Abstract

This paper presents a comprehensive theoretical derivation of a membrane potential formula based on the Association-Induction Hypothesis (AIH), challenging traditional membrane theory and the Goldman–Hodgkin–Katz equation (GHK equation). The study demonstrates that membrane potential is not primarily a result of transmembrane ion transport through channels and pumps, but rather a consequence of the Boltzmann distribution of mobile ions influenced by their adsorption onto cell constituents. By employing a variational principle to minimize the total free energy of the system—consisting of ion mixing entropy, electrostatic energy, and adsorption energy—the authors derive a generalized membrane potential formula. Unlike the GHK equation, this model explicitly incorporates fixed charge density and the specific adsorption affinity of ion species such as K+ and NH3+ onto carboxyl (COO−) groups. The derivation shows that cell potential (so-called membrane potential) can be generated even in the absence of a plasma membrane, suggesting that the transmembrane ion transport mediated by channels and pumps may not be the principal cause of the membrane potential generation but rather that the ion adsorption and desorption must govern the membrane potential generation. Ultimately, this research suggests that the fundamental mechanism of potential generation in biological systems is the equilibrium distribution of ions governed by thermodynamic stability rather than non-equilibrium steady-state flux.

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