E3: Membrane voltage

If there is a membrane, permeable only to one ion, then the voltage across the membrane is given by the Nernst potential for that ion.

$$\Delta V = \frac{RT}{zF}\ln\frac{[Ion]_{\text{out}}}{[Ion]_{\text{in}}}$$

where R is the gas constant, T is the absolute temperature, z is the ion valence, and F is the Faraday constant. \(\frac{RT}{F} = 26.7\text{mV}\).

This gives a good way to understand the opening of an ion channel - it "drags the membrane voltage towards the Nernst potential for that ion".

This is an extension of the Nerst equations to account for multiple ions:

$$\Delta V = \frac{\sum_{\text{Cations C}} P_C[C]_out + \sum_{text{Anions A}} P_A}[A]_in}{\sum_{\text{Cations C}} P_C[C]_in + \sum_{text{Anions A}} P_A}[A]_out}$$

When the permiability of all but one ion is set to zero, this reduces to the Nerst equation.

This occurs when there is an impermiable ion on one side of a semipermiable membrane. Consider the case of anionic protein inside a cell, with a membrane permiable to chloride.

1. The chloride diffuses down its concerntration gradient
2. This creates a negative charge in the inside of the cell
3. This drags some cations, against their concerntration gradient, into the cell
4. The overall effect is to create a negative intracellular charge and an increase in intracellular osmolality
5. The osmolality change is counteracted by sodium export from the Na/K pump in vivo

This effect also amplifies the oncotic pressure exerted by plasma proteins, with exert a Gibbs-Donnan influence by dragging extra cations into the plasma (in addition to what would be expected from their charge).