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Biophysics Insight?
Warning: This message may seem a little esoteric unless you are into membrane biophysics/neural excitability.
My adviser posed to me the following question today (and warned that thinking about it may lead to some sleepless nights):
On biological membranes, there are fixed negative charges which generate a surface potential and alter the concentration of ions near the membrane surface which leads to charge screening; thus to accurately use the Goldman (Constant Field/Goldman-Hodgkin-Katz actually) equation to calculate the membrane potential, one must apply a Boltzmann ?correction factor? for the ion(s) of interest. However, there is no need to make this correction to calculate the equilibrium potential for a single ion using the Nernst equation. Why so?
I have come up with some intuitive arguments but want to show it mathematically to convince myself before getting back to him ? any insight from the real physicists would be most appreciated (I have a feeling that the solution is actually fairly trivial). Hope it doesn?t give any of you sleepless nights!
My adviser posed to me the following question today (and warned that thinking about it may lead to some sleepless nights):
On biological membranes, there are fixed negative charges which generate a surface potential and alter the concentration of ions near the membrane surface which leads to charge screening; thus to accurately use the Goldman (Constant Field/Goldman-Hodgkin-Katz actually) equation to calculate the membrane potential, one must apply a Boltzmann ?correction factor? for the ion(s) of interest. However, there is no need to make this correction to calculate the equilibrium potential for a single ion using the Nernst equation. Why so?
I have come up with some intuitive arguments but want to show it mathematically to convince myself before getting back to him ? any insight from the real physicists would be most appreciated (I have a feeling that the solution is actually fairly trivial). Hope it doesn?t give any of you sleepless nights!
Comments on this journal
Warning 2: Googling, I just had a 15 minute crash course in biophysics and looked at the symbolic form of the equations.
Warning 3: What follows is my best GUESS based on my physics knowledge.
If we look at the derivation of Nernst equation, we can "see" all the Boltzman factors. In other words, the equation is based on Boltzmann's statistics. Goldman's equation, on the other hand, isn't based on Boltzmann statistics (is it?)
When we have a surface voltage, the charges in the vicnity will acquire an energy of E = q*V and therfore we have to manually put in the contribution of that energy through boltzmann factor. I think that in Nernst equation we have already accounted for this energy in our derivation and so no need for any correction terms.
We can also think of the problem in terms of a capacitor with some dielectric in it. So potential will be the voltage across the plates of this capacitor. Then I can say that adding an extra boltzmann factor is same as accounting for self-energy of the dielectric....?
It's an interesting problem...would love to know the answer.....
All the Best