title: Bursting excitable cell models by a slow Ca2+ current.
abstract: Bursting in excitable cells is a phenomenon that has attracted the interest of many electrophysiologists and non-linear dynamicists. In this paper, we present two models that give rise to bursting in action potentials. The membrane of the first model contains a voltage-activated Ca2+ channel that inactivates very slowly upon depolarization and a delayed K+ channel that is activated by voltage. This model consists of three dynamic variables--the gating variable of K+ channel (n), inactivation gating variable of the Ca2+ channel (f), and membrane potential (V). The membrane of the second model contains a voltage-activated Na+ channel that inactivates rather fast upon depolarization. This model contains altogether five dynamic variables--the Na+ inactivation gating variable (h) and Ca2+ activation variable (d), in addition to the three dynamic variables in the first model. With the first model, we show how various interesting bursting patterns may arise from such a simple three dynamic variable model. We also demonstrate that a slowly inactivating voltage-dependent Ca2+ channel may play the key role in the genesis of bursting. With the second model, we show how the participation of a quickly inactivating fast inward current may lead to a neuronal type of bursting, multi-peaked oscillations, and chaos, as the rates of the gating variables change.
authors.affiliation: Department of Biological Sciences, University of Pittsburgh, PA 15260.
authors.forename: T R
authors.initials: TR
authors.lastname: Chay
mesh_terms: D000200:Action Potentials / Q000502:physiology; D000818:Animals; D002118:Calcium / Q000502:physiology*; D015220:Calcium Channels / Q000502:physiology; D002462:Cell Membrane / Q000502:physiology; D015640:Ion Channel Gating / Q000502:physiology; D008954:Models, Biological; D009474:Neurons / Q000502:physiology*; D015221:Potassium Channels / Q000502:physiology; D012964:Sodium / Q000502:physiology
chemical_list: D015220:Calcium Channels; D015221:Potassium Channels; D012964:Sodium; D002118:Calcium