Electrodiffusion active pump model with asymmetric immersed chemical potentials

Electrodiffusion is essential in understanding the mechanisms of electrophysiology. Active exchange pumps are critical regarding volume homeostasis, and are also significant in the mechanisms of cell division, growth, and apoptosis. In the formalism of the immersed boundary (IB) method, we replace classical interface conditions across the membrane with regularized chemical potentials to control the permeation of each ionic species governed by the Poisson-Nernst-Planck equation. In asymmetry, to regulate ionic transport, continuous chemical potential barriers are augmented with energetic gradients represented by smoothed Heaviside kernels specifying the directions of active pumps. We obtain steadystate concentrations from electrodiffusion active pumps using Na⁺, K⁺, Cl^- ionic species, with background charges in the entire unified domain under periodic boundary conditions. As a consequence of the model simulation, electroneutrality, except for the thin space charge layers along the membrane, is well satisfied. The electrodiffusion active pump model for the exchange of sodium and potassium (NKE) exhibits a good fit to the theoretical formula over a broad range of perturbations in ionic concentrations, ensuring volume conservation in the steady state only when active pumps are functioning. It is also shown that van't Hoff's law is satisfied without active pumps. This is a foundation for applying the IB electrodiffusion active pump model for subcellular transport of water and molecules, possibly involving cell motility and migration.