On chemomechanical coupling of the F(1)-ATPase molecular motor

Estimating the rotation rate in the vacuolar proton-ATPase in native yeast vacuolar membranes

The rate of rotation of the rotor in the yeast vacuolar proton-ATPase (V-ATPase), relative to the stator or steady parts of the enzyme, is estimated in native vacuolar membrane vesicles from Saccharomyces cerevisiae under standardised conditions. Membrane vesicles are formed spontaneously after exposing purified yeast vacuoles to osmotic shock. The fraction of total ATPase activity originating from the V-ATPase is determined by using the potent and specific inhibitor of the enzyme, concanamycin A. Inorganic phosphate liberated from ATP in the vacuolar membrane vesicle system, during ten min of ATPase activity at 20 °C, is assayed spectrophotometrically for different concanamycin A concentrations. A fit of the quadratic binding equation, assuming a single concanamycin A binding site on a monomeric V-ATPase (our data are incompatible with models assuming multiple binding sites), to the inhibitor titration curve determines the concentration of the enzyme. Combining this with the known ATP/rotation stoichiometry of the V-ATPase and the assayed concentration of inorganic phosphate liberated by the V-ATPase, leads to an average rate of ~10 Hz for full 360° rotation (and a range of 6-32 Hz, considering the ± standard deviation of the enzyme concentration), which, from the time-dependence of the activity, extrapolates to ~14 Hz (8-48 Hz) at the beginning of the reaction. These are lower-limit estimates. To our knowledge, this is the first report of the rotation rate in a V-ATPase that is not subjected to genetic or chemical modification and is not fixed to a solid support; instead it is functioning in its native membrane environment.

CHEMOMECHANICAL COUPLING AND STOCHASTIC THERMODYNAMICS OF THE F1-ATPase MOLECULAR MOTOR WITH AN APPLIED EXTERNAL TORQUE

The effects of external torque on the F 1-ATPase rotary molecular motor are studied from the viewpoint of recent advances in stochastic thermodynamics. This motor is modeled in terms of discrete-state and continuous-state stochastic processes. The dependence of the discrete-state description on external torque and friction is obtained by fitting its transition rates to a continuous-angle model based on Newtonian mechanics with Langevin fluctuating forces and reproducing experimental data on this motor. In this approach, the continuous-angle model is coarse-grained into discrete states separated by both mechanical and chemical transitions. The resulting discrete-state model allows us to identify the regime of tight chemomechanical coupling of the F 1 motor and to infer that its chemical and mechanical efficiencies may reach values close to the thermodynamically allowed maxima near the stalling torque. We also show that, under physiological conditions, the F 1 motor is functioning in a highly-nonlinear-response regime, providing a rotation rate a million times faster than would be possible in the linear-response regime of nonequilibrium thermodynamics. Furthermore, the counting statistics of fluctuations can be obtained in the tight-coupling regime thanks to the discrete-state stochastic process and we demonstrate that the so-called fluctuation theorem provides a useful method for measuring the thermodynamic forces driving the motor out of equilibrium.