VERA MAURA FERNANDES DE LIMA
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Artigo IPEN-doc 28171 Analyses of HH and GHK equations with another perspective2021 - TAMAGAWA, HIROHISA; MULEMBO, TITUS; LIMA, VERA M.F. de; HANKE, WOLFGANGTwo mathematically distinct physiological concepts, the Goldman-Hodgkin-Katz eq. (GHK eq.) and the Hodgkin-Huxley model (HH model) were successfully associated with each other in a prior work. The previous work was performed on the following premises (i) The membrane potential is generated by ion adsorption, as opposed to the classical ion transport mechanisms, (ii) The living cell is a thermodynamically real system rather than an ideal system, and (iii) The conductance employed in the HH model is replaced by the ion activity coefficient, which is weighted with the role of conductance. Consequently, the GHK eq. was mathematically associated with the HH model through the intermediary of Boltzmann ion distribution and mass action law. To verify if our theoretical formularization could afford a physiologically, physically and chemically viable model, we performed computational analysis using the formulae (quantitative correlations between various variables) we derived in the previous work. The computational results obtained through associating the GHK eq. with the HH model validated our model and its predictions. This outcome suggests that the current prevailing physiological concepts could be expanded further, to incorporate the newly proposed mechanisms. That is, GHK eq. and HH model could be interpreted via another set of founding principles that incorporate the ubiquitous phenomena of ion-adsorption.Artigo IPEN-doc 27431 GHK eq. and HH eq. for a real system is mathematically associable to each other but their physiological interpretation needs a reconsideration2020 - TAMAGAWA, HIROHISA; MULEMBO, TITUS; LIMA, VERA M.F. de; HANKE, WOLFGANGDespite the long and broad acceptance of the Goldman - Hodgkin - Katz equation (GHK eq.) and the Hodgkin - Huxley equation (HH eq.) as strong tools for the quantitative analysis of the membrane potential behavior, for a long time they have been utilized as separate concepts. That is the GHK eq. and the HH eq. have not been associated with each other mathematically. In this paper, an attempt to associate these equations to each other mathematically was demonstrated and was successful by viewing the system in question as a thermodynamically real system rather than an ideal system. For achieving that, two fundamental physical chemistry concepts, the mass action law, and the Boltzmann distribution were employed. Hence, this paper’s achievement is completely within the framework of common thermodynamics. Through this work, the origin of the membrane potential generation attributed to the ion adsorption-desorption process and governed by the mass action law and the Boltzmann distribution is expressed to be plausible, whereas the existing membrane potential generation mechanism states that membrane potential is generated by transmembrane ion transport. As at this moment, this work does not intend to deny the transmembrane ion transport as a membrane potential generation mechanism but urges the readers to reconsider its validity, since this work suggests that the ion adsorptiondesorption mechanism is as plausible as the transmembrane ion transport mechanism as a cause of membrane potential generation.