BISTABILITY IN CEREBELLAR PURKINJE-CELL DENDRITES MODELED WITH HIGH-THRESHOLD CALCIUM AND DELAYED-RECTIFIER POTASSIUM CHANNELS

Phase-plane analysis of the ionic currents underlying dendritic platea u potentials was carried out to study the nonlinear dynamics and stead y-state transfer properties of the dendritic tree in cerebellar Purkin je 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 rel ationship, we derive concise, algebraic expressions for the voltage an d current thresholds of state transitions as functions of specific con ductance. The significance of bistability in this ion-channel system i s discussed with respect to the generation of plateau potentials in Pu rkinje cells dendrites and the role of the cerebellum in motor control .