Biophysical Journal 19: 125-140 (1977)
© 1977 the Biophysical Society

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A Single-File Model for Potassium Transport in Squid Giant Axon

Simulation of Potassium Currents at Normal Ionic Concentrations

ABSTRACT

A physical model for potassium transport in squid giant axon is proposed. The model is designed to explain the empirical data given by the Hodgkin-Huxley model and related experiments. It is assumed that K⁺ moves across the axon membrane by single-file diffusion through narrow pores. In the model a pore has three negatively charged sites that can be occupied alternatively by K⁺ or by a gating particle, GP⁺⁺, coming from the external surface. GP⁺⁺ is considered to be part of the membrane rather than a diffusible component of the surrounding solutions. A high activation barrier for GP⁺⁺ is supposed at the inner membrane border so that it cannot change over to the internal surface. Therefore potassium diffusion can be blocked by GP⁺⁺ penetrating into the pores. This mechanism controls the dynamic behaviour of the model. The time-dependent probabilities of the pore states are described by a system of differential equations. The rate constants in these equations depend on the ionic concentrations, the membrane voltage, and the electrostatic interaction between ions in a single pore. Detailed computational tests for normal composition of external and internal solutions show that the model agrees remarkably well with the stationary and dynamic behaviour of the Hodgkin-Huxley model. However, the hyperpolarization delay is not reproduced. A structural modification, concerning this delay and the way in which GP⁺⁺ is attached to the membrane, is proposed, and the qualitative behavior of the model at varied external and internal concentrations is discussed.