Electrostatic origin of the unidirectionality of walking myosin V motors

Kinetic Asymmetry and Directionality of Nonequilibrium Molecular Systems

Scientists have long been fascinated by the biomolecular machines in living systems that process energy and information to sustain life. The first synthetic molecular rotor capable of performing repeated 360° rotations due to a combination of photo- and thermally activated processes was reported in 1999. The progress in designing different molecular machines in the intervening years has been remarkable, with several outstanding examples appearing in the last few years. Despite the synthetic accomplishments, there remains confusion regarding the fundamental design principles by which the motions of molecules can be controlled, with significant intellectual tension between mechanical and chemical ways of thinking about and describing molecular machines. A thermodynamically consistent analysis of the kinetics of several molecular rotors and pumps shows that while light driven rotors operate by a power-stroke mechanism, kinetic asymmetry-the relative heights of energy barriers-is the sole determinant of the directionality of catalysis driven machines. Power-strokes-the relative depths of energy wells-play no role whatsoever in determining the sign of the directionality. These results, elaborated using trajectory thermodynamics and the nonequilibrium pump equality, show that kinetic asymmetry governs the response of many non-equilibrium chemical phenomena.

Identifying a Feasible Transition Pathway between Two Conformational States for a Protein

Proteins usually need to transit between different conformational states to fulfill their biological functions. In the mechanistic study of such transition processes by molecular dynamics simulations, identification of the minimum free energy path (MFEP) can substantially reduce the sampling space, thus enabling rigorous thermodynamic evaluation of the process. Conventionally, the MFEP is derived by iterative local optimization from an initial path, which is typically generated by simple brute force techniques like the targeted molecular dynamics (tMD). Therefore, the quality of the initial path determines the successfulness of MFEP estimation. In this work, we propose a method to improve derivation of the initial path. Through iterative relaxation-biasing simulations in a bidirectional manner, this method can construct a feasible transition pathway connecting two known states for a protein. Evaluation on small, fast-folding proteins against long equilibrium trajectories supports the good sampling efficiency of our method. When applied to larger proteins including the catalytic domain of human c-Src kinase as well as the converter domain of myosin VI, the paths generated by our method deviate significantly from those computed with the generic tMD approach. More importantly, free energy profiles and intermediate states obtained from our paths exhibit remarkable improvements over those from tMD paths with respect to both physical rationality and consistency with a priori knowledge.

Molecular Pumps and Motors

Pumps and motors are essential components of the world as we know it. From the complex proteins that sustain our cells, to the mechanical marvels that power industries, much we take for granted is only possible because of pumps and motors. Although molecular pumps and motors have supported life for eons, it is only recently that chemists have made progress toward designing and building artificial forms of the microscopic machinery present in nature. The advent of artificial molecular machines has granted scientists an unprecedented level of control over the relative motion of components of molecules through the development of kinetically controlled, away-from-thermodynamic equilibrium chemistry. We outline the history of pumps and motors, focusing specifically on the innovations that enable the design and synthesis of the artificial molecular machines central to this Perspective. A key insight connecting biomolecular and artificial molecular machines is that the physical motions by which these machines carry out their function are unambiguously in mechanical equilibrium at every instant. The operation of molecular motors and pumps can be described by trajectory thermodynamics, a theory based on the work of Onsager, which is grounded on the firm foundation of the principle of microscopic reversibility. Free energy derived from thermodynamically non-equilibrium reactions kinetically favors some reaction pathways over others. By designing molecules with kinetic asymmetry, one can engineer potential landscapes to harness external energy to drive the formation and maintenance of geometries of component parts of molecules away-from-equilibrium, that would be impossible to achieve by standard synthetic approaches.

The mechanism of DNA unwinding by the eukaryotic replicative helicase

Accurate DNA replication is tightly regulated in eukaryotes to ensure genome stability during cell division and is performed by the multi-protein replisome. At the core an AAA+ hetero-hexameric complex, Mcm2-7, together with GINS and Cdc45 form the active replicative helicase Cdc45/Mcm2-7/GINS (CMG). It is not clear how this replicative ring helicase translocates on, and unwinds, DNA. We measure real-time dynamics of purified recombinant Drosophila melanogaster CMG unwinding DNA with single-molecule magnetic tweezers. Our data demonstrates that CMG exhibits a biased random walk, not the expected unidirectional motion. Through building a kinetic model we find CMG may enter up to three paused states rather than unwinding, and should these be prevented, in vivo fork rates would be recovered in vitro. We propose a mechanism in which CMG couples ATP hydrolysis to unwinding by acting as a lazy Brownian ratchet, thus providing quantitative understanding of the central process in eukaryotic DNA replication.

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.

The FOF1 ATP synthase: from atomistic three-dimensional structure to the rotary-chemical function

Molecular motors are multi-subunit complexes that are indispensable for accomplishing various tasks of the living cells. One such molecular motor is the F_OF₁ ATP synthase that synthesizes ATP at the expense of the membrane proton gradient. Elucidating the molecular origin of the motor function is challenging despite significant advances in various experimental fields. Currently atomic simulations of whole motor complexes cannot reach to functionally relevant time scales that extend beyond the millisecond regime. Moreover, to reveal the underlying molecular origin of the function, one must model the coupled chemical and conformational events using physically and chemically meaningful multiscaling techniques. In this review, we discuss our approach to model the action of the F₁ and F_O molecular motors, where emphasis is laid on elucidating the molecular origin of the driving force that leads to directional rotation at the expense of ATP hydrolysis or proton gradients. We have used atomic structures of the motors and used hierarchical multiscaling techniques to generate low dimensional functional free energy surfaces of the complete mechano-chemical process. These free energy surfaces were studied further to calculate important characteristics of the motors, such as, rotational torque, temporal dynamics, occurrence of intermittent dwell states, etc. We also studied the result of mutating various parts of the motor domains and our observations correspond very well with the experimental findings. Overall, our studies have generated a cumulative understanding of the motor action, and especially highlight the crucial role of electrostatics in establishing the mechano-chemical coupling.

Reexamining the origin of the directionality of myosin V

The nature of the conversion of chemical energy to directional motion in myosin V is examined by careful simulations that include two complementary methods: direct Langevin Dynamics (LD) simulations with a scaled-down potential that provided a detailed time-resolved mechanism, and kinetic equations solution for the ensemble long-time propagation (based on information collected for segments of the landscape using LD simulations and experimental information). It is found that the directionality is due to the rate-limiting ADP release step rather than the potential energy of the lever arm angle. We show that the energy of the power stroke and the barriers involved in it are of minor consequence to the selectivity of forward over backward steps and instead suggest that the selective release of ADP from a postrigor myosin motor head promotes highly selective and processive myosin V. Our model is supported by different computational methods-LD simulations, Monte Carlo simulations, and kinetic equations solution-as well as by structure-based binding energy calculations.

Simulating the dynamics of the mechanochemical cycle of myosin-V

The detailed dynamics of the cycle of myosin-V are explored by simulation approaches, examining the nature of the energy-driven motion. Our study started with Langevin dynamics (LD) simulations on a very coarse landscape with a single rate-limiting barrier and reproduced the stall force and the hand-over-hand dynamics. We then considered a more realistic landscape and used time-dependent Monte Carlo (MC) simulations that allowed trajectories long enough to reproduce the force/velocity characteristic sigmoidal correlation, while also reproducing the hand-over-hand motion. Overall, our study indicated that the notion of a downhill lever-up to lever-down process (popularly known as the powerstroke mechanism) is the result of the energetics of the complete myosin-V cycle and is not the source of directional motion or force generation on its own. The present work further emphasizes the need to use well-defined energy landscapes in studying molecular motors in general and myosin in particular.

ATP-dependent interplay between local and global conformational changes in the myosin motor

The ATPase active site of myosin is located at the core of the motor head. During the Lymn-Taylor actomyosin contractile cycle, small conformational changes in the active site upon ATP binding, ATP hydrolysis and ADP/P_i release are accompanied by large conformational transitions of the motor domains, such as opening and closing of the actin binding cleft and the movement of lever arm. Here, our previous computational studies of myosin are summarized in a comprehensive model at the level of atomic detail. Molecular movies show how the successive domain motions during the ATP induced actin dissociation and the recovery stroke are coupled with the precise positioning of the key catalytic groups in the active site. This leads to a precise timing of the activation of the ATPase function: it allows ATP hydrolysis only after unbinding from actin and the priming of the lever arm, both pre-requisites for an efficient functioning of the motor during the subsequent power stroke. These coupling mechanisms constitute essential principles of every myosin motor, of which the ATP-site can be seen as the central allosteric control unit. © 2016 Wiley Periodicals, Inc.

Strain Mediated Adaptation Is Key for Myosin Mechanochemistry: Discovering General Rules for Motor Activity

A structure-based model of myosin motor is built in the same spirit of our early work for kinesin-1 and Ncd towards physical understanding of its mechanochemical cycle. We find a structural adaptation of the motor head domain in post-powerstroke state that signals faster ADP release from it compared to the same from the motor head in the pre-powerstroke state. For dimeric myosin, an additional forward strain on the trailing head, originating from the postponed powerstroke state of the leading head in the waiting state of myosin, further increases the rate of ADP release. This coordination between the two heads is the essence of the processivity of the cycle. Our model provides a structural description of the powerstroke step of the cycle as an allosteric transition of the converter domain in response to the P_i release. Additionally, the variation in structural elements peripheral to catalytic motor domain is the deciding factor behind diverse directionalities of myosin motors (myosin V & VI). Finally, we observe that there are general rules for functional molecular motors across the different families. Allosteric structural adaptation of the catalytic motor head in different nucleotide states is crucial for mechanochemistry. Strain-mediated coordination between motor heads is essential for processivity and the variation of peripheral structural elements is essential for their diverse functionalities.

Molecular motors are perhaps the most important proteins present in the cell. The importance specifically lies with the fact that these proteins use the chemical energy source (such as ATP) of the cell to generate mechanical work and perform a wide range of functionalities. In this article, we generalize the idea of using structure-based models to explore the mechanochemistry of myosin molecular motors in structural terms. We find that a structural adaptation of the motor head domain in post-powerstroke state signals faster ADP release from the trailing head to maintain its processivity while directionality arises from a careful design of peripheral structural elements. These results along with our earlier results on other motors provide a general rule for motor activity.

Quantum mechanical calculation of electric fields and vibrational Stark shifts at active site of human aldose reductase

Recent advance in biophysics has made it possible to directly measure site-specific electric field at internal sites of proteins using molecular probes with C = O or C≡N groups in the context of vibrational Stark effect. These measurements directly probe changes of electric field at specific protein sites due to, e.g., mutation and are very useful in protein design. Computational simulation of the Stark effect based on force fields such as AMBER and OPLS, while providing good insight, shows large errors in comparison to experimental measurement due to inherent difficulties associated with point charge based representation of force fields. In this study, quantum mechanical calculation of protein's internal electrostatic properties and vibrational Stark shifts was carried out by using electrostatically embedded generalized molecular fractionation with conjugate caps method. Quantum calculated change of mutation-induced electric field and vibrational Stark shift is reported at the internal probing site of enzyme human aldose reductase. The quantum result is in much better agreement with experimental data than those predicted by force fields, underscoring the deficiency of traditional point charge models describing intra-protein electrostatic properties.

The Physics and Physical Chemistry of Molecular Machines

The concept of a "power stroke"-a free-energy releasing conformational change-appears in almost every textbook that deals with the molecular details of muscle, the flagellar rotor, and many other biomolecular machines. Here, it is shown by using the constraints of microscopic reversibility that the power stroke model is incorrect as an explanation of how chemical energy is used by a molecular machine to do mechanical work. Instead, chemically driven molecular machines operating under thermodynamic constraints imposed by the reactant and product concentrations in the bulk function as information ratchets in which the directionality and stopping torque or stopping force are controlled entirely by the gating of the chemical reaction that provides the fuel for the machine. The gating of the chemical free energy occurs through chemical state dependent conformational changes of the molecular machine that, in turn, are capable of generating directional mechanical motions. In strong contrast to this general conclusion for molecular machines driven by catalysis of a chemical reaction, a power stroke may be (and often is) an essential component for a molecular machine driven by external modulation of pH or redox potential or by light. This difference between optical and chemical driving properties arises from the fundamental symmetry difference between the physics of optical processes, governed by the Bose-Einstein relations, and the constraints of microscopic reversibility for thermally activated processes.

Principles and Overview of Sampling Methods for Modeling Macromolecular Structure and Dynamics

Investigation of macromolecular structure and dynamics is fundamental to understanding how macromolecules carry out their functions in the cell. Significant advances have been made toward this end in silico, with a growing number of computational methods proposed yearly to study and simulate various aspects of macromolecular structure and dynamics. This review aims to provide an overview of recent advances, focusing primarily on methods proposed for exploring the structure space of macromolecules in isolation and in assemblies for the purpose of characterizing equilibrium structure and dynamics. In addition to surveying recent applications that showcase current capabilities of computational methods, this review highlights state-of-the-art algorithmic techniques proposed to overcome challenges posed in silico by the disparate spatial and time scales accessed by dynamic macromolecules. This review is not meant to be exhaustive, as such an endeavor is impossible, but rather aims to balance breadth and depth of strategies for modeling macromolecular structure and dynamics for a broad audience of novices and experts.

Irrelevance of the power stroke for the directionality, stopping force, and optimal efficiency of chemically driven molecular machines

A simple model for a chemically driven molecular walker shows that the elastic energy stored by the molecule and released during the conformational change known as the power-stroke (i.e., the free-energy difference between the pre- and post-power-stroke states) is irrelevant for determining the directionality, stopping force, and efficiency of the motor. Further, the apportionment of the dependence on the externally applied force between the forward and reverse rate constants of the power-stroke (or indeed among all rate constants) is irrelevant for determining the directionality, stopping force, and efficiency of the motor. Arguments based on the principle of microscopic reversibility demonstrate that this result is general for all chemically driven molecular machines, and even more broadly that the relative energies of the states of the motor have no role in determining the directionality, stopping force, or optimal efficiency of the machine. Instead, the directionality, stopping force, and optimal efficiency are determined solely by the relative heights of the energy barriers between the states. Molecular recognition--the ability of a molecular machine to discriminate between substrate and product depending on the state of the machine--is far more important for determining the intrinsic directionality and thermodynamics of chemo-mechanical coupling than are the details of the internal mechanical conformational motions of the machine. In contrast to the conclusions for chemical driving, a power-stroke is very important for the directionality and efficiency of light-driven molecular machines and for molecular machines driven by external modulation of thermodynamic parameters.

Huxley's Model for Muscle Contraction Revisited: The Importance of Microscopic Reversibility

Andrew Huxley's model for muscle contraction is the first mechanistic description of how an energy-providing chemical reaction, ATP hydrolysis, can be coupled by a molecule (myosin) to do work in the environment in a cyclic process. The model was originally used to fit experimentally obtained force vs velocity curves, and has served as a paradigm for understanding mechanochemical coupling ever since. Despite the remarkable success in fitting kinetic data, Huxley's model is thermodynamically inconsistent in several regards, most notably in its failure to include thermal noise in the description of the mechanical transitions by which motion occurs. This inconsistency has led subsequent workers to incorrect conclusions regarding the importance of mechanical transitions for determining the direction of motion, the efficiency of energy conversion, the ratio of forward to backward steps, and the applied force necessary to stop the motion of chemically driven molecular motors. In this chapter an extension of Huxley's model is described where the principle of microscopic reversibility provides a framework for developing a thermodynamically consistent description of a molecular machine. The results show clearly that mechanical strain and the so-called "power stroke" are irrelevant for determining the directionality and thermodynamic properties of any chemically driven molecular motor. Instead these properties are controlled entirely by the chemical specificity that describes how the relative rates of the ATP hydrolysis reaction depend, by allosteric interactions, on the mechanical state of the molecule. This mechanism has been termed an "information ratchet" in the literature. In contrast to the results for chemical driving, a power stroke can be a key component for the operation of an optically driven motor, the transitions of which do not obey microscopic reversibility.