Nernst Equation - Nernst Potential

Nernst Potential

The Nernst equation has a physiological application when used to calculate the potential of an ion of charge z across a membrane. This potential is determined using the concentration of the ion both inside and outside the cell:

When the membrane is in thermodynamic equilibrium (i.e., no net flux of ions), the membrane potential must be equal to the Nernst potential. However, in physiology, due to active ion pumps, the inside and outside of a cell are not in equilibrium. In this case, the resting potential can be determined from the Goldman equation:

• = The membrane potential (in volts, equivalent to joules per coulomb)
• = the permeability for that ion (in meters per second)
• = the extracellular concentration of that ion (in moles per cubic meter, to match the other SI units, though the units strictly don't matter, as the ion concentration terms become a dimensionless ratio)
• = the intracellular concentration of that ion (in moles per cubic meter)
• = The ideal gas constant (joules per kelvin per mole)
• = The temperature in kelvin
• = Faraday's constant (coulombs per mole)

The potential across the cell membrane that exactly opposes net diffusion of a particular ion through the membrane is called the Nernst potential for that ion. As seen above, the magnitude of the Nernst potential is determined by the ratio of the concentrations of that specific ion on the two sides of the membrane. The greater this ratio the greater the tendency for the ion to diffuse in one direction, and therefore the greater the Nernst potential required to prevent the diffusion.

A similar expression exists that includes r (the absolute value of the transport ratio). This takes transporters with unequal exchanges into account. See: Sodium-Potassium Pump where the transport ratio would be 2/3. The other variables are the same as above. The following example includes two ions: Potassium (K+) and sodium (Na+). Chloride is assumed to be in equilibrium.

When Chloride (Cl−) is taken into account, its part is flipped to account for the negative charge.