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Equilibrium Potential: Nernst Equation Derived
If a particular ion is in equilibrium, the following relationship holds:
where dC/dx is the concentration
gradient across the membrane for that ion, and dV/dx is the voltage gradient across the membrane.
If we solve this equation for V (the voltage that has to exist across the membrane for the ion to be in equilibrium), the following expression results:
where ln signifies the natural log (log base e) of the quotient.
This equation, the Nernst Equation, is very important for understanding the electrophysiological properties of cell membranes. You do not need to know how to derive it, but you need to commit it to memory, understand its significance, and know how to apply it.
The Nernst equilibrium potential for an ion (usually referred to as either the Nernst potential or the equilibrium potential and abbreviated Ei) is a calculated quantity. It is calculated for each species of charged particle (and only for charged particles) in solution. It is the potential across the membrane that, if it existed, would produce an electrical force on an ion that exactly opposes the force on that ion due to the concentration gradient of the ion.
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