Catalytic strategy used by the motor to PNAS PLUS hydrolyze ATP

Farooq Ahmad Kiani and Stefan Fischer1

Computational Biochemistry, Interdisciplinary Center for Scientific Computing, University of Heidelberg, D-69120 Heidelberg, Germany

Edited by Donald G. Truhlar, University of Minnesota, Minneapolis, MN, and approved June 6, 2014 (received for review January 30, 2014) − + Myosin is a responsible for biological motions triphosphate4 /Mg2 moiety of ATP. A structure of myosin such as muscle contraction and intracellular cargo transport, for bound to the dissociated product (ADP/Pi) has not been which it hydrolyzes adenosine 5’-triphosphate (ATP). Early steps of available so far. This product state is important, because the the mechanism by which myosin catalyzes ATP hydrolysis have inorganic phosphate (Pi) and ADP products are only released been investigated, but still missing are the structure of the final later by myosin, upon rebinding to the actin filament during the ADP·inorganic phosphate (Pi) product and the complete pathway power stroke. This rebinding can only take place when the nu- leading to it. Here, a comprehensive description of the catalytic cleotide is in the ADP/Pi product state. Some residues thought strategy of myosin is formulated, based on combined quantum– to be catalytically relevant are Glu459 (22), Ser181 (23), Ser236 classical molecular mechanics calculations. A full exploration of (24–25), and Gly457 (26) (using the residue numbering of Dic- catalytic pathways was performed and a final product structure tyostelium discoideum), which are all strictly conserved. Whereas was found that is consistent with all experiments. Molecular movies Glu459 has been proposed to act as a general base in the catalysis, of the relevant pathways show the different reorganizations of the exact role played by the other residues remained unclear. Both the H-bond network that lead to the final product, whose associative (9, 17, 21) and dissociative (18, 19) pathways in myosin 2− γ-phosphate is not in the previously reported HPγO4 state, but − have been investigated by combined quantum-classical (QM/MM) in the H2PγO4 state. The simulations reveal that the catalytic strat- simulations. In an associative mechanism, the breaking of the i egy of myosin employs a three-pronged tactic: ( ) Stabilization of Pβ–Oβγ bond is concerted with the attack of water onto the γ − the -phosphate of ATP in a dissociated metaphosphate (PγO3 ) γ-phosphate (Fig. 2A), whereas in a dissociative mechanism state. (ii) Polarization of the attacking water molecule, to abstract they are sequential (Fig. 2B). The simulations have shown that a proton from that water. (iii) Formation of multiple proton wires only dissociative pathways have transition barriers that are low in the , for efficient transfer of the abstracted proton to enough to be consistent with the experimental rates (9, 18, 19). various product precursors. The specific role played in this strategy Recently, we have explained how myosin achieves the stabiliza- by each of the three loops enclosing ATP is identified unambigu- − tion of the metaphosphate (PγO3 ) that is generated by the ously. It explains how the precise timing of the ATPase activation dissociative mechanism (20). Furthermore, Nemukhin and co- during the force generating cycle is achieved in myosin. The cata- workers have shown that Glu459 can promote the abstraction of lytic strategy described here for myosin is likely to be very similar a proton from a close-by water (Wa in Fig. 1A) to produce the BIOPHYSICS AND in most nucleotide hydrolyzing . −

attacking OH hydroxyl (Fig. 2B) (18, 19). However, the fate of COMPUTATIONAL BIOLOGY the abstracted proton in the final myosin-bound ADP/Pi product he molecular motor myosin cyclically interacts with the actin has not been elucidated. Without this knowledge the catalytic Tfilament to generate the mechanical force that is used in pathway remains incomplete. living cells to achieve muscle contraction (1), cytokinesis (2, 3), Here we address the open questions about the catalytic and intracellular cargo transport (4). Hydrolysis of one ATP mechanism and present a comprehensive view of the strategy molecule per cycle provides the free energy that drives the acto– used by myosin to catalyze ATP hydrolysis. In particular: (i) myosin interaction cycle, as originally described by Lymn and Taylor (5). ATP is the common energy currency in biology, and is Significance extremely stable in aqueous solution (6, 7). , the – – enzymes that catalyze the hydrolysis of the Pβ O Pγ anhydride Biomolecular motor proteins like myosin generate mechanical linkage in ATP, are ubiquitous in biology because they are force from the chemical energy of ATP. Like gas engines, they needed to accelerate the release of free energy stored in ATP. 7 have different parts (protein domains) that run through a well- Myosin manages to speed up the hydrolysis by a factor of 10 over defined cycle of motions, consuming one ATP per cycle. Be- the uncatalyzed rate in solution. The experimental uncatalyzed − cause ATP is very stable, motor proteins catalyze its breakdown energy barrier is 29 kcal mol 1 (7, 8), and the catalyzed barrier has − (hydrolysis). The catalytic mechanism is at the core of un- been determined experimentally between 14.4 kcal mol 1 (9) and −1 derstanding how these motors work, because the activation of 14.8 kcal mol (10). Understanding how myosin achieves its the catalytic ATPase-function coordinates the motion of the ATPase function is necessary to understand how myosin works as different domains. Identifying which protein groups are es- a motor, but also helps one to understand the functioning of the sential for catalysis allows one to understand how the precise multitude of other nucleotide hydrolyzing enzymes. The cat- coupling between ATPase activation and mechanical motion is alytic mechanism of ATP hydrolysis in myosin has been stud- achieved. Moreover, ATPases are involved in most biochemical ied extensively with methods such as protein crystallography processes and are expected to have a catalytic strategy very – (11 14), mutagenesis (15, 16), photochemical kinetics (10), and similar to the one reported here. quantum-mechanical simulations of the active site (9, 17–21). This has yielded structures of analogs of the reactant and Author contributions: S.F. designed research; F.A.K. performed research; F.A.K. and S.F. transition states, a list of residues affecting the catalytic pro- analyzed data; and F.A.K. and S.F. wrote the paper. cess, and a number of proposed catalytic pathways. A reactant The authors declare no conflict of interest. (ATP-bound) structure of the catalytically competent state This article is a PNAS Direct Submission. of the Lymn–Taylor cycle, such as the one shown in Fig. 1A, 1To whom correspondence should be addressed. Email: [email protected]. can be derived from the crystals. In that state, three loops (called This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. the Switch 1, the Switch 2, and the P loop) are closed over the 1073/pnas.1401862111/-/DCSupplemental.

www.pnas.org/cgi/doi/10.1073/pnas.1401862111 PNAS | Published online July 8, 2014 | E2947–E2956 Downloaded by guest on October 1, 2021 catalytic strategy of myosin combines three tactics, and the role of the protein residues that are specifically involved in each tactic can now be identified: The initial metaphosphate intermediate is stabilized by interactions with the P-loop backbone and the + Lys185 side chain (Fig. 1A), which pull negative charge from the γ-phosphate to the α- and β-phosphate groups, thereby fa- voring the dissociation (compare the charge distribution in Fig. 2 A and B). The backbone carbonyl of Ser237 activates the attacking water Wa by polarizing it with a H-bond (Fig. 1A). We find that the role of the Glu459 carboxylic side chain is to po- larize a “helping” water molecule (Wh in Fig. 1A), rather than serving as a general base itself and accepting a proton as pre- viously proposed (18, 19). Water Wh accepts the proton ab- stracted from the attacking water and transiently becomes a + H3O hydronium. The precise positioning of this helping water is achieved by Gly457. The abstracted proton is then transferred from the helping water to the inorganic γ-phosphate group via a proton wire through the side chain of Ser181. Thus, the specific role of the residues involved in the catalytic strategy is now identified for myosin. Significantly, residues that are central to the strategy are located on each of the three active-site loops, so that a primary role can be assigned to each loop: The P loop, the Switch 1, and the Switch 2 are, respectively, responsible for metaphosphate stabilization, polarization of water Wa, and po- larization of water Wh. An overlap of the crystal structures of different in the ATPase competent conformation (listed − in Table 1) shows that they all have identical configurations of Fig. 1. End states of ATP hydrolysis in myosin. (A) ATP4 reactant state R.(B) 3− − the active site, indicating that probably all myosins use the same Final ADP /H2PγO4 product state P. The phosphorus atoms of ATP are colored gold. The adenosine and the two waters coordinating the Mg2+ are catalytic strategy. Analogous active sites are found in other not displayed. Interatomic distances are in Å. All hydrogen bonds of less than motors and ATPases (20), and a similar catalytic strategy is seen 2.8 Å length (between the heavy atoms) are shown as dotted lines. in enzymes catalyzing the hydrolysis of other types of P–O bonds, such as DNA restriction endonucleases (31).

Where are the protons positioned in the final ADP/Pi product Results (before F-actin binding)? (ii) How is the abstracted proton The Reactant and Product Structures. The energy-optimized struc- − + transferred from the attacking water to its final position in the ture of the ATP4 –Mg2 -bound reactant state (R) is shown in Fig. product state? (iii) What are the respective roles of the residues 1A. There are no significant changes in the positions of the in active site? To answer these questions, we have used QM/MM protein atoms compared with the crystal structure of myosin calculations to find the most stable ADP/Pi product structure bound to either vanadate/ADP (12) or to beryllium fluoride/ADP in the active site. Then, we computed minimum energy paths (32). The length of the Pγ–Oβγ bond is 1.78 Å, which is signifi- (MEPs) of all of the substeps from the reactant (ATP) to this cantly longer than the 1.6 Å typical of the phospho–ester bonds in final product state (MEPs and how they are computed is de- isolated ATP. This shows that the is using some of the scribed in SI Methods), trying different reaction mechanisms. We find that in the final product (Fig. 1B), the inorganic γ-phosphate − is doubly protonated and can be formally written as H2PγO4 . Its − calculated energy is –2(±1) kcal mol 1 relative to the ATP re- actant, in very good agreement with the experimental values − − between –1.5 kcal mol 1(9) and −2.6 kcal mol 1(10) for the re- action energy in prepower stroke myosin. We show how this product structure is consistent with the well-known reversibility of the hydrolysis reaction in myosin (27–30). The most favorable MEP transition has four stable intermediates between the ATP reactant state and the final ADP/Pi product state, separated by five transition states (MEP1 in Fig. 3). Unlike often assumed, there is no dominant rate-limiting step. Instead, three of the five − substeps have similarly high barriers (in the 8.7–10.4-kcal mol 1 range, consistent with experimental rates), and jointly contribute in limiting the overall reaction rate. The present calculations confirm that the reaction is dissociative. The catalytic mechanism is found to have three main phases: (i) Dissociation of the − γ-phosphate as a stable PγO3 metaphosphate (as in Fig. 2B), to − provide a better target for the subsequent attack by an OH group. (ii) Abstraction of a proton from the attacking water (Wa − − in Fig. 1A) and attack of the resulting OaH onto the PγO3 .(iii) Fig. 2. Associative versus dissociative mechanisms. (A)Associativemech- Transfer of the abstracted proton to the inorganic γ-phosphate 4− anism: ATP dissociation is concerted with the attack by water Wa.(B) − via a proton wire and rearrangement of the H-bond network Dissociative mechanism: the PγO metaphosphate dissociates before − 3 to yield the final H2PγO4 product (Fig. 1B). Accordingly, the water attack.

E2948 | www.pnas.org/cgi/doi/10.1073/pnas.1401862111 Kiani and Fischer Downloaded by guest on October 1, 2021 this structure, the inorganic γ-phosphate is doubly protonated, PNAS PLUS − H2PγO4 . One of the two protons is bound to oxygen atom Oa (which was the oxygen of the attacking water, Wa), where it retains its H-bond to the backbone carbonyl of Ser237 (compare with Fig. 1A). The second proton is bound to the oxygen that receives a H-bond from the Ser181 side chain (Fig. 4F), and − makes a H-bond to the β-phosphate group of the ADP3 (to the oxygen labeled Oβγ in Fig. 2B). This H-bond is important, be- − cause it keeps the inorganic H2PγO4 in close proximity to the β-phosphate group, despite the strong electrostatic repulsion − with the negative charges on the β-phosphates of ADP3 .Asa result, the H-bond network in the active site of the product is identical to that of the reactant state (except for water Wh, which accepts a H-bond from the NH of Gly457 in P instead from water Wa in R). In particular, the groups involved in the sixfold co- + ordination sphere of the Mg2 ion are the same as in the reactant (unlike previously speculated) (9). The implication of this simi- larity between reactant and product conformations with respect to the reversibility of ATP hydrolysis is addressed below (see Discussion). Fig. 3. Transition network of the ATP hydrolysis in myosin. The names of A very similar product structure (g2, not displayed), with stable states and their energies are shown inside circles (their structures are −1 similar energy (−2.6 kcal mol ), is found when water Wh is shown in Figs. 4 and 5). R is the ATP reactant state (shown in Fig. 1A). P is the turned to make a H-bond with the Oa oxygen of the inorganic most stable ADP/Pi product state (shown in Fig. 1B). Intermediates m1, m2, − γ and m3 are metaphosphate states (i.e., with a dissociated PγO ). Inter- -phosphate instead of Gly457 (Fig. 6E). Another low-energy 3 −1 mediates e1, e2, and e3 are states where the side chain of E459 is pro- product state (−1.5 kcal mol ), labeled here g1, is shown in Figs. tonated. g1 to g4 are product precursors, with two protons on the inorganic 4E and 6C. It is like g2, except that one of the protons of the γ − − -phosphate (H2PγO4 ). The computed MEPs are shown as lines connecting H2PγO4 is turned toward the Ser181 side chain (instead of to- the circles, the corresponding transition state energy labeling each line. The ward the β-phosphate), which itself is turned toward the oxygen most favorable transition from R to P is shown in bold and named MEP1. All −1 of water Wh. In the present calculations, the g1 and g2 states ap- energies (in kcal mol ) are given relative to the reactant R. Values in pa- pear as precursors of the P structure (Fig. 3). However, the ener- rentheses are energies obtained when water W3 is treated quantum- −1 mechanically instead of classically (Methods). gies of these three structures are within a narrow (1.5 kcal mol ) range, so that they might easily interchange in nature (for example, the H-bond distances in a crystal structure of the binding energy of ATP to destabilize the reactant ground-state product would reflect an average of their H-bond networks). In structure, distorting it in the direction of the subsequent reaction contrast, all configurations (states e1, e2, e3,inFig.3)withone BIOPHYSICS AND − step (i.e., Pγ–Oβγ bond dissociation). The attacking water (Wa in proton placed on the Glu459 side chain (i.e., the nucleotide is COMPUTATIONAL BIOLOGY 3− 2− Fig. 1A) is in apical position relative to Oβγ and 3.04 Å distant in the ADP /HPγO4 state) have significantly higher ener- −1 from the Pγ. gies. Structure e1 (Fig. 5D) starts at 6.8 kcal mol , which is much In the final product state (P), of ADP/Pi bound to myosin higher than found experimentally for the hydrolysis product. protein, the two protons from the attacking water Wa need to be Therefore, none of the states with a protonated Glu459 can be placed somewhere to account for the proton stoichiometry in the considered to be the final product state of the ATP hydrolysis active site. Several proton positions and orientations were tried, (before myosin binds F-actin). Finally, a P-like structure was tried − on either the phosphate groups or the Glu459 side chain. The in which the proton between the γ- and the β-phosphates is bonded structure with the lowest energy is shown in Fig. 1B. Its com- to the β-oxygenratherthantotheγ-oxygen (not displayed). −1 2−. 2− puted energy is −3.0 kcal mol (unless mentioned otherwise, The formula for this P′ structure is then ADPH HPγO4 . − all energies are given here relative to the ATP reactant structure It has an energy of +2.1 kcal mol 1 and is unstable, the proton R), consistent with the experimental reaction energy (9, 10). In tending to jump back onto the γ-oxygen.

Table 1. Crystal structures of myosin in the ATPase-competent conformation † ‡ § ¶ PDB ID code Organism Myosin type Bound nucleotide analog Water Wa Water Wh Water W3

1VOM Dictyostelium discoideum II ADP-VO4 +++

2JJ9 Dictyostelium discoideum II ADP-VO4 +++ 3MKD Dictyostelium discoideum II ADP-VO4 +++

1MND Dictyostelium discoideum II ADP-AlF4 n.a. ++

2V26 Sus scrofa VI ADP-VO4 +++

4ANJ Sus scrofa VI ADP-AlF4 n.a. ++ 4BYF Homo sapiens 1c ADP-VO4 ++—

1DFL Argopectin irradians II ADP-VO4 + kk

Entries in the PDB having a structure with the Converter domain (which carries the lever arm) in the postrecovery–prepower stroke conformation. All have the Switch 1 and Switch 2 loops in the same closed–closed configuration over the P loop. n.a., not applicable. † + Nucleotide analog makes the same H-bonds to the protein and the Mg2 as those shown for ATP in Fig. 1A. ‡ “+” means that the apical oxygen of the vanadate is positioned like water Wa in Fig. 1A. § “+” means that a crystal water molecule is present in the same position as water Wh in Fig. 1A. ¶ “+” means that a crystal water molecule is present in the same position as water W3 in Fig. 1A. k1DFL does not show any water positions.

Kiani and Fischer PNAS | Published online July 8, 2014 | E2949 Downloaded by guest on October 1, 2021 a protonated Glu459 side chain and the γ-phosphate in the 2− HPγO4 state. The other transition, MEP2, is shown on the left side of Fig. 3 and proceeds via the intermediates m3, e1, e2, and g4. The highest energy along the MEP1 transition is 10.4 − kcal mol 1 relative to the reactant R, which is consistent with the experimental barrier. Along MEP2, the highest energy is 18.5 − kcal mol 1. It follows that the MEP1 transition is significantly more likely than the MEP2 transition. The events along the MEP1 and MEP2 transitions are shown in molecular movies (Movies S1 and S2), as well as schematically illustrated in Figs. 6 and 7, respectively, and are described in the next sections.

Metaphosphate Formation. The first step in both the MEP1 and MEP2 transitions (R→m1)isthecleavageofthePγ–Oβγ bond − which produces a PγO3 metaphosphate (Fig. 6A). The resulting − structure m1 (shown in Fig. 5A) has an energy of 2.7 kcal mol 1 and is nearly identical to the reactant R except for a small (1.1 Å) motion of the γ-phosphate toward the oxygen of the attacking −1 water Wa (Movie S1). Nevertheless, an 8.7-kcal mol barrier clearly separates m1 from R (Fig. 3). m1 is also separated by significant barriers from the ensuing intermediate along the two − − transition pathways (10.4 kcal mol 1 and 10.9 kcal mol 1 from states m2 and m3, respectively, Fig. 3). Consequently, the m1 state constitutes a distinctive intermediate of the catalytic mechanism. Using a basis set [B3LYP/6–31+G(d,p)] of even higher quality than was used for Fig. 3 (Methods), the energy of − m1 drops further to 2.3 kcal mol 1. The energy of the m1 metaphosphate state is remarkably low. Indeed, when the surrounding protein is removed, then the + vacuum energy of the nucleotide (including the Mg2 and its coordination shell) is calculated to be very much higher (by 44.3 Fig. 4. Structures along the MEP1 transition. (A)ATP4− reactant state −1 3− − kcal mol ) in the ADP ·PγO3 conformation of m1 than in the 3− − − (R,sameasFig.1A). (B) Stable metaphosphate (ATP /PγO3 )interme- ATP4 conformation of R. This means that myosin stabilizes the diate m2.(C) Transition state m2-g3: a proton wire ring composed of −1 + metaphosphate state of the nucleotide by more than 40 kcal mol . 6 atoms is formed by water Wa,waterWh (in H3O hydronium state), and − We have recently shown how myosin combines two strategies to PγO3 .(D) Transition state m2-g1: a proton-wire ring composed of + achieve this stabilization (20): (i) Myosin exploits the charge 8 atoms is formed by water Wa,waterWh (H3O ),theSer181sidechain − 3− − γ α–β and PγO3 .(E)ADP /H2PO4 product precursor g1.(F)FinalADP·Pi product shiftof1efromthe -tothe -phosphates when meta- state (P,sameasFig.1B). Atoms that are not displayed have essentially the phosphate is formed (compare Fig. 2 A and B). The backbone same positions as in the reactant R (Fig. 1A).SeeFigs.1and3fordisplayand NH groups of residues 182–187 of the P loop and the side chain + naming conventions. of Lys185 preferentially interact with the α-andβ-phosphate groups (Fig. 1A), thus contributing 52% (P-loop backbone) and 25% (Lys185) of the overall stabilization of the m1 state, Reaction Pathways. We had previously explored a variety of path- respectively. (ii) Myosin promotes the formation of hydrate ways for the associative mechanism of catalysis (9), and had found − complex between the attacking water W and the PγO meta- – −1 a 3 that they all have much higher energy barriers (30 40 kcal mol ) phosphate (the distance between them is only 1.84 Å, Fig. 5A). It than the experimental barrier. Recently, Nemukhin and coworkers does so by polarizing W with a H-bond to the backbone C = O γ a (18, 19) have shown that the early dissociation of the -phosphate of Ser237 (Fig. 5A), which contributes 16% of further stabiliza- (leading to a product precursor with the abstracted proton on −1 tion. A detailed description of the contribution from the other Glu459) has a barrier on the order of 10 kcal mol . Therefore, protein residues to the stabilization of the m1 metaphosphate we focused on further exploring and extending the pathways of state is given in ref. 20. the dissociative mechanism. Several MEPs and their transition The formation of the metaphosphate intermediate is one of state barriers were computed, varying the positions of the waters, the crucial features of the catalytic strategy of myosin (and of + − trying proton transfer from Lys185 to the phosphates, changing other ATPases as well) (20). Indeed, the PγO3 metaphosphate the configurations of the hydrogen-bond network in the active has a planar geometry and a single negative charge, which both site, and using alternative proton wires for the reshuffling of make the metaphosphate a much better target for the attack − protons from the reactant to the product configuration. This was by an OH ion later in the reaction (Fig. 2B) than the tetra- 2− done in particular for (i) transitions in which the side chain of γ − hedral and doubly negative P O4 moiety of ATP (Fig. 2A). Glu459 never gets protonated, and (ii) transitions in which the This is one of the reasons for the remarkably low transition − − side chain of Glu459 gets protonated in some intermediates. The barrier (10.3 kcal mol 1 in MEP1 and 10.7 kcal mol 1 in MEP2) best of each of these two sorts of transitions are shown in Fig. 3 of the subsequent attack by water Wa onto the metaphosphate and are labeled, respectively, as MEP1 and MEP2. (see Discussion, Catalytic Strategy I). The MEP1 and MEP2 The substates and energy levels along the MEP1 transition are transitions diverge after m1 (Fig. 3). The essential difference shown on the right side of Fig. 3. They connect the reactant state between these two transitions is the way one of the protons of R to the final product P via intermediates called here m1, m2, g1, water Wa istransferredtotheγ-phosphate in the final product: and g2, which are local minima of the potential energy. The In MEP2, this transfer involves stable intermediates (e1, e2)in intermediates were named according to their chemical state: m1, which the side chain of Glu459 is protonated, whereas in MEP1 − m2, and m3 have a metaphosphate PγO3 ; g1 to g4 have a doubly this side chain never gets stably protonated. The two transitions 2− protonated inorganic γ-phosphate H2PγO4 ; e1 to e3 have are described in the next sections.

E2950 | www.pnas.org/cgi/doi/10.1073/pnas.1401862111 Kiani and Fischer Downloaded by guest on October 1, 2021 PNAS PLUS BIOPHYSICS AND COMPUTATIONAL BIOLOGY

3− − Fig. 5. Structures along MEP2 transition (starting from m1 in Fig. 3). (A) m1 metaphosphate (ADP ·PγO3 ) intermediate. (B) m3 metaphosphate in- 3− 2− termediate. (C) m3-e1 transition state: a proton wire is formed along Wa→ Wh→Glu459. (D) e1, an ADP /HPγO4 intermediate with a protonated 3− − Glu459. (E) e2-g4 transition state: a proton wire is formed along Glu459→W3→Ser181→γ-phosphate. (F) g4,anADP /H2PγO4 product precursor with unprotonated Glu459.

The MEP1 transition. + − + The transfer of the proton from Wa to the Ha ,theOaH binding to Pγ and the Ha binding to Oh of water γ + -phosphate proceeds via a proton wire through the helping Wh, which transiently becomes a hydronium H3Oh .Simulta- water Wh. This first requires reorientation of Wh to form the neously, the protons in the eight-membered H-bond ring ...... proton wire: In the reactant, water Wh makes a H-bond with the Pγ Oa–Ha Oh–Hh OSer181–H O–Pγ (where ... denotes a = ...... C O of Gly457 (Fig. 1A) which is still present in m1 (Fig. 5A). H-bond)switchtoPγ–Oa Ha–Oh Hh–OSer181 H–O–Pγ, → In step m1 m2, water Wh breaks this H-bond and moves (see which results in the net transfer of one proton from Wa to the the white-headed arrow in Fig. 6B and Movie S1)toforma γ-phosphate (see the black-headed arrows in Fig. 6D). The H-bond with the side chain of Ser181. This involves the crossing corresponding transition state structure (m2–g1)isshownin − − − of a 10.4-kcal mol 1 energy barrier (7.7 kcal mol 1 relative to m1). Fig. 4D and has an energy of 10.3 kcal mol 1. It is noteworthy − Thekeyfeatureoftheresultingm2 metaphosphate state is that the energy barrier taken relative to m2 is only 2.6 kcal mol 1 its extreme polarization of water Wa, which is due to the two (=10.3–7.7). This is remarkably low for a reaction step involving H-bonds Wa makes with the C = O of Ser237 and with water Wh the breakup of a water molecule. Myosin achieves this by simul- − (itself polarized by Glu459 ), Fig. 4B. This tightens the taneously presenting a good electrophile (i.e., the phosphorus of · − − Wa PγO3 hydrate (the distance between Pγ and Oa is only 1.87 the PγO3 metaphosphate) and a good base (i.e., the polarized – − + Å), and weakens the Oa H-bonds of water Wa. water Wh), respectively, to the OaH and the Ha moieties of All this sets the stage for the hydrolysis of water Wa, its si- water Wa. Water Wa readily breaks up into these two moieties γ multaneous attack on the -phosphorus, and proton transfer because of the strong polarization of Wa in the m2 state (de- along a proton wire Wa→Wh→Ser181→Pγ. They happen in step scribed above). The resulting structure g1 is shown in Fig. 4E −1 m2→g1 (Fig. 6D): Because water Wh is highly polarized by the and has an energy of −1.5 kcal mol . − H-bond with the -COO side chain of Glu459, it can act as An alternative route to go from m2 to g1 is via g3 (Fig. 3). In a proton acceptor and abstract one proton from water Wa. that case, water Wh breaks its H-bond with Ser181 and instead − Water Wa breaks up (i.e., undergoes hydrolysis) into OaH and makes a H-bond with the γ-phosphate (Movie S3). This forms

Kiani and Fischer PNAS | Published online July 8, 2014 | E2951 Downloaded by guest on October 1, 2021 Fig. 6. Events along the MEP1 transition of Fig. 3. The actions occurring from one panel to the next are represented as curved arrows: Arrows with a black arrowhead indicate bond breaking and -making; white arrowheads indicate motions leading to switches in the H-bond network (i.e., without changes in the covalent bond structure). These events can be watched in Movie S1. Values in parentheses give the energy of the state; values next to the arrows between − panels (which indicate the order of events) give the energy of the corresponding transition state. All energies (in kcal mol 1) are relative to the reactant state R. Hydrogen bonds are indicated by broken lines. (A) state R, (B) state m1, (C) state g1, (D) m2, (E) state g2, and (F) state P.

− a six-membered H-bond ring (as opposed to the eight-membered side chain of Glu459 via the proton wire W →W →Glu459 ...... a h H-bond ring described above), Pγ O –H O –H O–Pγ, (Fig. 1A) (18, 19). However, when this transfer is performed in a ... h ...h which undergoes a proton wire switch to Pγ-Oa H–Oh Hh–O–Pγ. the m1 conformation, the resulting structure (e3)isunstable The corresponding transition state structure m2-g3 is shown in (Fig. 3): The proton only remains on the Glu459 side chain with − Fig. 4C and has an energy barrier of 12.6 kcal mol 1.Instepg3→g1, the help of an artificial restraining force. The energy of e3 is −1 Ser181 reforms a H-bond with water Wh (not displayed), over a quite high at 9.2 kcal mol (without counting the restraining − 9.1-kcal mol 1 barrier (Fig. 3). The barriers of the direct m2→g1 energy). This is because there is another water molecule (labeled −1 route and of the m2→g3→g1 route differ by only 2.6 kcal mol , here W3) in the crystal structure (Methods) that donates a − which is within the accuracy range of the calculations, so that H-bond to the Glu459 side chain (Fig. 5A). Moreover, Glu459 is + both routes may occur. engaged in a salt bridge with Arg238 (Fig. 1A). Altogether, this 3− − − In g1, the nucleotide is already in the same ADP /H2PO4 makes the Glu459 side chain a poorer proton acceptor. Nev- state as the final product, but the H-bond network is not yet fully ertheless, we found that the side chain can get stably protonated − optimal. The next two steps, g1→g2 and g2→P, involve only if water W3 breaks its H-bond to Glu459 and rotates to make rearrangements of the H-bond network (Movie S1). First, the a H-bond with the side chain of Thr230 (Movie S2), which itself Ser181 side chain breaks its H-bond with Oh and rotates to do- switches from water W3 to the backbone carbonyl of Asn233 (see nate a H-bond to the γ-phosphate, which itself switches from the white-headed arrows in Fig. 7A). This transition has a barrier − donating a H-bond to Ser181 to donating this H-bond to the of 10.9 kcal mol 1. The resulting structure m3 (shown in Fig. 5B) − β-phosphate (white-headed arrows in Fig. 6C). This involves has an energy of 9.9 kcal mol 1. From m3, the hydrolysis of water −1 a 0.1-kcal mol barrier. The energy of the resulting structure g2 Wa and the concerted transfer of one proton along the proton −1 is −2.6 kcal mol . Finally, water Wh moves back to the position wire from Wa to Glu459 (black-headed arrows in Fig. 7B) has − it had in R (see the white-headed arrows in Fig. 6E), which only a small barrier of 0.8 kcal mol 1 relative to m3. This easy −1 involves a 0.7-kcal mol barrier relative to g2, thereby reforming breakup of water Wa results from its high polarization by Ser237 the H-bond with the C = O of Gly457 and reaching the final and Wh (Fig. 5B), just as described above for state m2. The product P. transition state, m3-e1, is shown in Fig. 5C. The MEP2 transition. As mentioned, it had been proposed that after This then yields a stable structure (e1,showninFig.5D) reaching the metaphosphate state, the hydrolysis in myosin would with a protonated Glu459 side chain and the nucleotide in an 3− 2− −1 proceed by stably transferring a proton from water Wa onto the ADP /HPO4 state. Its energy is 6.8 kcal mol , significantly

E2952 | www.pnas.org/cgi/doi/10.1073/pnas.1401862111 Kiani and Fischer Downloaded by guest on October 1, 2021 PNAS PLUS

Fig. 7. Events along the MEP2 transition (starting from state m1 in Fig. 3). See legend of Fig. 6 for the meaning of numbers and arrows. The events shown in BIOPHYSICS AND

this figure can be observed in Movie S2.(A) state m1, (B) state m3, (C) state e2, (D) state e1, (E) state g4, and (F) state P. COMPUTATIONAL BIOLOGY

higher than the reactant R, which is inconsistent with the ex- Discussion perimental data (9, 10) showing that the energy of the final What Are the Reactant and Product Structures? Only cocrystals of product is clearly lower than the reactant. Because the product myosin with analogs of ATP, not actual ATP, have been avail- 3− − – P (in the ADP /H2PγO4 state, described above) does fulfill this able so far in the postrecovery prepower stroke conformation (in condition, we searched for transition routes between state e1 and which catalysis takes place). By using a high-level quantum the product P. The route of lowest energy is shown on the left method for the ATP and the relevant active site residues side of Fig. 3. First (e1→e2), the proton on the Glu459 side chain (Methods), we find a catalytically competent structure of myosin/ rotates to form a H-bond with water W (white-headed arrow in ATP (R) from which the hydrolysis reaction can proceed over 3 low-energy barriers (MEP1, Fig. 3) that are consistent with the Fig. 7D). This involves the crossing of a high barrier of 16.6 − experimental rate. This already is a very good indication that it is kcal mol 1.Then(e2→g4), a proton wire transfers one proton from γ the correct reactant structure. Moreover, the energy difference the Glu459 side chain to the -phosphate, by switching the between R and the final product state P again matches the ex- – ... – ... – ... – 2− H-bond network from Glu459 H O3 H3 OSer181 H O PγO3H perimental reaction energy. This simultaneous consistency of −... – ... – ... – – − to Glu459 H O3 H3 OSer181 H O PγO3H (Fig. 7C). The energy barrier and reaction energy is strong evidence that the corresponding transition state e2-g4 is shown in Fig. 5E and has correct pair of reactant–product structures has been found here. − an energy of 18.5 kcal mol 1. The resulting structure g4 has the Note that the H-bond networks displayed in Fig. 1 are also 3− − nucleotide in the ADP /H2PO4 state (Fig. 5F) and an energy compelling by their perfection, every H-bond having a near- − of 5.5 kcal mol 1. Finally, proton reorientations (see the white- ideal geometry. This is important, because the above description headed arrows in Fig. 7E) convert g4 into the final product of the transition pathways has made it clear that the positioning − P over a 15.5-kcal mol 1 barrier. All steps of the second part of the protons in the active site is determinant for the catalytic → → → pathway. of the MEP2 transition (e1 e2 g4 P) involve high transition · – −1 The protonation state of ADP Pi in the final product structure is states (with energies in a range 15.5 18.5 kcal mol above R). 3−· − → found to be ADP H2PO4 . The most remarkable thing is the We tried to find alternative e1 P routes with lower energy similarity between the product (P,Fig.1B) and the reactant barriers, for example, involving proton wires via water Wh,but structures (R,Fig.1A). This is achieved by the H-bond between → without success. Therefore, unless lower e1 P pathway can the β-andtheγ-phosphate groups that keeps these two groups in be found, a hydrolysis mechanism with intermediates having a close contact, even though the covalent Pγ–Oβγ–Pβ linkage is protonated Glu459 side chain appears unlikely. The whole broken after the hydrolysis. This explains the much-studied re- MEP2 transition is shown in Movie S2. versibility of ATP hydrolysis in myosin (27–30): Isotope exchange

Kiani and Fischer PNAS | Published online July 8, 2014 | E2953 Downloaded by guest on October 1, 2021 experiments have shown that, by reversal of the hydrolysis re- water Wa has the role of polarizing water Wa, splitting it into − + action in the absence of F-actin, oxygen atoms of the solvent OaH and Ha , and then accepting the abstracted proton become incorporated into the γ-phosphate of ATP. For this to (BHa). Examples of P–O bond cleaving enzymes where this happen, it is necessary that the ADP and Pi products of hydro- is the case are EcoRV (31) and RAS-GAP (33). In myosin, lysis remain in close contact in the product state, as is the case in the role of the general base is shared by water Wh, the − − the present P structure. Glu459 side chain, and the PγO3 metaphosphate itself. Indeed, as illustrated in the transition state m2-g1 (Fig. Catalytic Strategy I: Why is the Dissociative Mechanism Preferred? 4D), the polarization of water Wa is performed by water − The energy barrier of ATP hydrolysis in myosin calculated for Wh, itself polarized by Glu459 . Whereas the direct acceptor −1 + + associative mechanisms (38–42 kcal mol ) (9) has a similar of the Ha proton is Wh (transiently becoming a H3O hy- value as the barrier for uncatalyzed hydrolysis of ATP in gas dronium), the final acceptor of the abstracted proton is the − phase (40–42 kcal mol 1) (20). This means that the catalytic γ-phosphate (after transfer through a proton wire, Fig. 6D). machinery of myosin is definitely not laid out to hydrolyze ATP This complex situation makes it difficult to pin the role of via an associative mechanism. On the other hand and as found general base to any single residue in myosin. It is not un- previously (18, 19), the catalytic barrier via a dissociative mech- common in enzymes that a helping water interca- − anism is found here to be significantly lower (10.4 kcal mol 1). lates between the “general base” and the attacking water, this then resulting in the transient formation of a hydronium The key to this lowering is twofold: First, a dissociative mech- + anism uncouples the energy barrier due to the breaking of the (H3O ) ion. Such a hydronium has been directly observed in – Pγ–Oβγ from the barrier due to the breaking of the attacking some enzymatic pockets by joint X-ray neutron diffraction − + water into OaH and H . Secondly, the dissociated meta- (34), and the possible involvement of a hydronium in the − phosphate (PγO3 ) is a much better target for the attack by catalytic mechanism of ATP hydrolysis had been inferred − from the crystal structures of myosin (35) and (36). a negatively charged OaH than the undissociated γ-phosphate 2− The H-bond of water W with the backbone C = O of Ser237 group of ATP (–O–PγO3 ), both in terms of geometry and of a − on loop Switch 1 polarizes W further, and thereby contrib- charge (Fig. 2). The PγO3 is planar, allowing a closer approach a − − – 2 utes to the weakening of its Oa–H-bonds. Moreover, polar- of the OaH than the tetrahedral OPγO3 .Moreover,the − − ization of Glu459 also plays a role. This can be seen when former is singly negative, creating less repulsion with the OaH than the double-negative charge of the latter. the Glu459 side chain is not treated quantum-mechanically, Experimental testing for the presence of the metaphosphate but classically. In that case, the barrier of the m2-g1 step state could be envisioned by spectroscopic methods, taking ad- increases slightly. Mutagenesis studies confirm that hydroly- sis is abolished when neither residue of the 238/459 salt vantage of the spectral differences between the tetrahedral PO4 and the planar PO species. Rather than in solution, where the bridge has a carboxylic acid side chain (22, 26, 37). However, 3 the high barriers along the MEP2 transition (Fig. 3) show signals from ATP and ADP would be overwhelming, this might − be done with myosin in the crystalline state, because the hy- that Glu459 is not the final acceptor of the proton, which γ g1 drolysis reaction is known to be reversible as long as the protein instead gets shuttled to the -phosphate (see in Fig. 4E). iii remains in the postrecovery–prepower stroke conformation. ) Transfer of the abstracted proton along proton wires. The most likely proton wire that shuttles a proton away from Detecting the metaphosphate intermediate in kinetic experi- + the Wh hydronium proceeds via the side chain of Ser181 ments will be difficult because, based on the energies calculated − (W →W →Ser181→PγO ,Figs.6D and 4D). However, here, that state is ∼100 times less populated than the ATP re- a h 3 the point mutant Ser181Ala has been shown to have actant and 4,000 times less populated than the final ADP/ a nearly normal ATPase rate (38). In that mutant, the Pi state. proton transfer may occur along the more direct proton − → → γ C Catalytic Strategy II: What Are the Roles of the Protein Residues? wire (Wa Wh P O3 ,Fig.4 ), whose energy barrier is not significantly higher. In m2, the Ser236 side chain From the MEP1 transition (Fig. 6), it can be seen that myosin − is H-bonded to the PγO (2.66 Å, not displayed). There- facilitates the dissociative hydrolysis mechanism by using a three- 3 fore, a proton wire involving the side chain of Ser236 (via pronged tactic: − Wa→Ser236→PγO3 ) might be envisioned. However, this is i) Stabilization of a metaphosphate state, in which the γ-phos- not likely, because it is now clear that the proton transfer from − phate of ATP dissociates as PγO3 . Wa must first get through water Wh, which is the primary ii) Activation of the attacking water Wa by a composite base, to proton acceptor as described above. A proton wire along − − promote the breaking of water Wa into an OaH hydroxyl W →W →Ser236→PγO is just as unlikely, due to the large + a h 3 and Ha proton. distance between W and Ser236 (3.5 Å between the oxygen + h iii) Transfer of the abstracted proton Ha via a proton wire to atoms in m2) that makes a proton jump difficult. Thus, Ser236 2− − the HPγO4 formed by the attack of the OaH onto is probably not involved in the proton transfers. To verify this, − the PγO3 . it would be necessary to test the double mutant Ser181/ Ser236, in which the proton transfer is predicted to still be The protein residues specifically involved in each tactic can be possible along the direct proton wire (which does only involve identified: water Wh,Fig.4C). i) Metaphosphate stabilization. As mentioned above, Pγ–Oβγ − bond cleavage is accompanied by a charge shift of 1e from Why is Protonation of Glu459 Unlikely? When, during the MEP2 the γ-phosphate of ATP to the β-phosphate of ADP (Fig. + transition, one proton is stably transferred from the Wh hydro- 2B). The protein promotes this charge shift by placing − nium to the Glu459 side chain (m3→e1,Fig.7B), the energy of H-bond donors of the P-loop backbone (residues 182–187) − + e1 D 1 and the side chain of Lys185 in such a way that they interact the resulting structure (Fig. 5 ) is 6.8 kcal mol higher than α β the reactant. A similar structure reported by Nemukhin et al. was preferentially with the -and -phosphate groups (Fig. 1A), − also 3.2 kcal mol 1 higher than the reactant (18, 19). Because it is thereby pulling negative charge toward the ADP moiety and − 3− − – 1 – favoring the ADP + PγO state. known that the experimental product is 1.5 kcal mol to 2.5 3 − ii) Activation of the attacking water. In the standard textbook kcal mol 1 lower than the reactant (9, 10), the protonated state of − case, a general base B in direct contact with the attacking Glu459 is not the final product state.

E2954 | www.pnas.org/cgi/doi/10.1073/pnas.1401862111 Kiani and Fischer Downloaded by guest on October 1, 2021 Moreover, the energy barriers for shuttling the proton from the lever arm while myosin rebinds to the actin filament. To PNAS PLUS Glu459 to the γ-phosphate (i.e., the remaining of the MEP2 ensure this precise timing in activating the ATPase function, the transition) are too high (Fig. 3). There are two reasons for that: closing of the Switch 2 loop is mechanically coupled to the lever- (i) Water W3 is strongly held by three H-bonds, donating two arm swing (44), whereas the closing of the Switch 1 is mechan- toGlu459andtoSer181(Fig.1A), and accepting one from ically coupled to the opening of the actin-binding cleft (45). Thr230 (Fig. 5A). This stabilizes the position of the Glu459 However, why does the ATPase only become active when both side chain during the catalytic transition by forming a bridge Switch 1 and Switch 2 loops are closed onto the P loop? The between Glu459 and Ser181 (Fig. 1A). When W3 breaks its catalytic strategy presented here explains how this is achieved: H-bond to Glu459 in step m1→m3 of MEP2 (Fig. 7A), this Each of the three loops carries at least one of the groups that are results in a poorer geometry of this salt bridge from states m3 essential to the ATPase function. Indeed, the groups that pro- to g4 (Movie S2). This is one of the reasons for the higher mote the dissociation of the γ-phosphate are mainly on the P energies along the MEP2. (ii) The distance between the excess loop (backbone NH and Lys185), the group that directly polar- + H (that is shuttled around the active site) and the negatively izes water Wa is on Switch 1 (C = O of Ser237), and the group 2− charged HPγO4 becomes much larger during the MEP2 than that turns water Wh into a proton acceptor is on Switch 2 during the MEP1 transition: In MEP1 transition state m2-g1 (Glu459 side chain). This means that the closing of any two loops + 2− (Fig. 4D), the Wh ··· HPγO4 distance is 3.6 Å (between Oh is still not sufficient to activate the ATPase. Only when all three and Pγ), whereas in MEP2 transition state e2-g4 (Fig. 5E), the loops come together are all essential groups in place. In this way, + 2− W3 ··· HPγO4 distance is 5.1 Å (between O3 and Pγ). This the protein ensures that ATP will not be hydrolyzed at the wrong larger separation between two groups of opposite charge is point in the motor cycle, which would be a wasteful loss of energy unfavorable, and is the other reason for the high transition for the cell. This nicely shows how the catalytic machinery of barriers along MEP2. All this indicates that a state with an ATPase enzyme has been evolved in myosin to become the a protonated Glu459 is unlikely to be a necessary intermediate control center that coordinates the motion of the force-generating of the catalytic mechanism. domains, thereby making it an efficient motor. A structure of the final ADP·Pi product (P) that is consistent Conclusions with biochemical (reversibility of ATP hydrolysis) and kinetic A comprehensive description of the catalytic strategy of the (reaction and barrier energies) data is now available. This ATPase in myosin has been formulated. The role of the key product structure is important for a functional understanding residues has been identified for each of the three tactics used by of the myosin motor cycle. Indeed, the rebinding of myosin to myosin: (i) Stabilization of the charge shift occurring during the the actin filament and the subsequent power stroke requires − initial dissociation of the PγO3 metaphosphate. (ii) Activation the separation of the Switch 1 loop from the P loop (45). This of the attacking water by a composite base composed of a protein opening of the active site can only occur when the nucleotide side chain (Glu459), a helping water, and the γ-phosphate. (iii) is in the ADP·Pi state, not in the ATP state. How the state of Formation of a H-bond network that allows the efficient transfer the nucleotide controls Switch 1–P-loop separation is still of protons along proton wires. This description can serve as completely unknown. Having structures now for both the ATP a blueprint for the interpretation of mutational and kinetic and the ADP·Pi states will allow a comparative study of the experiments in myosins in general: Crystal structures of myosins interaction forces in the active site that may explain this BIOPHYSICS AND

from different organisms and of different myosin types having control mechanism. COMPUTATIONAL BIOLOGY the “Converter” domain (which carries the lever arm) in the postrecovery–prepower stroke conformation (i.e., in the ATPase Methods competent stage of the Lymn–Taylor cycle) are listed in Table 1. The setups of the protein and of the energy function are identical to those They all have the Switch 1 and Switch 2 loops in the same recently described in ref. 20 and are summarized here (see also SI Methods): closed–closed configuration over the P loop. An overlap of their Atomic coordinates were taken from crystal structures of myosin bound to · · · active site shows that these independently refined crystal struc- the ATP analogs ADP Be F3 (32) and ADP VO4 (12). In the so-called reactant tures have water molecules in the exact same positions (relative state, the ATP atoms were positioned as in the vanadate analog. The γ-phosphate group of ATP was placed so as to make the same H-bonds as the to the surrounding protein) as do waters Wa,Wh, and W3 shown 2+ vanadate group, and water Wa was positioned where the apical oxygen of in Fig. 1. Moreover, in all structures of Table 1, the Mg ion is the vanadate is located. The density functional theory method with B3LYP in the same position and has the same coordination partners as functional and a 6–31G(d,p) basis set was used to treat 84 atoms in the active + shown in Fig. 1. This great similarity suggests that the same site, which include the triphosphate, Mg2 and its two coordinating waters,

catalytic strategy is used by all myosins. Given the similarity of waters Wa and Wh, all of the side chains shown in Fig. 1A (except Lys185 and their active sites, the catalytic strategy presented here will most Asn233), and the backbone peptide group 181/182. For the calculation of likely be similar in the kinesin motor (36, 39), in the F1-ATPase some MEP2 subpathways, water molecule W3 [water number 103 in the (40, 41,) and in other ATPase and GTPase enzymes, (33, 42, 43,) Protein Data Bank (PDB) ID code 1VOM] (12) was also included in this most of which have been shown to involve the formation of quantum-mechanical region. All of the remaining atoms of the myosin head were included explicitly in the simulation, using a classical energy that was a metaphosphate intermediate as well. Even the strategy used by computed with the CHARMM force field and parameters described pre- the EcoRV restriction enzyme to cleave the P–Obondinthe – – viously. (46, 47,) The link atom approach (48) was used to treat the QM/MM P O C phosphodiester linkage of the DNA backbone (as op- boundary. The strong polarization of some active site peptide groups by the posedtotheP–O–P anhydride linkage in ATP) has great −4e charge on the triphosphate moiety was accounted for by individually similarity (31): EcoRV cleaves the P–O bond before the water up-scaling the atomic point charges of these peptide groups, as described in activation, thus generating a planar phosphate intermediate of detail in ref. 20. Nonuniform charge scaling (49), an implicit solvent model, − was used to account for the solvent screening effects. the form R–O–PO2 (equivalent to the PγO3 metaphosphate in myosin). The nearby Asp90 then acts as general base (similarly The conjugate peak refinement (CPR) algorithm (50) as implemented in CHARMM (51) was used to determine the MEPs and their transition state to the Glu459–Wh complex in myosin) and activates the − attacking water to generate an OH , whose attack onto the structures. CPR finds the exact transition state structure and the whole path (consisting of a series of structures, which are used to make the phosphorus atom completes the reaction. frames of the molecular movie) that connects the desired reactant to the For myosin to function efficiently as a motor, the ATP hy- desired product structures, thus making sure that the relevant energy drolysis must take place at a very well-defined point along the barrier is identified. The method allows determination of the mechanism Lymn–Taylor motor cycle (5): just after the recovery stroke that of complex reactions in proteins. CPR has been used successfully in con- primes the lever arm and just before the power stroke that swings junction with QM/MM energy functions, for example to study proton

Kiani and Fischer PNAS | Published online July 8, 2014 | E2955 Downloaded by guest on October 1, 2021 − − − transfer along proton wires (52, 53), the cleavage of P ̶O bonds (9, 31), or found was that a gradient of less than 10 2 kcal mol 1·Å 1 is obtained for isomerization reactions (54–56). Unlike molecular dynamics simulations, 55 successive line minimizations. the MEP shows only the motions that are essential for the reaction, but gives no information on the time needed to get from one movie frame to ACKNOWLEDGMENTS. Financial support by the German Science Foundation the next. MEPs and the CPR method are described in more detail in SI through the module SFB 623, Molecular Catalysts: Structure and Functional Methods. The CPR criterion for deciding that a transition state has been Design is gratefully acknowledged.

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