A non-equilibrium thermodynamics model of reconstituted Ca²⁺-ATPase

Abstract

A non-equilibrium thermodynamics (NET) model describing the action of completely coupled or `slipping' reconstituted Ca<sup>2+</sup>-ATPase is presented. Variation of the coupling stoichiometries with the magnitude of the electrochemical gradients, as the ATPase hydrolyzes ATP, is an indication of molecular slip. However, the Ca<sup>2+</sup> and H<sup>+</sup> membrane-leak conductances may also be a function of their respective gradients. Such non-ohmic leak typically yields `flow-force' relationships that are similar to those that are obtained when the pump slips; hence, caution needs to be exercised when interpreting data of Ca²⁺-ATPase-mediated fluxes that display a non-linear dependence on the electrochemical proton (Δµ˜_H) and/or calcium gradients (Δµ˜_Ca). To address this issue, three experimentally verifiable relationships differentiating between membrane leak and enzymic slip were derived. First, by measuring Δµ˜_H as a function of the rate of ATP hydrolysis by the enzyme. Second, by measuring the overall `efficiency' of the pump as a function of Δµ˜_H. Third, by measuring the proton ejection rate by the pump as a function of its ATP hydrolysis rate.