A coarse-grained normal mode approach for macromolecules: an efficient implementation and application to Ca(2+)-ATPase

A block normal mode (BNM) algorithm, originally proposed by Tama et al., (Proteins Struct. Func. Genet. 41:1-7, 2000) was implemented into the simulation program CHARMM. The BNM approach projects the hessian matrix into local translation/rotation basis vectors and, therefore, dramatically reduces the size of the matrix involved in diagonalization. In the current work, by constructing the atomic hessian elements required in the projection operation on the fly, the memory requirement for the BNM approach has been significantly reduced from that of standard normal mode analysis and previous implementation of BNM. As a result, low frequency modes, which are of interest in large-scale conformational changes of large proteins or protein-nucleic acid complexes, can be readily obtained. Comparison of the BNM results with standard normal mode analysis for a number of small proteins and nucleic acids indicates that many properties dominated by low frequency motions are well reproduced by BNM; these include atomic fluctuations, the displacement covariance matrix, vibrational entropies, and involvement coefficients for conformational transitions. Preliminary application to a fairly large system, Ca(2+)-ATPase (994 residues), is described as an example. The structural flexibility of the cytoplasmic domains (especially domain N), correlated motions among residues on domain interfaces and displacement patterns for the transmembrane helices observed in the BNM results are discussed in relation to the function of Ca(2+)-ATPase. The current implementation of the BNM approach has paved the way for developing efficient sampling algorithms with molecular dynamics or Monte Carlo for studying long-time scale dynamics of macromolecules.     

Cooperativity in the motor activities of the ATP-fueled molecular motors

Kinesin, myosin and F1-ATPase are multi-domain molecular motors with multiple catalytic subunits. The motor mechanochemics are achieved via the conversion of ATP hydrolysis energy into forces and motions. We find that the catalysis of these molecular motors do not follow the simple Michaelis-Menten mechanism. The motor activities, such as the hydrolysis or processive rates, of kinesin, myosin and F1-ATPase have a complex ATP-dependent cooperativity. To understand this complexity in kinetics and mechanochemics, we develop a conformation correlation theory of cooperativity for the ATP-fueled motor proteins. The quantitative analysis and simulations indicate that cooperativity is induced by the conformational coupling of binding states of different subunits and prevails in the motor activities.     

Dynamic and coordinating domain motions in the active subunits of the F1-ATPase molecular motor

F1-ATPase is a rotary molecular motor crucial for various cellular functions. In F1-ATPase, the rotation of the gammadeltaepsilon subunits against the hexameric alpha(3)beta(3) subunits is highly coordinative, driven by ATP hydrolysis and structural changes at three beta subunits. However, the dynamical and coordinating structural transitions in the beta subunits are not fully understood at the molecular level. Here we examine structural transitions and domain motions in the active subunits of F1-ATPase via dynamical domain analysis of the alpha(3)beta(3)gammadeltaepsilon complex. The domain movement and hinge axes and bending residues have been identified and determined for various conformational changes of the beta-subunits. P-loop and the ATP-binding pocket are for the first time found to play essential mechanical functions additional to the catalytic roles. The cooperative conformational changes pertaining to the rotary mechanism of F1-ATPase appears to be more complex than Boyer's 'bi-site' activity. These findings provide unique molecular insights into dynamic and cooperative domain motions in F1-ATPase.     

A normal mode analysis of structural plasticity in the biomolecular motor F(1)-ATPase

Normal modes have been used to explore the inherent flexibility of the alpha, beta and gamma subunits of F(1)-ATPase in isolation and as part of the alpha(3)beta(3)gamma complex. It was found that the structural plasticity of the gamma and beta subunits, in particular, correlates with their functions. The N and C-terminal helices forming the coiled-coil domain of the gamma subunit are highly flexible in the isolated subunit, but more rigid in the alpha(3)beta(3)gamma complex due to interactions with other subunits. The globular domain of the gamma subunit is structurally relatively rigid when isolated and in the alpha(3)beta(3)gamma complex; this is important for its functional role in coupling the F(0) and F(1) complex of ATP synthase and in inducing the conformational changes of the beta subunits in synthesis. Most important, the character of the lowest-frequency modes of the beta(E) subunit is highly correlated with the large beta(E) --> beta(TP) transition. This holds for the C-terminal domain and the nucleotide-binding domain, which undergo significant conformational transitions in the functional cycle of F(1)-ATPase. This is most evident in the ligand-free beta(E) subunit; the flexibility in the nucleotide-binding domain is reduced somewhat in the beta(TP) subunit in the presence of Mg(2+).ATP. The low-frequency modes of the alpha(3)beta(3)gamma complex show that the motions of the globular domain of the gamma subunit and of the C-terminal and nucleotide binding domains of the beta(E) subunits are coupled, in accord with their function. Overall, the normal mode analysis reveals that F(1)-ATPase, like other macromolecular assemblies, has the intrinsic structural flexibility required for its function encoded in its sequence and three-dimensional structure. This inherent plasticity is an essential aspect of assuring a small free energy cost for the large-scale conformational transition that occurs in molecular motors.     

The requirement for mechanical coupling between head and S2 domains in smooth muscle myosin ATPase regulation and its implications for dimeric motor function

A combination of experimental structural data, homology modelling and elastic network normal mode analysis is used to explore how coupled motions between the two myosin heads and the dimerization domain (S2) in smooth muscle myosin II determine the domain movements required to achieve the inhibited state of this ATP-dependent molecular motor. These physical models rationalize the empirical requirement for at least two heptads of non-coiled alpha-helix at the junction between the myosin heads and S2, and the dependence of regulation on S2 length. The results correlate well with biochemical data regarding altered conformational-dependent solubility and stability. Structural models of the conformational transition between putative active states and the inhibited state show that torsional flexibility of the S2 alpha-helices is a key mechanical requirement for myosin II regulation. These torsional motions of the myosin heads about their coiled coil alpha-helices affect the S2 domain structure, which reciprocally affects the motions of the myosin heads. This inter-relationship may explain a large body of data on function of molecular motors that form dimers through a coiled-coil domain.     

Electrostatic interactions in catalytic centers of F1-ATPase

The first part of this paper is a brief review of works concerned with the mechanisms of functioning of F0F1-ATP synthases. F0F1-ATP syntheses operate as rotating molecular machines that provide the synthesis of ATP from ADP and inorganic phosphate (Pi) in mitochondria, chloroplasts, and bacteria at the expense of the energy of electrochemical gradient of hydrogen ions generated across energy-transducing mitochondrial, chloroplast or, bacterial membranes. A distinguishing feature of these enzymes is that they operate as rotary molecular motors. In the second part of the work, we calculated the contribution of electrostatic interactions between charged groups of a substrate (MgATP), reaction products (MgADP and Pi), and charged amino acid residues of the F1-ATPase molecule to energy changes associated with the binding of ATP and its chemical transformations in the catalytic centers located at the interface of the alpha- and beta-subunits of the enzyme (oligomer complex alpha 3 beta 3 gamma of bovine mitochondrial ATPase). The catalytic cycle of ATP hydrolysis considered in the work includes conformational changes of alpha- and beta-subunits caused by unidirectional rotations of the central gamma-subunit. The results of our calculations are consistent with the idea that the energetically favorable process of ATP binding to the "open" catalytic center of F1-ATPase initiates the rotation of the gamma-subunit followed by ATP hydrolysis in another ("closed") catalytic center of the enzyme.     

Single molecule measurements and molecular motors

Single molecule imaging and manipulation are powerful tools in describing the operations of molecular machines like molecular motors. The single molecule measurements allow a dynamic behaviour of individual biomolecules to be measured. In this paper, we describe how we have developed single molecule measurements to understand the mechanism of molecular motors. The step movement of molecular motors associated with a single cycle of ATP hydrolysis has been identified. The single molecule measurements that have sensitivity to monitor thermal fluctuation have revealed that thermal Brownian motion is involved in the step movement of molecular motors. Several mechanisms have been suggested in different motors to bias random thermal motion to directional movement.     

Effect of medium viscosity on the activity of myosin ATPase

The influence of increased medium viscosity on the activity of myosin Ca2+-ATPase has been studied in 28, 45 and 60% water-sucrose solutions at 25 degrees C. In the wide range of viscosities (10 divided by 430 mp) the rate constant of ATP hydrolysis displays the negative power-law dependence on solution viscosity with an index approximately -0,5. The obtained data confirm an idea about the existence of direct connection between the low-frequency liquid relaxations and structural dynamics of proteins and enzymes.     

Direct observation of the myosin Va recovery stroke that contributes to unidirectional stepping along actin

Myosins are ATP-driven linear molecular motors that work as cellular force generators, transporters, and force sensors. These functions are driven by large-scale nucleotide-dependent conformational changes, termed "strokes"; the "power stroke" is the force-generating swinging of the myosin light chain-binding "neck" domain relative to the motor domain "head" while bound to actin; the "recovery stroke" is the necessary initial motion that primes, or "cocks," myosin while detached from actin. Myosin Va is a processive dimer that steps unidirectionally along actin following a "hand over hand" mechanism in which the trailing head detaches and steps forward ～72 nm. Despite large rotational Brownian motion of the detached head about a free joint adjoining the two necks, unidirectional stepping is achieved, in part by the power stroke of the attached head that moves the joint forward. However, the power stroke alone cannot fully account for preferential forward site binding since the orientation and angle stability of the detached head, which is determined by the properties of the recovery stroke, dictate actin binding site accessibility. Here, we directly observe the recovery stroke dynamics and fluctuations of myosin Va using a novel, transient caged ATP-controlling system that maintains constant ATP levels through stepwise UV-pulse sequences of varying intensity. We immobilized the neck of monomeric myosin Va on a surface and observed real time motions of bead(s) attached site-specifically to the head. ATP induces a transient swing of the neck to the post-recovery stroke conformation, where it remains for ～40 s, until ATP hydrolysis products are released. Angle distributions indicate that the post-recovery stroke conformation is stabilized by ≥ 5 k(B)T of energy. The high kinetic and energetic stability of the post-recovery stroke conformation favors preferential binding of the detached head to a forward site 72 nm away. Thus, the recovery stroke contributes to unidirectional stepping of myosin Va.     

Dynamic conformational changes due to the ATP hydrolysis in the motor domain of myosin: 10-ns molecular dynamics simulations

Muscle contraction is caused by directed movement of myosin heads along actin filaments. This movement is triggered by ATP hydrolysis, which occurs within the motor domain of myosin. The mechanism for this intramolecular process remains unknown owing to a lack of ways to observe the detailed motions of each atom in the myosin molecule. We carried out 10-ns all-atom molecular dynamics simulations to investigate the types of dynamic conformational changes produced in the motor domain by the energy released from ATP hydrolysis. The results revealed that the thermal fluctuations modulated by perturbation of ATP hydrolysis are biased in one direction that is relevant to directed movement of the myosin head along the actin filament.     

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 Å away.     

Three myosin V structures delineate essential features of chemo-mechanical transduction

The molecular motor, myosin, undergoes conformational changes in order to convert chemical energy into force production. Based on kinetic and structural considerations, we assert that three crystal forms of the myosin V motor delineate the conformational changes that myosin motors undergo upon detachment from actin. First, a motor domain structure demonstrates that nucleotide-free myosin V adopts a specific state (rigor-like) that is not influenced by crystal packing. A second structure reveals an actomyosin state that favors rapid release of ADP, and differs from the rigor-like state by a P-loop rearrangement. Comparison of these structures with a third structure, a 2.0 angstroms resolution structure of the motor bound to an ATP analog, illuminates the structural features that provide communication between the actin interface and nucleotide-binding site. Paramount among these is a region we name the transducer, which is composed of the seven-stranded beta-sheet and associated loops and linkers. Reminiscent of the beta-sheet distortion of the F1-ATPase, sequential distortion of this transducer region likely controls sequential release of products from the nucleotide pocket during force generation.     

Nanoseconds molecular dynamics simulation of primary mechanical energy transfer steps in F1-ATP synthase

The mitochondrial membrane protein FoF1-ATP synthase synthesizes adenosine triphosphate (ATP), the universal currency of energy in the cell. This process involves mechanochemical energy transfer from a rotating asymmetric gamma-'stalk' to the three active sites of the F1 unit, which drives the bound ATP out of the binding pocket. Here, the primary structural changes associated with this energy transfer in F1-ATP synthase were studied with multi-nanosecond molecular dynamics simulations. By forced rotation of the gamma-stalk that mimics the effect of proton motive Fo-rotation during ATP synthesis, a time-resolved atomic model for the structural changes in the F1 part in terms of propagating conformational motions is obtained. For these, different time scales are found, which allows the separation of nanosecond from microsecond conformational motions. In the simulations, rotation of the gamma-stalk lowers the ATP affinity of the betaTP binding pocket and triggers fast, spontaneous closure of the empty betaE subunit. The simulations explain several mutation studies and the reduced hydrolysis rate of gamma-depleted F1-ATPase.     

Coupling of Lever Arm Swing and Biased Brownian Motion in Actomyosin

An important unresolved problem associated with actomyosin motors is the role of Brownian motion in the process of force generation. On the basis of structural observations of myosins and actins, the widely held lever-arm hypothesis has been proposed, in which proteins are assumed to show sequential structural changes among observed and hypothesized structures to exert mechanical force. An alternative hypothesis, the Brownian motion hypothesis, has been supported by single-molecule experiments and emphasizes more on the roles of fluctuating protein movement. In this study, we address the long-standing controversy between the lever-arm hypothesis and the Brownian motion hypothesis through in silico observations of an actomyosin system. We study a system composed of myosin II and actin filament by calculating free-energy landscapes of actin-myosin interactions using the molecular dynamics method and by simulating transitions among dynamically changing free-energy landscapes using the Monte Carlo method. The results obtained by this combined multi-scale calculation show that myosin with inorganic phosphate (P_i) and ADP weakly binds to actin and that after releasing P_i and ADP, myosin moves along the actin filament toward the strong-binding site by exhibiting the biased Brownian motion, a behavior consistent with the observed single-molecular behavior of myosin. Conformational flexibility of loops at the actin-interface of myosin and the N-terminus of actin subunit is necessary for the distinct bias in the Brownian motion. Both the 5.5–11 nm displacement due to the biased Brownian motion and the 3–5 nm displacement due to lever-arm swing contribute to the net displacement of myosin. The calculated results further suggest that the recovery stroke of the lever arm plays an important role in enhancing the displacement of myosin through multiple cycles of ATP hydrolysis, suggesting a unified movement mechanism for various members of the myosin family.     

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

Although the major structural transitions in molecular motors are often argued to couple to the binding of Adenosine triphosphate (ATP), the recovery stroke in the conventional myosin has been shown to be dependent on the hydrolysis of ATP. To obtain a clearer mechanistic picture for such "mechanochemical coupling" in myosin, equilibrium active-site simulations with explicit solvent have been carried out to probe the behavior of the motor domain as functions of the nucleotide chemical state and conformation of the converter/relay helix. In conjunction with previous studies of ATP hydrolysis with different active-site conformations and normal mode analysis of structural flexibility, the results help establish an energetics-based framework for understanding the mechanochemical coupling. It is proposed that the activation of hydrolysis does not require the rotation of the lever arm per se, but the two processes are tightly coordinated because both strongly couple to the open/close transition of the active site. The underlying picture involves shifts in the dominant population of different structural motifs as a consequence of changes elsewhere in the motor domain. The contribution of this work and the accompanying paper [] is to propose the actual mechanism behind these "population shifts" and residues that play important roles in the process. It is suggested that structural flexibilities at both the small and large scales inherent to the motor domain make it possible to implement tight couplings between different structural motifs while maintaining small free-energy drops for processes that occur in the detached states, which is likely a feature shared among many molecular motors. The significantly different flexibility of the active site in different X-ray structures with variable level arm orientations supports the notation that external force sensed by the lever arm may transmit into the active site and influence the chemical steps (nucleotide hydrolysis and/or binding).     

Predicting order of conformational changes during protein conformational transitions using an interpolated elastic network model

The decryption of sequence of structural events during protein conformational transitions is essential to a detailed understanding of molecular functions ofvarious biological nanomachines. Coarse‐grained models have proven useful by allowing highly efficient simulations of protein conformational dynamics. By combining two coarse‐grained elastic network models constructed based on the beginning and end conformations of a transition, we have developed an interpolated elastic network model to generate a transition pathway between the two protein conformations. For validation, we have predicted the order of local and global conformational changes during key ATP‐driven transitions in three important biological nanomachines (myosin, F₁ ATPase and chaperonin GroEL). We have found that the local conformational change associated with the closing of active site precedes the global conformational change leading to mechanical motions. Our finding is in good agreement with the distribution of intermediate experimental structures, and it supports the importance of local motions at active site to drive or gate various conformational transitions underlying the workings of a diverse range of biological nanomachines. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

Structural Plasticity and Conformational Transitions of HIV Envelope Glycoprotein gp120

HIV envelope glycoproteins undergo large-scale conformational changes as they interact with cellular receptors to cause the fusion of viral and cellular membranes that permits viral entry to infect targeted cells. Conformational dynamics in HIV gp120 are also important in masking conserved receptor epitopes from being detected for effective neutralization by the human immune system. Crystal structures of HIV gp120 and its complexes with receptors and antibody fragments provide high-resolution pictures of selected conformational states accessible to gp120. Here we describe systematic computational analyses of HIV gp120 plasticity in such complexes with CD4 binding fragments, CD4 mimetic proteins, and various antibody fragments. We used three computational approaches: an isotropic elastic network analysis of conformational plasticity, a full atomic normal mode analysis, and simulation of conformational transitions with our coarse-grained virtual atom molecular mechanics (VAMM) potential function. We observe collective sub-domain motions about hinge points that coordinate those motions, correlated local fluctuations at the interfacial cavity formed when gp120 binds to CD4, and concerted changes in structural elements that form at the CD4 interface during large-scale conformational transitions to the CD4-bound state from the deformed states of gp120 in certain antibody complexes.     

Weak Intra-Ring Allosteric Communications of the Archaeal Chaperonin Thermosome Revealed by Normal Mode Analysis

Chaperonins are molecular machines that use ATP-driven cycles to assist misfolded substrate proteins to reach the native state. During the functional cycle, these machines adopt distinct nucleotide-dependent conformational states, which reflect large-scale allosteric changes in individual subunits. Distinct allosteric kinetics has been described for the two chaperonin classes. Bacterial (group I) chaperonins, such as GroEL, undergo concerted subunit motions within each ring, whereas archaeal and eukaryotic chaperonins (group II) undergo sequential subunit motions. We study these distinct mechanisms through a comparative normal mode analysis of monomer and double-ring structures of the archaeal chaperonin thermosome and GroEL. We find that thermosome monomers of each type exhibit common low-frequency behavior of normal modes. The observed distinct higher-frequency modes are attributed to functional specialization of these subunit types. The thermosome double-ring structure has larger contribution from higher-frequency modes, as it is found in the GroEL case. We find that long-range intersubunit correlation of amino-acid pairs is weaker in the thermosome ring than in GroEL. Overall, our results indicate that distinct allosteric behavior of the two chaperonin classes originates from different wiring of individual subunits as well as of the intersubunit communications.