Anatomy & Physiology

Calculating membrane potential

The Nernst Equation describes the relationships between ion concentrations and membrane potential (or voltage). In its simple form, the Nernst equation is:

RT [X]^I

E_x = ---- ln -----

Fz [X] ^II

Where,

E_x = voltage of membrane with respect to ion X

R = the gas constant

T = temperature (Kelvin)

F = the Faraday constant (96,500 coulombs/g-equivalent charge)

z = the valance of the ion

[X] = the concentration of the ion, X on one side (I) or the other side

(II) of the membrane

The formula reduces to:

[X]^I

Ex = .058 log -----

[X]^II

The formula is most useful when more than one ion is considered. The two ions that contribute to the resting membrane potential are sodium (Na) and potassium (K). The formula, as written above, considers only a fully permeable membrane. In practice, the cell membrane is selectively permeable. In particular, the cell membrane is about 100 times more permeable ( ^P_x) to K than to Na. The working formula to calculate membrane potential is:

Pk[K⁺]0 + Pna[Na⁺]0

E_x = .058 log ----------------------

PK[K⁺]i + PN_A[Na⁺]i

Where,

Ions are in molar concentrations and the letters o and i refer to inside and outside of the cell.

To be complete, permeabilities and concentrations of each ion should be included. The next most important ions are Ca ⁺⁺ and CI but inclusion of these in the calculations does not change the membrane potential much since these ions have low concentrations and low permeabilities.