A Discontinuous Model for Membrane Activity
A model for the excitable membrane is described. The model exhibits many types of firing patterns seen in excitable cells. The model includes potassium, sodium and calcium ions. These are affected by an active calcium pump, by potential dependent calcium, sodium and potassium conductances, and a calcium dependent potassium conductance. The cytosolic calcium concentration is buffered. Inactivation or time-delays of the conductances are not included, and the membrane capacity is zero. This leads to a discontinuous model, which is nevertheless capable of showing stable behavior, slow or fast spontaneous oscillations or bursting. To illustrate the generality of the model, it is adopted to mimic two specific cell types: a pancreatic β-cell and a cerebellar Purkinje cell.
KeywordsPurkinje Cell Membrane Capacity Cerebellar Purkinje Cell Catastrophe Theory Potassium Conductance
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