[Mathematical model of neuronal adaptation taking into account the effect of calcium on membrane permeability to potassium ions]

Abstract

A model of the adaptive neurone was suggested to base on the effect of increasing the potassium permeability during the increasing the intracellular calcium concentration. Calcium accumulation occurs due to entrance of calcium ions into the cell in the course of the potential action development. Extent of influence of the intracellular calcium on the potassium permeability and velocity of moving the calcium off the cell was obtained from Meech's results. Frankenhauzer--Huxley equation was used for computation of membrane excitation, however, in our case the subthreshold potassium inactivation was reduced. Thus, the adaptation phenomenon was simulated in the following succession: 1) calcium accumulation in the cell, 2) increasing the potassium permeability, 3) increasing the after hyperpolarization and 4) increasing the interspike intervals.