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Home/Biophysics, Fluids & Geoscience/Nernst Potentials & Membrane

Nernst Potentials & Membrane

Ion concentrations on either side of a semipermeable membrane set the Nernst equilibrium voltage for each species. When several ions permeate with different permeabilities, the Goldman–Hodgkin–Katz equation estimates the zero-current (resting) potential. Sliders expose how extracellular potassium or relative sodium permeability shifts V_m.

Who it's for: Introductory biophysics or physiology students.

Key terms

  • Nernst equation
  • GHK voltage
  • Resting potential
  • Permeability

Cl⁻ uses fixed demo concentrations; tune P_K : P_Na : P_Cl to see how resting voltage shifts toward the dominant permeant ion.

Live graphs

Concentrations & permeabilities

310 K
140 mM
5 mM
15 mM
145 mM
1
0.05
0.45

Nernst for each ion: E = (RT/zF) ln(a_out/a_in). GHK resting estimate uses constant [Cl] example (5 / 120 mM) with your P ratios — illustrative, not fitted cell data. Nernst–Planck flux (1D, dilute): J_i = −D_i ∂c_i/∂x − μ_i z_i F c_i ∂V/∂x; near equilibrium the net K⁺ current is often discussed as proportional to P_K(V_m − E_K) in linearized treatments — see the sidebar driver (arbitrary scale).

Measured values

E_K (Nernst)-89.0 mV
E_Na (Nernst)60.6 mV
E_Cl (example)-84.9 mV
V_m (GHK)-69.4 mV
K⁺ driver P_K(V_m−E_K)19.62 a.u.

How it works

Thermodynamic reversal potentials from concentration ratios, plus a Goldman–Hodgkin–Katz estimate of zero-current voltage when multiple ions permeate.

Frequently asked questions

Why fix chloride concentrations in the GHK example?
To keep the control panel tractable; chloride is included with illustrative intracellular/extracellular values so the GHK denominator is well posed.