Energy transduction in the F 1 motorofATPsynthase

ATP synthase is the universal enzyme that manufactures ATP from ADP and phosphate by using the energy derived from a transmembrane protonmotive gradient. It can also reverse itself and hydrolyse ATP to pump protons against an electrochemical gradient. ATP synthase carries out both its synthetic and hydrolytic cycles by a rotary mechanism. This has been con®rmed in the direction of hydrolysis after isolation of the soluble F1 portion of the protein and visualization of the actual rotation of the central `shaft' of the enzyme with respect to the rest of the molecule, making ATP synthase the world's smallest rotary engine. Here we present a model for this engine that accounts for its mechanochemical behaviour in both the hydrolysing and synthesizing directions. We conclude that the F1 motor achieves its high mechanical torque and almost 100% ef®ciency because it converts the free energy of ATP binding into elastic strain, which is then released by a coordinated kinetic and tightly coupled conformational mechanism to create a rotary torque. The general structure of ATP synthase is shown in Fig. 1. It consists of two portions: a soluble component, F1, containing the catalytic sites, and a membrane-spanning component, Fo, comprising the proton channel. The entire FoF1 structure is arranged as a counter-rotating `rotor' and `stator' assembly. The stator portion consists of the catalytic sites contained in the a3b3 hexamer, together with subunits a, b2 and d. The rotor consists of 9±12 c-subunits arranged in a ring and connected to the gand esubunits that form the central `shaft'. The mechanism of protonmotive force transduction has been discussed elsewhere; we now focus on the mechanochemistry of F1, which synthesizes ATP when the g±e shaft is turned clockwise (viewed from the membrane) by the protonmotive force, and which rotates counterclockwise to pump protons when hydrolysing ATP. Any mechanism proposed to explain the experimental results is strongly constrained by thermodynamic, kinetic, structural and mechanical considerations. In the hydrolysis direction, it must reproduce the large torque and almost 100% mechanical ef®ciency; in the synthesis direction, ATP must be produced at the measured rate when driven by torques generated by the protonmotive force in Fo. Kinetic constants and free energies must correspond to measured values. A model must also be geometrically compatible with the detailed structural information now available. We constructed the model in three steps. First, kinematic motions of the F1 subunits were analysed to determine the conformational changes that drive rotation of the g-subunit. From this, we constructed a mathematical model describing the principal mechanical and electrostatic interactions between the subunits. Finally, the reaction sequences were incorporated to create a complete mechanochemical model. The outline of this model can be summarized as follows. The reactivity of a catalytic site depends on its local conformation and composition. The unique feature of F1 is that the reactivity of each site depends on the states of the other two sites, and the position of g. Each of the three catalytic sites, b1, b2 and b3, passes through at least four chemical states: