Goldman-Hodgkin-Katz constant field

Q.23.3 (a) What are the assumptions in the Goldman-Hodgkin-Katz constant field equation (b) Under what circumstances does the equation tend to fail (c) Choose one assumption and hypothesize a specific situation that it might not be applicable. 

Figure 26. Membrane potential profiles (A) Goldman-Hodgkin-Katz constant field model (diffusion potential-dominated) (B) fixed-charge membrane model with positive fixed charges.

An equation (also referred to as the constant field equation, the Goldman-Hodgkin-Katz equation, and the GHK equation) which relates the membrane potential (Ai/r) to the individual permeabilities of the ions (and their concentrations) on both sides of the membrane. Thus,... 

Three assumptions are usually made in calculating ion current density through a membrane (a) an ion does not interact with any other ion while traversing the membrane (independence principle) (b) the membrane is homogeneous and (c) the electric field in the membrane is constant in space. The linear transport equation then leads to the Goldman-Hodgkin-Katz equation - for the I -V relation ... 

We next explored the fit of the data to a more detailed relationship than that forming the basis of Nernst equation. We wrote the Goldman constant field equation (3) in the form used by Hodgkin and Katz (4) in the exponential form shown here as equation 3. 

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