PMC

Rate of ATP synthesis and hydrolysis as a function of the transmembrane ΔpH. The initial rates and their errors obtained from , and additional measurements, were plotted as a function of ΔpH. Some error bars are not visible, because they are smaller than the size of the symbols. Each curve represents catalysis rates measured at a constant stoichiometric product, Q. The data were fitted, using their errors as weight, by a function that was the product of a linear function (describing the rate-force relation near equilibrium) and of a sigmoidal function (describing the ΔpH dependence of activation). The fitting functions were used to interpolate the point at which the rate is zero [ΔpH(eq)]. (Left) CF₀F₁ proteoliposomes. (Right) EF₀F₁ proteoliposomes.

ATP synthesis and ATP hydrolysis after generation of a transmembrane ΔpH. The basic medium (900 μl) with the preestablished Q value and with luciferin/luciferase was placed into a cuvette in the luminometer, and the baseline was registered. The acid-base transitions were carried out by injection of 100 μl of proteoliposomes, incubated in the acidic reconstitution medium at different pH_in. The final pH_out was 8.47 ± 0.02, and the ΔpH values are given next to each trace. The addition gives rise to an immediate jump of the baseline. For clarity, the baseline was shifted back to the original luminescence level. The luminescence increase indicates ATP synthesis, the decrease indicates ATP hydrolysis. The different panels refer to different stoichiometric ratios Q as indicated. The luminescence was calibrated by addition of standard ATP. The solid lines show a biexponential fit of the complete time trace. The initial rates and their errors are given in units of 10⁻³ s⁻¹; they were calculated from the monoexponential fit of the first part of the traces, as detailed in SI Fig. 6. (Left) CF₀F₁ proteoliposomes. The final CF₀F₁ concentration was 7.6 nM. (Right) EF₀F₁ proteoliposomes. The final EF₀F₁ concentration was 23 nM.

Determination of the thermodynamic H⁺/ATP ratio. ΔpH(eq) was plotted versus the stoichiometric product Q according to (data from ). (Upper Left) CF₀F₁ data (from Left). The error associated with ΔpH(eq) has been taken to coincide with the error estimated for ΔpH determination by the pH electrode (±0.03). The data were fitted by a straight line, using their errors as weight. The slope of the linear regression gives the H⁺/ATP ratio. The y intercept gives the standard Gibbs free energy −ΔG_p⁰′ at pH_out = 8.47. The arrow marked as R&S indicates the value of −ΔG_p⁰′ published in ref. . (Upper Right) EF₀F₁ data (from Right). The −ΔG_p⁰′ value (diamond) is the best-fitting parameter out of the CF₀F₁ data (Left) and has been included in the linear regression of the EF₀F₁ data. The data were fitted by a straight line, using their errors as weight. The slope of the linear regression gives the H⁺/ATP ratio. To account for the error on the y axis of the ΔG_p⁰′ value, two additional linear fits were calculated, using its two extreme values of 35 and 41; the resulting H⁺/ATP values were 3.7 and 4.3 respectively, whose difference from 4.0, being higher than the error resulting from each linear regression, has been taken as the error in the determination of this parameter. (Lower) The CF₀F₁ (circles) and EF₀F₁ (triangles) data from Upper are plotted together for better comparison; the squares are CF₀F₁ data from ref. , in which the Δϕ component has been converted in ΔpH units (15 mV, corresponding to 0.26 ΔpH units). The straight line is the regression line of Upper Left.