Bistability in cerebellar Purkinje cell dendrites modelled with high-threshold calcium and delayed-rectifier potassium channels

Phase-plane analysis of the ionic currents underlying dendritic plateau potentials was carried out to study the nonlinear dynamics and steady-state transfer properties of the dendritic tree in cerebellar Purkinje cells. The results of an analysis of the P-type calcium and delayed rectifier potassium channel system are presented in this study. These channels constitute a simple system that can support bistability and plateau potentials. By requiring both the steady-state current-voltage curve and nullclines to mimic basic plateau potential properties, we obtained well-defined ranges of specific conductance that can support bistability. Hysteresis was found to be surprisingly prevalent in this simple ion-channel system. Using the steady-state current voltage relationship, we derive concise, algebraic expressions for the voltage and current thresholds of state transitions as functions of specific conductance. The significance of bistability in this ion-channel system is discussed with respect to the generation of plateau potentials in Purkinje cells dendrites and the role of the cerebellum in motor control.