Gibbsdonnan Equilibrium Ion Pumps And Maintenance Of Cell Volume

So far we have considered three of the functions that are fulfilled by the operation of (Na+-K+) pumps. First, they are responsible for the high K+ and low Na+ concentrations characteristic of the intracellular fluid of higher animals. A number of enzymes involved in intermediary metabolism and protein synthesis appear to require relatively high concentrations of K+ for optimal activity and are inhibited by high concentrations of Na+; the activities of these enzymes would be markedly impaired if the intracellular Na+ and K+

concentrations were the same as those in the extracellular fluid. Second, these ionic asymmetries are largely responsible for establishing the electrical potential differences across membranes and the bioelectrical phenomena essential for the functions of excitable cells such as nerve and muscles as well as many cells that are not in this category. Finally, the Na+ gradients established by these pumps energize the secondary active transport of a number of solutes whose movements are coupled to those of Na+ (cotransport or counter-transport).

(Na+-K+) pumps fulfill yet another, extremely vital function in cells that do not possess a rigid cell wall; namely, they are in part responsible for maintaining the intracellular osmolarity equal to that of the extracellular fluid, thereby preventing osmotic water flow into the cells and, in turn, cell swelling. To appreciate why ion pumps are necessary for the maintenance of cell volume, we should first consider the artificial system illustrated in Fig. 23. The two compartments illustrated are assumed to be closed to the atmosphere and separated by a membrane that is freely permeable to Na+, Cl—, and water but is impermeable to proteins. A solution of NaCl is added to compartment o, and a solution of the sodium salt of a protein (Na+-proteinate [NaP]) is added to compartment i; assume that at the outset [Na+]o = [Na+]z. The system is then left undisturbed for a sufficiently long time until equilibrium is achieved.

Let us now consider the characteristics of this final, time-independent, equilibrium condition, which was derived by Josiah Willard Gibbs (1839-1903) and

Gibbs Donnan Equilibrium

FIGURE 23 The development of the Gibbs-Donnan equilibrium condition. AP, difference in hydrostatic pressure; Pr, protein anion.

Frederick George Donnan (1870-1956) and is often referred to as the Gibbs-Donnan equilibrium, Donnan equilibrium, or Donnan distribution. Because the membrane is permeable to Na+ and Cl—, but there is no Cl— initially present in compartment i, some Cl— must diffuse from compartment o into compartment i, but this must be also accompanied by an equal amount of Na+; otherwise, electroneutrality would be violated.

At all times, the system must obey a balance of electrical charges such that:

[Na+]0 = [Cl—]0 and [Na+]; = [Cl—+ Zp[P—]t (33)

where zp is the net anionic valence of the protein molecule.

When equilibrium is achieved, the system will be characterized by three properties:

1. Because we started out with equal Na+ concentrations in both compartments and Na+ and Cl— subsequently diffused into compartment i (at equal rates), the equilibrium condition must be characterized by asymmetrical distributions of both of these permeant ions across the membrane. As we have already learned, if there is an asymmetric distribution of a passively transported ion across a membrane, then, at equilibrium, there must be an electrical potential difference, Vm, across that membrane that balances the concentration difference and is given by the Nernst equation. Thus, one value of Vm must simultaneously satisfy the equilibrium distributions of both Na+ and Cl—, namely,

Vm = 60 log([Na+]0/[Na+]i) = 60 log([Cl—/[Cl—]o)

2. It follows from Eq. 34 that:

FIGURE 23 The development of the Gibbs-Donnan equilibrium condition. AP, difference in hydrostatic pressure; Pr, protein anion.

If we consider the initial and final (equilibrium) conditions illustrated in Fig. 23 together with Eq. 33, it should be clear that when equilibrium is achieved [Na+]o < [Na+L- and [CP]; < [Cl"]o) with the precise relation given by Eq. 35. Furthermore, it follows from Eq. 34 that compartment i will be electrically negative with respect to compartment o.

3. Finally, if we consider the initial and final conditions together with Eq. 33, it should be clear that when equilibrium is achieved, the concentration of osmo-tically active solutes in compartment i will be greater than that in compartment o, so that a pressure will have developed across the membrane given by van't Hoffs law, Eq. 19. Furthermore, if instead of being rigid the membrane is distensible, it would bulge into compartment o.

We chose the initial condition [Na+]o = [Na+]i simply to make it easier for students to comprehend the evolution of the asymmetries that characterize this equilibrium condition, but these equilibrium characteristics can be formally generalized to any set of initial conditions. Thus, if compartment i has a greater concentration of impermeant charged species than compartment o, the three additional asymmetries that will characterize the Gibbs-Donnan equilibrium when it is reached are as follows:

1. There will be an asymmetric distribution of all permeant monovalent cations (C+) and anions (C—) that conforms to the relation:

C+/C+ = C—/C— = r where r is often referred to as the Donnan ratio and is, in part, a function of the difference in total charge between compartments o and i borne by impermeant ions. If compartment i contains a preponderance of impermeant anions, then Co+ < C\ and CL < Co; if the impermeant species are predominantly cationic, then these relations will be reversed.

2. There will be an electrical potential difference across the membrane given by the relation:

If compartment i contains a preponderance of impermeant anions then Vm will be oriented such that compartment i is electrically negative with respect to compartment o; if the impermeant species are predominantly cationic, then this orientation will be reversed.

3. Regardless of the sign of the total charge carried by the preponderance of impermeant species in compartment i, at equilibrium that compartment will contain a greater number of osmotically active particles than compartment o. Thus, there will be an osmotic driving force for the movement of water into compartment i. If the membrane is rigid then an osmotic pressure would balance that driving force; if the membrane is distensible, then it would bulge into compartment o.

We can appreciate the function of ion pumps in the maintenance of cell volume by considering what would happen if there were no ion pumps. Because the intracellular concentration of charged, largely anionic, impermeant macromolecules is much greater than that in the extracellular fluid, cells lacking ion pumps would resemble the passive system illustrated in Fig. 23 and would move toward the direction of achieving a Gibbs-Donnan equilibrium. The total osmotic activity of intracellular solutes would exceed that in the surrounding fluid, and there would be a driving force for osmotic water flow into the cell. If the cells possess rigid cell walls that prevent any increase in cell volume, an osmotic pressure difference would develop across the cell walls and the cell interiors would be subjected to a pressure greater than the extracellular fluid (''turgor''). If, as in the case of animal cells, the membrane is distensible, water would flow into the cell, leading to cell swelling and, perhaps, rupture.

The (Na+-K+) pumps in animal cell membranes serve to reduce the intracellular content of osmotically active solutes, thereby counteracting the osmotic effect of intracellular macromolecules. The pumps extrude three sodium ions in exchange for two potassium ions and also establish an electrical potential difference across the membrane (negative cell interior) that reduces the steady-state intracellular concentrations of permeant, passively distributed anions (mainly Cl—).

If the (Na+-K+) pumps are inhibited by digitalis glycosides or metabolic poisons, the cells will lose K+ and gain Na+ and Cl—; in many cells, three Na+ plus one Cl— will be gained for every two K+ lost, so that the total amount of Na+ and Cl— gained by the cell exceeds the amount of K+ lost, and the total intracellular solute concentration will increase. This will result in an osmotic uptake of water and cell swelling and may lead to the destruction of the integrity of the cell membrane. (Recall that inhibition of the pump would not only lead to the dissipation of the asymmetric distributions of Na+ and K+, but also the Vm (cell interior negative) arising from these asymmetries. According to Eq. 32, if Vm becomes less negative, then intracellular Cl— will increase. Also note that the redistribution of ions following inhibition of the pump does not, indeed cannot, violate the law of bulk electroneutrality.)

In summary, the membranes that surround most animal cells are distensible and highly permeable to water. If these cells are immersed in a hypertonic fluid, water rapidly leaves the intracellular compartment and they shrink. If these cells are immersed in a hypotonic solution, water flows rapidly into them and they swell, possibly rupturing. In higher animals, the osmolarity of the extracellular fluid is carefully regulated by the kidneys in response to neurohormonal stimuli so that it normally remains within very narrow limits. However, the maintenance of isotonicity between the intracellular and extracellular fluids depends, in part, on the presence of ion, particularly (Na+-K+), pumps in the cell membranes. These pumps serve to lower the intracellular concentration of permeant solutes and thereby balance and offset the osmotic effects of impermeant intracellular macromolecules. (Other transport mechanisms come into play when the preservation of cell volume is threatened by conditions that lead to swelling and, in some instances, shrinking; a discussion of these mechanisms is beyond the scope of this introductory text but can be found in the suggested readings.)

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  • medardo
    What is law of bulk electroneutrality?
    6 years ago

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