Unidirectional Brownian motion observed in an in silico single molecule experiment of an actomyosin motor

Electrostatic Ratchet for Successive Peptide Synthesis in Nonribosomal Molecular Machine RimK

A nonribosomal peptide-synthesizing molecular machine, RimK, adds l-glutamic acids to the C-terminus of ribosomal protein S6 (RpsF) in vivo and synthesizes poly-α-glutamates in vitro. However, the mechanism of the successive glutamate addition, which is fueled by ATP, remains unclear. Here, we investigate the successive peptide-synthesizing mechanism of RimK via the molecular dynamics (MD) simulation of glutamate binding. We first show that RimK adopts three stable structural states with respect to the ATP-binding loop and the triphosphate chain of the bound ATP. We then show that a glutamate in solution preferentially binds to a positively charged belt-like region of RimK and the bound glutamate exhibits Brownian motion along the belt. The binding-energy landscape shows that the open-to-closed transition of the ATP-binding loop and the bent-to-straight transition of the triphosphate chain of ATP can function as an electrostatic ratchet that guides the bound glutamate to the active site. We then show the binding site of the second glutamate, which allows us to infer the ligation mechanism. Consistent with MD results, the crystal structure of RimK we obtained in the presence of RpsF presents an electron density that is presumed to correspond to the C-terminus of RpsF. We finally propose a mechanism for the successive peptide synthesis by RimK and discuss its similarity to other molecular machines.

Landscape-Based View on the Stepping Movement of Myosin VI

Myosin VI dimer walks toward the minus end of the actin filament with a large and variable step size of 25–36 nm. Two competing models have been put forward to explain this large step size. The Spudich model assumes that the myosin VI dimer associates at a distal tail near the cargo-binding domain, which makes two full-length single α-helix (SAH) domains serve as long legs. In contrast, the Houdusse–Sweeney model assumes that the association occurs in the middle (between residues 913 and 940) of the SAH domain and that the three-helix bundles unfold to ensure the large step size. Their consistency with the observation of stepping motion with a large and variable step size has not been examined in detail. To compare the two proposed models of myosin VI, we computationally characterized the free energy landscape experienced by the leading head during the stepping movement along the actin filament using the elastic network model of two heads and an implicit model of the SAH domains. Our results showed that the Spudich model is more consistent with the 25–36 nm step size than the Houdusse–Sweeney model. The unfolding of the three-helix bundles gives rise to the free energy bias toward a shorter distance between two heads. Besides, the stiffness of the SAH domain is a key factor for giving strong energetic bias toward the longer distance of stepping. Free energy analysis of the stepping motion complements the visual inspection of static structures and enables a deeper understanding of underlying mechanisms of molecular motors.

Structure and Dynamics of the Flexible Cardiac Troponin T Linker Domain in a Fully Reconstituted Thin Filament

The structural analysis of large protein complexes has been greatly enhanced through the application of electron microscopy techniques. One such multiprotein complex, the cardiac thin filament (cTF), has cyclic interactions with thick filament proteins to drive contraction of the heart that has recently been the subject of such studies. As important as these studies are, they provide limited or no information on highly flexible regions that in isolation would be characterized as inherently disordered. One such region is the extended cardiac troponin T (cTnT) linker between the regions of cTnT which have been labeled TNT1 and TNT2. It comprises a hinge region (residues 158-166) and a highly flexible region (residues 167-203). Critically, this region modulates the troponin/tropomyosin complex's position across the actin filament. Thus, the cTnT linker structure and dynamics are central to the regulation of the function of cardiac muscles, but up to now, it was ill-understood. To establish the cTnT linker structure, we coupled an atomistic computational cTF model with time-resolved fluorescence resonance energy transfer measurements in both ±Ca²⁺ conditions utilizing fully reconstituted cTFs. We mapped the cTnT linker's positioning across the actin filament, and by coupling the experimental results to computation, we found mean structures and ranges of motion of this part of the complex. With this new insight, we can now address cTnT linker structural dynamics in both myofilament activation and disease.

Five-Site Model for Brownian Dynamics Simulations of a Molecular Walker in Three Dimensions

Motor proteins play an important role in many biological processes and have inspired the development of synthetic analogues. Molecular walkers, such as kinesin, dynein, and myosin V, fulfill a diverse set of functions including transporting cargo along tracks, pulling molecules through membranes, and deforming fibers. The complexity of molecular motors and their environment makes it difficult to model the detailed dynamics of molecular walkers over long time scales. In this work, we present a simple, three-dimensional model for a molecular walker on a bead-spring substrate. The walker is represented by five spherically symmetric particles that interact through common intermolecular potentials and can be simulated efficiently in Brownian dynamics simulations. The movement of motor protein walkers entails energy conversion through ATP hydrolysis while artificial motors typically rely on a local conversion of energy supplied through external fields. We model energy conversion through rate equations for mechanochemical states that couple positional and chemical degrees of freedom and determine the walker conformation through interaction potential parameters. We perform Brownian dynamics simulations for two scenarios: In the first, the model walker transports cargo by walking on a substrate whose ends are fixed. In the second, a tethered motor pulls a mobile substrate chain against a variable force. We measure relative displacements and determine the effects of cargo size and retarding force on the efficiency of the walker. We find that, while the efficiency of our model walker is less than for the biological system, our simulations reproduce trends observed in single-molecule experiments on kinesin. In addition, the model and simulation method presented here can be readily adapted to biological and synthetic systems with multiple walkers.

Biased Brownian Motion of KIF1A and the Role of Tubulin's C-Terminal Tail Studied by Molecular Dynamics Simulation

KIF1A is a kinesin family protein that moves over a long distance along the microtubule (MT) to transport synaptic vesicle precursors in neurons. A single KIF1A molecule can move toward the plus-end of MT in the monomeric form, exhibiting the characteristics of biased Brownian motion. However, how the bias is generated in the Brownian motion of KIF1A has not yet been firmly established. To elucidate this, we conducted a set of molecular dynamics simulations and observed the binding of KIF1A to MT. We found that KIF1A exhibits biased Brownian motion along MT as it binds to MT. Furthermore, we show that the bias toward the plus-end is generated by the ratchet-like energy landscape for the KIF1A-MT interaction, in which the electrostatic interaction and the negatively-charged C-terminal tail (CTT) of tubulin play an essential role. The relevance to the post-translational modifications of CTT is also discussed.

Gene Silencing Mechanisms Revealed by Dynamics of Guide, Target, and Duplex Binding to Argonaute

Argonaute (Ago) protein plays a central role in silencing gene expression by binding a "guide" strand to the base-pair with a complementary mRNA and degrading the mRNA. The current understanding of how Ago-guide and Ago-guide-mRNA complexes assemble is based mainly on static crystal structures; the associated kinetic pathways remain unknown/unclear. By simulating the successive binding of guide/target strand to Thermus thermophilus Ago (TtAgo) and computing the respective free energy landscapes, we directly visualize how TtAgo silencing complexes form and function. We show that the guide binding rate depends on its initial loading position onto TtAgo. Subsequent target recognition beyond the scissile 10-11 nucleotides must overcome a substantial energy barrier for TtAgo's nucleotide-binding groove to expand widely. This work reveals novel roles for the core TtAgo domains and shows how the kinetic barriers that must be overcome for critical structural changes to occur lead to target repression/cleavage.

The Work of Titin Protein Folding as a Major Driver in Muscle Contraction

Single-molecule atomic force microscopy and magnetic tweezers experiments have demonstrated that titin immunoglobulin (Ig) domains are capable of folding against a pulling force, generating mechanical work that exceeds that produced by a myosin motor. We hypothesize that upon muscle activation, formation of actomyosin cross bridges reduces the force on titin, causing entropic recoil of the titin polymer and triggering the folding of the titin Ig domains. In the physiological force range of 4-15 pN under which titin operates in muscle, the folding contraction of a single Ig domain can generate 200% of the work of entropic recoil and occurs at forces that exceed the maximum stalling force of single myosin motors. Thus, titin operates like a mechanical battery, storing elastic energy efficiently by unfolding Ig domains and delivering the charge back by folding when the motors are activated during a contraction. We advance the hypothesis that titin folding and myosin activation act as inextricable partners during muscle contraction.

Moving beyond simple answers to complex disorders in sarcomeric cardiomyopathies: the role of integrated systems

The classic clinical definition of hypertrophic cardiomyopathy (HCM) as originally described by Teare is deceptively simple, "left ventricular hypertrophy in the absence of any identifiable cause." Longitudinal studies, however, including a seminal study performed by Frank and Braunwald in 1968, clearly described the disorder much as we know it today, a complex, progressive, and highly variable cardiomyopathy affecting ~ 1/500 individuals worldwide. Subsequent genetic linkage studies in the early 1990s identified mutations in virtually all of the protein components of the cardiac sarcomere as the primary molecular cause of HCM. In addition, a substantial proportion of inherited dilated cardiomyopathy (DCM) has also been linked to sarcomeric protein mutations. Despite our deep understanding of the overall function of the sarcomere as the primary driver of cardiac contractility, the ability to use genotype in patient management remains elusive. A persistent challenge in the field from both the biophysical and clinical standpoints is how to rigorously link high-resolution protein dynamics and mechanics to the long-term cardiovascular remodeling process that characterizes these complex disorders. In this review, we will explore the depth of the problem from both the standpoint of a multi-subunit, highly conserved and dynamic "machine" to the resultant clinical and structural human phenotype with an emphasis on new, integrative approaches that can be widely applied to identify both novel disease mechanisms and new therapeutic targets for these primary biophysical disorders of the cardiac sarcomere.

Coarse-Grained Protein Dynamics Studies Using Elastic Network Models

Elastic networks have been used as simple models of proteins to study their slow structural dynamics. They consist of point-like particles connected by linear Hookean springs and hence are convenient for linear normal mode analysis around a given reference structure. Furthermore, dynamic simulations using these models can provide new insights. As the computational cost associated with these models is considerably lower compared to that of all-atom models, they are also convenient for comparative studies between multiple protein structures. In this review, we introduce examples of coarse-grained molecular dynamics studies using elastic network models and their derivatives, focusing on the nonlinear phenomena, and discuss their applicability to large-scale macromolecular assemblies.

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.

Ultra-fast vapor generation by a graphene nano-ratchet: a theoretical and simulation study

Vapor generation is of prime importance for a broad range of applications: domestic water heating, desalination and wastewater treatment, etc. However, slow and inefficient evaporation limits its development. In this study, a nano-ratchet, a multilayer graphene with cone-shaped nanopores (MGCN), to accelerate vapor generation has been proposed. By performing molecular dynamics simulation, we found that air molecules were spontaneously transported across MGCN and resulted in a remarkable pressure difference, 21 kPa, between the two sides of MGCN. We studied the dependence of the pressure difference on the ambient temperature and geometry of MGCN in detail. Through further analysis of the diffusive transport, we found that pressure difference depended on the competition between ratchet transport and Knudsen diffusion and it was further found that ratchet transport is dominant. The significant pressure difference could lead to a 15-fold or greater enhancement of vapor generation, which shows the wide applications of this nano-ratchet.

Geometric somersaults of a polymer chain through cyclic twisting motions

This study explores the significance of geometric angle shifts, which we call geometric somersaults, arising from cyclic twisting motions of a polymer chain. A five-bead polymer chain serves as a concise and minimal model of a molecular shaft throughout this study. We first show that this polymer chain can change its orientation about its longitudinal axis largely, e.g., 120^{∘}, under conditions of zero total angular momentum by changing the two dihedral angles in a cyclic manner. This phenomenon is an example of the so-called "falling cat" phenomenon, where a falling cat undergoes a geometric somersault by changing its body shape under conditions of zero total angular momentum. We then extend the geometric somersault of the polymer chain to a noisy and viscous environment, where the polymer chain is steered by external driving forces. This extension shows that the polymer chain can achieve an orientation change keeping its total angular momentum and total external torque fluctuating around zero in a noisy and viscous environment. As an application, we argue that the geometric somersault of the polymer chain by 120^{∘} may serve as a prototypical and coarse-grained model for the rotary motion of the central shaft of ATP synthase (F_{O}F_{1}-ATPase). This geometric somersault is in clear contrast to the standard picture for the rotary motion of the central shaft as a rigid body, which generally incurs nonzero total angular momentum and nonzero total external torque. The power profile of the geometric somersault implies a preliminary mechanism for elastic power transmission. The results of this study may be of fundamental interest in twisting and rotary motions of biomolecules.

Dielectric Allostery of Protein: Response of Myosin to ATP Binding

Protein uses allostery to execute biological function. The physical mechanism underlying the allostery has long been studied, with the focus on the mechanical response by ligand binding. Here, we highlight the electrostatic response, presenting an idea of "dielectric allostery". We conducted molecular dynamics simulations of myosin, a motor protein with allostery, and analyzed the response to ATP binding which is a crucial step in force-generating function, forcing myosin to unbind from the actin filament. We found that the net negative charge of ATP causes a large-scale, anisotropic dielectric response in myosin, altering the electrostatic potential in the distant actin-binding region and accordingly retracting a positively charged actin-binding loop. A large-scale rearrangement of electrostatic bond network was found to occur upon ATP binding. Since proteins are dielectric and ligands are charged/polar in general, the dielectric allostery might underlie a wide spectrum of functions by proteins.

Including Thermal Fluctuations in Actomyosin Stable States Increases the Predicted Force per Motor and Macroscopic Efficiency in Muscle Modelling

Muscle contractions are generated by cyclical interactions of myosin heads with actin filaments to form the actomyosin complex. To simulate actomyosin complex stable states, mathematical models usually define an energy landscape with a corresponding number of wells. The jumps between these wells are defined through rate constants. Almost all previous models assign these wells an infinite sharpness by imposing a relatively simple expression for the detailed balance, i.e., the ratio of the rate constants depends exponentially on the sole myosin elastic energy. Physically, this assumption corresponds to neglecting thermal fluctuations in the actomyosin complex stable states. By comparing three mathematical models, we examine the extent to which this hypothesis affects muscle model predictions at the single cross-bridge, single fiber, and organ levels in a ceteris paribus analysis. We show that including fluctuations in stable states allows the lever arm of the myosin to easily and dynamically explore all possible minima in the energy landscape, generating several backward and forward jumps between states during the lifetime of the actomyosin complex, whereas the infinitely sharp minima case is characterized by fewer jumps between states. Moreover, the analysis predicts that thermal fluctuations enable a more efficient contraction mechanism, in which a higher force is sustained by fewer attached cross-bridges.

Mathematical models are of fundamental importance in the quantitative verification of biological hypotheses. Muscle contraction models assume the existence of several stable states for the myosin head, whereas the transition rates between states are defined to fit experimental data. The ratio of the forward and backward rates is linked to the ratio of the probabilities of being in one or other stable state at equilibrium through a detailed balance condition. A commonly used assumption leads to a relatively simple expression for this balance condition that depends only on the values of the energy at the minima and not on the minima shape. Mathematically, this hypothesis corresponds to infinite sharpness at these minima; physically, it neglects the small thermal fluctuations within actomyosin stable states. In this work, we compare this classical approach with a model that includes thermal fluctuations within wide minima, and quantitatively assess how much this hypothesis affects the model outcomes at the single molecule, single fiber, and whole heart levels. It is shown that, using parameters compatible with known behavior in muscle mechanics, relaxing the infinitely sharp minima hypothesis improves the predicted force generation and efficiency at the macroscopic level.

Piezoelectric allostery of protein

Allostery is indispensable for a protein to work, where a locally applied stimulus is transmitted to a distant part of the molecule. While the allostery due to chemical stimuli such as ligand binding has long been studied, the growing interest in mechanobiology prompts the study of the mechanically stimulated allostery, the physical mechanism of which has not been established. By molecular dynamics simulation of a motor protein myosin, we found that a locally applied mechanical stimulus induces electrostatic potential change at distant regions, just like the piezoelectricity. This novel allosteric mechanism, "piezoelectric allostery", should be of particularly high value for mechanosensor/transducer proteins.

The path to visualization of walking myosin V by high-speed atomic force microscopy

The quest for understanding the mechanism of myosin-based motility started with studies on muscle contraction. From numerous studies, the basic frameworks for this mechanism were constructed and brilliant hypotheses were put forward. However, the argument about the most crucial issue of how the actin-myosin interaction generates contractile force and shortening has not been definitive. To increase the "directness of measurement", in vitro motility assays and single-molecule optical techniques were created and used. Consequently, detailed knowledge of the motility of muscle myosin evolved, which resulted in provoking more arguments to a higher level. In parallel with technical progress, advances in cell biology led to the discovery of many classes of myosins. Myosin V was discovered to be a processive motor, unlike myosin II. The processivity reduced experimental difficulties because it allowed continuous tracing of the motor action of single myosin V molecules. Extensive studies of myosin V were expected to resolve arguments and build a consensus but did not necessarily do so. The directness of measurement was further enhanced by the recent advent of high-speed atomic force microscopy capable of directly visualizing biological molecules in action at high spatiotemporal resolution. This microscopy clearly visualized myosin V molecules walking on actin filaments and at last provided irrefutable evidence for the swinging lever-arm motion propelling the molecules. However, a peculiar foot stomp behavior also appeared in the AFM movie, raising new questions of the chemo-mechanical coupling in this motor and myosin motors in general. This article reviews these changes in the research of myosin motility and proposes new ideas to resolve the newly raised questions.

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.

Myosin II is a molecular motor that is fueled by ATP hydrolysis and generates mechanical force by interacting with actin filament. Comparison among various myosin structures obtained by X-ray and electron microscope analyses has led to the hypothesis that structural change of myosin in ATP hydrolysis cycle is the driving mechanism of force generation. However, single-molecule experiments have suggested an alternative mechanism in which myosin moves stochastically in a biased direction along actin filament. Computer simulation serves as a platform for assessing these hypotheses by revealing the prominent features of the dynamically changing landscape of actin-myosin interaction. The calculated results show that myosin binds to actin at different locations of actin filament in the weak- and strong-binding states and that the free energy has a global gradient from the weak-binding site to the strong-binding site. Myosin relaxing into the strong-binding state therefore necessarily shows the biased Brownian motion toward the strong-binding site. Lever-arm swing is induced during this relaxation process; therefore, lever-arm swing and the biased Brownian motion are coupled to contribute to the net displacement of myosin. This coupling should affect the dynamical behaviors of muscle and cardiac systems.

Molecular dynamics simulation of a myosin subfragment-1 docking with an actin filament

Myosins are typical molecular motor proteins, which convert the chemical energy of ATP into mechanical work. The fundamental mechanism of this energy conversion is still unknown. To explain the experimental results observed in molecular motors, Masuda has proposed a theory called the "Driven by Detachment (DbD)" mechanism for the working principle of myosins. Based on this theory, the energy used during the power stroke of the myosins originates from the attractive force between a detached myosin head and an actin filament, and does not directly arise from the energy of ATP. According to this theory, every step in the myosin working process may be reproduced by molecular dynamics (MD) simulations, except for the ATP hydrolysis step. Therefore, MD simulations were conducted to reproduce the docking process of a myosin subfragment-1 (S1) against an actin filament. A myosin S1 directed toward the barbed end of an actin filament was placed at three different positions by shifting it away from the filament axis. After 30 ns of MD simulations, in three cases out of ten trials on average, the myosin made a close contact with two actin monomers by changing the positions and the orientation of both the myosin and the actin as predicted in previous studies. Once the docking was achieved, the distance between the myosin and the actin showed smaller fluctuations, indicating that the docking is stable over time. If the docking was not achieved, the myosin moved randomly around the initial position or moved away from the actin filament. MD simulations thus successfully reproduced the docking of a myosin S1 with an actin filament. By extending the similar MD simulations to the other steps of the myosin working process, the validity of the DbD theory may be computationally demonstrated.

Entropic mechanism of allosteric communication in conformational transitions of dihydrofolate reductase

The mechanism of allosteric conformational transitions of Escherichia coli dihydrofolate reductase (DHFR) is investigated theoretically by applying a newly developed coarse-grained model. Functional forms of interaction potentials in the model depend on the local structural environments around those interactions to represent the many-residue effects due to atomic packing in each local region, and hence, this model is called "the chameleon model". The chameleon model consistently describes the free-energy landscape of two conformational transitions in the catalytic cycle of DHFR, which we call conformational transition 1 (CT1) and conformational transition 2 (CT2); CT1 is accompanied by the hydride transfer reaction, and CT2 is accompanied by the product ligand release. The transition state of CT1 is entropically stabilized by the disordering of loops at the peripheral regions of the protein, which enhances the positively correlated fluctuations at the center part of the protein, showing that the allosteric communication between distant regions through the central region is intrinsically associated with the entropic stabilization of the transition state. The transition state of CT2 is entropically stabilized through the mechanism that enhances the breathing motion of two domains, showing that the difference in the distribution of interactions brings about the difference in the transition mechanism between CT1 and CT2. The chameleon model opens a way to consistently describe the dynamical energy landscape of enzymatic reactions.

Attached molecular motor in a trapped single molecule assay as a bidimensional Brownian multistable system

To elucidate the physical properties of the force generation mechanism in molecular motors, we have obtained an analytical solution of the bidimensional Fokker-Plank equation which describes a common setup used in single molecule experiments. As a first application of this general result, we have shown that the size of the trapping system affects the dwell time of a multistable particle linearly. A quantitative application to skeletal actomyosin complex, using direct observation of force generation dynamics in the literature, shows that the size of the trapping system used was important for increasing the dwell time of the myosin head stable states to an observable time scale.

Single-molecule nanometry for biological physics

Precision measurement is a hallmark of physics but the small length scale (∼nanometer) of elementary biological components and thermal fluctuations surrounding them challenge our ability to visualize their action. Here, we highlight the recent developments in single-molecule nanometry where the position of a single fluorescent molecule can be determined with nanometer precision, reaching the limit imposed by the shot noise, and the relative motion between two molecules can be determined with ∼0.3 nm precision at ∼1 ms time resolution, as well as how these new tools are providing fundamental insights into how motor proteins move on cellular highways. We will also discuss how interactions between three and four fluorescent molecules can be used to measure three and six coordinates, respectively, allowing us to correlate the movements of multiple components. Finally, we will discuss recent progress in combining angstrom-precision optical tweezers with single-molecule fluorescent detection, opening new windows for multi-dimensional single-molecule nanometry for biological physics.

The origin of minus-end directionality and mechanochemistry of Ncd motors

Adaptation of molecular structure to the ligand chemistry and interaction with the cytoskeletal filament are key to understanding the mechanochemistry of molecular motors. Despite the striking structural similarity with kinesin-1, which moves towards plus-end, Ncd motors exhibit minus-end directionality on microtubules (MTs). Here, by employing a structure-based model of protein folding, we show that a simple repositioning of the neck-helix makes the dynamics of Ncd non-processive and minus-end directed as opposed to kinesin-1. Our computational model shows that Ncd in solution can have both symmetric and asymmetric conformations with disparate ADP binding affinity, also revealing that there is a strong correlation between distortion of motor head and decrease in ADP binding affinity in the asymmetric state. The nucleotide (NT) free-ADP (φ-ADP) state bound to MTs favors the symmetric conformation whose coiled-coil stalk points to the plus-end. Upon ATP binding, an enhanced flexibility near the head-neck junction region, which we have identified as the important structural element for directional motility, leads to reorienting the coiled-coil stalk towards the minus-end by stabilizing the asymmetric conformation. The minus-end directionality of the Ncd motor is a remarkable example that demonstrates how motor proteins in the kinesin superfamily diversify their functions by simply rearranging the structural elements peripheral to the catalytic motor head domain.

Proteins belonging to the kinesin superfamily are responsible for vesicle or organelle transport, spindle morphogenesis, and chromosome sorting during cell division. Interestingly, while most proteins in kinesin superfamily that share the common catalytic motor head domain have plus-end directionality along microtubules, kinesin-14 (Ncd) exhibits minus-end directionality. Despite the several circumstantial evidences on the determining factors for the motor directionality in the last decade, a comprehensive understanding of the mechanism governing the Ncd minus-end directionality is still missing. Our studies provide a clear explanation for this minus-end directionality and the associated mechanochemical cycle. Here, we modeled an Ncd motor by employing structural details available in the literature to simulate its conformational dynamics. Simulations using our structure-based model of Ncd assert that the dynamics due to a simple rearrangement of structural elements, peripheral to the catalytic motor domain, is the key player in determining both the directionality and mechanochemistry unique to Ncd motors. Although Ncd has a different directionality, it uses a similar strategy to kinesin-1 of structural adaptation of the catalytic motor domain. Therefore using the same physical principle of protein folding and very similar structural elements, motors in the kinesin superfamily are able to achieve a variety of biological function.

From single molecule fluctuations to muscle contraction: a Brownian model of A.F. Huxley's hypotheses

Muscular force generation in response to external stimuli is the result of thermally fluctuating, cyclical interactions between myosin and actin, which together form the actomyosin complex. Normally, these fluctuations are modelled using transition rate functions that are based on muscle fiber behaviour, in a phenomenological fashion. However, such a basis reduces the predictive power of these models. As an alternative, we propose a model which uses direct single molecule observations of actomyosin fluctuations reported in the literature. We precisely estimate the actomyosin potential bias and use diffusion theory to obtain a brownian ratchet model that reproduces the complete cross-bridge cycle. The model is validated by simulating several macroscopic experimental conditions, while its interpretation is compatible with two different force-generating scenarios.

Temperature-enhanced association of proteins due to electrostatic interaction: a coarse-grained simulation of actin-myosin binding

Association of protein molecules constitutes the basis for the interaction network in a cell. Despite its fundamental importance, the thermodynamic aspect of protein-protein binding, particularly the issues relating to the entropy change upon binding, remains elusive. The binding of actin and myosin, which are vital proteins in motility, is a typical example, in which two different binding mechanisms have been argued: the binding affinity increases with increasing temperature and with decreasing salt-concentration, indicating the entropy-driven binding and the enthalpy-driven binding, respectively. How can these thermodynamically different binding mechanisms coexist? To address this question, which is of general importance in understanding protein-protein bindings, we conducted an in silico titration of the actin-myosin system by molecular dynamics simulation using a residue-level coarse-grained model, with particular focus on the role of the electrostatic interaction. We found a good agreement between in silico and in vitro experiments on the salt-concentration dependence and the temperature dependence of the binding affinity. We then figured out how the two binding mechanisms can coexist: the enthalpy (due to electrostatic interaction between actin and myosin) provides the basal binding affinity, and the entropy (due to the orientational disorder of water molecules) enhances it at higher temperatures. In addition, we analyzed the actin-myosin complex structures observed during the simulation and obtained a variety of weak-binding complex structures, among which were found an unusual binding mode suggested by an earlier experiment and precursor structures of the strong-binding complex proposed by electron microscopy. These results collectively indicate the potential capability of a residue-level coarse-grained model to simulate the association-dissociation dynamics (particularly for transient weak-bindings) exhibited by larger and more complicated systems, as in a cell.

A structural perspective on the dynamics of kinesin motors

Despite significant fluctuation under thermal noise, biological machines in cells perform their tasks with exquisite precision. Using molecular simulation of a coarse-grained model and theoretical arguments, we envisaged how kinesin, a prototype of biological machines, generates force and regulates its dynamics to sustain persistent motor action. A structure-based model, which can be versatile in adapting its structure to external stresses while maintaining its native fold, was employed to account for several features of kinesin dynamics along the biochemical cycle. This analysis complements our current understandings of kinesin dynamics and connections to experiments. We propose a thermodynamic cycle for kinesin that emphasizes the mechanical and regulatory role of the neck linker and clarify issues related to the motor directionality, and the difference between the external stalling force and the internal tension responsible for the head-head coordination. The comparison between the thermodynamic cycle of kinesin and macroscopic heat engines highlights the importance of structural change as the source of work production in biomolecular machines.

Coarse-grained molecular simulations of large biomolecules

Recently, we saw a dramatic increase in the number of researches that rely on coarse-grained (CG) simulations for large biomolecules. Here, first, we briefly describe recently developed and used CG models for proteins and nucleic acids. Balance between structure-based and physico-chemical terms is a key issue. We also discuss the multiscale algorithms used to derive CG parameters. Next, we comment on the dynamics used in CG simulations with an emphasis on the importance of hydrodynamic interactions. We then discuss the pros and cons of CG simulations. Finally, we overview recent exciting applications of CG simulations. Publicly available tools and software for CG simulations are also summarized.

Myosin-V as a mechanical sensor: an elastic network study

According to recent experiments, the molecular-motor myosin behaves like a strain sensor, exhibiting different functional responses when loads in opposite directions are applied to its tail. Within an elastic-network model, we explore the sensitivity of the protein to the forces acting on the tail and find, in agreement with experiments, that such forces invoke conformational changes that should affect filament binding and ADP release. Furthermore, conformational responses of myosin to the application of forces to individual residues in its principal functional regions are systematically investigated and a detailed sensitivity map of myosin-V is thus obtained. The results suggest that the strain-sensor behavior is involved in the intrinsic operation of this molecular motor.

The Zebrafish Neurophenome Database (ZND): a dynamic open-access resource for zebrafish neurophenotypic data

Zebrafish (Danio rerio) are widely used in neuroscience research, where their utility as a model organism is rapidly expanding. Low cost, ease of experimental manipulations, and sufficient behavioral complexity make zebrafish a valuable tool for high-throughput studies in biomedicine. To complement the available repositories for zebrafish genetic information, there is a growing need for the collection of zebrafish neurobehavioral and neurological phenotypes. For this, we are establishing the Zebrafish Neurophenome Database (ZND; www.tulane.edu/∼znpindex/search ) as a new dynamic online open-access data repository for behavioral and related physiological data. ZND, currently focusing on adult zebrafish, combines zebrafish neurophenotypic data with a simple, easily searchable user interface, which allow scientists to view and compare results obtained by other laboratories using various treatments in different testing paradigms. As a developing community effort, ZND is expected to foster innovative research using zebrafish by federating the growing body of zebrafish neurophenotypic data.

Thin filament mutations: developing an integrative approach to a complex disorder

Sixteen years ago, mutations in cardiac troponin (Tn)T and α-tropomyosin were linked to familial hypertrophic cardiomyopathy, thus transforming the disorder from a disease of the β-myosin heavy chain to a disease of the cardiac sarcomere. From the outset, studies suggested that mutations in the regulatory thin filament caused a complex, heterogeneous pattern of ventricular remodeling with wide variations in clinical expression. To date, the clinical heterogeneity is well matched by an extensive array of nearly 100 independent mutations in all components of the cardiac thin filament. Significant advances in our understanding of the biophysics of myofilament activation, coupled to the emerging evidence that thin filament linked cardiomyopathies are progressive, suggests that a renewed focus on the most proximal events in both the molecular and clinical pathogenesis of the disease will be necessary to achieve the central goal of using genotype information to manage affected patients. In this review, we examine the existing biophysical and clinical evidence in support of a more proximal definition of thin filament cardiomyopathies. In addition, new high-resolution, integrated approaches are presented to help define the way forward as the field works toward developing a more robust link between genotype and phenotype in this complex disorder.

Membrane traffic and fusion at post-Golgi compartments

Complete sequencing of the Arabidopsis genome a decade ago has facilitated the functional analysis of various biological processes including membrane traffic by which many proteins are delivered to their sites of action and turnover. In particular, membrane traffic between post-Golgi compartments plays an important role in cell signaling, taking care of receptor-ligand interaction and inactivation, which requires secretion, endocytosis, and recycling or targeting to the vacuole for degradation. Here, we discuss recent studies that address the identity of post-Golgi compartments, the machinery involved in traffic and fusion or functionally characterized cargo proteins that are delivered to or pass through post-Golgi compartments. We also provide an outlook on future challenges in this area of research.

Entropic potential field formed for a linear-motor protein near a filament: Statistical-mechanical analyses using simple models

We report a new progress in elucidating the mechanism of the unidirectional movement of a linear-motor protein (e.g., myosin) along a filament (e.g., F-actin). The basic concept emphasized here is that a potential field is entropically formed for the protein on the filament immersed in solvent due to the effect of the translational displacement of solvent molecules. The entropic potential field is strongly dependent on geometric features of the protein and the filament, their overall shapes as well as details of the polyatomic structures. The features and the corresponding field are judiciously adjusted by the binding of adenosine triphosphate (ATP) to the protein, hydrolysis of ATP into adenosine diphosphate (ADP)+Pi, and release of Pi and ADP. As the first step, we propose the following physical picture: The potential field formed along the filament for the protein without the binding of ATP or ADP+Pi to it is largely different from that for the protein with the binding, and the directed movement is realized by repeated switches from one of the fields to the other. To illustrate the picture, we analyze the spatial distribution of the entropic potential between a large solute and a large body using the three-dimensional integral equation theory. The solute is modeled as a large hard sphere. Two model filaments are considered as the body: model 1 is a set of one-dimensionally connected large hard spheres and model 2 is a double helical structure formed by two sets of connected large hard spheres. The solute and the filament are immersed in small hard spheres forming the solvent. The major findings are as follows. The solute is strongly confined within a narrow space in contact with the filament. Within the space there are locations with sharply deep local potential minima along the filament, and the distance between two adjacent locations is equal to the diameter of the large spheres constituting the filament. The potential minima form a ringlike domain in model 1 while they form a pointlike one in model 2. We then examine the effects of geometric features of the solute on the amplitudes and asymmetry of the entropic potential field acting on the solute along the filament. A large aspherical solute with a cleft near the solute-filament interface, which mimics the myosin motor domain, is considered in the examination. Thus, the two fields in our physical picture described above are qualitatively reproduced. The factors to be taken into account in further studies are also discussed.

Whole-cell-analysis of live cardiomyocytes using wide-field interferometric phase microscopy

We apply wide-field interferometric microscopy techniques to acquire quantitative phase profiles of ventricular cardiomyocytes in vitro during their rapid contraction with high temporal and spatial resolution. The whole-cell phase profiles are analyzed to yield valuable quantitative parameters characterizing the cell dynamics, without the need to decouple thickness from refractive index differences. Our experimental results verify that these new parameters can be used with wide field interferometric microscopy to discriminate the modulation of cardiomyocyte contraction dynamics due to temperature variation. To demonstrate the necessity of the proposed numerical analysis for cardiomyocytes, we present confocal dual-fluorescence-channel microscopy results which show that the rapid motion of the cell organelles during contraction preclude assuming a homogenous refractive index over the entire cell contents, or using multiple-exposure or scanning microscopy.