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

摘要

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 I_K=g_K( V- E_k), where g)K is the membrane's K~+ current conductance and E_K is the K~+ Nernst potential. However, I_K has a nonlinear dependence on (V-E_K) well described by the Goldman-Hodgkin-Katz equation that determines the voltage dependence of G_K 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 I_K =g_K( V- E_K) to describe K+ currents in a wide variety of biological preparations.