Theoretical Study on the Permeability Coefficient of Hodgkin and Katz
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概要
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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, <I>P</I><SUB>κ</SUB>, which is defined as <I>B</I><SUB>κ</SUB>β<SUB>κ</SUB><I>RT/F<SUB>A</SUB>L</I>, where <I>B</I><SUB>κ</SUB> is mobility of κ-th ion in membrane, <I>B</I>κ is partition coefficient of κ-th ion and <I>L</I> is thickness of the membrane. So, the permeability coefficients play very important part on the study of membrane potential, but <I>P</I><SUB>κ</SUB> is used to be treated as a variable parameter determined by experimental data and theoretical study on <I>P</I><SUB>κ</SUB> has not been made so far. In this paper, <I>P</I><SUB>κ</SUB> 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:<BR>_??_<BR>where <I>i</I>, <I>j</I> show cations and a shows anions, <I>z</I> is charge of ions, gκ=γκ<I>M</I>/<I>b</I><SUB>κ</SUB>γ<SUB>κ<I>B</I></SUB>, <SUB>b</SUB><SUB>κ</SUB>=exp (-Δμ<SUB>κ</SUB><SUP>0</SUP>/<I>RT</I>), γκ is activity coefficient of κ-th ion and suffixes <I>M</I> and <I>B</I> show membrane and bulk, respectively. Δ<I>E</I><I><SUB>D</SUB></I><SUB>1</SUB> and Δ<I><SUB>D</SUB></I><SUB>2</SUB> 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, <I>B</I><SUB>κ</SUB> and <I>P</I><SUB>κ</SUB>. 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 β<SUB>κ</SUB>.
- 日本膜学会の論文
著者
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Nakagaki Masayuki
Faculty Of Pharmaceutical Sciences Kyoto University
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Takagi Ryosuke
Faculty Of Science Kwansei Gakuin University
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Nakagaki Masayuki
Faculty of Living Science Osaka City University
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Takagi Ryosuke
Faculty of Pharmaceutical Sciences, Kyoto University
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