On the relationship between the number of negative slope regions in the voltage-current curve of the Hodgkin-Huxley model and its parameter values.

We consider the problem of the existence of a negative slope region (NSR) in the voltage-current curve of the neuronal membrane and the relationship between this phenomenon and the membrane parameters. For the Hodgkin-Huxley model it is proposed to determine the dependence of the number of NSR on the values of the maximal sodium (gNa) and potassium (gk) conductances. The method is suggested for constructing the boundaries on the (gNa, gk) plane, in passing through which the number of NSR changes to 1. Using the method we partition the (gNa, gk) plane into the regions corresponding to the curves with the different number of NSR. This number can be changed from 0 to 2 in changing the values of gNa and gk over the physiologically possible range.