[Time dependence of the reaction rate constant of potassium permeability of Ranvier's node membrane]

Abstract

To describe the kinetics of potassium permeability (conductance) changes in the squid giant axon membrane the Hodgkin--Huxley formulation uses a single first-order in time variable n with forward and backward rate constants, respectively alpha-n and beta-n, potential-dependent but time-independent. It has been shown by Frankenhaeuser that in the potassium-carrying system of the myelinated nerve fiber membrane of Xenopus laevis the rate constant beta-n is dependent on the duration of previous depolarization, i. e. the beta-n of this membrane is time-dependent. Started from the FitzHugh--Cole--Moore translation principle for potassium current experimental data of Frankenhaeuser have been analysed to show that the rate constant alpha-n in the X. laevis nerve fiber membrane is also time-dependent. To keep the conventional Hodgkin--Huxley formulation valid in case of the potassium-carrying system of the X. laevis nodal membrane involvement of an additional first--order in time component (n-II) has been postulated, which is compatible with Frankenhaeuser's experimental results. This component n-II appears to be identical to the n-II-component in the potassium-carrying system of the Rana ridibunda nerve fiber membrane. Both are rather slow and activated within the potential range more negative than the basic n-I-component (corresponding to Frankenhaeuser's variable n). The component n-I seems to be identical to the n-component of many other excitable membranes with fast action potentials. The existence of the third, very slow nIII-component is also possible. The independent components in question are believed to be associated with different independent potassium channels within the same membrane. It is likely that the existence of several independent components is a general feature of the potassium-carrying mechanism in the excitable membranes essential for a particular type of electrogenesis.