Myosin-V makes two brownian 90 degrees rotations per 36-nm step

Dynamics of multicellular swirling on micropatterned substrates

Chirality plays a crucial role in biology, as it is highly conserved and fundamentally important in the developmental process. To better understand the relationship between the chirality of individual cells and that of tissues and organisms, we develop a generalized mechanics model of chiral polarized particles to investigate the swirling dynamics of cell populations on substrates. Our analysis reveals that cells with the same chirality can form distinct chiral patterns on ring-shaped or rectangular substrates. Interestingly, our studies indicate that an excessively strong or weak individual cellular chirality hinders the formation of such chiral patterns. Our studies also indicate that there exists the influence distance of substrate boundaries in chiral patterns. Smaller influence distances are observed when cell-cell interactions are weaker. Conversely, when cell-cell interactions are too strong, multiple cells tend to be stacked together, preventing the formation of chiral patterns on substrates in our analysis. Additionally, we demonstrate that the interaction between cells and substrate boundaries effectively controls the chiral distribution of cellular orientations on ring-shaped substrates. This research highlights the significance of coordinating boundary features, individual cellular chirality, and cell-cell interactions in governing the chiral movement of cell populations and provides valuable mechanics insights into comprehending the intricate connection between the chirality of single cells and that of tissues and organisms.

How torque on formins is relaxed strongly affects cellular swirling

Chirality is a common and essential characteristic at varied scales of living organisms. By adapting the rotational clutch-filament model we previously developed, we investigate the effect of torque relaxation of a formin on cellular chiral swirling. Since it is still unclear how the torque on a formin is exactly relaxed, we probe three types of torque relaxation, as suggested in the literature. Our analysis indicates that, when a formin periodically undergoes positive and negative rotation during processive capping to relax the torque, cells hardly rotate. When the switch between the positive and the negative rotation during the processive capping is randomly regulated by the torque, our analysis indicates that cells can only slightly rotate either counterclockwise or clockwise. When a formin relaxes the torque by transiently loosening its contact either with the membrane at its anchored site or with the actin filament, we find that cells can prominently rotate either counterclockwise or clockwise, in good consistency with the experiment. Thus, our studies indicate that how the torque on a formin is relaxed strongly affects cellular swirling and suggest an efficient type of torque relaxation in switching cellular swirling.

Flagella-Driven Motility of Bacteria

The bacterial flagellum is a helical filamentous organelle responsible for motility. In bacterial species possessing flagella at the cell exterior, the long helical flagellar filament acts as a molecular screw to generate thrust. Meanwhile, the flagella of spirochetes reside within the periplasmic space and not only act as a cytoskeleton to determine the helicity of the cell body, but also rotate or undulate the helical cell body for propulsion. Despite structural diversity of the flagella among bacterial species, flagellated bacteria share a common rotary nanomachine, namely the flagellar motor, which is located at the base of the filament. The flagellar motor is composed of a rotor ring complex and multiple transmembrane stator units and converts the ion flux through an ion channel of each stator unit into the mechanical work required for motor rotation. Intracellular chemotactic signaling pathways regulate the direction of flagella-driven motility in response to changes in the environments, allowing bacteria to migrate towards more desirable environments for their survival. Recent experimental and theoretical studies have been deepening our understanding of the molecular mechanisms of the flagellar motor. In this review article, we describe the current understanding of the structure and dynamics of the bacterial flagellum.

Characteristics of Myosin V Processivity

Myosin V is a processive doubled-headed biomolecular motor involved in many intracellular organelle and vesicle transport. The unidirectional movement is coupled with the adenosine triphosphate (ATP) hydrolysis and product release cycle. With the progress of experimental techniques and the enhancement of measuring directness, detailed knowledge of the motility of myosin V has been obtained. Following the ATPase cycle, the 4-state mechanochemical model of the myosin V's processive movement is used. The transitions between various states take place in a stochastic manner. We can use the master equation to analyze and calculate quantitatively. Meanwhile, the effect of the reverse reaction is taken fully into account. We fit the mean velocity, the mean dwell time, the mean run length, and the ratio of forward/backward steps as a functionof ATP, ADP, and Pi concertration. The theoretical curves are generally in line with the experimental data. This work provides a new insight for the characteristic of myosin V.

Structural dynamics of myosin 5 during processive motion revealed by interferometric scattering microscopy

Myosin 5a is a dual-headed molecular motor that transports cargo along actin filaments. By following the motion of individual heads with interferometric scattering microscopy at nm spatial and ms temporal precision we found that the detached head occupies a loosely fixed position to one side of actin from which it rebinds in a controlled manner while executing a step. Improving the spatial precision to the sub-nm regime provided evidence for an ångstrom-level structural transition in the motor domain associated with the power stroke. Simultaneous tracking of both heads revealed that consecutive steps follow identical paths to the same side of actin in a compass-like spinning motion demonstrating a symmetrical walking pattern. These results visualize many of the critical unknown aspects of the stepping mechanism of myosin 5 including head-head coordination, the origin of lever-arm motion and the spatiotemporal dynamics of the translocating head during individual steps.

Structural dynamics of myosin 5 during processive motion revealed by interferometric scattering microscopy

Myosin 5a is a dual-headed molecular motor that transports cargo along actin filaments. By following the motion of individual heads with interferometric scattering microscopy at nm spatial and ms temporal precision we found that the detached head occupies a loosely fixed position to one side of actin from which it rebinds in a controlled manner while executing a step. Improving the spatial precision to the sub-nm regime provided evidence for an ångstrom-level structural transition in the motor domain associated with the power stroke. Simultaneous tracking of both heads revealed that consecutive steps follow identical paths to the same side of actin in a compass-like spinning motion demonstrating a symmetrical walking pattern. These results visualize many of the critical unknown aspects of the stepping mechanism of myosin 5 including head-head coordination, the origin of lever-arm motion and the spatiotemporal dynamics of the translocating head during individual steps.

Design principles governing the motility of myosin V

The molecular motor myosin V (MyoV) exhibits a wide repertoire of pathways during the stepping process, which is intimately connected to its biological function. The best understood of these is the hand-over-hand stepping by a swinging lever arm movement toward the plus end of actin filaments. Single-molecule experiments have also shown that the motor "foot stomps," with one hand detaching and rebinding to the same site, and back-steps under sufficient load. The complete taxonomy of MyoV's load-dependent stepping pathways, and the extent to which these are constrained by motor structure and mechanochemistry, are not understood. Using a polymer model, we develop an analytical theory to describe the minimal physical properties that govern motor dynamics. We solve the first-passage problem of the head reaching the target-binding site, investigating the competing effects of backward load, strain in the leading head biasing the diffusion in the direction of the target, and the possibility of preferential binding to the forward site due to the recovery stroke. The theory reproduces a variety of experimental data, including the power stroke and slow diffusive search regimes in the mean trajectory of the detached head, and the force dependence of the forward-to-backward step ratio, run length, and velocity. We derive a stall force formula, determined by lever arm compliance and chemical cycle rates. By exploring the MyoV design space, we predict that it is a robust motor whose dynamical behavior is not compromised by reasonable perturbations to the reaction cycle and changes in the architecture of the lever arm.

Torque measurement at the single-molecule level

Methods for exerting and measuring forces on single molecules have revolutionized the study of the physics of biology. However, it is often the case that biological processes involve rotation or torque generation, and these parameters have been more difficult to access experimentally. Recent advances in the single-molecule field have led to the development of techniques that add the capability of torque measurement. By combining force, displacement, torque, and rotational data, a more comprehensive description of the mechanics of a biomolecule can be achieved. In this review, we highlight a number of biological processes for which torque plays a key mechanical role. We describe the various techniques that have been developed to directly probe the torque experienced by a single molecule, and detail a variety of measurements made to date using these new technologies. We conclude by discussing a number of open questions and propose systems of study that would be well suited for analysis with torsional measurement techniques.

Tilting and wobble of myosin V by high-speed single-molecule polarized fluorescence microscopy

Myosin V is biomolecular motor with two actin-binding domains (heads) that take multiple steps along actin by a hand-over-hand mechanism. We used high-speed polarized total internal reflection fluorescence (polTIRF) microscopy to study the structural dynamics of single myosin V molecules that had been labeled with bifunctional rhodamine linked to one of the calmodulins along the lever arm. With the use of time-correlated single-photon counting technology, the temporal resolution of the polTIRF microscope was improved ~50-fold relative to earlier studies, and a maximum-likelihood, multitrace change-point algorithm was used to objectively determine the times when structural changes occurred. Short-lived substeps that displayed an abrupt increase in rotational mobility were detected during stepping, likely corresponding to random thermal fluctuations of the stepping head while it searched for its next actin-binding site. Thus, myosin V harnesses its fluctuating environment to extend its reach. Additional, less frequent angle changes, probably not directly associated with steps, were detected in both leading and trailing heads. The high-speed polTIRF method and change-point analysis may be applicable to single-molecule studies of other biological systems.

Dwell time distributions of the molecular motor myosin V

The dwell times between two successive steps of the two-headed molecular motor myosin V are governed by non-exponential distributions. These distributions have been determined experimentally for various control parameters such as nucleotide concentrations and external load force. First, we use a simplified network representation to determine the dwell time distributions of myosin V, with the associated dynamics described by a Markov process on networks with absorbing boundaries. Our approach provides a direct relation between the motor’s chemical kinetics and its stepping properties. In the absence of an external load, the theoretical distributions quantitatively agree with experimental findings for various nucleotide concentrations. Second, using a more complex branched network, which includes ADP release from the leading head, we are able to elucidate the motor’s gating effect. This effect is caused by an asymmetry in the chemical properties of the leading and the trailing head of the motor molecule. In the case of an external load acting on the motor, the corresponding dwell time distributions reveal details about the motor’s backsteps.

F(1)-ATPase: a prototypical rotary molecular motor

F(1)-ATPase, the soluble portion of ATP synthase, has been shown to be a rotary molecular motor in which the central γ subunit rotates inside the cylinder made of α(3)β(3) subunits. The rotation is powered by ATP hydrolysis in three catalytic sites, and reverse rotation of the γ subunit by an external force leads to ATP synthesis in the catalytic sites. Here I look back how our lab became involved in the study of this marvelous rotary machine, and discuss some aspects of its rotary mechanism while confessing we are far from understanding. This article is a very personal essay, not a scientific review, for this otherwise viral machines book.

Fluorescence microscopy for simultaneous observation of 3D orientation and movement and its application to quantum rod-tagged myosin V

Single molecule fluorescence polarization techniques have been used for three-dimensional (3D) orientation measurements to observe the dynamic properties of single molecules. However, only few techniques can simultaneously measure 3D orientation and position. Furthermore, these techniques often require complex equipment and cumbersome analysis. We have developed a microscopy system and synthesized highly fluorescent, rod-like shaped quantum dots (Q rods), which have linear polarizations, to simultaneously measure the position and 3D orientation of a single fluorescent probe. The optics splits the fluorescence from the probe into four different spots depending on the polarization angle and projects them onto a CCD camera. These spots are used to determine the 2D position and 3D orientation. Q rod orientations could be determined with better than 10° accuracy at 33 ms time resolution. We applied our microscopy and Q rods to simultaneously measure myosin V movement along an actin filament and rotation around its own axis, finding that myosin V rotates 90° for each step. From this result, we suggest that in the two-headed bound state, myosin V necks are perpendicular to one another, while in the one-headed bound state the detached trailing myosin V head is biased forward in part by rotating its lever arm about its own axis. This microscopy system should be applicable to a wide range of dynamic biological processes that depend on single molecule orientation dynamics.

Chemomechanical coupling and motor cycles of myosin V

The molecular motor myosin V has been studied extensively both in bulk and single molecule experiments. Based on the chemical states of the motor, we construct a systematic network theory that includes experimental observations about the stepping behavior of myosin V. We utilize constraints arising from nonequilibrium thermodynamics to determine motor parameters and demonstrate that the motor behavior is governed by three chemomechanical motor cycles. The competition between these cycles can be understood via the influence of external load forces onto the chemical transition rates for the binding of adenosine triphosphate and adenosine diphosphate. In addition, we also investigate the functional dependence of the mechanical stepping rates on these forces. For substall forces, the dominant pathway of the motor network is profoundly different from the one for superstall forces, which leads to a stepping behavior that is in agreement with the experimental observations. Our theory provides a unified description of the experimental data as obtained for myosin V in single motor experiments.

Moving into the cell: single-molecule studies of molecular motors in complex environments

Much has been learned in the past decades about molecular force generation. Single-molecule techniques, such as atomic force microscopy, single-molecule fluorescence microscopy and optical tweezers, have been key in resolving the mechanisms behind the power strokes, 'processive' steps and forces of cytoskeletal motors. However, it remains unclear how single force generators are integrated into composite mechanical machines in cells to generate complex functions such as mitosis, locomotion, intracellular transport or mechanical sensory transduction. Using dynamic single-molecule techniques to track, manipulate and probe cytoskeletal motor proteins will be crucial in providing new insights.

A coarse-grained molecular model for actin-myosin simulation

We describe a very coarse-grained molecular model for the simulation of myosin V on an actin filament. The molecular representation is hierarchical with the finest level representing secondary structure elements (end-points) which are grouped into domains which are then grouped into molecules. Each level moves with a Brownian-like motion both in translation and rotation. Molecular integrity is maintained by steric exclusion and inter-domain restraints. A molecular description is developed for a myosin dimer on a actin filament with binding interactions also specified between domains to simulate both loose and tight binding. The stability of the model was tested in the pre- and post-power-stroke conformations with simulations in both states being used to test the preferred binding site of the myosin on the filament. The effects of the myosin twofold symmetry and the restriction of an attached cargo were also tested. These results provide the basis for the development of a dynamic model of processive motion.

Myosin individualized: single nucleotide polymorphisms in energy transduction

BACKGROUND

Myosin performs ATP free energy transduction into mechanical work in the motor domain of the myosin heavy chain (MHC). Energy transduction is the definitive systemic feature of the myosin motor performed by coordinating in a time ordered sequence: ATP hydrolysis at the active site, actin affinity modulation at the actin binding site, and the lever-arm rotation of the power stroke. These functions are carried out by several conserved sub-domains within the motor domain. Single nucleotide polymorphisms (SNPs) affect the MHC sequence of many isoforms expressed in striated muscle, smooth muscle, and non-muscle tissue. The purpose of this work is to provide a rationale for using SNPs as a functional genomics tool to investigate structurefunction relationships in myosin. In particular, to discover SNP distribution over the conserved sub-domains and surmise what it implies about sub-domain stability and criticality in the energy transduction mechanism.

RESULTS

An automated routine identifying human nonsynonymous SNP amino acid missense substitutions for any MHC gene mined the NCBI SNP data base. The routine tested 22 MHC genes coding muscle and non-muscle isoforms and identified 89 missense mutation positions in the motor domain with 10 already implicated in heart disease and another 8 lacking sequence homology with a skeletal MHC isoform for which a crystallographic model is available. The remaining 71 SNP substitutions were found to be distributed over MHC with 22 falling outside identified functional sub-domains and 49 in or very near to myosin sub-domains assigned specific crucial functions in energy transduction. The latter includes the active site, the actin binding site, the rigid lever-arm, and regions facilitating their communication. Most MHC isoforms contained SNPs somewhere in the motor domain.

CONCLUSIONS

Several functional-crucial sub-domains are infiltrated by a large number of SNP substitution sites suggesting these domains are engineered by evolution to be too-robust to be disturbed by otherwise intrusive sequence changes. Two functional sub-domains are SNP-free or relatively SNP-deficient but contain many disease implicated mutants. These sub-domains are apparently highly sensitive to any missense substitution suggesting they have failed to evolve a robust sequence paradigm for performing their function.

Direct measurements of kinesin torsional properties reveal flexible domains and occasional stalk reversals during stepping

Kinesin is a homodimeric motor with two catalytic heads joined to a stalk via short neck linkers (NLs). We measured the torsional properties of single recombinant molecules by tracking the thermal angular motions of fluorescently labeled beads bound to the C terminus of the stalk. When kinesin heads were immobilized on microtubules (MTs) under varied nucleotide conditions, we observed bounded or unbounded angular diffusion, depending on whether one or both heads were attached to the MT. Free rotation implies that NLs act as swivels. From data on constrained diffusion, we conclude that the coiled-coil stalk domains are approximately 30-fold stiffer than its flexible "hinge" regions. Surprisingly, while tracking processive kinesin motion at low ATP concentrations, we observed occasional abrupt reversals in the directional orientations of the stalk. Our results impose constraints on kinesin walking models and suggest a role for rotational freedom in cargo transport.

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.

Mesoscale modeling of molecular machines: cyclic dynamics and hydrodynamical fluctuations

Proteins acting as molecular machines can undergo cyclic internal conformational motions that are coupled to ligand binding and dissociation events. In contrast to their macroscopic counterparts, nanomachines operate in a highly fluctuating environment, which influences their operation. To bridge the gap between detailed microscopic and simple phenomenological descriptions, a mesoscale approach, which combines an elastic network model of a machine with a particle-based mesoscale description of the solvent, is employed. The time scale of the cyclic hinge motions of the machine prototype is strongly affected by hydrodynamical coupling to the solvent.

Myosin V from head to tail

Myosin V (myoV), a processive cargo transporter, has arguably been the most well-studied unconventional myosin of the past decade. Considerable structural information is available for the motor domain, the IQ motifs with bound calmodulin or light chains, and the cargo-binding globular tail, all of which have been crystallized. The repertoire of adapter proteins that link myoV to a particular cargo is becoming better understood, enabling cellular transport processes to be dissected. MyoV is processive, meaning that it takes many steps on actin filaments without dissociating. Its extended lever arm results in long 36-nm steps, making it ideal for single molecule studies of processive movement. In addition, electron microscopy revealed the structure of the inactive, folded conformation of myoV when it is not transporting cargo. This review provides a background on myoV, and highlights recent discoveries that show why myoV will continue to be an active focus of investigation.

Measurement system for simultaneous observation of myosin V chemical and mechanical events

Myosin V is an actin-based processive molecular motor driven by the chemical energy of ATP hydrolysis. Although the chemo-mechanical coupling in processive movement has been postulated by separate structural, mechanical and biochemical studies, no experiment has been able to directly test these conclusions. Therefore the relationship between ATP-turnover and force generation remains unclear. Currently, the most direct method to measure the chemo-mechanical coupling in processive motors is to simultaneously observe ATP-turnover cycles and displacement at the single molecule level. In this study, we developed a simultaneous measurement system suitable for mechanical and chemical assays of myosin V in order to directly elucidate its chemo-mechanical coupling.