A model for rebound bursting in mammalian neurons.

In this paper we begin by simplifying our previous model of a thalamic neuron (Rose & Hindmarsh Proc. R. Soc. Lond. B 237, 289-312 (1989b)) by removal of the A current. A Ca(2+)-activated K+ current, with Ca2+ entering through T channels, is then added to give a model for a class of mammalian neurons in which the membrane potential oscillates in the subthreshold region following a hyperpolarizing current step. The properties of the model are represented using an experimentally observable bifurcation diagram. In the subthreshold region only three variables are required to explain the essential dynamic properties of the cell. In this three-dimensional space the solutions tend to lie on a surface which resembles a paraboloid. We use a simplified model of this model to explain both the dynamics of the solutions on this surface and the form of the bifurcation diagram.