Ion Transport and Membrane Potential

Ions, too, can cross membranes. Their diffusion properties generate an electric gradient. This gradient cannot be kept upright without energy consumption. Cations and anions (M⁺ and A^-) pass the membrane according to their selectivity. This means that the flow of cations is not solely dependent on the cation concentration [M⁺] but also on the anion concentration [A^-]. The influx of [M⁺] into the cell - or any other compartment - is consequently described by FICK's diffusion law:

influx M = P_M [M⁺]_e [A ]_e

where P_M is the permeability coefficient and [M⁺]_e and [A^-]_e, respectively, are the extracellular ion concentrations. The efflux of the cell is:

efflux_M = P_M [M⁺]_i [A ]_i

[M⁺]_i and [A^-]_i are the ion concentrations within the cell. At an equilibrium (same ion distribution at the in- and the outside and therefore no overall electric charge) are

[M⁺]_i [A^-]_i = [M⁺]_e [A^-]_e

or

g = [M⁺]_e / [M⁺]_i = [A^-]_i / [A^-]_e

where g is the so-called DONNAN equilibrium. It is 1, if only freely permeating ions are present. But in a cell can usually a high proportion of bound ions be found, for example in most negatively charged proteins (P_r). To achieve electric neutrality have

[M⁺]_e = [A^-]_e

to meet the requirement

[M⁺]_i = [A^-]_i + [P_r-]_i

This means that

[M⁺]_i > [A^-]_i

and that the DONNAN - equilibrium has a value clearly smaller than 1. Consequently is the concentration of freely diffusing ions always higher at the inside than at the outside. The ion distribution of both sides of the membrane is uneven: a membrane potential (E_D) exists. It is described by the NERNST equation:

E_D = (RT / FZ) ln ([M⁺]_e / [M⁺]_i) = RT / FZ ln ([A^-]_i / [A^-]_e)

where R is the gas constant, T is the absolute temperature, F is the FARADAY constant and Z is the charge of the ion in question. By transformation of the equation and after putting in the corresponding numbers is the following equation obtained

E_D [mV] = 62 log [M⁺]_e / [M⁺]_i

The net flow through a membrane is the difference between influx and efflux. In any given membrane potential is the ion diffusion influenced by the concentration and the electric gradient. The influx is decisively affected by the extracellular concentration. The potential which goes with it is the potential difference between the extracellular space and the membrane: the driving force is the electrochemical potential B_e:

B_e = C_e e (ZFE_e / RT)

where C_e is the extracellular ion concentration. The ratio of efflux and influx is

efflux / influx = B_i/ B_e = (C_i / C_e) e (ZFE_D/ RT)

where E_D is the difference between E_i and E_e. This relation is called the USING flux relation. It can be applied to find out whether a measured potential difference tallies with a calculated one. If the efflux to influx ratio is larger than B_i/ B_e (efflux / influx > B_i/ B_e) then has it to be assumed that additional energy has been invested in order to attain the measured potential difference. That is, the formula offers a test to distinguish between active and passive transport.

© Peter v. Sengbusch - Impressum