Biophysical comparison of ATP synthesis mechanisms shows a kinetic advantage for the rotary process

Abstract

The ATP synthase (F-ATPase) is a highly complex rotary machine that synthesizes ATP, powered by a proton electrochemical gradient. Why did evolution select such an elaborate mechanism over arguably simpler alternating-access processes that can be reversed to perform ATP synthesis? We studied a systematic enumeration of alternative mechanisms, using numerical and theoretical means. When the alternative models are optimized subject to fundamental thermodynamic constraints, they fail to match the kinetic ability of the rotary mechanism over a wide range of conditions, particularly under low-energy conditions. We used a physically interpretable, closed-form solution for the steady-state rate for an arbitrary chemical cycle, which clarifies kinetic effects of complex free-energy landscapes. Our analysis also yields insights into the debated "kinetic equivalence" of ATP synthesis driven by transmembrane pH and potential difference. Overall, our study suggests that the complexity of the F-ATPase may have resulted from positive selection for its kinetic advantage.

Keywords: ATP synthase; evolution; free-energy landscape; kinetic mechanism; nonequilibrium steady state.

Fig. 1.

ATP synthesis by rotary and alternating-access mechanisms. H⁺ transport across the membrane is driven by transmembrane differences in pH and electric potential ψ. (A) In the rotary mechanism, H⁺ transport drives the rotation of the transmembrane ring, which induces conformational changes that catalyze phosphorylation of ADP. (B) In the alternating-access mechanism, H⁺ binding allosterically produces the conformational changes necessary to catalyze phosphorylation of ADP.

Fig. 2.

Minimalist kinetic modeling of rotary and alternative mechanisms for ATP synthesis. (A) Synthesis cycles for the rotary and basic alternating-access mechanisms, which are (kinetically) distinguished by their orders of proton transport. (B) Other possible mechanisms based on proton transport order for a 3:1 H⁺:ATP stoichiometry. Note that conformational processes, such as rotation, are implicitly included in the binding and chemical processes shown, in a thermodynamically consistent way. Alternative stoichiometries as well as event orders (binding and reaction sequences) were also considered as described in the text and SI Appendix.

Fig. 3.

Performance of ATP synthesis mechanisms. (A and B) Performance relative to rotary calculated as the geometric average ratio for each mechanism relative to the rotary process, for a wide range of conditions. (A) Varying model assumptions—event order, optimization protocol, parameter values, and pH_out range—show that relative performance is qualitatively insensitive to these assumptions. (B) The advantage of the rotary mechanism is the greatest under challenging conditions (low driving potential $\mathrm{\Delta }{G}_{\text{driv}}$). (C) The average rate of ATP synthesis is quantitatively and qualitatively similar to experimentally reported values when pmf is varied (39, 43), providing further support for these results. Error bars show the standard error of the mean when sampling over a range of conditions. Data for B and C are from the default set of models described in SI Appendix.

Fig. 4.

Free-energy (FE) landscape effects on ATP synthesis rate: the maximum FE climb. FE landscapes are shown for the rotary and basic alternating-access mechanisms represented in Fig. 2A, with a representative set of kinetic parameters determined by the parameter optimization protocol, and typical physiological conditions, as described in Methods. The specific parameter and condition values are listed in SI Appendix. For the example shown here, the maximum FE climbs are 3.7 and 7.2 kcal/mol for the rotary and alternating-access mechanisms, respectively, with corresponding rates of 9.5 and 2.5 ATP per s.

Fig. 5.

Sensitivity of apparent kinetic equivalence of pmf components to driving conditions. (A) Synthesis rate as a function of $\mathrm{\Delta }$ pH for different fixed values of membrane potential $\mathrm{\Delta }\psi$. (B) Synthesis rate as a function of $\mathrm{\Delta }\psi$ for different fixed values of $\mathrm{\Delta }$ pH. Condition values, other than those for $\mathrm{\Delta }\psi$ and $\mathrm{\Delta }$ pH, represent typical physiological conditions (48). Parameter values are from the parameter optimization protocol for the rotary mechanism. See Methods. Atypical ranges for $\mathrm{\Delta }$ pH (−4 to 4) and $\mathrm{\Delta }\psi$ (−500 to 500 mV) were used to extend the performance curves sufficiently.

Fig. 6.

Stoichiometry effect on ranges of productive operating conditions. Green arrows represent range of productive operating condition for each of the ATPases shown. Red circles represent examples of reported stoichiometry and physiological conditions (, , , , –67). The diagonal represents equilibrium behavior where the efficiency, as defined in the text, is maximum but the rate of synthesis or pumping would vanish. “Mitochondria” refers to animal mitochondria.