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-dimensional cell model. We introduce one-and-two dimensional phase portraits to illustrate the 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 release are sufficient for all cases. We divided the behaviors of a single cell into six different types and examined the joint behaviors arising from every combination of pairs of cells with behaviors drawn from these six types. For the case of two quiescent cells or two cells each having plateau potentials, bifurcation diagrams demonstrate the relations between synaptic threshold and synaptic strength necessary for oscillations by escape, oscillations by release, or network-generated plateau potentials. Thus we clarify the relationship between plateau potentials and oscillations in a cell. Using the two dimensional cell model we examine 1:N beating between cells and find that our simple model displays many of the essential dynamical properties displayed by more sophisticated models, some of which relate to thalamocortical spindling.