Question

I'm calculating the equilibrium potentials of sodium ions and potassium ions using the Nernst equation. In the problem I just did, I calculated Ena= +69.9 mV and Ek=-92.0 mV.

The next part of the question asks, "If the conditions are the same as above, at which membrane potential would you expect the movement of the Na and K ions to cancel each other out and there be no net change in membrane potential?"

Do I average their equilibrium potentials or is it more complicated than that?

Answer 1

Equilibrium potential is the electric potential difference which counter acts the movement of ions by diffusion ( due to concentration gradient) . Positive and negative signs for equilibrium potential is indicative of the direction of membrane potential. For instance, concentration of sodium ion is lower in the intracellular melieu, it should have positive equilibrium potential to drive Na+ ions out, similarly its negative for K+ ions. In a given cell if there's only K+ or Na+ ions resting potential is close to respective equilibrium potentials. However in reality both ion/ ion pumps contribute to the resting membrane potential. In the present situation, when both ions can move across membrane, you are asked to calculate membrane potential. you cannot average out the equilibrium potentials, this is because for every three sodium ions exported two potassium ions are imported into the cells. Typically membrane potential is -65 to -85 MV which is closer to potassium equivalent owing to its highest permeability.

Exact resting membrane potential can be calculated by Gold man-Hodgkin-Katz equation which primarily takes individual ion concentration of all the contributing ions into consideration mainly Na+ and K+ to arrive at resting membrane potential. ( This may not be part of your syllabus).

Vm=RT/Fln Pk[K+]o+Pk[Na+]o+Pk[Cl-]i/Pk[K+]i+Pk[Na+]i+Pk[Cl-]o