 When an ion on one side of a membrane cannot diffuse through the membrane, the distribution of other ions to which the membrane is permeable is affected in a predictable way. For example, the negative charge of a nondiffusible anion hinders diffusion of the diffusible cations and favors diffusion of the diffusible anions. See example below: In the example on the left, the membrane (we call it “m”) between compartments X and Y is impermeable to charged proteins (Prot) but freely permeable to K+ and Cl. Assume that the concentrations of the anions and of the cations on the two sides are initially equal. Cl diffuses down its concentration gradient from Y to X, and some K+ moves with the negatively charged Cl because of its opposite charge. Therefore,

[K+X] > [K+Y]

Furthermore,

[K+X] + [ClX] + [ProtX] > [K+Y] + [ClY]

that is, more osmotically active particles are on side X than on side Y. Donnan and Gibbs showed that in the presence of a nondiffusible ion, the diffusible ions distribute themselves so that at equilibrium their concentgration ratios are equal:

[K+X] * [ClX] = [K+Y] * [ClY]

This is the Gibbs-Donnan equation. It holds for any pair of cations and anions of the same valence.

Significance

The Donnan effect on the distribution of ions has tree effects in the body introduced here and discussed below.

1. Because of  charged proteins (Prot) in cells, there are more osmotically active particles in cells than in interstitial fluid, and because animal cells have flexible walls, osmosis would make them swell and eventually rupture if it were not for Na, K ATPase pumping ions back out of cells. Thus, normal cell volume and pressure depend on Na, K ATPase.

2. Because at equilibrium the distribution of permeant ions across the membrane (m in the example used here) is asymmetric, an electrical difference exists across the membrane whose magnitude can be determined by the Nernst equation. In the example of the figure, side X will be negative relative to side Y. The charges line up along the membrane, with the concentration gradient for Cl exactly balanced by the oppositely directed electrical gradient, and the same holds true for K+.

3. Because there are more proteins in plasma than in interstitial fluid, there is a Donnan effect on ion movement across the capillary wall.

Genesis of The Membrane Potential

The distribution of ions across the cell membrane and the nature of this membrane provide the explanation for the membrane potential. The resting membrane potential is -70 mV. The concentration gradient for K+ facilitates its movement out of the cell via K+ channels (chemical gradient), but its electrical gradient is in the opposite (inward) direction. Consequently, an equilibrium is reached in which the tendency of K+ to move out of the cell (chemical gradient) is balanced by its tendency to move into the cell (electrical gradient), and at that equilibrium there is a slight excess of cation on the outside and anions on the inside. The slight excess of cation on the outside and anions on the inside is maintained by Na, K ATPase, and because the Na, K ATPase moves three Na+ out of the cell for every two K+ moved in, therefore it also contributes to the membrane potential and thus is termed an electrogenic pump.

Attention must be paid that the number of ions responsible for the membrane potential is a minute fraction of the total number present and that the total concentrations of positive and negative ions are equal everywhere except along the membrane.

The resting membrane potential is -70 mV, and the equilibrium potential of Na+, K+, and Cl  are list in the figure below. According to the relationship between the equilibrium potential and the resting membrane potential, the electrical gradient of Na+ is inward, as same as the chemical gradient of it. Conversely, the electrical gradient of K+ is outward since the equilibrium potential of K+ is -90 mv and the actual resting potential is -90 mv, whose power is somewhat smaller than the force of chemical gradient.

Therefore, plenty of Na+ would come into the cell automatically, a few of K+ would come out of the cell spontaneously too. Thank goodness to the Na, K ATPase, which maintain the natural distribution of ions across the cell membrane, and the resting membrane potential.