Model calculations of ion transport against its concentration gradient when the driving force is a pH difference across a charged membrane

Model calculations of the steady-state ion transport against its external concentration gradient when the driving force of this transport is a pH difference across a charged membrane are presented. We have solved numerically the exact Nernst-Planck equations without any additional simplifying approximation, such as the Goldman constant field assumption within the membrane. The validity of this assumption for a broad range of pH values, and salt and membrane fixed charge concentrations was analyzed critically. Thr membrane characteristics studied are the ionic fluxes and the membrane potential. Special attention is paid to the physical mechanism which leads to the ion transport against the concentration gradient, and the experimental conditions for which this transport can occur. The case of a system with ions of different charge numbers is also considered.