Electric potential generation of electrocytes: Modelling, analysis, and computation

•A PNP (or PDE) model is formulated for the mechanism of electrocyte.•The superposition of two membrane potentials is rigorously explained by PNP model.•Classical membrane (or ODE) model can not explain the above superposition principle.•PNP model reduces to the membrane model at leading order by asymptotic analysis. In this paper, we developed a one-dimensional model for electric potential generation of electrocytes in electric eels. The model is based on the Poisson–Nernst–Planck system for ion transport coupled with membrane fluxes including the Hodgkin–Huxley type. Using asymptotic analysis, we derived a simplified zero-dimensional model, which we denote as the membrane model in this paper, as a leading order approximation. Our analysis provides justification for the assumption in membrane models that electric potential is constant in the intracellular space. This is essential to explain the superposition of two membrane potentials that leads to a significant transcellular potential. Numerical simulations are also carried out to support our analytical findings.