The single-channel conductance in the classic cell membrane model

For a problem of dipolar polarization, the statistical field theory approach is used to investigate the nonlinear behaviour of the classic cell membrane model. We describe the ensemble of gating particles as a dipole distribution with fixed location in order to study the interaction with the transmembrane potential. It is shown that both polarization and random fluctuations modify the Hodgkin-Huxley equation of the cell membrane voltage. Within the framework of the Gaussian statistics, we derive the nonlinear evolution equation of a Brownian oscillating dipole with time-dependent characteristic frequency. By coupling the polarization to radiative transfer, a nonlinear PDE of reaction-diffusion type is derived which reduces in the linear approximation to the voltage cable type equation. The analysis is carried out within the framework of different forms of microcanonical description. The conceptual steps of the procedure are (i) the identification of the single-channel conductance as the time-dependent variance associated with the gyromotion of the gating particles, and (ii) the onset of propagation of the polarization front. It appears that the approach provides analytical tools suitable for applications in studying nonlinear models of excitable cells. (C) 2000 Elsevier Science Ltd. All rights reserved.