Functional states of an excitable membrane and their dependence on its parameter values

The property of an excitable membrane of a nerve cell to change the type of electrical activity has been examined with the change of the value of applied current (I). The dependence of this property on the values of the membrane parameters is determined. Two different functional states depending on the values of the membrane parameters are considered. For one of the states a change in the value of I is accompanied by a change in the type of activity (damped periodic oscillations jump to undamped periodic oscillations or vice versa). For the other state the type of activity remains phasic (damped periodic oscillations) for each value of I. For the mathematical model of a membrane we have considered the problem of obtaining the boundary, partitioning the parameter space into the regions to which these functional states correspond. We suggest a mathematical set of this problem and give its algorithm. These boundaries have been constructed for two different variable parameters of the model. A good agreement between the boundaries and the experimental values of sodium and potassium conductances for different excitable membranes has been obtained.