Question

"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 alpha = permeability to Na+ / permeability to K+: [K+]out + a[Na+]out Vm = 61log m [K+]in + a[Na+]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.

QUESTIONS:
(a) What is the membrane potential given an alpha value of 0.025 and the following ion concentrations:
Na+ ICF = 5mM, ECF = 135mM
K+ ICF = 150mM, ECF = 4mM

(b) The Na+ permeability of the cell in (a) suddenly increases so that alpha = 20. Now what is the cell's membrane potential?

(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), now what is the membrane potential?

(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 the membrane potential?"

Answer 1

The membrane potential of a cell is calculated using the GHK equation, which takes into account ion concentrations and membrane ion permeabilities. Values of ion concentrations and permeabilities are plugged into the equation to determine changes in membrane potential under different scenarios.

Step-by-step explanation:

The GHK equation allows for the calculation of the membrane potential of a cell given the concentrations of ions inside and outside the cell and the membrane's relative permeabilities to those ions. Below are the solved parts of the question:

• (a) With an alpha value of 0.025, Na+ ICF = 5mM, Na+ ECF = 135mM, K+ ICF = 150mM, and K+ ECF = 4mM; the membrane potential (Vm) can be calculated using the provided GHK equation.
• (b) If the Na+ permeability increases so that alpha = 20, the membrane potential of the cell will change accordingly when re-calculated using the GHK equation.
• (c) If Mrs. Nguyen's plasma K+ concentration decreases from 4 mM to 2.5 mM, there will be an effect on the membrane potential when using the initial GHK equation values.
• (d) If Mrs. Nguyen's plasma K+ concentration increases to 6 mM from an optimal supplementation, the membrane potential will again change, which can be determined by recalculating using the GHK equation.

For each part of the question, insert the respective values into the GHK equation and solve for the membrane potential, keeping in mind the roles of various channels and pumps such as the Na+/K+ ATPase in the overall maintenance of membrane potential.