The Goldman–Hodgkin–Katz voltage equation, sometimes called the Goldman equation, is used in cell membrane physiology to determine the resting potential across a cell's membrane, taking into account all of the ions that are permeant through that membrane. The discoverers of this are David E. Goldman of Columbia University, and the Medicine Nobel laureates Alan Lloyd Hodgkin and Bernard Katz.
Equation for monovalent ions The GHK voltage equation for n {\displaystyle n} monovalent positive ionic species M i {\displaystyle M_{i}} and m {\displaystyle m} negative species A j {\displaystyle A_{j}} :
E m = R T F ln ( ∑ i n P M i + [ M i + ] o u t + ∑ j m P A j − [ A j − ] i n ∑ i n P M i + [ M i + ] i n + ∑ j m P A j − [ A j − ] o u t ) {\displaystyle E_{m}={\frac {RT}{F}}\ln {\left({\frac {\sum _{i}^{n}P_{M_{i}^{+}}[M_{i}^{+}]_{\mathrm {out} }+\sum _{j}^{m}P_{A_{j}^{-}}[A_{j}^{-}]_{\mathrm {in} }}{\sum _{i}^{n}P_{M_{i}^{+}}[M_{i}^{+}]_{\mathrm {in} }+\sum _{j}^{m}P_{A_{j}^{-}}[A_{j}^{-}]_{\mathrm {out} }}}\right)}}
This results in the following if we consider a membrane separating two K x N a 1 − x C l {\displaystyle \mathrm {K} _{x}\mathrm {Na} _{1-x}\mathrm {Cl} } -solutions:
… excerpt ends here. Continue reading the full article.
