Electrodiffusion in Membranes

Abstract

Of the many membrane transport processes now known, those of diffusion and electric current flow were the earliest to be studied, are the simplest, and together are especially suited to the analysis of problems of ionic movement. Electrodiffusion is a passive process by which charged particles are transported through a medium under the influence of two simultaneously acting forces, namely, the gradients of particle density and electric potential. The particle flows are given as the sum of these two forces, each multiplied by a coefficient that serves as a facilitating factor or conductance. When the particles are relatively small and the media are very dilute aqueous solutions, the diffusional force is the particle concentration; otherwise the thermodynamic activity, as defined by G. N. Lewis, takes its place. The complexity of the conductance factor depends on the nature of the ions and the structure of the medium. These conductances are not well understood in any but the simplest cases. In addition, in real systems additional forces are usually present, for example, thermal, mechanical, and magnetic; fortunately, in most systems of practical interest to the physical chemist and the biologist, these can be neglected or treated as minor perturbations. The equation expressing the electrodiffusion process is known as the Nernst-Planck equation. There is one such equation for each participating ion species, but because the electric field strength is also a variable, another equation is needed to complete the system. This is the Poisson equation, which relates the electric field strength to the net charge density at any point. The charge density in turn depends on all the ions present, whether mobile or fixed. This equation is the differential form of Gauss’s law of electrostatics. In addition, there are both physical and geometrical boundary conditions that must be met.