Buffered Diffusion around a Spherical Proton Pumping Cell: A Theoretical Analysis

H+ ions are a substrate of many active and passive membrane transporters in all cells. Absolute proton fluxes are often quantified using intracellular pH sensitive microelectrodes or pH sensitive dyes. These measurements, however, rely on a priori estimates of the intracellular buffer capacity and on the assumption of diffusive equilibrium inside the cell. Here, assuming local equilibrium of protons with a single mobile buffer, we model the diffusion of H+ in the extracellular medium around an H+ pumping cell to estimate the expected pH changes as a function of time, distance from the cell, extracellular buffer capacity, and the absolute proton flux across the membrane. In particular, using accurate numerical simulation, we gauge the range of validity of an explicit, analytical solution of the linearized, nonstationary diffusion equation. Our results provide a framework to quantify the absolute membrane proton flux, if spatiotemporal information about the extracellular pH change is available, e.g., using imaging of pH dependent fluorescent dyes.