Multi-Ion And Transient Electrodiffusion

Abstract

In Chapter 7, we reviewed the theory of electrodiffusion as applied to a membrane traversed by a steady current of a single species of ions. Let us now consider two complications: multi-ion electrodiffusion and time-dependent electrodiffusion. We will also note that the system of electrodiffusion equations obeys a set of scaling rules. We close this chapter with a critique of the classical electrodiffusion model as applied to membranes containing voltage-sensitive ion channels. 1. MULTIPLE SPECIES OF PERMEANT IONS, STEADY STATE We now extend the discussion of the classical electrodiffusion model to the multi-ion case, which is important because membranes are permeated by multiple species of ions, and because of the role multiple ions play in ion-channel theory. We see from Equations 2.9 and 4.4 of Chapter 7, to be designated 7.2.9 and 7.4.4, that we have characterized ions by two properties, charge q (or valency Z) and mobility u. Let us begin by considering two ion species of the same charge; of course they will generally have different mobilities, say u 1 and u 2. We can say that they belong to the same charge class, and that they have the same valency. For example, Na + , K + , Li + and NH 4 + belong to the charge class with valency +1. Ions with valency-1, e.g. Cl-and Br-form a different charge class, and those with valency +2, e.g. Ca 2+ and Mg 2+ , a different one yet. The electrodiffusion problem of a system of ions in the same charge class, albeit of different mobilities, is much simpler than the more general problem in which valency also differs. 1.1. Ions of the same charge We can write the generalizations of Equations 7.2.9 and 7.4.4 for two ion species of the same charge class by the equations