Question 14

College Answer

A good answer included a definition of the resting membrane potential and a clear description of
the factors that determine it. Explanation of these factors should have included a detailed
description of the selective permeability of the membrane, electrochemical gradients and active
transport mechanisms. Answers should demonstrate awareness of the Nernst equation and the
Goldman-Hodgkin-Katz equation. These were often confused, sometimes with the GibbsDonnan
effect. Descriptions of the Gibbs-Donnan effect generally lacked detail and
understanding. The better answers included a definition and discussed in detail the influence of
non-diffusible ions (intracellular proteins) on the distribution of diffusible ions.

Discussion

a) 

This is a topic which generally takes an entire book chapter to describe. What follows is an attempt to explain/describe the main concepts as briefly as possible while including the essential details.

Resting membrane potential: the voltage (charge) difference between the intracellular and extracellular fluid, when the cell is at rest (i.e not depolarised by an action potential).

Mechanisms responsible for the resting membrane potential:

• Chemical gradients generated by active transport pumps: the concentration of ions are significantly different between the intracellular and extracellular fluid, eg. the ratio of potassium ions is 35:1.
• Selective membrane permeability: the cell membrane is selectively ion-permeable, specifically it is much more permeable to potassium ions
• Electrical gradients are generated because potassium leak (via K_2P channels) from the intracellular fluid creates a negative intracellular charge. This charge attracts potassium ions back into the cell and thus opposes the chemical gradient.
• Electrochemical equilibrium develops when electrical and chemical forces are in balance for each specific ion species, and this is described by the Nernst equation.
• The Nernst potential for each ion is the transmembrane potential difference generated when that ion is at electrochemical equilibrium
• The total membrane resting potential for all important ion species is described by the Goldman-Hodgkin-Katz equation, which takes into account the different membrane permeabilities for each ion.
• At rest, with normal intracellular and extracellular electrolyte concentrations, the net charge of the intracellular side of the cell membrane is negative, and is approximately -70 to -90 mV for mammalian neurons.

Now, as for the Gibbs-Donnan effect:

• The Gibbs-Donnan effect describes the unequal distribution of permeant charged ions on either side of a semipermeable membrane which occurs in the presence of impermeant charged ions. 
• At Gibbs-Donnan equilibrium,
  • On each side of the membrane, each solution will be electrically neutral
  • The product of diffusible ions on one side of the membrane will be equal to the product of diffusible ions on the other side of the membrane
  • The electrochemical gradients produced by unequal distribution of charged ions produces a transmembrane potential difference which can be calculated using the Nernst equation
  • The presence of impermeant ions on one side of the membrane creates an osmotic diffusion gradident attracting water into that compartment.
• The mechanisms which maintain the resting membrane potential and the mechanisms of the Gibbs-Donnan effect are different phenomena:
  • The Donnan equlibrium is a completely passive process: i.e. no active transporters are involved in maintaining this equilibrium.
  • A Donnan equilibrium is an equilibrium, i.e. ion concentrations on either side of the barrier are static. 
  • If the Donnan equilibrium were to become fully established,  the increase in intracellular ions would cause cells to swell due to the osmotic influx of water.
  • At a Donnan equilibrium, the resting membrane potential would be only about -20 mV. This potential would exist even if the membrane permeability for all ions was the same.
  • The resting membrane potential, in contrast, requires different permeabilities for potassium and for sodium, and is maintained actively by constant Na⁺/K⁺ ATPase activity.
  • Because biological membranes (especially of exciteable tissues) are never at equilibrium, the Goldman-Hodgkin-Katz equation is usually a better choice for explaining their electrochemical behaviour.

Wright, Stephen H. "Generation of resting membrane potential." Advances in physiology education 28.4 (2004): 139-142.

Tasaki, I., A. Watanabe, and T. Takenaka. "Resting and action potential of intracellularly perfused squid giant axon." Proceedings of the National Academy of Sciences of the United States of America 48.7 (1962): 1177.

Lodish, Harvey, et al. "Intracellular ion environment and membrane electric potential." Molecular Cell Biology. 4th edition. WH Freeman, 2000.

Lesage, Florian, and Michel Lazdunski. "Molecular and functional properties of two-pore-domain potassium channels." American Journal of Physiology-Renal Physiology 279.5 (2000): F793-F801.

Ling, G. N., Zelling, Niu, and M. Ochsenfeld. "Predictions of polarized multilayer theory of solute distribution confirmed from a study of the equilibrium distribution in frog muscle of twenty-one nonelectrolytes including five cryoprotectants." Physiological chemistry and physics and medical NMR 25.3 (1993): 177-208.

Stanton, M. G. "Origin and magnitude of transmembrane resting potential in living cells." Philosophical Transactions of the Royal Society of London. B, Biological Sciences 301.1104 (1983): 85-141.

Sperelakis, Nicholas. "Origin of resting membrane potentials." Cell physiology source book. Academic Press, 1995. 67-90.

Donnan, Frederick George. "Theory of membrane equilibria and membrane potentials in the presence of non-dialysing electrolytes. A contribution to physical-chemical physiology." Journal of Membrane Science 100.1 (1995): 45-55.

Adair, G. S. "On the Donnan equilibrium and the equation of Gibbs." Science 58.1488 (1923): 13-13.

Donnan, Frederick George. "The theory of membrane equilibria." Chemical Reviews 1.1 (1924): 73-90.

Nguyen, Minhtri K., and Ira Kurtz. "Quantitative interrelationship between Gibbs-Donnan equilibrium, osmolality of body fluid compartments, and plasma water sodium concentration." Journal of Applied Physiology 100.4 (2006): 1293-1300.

Masuda, Takashi, Geoffrey P. Dobson, and Richard L. Veech. "The Gibbs-Donnan near-equilibrium system of heart." Journal of Biological Chemistry 265.33 (1990): 20321-20334.