Rate of hydrolysis in ATP synthase is fine-tuned by α-subunit motif controlling active site conformation

Abstract

Computer-designed artificial enzymes will require precise understanding of how conformation of active sites may control barrier heights of key transition states, including dependence on structure and dynamics at larger molecular scale. F_oF₁ ATP synthase is interesting as a model system: a delicate molecular machine synthesizing or hydrolyzing ATP using a rotary motor. Isolated F₁ performs hydrolysis with a rate very sensitive to ATP concentration. Experimental and theoretical results show that, at low ATP concentrations, ATP is slowly hydrolyzed in the so-called tight binding site, whereas at higher concentrations, the binding of additional ATP molecules induces rotation of the central γ-subunit, thereby forcing the site to transform through subtle conformational changes into a loose binding site in which hydrolysis occurs faster. How the 1-Å-scale rearrangements are controlled is not yet fully understood. By a combination of theoretical approaches, we address how large macromolecular rearrangements may manipulate the active site and how the reaction rate changes with active site conformation. Simulations reveal that, in response to γ-subunit position, the active site conformation is fine-tuned mainly by small α-subunit changes. Quantum mechanics-based results confirm that the sub-Ångström gradual changes between tight and loose binding site structures dramatically alter the hydrolysis rate.

Most cellular processes depend on ATP as a free energy source. Among a wide spectrum of organisms, the key enzyme responsible for maintaining the ATP concentration is F_oF₁ ATP synthase, with synthesis being driven by a transmembrane electrochemical gradient (1). The chemical reaction takes place in the F₁ domain at active sites located in the three αβ-subunit pairs surrounding a central α-helical coiled coil, the γ-subunit. It has been shown in single-molecule experiments on F₁ that ATP synthesis and ATP hydrolysis are coupled to γ-subunit rotations of opposite directions (1, 2). Early kinetic studies revealed a strong ATP concentration dependence for the hydrolysis rate that was explained involving both unisite and multisite catalysis: low ATP concentrations, with only one active site populated by unisite catalysis (3, 4), whereas at physiological (high) ATP concentrations, multisite catalysis takes over, resulting in several orders of magnitude increase in hydrolysis rate (5). This remarkable catalytic cooperativity of the enzyme could be an effect of the mechanochemical coupling between the active sites. In crystal structures, three conformations of the catalytically active sites can be seen, assigned as tight binding site (α_TP/β_TP; T), loose binding site (α_DP/β_DP; D), and empty site (α_E/β_E; E) (6–10). During ATP hydrolysis, each α/β-subunit pair changes conformation along the cycle: E→T→D→E, each step associated with a 120° rotation of the γ-subunit (5, 7, 10, 11). Single-molecule studies supported by simulations indicate that the 120° rotation steps (11) can be further resolved into one 90° and one 30° substep during hydrolysis (2, 12, 13). The binding of ATP and release of product ADP are associated with larger conformational changes in the β-subunit.

By contrast, the crucial chemical step, the phosphate ester bond breaking of ATP hydrolysis, occurs in an already closed active site. High-resolution X-ray structures show minuscule variations between the two closed active site conformations, T and D (6–8, 14). According to single-molecule experiments, the bond-breaking step takes place after an ∼90° rotation of the γ-subunit, thus in between the two conformations, most likely in a near-D structure (12). This conclusion was supported by theoretical studies (13, 15, 16), and recently, we provided indications that the barrier height for the hydrolysis step decreases significantly when the active site conformation changes from T to D (15, 16). Additional support was obtained from single-molecule manipulations (17). The coarse-grained simulations by Mukherjee and Warshel (13) for the energy surface of the whole F₁ complex were instrumental here, showing the electrostatic origin of the rotary mechanism. Based on these results and the threefold symmetry of F₁-ATPase, an energy-phase shift mechanism was proposed, by which macroscopic-scale changes are speculated to be energetically coupled to contribute to reduce conformational barriers because of destructive interference during the rotary mechanism (18).

However, how the change of chemical barrier may be connected to structural change at an atomic level is yet a remaining challenge, and more specifically, one may ask if macroscopic-scale changes could control the chemical reaction rates? Clearly, the reactions run much faster than the conformational changes that are occurring on a millisecond timescale. In particular, the role of small conformational differences between the closed active sites in T and D is important to find out. Using multiple computational approaches, we address (at an atomic level) the mechanism of larger-scale changes in the enzyme complex, how these changes can be connected to fine-tuning of the active site conformation, and how conformational changes in the active site are related to control of reaction rate. When T and D were superposed, the largest change in the active site is the ∼1.1-Å shift of the αR373 residue (7). This residue has earlier been shown important for the reaction (5, 15, 19), although how its position may constitute a control mechanism is not understood; also, it is not understood how long-range interactions may connect the conformation at the reaction center to the rotary position of the γ-subunit.

Results and Discussion

Defining Problem and Model.

There is solid experimental evidence that the 120° γ-subunit rotation is induced by binding of ATP into an E site, which is then converted into T (1, 2, 8, 20). In the WT enzyme, the rate of unisite catalysis is the same as in cross-linked mutants in which the γ-subunit is immobilized (21). This observation indicates that ATP hydrolysis is not coupled to the γ-subunit rotation but takes place in a near-T conformation (Fig. 1). For the case of multisite catalysis, when ATP populates also a second site, the first T site containing ATP is converted to a near-D conformation, and ATP is hydrolyzed at a much faster rate (Fig. 1) (2, 17). Thus, how the chemical reaction is affected as the active site conformation is altered from T→D is the key to understanding the difference between the unisite and multisite catalysis. This relation may also be a key to understanding the nature of the coupling between mechanical energy transferred by rotation of the γ-subunit and the change of chemical activation energy along the reaction path. Earlier theoretical work has shown how the energetic preference for ATP or ADP and P_i changes between the active sites (13, 19, 22, 23).

Fig. 1.

Schematic energy landscape describing coupling between mechanical and chemical processes in an α/β-subunit pair.

The structural differences between the closed active sites is so small (7) that the T→D change can, in principle, be followed using, other than standard molecular dynamics (MD), quantum mechanics (QM)-based models, where transformation of the isolated active site may be approximated as a linear combination of atomic positions between initial X-ray coordinates of active sites in tight and loose conformation. Although the MD modeling could provide clarifying information of how the larger-scale rearrangements may effectuate the T to D active site conformational change, the QM and QM/molecular mechanics (MM) models can quantify how such structural rearrangements will alter the hydrolysis barrier height.

Based on the above-described structural considerations and the overall timing of the substeps put together from available structural, kinetic, and single-molecule sources (1, 2, 5, 20), using all-atom MD simulations, we set out to trace the structural changes that regulate the active site rearrangement along the T→D pathway. Several MD simulations of the full F₁ complex have been performed in the past; however, they did not focus on this conformational energetic fine-tuning (24–27). The few studies that have explored conformational effects on barrier have not focused on the change along the conformational coordinate. The transition of T into D in F₁ takes place during the 120° rotation of γ-subunit between one state (e.g., DTE) and the following EDT state (Fig. 2). Here, most likely an intermediate structure is present containing two Ts: one binding ATP (E→T), forcing rotation of the γ-subunit, and the other translocating from T to D (1, 2, 20). Because such an intermediate structure is not yet available from experiments, we built an F₁ model ET*T, with T* denoting the tight α/β-subunit before relaxing into D (Fig. 2). At this point, ATP binding and large γ-subunit rotation are both assumed to be completed, and multisite hydrolysis will commence.

Fig. 2.

Schematic timing of structural changes in α-subunit manipulating the active site geometry during 120° rotation of γ-subunit (central red oval). Relaxation of one T subunit (T*) into D from DTE state to the next (EDT) state is achieved through ET*T. Relevant microscopic changes are indicated by highlighting ATP (red sticks) and NVISIT helix and Tuning motif (gray cartoon). Residues αS344, αR373, and αK391 are shown as balls and sticks, and close contacts C1-7, which are important for the T→D transition, are indicated as red dashed lines (Table 1).

Macroscopic Changes Along T→D.

To understand the control of microscopic change in the active site, we first followed larger-scale changes and structural rearrangements in the tight site T* of the ET*T model. The overall T*→D relaxation was enhanced by using restrained MD (RMD), with distance restraints introduced far away from the active site after the initial 16-ns unrestrained simulation (Methods and SI Text). The macroscale changes were followed for T*→D using both T and D as a reference. RMSD of the T* subunit relative to T clearly increases (Fig. S1A). By contrast, when using D as reference, after an initial period, RMSD is decreasing slightly and then stays significantly smaller, indicating that T* transforms away from T and to D. When comparing the α- and β-subunits of T* separately, the larger changes of the RMSD plot with T as reference clearly take place in the α- and not the β-subunit (Fig. S1B). Zooming closer to the region surrounding the active site, the overall process is accompanied by several structural rearrangements, with formation of H-bonds and salt bridges mainly involving the α³³³D-T⁴¹⁴ region in the α-subunit. Most of these structural changes are intersubunit contacts with surrounding subunits, and their presence or absence is characteristic for the difference between T and D (Table 1). Our numbering of these contacts follows the timing of their breakup or formation. They will be discussed below in other contexts (e.g., C1 and C2 in relation to the microscopic change in the active site).

Table 1.

Emerging close contacts between subunits differentiating T from D

C1	αTP	333DVSA336	γ	252R
C2		341NVISIT346		ATP
C3	αDP	353ETELFYK359	βTP	381S (DELSEED loop)
C4	αDP	370SVSR373	αDP	386VAGTMK391
C5	αDP	395AQYRE399	βDP	341ELG343
C6	αDP	395AQYRE399	βDP	408R, 412R (DELSEED loop)
C7	αDP	411DAAT414	βDP	453PEQA456

Residues involved in formation of H-bonds or salt bridges are marked as bold letters.

Most interestingly and a summit of our study regarding the local regions of the active site, the simulations provide intermediates that cannot be traced from the end states found in the X-ray structures. The closer region of the key αR373 residue displays three distinct conformational states as T* converts to D (Fig. 3). Within this region, the smaller α³⁷⁰S-E³⁹³ segment, which we term the Tuning motif, shows a rapid distortion right from the early stages of the simulation (Fig. 4).

Fig. 3.

RMSD of the α³⁵³E-E³⁹³ amino acid sequence region around the αR373 calculated with the corresponding region of T as reference (red with yellow smoothed average) and calculated with the same region of the ground-state D subunit pair as reference (blue with cyan smoothed average) (7).

Fig. 4.

Overview of α-subunit Tuning motifs (α³⁷⁰S -E³⁹³) relevant for manipulating active site conformation. (A) Surface view of full F₁: γ-subunit is in red and Tuning motifs in T and D are colored blue and green, respectively. The two αR373 residues and the two ATPs are shown as red sticks. (B) Gradual transition of Tuning motif from the conformation found in T (i.e., T* at 0 ns) to the conformation found in D. The most significant change is the partial unfolding of the 6-residue-long segment, α³⁸⁶VAGTMK³⁹¹, in the helix region. (C) Variation of overall Tuning motif conformation in T* and H-bond formation between αK391 and αS370, αS372. By end of the simulation (green), H-bonds (magenta dashed lines) are formed, and the position of αR373 is shifted compared with T conformation at 0 ns (blue).

The first change occurs spontaneously after 2.8 ns: the partial unfolding of a 6-residue fragment ending with αK391 in the longer helix of the Tuning motif. This change is coupled to partial formation of C6, involving αQ396, αE399, and βR408 and βR412 residues in β-subunit of T* (Table 1 and Fig. S2). The latter two residues are part of a key region close to the β³⁹⁴DELSEED⁴⁰⁰ loop, which has important interactions with the central γ-subunit (27–29).

The transition to the second conformational state takes place when restraints are introduced after ∼16 ns. These restraints guide the formation of C3 close to αR373 (Fig. 2). Close-contact C3 is present between the α-subunit of T* in ET*T and the DELSEED loop of the neighboring β-subunit in the subsequent T. This contact is, again, a clear difference between the crystal structures of the final T and D conformations, because α_TP in T does not have any similar interaction with the subsequent β_E in E (7). This difference may be important for the correct final positioning of αR373, justifying the introduced restraints. Because of the applied restraints for this second stage, the actual timing of structural changes has no physical relevance; nevertheless, the structural changes are judged to be realistic.

The transition into the third and final state can be observed after ∼34.6 ns, and the structural change corresponds to the further shift of the second part of the Tuning motif towards the β-subunit in T*. At this point, the α-helical H-bond pattern in the helical region of the Tuning motif is completely disrupted, and C4 forms (Figs. 2 and 4). Additional structural changes in the later stage of the simulation include the formation of close contacts C5 and C7 and the final form of C6 between loops of α and β in T*, similar to what is seen in the crystal structure of D (7). These contacts close the interface between the α- and β-subunits, and their formation also indicates that the T*→D transition is essentially concluded.

In crystals from mitochondrial F₁ (7, 8), conformational changes and variations between T and D show close similarity to the changes observed in the simulations. In the α_DP-subunit of D, the Tuning motif is distorted almost the same way as found by the end of the simulation, whereas in α_TP, it exhibits no deformation (Figs. 2 and 4 and Fig. S2) (7–9). The spontaneously formed contacts in T* (i.e., between α and β; C5, C6, C7) can all be found similarly in the D (α_DP/β_DP) subunit pairs of the X-ray structures. The importance of forming these contacts is accentuated by the fact that they are not present in the corresponding regions in T (for α_TP/β_TP). This difference most likely originates from the different relative positions of T and D with respect to the γ-subunit. The intersubunit contacts (α_DP↔β_TP, α_DP↔γ) seem important in aiding the T→D relaxation path in F₁, because when closed subunits were studied alone, they rather tended to relax to the more open empty site (30).

Microscopic Changes.

The above-described macroscopic changes contribute to the rearrangement of the active site structure in T*. However, tracking microscopic changes in the active site is hard, because the differences between tight and loose active sites are only ∼1.0 Å or less (i.e., subtle compared with the 100-Å-scale size of the ∼350 kDa F₁ complex or the positional fluctuations, which are also on the scale of a few angstroms for proteins). Therefore, active site changes were monitored by both residue–residue distances along the timeline of the simulation and radial distribution functions for those pairs of residues, which showed the largest positional difference between T and D in crystal (Fig. 5). These residues include βE188, βR260, βR189, and αR373, which are responsible for coordinating the key components of the hydrolysis reaction: the nucleophilic water molecule, the γ-phosphate, and the oxygen atom connecting γP and βP in ATP.

Fig. 5.

Timeline for the selected characteristic distances of the active site of T (blue with cyan smoothed average) and T* (green with yellow smoothed average) during the MD simulation of the modified F₁ model ET*T. (Left) The αS344 side chain flips and becomes H-bonded to ATP at 9.7 ns; then, the Cα-Cα distances start to decrease spontaneously to values found in the D conformation. By the end of simulation, all three distances show a marked drop in T* compared with T, indicating that the active site is transformed into a near-D conformation. (Right) The same Cα-Cα distances measured by radial distribution functions in 10-ns windows of the simulation (shown up to 50 ns).

Changes in the relative positions of these residues can have a crucial effect on the rate of hydrolysis. The initial partial unfold of the helical region in the Tuning motif at 2.8 ns seems, at first, to expand the active site rather than contract it (Fig. 5). However, all of the interresidue distances eventually spontaneously decrease to the distance values observed in D, enhanced also by a contribution from αS344 forming C2. We and others have earlier shown that αSer344 in the α³⁴¹NVISIT³⁴⁶ helix plays an important role in the preparation of the transition state (TS) (15, 31). Our QM results have also suggested that the side chain of αS344 has to turn to the active site and form a hydrogen bond with O=γP of ATP (15). This flipping of the Ser side chain can be observed in the MD simulation in T* after ∼9.7 ns (Fig. S3). Precisely at the same time when the -OH side chain is turned to ATP, the active site geometry shows a rapid contraction to its final conformation in D (Fig. 5).

Interestingly, the same side chain rotation can be observed also for the αS344 in T at ∼30 ns but in this case, with no apparent effect on the overall conformation of the tight site (Fig. 5). The major difference between T and D for the sequential region of the NVISIT helix is caused by their positions relative to the γ-subunit. In T, the helix is held firmly, close to the larger helix of the γ-subunit by hydrogen bonds (C1), whereas in T*, the helix diverts freely from the γ-subunit to the active site (Fig. 2, SI Text, and Fig. S4).

The final substantial contraction that locks αR373 into its position in D has a timing closely related to the 34.6-ns conformational change in the Tuning motif but occurs some 3 ns earlier. It is initiated by the breakup of the H-bond between αD347 and the C=O group of αR373 and formation of C4 in the Tuning motif. It also shows why partial unfold of the helical region in the Tuning motif is crucial for formation of C4: in this way, αK391 gets close to αS370 and αS372 and can pull these residues (and αR373) into their positions in D (Fig. 4).

The flip of the αS344 side chain, the initial divergence of the NVISIT helix from the γ-subunit, and the initial involvement of αS372 in C4 cannot be seen from the X-ray structures. These intermediate states evidenced from the simulations are important for understanding the true mechanism of the T→D transition. To confirm that the transition is completed and test robustness of the achieved near-D conformation, after RMD, an additional 30-ns fully unrestrained MD was performed, up to a total of 80 ns. By the end, it is clear that, in contrast to the residue–residue distances measured in T, all T* values have decreased significantly, indicating that most of the T*→D microscopic residual rearrangements in the active site are completed (Fig. 5). The radial distributions of the distances measured in 10-ns windows also support that most of the changes affect the tested distances similarly and that a gradual contraction of the key positions of active site is observed. The full relaxation of T* cannot be achieved on the available timescale but most likely requires orders of magnitude longer time. Nevertheless, the all-atom simulation on ET*T shows that most of the significant differences between crystal structures of T and D can be tracked and are well-reproduced.

Effect of T→D on the Rate of Hydrolysis.

To assess how the hydrolysis reaction is affected along T→D, in parallel to the MD simulations, several QM active site models were combined with QM/MM models for both end states, T and D, using a large 152-atom QM layer (QM₁₅₂/MM) and also, a linear shift approach on previous QM models (15) scanning the gradual changes of the active site conformation. In this way, we obtained an approximate energy surface (ES) to probe reaction paths and changes of barrier height along T→D (Fig. 6).

Fig. 6.

Energy surface of the hydrolysis step in F₁ ATPase as the active site changes from T to D conformation. Schematic trajectories of unisite (black) and multisite (red) catalysis are drawn based on the experimental barrier heights. The ES is obtained using a combination of QM/MM and QM simulations tracking conformational changes of active sites using a linear shift method.

Small structural variations between T and D in the initial ATP + H₂O state and subsequent reaction steps have been described in detail (7, 15, 16). The QM/MM models used here support that, in T, the distance between ATP and the nucleophilic H₂O is longer and the fragments directly participating in the hydrolysis reaction are in a bent, less favorable position than in D (Fig. S5). To accommodate the TS geometry in T, relatively large rearrangements are required from the ATP state: βE188, which coordinates the nucleophilic water, has to shift ∼0.6 Å from ATP to the TS geometry, whereas in D, this shift is only ∼0.2 Å. These rearrangements result in an energetically less favorable TS for T. Thus, the difference in barrier heights between T and D in the QM/MM models arises not only from differences in the QM region but more because of effects of the protein environment described in the MM layer. Relative values of the stretching, the van der Waals, and the bending energy terms are significantly larger for the TS in T than in the D models (SI Text and Fig. S5).

The results from the combined QM-based models indicate a significant decrease in barrier height when the active site conformation changes from T to D: the decrease of barrier height near T is rapid, but as it approaches the D region, it becomes less steep (Fig. 6). Note that experimental barrier heights suggest a range of 52–67 kJ/mol (2, 32) for multisite hydrolysis, which corresponds to a region closer to the D active site conformation. However, the barrier for unisite catalysis is around 80 kJ/mol according to experiments (33), which corresponds to a near-T region. The shallower barrier height decrease observed near the D conformation indeed supports that, on multisite catalysis, the ∼90° rotation of the γ-subunit changes one of the T conformations into a near-D conformation, where the bond-breaking step occurs (2). Under unisite conditions, the γ-subunit, because of lack of rotation, cannot exert any large changes on T. Consequently, the reaction will then progress more slowly with a barrier height corresponding to the high-energy TS region of a near-T conformation. If one assumes for simplicity a linear relation between conformational change and γ-position, the barrier height obtained after performing about 75% of the steps along T→D is consistent with hydrolysis occurring after ∼80–90° rotation. This observation would suggest that a majority of the conformational shifts in the active site have been already performed at this point.

In the final D conformation, the barrier height is predicted to be significantly decreased. This decrease is most pronounced in the set of fully relaxed QM/MM models, which have electronic embedding and therefore, wave functions of the QM region polarized by the electrostatic potential of the MM layer. For the D site, the average of the activation enthalpies obtained by the QM/MM models is 46 kJ/mol, thus lower than observed experimentally in WT F₁-ATPase. This lower value suggests that, if the γ-subunit rotation were not split in two substeps but 120° in one step, a faster turnover rate should be obtained. Indeed, when a crucial region of the DELSEED loop close to the γ-subunit was deleted, a several-fold increase in experimental turnover rate was observed, and activation enthalpy dropped to 34.1 kJ/mol (28). On the energy surface obtained from the combination of QM/MM and QM models, gradually tracking all structural changes, the experimental barrier height differences for unisite, multisite, and mutation studies are satisfactorily reproduced. Moreover, the results also show that, in direction to hydrolysis, the barrier height strongly decreases as the active site changes, whereas in the direction of synthesis, it deviates by only a few kilojoules per mole (Fig. S6). The smooth continuous decrease of the barrier height along T→D in our ES is the consequence of the applied linear shift method, which takes the differences between average conformations of T and D found in the crystal structures. The barrier height alterations presented here are in agreement with experimental results testing a smaller angular range of γ-subunit rotation (17). A word of caution: using snapshot structures to reproduce T→D conversion from a millisecond timescale simulation, where the γ-subunit is gradually rotated and active site side chains are given time to relax, would probably produce intermediate energetics with large energetic fluctuations. Because they might last orders of magnitude longer than available simulation times, a direct coupling between current MD and QM/MM calculations is not considered meaningful. However, in the present MD simulation, the residue–residue distances in the active site of T* measured also in 10-ns windows all show similar continuous decreases for the selected C_α-C_α distances (Fig. 5). These decreases indicate that active site contraction during T→D goes most likely without large positional fluctuations of the key residues but rather, that they move to each other in a synchronous manner. Thus, our linear shift approach of the active site contraction may be a justified approximation.

The MD simulations initiated from ET*T reproduce most of the macroscopic and microscopic conformational changes from loose to tight binding site and thus, provide a mechanistic basis for how the subtle control of active site conformation and larger-scale conformational changes may cooperate. Interestingly, all major change is observed in the α- and not β-subunit. The three-stage conformational changes occurring around the Tuning motif and involving H-bond formation between αK391 and αS370/αS372 have a clear contribution in the repositioning of αR373. In addition, the increasing distance of the α³⁴¹NVISIT³⁴⁶ helix from the γ-subunit and the accompanying flip of the αS344 side chain, which makes it H-bonded to ATP, pushes farther the contraction of the active site. The simulations not only provide insight into these intermediate changes, which cannot be seen from the T and D end states, but also reproduce the final close contacts between α- and β-subunits, which are present for D in the crystal structures.

As for effects of subtle structural changes, the energy surface of the hydrolysis step clearly shows that the 1-Å-scale fine-tuning between tight to loose active site conformation results in large hydrolysis rate variations. The relative change of barrier height in the QM/MM models provides new pieces of insight about the overall mechanism of the enzyme, because it seemingly does not exhibit maximum efficiency in catalyzing the hydrolysis step by stopping at ∼80° rotation. The experimentally observed dwelling with relatively long pauses might be because of effects of relaxing the integral F₁ system put into a more mechanical perspective: the position of the γ-subunit playing a role in minimizing total balancing overlapping and phase-shifted potentials (18). By the parallel use of the QM and MD simulations, the mechanistic details of how the position of the γ-subunit may control the rate of hydrolysis through the T→D relaxation may now be understood at a molecular level.

Note that K_eq ∼ 1 for the hydrolysis step in F₁ (3, 16, 33), and with single-molecule studies, the released nucleotides were often observed to rebind (2), which in case of ATP synthesis, would probably mean an E→T backward transition. Thus, during synthesis, the increasing hydrolysis barrier along D→T and the separation of these two conformations by a 120° γ-subunit rotation may result in a ratchet mechanism ensuring kinetic control of the unwanted (backward) hydrolysis step of the rebound product and in this way, increase the efficiency of ATP synthesis.

Our understanding of the function of the enzyme is far from perfect; several problems clearly remain to be addressed in the future. One concern is the entropy difference between tight and loose active sites: the size of the QM layer required to describe the proper chemical steps (15) has so far prohibited additional calculation of the conformational entropy contributions of the larger enzymatic environment. The entropy terms for the WT F₁ were described to be small compared with the enthalpy values in both unisite and multisite kinetic studies (28, 33), and they were also similar in magnitude, thus further decreasing the differential; therefore, they may cancel out in comparison of T with D. Nevertheless, quantitative evaluation is motivated. Another even more challenging issue that remains to be resolved depends on whether the overall F₁ free energy described recently (13) may be separated into enthalpy and entropy terms and if so, whether they could contribute phase-shifted potentials to the individual subunits (18). Both problems are currently subject to investigation in our laboratory.

Methods

All-atom MD simulations were performed using the AMBER 11 software package (34). Initial geometries were taken from the ground-state F₁ with 1.8-Å resolution (7). ET*T with two tight sites was built by superposing α_TP/β_TP to α_DP/β_DP. Before MD simulations, the model was carefully checked at the subunit interfaces, minimized in several steps to eliminate clashes and positional overlaps, and it was surrounded with an 8-Å truncated octahedral box of TIP3P water (Fig. S7). The inner matrix of the mitochondria has lower salt concentration than cytoplasm (35), and thus, charges of the models were only neutralized by adding Na⁺ ions, resulting a 45 mM salt concentration. The ET*T model was submitted to a total of an 80-ns MD simulation, where RMD was applied after the initial 16-ns unbiased MD simulation. The restraints include H-bond distances and backbone dihedral angles in the α³⁷⁴V-K³⁸⁴ region and αE355, αK359 in T* as well as between αE399 and βR408, βR412 in T. Restraints were kept until 50-ns total simulation time. The system was then equilibrated 30 ns further in a fully unrestrained MD simulation. Periodic boundary conditions were used in an isothermal-isobaric (NPT) ensemble using the Langevin piston pressure control (300 K, 1 atm). Long-range electrostatics was treated with the Particle Mesh Ewald method. The SHAKE algorithm was used to constrain bonds involving hydrogen.

The reaction steps of the mechanism were identified earlier (15, 16, 23). Here, focus was put on obtaining the ATP + H₂O state found in the crystal structure (7), the bond-breaking TS, and two ADP + P_i states, one being immediately after the TS and the other being the final product state. To produce the energy surface of the hydrolysis step, active site conformations along T→D change were obtained by applying a linear shift method on the residual positions from positions in T to positions in D, describing the transformation in 11 steps in a 152-atom QM model (15, 16). Energy corrections were considered at the B3LYP/6–311++G(d,p)//B3LYP/6–31G(d) level of theory. The critical points were obtained also using ONIOM(QM/MM) simulations in two sets of models: in one, each had 152 atoms in the QM layer and an additional set for the D site with 148 atoms. Initial geometries were taken from MD simulations described in SI Text. The QM/MM models included all atoms within 20 Å of ATP or Mg²⁺. Atoms farther than 15 Å from Mg²⁺ were frozen, and the critical points were obtained with a B3LYP/6–31G(d):AMBER setup. Charges of the active site atoms were determined using the Merz–Singh–Kollman scheme (36) in the QM models of the ATP state. To avoid energetic differences caused by structural variations, several (four to five) iterations were made between the ATP and ADP + P_i states for every model. Final optimization included electronic embedding (37). Because of the large QM layer required for the localization of the TSs (15), loose convergence criteria were applied for one set of optimizations. Energy corrections were considered at the B3LYP/6–311++G(d,p):AMBER level. Validation of the critical points, zero point and thermal corrections to the energy, and entropy contributions were obtained from normal mode analysis. Additional expanded details on the computational methods are given in SI Text. All QM calculations were performed using the Gaussian 09 software package (38). Figs. 2 and 4 were made using PYMOL (39).