Chapter 8, Problem 32RQ

The GHK equation is sometimes abbreviated to exclude chloride, which plays a minimal role in membrane potential for most cells. In addition, because it is difficult to determine absolute membrane permeability values for Na⁺ and K⁺, the equation is revised to use the ratio of the two ion permeabilities, expressed as α = P_Na/P_K:

${\text{V}}_{\text{m}}=61\log \frac{{\left[{\text{K}}^{+}\right]}_{\text{out}}+\alpha {\left[{\text{Na}}^{+}\right]}_{\text{out}}}{{\left[{\text{K}}^{+}\right]}_{\text{in}}+\alpha {\left[{\text{Na}}^{+}\right]}_{\text{in}}}$

Thus, if you know the relative membrane permeabilities of the two ions and their intracellular (ICF) and extracellular (ECF) concentrations, you can predict the membrane potential for a cell.

Using a calculator with log function or the free online Nernst/Goldman equation simulator from the University of Arizona (www.nernstgoldman.physiology.arizona.edu/), do the following calculations.

1. (a) A resting cell has an alpha (a) value of 0.025 and the following ion concentrations:

   Na⁺: ICF = 5 mM, ECF = 135 mM

   K⁺: ICF = 150 mM, ECF = 4 mM

   What is the cell’s membrane potential?

2. (b) The Na⁺ permeability of the cell in (a) suddenly increases so that α = 20. Now what is the cell’s membrane potential?
3. (c) Mrs. Nguyen has high blood pressure, and her physician puts her on a drug whose side effect decreases her plasma (ECF) K⁺ from 4 mM to 2.5 mM. Using the other values in (a), calculate the membrane potential with decreased plasma K⁺.
4. (d) The physician prescribes a potassium supplement for Mrs. Nguyen, who decides that if two pills are good, four must be better. Her plasma (ECF) K⁺ now goes to 6 mM. What happens to her membrane potential?