Abstract
To analyze the biomembrane potential, Hodgkin-Katz equation is usually used, which has the same assumption as Goldman equation. In addition to the constant field assumption, they assume that ion concentration in membrane is directly proportional to ion concentration in bulk solution at bulk-membrane interface. In Hodgkin-Katz equation, the contributions to membrane potential from the interface are included in the permeability coefficient, Pκ, which is defined as BκβκRT/FAL, where Bκ is mobility of κ-th ion in membrane, Bκ is partition coefficient of κ-th ion and L is thickness of the membrane. So, the permeability coefficients play very important part on the study of membrane potential, but Pκ is used to be treated as a variable parameter determined by experimental data and theoretical study on Pκ has not been made so far. In this paper, Pκ is studied theoretically and it is pointed out that Hodgkin-Katz equation is quit equivalent to Goldman equation if the ratio of the partition coefficients are set as follows:
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where i, j show cations and a shows anions, z is charge of ions, gκ=γκM/bκγκB, bκ=exp (-Δμκ0/RT), γκ is activity coefficient of κ-th ion and suffixes M and B show membrane and bulk, respectively. ΔED1 and ΔD2 show interfacial potentials at the interfaces 1 and 2, respectively. For a two ion system and a three ion system, the experimental conditions and methods are investigated in order to determine the value of parameters, Bκ and Pκ. It is also pointed out that the measured membrane potential can be separated into the diffusion potential and the interfacial potential by use of the value of βκ.
