1. Donnan equilibrium

• The Nernst equation for potassium is:
  V_K = (62/+1)*log₁₀(K_out/K_in)
• And, the Nernst equation for chloride is:
  V_Cl = (62/-1)*log₁₀(Cl_out/Cl_in), or,

  V_Cl = (62/+1)*log₁₀(Cl_in/Cl_out)

• If the permeability of the membrane to potassium and chloride is equal and these ions are permeable through the membrane to a much greater extent than any other ions, then either V_K or V_Cl will predict the actual membrane potential across the membrane. So, V_K = V_Cl and thus,
  62*log₁₀(K_out/K_in) = 62*log₁₀(Cl_in/Cl_out)

  K_out/K_in = Cl_in/Cl_out

  This is the Gibbs-Donnan equlibrium!
• (How might the Gibbs-Donnan equlibrium equation look if calcium and potassium are the only permeable, and equally permeable, ions? Or what might the equation look like if calcium (+2) and phosphate (-2) were the only, and equally permeable, ions?)
• Now, we see that if external chloride is replaced by sulfate and external potassium concentration is lowered, the membrane potential obeys the Nernst potential equation for potassium EXCEPT at low potassium concentrations. Why?

2. Goldman constant-field equation

For Frog muscle, where the permeability of Sodium is about 1/100 of that for Potassium or Chloride, and where some impermeable solute is substituted for Chloride,

3. The Goldman equation requires knowledge of the permeabilities of membrane to ions. Permeability is a measure of how easily mass moves through membrane channels. The measurement of mass movement in real time is difficult. However, physiologists can make use of the fact that mass movement of ions is accompanied by charge movement. Charge movement is electrical "current", which can be measured with relative ease. (Eckert, Fig. 5-8)

• Ohm's Law is V = I R (or E = I R). But, resistance (R) = 1/g where g, conductance, is 1/R. (Eckert, Fig. 5-10) Conductance is very similar to permeability - Greater permeability is equivalent to greater conductivity.
• At this point in the lecture, we discuss electrical circuits and how potential differences result in the flow of current.
• We can show that the membrane potential is comprised of a sum of Nernst potentials V_Na, V_K, and V_Cl (and terms for any other ions with significant conductance), with each term weighted (multiplied) by the fraction of the total conductance that each ion is responsible for. This "conductance equation" is discussed in Eckert as a means of analyzing the so-called "reversal potential". However, the conductance equation is generally useful because the components of the conductance equation can be calculated from easily measured quantities: Nernst potentials can be calculated from ion concentrations and conductances can be determined from electrical measurements.

All text and images, not attributed to others, including course examinations and sample questions, are Copyright, 2007, Thomas J. Herbert and may not be used for any commercial purpose without the express written permission of Thomas J. Herbert.