The interactions that generate the resting potential are modeled by the Goldman equation.

In this case, the resting potential can be determined from the Goldman equation:

This results is a slightly more depolarized membrane potential of the fiber during repeated action potentials, see Goldman equation.

In a more formal notation, the membrane potential is the weighted average of each contributing ion's equilibrium potential (Goldman equation).

The Nernst equation can be considered a special case of the Goldman equation for only one ion:

This hyperpolarization is caused by the effect of the altered potassium gradient on resting membrane potential as defined by the Goldman equation.

If this function is interfered with, the extracellular concentration of potassium will rise, leading to neuronal depolarization by the Goldman equation.

Two important equations that can determine membrane potential differences based on ion concentrations are the Nernst Equation and the Goldman Equation.

David E. Goldman (1910 - 1998) was a scientist famous for the Goldman equation which he derived for his doctorate degree at Columbia University.

In most quantitative treatments of membrane potential, such as the derivation of Goldman equation, 'electroneutrality' is assumed; that is, that there is no measurable charge excess in any side of the membrane.

If divalent ions such as calcium are considered, terms such as e appear, which is the square of e; in this case, the formula for the Goldman equation can be solved using the quadratic formula.

Julius Bernstein was also the first to introduce the Nernst equation for resting potential across the membrane; this was generalized by David E. Goldman to the eponymous Goldman equation in 1943.

As can be derived from the Goldman equation shown above, the effect of increasing the permeability of a membrane to a particular type of ion shifts the membrane potential toward the reversal potential for that ion.

For fixed ion concentrations and fixed values of ion channel conductance, the equivalent circuit can be further reduced, using the Goldman equation as described below, to a circuit containing a capacitance in parallel with a battery and conductance.

Second, according to the Goldman equation, this change in permeability changes in the equilibrium potential E, and, thus, the membrane voltage V. Thus, the membrane potential affects the permeability, which then further affects the membrane potential.

The Goldman-Hodgkin-Katz voltage equation, more commonly known as 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.