\[V_m=\frac{RT}{F}\ln\left(\frac{P_K[K]_o+P_{Na}[Na]_o+P_{Cl}[Cl]_i}{P_K[K]_i+P_{Na}[Na]_i+P_{Cl}[Cl]_o}\right)\]
Variables
Vmmembrane potential (V)
Runiversal gas constant (J/mol·K)
Tabsolute temperature (K)
FFaraday constant (C/mol)
Pkpotassium permeability
Pnasodium permeability
Pclchloride permeability
Koextracellular potassium concentration
Kiintracellular potassium concentration
Naoextracellular sodium concentration
Naiintracellular sodium concentration
Cliintracellular chloride concentration
Cloextracellular chloride concentration
Description
What is this formula?
The Goldman-Hodgkin-Katz equation calculates the membrane potential considering the permeability and concentration gradients of multiple ions across a biological membrane.
When to use it
Use this formula in electrophysiology, neuroscience, or cellular biophysics when analyzing resting membrane potentials and ionic transport.
Example
At physiological temperature:
T=310 K
Assume:
Pk=1
Pna=0.04
Pcl=0.45
Ion concentrations:
Ko=5
Ki=140
Nao=145
Nai=12
Cli=4
Clo=110
Constants:
R=8.314
F=96485
Formula:
Vm=((R*T)/F)*ln(((Pk*Ko)+(Pna*Nao)+(Pcl*Cli))/((Pk*Ki)+(Pna*Nai)+(Pcl*Clo)))
Result:
Vm≈-0.070 V
The membrane resting potential is approximately -70 mV.
Applications
- Neuronal electrophysiology
- Cardiac membrane studies
- Ion transport analysis
- Cellular biophysics
- Neurophysiology