Full electro-hydro-osmotic solution for charged ion transport in the membrane tube model

Develop and solve a full electro-hydrodynamic–osmotic model for the active membrane tube with unidirectional ion pumps and passive channels that explicitly includes charged ion transport, counterion dynamics to maintain electroneutrality, and electrostatics, rather than assuming neutral osmolytes; determine the resulting pressure and concentration profiles and transport conditions under physiologically relevant parameters.

Background

In the main analysis the paper assumes neutral osmolytes and neglects electrostatics and pH to obtain tractable expressions for pressure and concentration profiles in actively pumped membrane tubes. However, real biological systems involve charged species and counterions, and electrostatic effects can impact membrane mechanics and transport.

The authors explicitly note that a complete treatment should incorporate electro-hydrodynamics with charge and counterion balance. This more realistic model may alter transport thresholds, screening lengths, and stability properties relevant to vacuole formation and water pumping efficiency.