Gibbs-Donnan Equilibrium
These animations have been prepared with the objective of serving as teaching tutorials to assist undergraduate students in conceptualizing the complex dynamics of physiological processes –– especially as they relate to insects. I am sharing these animations with my colleagues that wish to link to them, or refer them to their students for the purpose of illustrating course lecture topics.
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Summary
The Gibbs–Donnan equilibrium is a phenomenon of solutions that contributes to the formation of an electrical potential across a cell membrane.
Scene 1: Solution Equilibrium
The Gibbs–Donnan equilibrium can be illustrated using a vessel separated into two chambers by a semi–permeable membrane. A KCl solution is added to one side of the vessel (I) and water to the other side (II). The membrane is completely permeable to the K+ and Cl– ions. The K+ and Cl– ions diffuse passively through the membrane from one side of the vessel to the other. Ions diffuse from high concentrations (I) to low concentrations (II) until equilibrium is attained, then the final solution on each side contains equal concentrations for both the K+ and the Cl– ions.
At equilibrium, K+ ions move along with Cl– ions from one side of the membrane to the other, and an equal number of the same ions will move from the second side back to the first. In this manner the solutions on each side of the membrane maintain both equal concentrations of ions and electrical neutrality.
The system becomes more complicated if an anion is present that is not permeable to the membrane.
Scene 2: Permeability Properties
In this representation, the impermeable anion is Pr– which represents anionic protein – a common constituent of cells. K+ and Cl– are permeable to the membrane. K+ and Cl– easily penetrate the membrane separating the two chambers. Pr– is not permeable and is retained on side I.
Scene 3: Gibbs-Donnan Equilibrium
An unstable situation occurs in a solution if one side (I) of the semi–permeable membrane contains a solution consisting of a permeable cation such as K+ with an impermeable anion (Pr–), whereas the other side (II) contains a solution of K+ and Cl–, both of which are permeable to the membrane. The K+ concentrations are equimolar on both sides I and II.
Since side I does not contain Cl–, the Cl– from side II will diffuse along the Cl– concentration gradient from side II to side I. This results in a negative charge on side I relative to side II due to the excess concentration of anions ( Pr– I + Cl–I > Cl–II ) on side I. The Cl– concentrations will not become equal on sides I and II because the negative charge on side I will repel Cl– movement from side II to side I so that side II will have the higher concentration of Cl–.
The presence of excess anion in the form of Cl– on side I establishes a negative electrical gradient between side I and side II. The negative electrical gradient attracts K+ to migrate from side II to side I. However, the [K+] on side I now exceeds that of side II , hence K+ will move back from side I to side II along a K+ -concentration gradient.
The net result at equilibrium is that K+ and Cl– move in equimolar amounts together from one side to the other. Each side is electrically neutral within itself due to equimolar concentrations of cations and anions, but there is an unequal concentration of the diffusible ions with [K+] highest on side I and [Cl-] highest on side II.