A simplified model for V-ATPase H+ extrusion

An analytical model of V-type H⁺-translocating ATPase (V-ATPase) was developed based on an approximation to the mechanochemical model of Grabe et al. (Biophys. J., pp. 2798-2813, vol. 78, 2000). Grabe\´s work utilizes structural information and physiological assumptions to construct a detailed mechanochemical model of the V-ATPase. Due to the complexity of their model, it does not give a readily usable mathematical expression for the V-ATPase current. Based on their analysis of the structure of the proton pump, we develop a two-compartment model of the V-ATPase, which contains a membrane "half-channel" for proton translocation separated by a hydrophilic strip and a hydrophobic wall from the cytoplasm. Using the Langevin equation to describe proton transport across the membrane, we simplify the model based on their assumptions on the molecular structure of the pump and arrive at a general form of solution to the proton pump flux driven by ATP hydrolysis based on assumptions on the physiological properties of the strip and the wall, as well as the two fluid compartments. In this process of simplification, we explicitly relate V-ATPase structure, stoichiometry, pump efficiency, and ATP hydrolysis energy to the active pump current. The simplified model is used to provide model-generated approximations to measured data from a variety of laboratories. In addition, it provides a very compact characterization of V-ATPase, which can be used as a proton extruder in a variety of different cell membranes, as well as in the membranes of intracellular organelles.