Goldman equation

Goldman equation is a fundamental concept in physiology and biophysics, particularly in the study of cell membranes. It is named after the American physiologist David E. Goldman who first proposed the equation in 1943.

Overview

The Goldman equation calculates the membrane potential that results from multiple ions. It is an extension of the Nernst equation which calculates the membrane potential of a single ion. The Goldman equation takes into account the relative permeability of the membrane to different ions, as well as their concentrations on either side of the membrane.

Mathematical Formulation

The Goldman equation is usually written as follows:

V = RT/F * ln((P_K[K+]_o + P_Na[Na+]_o + P_Cl[Cl-]_i) / (P_K[K+]_i + P_Na[Na+]_i + P_Cl[Cl-]_o))

Where:

• V is the membrane potential
• R is the universal gas constant
• T is the absolute temperature
• F is Faraday's constant
• P_K, P_Na, and P_Cl are the relative permeabilities of potassium, sodium, and chloride ions, respectively
• [K+]_o, [Na+]_o, and [Cl-]_o are the concentrations of potassium, sodium, and chloride ions outside the cell, respectively
• [K+]_i, [Na+]_i, and [Cl-]_i are the concentrations of potassium, sodium, and chloride ions inside the cell, respectively

Applications

The Goldman equation is used in many areas of physiology and biophysics, including:

• Understanding the resting membrane potential of cells
• Predicting changes in membrane potential due to changes in ion concentrations or permeabilities
• Studying the effects of ion channel mutations on membrane potential

See Also

• Nernst equation
• Hodgkin-Huxley model
• Resting potential
• Action potential