Domain compliance and elastic power transmission in rotary F(O)F(1)-ATPase

Abstract

The 2 nanomotors of rotary ATP synthase, ionmotive F(O) and chemically active F(1), are mechanically coupled by a central rotor and an eccentric bearing. Both motors rotate, with 3 steps in F(1) and 10-15 in F(O). Simulation by statistical mechanics has revealed that an elastic power transmission is required for a high rate of coupled turnover. Here, we investigate the distribution in the F(O)F(1) structure of compliant and stiff domains. The compliance of certain domains was restricted by engineered disulfide bridges between rotor and stator, and the torsional stiffness (kappa) of unrestricted domains was determined by analyzing their thermal rotary fluctuations. A fluorescent magnetic bead was attached to single molecules of F(1) and a fluorescent actin filament to F(O)F(1), respectively. They served to probe first the functional rotation and, after formation of the given disulfide bridge, the stochastic rotational motion. Most parts of the enzyme, in particular the central shaft in F(1), and the long eccentric bearing were rather stiff (torsional stiffness kappa > 750 pNnm). One domain of the rotor, namely where the globular portions of subunits gamma and epsilon of F(1) contact the c-ring of F(O), was more compliant (kappa congruent with 68 pNnm). This elastic buffer smoothes the cooperation of the 2 stepping motors. It is located were needed, between the 2 sites where the power strokes in F(O) and F(1) are generated and consumed.

Fig. 1.

Immobilized EF₁ with attached magnetic bead (A), the yield of magnetically forced rotation as function of oxidation-reduction cycles (B), and histograms of thermally driven rotational fluctuations (magnetic field off) after the formation of a disulfide cross-link between the rotor and the stator (C). The green and magenta arrows in A indicate the position of the particular disulfide cross-links in EF₁. They are encircled in green and magenta, respectively, in C Inset. The arrows in B indicate the time when the solution was changed from reducing to oxidizing and vice versa. The points in C are experimental, and the lines are the respective fits by a single Gaussian. For details, see Results.

Fig. 2.

Immobilized EF_OF₁ with attached actin filament of short length, typically 0.5 μm (A), and histograms of thermally driven rotational fluctuations after the formation of a disulfide cross-link between the rotor and the stator (B). The positions of 3 different disulfide cross-links are indicated in colors in A and in the Inset in B, with matching colors of the respective histograms. For details, see Results.

Fig. 3.

Rotary trajectory under hydrolysis of ATP by active EF_OF₁ (A) and histogram of a more extended trajectory (B). The trajectory was recorded at 50 μM ATP with 5 mM Mg²⁺ present. As discussed in ref. , the halt positions represent the ATP-waiting dwells that follow each other with a period of 120°. The duration of these dwells, some 100 ms, was typical for immobilized EF_OF₁. The waiting for ATP binding was not diffusion-controlled. The orange histogram represents fluctuations after the molecule has fallen into its ADP-saturated state. Its peak was always displaced by −40° relative to the nearest one of the 3 ATP-waiting dwells. Details of the relation between the stepping motion and the crystal structure have been published in ref. .

Fig. 4.

Immobilized EF_OF₁ with a Q-dot-doped magnetic bead attached to the C-terminal end of both copies of subunit b (A) and histograms of rotary fluctuations (B) with the magnetic field off (Upper) and slowly (0.125 revolutions per second) rotating (Lower). The rotation was either clockwise (when viewed from the F_O side), shown in blue, or counterclockwise, shown in red. The fluctuations in the absence of the magnetic field (Upper) shown in blue and red, respectively, were observed subsequent to a previous clockwise and counterclockwise motion. The points are experimental, and the lines fits with a single Gaussian (Upper) and with 2 Gaussians each (Lower).

Fig. 5.

Structural model of EF_OF₁ (stator subunits in dark gray, rotor in light gray) and, at the very right side, of the homodimer of subunit b, and numbers for the torsional stiffness of various domains. Numbers given on the left side resulted from data obtained with EF₁ in the setup shown in Fig. 1A, those on the right side from EF_OF₁ as in Fig. 2A, and the one at the far right from EF_OF₁ as in Fig. 4A. The stiffness κ comes in units of pNnm. Numbers associated with horizontal colored lines denote the resulting stiffness κ_result (see Eq. 3) as observed when the respective disulfide cross-link (its 2 cysteines shown in the same hue, dark on the stator or light on the rotor) was closed. The numbers between the black vertical arrows denote the stiffnesses of the rotor domain lying between the respective pairs of cross-link positions. The red arrow marks the region of greatest compliance in EF_OF₁, the dominant elastic buffer that is responsible for an elastic power transmission between F_O and F₁.