title: Bistability in cerebellar Purkinje cell dendrites modelled with high-threshold calcium and delayed-rectifier potassium channels.
abstract: 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.
authors.affiliation: Department of Physiology, Northwestern University Medical Center, Chicago, IL 60611, USA.
authors.forename: G L
authors.initials: GL
authors.lastname: Yuen
authors.forename: P E
authors.initials: PE
authors.lastname: Hockberger
authors.forename: J C
authors.initials: JC
authors.lastname: Houk
mesh_terms: D000200:Action Potentials; D000818:Animals; D015220:Calcium Channels / Q000502:physiology*; D051668:Delayed Rectifier Potassium Channels; D003712:Dendrites / Q000502:physiology*; D004553:Electric Conductivity; D008433:Mathematics; D008959:Models, Neurological; D015221:Potassium Channels / Q000502:physiology*; D024642:Potassium Channels, Voltage-Gated; D011689:Purkinje Cells / Q000502:physiology*
chemical_list: D015220:Calcium Channels; D051668:Delayed Rectifier Potassium Channels; D015221:Potassium Channels; D024642:Potassium Channels, Voltage-Gated