Structural Model of Weak Binding Actomyosin in the Prepowerstroke State*

Background: Actomyosin generates mechanical force in all eukaryotic cells including muscle. Results: By dynamic computational simulations we revealed structural rearrangements in myosin upon actin binding, leading to the initial state of force generation. Conclusion: The actin binding-induced structural rearrangements in myosin are transmitted specifically through the activation loop of the myosin. Significance: The first actomyosin atomic structural model of the initial state of force generation. We present the first in silico model of the weak binding actomyosin in the initial powerstroke state, representing the actin binding-induced major structural changes in myosin. First, we docked an actin trimer to prepowerstroke myosin then relaxed the complex by a 100-ns long unrestrained molecular dynamics. In the first few nanoseconds, actin binding induced an extra primed myosin state, i.e. the further priming of the myosin lever by 18° coupled to a further closure of switch 2 loop. We demonstrated that actin induces the extra primed state of myosin specifically through the actin N terminus-activation loop interaction. The applied in silico methodology was validated by forming rigor structures that perfectly fitted into an experimentally determined EM map of the rigor actomyosin. Our results unveiled the role of actin in the powerstroke by presenting that actin moves the myosin lever to the extra primed state that leads to the effective lever swing.

leading to strong actin binding (Fig. 1). Actin rebinding to the up-lever M⅐ADP⅐P i 4 state is weak, thermodynamically unfavorable, however, mechanistically the resulting weak actomyosin complex represents a key enzymatic state, i.e. the primed prepowerstroke state of the motor system. Actin must bind to the lever-up state of myosin to produce a mechanically effective, up-to-down lever swing, otherwise a non-productive, futile cycle occurs (4). Although actin binding to M⅐ADP⅐P i is thermodynamically unfavorable, a kinetic pathway selection mechanism channels the cycle into the effective route by the actindriven acceleration of the rate-limiting lever swing (4). In other words, in the absence of actin the rate-limiting step is the up-todown lever swing (5), which is accelerated by actin, resulting in a large flux toward the effective lever swing pathway (Fig. 1). Recently, we found that the activation loop located in the upper part of the relay region of myosin binds to the N-terminal segment of actin (6). This actomyosin interaction specifically accelerates the rate of the up-to-down lever swing of M⅐ADP⅐P i , thus it is responsible for maintaining the high ratio of flux of the effective versus futile lever swing pathways. Consequently, mutations that weaken the interaction between actin and the activation loop reduce the efficiency of the actomyosin system (6). Nevertheless, the molecular mechanism of the actin-induced acceleration of the lever swing is still unrevealed. This leads us to the fundamental question: what are the conformational rearrangements that occur upon actin binding to the uplever, prepowerstroke state of myosin?
The answer to this question is not easily accessible, as there are no crystal structures of the actomyosin complex. Atomic structural models of the rigor actomyosin complex have been presented based on high resolution electron microscopy (7)(8)(9)(10). Recently, ATP-induced actin dissociation from myosin has been modeled by in silico simulations (11). To understand the mechanism of the powerstroke, there is a great demand to solve the initial state of the powerstroke, i.e. the weak A⅐M⅐ADP⅐P i up-lever state complex. Determination of this weak binding actomyosin complex is experimentally challenging due to its low proportion and very short lifetime in equilibrium and steady-state systems, respectively. Thus, despite serious efforts (12), no high resolution EM-based structure is available of any weak actin-binding actomyosin complex. Therefore, we have determined the atomic model of the weak actomyosin, up-lever complex by in silico techniques using protein-protein docking and long time molecular dynamics simulation. For validation of the simulated weak actomyosin structures, rigor actomyosin complexes were also resolved by the same methods and compared with experimentally determined rigor structures. We found that upon actin binding, the closed switch 2 loop of prepowerstroke myosin becomes more closed, which conformational rearrangement is coupled to an 18 degrees further up movement of the up positioned lever, resulting in an "extra primed" state of myosin. We also demonstrate the specific role of the activation loop in the communication pathway between the actin-binding site, the nucleotide-binding pocket, and the converter domain.

EXPERIMENTAL PROCEDURES
Protein Structures Preparation-The Dictyostelium discoideum myosin 2 motor domain up-lever state (Protein Data Bank code 1VOM) (PDB) was extended with the missing amino acids (Ala 205 to Ser 208 , Asn 711 , Ala 716 to Ser 719 , Asp 724 to Leu 730 , and Ala 748 to Glu 759 ) based on the structure by Jon Kull 5 (referred to as M up ). Missing residues of the squid S1 apo state (PDB 2OVK referred to as M apo,sq : Lys 203 to Lys 216 , Pro 626 to Ala 642 ) were completed with Modeler 9.2 (13). Coordinates of all atoms of the Dictyostelium myosin 2 motor domain apo state (PDB 1Q5G, referred to as M apo,Dd ) are well defined. Vanadate in the nucleotide-binding pocket of PDB 1VOM was replaced by P i . We calculated the partial charges and coordinates using the AMBER force field. The ADP parameters applied in the AMBER force field were provided by Meagher et al. (14). Restrained electrostatic potential charges of H 2 PO 3 Ϫ (the most dominant ionized state at pH 7.2, verified by quantum mechanical calculations under CHARMM force field) were calculated by Gaussian 03 and ANTECHAMBER (15,16). The calculations were carried out for a set of structural conformations of the H 2 PO 3 Ϫ group by covering the accessible space in the system. The density functional algorithm with the B3LYP exchange and the 6 -312ϩg (d,p) basis set were selected for calculation in Gaussian 03. The resulting charges were averaged over all of the conformations. All crystal waters were stripped except for two in the nucleotide binding pocket of PDB 1VOM, which stabilize the position of ADP and P i through interactions with the magnesium ion. The missing N terminus of the actin trimer (17) was sequentially extended and capped with acetylate (acetyl-Asp-Glu-Asp-Glu-actin) preceding the molecular minimization.
Protein-Protein Docking-After a 20-ns long molecular dynamic relaxation of the prepared crystal structures ( rel M up , rel M apo,Dd , and rel M apo,sq ), the averaged myosin structures were docked to the refined actin trimer using the HADDOCK program (High Ambiguity Driven Docking), resulting in dock A⅐M up, dockA⅐M rigor,Dd , and dock A⅐M rigor,sq . Intermolecular restraint residues for docking were defined by the experimentally determined actomyosin interface (18 -20), regarded as flexible segments and divided into active and passive amino acids for protein-protein docking. Active residues take part in actomyosin binding and passive residues are the neighboring residues of active residues. Overall, six active and 10 passive residues were selected from myosin, five active and five passive residues were selected from actin. Ambiguous interaction restraints identified from these residues was used to drive the docking process, with a maximum effective distance of 8.0 Å (21), which was available for the active-active and active-passive, but not for the passive-passive residues. The best 200 of 1000 refined complexes were obtained from rigid body energy minimization and then submitted to the semi-rigid simulated annealing process. These structures were exposed to a 12-Å shell of TIP3P water solvent for molecular dynamic simulations with a cutoff value of 5 Å. The best 100 complexes were selected according to the evaluation score of their average interaction energies and buried surface area. The HADDOCK score, as the main criteria for selection, was calculated on the basis of the Equation 1, where E VWD is the Van der Waals, E ELEC is the electrostatic, E AIR is the ambiguous interaction restraint, and E DESO is the desolvation energy. Finally, optimal candidates with the lowest HADDOCK scores were collected into subsets with more than 10 structures by a backbone-based root mean square deviation clustering with a cut-off value of 7.5 Å. All parameters and processes were carried out through the HADDOCK online service. Molecular Dynamic Simulations-The module of sander in molecular dynamics package AMBER11 was used for molecular dynamics simulations (22). The prepared crystal structures and the refined actin trimer before docking were relaxed for 20 ns ( rel M up , rel M apo,Dd , and rel M apo,sq ). After docking, the actomyosin structures were also relaxed by a 100-ns long molecular dynamics, resulting in rel A⅐M up , rel A⅐M rigor,Dd , and rel A⅐M rigor,sq . After introducing mutations into the rel A⅐M up complex, the structures were relaxed for the same length of time leading to rel A⅐M up,R520Q , rel A⅐M up,R562Q , and rel A⅐M up,K622Q/K623Q complexes. All structures were neutralized by adding a discrete number of Na ϩ in the most appropriate electronegative areas around proteins. Complexes were then solvated in a truncated octahedron box of TIP3P water with a 12-Å cut-off value along each dimension (23). Longrange electrostatic interactions were treated by particle-mesh Ewald method in periodic boundary conditions (24). By a 1000 steps of the steepest descent and conjugate gradient energy minimization, the compact system was slowly heated up to 300 K and equilibrated at constant temperature (NVT) for 20 ns and then at constant pressure (NPT) for 80 ns. The Berendsen coupling algorithm was used for temperature control (25). The SHAKE algorithm was applied for constraints on covalent bonds and all hydrogen atoms (26).
Binding Free Energy Calculation-Binding free energies of actomyosin complexes from 2500 snapshots of the last 60 ns of the MD simulations were calculated by the molecular mechanic Poisson-Boltzmann surface area method (MM/PBSA) (27). The pbsa module in AMBER was used to evaluate the polar contribution (⌬G sol-pol ) to the solvation free energy (⌬G sol ) (Equation 2).
The structure of the docked and relaxed rigor actomyosin complexes. Actomyosin structures are fitted into the electron density map (transparent gray) of EM A⅐M rigor,ch with their actin trimers (yellow-red-green) as best fits for the map. Myosin (blue) outside the EM map is colored white. The root mean square deviations of the backbones of dock A⅐M rigor,Dd and rel A⅐M rigor,Dd from EM A⅐M rigor,ch are 6.0 Ϯ 1.9 and 4.7 Ϯ 1.7 Å, respectively. The root mean square deviations of the backbones of dock A⅐M rigor,sq and rel A⅐M rigor,sq from EM A⅐M rigor,ch are 5.8 Ϯ 1.8 and 5.5 Ϯ 1.7 Å, respectively.  The grid spacing of the cubic lattice was set at 2 Å, and the dielectric constant values for the interior and exterior of the system were 1 and 80. The non-polar contribution to the solva-tion free energy (⌬G sol-np ) was calculated from the solvent-accessible surface area (Equation 3) (28).
The surface tension ␥ and the offset ␤ were set to 0.00542 kcal mol Ϫ1 Å Ϫ1 and 0.92 kcal mol Ϫ1 , respectively. The contribution of entropy (ϪT⌬S) based on ligand receptor association was performed with normal-mode analysis (29). 1000 snapshots were collected and submitted to molecular minimization with a distance-dependent dielectric constant, E ϭ 4r. The end of convergence was not achieved until the root mean square deviations of the gradient vector were less than 1 ϫ 10 Ϫ4 kcal mol Ϫ1 Å Ϫ1 . Residues close to the binding surface with a distance less than 20 Å were acquired to estimate the contribution of entropy.

RESULTS
After completing the actin trimer (17) and the different myosin 2 structures (Table 1) with their missing residues, they were relaxed by molecular dynamics and docked to each other using the HADDOCK program. The docked structural models and the uncomplexed actin and myosin structures were placed into explicit water boxes and relaxed by a 100-ns long molecular  dynamics. To validate the structural simulation by molecular dynamics, we compared the rigor structures ( rel A⅐M rigor,Dd and rel A⅐M rigor,sq ) (supplemental relAMrigorDd.pdb and relAMrigorsq.pdb) with the rigor actomyosin model created using the electron microscopy density map ( EM A⅐M rigor,ch ) (7). The comparison validated the applied in silico procedures as the nondirected protein-protein docking and molecular dynamics simulations resulted in a highly similar structure to the experimentally determined one. During the molecular dynamic relaxation, actin induced the closure of the actin-binding cleft of dock A⅐M rigor,Dd and dock A⅐M rigor,sq resulting in similarly closed clefts as in EM A⅐M rigor,ch ( Fig. 2 and further closed cleft states of Table 2). Actin-binding clefts of the non-actin-bound M apo states did not change upon relaxation (M apo,Dd/sq and rel M apo,Dd/sq of Table 2). Furthermore, we found that the orientation of myosin relative to the actin filament in dock A⅐M rigor,Dd and dock A⅐M rigor,sq did not match well with EM A⅐M rigor,ch , whereas in the first 10 ns of the molecular dynamics, myosin oriented to the experimentally determined position of EM A⅐M rigor,ch (Fig. 2). A further validation of the applied in silico method is that the difference of the binding free energy (⌬G bind ) between the weak and strong actomyosin complexes (⌬⌬G bind ) in the simulated and experimentally determined values do not differ significantly ( SIM ⌬⌬G bind ϭ 4.8 Ϯ 1.1 kcal mol Ϫ1 , EXP ⌬⌬G bind ϭ 4.2 kcal mol Ϫ1 ) (5, 6, 30, 31) ( Table 3).
The binding surface areas of myosin increased upon molecular dynamics in all docked actomyosin complexes (from 1477.5 Å of dock A⅐M up to 1997.1 Å of rel A⅐M up , from 1753 Å of dock A⅐M rigor,Dd to 2205.3 Å of rel A⅐M rigor,Dd and from 1468 Å of dock A⅐M rigor,sq to 2707 Å of rel A⅐M rigor,sq ). All actomyosin inter-actions are listed in Table 4. The comparison of the rel A⅐M up (supplemental relAMup.pdb) and rel A⅐M rigor,Dd/sq structures demonstrates that the actin-binding surface area of myosin expands during the weak to strong actin-binding transition due to the increasing contribution of loop 4 and cardiomyopathy loop in actin binding ( Fig. 3A and Table 4). These results are in accordance with the interactions depicted by the electron micrography-based actomyosin structure, EM A⅐M rigor,ch .
The simulations confirmed the existence of the interaction between the recently described activation loop (residues 519 -524 of D. discoideum) and the N-terminal segment of actin (residues 1-4) (6). Recently we described that the activation loop of myosin plays a key role in actin activation of the ATPase activity of myosin. In all relaxed states Arg 520 located in the activation loop interacts with the negatively charged N-terminal segment of actin ( Fig. 3B and Table 4). This interaction was not established in the protein-protein docking procedures, whereas it was formed spontaneously in the first few nanoseconds of the molecular dynamics relaxations. In the EM A⅐M rigor,ch model, this interaction was not described because the N-terminal region of actin was missing from the actin crystal structure used for creating the model. In the weak actinbinding state, conformation of the activation loop is different from that of the rigors. Arg 520 in rel A⅐M up has a salt bridge with Asp 1 of actin, whereas in rel A⅐M rigor it forms a more extended salt bridge cluster with Asp 3 and Glu 4 (Fig. 3B, Table 4). These interactions are stable as their occurrence is 95% throughout the whole molecular dynamics. Loop 2 goes through a large conformational change during the weak to strong actin-binding transition. In both states, there is a salt bridge between myosin The helix-loop-helix element (residues 530 -537), structurally coupled to the activation loop, has stronger hydrophobic interactions with residues 143-147 of actin in rigor compared with the weak binding state. These results are in agreement with previous indications that hydrophobic interactions create expanding networks of the actin-myosin interface during the weak to strong actin-binding transition (32). Furthermore, a conformational rearrangement of the interaction network occurs between the activation loop and the actin N-terminal region upon the up-to-down lever movement and the weak to strong actin-binding transition, which indicates that actin may directly affect the relay/converter/lever movement through their structural coupling to the activation loop.
Upon molecular dynamics of dock A⅐M up , significant conformational relaxations occurred in the relay/converter and the nucleotide-binding region. All conformational relaxations were completed in the first 10 ns and remained stable in the following 90 ns of the simulations. The most striking effect induced by actin binding was an 18°further up movement of the myosin lever (further up-lever state of rel A⅐M up in Table 5). The further up-lever movement occurred within 5 ns of the relaxation and remained stable in the following 95 ns (Fig. 4, A and B, left  panel). To investigate the role of the activation loop-actin interaction in this effect, Arg 520 of rel A⅐M up was mutated in silico to Gln ( rel A⅐M up,R520Q ) (supplemental file relAMupR520Q.pdb). This mutation interrupts the salt bridge interaction between the activation loop and the actin N-terminal region. The mutated construct was relaxed by molecular dynamics for 100 ns. In the first 5 ns the lever moved back to the same up position as that the actin detached myosin ( rel M up ). This specific effect on the extra priming caused by the activation loop-actin interaction is supported by the fact that mutations in other actinbinding regions (K622Q/K623Q in loop 2 and R562Q in loop 3) caused only slight "back" relaxations and the lever remained mainly in the further up position (Fig. 4B, left panel, and rel A⅐M up,K622Q/K623Q and rel A⅐M up,R562Q in Table 5) (supplemental file relAMupR562Q.pdb).
As expected, the further up-lever movement was coupled to another conformational relaxation that occurred in the nucleotide binding pocket ( Table 5). As a result, the C-terminal part of the switch 2 loop in rel A⅐M up possesses a further closed position (Fig. 4A). Similarly to the lever relaxation, when Arg 520 of the activation loop was mutated to Gln ( rel A⅐M up,R520Q ), the switch 2 loop relaxed to the same closed position as that of the actin detached, closed conformation ( rel M up ), whereas in loop 3 and loop 2 mutants ( rel A⅐M up,R562Q and rel A⅐M up,K622Q/K623Q ) switch 2 remained in the further closed position (Fig. 4B, right panel, and Table 5) without any back relaxations. The effect of  These results indicate that the activation loop is a specific sensor of actin binding and is responsible for transferring the information of actin binding to the nucleotide binding pocket and the relay/converter region.
We analyzed changes of the motional correlations of the functional regions of myosin upon actin binding. Positive motional correlation between the two regions is defined as their coupled dynamics is high. In the absence of actin ( rel M up and rel M apo ) the dynamics of switch 2 is weekly coupled to other functional regions of myosin (Fig. 6). The dynamic coupling between switch 2 and the relay is highly increased in the weakly and strongly actin-bound states ( rel A⅐M up and rel A⅐M rigor,Dd ). The dynamic coupling becomes very high between switch 2 and the upper relay, including the activation loop, the relay helix, and the wedge loop. When the salt bridge interaction between the activation loop and actin was interrupted by the R520Q mutation, the motional correlations between these regions decreased to the same level as that of the actin detached states ( rel A⅐M up,R520Q ). Mutations in loops 3 and 2 did not decrease the motional correlation of switch 2 to the level of the actin detached states ( rel A⅐M up,R562Q and rel A⅐M up,K622Q/K623Q ). These effects picture the same communication pathways found by the analysis of the structural rearrangements described above.

DISCUSSION
Recently, the mechanism of the powerstroke has been proposed on the basis of crystal structures and pseudoatomic cryo-EM models (7)(8)(9). However, neither the starting nor the end states of the powerstroke structures of actomyosin are available. Generally, the actin detached, up-lever myosin head complexed with an ADP⅐P i analog (PDB codes 1MMD, 1VOM, and 2V26) is discussed as the starting state of the powerstroke and additionally the formation of the ADP⅐P i up-lever state has been modeled recently (33). However, one may assume that an actin-detached state is not the initial state of the powerstroke, because an effective powerstroke must start in an actin-attached state (4). Also, the electron micrograph rigor structures (7-9) cannot be considered as part of the powerstroke, because the powerstroke ends in a nucleotide-bound state (34). The actin-induced conformational changes in the M up ⅐ADP⅐P i state were speculated based on comparison of the rigor cryo-EM model and the actin-detached M up ⅐ADP⅐VO 4 crystal structures (7,8). Actin-binding cleft closure was considered to be the major actin-induced conformational change that was supposed to initiate rearrangements in the nucleotide binding pocket leading to the powerstroke. To overcome the problem of the missing structure of the initial state of the actomyosin prepowerstroke, in this study we constructed the atomic model of the weak actin-binding state (A⅐M up ⅐ADP⅐P i ).
We demonstrate that the lower 50-kDa subdomain, including loop 3, H-loop, and the activation loop, is the major contributor for the initial, weak actin binding of myosin. We also confirm the interaction of loop 3 with two actin monomers (34,35), which are among the initial weak actin-binding interac-tions. Structural and mutational studies indicate that dynamic interactions of loop 2 with different regions of actin in the different states of actomyosin reflect its role in the weak to strong actin-binding transition of myosin (36,37). We found that loop 2 positioned differently in rigor compared with the weak actinbinding state. As actin binding strengthens, loop 2 starts to compete with the activation loop for the highly negatively charged N-terminal region of actin, while also still interacting with other regions of actin (Asp 24/25 ). Similarly to our results, a recently published in silico structural study also demonstrates that the activation loop and loop 2 interact with the actin N-terminal region in rigor actomyosin (38). Within the first 15 ns of their molecular dynamic simulation, the activation loop forms stable interactions with Glu 2 and Asp 3 , whereas it competes with loop 2 for Asp 1 of actin. In rigor actomyosin a similar "sandwich-like" pattern (actin Asp 24 /Asp 25 -myosin loop 2-actin N-terminal region-myosin activation loop) was found in the rigor actin-myosinIE complex (8). Former rigor models lack the interaction of the activation loop with actin, because of the missing N-terminal region of the applied actin structures (7,10), although this interaction is crucial for actin activation of myosin (6).
We found that actin binding causes a structural relaxation of the myosin structure. We note that conformational relaxations are not hindered by free energy barriers, and thus occur at the nanosecond time scale, therefore they must be distinguished from first-order kinetic steps. The major structural rearrangements occur in the relay/converter/lever region and the switch 2 loop: an 18°further up-lever movement is coupled to a further closure of the switch 2 loop. A minor actin-binding cleft closure was also detected upon molecular dynamics relaxation. We demonstrated that the activation loop has an essential role in the extra priming of myosin, because the actin-induced conformational changes are transmitted through the activation loop toward the relay and active sites. This structural finding is in accordance with recent experimental evidence that the activation loop is specifically responsible for actin activation of the ATPase activity of myosin by accelerating the up-to-down lever movement (6).
Irrespective of the lever swing occurring in ADP⅐P i or ADP states of myosin, the initial state of the powerstroke is undoubtedly the open actin-binding cleft rel A⅐M up state, which weakly binds to actin. Intriguingly, myosin 6 complexed with ADP⅐VO 4 (PDB 2V26) (39) is highly similar to the presented structure of rel A⅐M up , possessing a further up-lever and a further closed switch 2 (Fig. 7). The existence of such a state demonstrates that it is a structurally accessible state of myosin.
Here, we determined the relaxed conformational structure of the weak actomyosin complex in the prepowerstroke state. Its significance is that the powerstroke (including actin-binding cleft closure, switch movements and lever swing) starts from this initial state. The presented rel A⅐M up structure may lead to further experiments to reveal a more detailed reaction coordinate pathway of the powerstroke.