Electrodiffusion active pump model with asymmetric immersed chemical potentials

Electrodiffusion is essential in understanding the mechanisms of electrophysiology. Regarding volume homeostasis, active exchange pumps are critical, as is also significant in the mechanisms of cell division, growth, and apoptosis. In the sense 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. As a consequence of the model simulation, electroneutrality, except for the thin space charge layers along the membrane, is well satisfied. 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 steady-state concentrations from electrodiffusion active pumps with Na ^{+, K} +, Cl ^- ionic species and background charges in the unified entire domain with periodic boundary conditions. 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.

Active pumps are crucial for cellular homeostasis, keeping physiological states. The new computational model for active pump resolves sharply thin space charge layers around membranes in a non-asymptotic manner without the assumption of homogeneous local and global electroneutrality in electrodiffusion. The microscopic representation of kinetic interaction between the water semi-permeable membrane and solutes mediated by the prescribed continuous chemical potential barriers through fluctuation-dissipation satisfies the macroscopic osmotic balance, i.e. van't Hoff law, when there are no active pumps. The biophysical model shows the expected homeostatic volume regulation with active pumps and swelling phenomena without their working. The model framework is applicable to rigorously characterize physiological and disease states involving the coupled electrical and osmotic effects with possible membrane movement.