Goldman equation

The Goldman–Hodgkin–Katz voltage equation, sometimes called the Goldman equation, is used in cell membrane physiology to determine the reversal potential across a cell's membrane, taking into account all of the ions that are permeant through that membrane. The discoverers of this are David E. Goldman of Columbia University, and the Medicine Nobel laureates Alan Lloyd Hodgkin and Bernard Katz. The GHK voltage equation for monovalent positive ionic species and negative: This results in the following if we consider a membrane separating two -solutions: It is "Nernst-like" but has a term for each permeant ion: = the membrane potential (in volts, equivalent to joules per coulomb) = the selectivity for that ion (in meters per second) = the extracellular concentration of that ion (in moles per cubic meter, to match the other SI units) = the intracellular concentration of that ion (in moles per cubic meter) = the ideal gas constant (joules per kelvin per mole) = the temperature in kelvins = Faraday's constant (coulombs per mole) is approximately 26.7 mV at human body temperature (37 °C); when factoring in the change-of-base formula between the natural logarithm, ln, and logarithm with base 10 , it becomes , a value often used in neuroscience. The ionic charge determines the sign of the membrane potential contribution. During an action potential, although the membrane potential changes about 100mV, the concentrations of ions inside and outside the cell do not change significantly. They are always very close to their respective concentrations when the membrane is at their resting potential. Using , , (assuming body temperature) and the fact that one volt is equal to one joule of energy per coulomb of charge, the equation can be reduced to which is the Nernst equation. Goldman's equation seeks to determine the voltage Em across a membrane. A Cartesian coordinate system is used to describe the system, with the z direction being perpendicular to the membrane.