Mechanochemical coupling in the myosin motor domain. I. Insights from equilibrium active-site simulations

A weak coupling mechanism for the early steps of the recovery stroke of myosin VI: A free energy simulation and string method analysis

Myosin motors use the energy of ATP to produce force and directed movement on actin by a swing of the lever-arm. ATP is hydrolysed during the off-actin re-priming transition termed recovery stroke. To provide an understanding of chemo-mechanical transduction by myosin, it is critical to determine how the reverse swing of the lever-arm and ATP hydrolysis are coupled. Previous studies concluded that the recovery stroke of myosin II is initiated by closure of the Switch II loop in the nucleotide-binding site. Recently, we proposed that the recovery stroke of myosin VI starts with the spontaneous re-priming of the converter domain to a putative pre-transition state (PTS) intermediate that precedes Switch II closing and ATPase activation. Here, we investigate the transition from the pre-recovery, post-rigor (PR) state to PTS in myosin VI using geometric free energy simulations and the string method. First, our calculations rediscover the PTS state agnostically and show that it is accessible from PR via a low free energy transition path. Second, separate path calculations using the string method illuminate the mechanism of the PR to PTS transition with atomic resolution. In this mechanism, the initiating event is a large movement of the converter/lever-arm region that triggers rearrangements in the Relay-SH1 region and the formation of the kink in the Relay helix with no coupling to the active site. Analysis of the free-energy barriers along the path suggests that the converter-initiated mechanism is much faster than the one initiated by Switch II closure, which supports the biological relevance of PTS as a major on-pathway intermediate of the recovery stroke in myosin VI. Our analysis suggests that lever-arm re-priming and ATP hydrolysis are only weakly coupled, so that the myosin recovery stroke is initiated by thermal fluctuations and stabilised by nucleotide consumption via a ratchet-like mechanism.

Analysis of Phosphoryl-Transfer Enzymes with QM/MM Free Energy Simulations

We discuss the application of quantum mechanics/molecular mechanics (QM/MM) free energy simulations to the analysis of phosphoryl transfers catalyzed by two enzymes: alkaline phosphatase and myosin. We focus on the nature of the transition state and the issue of mechanochemical coupling, respectively, in the two enzymes. The results illustrate unique insights that emerged from the QM/MM simulations, especially concerning the interpretation of experimental data regarding the nature of enzymatic transition states and coupling between global structural transition and catalysis in the active site. We also highlight a number of technical issues worthy of attention when applying QM/MM free energy simulations, and comment on a number of technical and mechanistic issues that require further studies.

Long-range coupling between ATP-binding and lever-arm regions in myosin via dielectric allostery

A protein molecule is a dielectric substance, so the binding of a ligand is expected to induce dielectric response in the protein molecule, considering that ligands are charged or polar in general. We previously reported that binding of adenosine triphosphate (ATP) to molecular motor myosin actually induces such a dielectric response in myosin due to the net negative charge of ATP. By this dielectric response, referred to as "dielectric allostery," spatially separated two regions in myosin, the ATP-binding region and the actin-binding region, are allosterically coupled. In this study, from the statistically stringent analyses of the extensive molecular dynamics simulation data obtained in the ATP-free and the ATP-bound states, we show that there exists the dielectric allostery that transmits the signal of ATP binding toward the distant lever-arm region. The ATP-binding-induced electrostatic potential change observed on the surface of the main domain induced a movement of the converter subdomain from which the lever arm extends. The dielectric response was found to be caused by an underlying large-scale concerted rearrangement of the electrostatic bond network, in which highly conserved charged/polar residues are involved. Our study suggests the importance of the dielectric property for molecular machines in exerting their function.

An intermediate along the recovery stroke of myosin VI revealed by X-ray crystallography and molecular dynamics

Myosins form a class of actin-based, ATPase motor proteins that mediate important cellular functions such as cargo transport and cell motility. Their functional cycle involves two large-scale swings of the lever arm: the force-generating powerstroke, which takes place on actin, and the recovery stroke during which the lever arm is reprimed into an armed configuration. Previous analyses of the prerecovery (postrigor) and postrecovery (prepowerstroke) states predicted that closure of switch II in the ATP binding site precedes the movement of the converter and the lever arm. Here, we report on a crystal structure of myosin VI, called pretransition state (PTS), which was solved at 2.2 Å resolution. Structural analysis and all-atom molecular dynamics simulations are consistent with PTS being an intermediate along the recovery stroke, where the Relay/SH1 elements adopt a postrecovery conformation, and switch II remains open. In this state, the converter appears to be largely uncoupled from the motor domain and explores an ensemble of partially reprimed configurations through extensive, reversible fluctuations. Moreover, we found that the free energy cost of hydrogen-bonding switch II to ATP is lowered by more than 10 kcal/mol compared with the prerecovery state. These results support the conclusion that closing of switch II does not initiate the recovery stroke transition in myosin VI. Rather, they suggest a mechanism in which lever arm repriming would be mostly driven by thermal fluctuations and eventually stabilized by the switch II interaction with the nucleotide in a ratchet-like fashion.

Allosteric modulation of cardiac myosin dynamics by omecamtiv mecarbil

New promising avenues for the pharmacological treatment of skeletal and heart muscle diseases rely on direct sarcomeric modulators, which are molecules that can directly bind to sarcomeric proteins and either inhibit or enhance their activity. A recent breakthrough has been the discovery of the myosin activator omecamtiv mecarbil (OM), which has been shown to increase the power output of the cardiac muscle and is currently in clinical trials for the treatment of heart failure. While the overall effect of OM on the mechano-chemical cycle of myosin is to increase the fraction of myosin molecules in the sarcomere that are strongly bound to actin, the molecular basis of its action is still not completely clear. We present here a Molecular Dynamics study of the motor domain of human cardiac myosin bound to OM, where the effects of the drug on the dynamical properties of the protein are investigated for the first time with atomistic resolution. We found that OM has a double effect on myosin dynamics, inducing a) an increased coupling of the motions of the converter and lever arm subdomains to the rest of the protein and b) a rewiring of the network of dynamic correlations, which produces preferential communication pathways between the OM binding site and distant functional regions. The location of the residues responsible for these effects suggests possible strategies for the future development of improved drugs and the targeting of specific cardiomyopathy-related mutations.

Allocating dissipation across a molecular machine cycle to maximize flux

Biomolecular machines consume free energy to break symmetry and make directed progress. Nonequilibrium ATP concentrations are the typical free energy source, with one cycle of a molecular machine consuming a certain number of ATP, providing a fixed free energy budget. Since evolution is expected to favor rapid-turnover machines that operate efficiently, we investigate how this free energy budget can be allocated to maximize flux. Unconstrained optimization eliminates intermediate metastable states, indicating that flux is enhanced in molecular machines with fewer states. When maintaining a set number of states, we show that-in contrast to previous findings-the flux-maximizing allocation of dissipation is not even. This result is consistent with the coexistence of both "irreversible" and reversible transitions in molecular machine models that successfully describe experimental data, which suggests that, in evolved machines, different transitions differ significantly in their dissipation.

Regulation and Plasticity of Catalysis in Enzymes: Insights from Analysis of Mechanochemical Coupling in Myosin

The mechanism of ATP hydrolysis in the myosin motor domain is analyzed using a combination of DFTB3/CHARMM simulations and enhanced sampling techniques. The motor domain is modeled in the pre-powerstroke state, in the post-rigor state, and as a hybrid based on the post-rigor state with a closed nucleotide-binding pocket. The ATP hydrolysis activity is found to depend on the positioning of nearby water molecules, and a network of polar residues facilitates proton transfer and charge redistribution during hydrolysis. Comparison of the observed hydrolysis pathways and the corresponding free energy profiles leads to detailed models for the mechanism of ATP hydrolysis in the pre-powerstroke state and proposes factors that regulate the hydrolysis activity in different conformational states. In the pre-powerstroke state, the scissile P_γ-O_3β bond breaks early in the reaction. Proton transfer from the lytic water to the γ-phosphate through active site residues is an important part of the kinetic bottleneck; several hydrolysis pathways that feature distinct proton transfer routes are found to have similar free energy barriers, suggesting a significant degree of plasticity in the hydrolysis mechanism. Comparison of hydrolysis in the pre-powerstroke state and the closed post-rigor model suggests that optimization of residues beyond the active site for electrostatic stabilization and preorganization is likely important to enzyme design.

Highly selective inhibition of myosin motors provides the basis of potential therapeutic application

Direct inhibition of smooth muscle myosin (SMM) is a potential means to treat hypercontractile smooth muscle diseases. The selective inhibitor CK-2018571 prevents strong binding to actin and promotes muscle relaxation in vitro and in vivo. The crystal structure of the SMM/drug complex reveals that CK-2018571 binds to a novel allosteric pocket that opens up during the "recovery stroke" transition necessary to reprime the motor. Trapped in an intermediate of this fast transition, SMM is inhibited with high selectivity compared with skeletal muscle myosin (IC₅₀ = 9 nM and 11,300 nM, respectively), although all of the binding site residues are identical in these motors. This structure provides a starting point from which to design highly specific myosin modulators to treat several human diseases. It further illustrates the potential of targeting transition intermediates of molecular machines to develop exquisitely selective pharmacological agents.

Advances in quantum simulations of ATPase catalysis in the myosin motor

During its contraction cycle, the myosin motor catalyzes the hydrolysis of ATP. Several combined quantum/classical mechanics (QM/MM) studies of this step have been published, which substantially contributed to our thinking about the catalytic mechanism. The methodological difficulties encountered over the years in the simulation of this complex reaction are now understood: (a) Polarization of the protein peptide groups surrounding the highly charged ATP(4-) cannot be neglected. (b) Some unsuspected protein groups need to be treated QM. (c) Interactions with the γ-phosphate versus the β-phosphate favor a concurrent versus a sequential mechanism, respectively. Thus, these practical aspects strongly influence the computed mechanism, and should be considered when studying other catalyzed phosphor-ester hydrolysis reactions, such as in ATPases or GTPases.

Increasing the sampling efficiency of protein conformational transition using velocity-scaling optimized hybrid explicit/implicit solvent REMD simulation

The application of temperature replica exchange molecular dynamics (REMD) simulation on protein motion is limited by its huge requirement of computational resource, particularly when explicit solvent model is implemented. In the previous study, we developed a velocity-scaling optimized hybrid explicit/implicit solvent REMD method with the hope to reduce the temperature (replica) number on the premise of maintaining high sampling efficiency. In this study, we utilized this method to characterize and energetically identify the conformational transition pathway of a protein model, the N-terminal domain of calmodulin. In comparison to the standard explicit solvent REMD simulation, the hybrid REMD is much less computationally expensive but, meanwhile, gives accurate evaluation of the structural and thermodynamic properties of the conformational transition which are in well agreement with the standard REMD simulation. Therefore, the hybrid REMD could highly increase the computational efficiency and thus expand the application of REMD simulation to larger-size protein systems.

Parametrization of DFTB3/3OB for magnesium and zinc for chemical and biological applications

We report the parametrization of the approximate density functional theory, DFTB3, for magnesium and zinc for chemical and biological applications. The parametrization strategy follows that established in previous work that parametrized several key main group elements (O, N, C, H, P, and S). This 3OB set of parameters can thus be used to study many chemical and biochemical systems. The parameters are benchmarked using both gas-phase and condensed-phase systems. The gas-phase results are compared to DFT (mostly B3LYP), ab initio (MP2 and G3B3), and PM6, as well as to a previous DFTB parametrization (MIO). The results indicate that DFTB3/3OB is particularly successful at predicting structures, including rather complex dinuclear metalloenzyme active sites, while being semiquantitative (with a typical mean absolute deviation (MAD) of ∼3–5 kcal/mol) for energetics. Single-point calculations with high-level quantum mechanics (QM) methods generally lead to very satisfying (a typical MAD of ∼1 kcal/mol) energetic properties. DFTB3/MM simulations for solution and two enzyme systems also lead to encouraging structural and energetic properties in comparison to available experimental data. The remaining limitations of DFTB3, such as the treatment of interaction between metal ions and highly charged/polarizable ligands, are also discussed.

All-atom molecular dynamics simulations of actin-myosin interactions: a comparative study of cardiac α myosin, β myosin, and fast skeletal muscle myosin

Myosins are a superfamily of actin-binding motor proteins with significant variations in kinetic properties (such as actin binding affinity) between different isoforms. It remains unknown how such kinetic variations arise from the structural and dynamic tuning of the actin-myosin interface at the amino acid residue level. To address this key issue, we have employed molecular modeling and simulations to investigate, with atomistic details, the isoform dependence of actin-myosin interactions in the rigor state. By combining electron microscopy-based docking with homology modeling, we have constructed three all-atom models for human cardiac α and β and rabbit fast skeletal muscle myosin in complex with three actin subunits in the rigor state. Starting from these models, we have performed extensive all-atom molecular dynamics (MD) simulations (total of 100 ns per system) and then used the MD trajectories to calculate actin-myosin binding free energies with contributions from both electrostatic and nonpolar forces. Our binding calculations are in good agreement with the experimental finding of isoform-dependent differences in actin binding affinity between these myosin isoforms. Such differences are traced to changes in actin-myosin electrostatic interactions (i.e., hydrogen bonds and salt bridges) that are highly dynamic and involve several flexible actin-binding loops. By partitioning the actin-myosin binding free energy to individual myosin residues, we have also identified key myosin residues involved in the actin-myosin interactions, some of which were previously validated experimentally or implicated in cardiomyopathy mutations, and the rest make promising targets for future mutational experiments.

Stabilization of the ADP/metaphosphate intermediate during ATP hydrolysis in pre-power stroke myosin: quantitative anatomy of an enzyme

It has been proposed recently that ATP hydrolysis in ATPase enzymes proceeds via an initial intermediate in which the dissociated γ-phosphate of ATP is bound in the protein as a metaphosphate (PγO3(-)). A combined quantum/classical analysis of this dissociated nucleotide state inside myosin provides a quantitative understanding of how the enzyme stabilizes this unusual metaphosphate. Indeed, in vacuum, the energy of the ADP(3-) · PγO3(-) · Mg(2+) complex is much higher than that of the undissociated ATP(4-). The protein brings it to a surprisingly low value. Energy decomposition reveals how much each interaction in the protein stabilizes the metaphosphate state; backbone peptides of the P-loop contribute 50% of the stabilization energy, and the side chain of Lys-185(+) contributes 25%. This can be explained by the fact that these groups make strong favorable interactions with the α- and β-phosphates, thus favoring the charge distribution of the metaphosphate state over that of the ATP state. Further stabilization (16%) is achieved by a hydrogen bond between the backbone C=O of Ser-237 (on loop Switch-1) and a water molecule perfectly positioned to attack the PγO3(-) in the subsequent hydrolysis step. The planar and singly negative PγO3(-) is a much better target for the subsequent nucleophilic attack by a negatively charged OH(-) than the tetrahedral and doubly negative PγO4(2-) group of ATP. Therefore, we argue that the present mechanism of metaphosphate stabilization is common to the large family of nucleotide-hydrolyzing enzymes. Methodologically, this work presents a computational approach that allows us to obtain a truly quantitative conception of enzymatic strategy.

The mechanism of the converter domain rotation in the recovery stroke of myosin motor protein

Upon ATP binding, myosin motor protein is found in two alternative conformations, prerecovery state M* and postrecovery state M**. The transition from one state to the other, known as the recovery stroke, plays a key role in the myosin functional cycle. Despite much recent research, the microscopic details of this transition remain elusive. A critical step in the recovery stroke is the rotation of the converter domain from "up" position in prerecovery state to "down" position in postrecovery state that leads to the swing of the lever arm attached to it. In this work, we demonstrate that the two rotational states of the converter domain are determined by the interactions within a small structural motif in the force-generating region of the protein that can be accurately modeled on computers using atomic representation and explicit solvent. Our simulations show that the transition between the two states is controlled by a small helix (SH1) located next to the relay helix and relay loop. A small translation in the position of SH1 away from the relay helix is seen to trigger the transition from "up" state to "down" state. The transition is driven by a cluster of hydrophobic residues I687, F487, and F506 that make significant contributions to the stability of both states. The proposed mechanism agrees well with the available structural and mutational studies.

Mechanical transduction mechanisms of RecA-like molecular motors

A majority of ATP-dependent molecular motors are RecA-like proteins, performing diverse functions in biology. These RecA-like molecular motors consist of a highly conserved core containing the ATP-binding site. Here I examined how ATP binding within this core is coupled to the conformational changes of different RecA-like molecular motors. Conserved hydrogen bond networks and conformational changes revealed two major mechanical transduction mechanisms: (1) intra-domain conformational changes and (2) inter-domain conformational changes. The intra-domain mechanism has a significant hydrogen bond rearrangement within the domain containing the P-loop, causing relative motion between two parts of the protein. The inter-domain mechanism exhibits little conformational change in the P-loop domain. Instead, the major conformational change is observed between the P-loop domain and an adjacent domain or subunit containing the arginine finger. These differences in the mechanical transduction mechanisms may link to the underlying energy surface governing a Brownian ratchet or a power stroke.

Density-cluster NMA: A new protein decomposition technique for coarse-grained normal mode analysis

Normal mode analysis has emerged as a useful technique for investigating protein motions on long time scales. This is largely due to the advent of coarse-graining techniques, particularly Hooke's Law-based potentials and the rotational-translational blocking (RTB) method for reducing the size of the force-constant matrix, the Hessian. Here we present a new method for domain decomposition for use in RTB that is based on hierarchical clustering of atomic density gradients, which we call Density-Cluster RTB (DCRTB). The method reduces the number of degrees of freedom by 85-90% compared with the standard blocking approaches. We compared the normal modes from DCRTB against standard RTB using 1-4 residues in sequence in a single block, with good agreement between the two methods. We also show that Density-Cluster RTB and standard RTB perform well in capturing the experimentally determined direction of conformational change. Significantly, we report superior correlation of DCRTB with B-factors compared with 1-4 residue per block RTB. Finally, we show significant reduction in computational cost for Density-Cluster RTB that is nearly 100-fold for many examples.

Interactions between relay helix and Src homology 1 (SH1) domain helix drive the converter domain rotation during the recovery stroke of myosin II

Myosin motor protein exists in two alternative conformations, prerecovery state M* and postrecovery state M**, on adenosine triphosphate binding. The details of the M*-to-M** transition, known as the recovery stroke to reflect its role as the functional opposite of the force-generating power stroke, remain elusive. The defining feature of the postrecovery state is a kink in the relay helix, a key part of the protein involved in force generation. In this article, we determine the interactions that are responsible for the appearance of the kink. We design a series of computational models that contain three other segments, relay loop, converter domain, and Src homology 1 (SH1) domain helix, with which relay helix interacts and determine their structure in accurate replica exchange molecular dynamics simulations in explicit solvent. By conducting an exhaustive combinatorial search among different models, we find that: (1) the converter domain must be attached to the relay helix during the transition, so it does not interfere with other parts of the protein and (2) the structure of the relay helix is controlled by SH1 helix. The kink is strongly coupled to the position of SH1 helix. It arises as a result of direct interactions between SH1 and the relay helix and leads to a rotation of the C-terminal part of the relay helix, which is subsequently transmitted to the converter domain.

Early stages of the recovery stroke in myosin II studied by molecular dynamics simulations

The recovery stroke is a key step in the functional cycle of muscle motor protein myosin, during which pre-recovery conformation of the protein is changed into the active post-recovery conformation, ready to exersice force. We study the microscopic details of this transition using molecular dynamics simulations of atomistic models in implicit and explicit solvent. In more than 2 μs of aggregate simulation time, we uncover evidence that the recovery stroke is a two-step process consisting of two stages separated by a time delay. In our simulations, we directly observe the first stage at which switch II loop closes in the presence of adenosine triphosphate at the nucleotide binding site. The resulting configuration of the nucleotide binding site is identical to that detected experimentally. Distribution of inter-residue distances measured in the force generating region of myosin is in good agreement with the experimental data. The second stage of the recovery stroke structural transition, rotation of the converter domain, was not observed in our simulations. Apparently it occurs on a longer time scale. We suggest that the two parts of the recovery stroke need to be studied using separate computational models.

Computational modeling of allosteric communication reveals organizing principles of mutation-induced signaling in ABL and EGFR kinases

The emerging structural information about allosteric kinase complexes and the growing number of allosteric inhibitors call for a systematic strategy to delineate and classify mechanisms of allosteric regulation and long-range communication that control kinase activity. In this work, we have investigated mechanistic aspects of long-range communications in ABL and EGFR kinases based on the results of multiscale simulations of regulatory complexes and computational modeling of signal propagation in proteins. These approaches have been systematically employed to elucidate organizing molecular principles of allosteric signaling in the ABL and EGFR multi-domain regulatory complexes and analyze allosteric signatures of the gate-keeper cancer mutations. We have presented evidence that mechanisms of allosteric activation may have universally evolved in the ABL and EGFR regulatory complexes as a product of a functional cross-talk between the organizing αF-helix and conformationally adaptive αI-helix and αC-helix. These structural elements form a dynamic network of efficiently communicated clusters that may control the long-range interdomain coupling and allosteric activation. The results of this study have unveiled a unifying effect of the gate-keeper cancer mutations as catalysts of kinase activation, leading to the enhanced long-range communication among allosterically coupled segments and stabilization of the active kinase form. The results of this study can reconcile recent experimental studies of allosteric inhibition and long-range cooperativity between binding sites in protein kinases. The presented study offers a novel molecular insight into mechanistic aspects of allosteric kinase signaling and provides a quantitative picture of activation mechanisms in protein kinases at the atomic level.

Despite recent progress in computational and experimental studies of dynamic regulation in protein kinases, a mechanistic understanding of long-range communication and mechanisms of mutation-induced signaling controlling kinase activity remains largely qualitative. In this study, we have performed a systematic modeling and analysis of allosteric activation in ABL and EGFR kinases at the increasing level of complexity - from catalytic domain to multi-domain regulatory complexes. The results of this study have revealed organizing structural and mechanistic principles of allosteric signaling in protein kinases. Although activation mechanisms in ABL and EGFR kinases have evolved through acquisition of structurally different regulatory complexes, we have found that long-range interdomain communication between common functional segments (αF-helix and αC-helix) may be important for allosteric activation. The results of study have revealed molecular signatures of activating cancer mutations and have shed the light on general mechanistic aspects of mutation-induced signaling in protein kinases. An advanced understanding and further characterization of molecular signatures of kinase mutations may aid in a better rationalization of mutational effects on clinical outcomes and facilitate molecular-based therapeutic strategies to combat kinase mutation-dependent tumorigenesis.

The energy landscape analysis of cancer mutations in protein kinases

The growing interest in quantifying the molecular basis of protein kinase activation and allosteric regulation by cancer mutations has fueled computational studies of allosteric signaling in protein kinases. In the present study, we combined computer simulations and the energy landscape analysis of protein kinases to characterize the interplay between oncogenic mutations and locally frustrated sites as important catalysts of allostetric kinase activation. While structurally rigid kinase core constitutes a minimally frustrated hub of the catalytic domain, locally frustrated residue clusters, whose interaction networks are not energetically optimized, are prone to dynamic modulation and could enable allosteric conformational transitions. The results of this study have shown that the energy landscape effect of oncogenic mutations may be allosteric eliciting global changes in the spatial distribution of highly frustrated residues. We have found that mutation-induced allosteric signaling may involve a dynamic coupling between structurally rigid (minimally frustrated) and plastic (locally frustrated) clusters of residues. The presented study has demonstrated that activation cancer mutations may affect the thermodynamic equilibrium between kinase states by allosterically altering the distribution of locally frustrated sites and increasing the local frustration in the inactive form, while eliminating locally frustrated sites and restoring structural rigidity of the active form. The energy landsape analysis of protein kinases and the proposed role of locally frustrated sites in activation mechanisms may have useful implications for bioinformatics-based screening and detection of functional sites critical for allosteric regulation in complex biomolecular systems.

Coarse-grained modeling of conformational transitions underlying the processive stepping of myosin V dimer along filamentous actin

To explore the structural basis of processive stepping of myosin V along filamentous actin, we have performed comprehensive modeling of its key conformational states and transitions with an unprecedented residue level of details. We have built structural models for a myosin V monomer complexed with filamentous actin at four biochemical states [adenosine diphosphate (ATP)-, adenosine diphosphate (ADP)-phosphate-, ADP-bound or nucleotide-free]. Then we have modeled a myosin V dimer (consisting of lead and rear head) at various two-head-bound states with nearly straight lever arms rotated by intramolecular strain. Next, we have performed transition pathway modeling to determine the most favorable sequence of transitions (namely, phosphate release at the lead head followed by ADP release at the rear head, while ADP release at the lead head is inhibited), which underlie the kinetic coordination between the two heads. Finally, we have used transition pathway modeling to reveal the order of structural changes during three key biochemical transitions (phosphate release at the lead head, ADP release and ATP binding at the rear head), which shed lights on the strain-dependence of the allosterically coupled motions at various stages of myosin V's work cycle. Our modeling results are in agreement with and offer structural insights to many results of kinetic, single-molecule and structural studies of myosin V.

Simulations of allosteric transitions

Allosteric transitions are one of the subtler mechanisms used by nature to fine tune protein activity. Effector binding to a specific site on the protein surface induces significant activity change, and initiates a conformational transition that frequently includes domain motions and is very large. From a theoretical and biophysical perspective two problems are particularly intriguing. The first is the way in which a launching signal, which is spatially confined and includes only a few interacting atoms, is propagated to a large-scale conformational transition we frequently see in allosteric transitions. Hence, there is the question of how a small perturbation is magnified to yield motions of thousands of atoms. The second puzzle is of focus, coherence, and efficiency. The impact of the binding of the effector is sometimes extended over tens of angstroms. How the signal is transmitted and kept significant over such large distances in the 'noisy' molecular environment is another major direction of investigation. In the present review we examined different theoretical and computational attempts to solve the questions.

Multiscale modeling of structural dynamics underlying force generation and product release in actomyosin complex

To decrypt the mechanistic basis of myosin motor function, it is essential to probe the conformational changes in actomyosin with high spatial and temporal resolutions. In a computational effort to meet this challenge, we have performed a multiscale modeling of the allosteric couplings and transition pathway of actomyosin complex by combining coarse-grained modeling of the entire complex with all-atom molecular dynamics simulations of the active site. Our modeling of allosteric couplings at the pre-powerstroke state has pinpointed key actin-activated couplings to distant myosin parts which are critical to force generation and the sequential release of phosphate and ADP. At the post-powerstroke state, we have identified isoform-dependent couplings which underlie the reciprocal coupling between actin binding and nucleotide binding in fast Myosin II, and load-dependent ADP release in Myosin V. Our modeling of transition pathway during powerstroke has outlined a clear sequence of structural events triggered by actin binding, which lead to subsequent force generation, twisting of central beta-sheet, and the sequential release of phosphate and ADP. Finally we have performed atomistic simulations of active-site dynamics based on an on-path "transition-state" myosin conformation, which has revealed significantly weakened coordination of phosphate by Switch II, and a disrupted key salt bridge between Switch I and II. Meanwhile, the coordination of MgADP by Switch I and P loop is less perturbed. As a result, the phosphate can be released prior to MgADP. This study has shed new lights on the controversy over the structural mechanism of actin-activated phosphate release and force generation in myosin motor.

Atomically detailed simulation of the recovery stroke in myosin by Milestoning

Myosin II is a molecular motor that converts chemical to mechanical energy and enables muscle operations. After a power stroke, a recovery transition completes the cycle and returns the molecular motor to its prestroke state. Atomically detailed simulations in the framework of the Milestoning theory are used to calculate kinetics and mechanisms of the recovery stroke. Milestoning divides the process into transitions between hyper-surfaces (Milestones) along a reaction coordinate. Decorrelation of dynamics between sequential Milestones is assumed, which speeds up the atomically detailed simulations by a factor of millions. Two hundred trajectories of myosin with explicit water solvation are used to sample transitions between sequential pairs of Milestones. Collective motions of hundreds of atoms are described at atomic resolution and at the millisecond time scale. The experimentally measured transition time of about a millisecond is in good agreement with the computed time. The simulations support a sequential mechanism. In the first step the P-loop and switch 2 close on the ATP and in the second step the mechanical relaxation is induced via the relay and the SH1 helices. We propose that the entropy of switch 2 helps to drive the power stroke. Secondary structure elements are progressing through a small number of discrete states in a network of activated transitions and are assisted by side chain flips between rotameric states. The few-state sequential mechanism is likely to enhance the efficiency of the relaxation reducing the probability of off-pathway intermediates.

The hydrolysis activity of adenosine triphosphate in myosin: a theoretical analysis of anomeric effects and the nature of the transition state

Combined quantum mechanical/molecular mechanical (QM/MM) calculations with density functional theory are employed to analyze two issues related to the hydrolysis activity of adenosine triphosphate (ATP) in myosin. First, we compare the geometrical properties and electronic structure of ATP in the open (post-rigor) and closed (pre-powerstroke) active sites of the myosin motor domain. Compared to both solution and the open active site cases, the scissile P(gamma)-O(3beta) bond of ATP in the closed active site is shown to be substantially elongated. Natural bond orbital (NBO) analysis clearly shows that this structural feature is correlated with the stronger anomeric effects in the closed active site, which involve charge transfers from the lone pairs in the nonbridging oxygen in the gamma-phosphate to the antibonding orbital of the scissile bond. However, an energetic analysis finds that the ATP molecule is not significantly destabilized by the P(gamma)-O(3beta) bond elongation. Therefore, despite the notable perturbations in the geometry and electronic structure of ATP as its environment changes from solution to the hydrolysis-competent active site, ground-state destabilization is unlikely to play a major role in enhancing the hydrolysis activity in myosin. Second, two-dimensional potential energy maps are used to better characterize the energetic landscape near the hydrolysis transition state. The results indicate that the transition-state region is energetically flat and a range of structures representative of different mechanisms according to the classical nomenclature (e.g., "associative", "dissociative", and "concerted") are very close in energy. Therefore, at least in the case of ATP hydrolysis in myosin, the energetic distinction between different reaction mechanisms following the conventional nomenclature is likely small. This study highlights the importance of (i) explicitly evaluating the relevant energetic properties for determining whether a factor is essential to catalysis and (ii) broader explorations of the energy landscape beyond saddle points (even on free-energy surface) for characterizing the molecular mechanism of catalysis.

Coarse-Grained Structural Modeling of Molecular Motors Using Multibody Dynamics

Experimental and computational approaches are needed to uncover the mechanisms by which molecular motors convert chemical energy into mechanical work. In this article, we describe methods and software to generate structurally realistic models of molecular motor conformations compatible with experimental data from different sources. Coarse-grained models of molecular structures are constructed by combining groups of atoms into a system of rigid bodies connected by joints. Contacts between rigid bodies enforce excluded volume constraints, and spring potentials model system elasticity. This simplified representation allows the conformations of complex molecular motors to be simulated interactively, providing a tool for hypothesis building and quantitative comparisons between models and experiments. In an example calculation, we have used the software to construct atomically detailed models of the myosin V molecular motor bound to its actin track. The software is available at www.simtk.org.

Approximate normal mode analysis based on vibrational subsystem analysis with high accuracy and efficiency

Normal mode analysis (NMA) has been proven valuable in modeling slow conformational dynamics of biomolecular structures beyond the reach of direct molecular simulations. However, it remains computationally expensive to directly solve normal modes for large biomolecular systems. In this study, we have evaluated the accuracy and efficiency of two approximate NMA protocols-one based on our recently proposed vibrational subsystem analysis (VSA), the other based on the rotation translation block (RTB), in comparison with standard NMA that directly solves a full Hessian matrix. By properly accounting for flexibility within blocks of residues or atoms based on a subsystem-environment partition, VSA-based NMA has attained a much higher accuracy than RTB and much lower computing cost than standard NMA. Therefore, VSA enables accurate and efficient calculations of normal modes from all-atom or coarse-grained potential functions, which promise to improve conformational sampling driven by low-frequency normal modes.

Experimental investigation of the seesaw mechanism of the relay region that moves the myosin lever arm

A seesaw-like movement of the relay region upon the recovery step of myosin was recently simulated in silico. In this model the relay helix tilts around its pivoting point formed by a phenylalanine cluster (Phe(481), Phe(482), and Phe(652)), which moves the lever arm of myosin. To study the effect of the elimination of the proposed pivoting point, these phenylalanines were mutated to alanines in two Dictyostelium myosin II motor domain constructs (M(F481A, F482A) and M(F652A)). The relay movement was followed by the fluorescence change of Trp(501) located in the relay region. The steady-state and transient kinetic fluorescence experiments showed that the lack of the phenylalanine fulcrum perturbs the formation of the "up" lever arm state, and only moderate effects were found in the nucleotide binding, the formation of the "down" lever arm position, and the ATP hydrolysis steps. We conclude that the lack of the fulcrum decouples the distal part of the relay from the nucleotide binding site upon the recovery step. Our molecular dynamics simulations also showed that the conformation of the motor is not perturbed by the mutation in the down lever arm state, however, the lack of the pivoting point rearranges the dynamic pattern of the kink region of the relay helix.

Extensive conformational transitions are required to turn on ATP hydrolysis in myosin

Conventional myosin is representative of biomolecular motors in which the hydrolysis of adenosine triphosphate (ATP) is coupled to large-scale structural transitions both in and remote from the active site. The mechanism that underlies such "mechanochemical coupling," especially the causal relationship between hydrolysis and allosteric structural changes, has remained elusive despite extensive experimental and computational analyses. In this study, using combined quantum mechanical and molecular mechanical simulations and different conformations of the myosin motor domain, we provide evidence to support that regulation of ATP hydrolysis activity is not limited to residues in the immediate environment of the phosphate. Specifically, we illustrate that efficient hydrolysis of ATP depends not only on the proper orientation of the lytic water but also on the structural stability of several nearby residues, especially the Arg238-Glu459 salt bridge (the numbering of residues follows myosin II in Dictyostelium discoideum) and the water molecule that spans this salt bridge and the lytic water. More importantly, by comparing the hydrolysis activities in two motor conformations with very similar active-site (i.e., Switches I and II) configurations, which distinguished this work from our previous study, the results clearly indicate that the ability of these residues to perform crucial electrostatic stabilization relies on the configuration of residues in the nearby N-terminus of the relay helix and the "wedge loop." Without the structural support from those motifs, residues in a closed active site in the post-rigor motor domain undergo subtle structural variations that lead to consistently higher calculated ATP hydrolysis barriers than in the pre-powerstroke state. In other words, starting from the post-rigor state, turning on the ATPase activity requires not only displacement of Switch II to close the active site but also structural transitions in the N-terminus of the relay helix and the "wedge loop," which have been proposed previously to be ultimately coupled to the rotation of the converter subdomain 40 A away.

Allosteric communication in myosin V: from small conformational changes to large directed movements

The rigor to post-rigor transition in myosin, a consequence of ATP binding, plays an essential role in the Lymn–Taylor functional cycle because it results in the dissociation of the actomyosin complex after the powerstroke. On the basis of the X-ray structures of myosin V, we have developed a new normal mode superposition model for the transition path between the two states. Rigid-body motions of the various subdomains and specific residues at the subdomain interfaces are key elements in the transition. The allosteric communication between the nucleotide binding site and the U50/L50 cleft is shown to result from local changes due to ATP binding, which induce large amplitude motions that are encoded in the structure of the protein. The triggering event is the change in the interaction of switch I and the P-loop, which is stabilized by ATP binding. The motion of switch I, which is a relatively rigid element of the U50 subdomain, leads directly to a partial opening of the U50/L50 cleft; the latter is expected to weaken the binding of myosin to actin. The calculated transition path demonstrates the nature of the subdomain coupling and offers an explanation for the mutual exclusion of ATP and actin binding. The mechanism of the uncoupling of the converter from the motor head, an essential part of the transition, is elucidated. The origin of the partial untwisting of the central β-sheet in the rigor to post-rigor transition is described.

Myosins are molecular motor proteins that interact with actin filaments to perform a wide range of cellular functions. They use the universal energy storage molecule adenosine triphosphate (ATP). The functional cycle involves myosin binding to actin, a “powerstroke” leading to directed movement, and myosin release in preparation for the next step. A fundamental question concerns the mechanism by which the local structural changes due to ATP binding, hydrolysis, and products release can generate the large myosin changes of conformation required for this cycle. Here, we focus on the rigor to post-rigor transition of myosin V, which results in the release of myosin from actin. Starting from the X-ray structures of the two states, we have used the optimal superposition of normal modes to determine the transition path. The path shows the allosteric mechanism by which ATP binding leads to the opening of the U50/L50 cleft, the essential step in the unbinding of myosin from actin. More generally, the new normal-mode superposition model can be useful for describing large-amplitude conformational transitions encoded in protein structures by evolution.

Energetics of subdomain movements and fluorescence probe solvation environment change in ATP-bound myosin

Energetics of conformational changes experienced by an ATP-bound myosin head detached from actin was studied by all-atom explicit water umbrella sampling simulations. The statistics of coupling between large scale domain movements and smaller scale structural features were examined, including the closing of the ATP binding pocket, and a number of key hydrogen bond formations shown to play roles in structural and biochemical studies. The statistics for the ATP binding pocket open/close transition show an evolution of the relative stability from the open state in the early stages of the recovery stroke to the stable closed state after the stroke. The change in solvation environment of the fluorescence probe Trp507 (scallop numbering; 501 in Dictyostelium discoideum) indicates that the probe faithfully reflects the closing of the binding pocket as previously shown in experimental studies, while being directly coupled to roughly the early half of the overall large scale conformational change of the converter domain rotation. The free energy change of this solvation environment change, in particular, is -1.3 kcal/mol, in close agreement with experimental estimates. In addition, our results provide direct molecular level data allowing for interpretations of the fluorescence experiments of myosin conformational change in terms of the de-solvation of Trp side chain.

Myosin V movement: lessons from molecular dynamics studies of IQ peptides in the lever arm

Myosin V moves along actin filaments by an arm-over-arm motion, known as the lever mechanism. Each of its arms is composed of six consecutive IQ peptides that bind light chain proteins, such as calmodulin or calmodulin-like proteins. We have employed a multistage approach in order to investigate the mechanochemical structural basis of the movement of myosin V from the budding yeast Saccharomyces cerevisiae. For that purpose, we previously carried out molecular dynamics simulations of the Mlc1p-IQ2 and the Mlc1p-IQ4 protein-peptide complexes, and the present study deals with the structures of the IQ peptides when stripped from the Mlc1p protein. We have found that the crystalline structure of the IQ2 peptide retains a stable rodlike configuration in solution, whereas that of the IQ4 peptide grossly deviates from its X-ray conformation exhibiting an intrinsic tendency to curve and bend. The refolding process of the IQ4 peptide is initially driven by electrostatic interactions followed by nonpolar stabilization. Its bending appears to be affected by the ionic strength, when ionic strength higher than approximately 300 mM suppresses it from flexing. Considering that a poly-IQ sequence is the lever arm of myosin V, we suggest that the arm may harbor a joint, localized within the IQ4 sequence, enabling the elasticity of the neck of myosin V. Given that a poly-IQ sequence is present at the entire class of myosin V and the possibility that the yeast's myosin V molecule can exist either as a nonprocessive monomer or as a processive dimer depending on conditions (Krementsova, E. B., Hodges, A. R., Lu, H., and Trybus, K. M. (2006) J. Biol. Chem. 281, 6079-6086), our observations may account for a general structural feature for the myosins' arm embedded flexibility.

Intrinsic dynamics of enzymes in the unbound state and relation to allosteric regulation

In recent years, there has been a surge in the number of studies exploring the relationship between proteins' equilibrium dynamics and structural changes involved in function. An emerging concept, supported by both theory and experiments, is that under native state conditions proteins have an intrinsic ability to sample conformations that meet functional requirements. A typical example is the ability of enzymes to sample open and closed forms, irrespective of substrate, succeeded by the stabilization of one form (usually closed) upon substrate binding. This ability is structure-encoded, and plays a key role in facilitating allosteric regulation, which suggests complementing the sequence-encodes-structure paradigm of protein science by structure-encodes-dynamics-encodes-function. The emerging connection implies an evolutionary role in selecting/conserving structures based on their ability to achieve functional dynamics, and in turn, selecting sequences that fold into such 'apt' structures.

Predicting allosteric communication in myosin via a pathway of conserved residues

We present a computational method that predicts a pathway of residues that mediate protein allosteric communication. The pathway is predicted using only a combination of distance constraints between contiguous residues and evolutionary data. We applied this analysis to find pathways of conserved residues connecting the myosin ATP binding site to the lever arm. These pathway residues may mediate the allosteric communication that couples ATP hydrolysis to the lever arm recovery stroke. Having examined pre-stroke conformations of Dictyostelium, scallop, and chicken myosin II as well as Dictyostelium myosin I, we observed a conserved pathway traversing switch II and the relay helix, which is consistent with the understood need for allosteric communication in this conformation. We also examined post-rigor and rigor conformations across several myosin species. Although initial residues of these paths are more heterogeneous, all but one of these paths traverse a consistent set of relay helix residues to reach the beginning of the lever arm. We discuss our results in the context of structural elements and reported mutational experiments, which substantiate the significance of the pre-stroke pathways. Our method provides a simple, computationally efficient means of predicting a set of residues that mediate allosteric communication. We provide a refined, downloadable application and source code (on https://simtk.org) to share this tool with the wider community (https://simtk.org/home/allopathfinder).

The Structural Coupling between ATPase Activation and Recovery Stroke in the Myosin II Motor

Before the myosin motor head can perform the next power stroke, it undergoes a large conformational transition in which the converter domain, bearing the lever arm, rotates approximately 65 degrees . Simultaneous with this "recovery stroke," myosin activates its ATPase function by closing the Switch-2 loop over the bound ATP. This coupling between the motions of the converter domain and of the 40 A-distant Switch-2 loop is essential to avoid unproductive ATP hydrolysis. The coupling mechanism is determined here by finding a series of optimized intermediates between crystallographic end structures of the recovery stroke (Dictyostelium discoideum), yielding movies of the transition at atomic detail. The successive formation of two hydrogen bonds by the Switch-2 loop is correlated with the successive see-saw motions of the relay and SH1 helices that hold the converter domain. SH1 helix and Switch-2 loop communicate via a highly conserved loop that wedges against the SH1-helix upon Switch-2 closing.

Mechanochemical coupling in the myosin motor domain. II. Analysis of critical residues

An important challenge in the analysis of mechanochemical coupling in molecular motors is to identify residues that dictate the tight coupling between the chemical site and distant structural rearrangements. In this work, a systematic attempt is made to tackle this issue for the conventional myosin. By judiciously combining a range of computational techniques with different approximations and strength, which include targeted molecular dynamics, normal mode analysis, and statistical coupling analysis, we are able to identify a set of important residues and propose their relevant function during the recovery stroke of myosin. These analyses also allowed us to make connections with previous experimental and computational studies in a critical manner. The behavior of the widely used reporter residue, Trp501, in the simulations confirms the concern that its fluorescence does not simply reflect the relay loop conformation or active-site open/close but depends subtly on its microenvironment. The findings in the targeted molecular dynamics and a previous minimum energy path analysis of the recovery stroke have been compared and analyzed, which emphasized the difference and complementarity of the two approaches. In conjunction with our previous studies, the current set of investigations suggest that the modulation of structural flexibility at both the local (e.g., active-site) and domain scales with strategically placed "hotspot" residues and phosphate chemistry is likely the general feature for mechanochemical coupling in many molecular motors. The fundamental strategies of examining both collective and local changes and combining physically motivated methods and informatics-driven techniques are expected to be valuable to the study of other molecular motors and allosteric systems in general.