Nernst and Goldman Potentials

How ion gradients and permeability set membrane voltage

One ion, one equilibrium potential The Nernst potential is where electrical and concentration forces balance for K⁺.

Adjust a concentration or permeability and watch both the voltage markers and current balance move. Hover over graphs for numerical values.

How to use this simulation

Nernst mode asks where a single ion would be at electrochemical equilibrium. Choose an ion, adjust its concentrations, and compare its equilibrium potential with the test membrane voltage. The current graph shows the driving force Vm − Eion. Positive current is outward by electrophysiological convention. An anion such as Cl⁻ moves opposite to the direction of conventional current.

Eion = RT/(zF) ln([ion]out/[ion]in)

A tenfold concentration ratio produces about 61.5 mV at 37 °C for a monovalent ion. Ca²⁺ has twice the charge, so the same ratio produces half the voltage change. The sign reverses for Cl⁻ because its valence is negative.

Goldman mode describes a membrane simultaneously permeable to K⁺, Na⁺, and Cl⁻. The Goldman voltage is the zero-total-current voltage under the constant-field assumptions. It is influenced by both concentration gradients and relative permeabilities; it is not a simple arithmetic mean of the three Nernst potentials.

VGHK = RT/F ln[(PK[K]out + PNa[Na]out + PCl[Cl]in) / (PK[K]in + PNa[Na]in + PCl[Cl]out)]

Chloride concentrations appear in the opposite orientation because Cl⁻ is negatively charged. The current graph uses the constant-field current equation for each ion. At VGHK, the individual currents can be substantial and opposite, while their sum is zero. The voltage is therefore a steady-state zero-current potential, not equilibrium for every ion. Pumps and transporters are needed to maintain the concentration gradients.

Try this

  • In Nernst mode, increase external K⁺ tenfold and predict the change in EK before moving the slider.
  • Compare Na⁺ and Cl⁻ with the same inside-to-outside concentration ratio.
  • Compare a monovalent ion with Ca²⁺ to see the effect of valence.
  • Use the resting-neuron preset, then raise extracellular K⁺ to model hyperkalaemia.
  • Increase PNa and watch VGHK move toward ENa.
  • Increase PCl and ask whether the effect is depolarizing, hyperpolarizing, or mainly stabilizing.
  • Set equal Na⁺ and K⁺ permeability and explain why the resulting voltage is not halfway between ENa and EK.

Scope and assumptions

The Goldman calculation here is limited to the monovalent ions K⁺, Na⁺, and Cl⁻ and assumes a constant electric field, fixed concentrations, and independent passive ion movement. Relative permeabilities set scale ratios rather than absolute current density. Ca²⁺ is included only in the single-ion Nernst mode. Channel gating, electrogenic pumps, ion accumulation, and concentration changes over time are outside this model.

Model basis

  • Goldman (1943): the constant-field treatment of membrane potential, impedance, and rectification.
  • Hodgkin & Katz (1949): application of ionic concentration and permeability ideas to the squid giant axon.