A simple modification of the Hodgkin and Huxley equations explains type 3 excitability in squid giant axons

Abstract

The Hodgkin and Huxley (HH) model predicts sustained repetitive firing of nerve action potentials for a suprathreshold depolarizing current pulse for as long as the pulse is applied (type 2 excitability). Squid giant axons, the preparation for which the model was intended, fire only once at the beginning of the pulse (type 3 behaviour). This discrepancy between the theory and experiments can be removed by modifying a single parameter in the HH equations for the K+ current as determined from the analysis in this paper. K+ currents in general have been described by IK=gK(V-EK), where gK is the membrane's K+ current conductance and EK is the K+ Nernst potential. However, IK has a nonlinear dependence on (V-EK) well described by the Goldman-Hodgkin-Katz equation that determines the voltage dependence of gK. This experimental finding is the basis for the modification in the HH equations describing type 3 behaviour. Our analysis may have broad significance given the use of IK=gK(V-EK) to describe K+ currents in a wide variety of biological preparations.