Firing behavior in a nerve membrane model with long-term changes of a potassium conductance component

Abstract

The effects of an additional slow potassium conductance upon firing behavior have been investigated in a space-clamped nerve membrane model. The parameters were adjusted in such a way that in the resting state the equations were identical to the Hodgkin-Huxley equations for the space-clamped giant axon in squid. The firing behavior of this model was investigated for different forms of the steady-state relationship between slow potassium conductance and potential. Both continuous firing after an initial decrease of the firing frequency (typical adaptation), and either burst firing or accommodation, were found in most cases. In the cases of typical adaptation, the instantaneous time “constant” for reduction of the frequency decreased with time, that is, the firing frequency approached the steady-state level progressively faster than an exponential decay. In all cases it was found that the time constants for adaptation, durations of bursts and of the intervals between bursts, etc., were proportional to the time “constant” for the slow potassium conductance.