Supplemental Material for J . Gen . Physiol . Vol . 117 No . 4 p . 329 , Grabe and Oster Detailed Calculations and Discussion

We have constructed a mechanochemical model for the V-ATPase that predicts proton pumping rates over a wide range of environmental conditions. We have used this model to determine the acidification of organelles. The conventional paradigm for active transmembrane ion transport is the “alternating access” mechanism: ions are bound tightly on the low concentration side of the membrane and a conformational change exposes them to the high concentration side and weakens their binding affinity so that they dissociate. The pump then resets its conformation to repeat the cycle (Eisenberg and Hill, 1985; Alberts et al., 1994). The energy to drive the cycle is supplied by nucleotide hydrolysis or an ion gradient. The Na-K-ATPase conforms to this traditional view of alternating access (see below); however, the conformational change in the V-ATPase is a simple rotation. In our computations here, we assume that the V-ATPase is working under normal operating conditions and that ATP concentrations are sufficiently high that hydrolysis is not rate limiting. By analogy with the F-ATPases, the V-ATPase structure is conventionally divided into a counter-rotating “stator” and “rotor” (Boekema et al., 1997; Finbow and Harrison, 1997; Forgac, 2000). Hydrolysis of ATP in the V1-soluble headpiece provides the torque that rotates the membrane-bound section Vo. Two models have been suggested for the rotor–stator assemblies: a two-channel model and a one-channel model (Vik and Antonio, 1994; Junge et al., 1997; Elston et al., 1998; Grabe et al., 2000). They differ in the path that the protons take through the enzyme and in the degree to which protons bound to the rotor section communicate with the cytoplasm. There is significant debate about the true structure of the channel in the Vand F-ATPase enzymes. We have shown that both channels behave similarly within the context of our mechanochemical model (Dimroth et al., 1999; Grabe et al., 2000). More recently, experiments on sodium V-ATPases strongly support the one channel model (Murata et al., 2000). There-