Membrane potential theory
Membrane potential is the electrical voltage across a cell membrane, produced by unequal ion concentrations and selective permeability. The calculator estimates membrane potential in mV from intracellular and extracellular ion values together with relative permeability, so the result reflects both concentration gradients and how easily each ion crosses the membrane.
Core definitions and formulas
A single ion can be summarized with the Nernst equation, while a real resting membrane is better approximated with a simplified Goldman relationship that combines several ions. For K+ and Na+, a larger outside-to-inside ratio tends to make the equilibrium potential more positive. For Cl−, the concentration ratio appears in reverse because it is an anion.
\[
E_{\text{ion}}=\frac{R T}{zF}\ln\!\left(\frac{[\text{ion}]_{\text{out}}}{[\text{ion}]_{\text{in}}}\right)
\]
\[
V_m=\frac{R T}{F}\ln\!\left(\frac{P_K[K^+]_{\text{out}}+P_{Na}[Na^+]_{\text{out}}+P_{Cl}[Cl^-]_{\text{in}}}{P_K[K^+]_{\text{in}}+P_{Na}[Na^+]_{\text{in}}+P_{Cl}[Cl^-]_{\text{out}}}\right)
\]
Here, Vm is membrane voltage, R is the gas constant, T is absolute temperature, F is Faraday’s constant, z is ion charge, P is relative permeability, and brackets denote concentration, usually in mM. Reported voltage is usually given in mV.
How to interpret results
A more negative result means the cell interior is predicted to be more negative relative to the outside. Increasing K+ permeability usually pulls the voltage closer to the K+ equilibrium potential, while increasing Na+ permeability usually makes the membrane less negative. The output is most useful when read together with the ion contribution summary, the resting comparison, and the permeability-linked visualizations.
- Do not mix up inside and outside concentrations.
- Do not treat permeability as the same thing as concentration.
- Remember that Cl− enters the Goldman ratio with reversed sides.
- Use temperature in °C only if the tool converts it internally.
Micro example: with K+ = 140 mM inside and 5 mM outside, Na+ = 15 mM inside and 145 mM outside, Cl− = 10 mM inside and 110 mM outside, and relative permeabilities 1, 0.04, and 0.45, the predicted voltage is close to a typical resting value near −70 mV.
This tool is useful for studying resting voltage, permeability changes, and the effect of altered ion gradients in physiology or introductory biophysics. It is not a full electrophysiology simulator and does not replace channel kinetics, pumps, time-dependent currents, or action-potential models. A useful next step is the Nernst equation, Goldman-Hodgkin-Katz analysis, or action-potential modeling.
