Elastic coupling power stroke mechanism of the F1-ATPase molecular motor

Abstract

The angular velocity profile of the 120° F₁-ATPase power stroke was resolved as a function of temperature from 16.3 to 44.6 °C using a Δμ_ATP = -31.25 k_BT at a time resolution of 10 μs. Angular velocities during the first 60° of the power stroke (phase 1) varied inversely with temperature, resulting in negative activation energies with a parabolic dependence. This is direct evidence that phase 1 rotation derives from elastic energy (spring constant, κ = 50 k_BT·rad^-2). Phase 2 of the power stroke had an enthalpic component indicating that additional energy input occurred to enable the γ-subunit to overcome energy stored by the spring after rotating beyond its 34° equilibrium position. The correlation between the probability distribution of ATP binding to the empty catalytic site and the negative E_a values of the power stroke during phase 1 suggests that this additional energy is derived from the binding of ATP to the empty catalytic site. A second torsion spring (κ = 150 k_BT·rad^-2; equilibrium position, 90°) was also evident that mitigated the enthalpic cost of phase 2 rotation. The maximum ΔG^ǂ was 22.6 k_BT, and maximum efficiency was 72%. An elastic coupling mechanism is proposed that uses the coiled-coil domain of the γ-subunit rotor as a torsion spring during phase 1, and then as a crankshaft driven by ATP-binding-dependent conformational changes during phase 2 to drive the power stroke.

Keywords: F-type ATP synthase; F1-ATPase; FOF1 ATP synthase; power stroke mechanism; single molecule.

Fig. 1.

F₁-ATPase single-molecule rotation assay. (A) F₁-ATPase (PDB entry 1E79) view from membrane. (B) Cross-section of F₁ with β_E and β_D lever and catalytic domains, and γ−coiled-coil (green, pink) and foot (cyan) domains. (C) Light intensity from a nanorod versus time during an F₁ power stroke with 1 mM Mg²⁺ and 2 mM ATP (). Polarizer was aligned perpendicular to the nanorod during preceding catalytic dwell (●). Nanorod angular position relative to polarizer is shown with 0°:90° as min:max light intensities. (Inset) Schematic for measurements where (a) F₁ was attached to a Ni-coated slide by 6×His tags on β-subunit C termini, and to a 75 × 35-nm streptavidin-coated gold nanorod via specific γ-subunit biotinylation. Light scattered from the nanorod passed through a (b) pinhole; (c) bandpass filter to exclude all but red light; (d) polarizing filter; then collected by (e) avalanche photodiode sampled at 200 kHz.

Fig. 2.

Effects of temperature on F₁-ATPase–driven γ-subunit power stroke angular velocities versus rotational position. (A) Angular velocities measured at temperatures in degrees Celsius of 16.3° (), 22.0° (), 24.8° (), 27.6° (), 33.3° (), 38.9° (●), and 44.6° (), calculated using 3,522, 6,675, 3,987, 4,518, 4,383, 2,358, and 4,362 total power strokes from 24, 39, 30, 33, 39, 15, and 21 F₁ molecules. Data were binned every 3° of rotation from the end of the catalytic dwell. (Inset) Angular velocities at the 88° rotary position. (B and C) Årrhenius analyses of F₁-ATPase–driven power stroke angular velocity at rotational positions of 4° (), 16° (), 37° (), 76° (), 85° (), 109° (), and 121° (●).

Fig. 3.

Thermodynamic values at 298 K of F₁-ATPase–driven power stroke angular velocities. (A) Activation energy (●) during power strokes versus rotational position. Energy stored as a function of the extent of twist of a torsion spring with a spring constant, κ = 50 k_BT⋅rad⁻² () and 150 k_BT⋅rad⁻² () from equilibrium positions of 34° and 88°, respectively. (Inset) Probability ATP-binding dwell formation with 0.3 mM MgATP () from SI Appendix, Figs. S3 and S4. Fit of data to the inverse of energy stored from twist of a κ = 50 k_BT⋅rad⁻² torsional spring and 34° equilibrium position (). (B) Enthalpy of activation, ΔH^‡ (), and energy dissipation, TΔS^‡ (). Chemical energy, Δμ_ATP (), was determined from [ATP], [ADP], and [Pi] present during measurements. The free energy for ATP binding to the empty catalytic site, ΔG K_D-ATP (), determined from K_D for GsF₁-ATPase (46). (C) Free energy of activation, ΔG^‡ (), and the angular velocity of the power stroke, ω (). Catalytic dwell values for Pi release (▵), and for ATP hydrolysis (□) using GsF₁-ATPase (39). (D) F₁-ATPase–driven power stroke efficiency versus rotational position was determined from −ΔG^‡/Δμ_ATP.

Fig. 4.

Elastic coupling mechanism of the F₁-ATPase power stroke. (A) Catalytic dwell (0°) after ATP hydrolysis at β_D. Tightly wound γ−coiled-coil and (αβ)₃-ring are tethered (). Power stroke starts by β_E-Pi release to allow coiled-coil unwinding. (B) Phase 1 rotation (0°–60°): γ−coiled-coil torsion spring unwinds to equilibrium γ-foot domain position of 34°. β_E binds ATP at any phase 1 rotational position, 34° is optimal. β_D dissociates ADP optimally at 34° but can slow phase 2 if delayed. (C) Phase 1 → phase 2 switch at 60° when the γ−coiled-coil reaches the winding limit. Electrostatic interactions between Mg-ATP and groups on the β_E lever and catalytic domains force conformational changes to break γ−coiled-coil tether and push β_E lever against subunit γ to rotate foot and coiled-coil. A different tether () may cause a second spring (80°–100°). (D) Catalytic dwell begins when γ-foot reaches 120°, and β-subunit conformations change (β_E → β_T and β_D → β_E). ATP hydrolysis rewinds torsion spring.