2.4.3—
The Nature and Origin of the Membrane Potential

It is clear that electrical potential differences across membranes are of great importance in generating driving forces on ions. It is important, therefore, to try to understand how these potentials arise and how they are maintained.

An electric potential difference arises because positive and negative charges become separated. Since the cytoplasm of most cells is electrically negative relative to the surroundings it is very slightly enriched in anions relative to cations. This can be attributed to the differential permeability of the cell membrane and to the activity of ion pumps. First let us examine how differential permeability can create an electrical potential difference.

2.4.3.1—
Diffusion Potential

Imagine a simple system of two compartments separated by a membrane which has a much higher permeability to K⁺ than to Cl^– (Fig. 2.13). If the compartments are filled with potassium chloride solutions of different concentration, initially K⁺ will move through the membrane out of the more concentrated compartment, and for a very brief period, the more concentrated cell will lose K⁺ faster than Cl^– leaving it enriched in negative charge. The negative diffusion potential thus created slows down the further escape of K⁺ by attracting it back into the more concentrated compartment. When the potential has developed, a large concentration difference can be maintained between the compartments. Since the membrane has a finite permeability to Cl^– , albeit a low one, over a long period of time both the electrical potential difference (the diffusion potential) and the concentration difference would run down as Cl^– leaked through the membrane. If the membrane were completely impermeable to Cl^– , the

potential, once established, would be maintained indefinitely. In nature, membrane permeability to anions is a tenth to one hundredth of that for the monovalent cations; thus, the maintenance of a potential of the kind just considered depends on topping up the cell with anions at a rate comparable with their leakage into the surroundings. This is an 'uphill' transport and therefore requires the mediation of some ion pumping mechanism. Active transport is, therefore, necessary to maintain a diffusion potential.

Figure 2.13
Development of charge separation and a diffusion potential
in a model system containing a membrane selectively
permeable to cations. For further explanation see text.
(From Clarkson. 1974.)

In nature it is frequently possible to find cells where the electrical potential difference across the plasmalemma is, indeed, a diffusion potential of the kind just described which depends very closely on the concentration of either K⁺ or H⁺ in the medium and in the cytoplasm. In such circumstances its value can be predicted from the Goldman equation (2.6) which relates the concentration ratios of ions across the membrane and their permeabilities (P_K , P_Na , P_Cl etc.).

This relationship will apply strictly only to situations where the cell and the surroundings are in a steady state and hence limits its application to mature and non-growing cells. The last pair of terms in equation 2.6 has been put in to emphasize that other diffusing ions can be added to the equation; clearly H⁺ has an important effect on the membrane potential in some instances (Kitasato, 1968). Since the concentration ratio is multiplied by the permeability coefficient, the value of E will be most strongly influenced by the ionic asymmetry of the most rapidly diffusing ion. In the system considered above the value of E would have been given by

and be governed almost entirely by K⁺ since P_Cl was very small compared with P_K . Notice that the ratio of the chloride terms is inverted relative to the cationic terms. This is explained because the chloride concentration differential will tend to reduce any negative electrical potential set up by the asymmetric distribution of the cations.