The distortion–push mechanism for the γ subunit rotation in F₁-ATPase

Significance

F₁ -ATPase is a rotary molecular motor that forms part of the ATP synthase complex. The F₁ -ATPase from thermophilic Bacillus PS3 rotates in 120° steps upon ATP hydrolysis, consisting of two substeps of 80° and 40°. In this study, we analyzed the rotation mechanism of the 80° substep using all-atom molecular dynamics (MD) simulations. Transition path sampling and free energy analysis suggest that this rotation is driven by distortion of the stator and a pushing force acting into the rotor. This “distortion–push” mechanism improves our understanding of the chemo-mechanical energy conversion in F₁ -ATPase, providing detailed insight into how mechanical force is generated at the atomic level.

Abstract

F₁-ATPase comprises the stator ring consisting of α₃β₃ subunits and the rotor γ subunit. The γ subunit rotation mechanism has been extensively investigated by biochemical analyses, structural studies, single-molecule measurements, and computational studies. Recent cryoelectron microscopy (cryo-EM) structures of F₁-ATPase from the thermophilic bacterium Bacillus PS3 (TF₁) provide us with further possibilities for a better understanding of the γ-rotation mechanisms. Using cryo-EM structures having the γ-rotation angles close to the binding dwell and catalytic dwell states, we investigate the relationships between the γ subunit rotation, conformational changes of the stator α₃β₃ subunits, and the nucleotide-binding and release. We performed targeted molecular dynamics (MD) simulations with external forces on the α₃β₃ subunits and observed 80° substep rotations of the γ subunit. Then, we optimized the most probable transition pathway through the mean-force string method simulations with 64 images. Finally, using umbrella sampling, we calculated the potential of mean forces along the minimum free energy pathway during the 80° substep rotation. Our MD simulations suggest that 80° substep rotation is divided into the first rotation, resting, and the second rotation. Notably, the first rotation is driven by the distortion of the stator α₃β₃ subunits, and the second rotation is induced mainly by direct β/γ subunit interactions. This model, which we call the distortion–push mechanism, is consistent with the residue-level experimental analysis on F₁-ATPase and the atomic structures determined by X-ray crystallography and cryo-EM.

ATP, a primary energy source for many cellular activities, is synthesized by the ATP synthase, which is localized in the inner mitochondrial membrane, thylakoid membranes of chloroplasts, and the plasma membrane of bacteria. The ATP synthase consists of two rotary molecular motors: the proton-driven F_o and the ATP-driven F₁. The F_o complex (ab₂c_8-15) functions through passive proton transports, resulting in the clockwise rotation of the c-ring when viewed from the periplasmic side. In contrast, the F₁ complex (α₃β₃γδε) rotates counterclockwise during ATP hydrolysis (1). These two motors with opposite rotational directions interact through their respective stators and rotors, functioning cooperatively for their biological activities. When the clockwise rotation of F_o predominates, it transports protons accumulated in the electron transport chain to enable ATP synthesis by F₁. This reaction is reversible; when the counterclockwise rotation of F₁-ATPase dominates, F₁ hydrolyzes ATP, and F_o expels protons against the concentration gradient (2, 3).

The isolated F₁ is known to function as a rotary molecular motor in the form of the α₃β₃γ complex (F₁-ATPase), which excludes the ε and δ subunits (1) (Fig. 1A). F₁-ATPase comprises the stator ring consisting of α₃β₃ subunits and the rotor γ subunit. The rotor γ subunit rotates counterclockwise by hydrolyzing ATP at the three catalytic sites of the stator. The stator is a hexamer formed by assembling three heterodimers of the α and β subunits, each possessing an ATP catalytic site. Most catalytic residues are in the β subunits, which exhibit more flexible structures than the α subunits. The β subunits are responsible for recognizing nucleotide binding and dissociation at the catalytic sites, which facilitate the open-to-closed motions (4, 5). The γ subunit undergoes a 120° rotational step, accompanying the hydrolysis of one ATP molecule, as demonstrated by single-molecule rotation measurements using Bacillus PS3 F₁-ATPase (TF₁) (6). Furthermore, single-molecule rotation measurements under low ATP concentrations close to K_m elucidated that a 120° step of TF₁ can be divided into an 80° substep associated with ATP binding and a 40° substep linked to ATP hydrolysis (7, 8) (SI Appendix, Fig. S1). The pauses preceding each substep have been referred to as the binding dwell state and catalytic dwell state, respectively (8, 9). Interestingly, F₁-ATPases from other species have different substep rotation mechanisms. For instance, human mitochondrial F₁ (hMF₁) and bovine mitochondrial F₁ (bMF₁) have 65° + 25° + 30° substep rotations (10) and 10 ~ 20° + 70° ~ 60° + 40° substep rotations (11), respectively.

Fig. 1.

Structure of F₁-ATPase and angular rotation of γ subunit by Targeted MD. (A) F₁-ATPase viewed from the membrane side (Left) and from the side (Right) (PDB ID: 7L1Q). The rotor γ subunit (cyan) is embedded in the stator ring α₃β₃, which is formed by α subunits (red) and β subunits (yellow). The γ subunit rotates counterclockwise during hydrolysis. (B) Schematic representation of an 80° substep of TF₁. As experimentally demonstrated, the structures indicating binding dwell and catalytic dwell are illustrated with the α subunits (red) and β subunits (yellow) represented as rounded triangles and the occupancy states of the catalytic sites indicated. The blue sticks denote the direction of γ subunit. “Post-Binding” and “Pre-Catalytic” correspond to the binding dwell after ATP binding and the catalytic dwell structure where ADP or P_i has not yet dissociated, respectively. The three αβ pairs are uniquely identified as α_Iβ_I, α_IIβ_II, and α_IIIβ_III, and their conformations are represented as Open (O), Half-open (HO), Half-close (HC), and Close (C). (C) Structural changes illustrating the hinge motion of β_I and the loosening at the α_II–β_II interface from binding dwell to catalytic dwell, as explored through TMD. (D) Changes in the rotation angle of the γ subunit observed through TMD. The calculation time is the sum of the initial and subsequent movements, with 75 ns + 75 ns signifying that the initial movement was induced over 75 ns of TMD, followed by the subsequent movement over another 75 ns of TMD. The three-colored time-series data correspond to the color coding in Fig. 1C, with PATH1 (blue), PATH2 (orange), and PATH3 (green) representing the analysis results of angular change analyses.

The structural details of the dwell states have been predominantly elucidated through X-ray crystallography of bMF₁ (12–15). Since the first structure (PDB ID: 1BMF), the rotational angles in most of the subsequent crystal structures of bMF₁ have been within the range of −15° to +20° from the rotation angle of 1BMF (16). It has also been suggested that these rotation angles correspond to the catalytic dwell state (17). For the widely utilized TF₁, the crystal structures for the stator ring lacking the γ subunit (18) and the self-inhibited state where the ε subunit impedes rotation were reported (19). Recent structural studies of TF₁ using cryoelectron microscopy (cryo-EM) determined three structures: one for the temperature-sensitive (TS) dwell state (PDB ID: 7L1Q) and two for the catalytic dwell state (PDB ID: 7L1R, 7L1S). The TS dwell structure had the γ subunit rotating approximately 80° counterclockwise (or 40° before the γ subunit completed its rotation) compared to the catalytic dwell structures (20). This is highly similar to the binding dwell state (PDB ID: 8HHA) of TF_oF₁ cryo-EM structures (21). These cryo-EM structures with different rotation angles provide a better understanding of the molecular mechanism of substep rotation.

So far, molecular dynamics (MD) simulation studies of F₁-ATPase have been extensively conducted utilizing the catalytic dwell structures of bMF₁, Escherichia coli F₁, and yeast F₁. These MD studies can be broadly divided into three approaches. The first one involves inducing structural changes in the stator and examining the resulting changes in the rotor (22–24). The second approach applies an external force to the rotor to force it to rotate and examines the resulting structural changes in the stator (25–29). The third one focuses on observing combinations of stator and rotor structures (30–32). Coarse-grained (CG) MD studies have primarily employed the first and third approaches, investigating the origins of the rotational driving force. Several research groups suggested that the steric interactions between the β and γ subunits associated with the opening and closing motions of the β subunit can drive γ-rotation using CG MD simulations (22, 23). Contrasting results were reported that electrostatic interactions between the β and γ subunits play a significant role (30, 31). All-atom MD studies have usually employed the second approach, wherein the γ subunit is enforced to rotate. They investigated the dynamic properties of the γ subunit (25, 27, 33), the timing of phosphate release (26), and the prediction of ATP binding states (28). Also, most of the all-atom MD studies utilized only the catalytic dwell structures.

In this study, we conducted all-atom MD simulations of TF₁ to understand the molecular mechanisms underlying the 80° substep rotation. There are two key differences between the current MD study and previous ones. First, we utilized the recent cryo-EM structures that show rotation angles close to the binding dwell and catalytic dwell states, which are the two endpoint structures during the 80° substep rotation. Second, we utilized the first approach, wherein the conformational changes of the stator α₃β₃ are induced first, and spontaneous γ-rotations are examined. This approach is free from slow responses of the stator conformations upon rapid γ-rotations induced by strong external forces. For this purpose, we performed targeted MD (TMD) simulations (34) for initial transition path prediction, the mean-force string method (35) for the path optimization, and the umbrella sampling (US) (36) to obtain the potential mean force (PMF) along the optimized pathway. In the mean-force string method and the umbrella sampling simulations, 64 images of TF₁ solvated with explicit water, which consists of more than 500,000 atoms, were simulated in parallel. We used the supercomputer Fugaku at RIKEN Center for Computational Science and MD software GENESIS (37–39) to perform the computationally expensive simulations. Based on the simulation results, we propose an atomistic mechanism for the γ-rotation in F₁-ATPase, which we call the distortion–push mechanism. This mechanism can explain many experimental results and answer the long-term questions about the rotational mechanisms underlying detailed mechanisms for F₁-ATPase.

Results

TF₁ Structures Before and After 80° Substep Rotation.

Fig. 1B shows a schematic representation of 80° substep rotation, transitioning from the binding dwell to the catalytic dwell state. It is induced by ATP-binding at the catalytic site of one of the αβ dimers (α_Iβ_I). ADP at the catalytic site of the second αβ dimer (α_IIβ_II) is released during 80° substep rotation. ATP at the catalytic site of the third αβ dimer (α_IIIβ_III) remains intact during the substep rotation and is hydrolyzed into ADP and P_i in the following 40° substep rotation. Sobti et al. determined one structure in the TS-dwell state, wherein the β_I subunit is half-closed and ATP is loosely bound at the β_I catalytic site (PDB ID: 7L1Q), and two structures in the catalytic dwell state: one with ADP at the interface of the α_IIβ_II dimer (PDB ID: 7L1R) and another with P_i at the same interface (PDB ID: 7L1S)(20). The TS-dwell structure is very close to the binding dwell structure of TF_oF₁ (PDB ID: 8HHA), which was later determined with cryo-EM (21). The Cα atom RMSD between 7L1Q and 8HHA is 0.84 Å. The binding dwell structure (PDB ID: 8HHA) was unavailable when we started this study. We, therefore, used the TS-dwell structure as the starting conformation in the 80° substep rotation. We added P_i to the cryo-EM structure in the catalytic dwell state bound with ADP (PDB ID: 7L1R). These two structures, which are referred to as Post-Binding and Pre-Catalytic states, include identical nucleotides at three active sites: ATP at the catalytic sites of β_I and β_III; ADP and P_i at the interface of the α_IIβ_II dimer. Thus, we could focus on conformational changes of the stator α₃β₃ and the responded γ-rotation in MD simulations. The cryo-EM structures by Sobti et al. (20) retain the βE191D mutation, a substitution for a catalytically critical glutamate residue. This mutant has also been widely utilized in single-particle studies. Therefore, the same mutation was adopted here to ensure that the results of our MD simulations are consistently compared with the previously reported structural and experimental data.

Transition Pathways in 80° Substep Rotation Predicted With Targeted MD.

Sobti et al. found two essential conformational changes between the TS-dwell (7L1Q) and catalytic dwell (7L1R, 7L1S) structures (20): one is the hinge motion of β_I (from half-closed to closed), and another is the interface motion of the α_IIβ_II dimer (from tight to loose). Previous structural studies also pointed out the importance of these motions (16, 40). We designed three possible pathways during 80° substep rotation by changing the order of the two essential motions (Fig. 1C). In PATH1, the hinge motion of β_I precedes the interface relaxation of the α_IIβ_II dimer. The two motions undergo simultaneously in PATH2. PATH3 is opposite to PATH1: the interface relaxation of the α_IIβ_II precedes the hinge motion of β_I. To induce the conformational changes in F₁-ATPase with TMD, external forces were applied to β_I and the α_IIβ_II dimer interface.

TMD simulations from Post-Binding to Pre-Catalytic structure along PATH 1, 2, and 3 were performed over three simulation times: 150 ns, 160 ns, and 170 ns (SI Appendix, Fig. S2). The 80° substep rotation of the γ subunit was accomplished in two TMD simulations along PATH1 (150 ns and 160 ns) (Fig. 1D). TMD along PATH2 and PATH3 exhibited unidirectional counterclockwise rotations but did not achieve 80° rotation of the γ subunit. The TMD trajectory along PATH1 with a duration of 170 ns also did not result in an 80° rotation.

Since TMD employs external forces to drive conformational changes, the resulting pathways may not accurately reflect the minimum free energy path. To overcome this limitation, we applied the mean-force string method (35) to refine the transition pathway on the free energy surface. Although not the focus of this study, ATP always remains bound at the noncatalytic interfaces (α_Iβ_II, α_IIβ_III, α_IIIβ_I).

The Mean-Force String Method Suggests Two Rotational Steps With Resting in Between.

In the mean-force string method simulation, Cartesian coordinates of the Cα atoms near the subunit interface in F₁-ATPase were used as the collective variables (CVs) (41). From the TMD trajectory along PATH1 (160 ns), we selected 64 equally spaced structures in the high-dimensional CV space. Previous studies demonstrated the effectiveness of this method in elucidating the functional rotation pathway of the multidrug transporter AcrB (42) and in analyzing the E1P-E2P transition of the Sarcoplasmic Reticulum Ca²⁺-ATPase (43). By performing the string method simulations for 82 ns per image, the initial pathway was optimized to a free energy minimum pathway, with convergence evaluated based on the RMSD changes of each image (SI Appendix, Fig. S3). Subsequently, the umbrella sampling (US) simulation was performed over 100 ns for each replica representing this transition pathway (SI Appendix, Fig. S4). PMF was computed using the multistate Bennett acceptance ratio (MBAR) from the trajectories over the final 90 ns (Fig. 2A).

Fig. 2.

Conformational change mechanism of 80° substep rotation. (A) Rotational angle changes of the γ subunit predicted by the string method (blue) and the free energy profile (red). Error bars on the PMF were estimated by dividing the final 90 ns of umbrella sampling into three equal segments (each 30 ns), independently calculating the PMF for each segment, and computing the SD at each point along the CV. The five regions, color-coded in gray and white, represent the five phases classified based on the rotational angle changes. (B) Representative structures of the five phases, using configurations obtained after 100 ns of umbrella sampling.

We calculated the average γ-rotational angles from the trajectory of each replica and obtained five different phases using the change point detection: images 1 to 12, 13 to 25, 26 to 33, 34 to 53, and 54 to 64 (Fig. 2A). The phase including the image 1 to 12 has the average γ-rotational angle of 6.3 ± 3.7°, suggesting that this phase is stable with a minimal change of the γ-rotation. Similarly, the phase, including images 54 to 64, shows stable rotation angles with the highest average values (82.4 ± 3.5°). Thus, we refer to the first and 5th phases as Post-Binding and Pre-Catalytic states, respectively. Significant changes in the average γ-rotational angle were observed in the second (images 13 to 25: from 6.3° to 20.4°) and fourth phases (images 34 to 53: from 37.1° to 79.8°). We refer to them as T1 and T2 steps, respectively. Between T1 and T2, the γ-rotational angles do not change significantly. This “Rest” phase covers the images 26 to 33 (34.5 ± 4.1°). Two rotation steps (T1 and T2) and the Rest in between can characterize the 80° substep rotation from Post-Binding to Pre-Catalytic state (Movie S1).

Fig. 2A shows PMF along the minimum free-energy pathway obtained with the string method. The metastable states that represent Post-Binding, T1, Rest, T2, and Pre-Catalytic states are identified in images 11, 19, 32, 42, and 55, which reveal the γ-rotational angles of 3.8 ± 2.6°, 15.0 ± 3.8°, 37.9 ± 3.2°, 56.3 ± 3.1°, and 84.3 ± 2.8°, respectively (Fig. 2B). The relationship between the PMF and the rotation angle is also shown in SI Appendix, Fig. S5. The PMF in Fig. 2A is characterized by elevated free energy at both ends, suggesting a large free-energy difference between the binding dwell and Post-Binding, and that between the catalytic dwell and Pre-Catalytic state. Since the structural changes between them and the γ-rotational angle differences are small, such significant free-energy changes can be due to the differences in the nucleotide-bound states. To investigate this possibility, we performed two additional US simulations. In one US simulation from images 1 to 32, we removed ATP from the β_I active site, creating structures with the same substrate-bound state as the binding dwell state (SI Appendix, Fig. S6). As a result, image 11 (the binding dwell state) is 8.45 kcal/mol more stable than image 19 (T1) (SI Appendix, Table S1). The ATP binding at the β_I active site can create a downhill free-energy landscape to drive the initial rotation of the γ subunit (Fig. 2A). In the second US simulation, ADP at the interface of the α_IIβ_II dimer was removed to mimic the catalytic dwell structure. In this state, P_i remained bound to the catalytic site. We used images 33 to 64 in the US and found that image 55 is stabilized by 1.60 kcal/mol compared to image 42 (SI Appendix, Table S1). This result suggests the catalytic dwell structure is stabilized after ADP is released from the Pre-Catalytic state. By integrating the three US results, the reaction model from the binding dwell to the catalytic dwell state agrees with that proposed by single-molecule measurements (44).

The Stator-Ring Conformational Changes During 80° Substep Rotation.

Left panel of Fig. 3A suggests that the hinge motion of β_I starts from the half-closed state in T1 and continues toward the closed state in Rest and T2. At the same time, the α_IIβ_II interface relaxation remains unchanged before T2 (Right panel of Fig. 3B and SI Appendix, Fig. S7). This order of two essential motions is the same as PATH1 in TMD, while T2 includes both. The hinge motion of β_II happens from half-open to open form in T2 (Right panel of Fig. 3A), synchronizing the interface relaxation of the α_IIβ_II dimer. The α_Iβ_I interface becomes tighter during 80° substep rotation. The α_IIIβ_I interface completes tightening by image 32 in Rest, remaining stable since then (Left panel of Fig. 3B). These results indicate that the stator structure is distorted by the hinge motion of β_I, propagating in both directions: clockwise through α_III and counterclockwise through α_I. The movement of α_I leads to a slight hinge opening in β_II, which is observed during the transition from T1 to Rest (Right panel of Fig. 3A).

Fig. 3.

Domain motion of the stator during 80° substep. (A) Distance between the N-terminal domain (NTD) and the C-terminal domain (CTD) tip representing the hinge motion of β_I. (B) Distance between the CTD of the α and β subunits, indicating the relaxation at the α-β interface.

Interaction Between γ-Rotator and α₃β₃ Stator to Drive 80° Substep Rotation.

The stator ring and γ subunit make contacts at the top (orifice region) and bottom (switch II region and hydrophobic sleeve region) in the X-ray structures (12). As the orifice region containing the C-terminal domain (CTD) of the β subunit is known to be responsible for at least half of the torque generation (45, 46), we focus on interaction changes in the region. In T1, residues in the orifice region of β_I interact weakly with Q183 in the γ subunit (Fig. 4A), and there are no significant interaction changes between the γ and β_I subunits at the orifice and switch II regions (SI Appendix, Figs. S8 and S9, and Movie S2). Instead, the electrostatic interaction changes between the γ subunit and the α and β subunits opposite to β_I are essential in T1 (Fig. 4B and SI Appendix, Figs. S10 and S11 and Movie S3). At first, R88 and G89 in the loop region of the γ subunit change their interaction partners from β_IIE391 to β_IIIE391 and from α_IID401 to β_IIE391, respectively. In addition, a hydrogen bond between the backbone of γL90 and the sidechain of β_IIIE391 is broken. The interaction changes associated with the start of T1 also occur within the stator ring: the three interfaces of α_Iβ_I, α_IIIβ_III, and α_IIβ_II form new interactions by switching their interaction partners (SI Appendix, Fig. S12). Thus, T1, the 35° rotation in 80° substep rotation, is not driven by the direct interaction between the β_I and γ subunits, but rather by the distortion of the entire stator ring and the resulting electrostatic interactions between the γ subunit and the α and β subunits opposite to β_I.

Fig. 4.

Contacts changes between the α₃β₃ and the γ subunit. (A) Changes in the interaction between the CTD of the β_I subunit and the γ subunit. Residues in the β_I and γ subunits exhibiting notable interaction changes during the 80° rotation are highlighted as green and blue spheres in images 11, 32, and 55. The weakly interacting γG183 is shown as a light blue sphere. The graph below illustrates the interaction frequency for each residue pair, with higher frequencies observed during 900 frames of the 90 ns umbrella sampling indicated by darker colors. Interaction changes in the switch II between the β_I and γ subunits are provided in SI Appendix, Fig. S8. (B) Interaction changes between the upper CTD region of the α₃β₃ stator ring and the γ subunit are shown. Residues in the α, β, and γ subunits that form significant interactions between the upper CTD region of α₃β₃ and the γ subunit are highlighted as magenta, green, and blue spheres, respectively, in images 11, 32, and 55. The graph below represents the interaction changes involving γ88–90 and α₃β₃. Further details on the interaction changes in the upper CTD region (excluding these residues) and the lower CTD region are available in the SI Appendix (SI Appendix, Figs. S9 and S10, respectively). (C) The trajectories of residues located at the subunit interfaces during the 80° rotation. The positional changes of αF398 and βI386 at the CTD termini of the stator ring, as well as those of γ subunit residues I23 (N-terminal helix) and N253 (C-terminal helix) in contact with these residues, are plotted on a plane as viewed from the top of TF₁. The trajectories show transitions from Post-Binding and T2 states (darker colors) to T1 and Pre-Catalytic (brighter colors).

At the end of T1, just before Rest (image 24), β_IE391 interacts with R100 in Helix2 (γH2). This electrostatic interaction switches those between β_ID394 and γR100 in T2, which, in turn, shifts into those between β_IE391 and γL90. In addition, I386 at the CTD tip of β_I gradually strengthens the interaction with N253 in the γ-coiled coil, suggesting that T2, the second rotation after Rest, is driven by direct interactions between β_I and γ subunits.

This model is confirmed by the contact analysis between the stator ring and the γ subunit at the lower half of the orifice region (Fig. 4C and Movie S4). In the projection viewed from the top, β_II386 moves toward α_IIIF398 and γN253, and α_IIIF398 approaches β_II386 from Post-Binding to T1. At the end of T1, β_II386, and γN253 are still separated by about 5 Å (Fig. 4C and SI Appendix, Fig. S13). From T2 to Pre-Catalytic phase β_III386 moves away from the γ subunit, and the γI23 position rotates counterclockwise. β_II386 approaches γN253 and shifts to push γN253 counterclockwise. α_IIIF398 likely supports the motions around β_II386. In this phase, α_IIF398 and β_III386 moved away from each other because of the loosening of the α_IIβ_II interface (Fig. 3B and SI Appendix, Figs. S13 and S14). Thus, we found that atomic mechanisms for 80° substep rotation can be explained with the distortion of the stator ring and the electrostatic interaction changes in the first 35° rotation, and the direct pushing force from β_I to γ subunit in the last 45° rotation. Hereafter, we call this two-step rotation mechanism the distortion–push mechanism and relate this mechanism with the previous experimental observation in the Discussion section.

Roles of ATP Binding and ADP/P_i Release in 80° Rotation.

In Post-Binding, ATP, which is loosely bound to β_I, has its phosphate group wrapped in the P-loop (₁₅₈GxxGxGK[T/S]₁₆₅) during T1, forming a specific interaction with G161, V162, and G163, forming a particular interaction (Fig. 5A). The main chain dihedral angles of G161 and G163 changed significantly to create this interaction (SI Appendix, Fig. S15), confirming that P-loop utilizes the unique flexibility of Gly residues in the nucleotide binding. This interaction remains stable up to Pre-Catalytic and is consistent with the changes observed in the cryo-EM structures (SI Appendix, Fig. S16A). Previous studies have reported increased binding affinity between β_I and ATP as the major torque-generating event at the 80° substep (47). The tight binding of β_I and ATP at T1 can induce the β_I hinge motions and facilitate the γ-rotation.

Fig. 5.

Interaction changes at the catalytic site of the β subunit. (A) The structure of ATP bound to the catalytic site of β_I. During the transition from the Post-Binding state to T1, interactions between the phosphate groups in ATP and the P-loop residues G161, V162, and G163 are formed. The time-dependent changes in the β_IATP interactions are represented by brightness, with higher brightness indicating more frequent interactions observed during the 90 ns of umbrella sampling. (B) The structure of ADP and P_i bound to the catalytic site of β_II.

ADP and P_i bound at the α_IIβ_II interface reduce their interactions with catalytic residues β_IIR191, D252, and R256 in T2. Then ADP and P_i move upward of β_II with the CTD side of β_II (Fig. 5B). This movement coincides with the transition of β_II from the half-open to open state (Fig. 3A). In Rest, where these interactions remain intact, it transiently causes transitions from the half-open to open conformation before reverting. It returns to the half-open state again at the beginning of T2. These results suggest that cleavage of the interaction between ADP and β_IIR191, D252, and R256 is significant for β_II to maintain the open conformation. Furthermore, after T2 rotation, ADP lost its interaction with α_IIR365 and no longer interacted closely with α_II (SI Appendix, Fig. S17). This indicates that, in the Pre-Catalytic state, ADP does not contribute to the tightening of the α_IIβ_II interface. At the end of the Pre-Catalytic state (Image 64), P_i appears to be associated with β_IIY307 (Fig. 5B and SI Appendix, Fig. S16B). To examine the interaction between P_i and the β_II catalytic site, we performed 20 additional MD simulations of 100 ns each, starting from Image 64. P_i often contacts Y307, and other β_II residues near the original P_i-binding site, such as G159, A160, R253, R256, and R333 (SI Appendix, Fig. S18).

Discussion and Conclusions

Here, we discuss the relationship between the proposed distortion–push mechanism and previous experimental/computational studies of F₁-ATPase. Single-molecule rotation experiments have shown that the 80° substep rotation of TF₁ is driven by the binding of ATP to β_I as a trigger, followed by ADP dissociation from α_IIβ_II (44, 48). Although the present study did not directly simulate the nucleotide binding and dissociation, there was a clear trend toward an increase in the interaction between β_I and ATP in T1 and a decrease in the interaction between α_IIβ_II and ADP in T2. This order is consistent with the experimentally demonstrated binding-dissociation sequence. Furthermore, in T2, the loosening of the α_IIβ_II interface occurs after the contact formation between the β_I and γ subunits in Rest. These structural changes are consistent with the previous simulation results (24), which suggested that the propagation of structural changes due to β_I closure promotes α_IIβ_II interface loosening and ADP dissociation. Theoretical considerations based on rotation experiments (49) also suggested the presence of a short-lived state prior to the ADP dissociation at a rotation angle of 30° during 80° substep rotation of TF₁. Similar results have been confirmed in Escherichia coli F₁ rotation experiments (50) and simulations of synthetic rotation of bMF₁ (32). The rest around 35° can be interpreted as a rotational pause waiting to loosen the α_IIβ_II interface and the ADP dissociation.

In the cryo-EM structure (PDB ID: 7L1R), which shows the catalytic dwell state, only ADP is found to be bound to the α_IIβ_II interface. This structure cannot explain the conventional rotational catalysis scheme in which ADP already dissociates during the 80° substep (44). The authors (20) suggested that this ADP can dissociate once and then rejoin at the same binding site. In the present study, at the end of T2, ADP reduces most of the interaction with α_II and loses the role in tightening the α_IIβ_II interface. After the interactions between ADP and β_IIR191, D252, and R256 are cleaved in T2, the closing of the β_II hinge is likely hindered. These findings suggest that the functional role of ADP in the catalytic dwell state after 80° rotation is limited, and that rebinding of ADP to β_II may still occur. Recent cryo-EM structures under high ATP concentrations have shown that ATP can bind to α_Eβ_E (α_IIβ_II around 80° rotation) independent of rotation angle (21). The role of bound nucleotide at the β subunit in the rotation mechanism should be discussed carefully together with the F₁-ATPase structure and the detailed interaction modes.

Based on the proposed mechanism, residues potentially involved in the 80° substep rotation and related experimental findings are summarized in SI Appendix, Table S2. The involvement of βI386 in torque generation (within the DELSEED loop: β386 to 394) (51, 52) and the αR283–βD312 interaction in coordinating α–β subunits (53) has already been suggested by experimental studies. In contrast, although experimental validation of other distortion-related residues is limited, mutations at these sites may hinder the propagation of structural changes and reduce rotational efficiency.

The most dominant rotational driving force of the γ subunit rotation has been considered to be either electrostatic interaction (30, 31, 41) or steric hindrance (22, 23, 51). The distortion–push mechanism proposed here can answer the question, suggesting different driving forces for the two rotational steps intervening by Rest. In this mechanism, the first rotation is driven by the distortion of the stator and the electrostatic interaction, while the direct contact between the β and γ subunits. Therefore, this molecular mechanism can be considered as one that encompasses two different models. It also agrees with the previous free-energy calculations on the ATP synthesis rotation of bMF₁ (32), which suggested that the rotation is mediated by a more complex combination of electrostatic and steric interactions in the rotation after ATP dissociation.

In summary, the molecular mechanism underlying 80° substep rotation of F₁-ATPase (TF₁) from the thermophilic bacterium Bacillus PS3 was investigated using all-atom MD calculations. The optimized transition path and PMF along the path revealed that 80° substep rotation consists of two rotations separated by a rest around 35°. The distortion of the stator α₃β₃ and the electrostatic interaction changes between the γ subunit and α_IIβ_II or β_III subunits in the upper part of the orifice region drive the first rotation. The γ-rotational angle does not change significantly in Rest, while β_I continues the hinge-bending motion and approaches to form a tight interface with α_III. The CTD of β_I makes contact with the coiled-coil part of the γ subunit. In the second rotation, the CTD of β_I pushes the coiled-coil region of the γ subunit by steric repulsion. The interaction between the CTD of α_IIβ_II is broken. The α_IIβ_II interface gradually starts to loosen, and thereby ADP reduces interaction with the catalytic residues of β_II (R191, D252, R256) and β_II transitions to an open conformation. As we see in the current study, chemo-mechanical coupling in F₁-ATPase is explained with multiple factors, such as distortion of the stator α₃β₃ subunits, changes of the electrostatic interaction between the β and γ subunit, the strengths of nucleotide-binding at each αβ interface, and so on. Proper molecular modeling and simulations based on the cryo-EM structures could help our understanding of atomistic mechanisms for the substep rotation of the γ subunit. The current approach can apply to the following 40° substep rotation toward a complete understanding of an entire rotational cycle in F₁-ATPase.

Materials and Methods

Computational Setup for Modeling and Simulations of TF₁.

In this study, the binding dwell and catalytic dwell states of TF₁ were taken from the cryo-EM structures corresponding to the rotational angles of each state (PDB ID: 7L1Q and 7L1R, respectively). The protonation state of P_i at the ADP+P_i binding site of each state was set to a doubly protonated state (H₂PO₄⁻), as suggested by previous QM/MM studies (5, 54, 55). Furthermore, αE165 and αE272 were assigned to protonated form based on the pKa predictions from PROPKA (56, 57). The internal cavities of the protein were hydrated using Dowser++ (58), and the structures were modeled using the VMD plugin (59). Each structure was solvated in a cubic box with a side length of 174.8 Å, containing CHARMM TIP3P water molecules (60) and neutralized with 150 mM KCl. The total atom count of the solvated systems was approximately 513,000 atoms. The CHARMM c36m force-field parameters (61) were used for TF_1, and the refined parameters for nucleotides by Komuro et al. were employed (62). Water molecules are considered as rigid using SETTLE constraints (63). All bonds involving hydrogen atoms are constrainted using SHAKE/RATTLE (64, 65). All MD simulations were performed using the GENESIS software version 2.1 (37–39). The simulations were conducted in the NPT ensemble at 310 K and 1 atm, using the stochastic velocity rescaling thermostat and MTK style barostat (66, 67) using the refined temperature definition (68). Group temperature/pressure is used for evaluation of temperature/pressure in thermostat/barostat (69, 70). The nonbonded interactions were calculated using the CHARMM standard procedures: the LJ interaction was smoothly truncated from 10 Å to 12 Å using the force-based switch function (71), and the electrostatic interactions were computed with the particle mesh Ewald summation algorithm (72, 73). For all executions, except for equilibration, we utilized the r-RESPA (or multiple time step) integration with 2.5 and 5.0 fs time steps for the real- and reciprocal-space interactions, respectively (74).

Transition Pathways From the Binding Dwell to the Catalytic Dwell State.

Using targeted molecular dynamics (TMD) (34), we generated candidates of transition pathways from the binding dwell state to the catalytic dwell state by inducing the conformational changes in β_I, α_II, and β_II, which are involved in the TF₁ substrate binding and release. As shown in Fig. 1C, three distinct pathways (PATH1, 2, and 3), assuming sequential or simultaneous conformational changes in β_I and α_IIβ_II, were examined in TMD simulations. TMD simulations along with each pathway were performed three times on different time scales, 150 ns, 160 ns, and 170 ns. We selected a conformational transition predicted in a 160 ns TMD, assuming PATH1 as the initial pathway for the string method, comprising 64 images. The CVs were defined following the previous study for V₁-ATPase (41), where the CVs were specified by the Cartesian coordinates of the Cα atoms of the residues within 5 Å of the intersubunit interfaces of all the α, β, and γ subunits, as well as the heavy atoms of the substrates MgATP and MgADP, excluding P_i. In addition, the Cα atoms in the CTD of all β subunits were included as CVs, even if they were not within 5 Å of the interfaces. The transition pathway was initially equilibrated so that 64 images were evenly positioned in the CVs space. Each image was subjected to MD simulation with a positional restraint of 0.01 kcal/mol/Ų for 1 ns per image. Subsequently, the restraint strength was increased to 1.0 kcal/mol/Ų, and each image was equilibrated further with MD simulations of 50 ns per image. After equilibration, the transition pathway was refined using the string method under positional restraint of 1.0 kcal/mol/Ų, with MD simulations of 20 ns per image. During the refinement process, all images except for the endpoints were updated. Finally, MD simulations based on the string method with 64 images were carried out for 10 ns per image with a 0.1 kcal/mol/Ų positional restraint to obtain the converged minimum free-energy pathway without fixing the endpoint images.

Free-Energy Profiles From Umbrella Sampling.

We performed umbrella sampling simulations with 64 replicas along the minimum free-energy pathway, followed by the string-method simulations. The CVs used in the umbrella sampling were the exact Cartesian coordinates of the atoms, the same as those in the string-method simulations. The CVs were restrained using a force constant of 0.02 kcal/mol/Ų. Each umbrella window was simulated for 100 ns in the NPT MD simulations. The free-energy profile was analyzed using the MBAR (Multistate Bennett Acceptance Ratio) method (75), using the 90 ns of sampling data, excluding the initial 10 ns trajectories.

Rotational Angles of the γ Subunit.

To define the rotational angle of the γ subunit, we followed the viscoelastic model for segment 3 of MF₁ by Okazaki et al. (33) (Fig. 3A). First, we compute a vector connecting the center of mass (COM) of the Cα atoms of the entire region to the COM of the N-terminal helix (residues: 44 to 53) in the γ subunit with the highly rigid region (residues: 44 to 53, 78 to 82, 105 to 119, 134 to 139, 148 to 160, 162, 168, 170 to 174, 188 to 192, 222 to 231). This vector is projected onto the plane formed by the N-terminal domains (NTD, residues: 2 to 82) of the three β subunits. The projected vector can mimic the rotation vector measured in single-molecule rotational measurements and is referred to as the rotating vector. The rotational angle was computed by taking the inner product of the rotational vector of the reference structure (PDB ID: 7L1Q), which has the same rotation angle of the binding dwell state.

Hinge Motions of the β Subunit and Tightening/Relaxation Motions at the α-β Interface.

The hinge motion of the β subunit is quantified using the interdomain vector between the COMs of the NTD and the CTD tips of Cα atoms (residues: 385 to 388). This height component is quantified using the perpendicular component of the interdomain vector to the plane formed by the NTD of the three β subunits. The tightening and relaxation at the αβ interface are quantified using the distance between the COMs of the Cα atoms in the CTD of the α and β subunits (residues: 371 to 499 and 360 to 473).

Data-Sharing Plans.

The GENESIS software used for all the MD simulations is available online (https://github.com/genesis-release-r-ccs/genesis) as free software under the LGPLv3 license. Essential information on the MD simulations including initial PDB structures, parameter files, final structures of 64 images in the string-method simulations and umbrella samplings is available on the GitHub repository (https://github.com/RikenSugitaLab/TF1_80degree_substep_rotation).

Supplementary Material

Appendix 01 (PDF)

Movie S1.

The transition pathway of an 80° rotation obtained using the mean-force string method with 64 images. The CTDs of the α and β subunits are highlighted in red or yellow, while the other domains are shown in gray. The cyan dots in the upper left corner of the video indicate changes in the rotational angle of the γ subunit.

Movie S2.

Changes in the interaction between the βI and γ subunits in the orifice region, corresponding to Figure 4A. The movie is composed of 64 images obtained from the string method. Electrostatic interactions between the βI and γ subunits are indicated by magenta dotted lines and enclosed with circles. The values in parentheses at the top of the movie indicate the rotation angle of the γ subunit.

Movie S3.

Changes in the interaction between the stator ring and the γ subunit in the upper half of the orifice region, corresponding to Figure 4B. The movie consists of 64 images generated using the string method. Electrostatic interactions are highlighted with orange circles. The values in parentheses at the top of the movie indicate the rotation angle of the γ subunit.

Movie S4.

Behavior of the CTD tip residues of the stator ring and the γ subunit in the lower half of the orifice region, corresponding to Figure 4C. The movie consists of 64 images obtained using the string method. The values in parentheses at the top of the movie indicate the rotation angle of the γ subunit.

Data, Materials, and Software Availability

Input/output data of MD simulations data have been deposited in Github (https://doi.org/10.5281/zenodo.14807751) (76). All study data are included in the article and/or supporting information.