# GHK Equation and Action potential

Can GHK equation be used to predict the membrane potential even if the cell is not at resting state?

To say it again, can we use GHK equation at every moment during Action potential?

I'm confused because GHK equation is derived at the situation with total ionic current is zero, but is that true also during AP?

The GHK voltage equation also known as just "Goldman equation" is always valid for determining the voltage at which the net current is zero, given internal/external ion concentrations and their permeabilities. This includes times during the action potential, though the result you get from GHK will be changing faster than the actual membrane potential itself, since the change in membrane potential brings about changes in permeabilities.

It's still useful to think about this equation to determine in which direction the membrane potential is changing instantaneously: it will always be changing towards the equilibrium potential. You can also qualitatively estimate the relative rate of change: if the current voltage is very far away from the equilibrium potential, the voltage will change more rapidly than if it is close to equilibrium.

However, this equation is just a steady-state equation. It doesn't tell you how quickly you will get to the new voltage or exactly which ions will move. For this, you need some other equations and other parameters, namely the actual permeabilities (rather than relative permeabilities) of the ions and the membrane capacitance.

The GHK flux equation can help: this will give you the flux of each ion at a given membrane potential (Wikipedia shows how this equation is related algebraically to the Nernst equation, which in turn is equivalent to the Goldman/GHK voltage equation for a single ion). You can also think in terms of the Hodgkin-Huxley model and the simple differential equation for current.

In summary, with respect to your question:

Can GHK equation be used to predict the membrane potential even if the cell is not at resting state?

It can predict where the membrane potential is headed, but not what it actually is or how fast it's changing, and the voltage you get from GHK will itself change as membrane potential changes affect the parameters that go into the GHK equation itself.