ON BIOMEMBRANE ELECTRODIFFUSIVE MODELS

Two models are used in the literature, to study the electric behaviour of cellular membranes such as in protein aggregates, excitable media or ionic currents for examples. The first one is the Electroneutral Mo del based on Nernst-Planck and Poisson equations with a specific condi tion of microscopic electroneutrality. The second one is tile Cable Mo del valid for long wavelengths based on an analogy between an electric cable and a cell. Convincing experiments have justified the Cable equ ation. First, we show that these two models are in contradiction. More precisely the assumption of electroneutrality is not considered in th e Cable Model. The main difference between the two models is highlight ed by the analysis of the well known voltage instability due to a nega tive differential conductance. Then, we derive a new semi-microscopic model (the Biomembrane Electrodiffusive Model, called BEM) valid for p henomena at any wavelength. The BEM is based on Nernst-Planck and Pois son equations but, doesn't imply microscopic electroneutrality. It rev eals the capacitive behaviour of the membrane. In the limit of long wa velengths, one recovers the behaviour described within the Cable frame work, as shown precisely in the study of the negative differential con ductance analysis. Finally; we demonstrate the intimate link between t he last models: the Cable Model appears as the limit of the BEM for la rge wavelengths with some prerequisites which are discussed. The effec ts of geometry and asymmetrical media are introduced.