Membrane Potential

skandy

In membrane potential determination of a cell, the Goldman Hodgkin Katz equation says the contribution of an ion to diffusion potential is dependent on its membrane permeability.
So in case an ion, one that has a zero permeability, is present outside the cell, using the equation , one will get contribution to diffusion potential as zero but thinking rationally, the charge on the ion must contribute to the electrical potential across the membrane.
Though I see that the equation is meant for diffusion potential, I see that the same equation is being used to find the resting membrane potential.

Here my questions are
1. Are membrane potential and net diffusion potential the same?
2. Isn't there any contribution to membrane Potential by an ion with zero permeability? If so how? Is there a different equation for it? Or will its presence influence the membrane permeability for other ions and thus have an effect?

atyy

Usually we assume that the bulk of the solution starts off neutral, eg. the solution could be A⁺B^- both inside and outside the cell. Let's suppose AB has a high concentration inside the cell and a low concentration outside. If there is a concentration difference across an impermeable membrane, then since no ions can move, both sides will stay neutral, and there will be no membrane potential difference.

If the membrane is permeable to A and impermeable to B, then A will try to diffuse down the concentration gradient from the inside of the cell to the outside of the cell. This will cause a net positive charge inside the cell and a net negative charge outside the cell. This charge excess will try to couteract the diffusion of A, since negatively charged A will be attracted back to the now positive environment inside the cell. The steady membrane potential occurs when the excess positive charge caused inside the cell exactly balances the tendency of A to diffuse out of the cell according to the concentration gradient.

Together, these two pictures are why we only put (explicitly) the permeable ions into the equation. You can also see by this reasoning that if A and B were both permeable, then both would diffuse together down the concentration gradient, and there would be no electric charge separation.

One approximation we usually make is that in principle the diffusion of A from the inside to the outside changes the concentration in the cell. But we ignore this because it takes relatively few ions to move across the cell membrane to cause a big membrane potential difference, and these few ions don't change the concentrations inside and outside by much.

These approximations can break down, but they illustrate why impermeable ions don't have to be explicitly considered in most approximations.

Andy Resnick

Consider soluble proteins- they have lots of negative charge but cannot leave the cell. This leads to movement of *water* across the membrane (Donnan equilibrium). Small ions will move down their concentration gradient until a final equilibrium concentration and membrane potential is reached for each semipermeable ion species (GHZ equations) and water will move until the osmotic gradient and hydrostatic gradient are equalized.

As a specific example, consider the extracellular space to initially have 150mM of NaCl and the cytosol to have [Na+] = 150 mM, [Cl-] = 0 mM, and [protein] = 1mM = 150 mEq (each protein molecule has 150 negative charges). Initially, Cl moves down the concentration gradient into the cell, which draws additional Na in to maintain electroneutrality. Final equilibrium is reached when the extracellular space has [Na] = [Cl] = 100mM and the cytosol has [Na] = 200 mM, [Cl] = 50 mM, the membrane potential is -18.4 mV (cell is negative) and the hydrostatic pressure jump is 967 mmHg (cell is positive).