Editing Nernst equation (section)

===Goldman equation===
{{main|Goldman equation}}
When the membrane is permeable to more than one ion, as is inevitably the case, the [[resting potential]] can be determined from the Goldman equation, which is a solution of [[GHK flux equation|G-H-K influx equation]] under the constraints that total current density driven by electrochemical force is zero:

<math display="block">E_\mathrm{m} = \frac{RT}{F} \ln{ \left( \frac{ \displaystyle\sum_i^N P_{\mathrm{M}^+_i}\left[\mathrm{M}^+_i\right]_\mathrm{out} + \displaystyle\sum_j^M P_{\mathrm{A}^-_j}\left[\mathrm{A}^-_j\right]_\mathrm{in}}{ \displaystyle\sum_i^N P_{\mathrm{M}^+_i}\left[\mathrm{M}^+_i\right]_\mathrm{in} + \displaystyle\sum_j^M P_{\mathrm{A}^-_j}\left[\mathrm{A}^-_j\right]_\mathrm{out}} \right) },</math>

where

* {{math|''E''<sub>m</sub>}} is the membrane potential (in [[volt]]s, equivalent to [[joule]]s per [[coulomb]]),
* {{math|''P''<sub>ion</sub>}} is the permeability for that ion (in meters per second),
* {{math|[ion]<sub>out</sub>}} is the extracellular concentration of that ion (in [[Mole (unit)|moles]] per cubic meter, to match the other [[SI]] units, though the units strictly don't matter, as the ion concentration terms become a dimensionless ratio),
* {{math|[ion]<sub>in</sub>}} is the intracellular concentration of that ion (in moles per cubic meter),
* {{mvar|R}} is the [[ideal gas constant]] (joules per [[kelvin]] per mole),
* {{mvar|T}} is the temperature in [[kelvin]]s<!-- pluralized – see Kelvin#Usage conventions -->,
* {{mvar|F}} is the [[Faraday constant|Faraday's constant]] (coulombs per mole).

The potential across the cell membrane that exactly opposes net diffusion of a particular ion through the membrane is called the Nernst potential for that ion. As seen above, the magnitude of the Nernst potential is determined by the ratio of the concentrations of that specific ion on the two sides of the membrane. The greater this ratio the greater the tendency for the ion to diffuse in one direction, and therefore the greater the Nernst potential required to prevent the diffusion. A similar expression exists that includes {{mvar|r}} (the absolute value of the transport ratio). This takes transporters with unequal exchanges into account. See: [[sodium-potassium pump]] where the transport ratio would be 2/3, so r equals 1.5 in the formula below. The reason why we insert a factor r = 1.5 here is that current density ''by electrochemical force'' J<sub>e.c.</sub>(Na<sup>+</sup>) + J<sub>e.c.</sub>(K<sup>+</sup>) is no longer zero, but rather J<sub>e.c.</sub>(Na<sup>+</sup>) + 1.5J<sub>e.c.</sub>(K<sup>+</sup>) = 0 (as for both ions flux by electrochemical force is compensated by that by the pump, i.e. J<sub>e.c.</sub> = −J<sub>pump</sub>), altering the constraints for applying GHK equation. The other variables are the same as above. The following example includes two ions: potassium (K<sup>+</sup>) and sodium (Na<sup>+</sup>). Chloride is assumed to be in equilibrium.
<math display="block">E_{m} = \frac{RT}{F} \ln{ \left( \frac{ rP_{\mathrm{K}^+}\left[\mathrm{K}^+\right]_\mathrm{out} + P_{\mathrm{Na}^+}\left[\mathrm{Na}^+\right]_\mathrm{out}}{ rP_{\mathrm{K}^+}\left[\mathrm{K}^+\right]_\mathrm{in} + P_{\mathrm{Na}^+}\left[\mathrm{Na}^+\right]_\mathrm{in}} \right) }.</math>

When chloride (Cl<sup>−</sup>) is taken into account, 

<math display="block">E_{m} = \frac{RT}{F} \ln{ \left( \frac{r P_{\mathrm{K}^+}\left[\mathrm{K}^+\right]_\mathrm{out} + P_{\mathrm{Na}^+}\left[\mathrm{Na}^+\right]_\mathrm{out} + P_{\mathrm{Cl}^-}\left[\mathrm{Cl}^-\right]_\mathrm{in}}{r P_{\mathrm{K}^+}\left[\mathrm{K}^+\right]_\mathrm{in} + P_{\mathrm{Na}^+}\left[\mathrm{Na}^+\right]_\mathrm{in} + P_{\mathrm{Cl}^-}\left[\mathrm{Cl}^-\right]_\mathrm{out}} \right) }.</math>