducing the study of dynamical mechanisms to planar geometrical properties. We examined whether other mechanisms besides the escape and release mechanisms (Wang and Rinzel, 1992) might be needed for some cases of reciprocal inhibition, and show that, within the confines of a simple two-dimensional cell model, escape and releaseare sufficient for all cases. We divided the behaviors of a singlecell into six different types and examined the joint behaviors arising from every combination of pairs of cells with behaviors drawn from thesesix types. For the case of two quiescent cells or two cells eachhaving plateau potentials, bifurcation diagrams demonstrate therelations between synaptic threshold and synaptic strength necessaryfor oscillations by escape, oscillations by release, ornetwork-generated plateau potentials. Thus we clarify therelationship between plateau potentials and oscillations in a cell.Using the two dimensional cell model we examine 1:N beating betweencells and find that our simple model displays many of the essentialdynamical properties displayed by more sophisticated models, some ofwhich relate to thalamocortical spindling.