Phosphate release coupled to rotary motion of F₁-ATPase

Significance

F₁-ATPase is the catalytic domain of F_oF₁-ATP synthase, the rotary molecular motor at the core of the energy transduction machinery in all of life. We use atomistic molecular dynamics simulations to study a key event in its catalytic cycle, the release of inorganic phosphate (P_i) produced by the hydrolysis of ATP. We determine the timing, kinetics, and molecular mechanism of P_i release and clarify its role in torque generation. We also obtain an atomically detailed structure of a crystallographically unresolved intermediate formed after the 40° substep. Our results help reconcile conflicting interpretations of earlier biochemical, crystallographic, and single-molecule studies; shed light on the functional requirements of efficient ATP synthesis; and establish connections to other motors such as myosin.

Abstract

F₁-ATPase, the catalytic domain of ATP synthase, synthesizes most of the ATP in living organisms. Running in reverse powered by ATP hydrolysis, this hexameric ring-shaped molecular motor formed by three αβ-dimers creates torque on its central γ-subunit. This reverse operation enables detailed explorations of the mechanochemical coupling mechanisms in experiment and simulation. Here, we use molecular dynamics simulations to construct a first atomistic conformation of the intermediate state following the 40° substep of rotary motion, and to study the timing and molecular mechanism of inorganic phosphate (P_i) release coupled to the rotation. In response to torque-driven rotation of the γ-subunit in the hydrolysis direction, the nucleotide-free αβ_E interface forming the “empty” E site loosens and singly charged P_i readily escapes to the P loop. By contrast, the interface stays closed with doubly charged P_i. The γ-rotation tightens the ATP-bound αβ_TP interface, as required for hydrolysis. The calculated rate for the outward release of doubly charged P_i from the αβ_E interface 120° after ATP hydrolysis closely matches the ∼1-ms functional timescale. Conversely, P_i release from the ADP-bound αβ_DP interface postulated in earlier models would occur through a kinetically infeasible inward-directed pathway. Our simulations help reconcile conflicting interpretations of single-molecule experiments and crystallographic studies by clarifying the timing of P_i exit, its pathway and kinetics, associated changes in P_i protonation, and changes of the F₁-ATPase structure in the 40° substep. Important elements of the molecular mechanism of P_i release emerging from our simulations appear to be conserved in myosin despite the different functional motions.

F₁-ATPase (F₁), the catalytic domain of F_oF₁-ATP synthase, is a rotary molecular motor that reversibly interconverts ATP hydrolysis free energy and mechanical work associated with the rotation of the central stalk (1). The minimal functional F₁ consists of a hexameric ring formed by three αβ-subunit dimers, with the rod-like γ-subunit located at its center (2). The rotation of the γ-subunit is tightly coupled to the reactions in the three catalytic sites located at the αβ interfaces and hosted mainly by the β-subunits. As a result, F₁ is a unique reversible motor that rotates γ by converting ATP hydrolysis energy at high efficiency (3–5) and, conversely, synthesizes ATP from ADP and inorganic phosphate (P_i) by forced rotation of γ in the reverse direction (6, 7). The three nucleotide-binding sites are in different phases of catalysis, reflecting the asymmetric structure of the γ-subunit. Correspondingly, the αβ-subunits hosting the catalytic interfaces are in different conformational states, empty (E), ATP-bound (TP), and ADP+P_i-bound (DP), as seen in crystal structures (2). They communicate through the γ-subunit or directly within the α₃β₃ ring (8, 9) and cooperatively drive the rotation of the γ-subunit.

Single-molecule experiments have shown that the γ-subunit rotates in 120° steps (4). Distinct substeps of 80° and 40° (10) are driven by ATP binding plus ADP release, and ATP hydrolysis plus P_i release, respectively (10–13). We thus expect two metastable conformations of F₁, one before the 80° substep (binding dwell) and the other before the 40° substep (catalytic dwell) (14, 15) (Fig. 1A). Most crystal structures correspond to the catalytic dwell state (1, 14–19), with the F₁ conformation of the binding dwell state still elusive (16).

Fig. 1.

Mechanochemical coupling scheme and P_i release of F₁-ATPase. (A) Mechanochemical coupling scheme deduced from recent single-molecule experiments (13). ATP hydrolysis reaction steps in one of the three catalytic sites (yellow circles) as a function of the γ-rotation (red arrow). T, D−P, D+P, and P stand for ATP bound, hydrolyzing ATP, ADP+P_i bound, and P_i bound, respectively. At an angle of 0°, ATP is bound. States differing by integer multiples of 120° are functionally equivalent. The timing and pathway of P_i release (purple) has been controversial. (B) Crystal structure (PDB ID code 2jdi) of F₁-ATPase that represents the ∼80° catalytic dwell state, with α-, β-, γ-subunits colored in blue, orange, and red, respectively. (C) Tightly bound P_i in the E site modeled on the basis of yeast structures (SI Text). The blue and orange ribbon backbones correspond to the α_E- and β_E-subunit, respectively. The five residues that participate in P_i binding are shown with thick bonds. VMD was used to prepare structural figures (64).

The transition from the catalytic dwell to the binding dwell involves P_i release, but the release site and the exact timing in the full cycle remain controversial. In most kinetic models of F₁ (1), but not all (20), P_i is assumed to exit first, followed by ADP release. This order appears to be consistent with kinetic (21) and structural studies (22) showing all three sites occupied by nucleotide (22); by contrast, the single-molecule experiments of Watanabe et al. (13) and structural studies of yeast F₁ (23) suggest that ADP is released before P_i. With γ-rotation stalled in the catalytic dwell state by magnetic tweezers, the hydrolysis reaction was found to be reversible without excess P_i in solution (13), suggesting that P_i is released at 320°, i.e., from the E site (13, 24) (where ATP binding defines 0°; Fig. 1A).

Here, we reconcile these conflicting interpretations by determining the kinetics of P_i release from the E site and the DP site with atomistic molecular dynamics simulations. These simulations also allow us to explore the coupling between the 40° substep and P_i release, and to examine the underlying molecular mechanisms. F₁ has been studied by molecular simulations at various levels of resolution, including quantum chemical calculations of ATP hydrolysis (25–27), all-atom simulations of conformational changes in the β-subunit (28, 29), of ATP release (30), of fluctuations in the complex (31, 32), and of γ-rotation (33, 34), as well as coarse-grained simulations of γ-rotation (35–37). As in experiment and in earlier simulations (33), we apply external torque to modulate the rates of the functional processes, including P_i release.

We first characterize the molecular motions of F₁ during the 40° substep in atomically detailed simulations. By rotating the γ-subunit with the help of a newly developed flexible rotor method, we show how the γ-angle and the protonation state of P_i (i.e., HPO₄²⁻ or H₂PO₄⁻) affect the conformation of αβ-dimers and the stability of P_i binding in the E site. We then estimate rates of P_i release from the E site and from the DP site with the help of metadynamics simulations (38). From the simulations and by relating the calculated rates to experiment, we determine the timing, pathway, and charge state dependence of P_i release. Finally, we show that key elements of P_i release appear to be conserved in myosin, despite the different functional motions.

Results

Rotation of γ and Conformational Response of αβ-Dimers.

In all-atom explicit-solvent simulations of the F₁ motor, the γ-angle was rotated in the hydrolysis direction with an angular velocity of 1°/ns by the newly developed flexible rotor method (Methods, Fig. S1, and Movie S1). The angular velocity may seem higher than in experiment. However, the millisecond timescale of F₁ rotation in experiment mainly reflects the catalytic dwell waiting for hydrolysis and P_i release. The rotary motion during the 40° substep transition should thus be much faster, yet it has not been measured without load to the best of our knowledge. For structurally more complex transitions like protein and RNA folding, transition path times have been measured in the low-microsecond range, many orders of magnitude faster than the corresponding mean first-passage times of (un)folding (39, 40). With the γ-subunit allowed to twist freely in our simulations, the angle of its core lagged behind the average, while the protruded part moved ahead (Fig. 2B). This twisting in response to torque reflects both on the torsional stiffness of γ and on the friction experienced by the core part due to its tight interactions with the α₃β₃ ring. The enhanced rotation of the protruded part (or “foot”) seen here is consistent with large variations in its rotational angle in crystal structures (22, 41) and the low torsional stiffness of the γ-rotor (42). Importantly, despite the twisting the γ-subunit remains structurally intact, as indicated by root-mean-square deviations (RMSDs) of <3.5 Å (Fig. S2A). The bottom part of the C-terminal helix of γ resists rotation, which seems to be a main source of the twisting (Fig. S2B). The elastic energy stored in this region may contribute to the reversibility and efficiency of the F₁ motor (32).

Fig. 2.

Rotation of γ-subunit in the hydrolysis direction. (A) Rotation of γ against α₃β₃ ring in the hydrolysis direction. The N- and C-terminal helices (γ1–33, 224–273), colored in purple, form the core that penetrates the center of the α₃β₃ ring. The protruded part is colored in red. (B) Rotational angle for the whole (blue), the core (purple), and the protruded parts of γ (red) as a function of time for F₁ with H₂PO₄⁻ in the E site.

Rotation of the γ-subunit induces conformational changes in all three αβ dimers, αβ_E, αβ_TP, and αβ_DP. We monitor their conformational responses by projection onto the principal component axes PC1 and PC2 obtained previously from the analysis of X-ray structures (43). PC1 reports on the hinge closing motion of the β-subunit, and PC2 on the tightening motion of the αβ interface in response to ligand binding and γ-rotation. PC1 and PC2 are in units of Ångstroms. During the γ-rotation, the αβ_DP interface remained close to the X-ray structures (Fig. 3A). By contrast, the interface structure of αβ_TP tightened in both simulations, moving toward αβ_DP already after ∼20° γ-rotation (Fig. 3A, green points; and difference ΔD_RMSD of the RMSD with respect to the initial αβ_TP and αβ_DP structures in Fig. S2C). αβ_TP thus indeed moved in the direction expected for hydrolysis. This motion is concentrated mainly in α_TP (Fig. 3B, blue), with rotation of γ in the hydrolysis direction pushing a protruded β-hairpin of γ (γ165–173) away from the helix-turn-helix motif of the C-terminal domain of α_TP, and α_TP occupying the vacated space (Fig. 3B and Movie S1). We note that this conformational change was not observed in free simulations without torque (Fig. S3B).

Fig. 3.

Conformational response of αβ-dimers to γ-rotation in the hydrolysis direction. (A) Projections of αβ-dimer structures onto the principal component axes PC1 and PC2 obtained from the analysis of X-ray structures (43) during the (Upper) first and (Lower) second half of the simulations with H₂PO₄⁻ (Left) and HPO₄²⁻ (Right) in the E site. Red, green, and blue points correspond to αβ that starts from αβ_E, αβ_TP, and αβ_DP, respectively, and purple points correspond to X-ray crystal structures (43). The arrows indicate directions of αβ-motion in response to γ-subunit rotation in the hydrolysis direction. (B) Conformational change of αβ_TP in response to 30° rotation of the γ-subunit during the trajectory with HPO₄²⁻. The snapshot at 30 ns is colored as in Fig. 1B, and the reference structure at 0 ns is colored in cyan. Only the C-terminal domains of αβ are shown for the 0-ns conformation, and the β-hairpin and the C-terminal helix are shown for the γ-subunit. (C) Conformational change of αβ_E in response to 30° rotation of the γ-subunit during the trajectory with H₂PO₄⁻. The snapshots at 30 and 0 ns are shown as in B.

The αβ_E-subunit motions induced by γ-subunit rotation depend sensitively on the protonation state of P_i in the E site. To account for the near-neutral pK_a2 of 7.2, we studied HPO₄²⁻ and H₂PO₄⁻ in separate simulations. The interface of αβ_E loosened after a few degrees of rotation with H₂PO₄⁻, as reflected in the large change of PC2 to negative values (Fig. 3A, Left). The loosening of the αβ_E interface with γ-rotation in the hydrolysis direction is consistent with a yeast structure at a 12° γ-angle (23), as indicated by their PC2 values of −10 ± 5 Å (molecular dynamics at γ= 12°) and −7.9 Å (X-ray) (43). By contrast, the αβ_E interface remained relatively tight with HPO₄²⁻ (Fig. 3A, Right). The doubly charged P_i locks the interface, forcing α- and β-subunits to move together in response to γ-rotation (Fig. S2D). By comparison, with the singly charged P_i, the motion is concentrated in the α-subunit, reflecting the weaker interactions of P_i with the αβ_E dimer. Thus, the motion of α_E, pushed by the N-terminal helix of γ, is primarily responsible for the loosening of the E-site interface (Fig. 3C), which in turn weakens P_i binding to the E site, as studied below.

Protonation State of P_i, Interface Conformation, and Direction of γ-Rotation Affect Binding Stability in the E Site.

P_i moves in the E site as the γ-subunit is rotated. To cancel out the overall rotational motion, we superimposed the binding site on the initial structure, using residues within 10 Å from P_i in the initial structure. Fig. 4A shows the resulting P_i distance from the initial position as a function of time, with γ rotated in the hydrolysis direction by 1°/ns. H₂PO₄⁻ and HPO₄²⁻ in the E site responded quite differently to γ-rotation. The singly charged P_i readily moved toward the P-loop region. This motion of P_i was tightly coupled to the loosening of the interface conformation of αβ_E (Fig. 5A) and was not observed in the free simulation without torque (Fig. S3C). The observed coupling supports the earlier suggestion that P_i binding is regulated by the αβ_E interface conformation, as inferred from a comparison of different F₁ structures (43). The transient structure at 3.5 ns is shown in Fig. 4B, with αARG373 and βLYS162 coordinating P_i. The so-called Arg-finger, αARG373, seems to play a role of guiding P_i to the P loop. In fact, αARG373 remained coordinated to P_i even as P_i moved toward the P loop (Fig. 4A, green line). P_i stayed at the P loop for the rest of the trajectory, frequently interacting with αARG373. The rapid escape of P_i from the E site to the P loop during the 40° substep, as probed in the torque simulations, is consistent with the dramatic increase in the rate of P_i release between 320° and 360° reported from experiment (24). By contrast, the doubly charged P_i remained quite stably bound in the initial position and maintained interactions with its coordinating residues throughout the trajectory (Fig. 4C). With two negative charges, the doubly charged P_i was, in effect, trapped by the four positively charged residues in its immediate surrounding, holding the interface tight during the torque simulations.

Fig. 4.

P_i motion in the E site during rotation of γ in the hydrolysis direction. (A) P_i distance from the initial position during the torque simulations. The trajectories with H₂PO₄⁻ and HPO₄²⁻ are shown in red and blue, respectively. The distance between H₂PO₄⁻ and the Cζ atom of αARG373 is plotted in green. (B) P_i (H₂PO₄⁻) migration toward the P loop at 3.5 ns (Upper) and 39 ns (Lower). (C) Tightly bound P_i (HPO₄²⁻) at 20 ns (details as in Fig. 1C).

Fig. 5.

Interface conformation and γ-rotational–direction dependence of P_i binding stability. (A) PC2 of the E site (left scale; blue) reporting on αβ interface tightening, and P_i distance relative to starting conformation (right scale; red) during the first 10 ns of the hydrolytic torque simulation with H₂PO₄⁻. (B) PC2 of the E site in the hydrolytic (blue) and synthetic (purple) torque simulations with H₂PO₄⁻. (C) (Left) Distance of the singly charged P_i from its starting point for the hydrolytic (red) and synthetic (green) torque simulations. (Right) Distance of the doubly charged P_i for the hydrolytic (red) and synthetic (green) torque simulations.

We also studied the dependence of the P_i binding stability in the E site on the direction of γ-rotation. The singly charged P_i, with the γ-subunit rotated in the synthesis direction, stayed at the initial position for the first ∼30 ns (Fig. 5C, Left). After moving transiently to the P loop, P_i returned back to the initial position at around 70 ns and remained there. These motions suggest that P_i binding in the E site is more stable when γ is rotated in the synthesis direction than in the hydrolysis direction. This increased stability would be important for ATP synthesis, where ADP should bind into the E site already occupied by P_i (see below). The loosening of the αβ interface in response to γ-rotation in the hydrolysis direction, and the tightening in the synthesis direction (Fig. 5B), are likely the main factors changing the P_i binding stability. The doubly charged P_i (Fig. 5C, Right) stayed at the initial position, independent of the direction of the γ-rotation, and maintained tight interactions with the αβ_E residues.

As a direct demonstration of the coupling between P_i release and γ-rotation, three independent 40-ns free simulations without torque were conducted: (i) without P_i, and with (ii) singly and (iii) doubly charged P_i in the E site (Fig. S3D). The resulting γ-angles are distributed narrowly around 85° with doubly charged P_i, with a wider distribution for singly charged P_i indicating a looser γ-shaft. Importantly, after doubly charged P_i was released, γ indeed rotated by ∼10° in the hydrolysis direction (Fig. S3E). These free simulations thus further support the hypothesis that release of doubly charged P_i from the E site drives γ-rotation in the hydrolysis direction.

Metadynamics Simulation of P_i Release from the E Site and DP Site.

P_i exits the E site (at 320°) and DP site (at 200°) on entirely different pathways according to the metadynamics (38) simulations (Fig. 6A). From the E site, singly and doubly charged P_i both escaped outward via a transient intermediate at the P loop, consistent with the escape route of H₂PO₄⁻ in the torque simulations. In the DP site, this outward path is blocked by ADP, forcing P_i instead to escape inward and exit at the central hole of the ring subunits (Table S1). This alternate pathway was confirmed by separate simulations with a different metadynamics hill height (0.2 kcal/mol) and for a different F₁ structure with a slightly open DP site [Protein Data Bank (PDB) ID code 4asu; Fig. S4].

Fig. 6.

P_i release from the E site and DP site. (A) Pathways and (B) free-energy profiles of P_i release determined from metadynamics simulations of singly charged P_i (brown) and doubly charged P_i (yellow) from the E site, and of singly charged P_i from the DP site (green). In A, β_E (cyan cartoon) is superimposed on β_DP (orange cartoon), and the P loops are colored in purple. ADP, Mg²⁺, and P_i in the DP site are shown as sticks. (C) Cut through the binding site in the DP state, with arrows indicating exit pathways.

These two exit pathways have drastically different free-energy barriers (Fig. 6B). Escaping from the E site in the z direction, singly and doubly charged P_i face free-energy barriers of ∼5 and ∼10 kcal/mol, respectively, to transition from the tightly bound state to the P loop. The free-energy barrier for P_i to be released from the P loop into solution is ∼5 kcal/mol in both cases. By contrast, the free-energy barrier for P_i to be released from the DP site, moving along the x direction, is almost ∼30 kcal/mol in total, and thus insurmountable on the functional timescale. This high barrier is a result of the tight interface of the DP site, and of ADP blocking the pathway to the P loop, which effectively prevent P_i escape to the outside (Fig. 6C). Our results are consistent with the interpretation of recent single-molecule experiments (13) of P_i being released from the E site, i.e., at 320° in Fig. 1A during the catalytic dwell. The free-energy barriers were confirmed by additional long simulations with a different protocol (SI Text and Fig. S5).

As listed in Table 1, the calculated timescale of ∼2 ms for the release of doubly charged P_i agrees well with the ∼1-ms estimate from experiment (10, 12, 13). The mean first-passage times were calculated from the free-energy profiles and diffusion coefficients (SI Text, Fig. S6, and Table S2). As described above, the P_i movement from the tightly bound state to the P loop is coupled to the global interface motion that occurred within a few nanoseconds (Fig. 5A). This rapid conformational change prevents backtransfer of P_i, which is thus ignored in our timescale estimates. Overall, our simulations suggest that doubly charged P_i is released from the E site at 320° before the 40° substep.

Table 1.

Estimated mean first-passage times of P_i release from the E site

Pi	Tightly bound to P loop	P loop to tightly bound	P loop to release
H2PO4−	2.4 μs	0.11 μs	0.34 μs
HPO42−	2.0 ms	0.014 μs	41 μs

Discussion

We found that P_i release from the E site is kinetically realistic and that release from the DP site is not. The calculated time of ∼2 ms for the release of doubly charged P_i from the E site matches the rate of P_i release during the catalytic dwell reported from experiment (13). With this timescale matching also the catalytic dwell time, P_i release could thus be rate-limiting. Our results suggest the need to correct earlier models in which P_i was assumed to exit first from the DP site, just after the hydrolysis reaction, followed by ADP release. Instead, P_i is likely released from the E site at 320° (Fig. 1A), 120° after the hydrolysis reaction, and after ADP release.

Our simulation results help reconcile conflicting interpretations of earlier experiments. Shimo-Kon et al. (21) showed that P_i binding from solution inhibits ATP binding, concluding that the E site must be devoid of P_i. However, at 320°, P_i could have escaped with a ∼1/ms rate and ATP rebound with an estimated on rate of ∼1/ms at 1 mM concentration (24), making the empty E site short-lived in the cycle. Nucleotide binding to all three sites at ∼1 mM concentration (21) could also explain the presence of three ADPs in a recent F₁ crystal structure (22). With these ADPs not produced during turnover, but likely taken up from solution (1), P_i would not be kinetically trapped in the DP and E sites. By contrast, tightly bound P_i observed in the E site of some structures (23, 44) likely mimics a product P_i of hydrolysis before release in the catalytic dwell. Gao et al. (20), on the basis of kinetic data on the inhibition of ATP hydrolysis by ADP and P_i, concluded that P_i is released after ADP, consistent with our calculations. We also note that, in the synthesis direction, preferential binding of P_i in the empty E site is advantageous by favoring the subsequent binding of substrate ADP (45) over the abundant but inhibitory product ATP. The ADP/ATP preference with P_i bound could be probed in experiment (21).

The combination of experiment (13) and simulation suggests that P_i is released as HPO₄²⁻. According to quantum chemical calculations, P_i is doubly protonated (singly charged) just after hydrolysis (25). However, after ADP and Mg²⁺ (net charge is −1) leave the site, four positively charged residues surround P_i, shifting its pK_a. This electrostatic environment would indeed favor the loss of one proton, resulting in a singly protonated (doubly charged) P_i in the E site. Probing the pH dependence of the dwell time of the P_i release (or the 40° substep) could test this hypothesis, assuming protonic equilibrium with the solvent.

We also investigated the conformational changes of F₁ in response to the 40° rotation step of the γ-subunit, and their coupling to P_i release. γ was rotated both in the hydrolysis and synthesis directions, for two possible protonation states of P_i in the E site. By rotating for 40° in the hydrolysis direction relative to the available crystal structures, we obtained a first fully atomistic conformation of the intermediate state following the 40° substep. We found that the structure of the ATP-bound αβ_TP interface became as tight as that of ADP+P_i-bound αβ_DP interface, thus facilitating hydrolysis. By comparison, the αβ_E interface became looser, and P_i escaped to the P loop. We expect these structures to be representative of the conformations of the two sites in the binding dwell state. The αβ_DP site remains relatively tight and shows only a slight opening, as indicated by the displacement of purple and blue points in Fig. 3A. We conclude that αβ_DP motions in response to γ-rotation are considerably slower than those of αβ_E and αβ_TP (16). The salt bridges between γ and α₃β₃ formed in the intermediate state are listed in SI Text. To test whether the intermediate state is stable without torque applied to γ, two 40-ns free simulations were conducted with the torque switched off at 40° and 50° from the catalytic dwell, respectively. In both simulations, the γ-angle settled around 110° (30° from the catalytic dwell), indicating the formation of a metastable state (Fig. S7A). Importantly, the torque simulations drive the system out-of-equilibrium (as would the F_o motor in intact ATP synthase). In such a nonequilibrium process, the γ-rotor will be slightly over-twisted. Releasing the torque that drives the rotation is thus expected to result in a fast relaxation of the angle. We indeed observed a relaxation on a ∼5-ns timescale after releasing the torque at 120°, close to the presumed metastable minimum (Fig. S7A, green curve). When we released the torque at 130°, beyond the minimum, we again saw this fast recoil, and in addition a more gradual relaxation to a state at ∼110°, consistent with an overdamped, weakly driven motion in a metastable minimum at ∼110°. The interface conformations of αβ_E and αβ_TP relaxed partially, but importantly in a reversible way (Fig. S7B).

These interfacial motions are coupled to torque generation, which should make it possible to probe our results by mutation. Torque generation as a result of nucleotide binding/dissociation has been probed extensively by mutations of β–γ interactions (46). By contrast, relatively little is known about the specific mechanisms of torque generation as a result of P_i release. The interfacial motions seen in our simulations suggest that torque generation by P_i release should be sensitive to the hydrophobic interactions between αPHE403/αPHE406 and γILE16/γILE19/γLEU77, and the electrostatic interactions between αASP409 and γARG133, αASP411 and γLYS30, αGLU355 and γLYS11, and αGLU399 and γLYS18. Perturbations of these interactions by mutation should affect the coupling between the αβ_E interface and the γ-subunit, and should thus report directly on torque generation as a result of P_i release.

Remarkably, the two P_i exit pathways observed in this study appear to be conserved in myosin, and possibly other members of the large family of P-loop ATPases. In particular, a so-called “back door” exit pathway for P_i release has been proposed for myosin, to circumvent the “front door” pathway blocked by ADP in the binding pocket (47). Molecular dynamics simulations showed that the P_i release pathway is tightly linked to the cleft-closing motion of myosin upon binding to actin (48, 49). The back door route dominated for an open cleft and a closed binding site, whereas the front door and a variant of the back door route dominated for a closed cleft and an open binding site (49). We have a similar situation in F₁, although the global motions are quite different. With the binding site closed (DP site), P_i escaped via an inward route that corresponds to the back door in myosin (toward switch II). By contrast, with the binding site open (E site), we observed the outward route corresponding to the front door in myosin (Fig. S8). Despite large differences in the global functional motions of different P-loop ATPases, local motions during the hydrolysis cycle thus appear to be conserved. Functional requirements then dictate the dominant route of P_i exit in different ATPases, and possibly also GTPases. Myosin uses both back and front doors, whereas F₁ takes the front door exclusively, as shown here.

Methods

Initial Structures.

The initial structures of F₁ were taken from the azide-free crystal structure (PDB ID code 2jdi) (50). Residues 24–510 were used for the α-subunits, 9–478 were used for the β-subunits, and all residues were used for the γ-subunit. MODELER (51) was used to model structures of missing residues. Missing residues in the γ-subunit were modeled according to the dicyclohexylcarbodiimide-inhibited structure (PDB ID code 1e79) (52). In the azide-free structure, the TP site and DP site bind an ATP analog (AMPPNP) and Mg²⁺, and the E site is empty. For the simulation system, the ATP analog in the TP site was replaced with ATP, and that in the DP site was replaced with ADP and P_i (H₂PO₄⁻). P_i (HPO₄²⁻ or H₂PO₄⁻) was modeled in the E site, representing the catalytic dwell state just after ATP hydrolysis (SI Text). A variety of analyses (1, 14–19) consistently indicate that the initial crystal structure represents the catalytic dwell, which corresponds to a γ-angle of 80° by definition (Fig. 1A). The half-closed structure by Menz et al. (44) was not used here because it possibly corresponds to an E site occupied by ADP rebound from solution at high ADP concentration, and thus would not be part of the actual sequence of product release. P_i in the DP site was modeled as doubly protonated following the quantum chemical studies of ATP hydrolysis in this site (25). Crystal water molecules were retained unless they clearly overlap with replaced ligands.

Simulation Setups.

The modeled F₁ with crystal waters was solvated with TIP3P water (53) in a rectangular box such that the minimum distance to the edge of the box is 11 Å, and neutralized with potassium ions. Then, ∼100 mM KCl was added to the system. The total number of atoms is ∼313,000 (Fig. S1). The Amber ff99SB force field was used for the protein (54), with modified parameters for KCl (55), and for ATP and ADP (56). The point charges for singly and doubly protonated P_i were determined using Gaussian 03 (57) and the Antechamber module of Amber (58) (SI Text). The system was energy minimized and equilibrated at isothermal–isobaric (NPT) conditions with Ewald electrostatics and restraints on all heavy atoms in the protein for 500 ps, and subsequently, with restraints on only Cα atoms for 1 ns. After the equilibration, production runs were conducted with restraints on the Cα atoms of the 10 N-terminal residues of each of the three β-subunits, mimicking the role of His-tag anchoring in single-molecule experiments. NAMD 2.8 was used for the molecular dynamics simulations with periodic boundary condition (59). Langevin dynamics with 1 ps⁻¹ damping coefficient was used for temperature control at 310 K, and the Nose–Hoover Langevin piston was used for pressure control at 1 atm (60).

Flexible Rotor Simulation.

In the torque simulations, only the average rotational angle of the γ-subunit was restrained. As in an earlier method (61), the γ-subunit is allowed to twist freely, but here without arbitrary subdivision into slabs. We also allow free translation of its center of mass. Details of the method and explicit expressions for the restraint forces are in SI Text.

Metadynamics Simulation of P_i Release.

To enhance the sampling and estimate free-energy profiles for P_i release, metadynamics (38) simulations were conducted using the PLUMED 1.3 plugin with NAMD (62). The relative Cartesian coordinates x, y, and z of P_i from the binding site were used as collective variables (63), where the binding site was defined by the Cα atoms of β-subunit residues 188, 256, 257, 259, and 309–312, which are within 8 Å from P_i in the DP site. Flexible α and P-loop residues are excluded. Repulsive Gaussian potentials with heights of 0.1 kcal/mol and widths of 0.6 Å were deposited every 1 ps during the metadynamics simulations. The free-energy profiles were calculated by a PLUMED utility, sum_hills.