Load-dependent kinetics of force production by smooth muscle myosin measured with optical tweezers

Motor domain phosphorylation increases nucleotide exchange and turns MYO6 into a faster and stronger motor

Myosin motors perform many fundamental functions in eukaryotic cells by providing force generation, transport or tethering capacity. Motor activity control within the cell involves on/off switches, however, few examples are known of how myosins regulate speed or processivity and fine-tune their activity to a specific cellular task. Here, we describe a phosphorylation event for myosins of class VI (MYO6) in the motor domain, which accelerates its ATPase activity leading to a 4-fold increase in motor speed determined by actin-gliding assays, single molecule mechanics and stopped flow kinetics. We demonstrate that the serine/threonine kinase DYRK2 phosphorylates MYO6 at S267 in vitro. Single-molecule optical-tweezers studies at low load reveal that S267-phosphorylation results in faster nucleotide-exchange kinetics without change in the working stroke of the motor. The selective increase in stiffness of the acto-MYO6 complex when proceeding load-dependently into the nucleotide-free rigor state demonstrates that S267-phosphorylation turns MYO6 into a stronger motor. Finally, molecular dynamic simulations of the nucleotide-free motor reveal an alternative interaction network within insert-1 upon phosphorylation, suggesting a molecular mechanism, which regulates insert-1 positioning, turning the S267-phosphorylated MYO6 into a faster motor.

Muscle Torque-Velocity Relationships and Fatigue With Reduced Knee Joint Range of Motion in Young and Older Adults

The purpose of this study was to evaluate the influence of knee joint range of motion (RoM) on the torque-velocity relationship and fatigue in the knee extensor muscles of 7 young (median = 26 y) and 7 older (68 y) adults. Each leg was assigned a RoM (35° or 75°) over which to perform a torque-velocity protocol (maximal isokinetic contractions, 60-300°·s-1) and a fatigue protocol (120 maximal contractions at 120°·s-1, 0.5 Hz). Six older participants were unable to reach 300°·s-1 over 35°. Therefore, the velocity eliciting 75% of peak torque at 60°·s-1 (V75, °·s-1) was calculated for each RoM from a fit of individual torque-velocity curves (60-240°·s-1), and ΔV75 (35°-75°) was determined. Fatigue (final torque/initial torque) was used to calculate Δfatigue (35°-75°). ΔV75 was not different from 0 in young (-28.3°·s-1 [-158.6 to 55.7], median [range], P = .091) or older (-18.5°·s-1 [-95.0 to 23.9], P = .128), with no difference by age (P = .710). In contrast, fatigue was greater for 75° in young (Δfatigue = 25.9% [17.5-30.3], P = .018) and older (17.2% [11.9-52.9], P = .018), with no effect of age (P = .710). These data indicate that, regardless of age, RoM did not alter the torque-velocity relationship between 60 and 240°·s-1, and fatigue was greater with a larger RoM.

Control of Modular Tissue Flows Shaping the Embryo in Avian Gastrulation

Avian gastrulation requires coordinated flows of thousands of cells to form the body plan. We quantified these flows using their fundamental kinematic units: one attractor and two repellers constituting its Dynamic Morphoskeleton (DM). We have also elucidated the mechanistic origin of the attractor, marking the primitive streak (PS), and controlled its shape, inducing gastrulation flows in the chick embryo that are typical of other vertebrates. However, the origins of repellers and dynamic embryo shape remain unclear. Here, we address these questions using active matter physics and experiments. Repeller 1, separating the embryo proper (EP) from extraembryonic (EE) tissues, arises from the tug-of-war between EE epiboly and EP isotropic myosin-induced active stress. Repeller 2, bisecting the anterior and posterior PS and associated with embryo shape change, arises from anisotropic myosin-induced active intercalation in the mesendoderm. Combining mechanical confinement with inhibition of mesendoderm induction, we eliminated either one or both repellers, as predicted by our model. Our results reveal a remarkable modularity of avian gastrulation flows delineated by the DM, uncovering the mechanistic roles of EE epiboly, EP active constriction, mesendoderm intercalation and ingression. These findings offer a new perspective for deconstructing morphogenetic flows, uncovering their modular origin, and aiding synthetic morphogenesis.

The Geometric Basis of Epithelial Convergent Extension

Shape changes of epithelia during animal development, such as convergent extension, are achieved through concerted mechanical activity of individual cells. While much is known about the corresponding large scale tissue flow and its genetic drivers, fundamental questions regarding local control of contractile activity on cellular scale and its embryo-scale coordination remain open. To address these questions, we develop a quantitative, model-based analysis framework to relate cell geometry to local tension in recently obtained timelapse imaging data of gastrulating Drosophila embryos. This analysis provides a systematic decomposition of cell shape changes and T1-rearrangements into internally driven, active, and externally driven, passive, contributions. Our analysis provides evidence that germ band extension is driven by active T1 processes that self-organize through positive feedback acting on tensions. More generally, our findings suggest that epithelial convergent extension results from controlled transformation of internal force balance geometry which combines the effects of bottom-up local self-organization with the top-down, embryo-scale regulation by gene expression.

Modeling thick filament activation suggests a molecular basis for force depression

Multiscale models aiming to connect muscle's molecular and cellular function have been difficult to develop, in part due to a lack of self-consistent multiscale data. To address this gap, we measured the force response from single, skinned rabbit psoas muscle fibers to ramp shortenings and step stretches performed on the plateau region of the force-length relationship. We isolated myosin from the same muscles and, under similar conditions, performed single-molecule and ensemble measurements of myosin's ATP-dependent interaction with actin using laser trapping and in vitro motility assays. We fit the fiber data by developing a partial differential equation model that includes thick filament activation, whereby an increase in force on the thick filament pulls myosin out of an inhibited state. The model also includes a series elastic element and a parallel elastic element. This parallel elastic element models a titin-actin interaction proposed to account for the increase in isometric force after stretch (residual force enhancement). By optimizing the model fit to a subset of our fiber measurements, we specified seven unknown parameters. The model then successfully predicted the remainder of our fiber measurements and also our molecular measurements from the laser trap and in vitro motility. The success of the model suggests that our multiscale data are self-consistent and can serve as a testbed for other multiscale models. Moreover, the model captures the decrease in isometric force observed in our muscle fibers after active shortening (force depression), suggesting a molecular mechanism for force depression, whereby a parallel elastic element combines with thick filament activation to decrease the number of cycling cross-bridges.

Homologous mutations in human β, embryonic, and perinatal muscle myosins have divergent effects on molecular power generation

Mutations at a highly conserved homologous residue in three closely related muscle myosins cause three distinct diseases involving muscle defects: R671C in β-cardiac myosin causes hypertrophic cardiomyopathy, R672C and R672H in embryonic skeletal myosin cause Freeman-Sheldon syndrome, and R674Q in perinatal skeletal myosin causes trismus-pseudocamptodactyly syndrome. It is not known whether their effects at the molecular level are similar to one another or correlate with disease phenotype and severity. To this end, we investigated the effects of the homologous mutations on key factors of molecular power production using recombinantly expressed human β, embryonic, and perinatal myosin subfragment-1. We found large effects in the developmental myosins but minimal effects in β myosin, and magnitude of changes correlated partially with clinical severity. The mutations in the developmental myosins dramatically decreased the step size and load-sensitive actin-detachment rate of single molecules measured by optical tweezers, in addition to decreasing overall enzymatic (ATPase) cycle rate. In contrast, the only measured effect of R671C in β myosin was a larger step size. Our measurements of step size and bound times predicted velocities consistent with those measured in an in vitro motility assay. Finally, molecular dynamics simulations predicted that the arginine to cysteine mutation in embryonic, but not β, myosin may reduce pre-powerstroke lever arm priming and ADP pocket opening, providing a possible structural mechanism consistent with the experimental observations. This paper presents direct comparisons of homologous mutations in several different myosin isoforms, whose divergent functional effects are a testament to myosin's highly allosteric nature.

Limiting pool and actin architecture controls myosin cluster sizes in adherent cells

The actomyosin cytoskeleton generates mechanical forces that power important cellular processes, such as cell migration, cell division, and mechanosensing. Actomyosin self-assembles into contractile networks and bundles that underlie force generation and transmission in cells. A central step is the assembly of the myosin II filament from myosin monomers, regulation of which has been extensively studied. However, myosin filaments are almost always found as clusters within the cell cortex. While recent studies characterized cluster nucleation dynamics at the cell periphery, how myosin clusters grow on stress fibers remains poorly characterized. Here, we utilize a U2OS osteosarcoma cell line with endogenously tagged myosin II to measure the myosin cluster size distribution in the lamella of adherent cells. We find that myosin clusters can grow with Rho-kinase (ROCK) activity alone in the absence of myosin motor activity. Time-lapse imaging reveals that myosin clusters grow via increased myosin association to existing clusters, which is potentiated by ROCK-dependent myosin filament assembly. Enabling myosin motor activity allows further myosin cluster growth through myosin association that is dependent on F-actin architecture. Using a toy model, we show that myosin self-affinity is sufficient to recapitulate the experimentally observed myosin cluster size distribution, and that myosin cluster sizes are determined by the pool of myosin available for cluster growth. Together, our findings provide new insights into the regulation of myosin cluster sizes within the lamellar actomyosin cytoskeleton.

Intrafusal cross-bridge dynamics shape history-dependent muscle spindle responses to stretch

Computational models can be critical to linking complex properties of muscle spindle organs to the sensory information that they encode during behaviours such as postural sway and locomotion where few muscle spindle recordings exist. Here, we augment a biophysical muscle spindle model to predict the muscle spindle sensory signal. Muscle spindles comprise several intrafusal muscle fibres with varied myosin expression and are innervated by sensory neurons that fire during muscle stretch. We demonstrate how cross-bridge dynamics from thick and thin filament interactions affect the sensory receptor potential at the spike initiating region. Equivalent to the Ia afferent's instantaneous firing rate, the receptor potential is modelled as a linear sum of the force and rate change of force (yank) of a dynamic bag1 fibre and the force of a static bag2/chain fibre. We show the importance of inter-filament interactions in (i) generating large changes in force at stretch onset that drive initial bursts and (ii) faster recovery of bag fibre force and receptor potential following a shortening. We show how myosin attachment and detachment rates qualitatively alter the receptor potential. Finally, we show the effect of faster recovery of receptor potential on cyclic stretch-shorten cycles. Specifically, the model predicts history-dependence in muscle spindle receptor potentials as a function of inter-stretch interval (ISI), pre-stretch amplitude and the amplitude of sinusoidal stretches. This model provides a computational platform for predicting muscle spindle response in behaviourally relevant stretches and can link myosin expression seen in healthy and diseased intrafusal muscle fibres to muscle spindle function.

A mechanochemical model recapitulates distinct vertebrate gastrulation modes

During vertebrate gastrulation, an embryo transforms from a layer of epithelial cells into a multilayered gastrula. This process requires the coordinated movements of hundreds to tens of thousands of cells, depending on the organism. In the chick embryo, patterns of actomyosin cables spanning several cells drive coordinated tissue flows. Here, we derive a minimal theoretical framework that couples actomyosin activity to global tissue flows. Our model predicts the onset and development of gastrulation flows in normal and experimentally perturbed chick embryos, mimicking different gastrulation modes as an active stress instability. Varying initial conditions and a parameter associated with active cell ingression, our model recapitulates distinct vertebrate gastrulation morphologies, consistent with recently published experiments in the chick embryo. Altogether, our results show how changes in the patterning of critical cell behaviors associated with different force-generating mechanisms contribute to distinct vertebrate gastrulation modes via a self-organizing mechanochemical process.

Mechanochemical Active Feedback Generates Convergence Extension in Epithelial Tissue

Convergence extension, the simultaneous elongation of tissue along one axis while narrowing along a perpendicular axis, occurs during embryonic development. A fundamental process that contributes to shaping the organism, it happens in many different species and tissue types. Here, we present a minimal continuum model, that can be directly linked to the controlling microscopic biochemistry, which shows spontaneous convergence extension. It is comprised of a 2D viscoelastic active material with a mechanochemical active feedback mechanism coupled to a substrate via friction. Robust convergent extension behavior emerges beyond a critical value of the activity parameter and is controlled by the boundary conditions and the coupling to the substrate. Oscillations and spatial patterns emerge in this model when internal dissipation dominates over friction, as well as in the active elastic limit.

Modeling Thick Filament Activation Suggests a Molecular Basis for Force Depression

Multiscale models aiming to connect muscle's molecular and cellular function have been difficult to develop, in part, due to a lack of self-consistent multiscale data. To address this gap, we measured the force response from single skinned rabbit psoas muscle fibers to ramp shortenings and step stretches performed on the plateau region of the force-length relationship. We isolated myosin from the same muscles and, under similar conditions, performed single molecule and ensemble measurements of myosin's ATP-dependent interaction with actin using laser trapping and in vitro motility assays. We fit the fiber data by developing a partial differential equation model that includes thick filament activation, whereby an increase in force on the thick filament pulls myosin out of an inhibited state. The model also includes a series elastic element and a parallel elastic element. This parallel elastic element models a titin-actin interaction proposed to account for the increase in isometric force following stretch (residual force enhancement). By optimizing the model fit to a subset of our fiber measurements, we specified seven unknown parameters. The model then successfully predicted the remainder of our fiber measurements and also our molecular measurements from the laser trap and in vitro motility. The success of the model suggests that our multiscale data are self-consistent and can serve as a testbed for other multiscale models. Moreover, the model captures the decrease in isometric force observed in our muscle fibers after active shortening (force depression), suggesting a molecular mechanism for force depression, whereby a parallel elastic element combines with thick filament activation to decrease the number of cycling cross-bridges.

Homologous mutations in β, embryonic, and perinatal muscle myosins have divergent effects on molecular power generation

Mutations at a highly conserved homologous residue in three closely related muscle myosins cause three distinct diseases involving muscle defects: R671C in β -cardiac myosin causes hypertrophic cardiomyopathy, R672C and R672H in embryonic skeletal myosin cause Freeman Sheldon syndrome, and R674Q in perinatal skeletal myosin causes trismus-pseudocamptodactyly syndrome. It is not known if their effects at the molecular level are similar to one another or correlate with disease phenotype and severity. To this end, we investigated the effects of the homologous mutations on key factors of molecular power production using recombinantly expressed human β , embryonic, and perinatal myosin subfragment-1. We found large effects in the developmental myosins, with the most dramatic in perinatal, but minimal effects in β myosin, and magnitude of changes correlated partially with clinical severity. The mutations in the developmental myosins dramatically decreased the step size and load-sensitive actin-detachment rate of single molecules measured by optical tweezers, in addition to decreasing ATPase cycle rate. In contrast, the only measured effect of R671C in β myosin was a larger step size. Our measurements of step size and bound times predicted velocities consistent with those measured in an in vitro motility assay. Finally, molecular dynamics simulations predicted that the arginine to cysteine mutation in embryonic, but not β , myosin may reduce pre-powerstroke lever arm priming and ADP pocket opening, providing a possible structural mechanism consistent with the experimental observations. This paper presents the first direct comparisons of homologous mutations in several different myosin isoforms, whose divergent functional effects are yet another testament to myosin's highly allosteric nature.

Endocytic myosin-1 is a force-insensitive, power-generating motor

Myosins are required for clathrin-mediated endocytosis, but their precise molecular roles in this process are not known. This is, in part, because the biophysical properties of the relevant motors have not been investigated. Myosins have diverse mechanochemical activities, ranging from powerful contractility against mechanical loads to force-sensitive anchoring. To better understand the essential molecular contribution of myosin to endocytosis, we studied the in vitro force-dependent kinetics of the Saccharomyces cerevisiae endocytic type I myosin called Myo5, a motor whose role in clathrin-mediated endocytosis has been meticulously studied in vivo. We report that Myo5 is a low-duty-ratio motor that is activated ∼10-fold by phosphorylation, and that its working stroke and actin-detachment kinetics are relatively force-insensitive. Strikingly, the in vitro mechanochemistry of Myo5 is more like that of cardiac myosin than like that of slow anchoring myosin-1s found on endosomal membranes. We therefore propose that Myo5 generates power to augment actin assembly-based forces during endocytosis in cells.

Summary

Pedersen, Snoberger et al. measure the force-sensitivity of the yeast endocytic the myosin-1 called Myo5 and find that it is more likely to generate power than to serve as a force-sensitive anchor in cells. Implications for Myo5's role in clathrin-mediated endocytosis are discussed.

Limiting Pool and Actin Architecture Controls Myosin Cluster Sizes in Adherent Cells

The actomyosin cytoskeleton generates mechanical forces that power important cellular processes, such as cell migration, cell division, and mechanosensing. Actomyosin self-assembles into contractile networks and bundles that underlie force generation and transmission in cells. A central step is the assembly of the myosin II filament from myosin monomers, regulation of which has been extensively studied. However, myosin filaments are almost always found as clusters within the cell cortex. While recent studies characterized cluster nucleation dynamics at the cell periphery, how myosin clusters grow on stress fibers remains poorly characterized. Here, we utilize a U2OS osteosarcoma cell line with endogenously tagged myosin II to measure the myosin cluster size distribution in the lamella of adherent cells. We find that myosin clusters can grow with Rho-kinase (ROCK) activity alone in the absence of myosin motor activity. Time-lapse imaging reveals that myosin clusters grow via increased myosin association to existing clusters, which is potentiated by ROCK-dependent myosin filament assembly. Enabling myosin motor activity allows further myosin cluster growth through myosin association that is dependent on F-actin architecture. Using a toy model, we show that myosin self-affinity is sufficient to recapitulate the experimentally observed myosin cluster size distribution, and that myosin cluster sizes are determined by the pool of myosin available for cluster growth. Together, our findings provide new insights into the regulation of myosin cluster sizes within the lamellar actomyosin cytoskeleton.

A mutation in switch I alters the load-dependent kinetics of myosin Va

Myosin Va is the molecular motor that drives intracellular vesicular transport, powered by the transduction of chemical energy from ATP into mechanical work. The coupling of the powerstroke and phosphate (Pi) release is key to understanding the transduction process, and crucial details of this process remain unclear. Therefore, we determined the effect of elevated Pi on the force-generating capacity of a mini-ensemble of myosin Va S1 (WT) in a laser trap assay. By increasing the stiffness of the laser trap we determined the effect of increasing resistive loads on the rate of Pi-induced detachment from actin, and quantified this effect using the Bell approximation. We observed that WT myosin generated higher forces and larger displacements at the higher laser trap stiffnesses in the presence of 30 mM Pi, but binding event lifetimes decreased dramatically, which is most consistent with the powerstroke preceding the release of Pi from the active site. Repeating these experiments using a construct with a mutation in switch I of the active site (S217A) caused a seven-fold increase in the load-dependence of the Pi-induced detachment rate, suggesting that the S217A region of switch I may help mediate the load-dependence of Pi-rebinding.

Vascular mechanotransduction

This review aims to survey the current state of mechanotransduction in vascular smooth muscle cells (VSMCs) and endothelial cells (ECs), including their sensing of mechanical stimuli and transduction of mechanical signals that result in the acute functional modulation and longer-term transcriptomic and epigenetic regulation of blood vessels. The mechanosensors discussed include ion channels, plasma membrane-associated structures and receptors, and junction proteins. The mechanosignaling pathways presented include the cytoskeleton, integrins, extracellular matrix, and intracellular signaling molecules. These are followed by discussions on mechanical regulation of transcriptome and epigenetics, relevance of mechanotransduction to health and disease, and interactions between VSMCs and ECs. Throughout this review, we offer suggestions for specific topics that require further understanding. In the closing section on conclusions and perspectives, we summarize what is known and point out the need to treat the vasculature as a system, including not only VSMCs and ECs but also the extracellular matrix and other types of cells such as resident macrophages and pericytes, so that we can fully understand the physiology and pathophysiology of the blood vessel as a whole, thus enhancing the comprehension, diagnosis, treatment, and prevention of vascular diseases.

Thermodynamics and Kinetics of a Binary Mechanical System: Mechanisms of Muscle Contraction

Biological motors function at the interface of biology, physics, and chemistry, and it remains unsettled what rules from which disciplines account for how these motors work. Myosin motors are enzymes that catalyze the hydrolysis of ATP through a mechanism involving a switch-like myosin structural change (a lever arm rotation) induced by actin binding that generates a small displacement of an actin filament. In muscle, individual myosin motors are widely assumed to function as molecular machines having mechanical properties that resemble those of muscle. In a fundamental departure from this perspective, here, I show that muscle more closely resembles a heat engine with mechanical properties that emerge from the thermodynamics of a myosin motor ensemble. The transformative impact of thermodynamics on our understanding of how a heat engine works guides a parallel transformation in our understanding of how muscle works. I consider the simplest possible model of force generation: a binary mechanical system. I develop the mechanics, energetics, and kinetics of this system and show that a single binding reaction generates force when muscle is held at a fixed length and performs work when muscle is allowed to shorten. This creates a network of thermodynamic binding pathways that resembles many of the characteristic mechanical and energetic behaviors of muscle including the muscle force-velocity relationship, heat output by shortening muscle, four phases of a muscle tension transient, spontaneous oscillatory contractions, and force redevelopment. Analogous to the thermodynamic (Carnot) cycle for a heat engine, isothermal and adiabatic binding and detachment reactions create a thermodynamic cycle for muscle that resembles cardiac pressure-volume loops (i.e., how the heart works). This paper provides an outline for how to re-interpret muscle mechanic data using thermodynamics - an ongoing effort that will continue providing novel insights into how muscle and molecular motors work.

Forces of Change: Optical Tweezers in Membrane Remodeling Studies

Optical tweezers allow precise measurement of forces and distances with piconewton and nanometer precision, and have thus been instrumental in elucidating the mechanistic details of various biological processes. Some examples include the characterization of motor protein activity, studies of protein-DNA interactions, and characterizing protein folding trajectories. The use of optical tweezers (OT) to study membranes is, however, much less abundant. Here, we review biophysical studies of membranes that utilize optical tweezers, with emphasis on various assays that have been developed and their benefits and limitations. First, we discuss assays that employ membrane-coated beads, and overview protein-membrane interactions studies based on manipulation of such beads. We further overview a body of studies that make use of a very powerful experimental tool, the combination of OT, micropipette aspiration, and fluorescence microscopy, that allow detailed studies of membrane curvature generation and sensitivity. Finally, we describe studies focused on membrane fusion and fission. We then summarize the overall progress in the field and outline future directions.

F-actin architecture determines constraints on myosin thick filament motion

Active stresses are generated and transmitted throughout diverse F-actin architectures within the cell cytoskeleton, and drive essential behaviors of the cell, from cell division to migration. However, while the impact of F-actin architecture on the transmission of stress is well studied, the role of architecture on the ab initio generation of stresses remains less understood. Here, we assemble F-actin networks in vitro, whose architectures are varied from branched to bundled through F-actin nucleation via Arp2/3 and the formin mDia1. Within these architectures, we track the motions of embedded myosin thick filaments and connect them to the extent of F-actin network deformation. While mDia1-nucleated networks facilitate the accumulation of stress and drive contractility through enhanced actomyosin sliding, branched networks prevent stress accumulation through the inhibited processivity of thick filaments. The reduction in processivity is due to a decrease in translational and rotational motions constrained by the local density and geometry of F-actin.

Hypertrophic cardiomyopathy: Mutations to mechanisms to therapies

Hypertrophic cardiomyopathy (HCM) affects more than 1 in 500 people in the general population with an extensive burden of morbidity in the form of arrhythmia, heart failure, and sudden death. More than 25 years since the discovery of the genetic underpinnings of HCM, the field has unveiled significant insights into the primary effects of these genetic mutations, especially for the myosin heavy chain gene, which is one of the most commonly mutated genes. Our group has studied the molecular effects of HCM mutations on human β-cardiac myosin heavy chain using state-of-the-art biochemical and biophysical tools for the past 10 years, combining insights from clinical genetics and structural analyses of cardiac myosin. The overarching hypothesis is that HCM-causing mutations in sarcomere proteins cause hypercontractility at the sarcomere level, and we have shown that an increase in the number of myosin molecules available for interaction with actin is a primary driver. Recently, two pharmaceutical companies have developed small molecule inhibitors of human cardiac myosin to counteract the molecular consequences of HCM pathogenesis. One of these inhibitors (mavacamten) has recently been approved by the FDA after completing a successful phase III trial in HCM patients, and the other (aficamten) is currently being evaluated in a phase III trial. Myosin inhibitors will be the first class of medication used to treat HCM that has both robust clinical trial evidence of efficacy and that targets the fundamental mechanism of HCM pathogenesis. The success of myosin inhibitors in HCM opens the door to finding other new drugs that target the sarcomere directly, as we learn more about the genetics and fundamental mechanisms of this disease.

A chemical thermodynamic model of motor enzymes unifies chemical-Fx and powerstroke models

Molecular motors play a central role in many biological processes, ranging from pumping blood and breathing to growth and wound healing. Through motor-catalyzed chemical reactions, these nanomachines convert the chemical free energy from ATP hydrolysis into two different forms of mechanical work. Motor enzymes perform reversible work, wrev, through an intermediate step in their catalyzed reaction cycle referred to as a working step, and they perform Fx work when they move a distance, x, against a force, F. In a powerstroke model, wrev is performed when the working step stretches a spring within a given motor enzyme. In a chemical-Fx model, wrev is performed in generating a conserved Fx potential defined external to the motor enzyme. It is difficult to find any common ground between these models even though both have been shown to account for mechanochemical measurements of motor enzymes with reasonable accuracy. Here, I show that, by changing one simple assumption in each model, the powerstroke and chemical-Fx model can be reconciled through a chemical thermodynamic model. The formal and experimental justifications for changing these assumptions are presented. The result is a unifying model for mechanochemical coupling in motor enzymes first presented by A.V. Hill in 1938 that is consistent with single-molecule structural and mechanical data.

Deconstructing the role of myosin contractility in force fluctuations within focal adhesions

Force fluctuations exhibited in focal adhesions that connect a cell to its extracellular environment point to the complex role of the underlying machinery that controls cell migration. To elucidate the explicit role of myosin motors in the temporal traction force oscillations, we vary the contractility of these motors in a dynamical model based on the molecular clutch hypothesis. As the contractility is lowered, effected both by changing the motor velocity and the rate of attachment/detachment, we show analytically in an experimentally relevant parameter space, that the system goes from decaying oscillations to stable limit cycle oscillations through a supercritical Hopf bifurcation. As a function of the motor activity and the number of clutches, the system exhibits a rich array of dynamical states. We corroborate our analytical results with stochastic simulations of the motor-clutch system. We obtain limit cycle oscillations in the parameter regime as predicted by our model. The frequency range of oscillations in the average clutch and motor deformation compares well with experimental results.

Force Measurements From Myofibril to Filament

Contractility, the generation of force and movement by molecular motors, is the hallmark of all muscles, including striated muscle. Contractility can be studied at every level of organization from a whole animal to single molecules. Measurements at sub-cellular level are particularly useful since, in the absence of the excitation-contraction coupling system, the properties of the contractile proteins can be directly investigated; revealing mechanistic details not accessible in intact muscle. Moreover, the conditions can be manipulated with ease, for instance changes in activator Ca²⁺, small molecule effector concentration or phosphorylation levels and introducing mutations. Subcellular methods can be successfully applied to frozen materials and generally require the smallest amount of tissue, thus greatly increasing the range of possible experiments compared with the study of intact muscle and cells. Whilst measurement of movement at the subcellular level is relatively simple, measurement of force is more challenging. This mini review will describe current methods for measuring force production at the subcellular level including single myofibril and single myofilament techniques.

High-Speed Optical Traps Address Dynamics of Processive and Non-Processive Molecular Motors

Interactions between biological molecules occur on very different time scales, from the minutes of strong protein-protein bonds, down to below the millisecond duration of rapid biomolecular interactions. Conformational changes occurring on sub-ms time scales and their mechanical force dependence underlie the functioning of enzymes (e.g., motor proteins) that are fundamental for life. However, such rapid interactions are beyond the temporal resolution of most single-molecule methods. We developed ultrafast force-clamp spectroscopy (UFFCS), a single-molecule technique based on laser tweezers that allows us to investigate early and very fast dynamics of a variety of enzymes and their regulation by mechanical load. The technique was developed to investigate the rapid interactions between skeletal muscle myosin and actin, and then applied to the study of different biological systems, from cardiac myosin to processive myosin V, microtubule-binding proteins, transcription factors, and mechanotransducer proteins. Here, we describe two different implementations of UFFCS instrumentation and protocols using either acousto- or electro-optic laser beam deflectors, and their application to the study of processive and non-processive motor proteins.

Velocity of myosin-based actin sliding depends on attachment and detachment kinetics and reaches a maximum when myosin-binding sites on actin saturate

Molecular motors such as kinesin and myosin often work in groups to generate the directed movements and forces critical for many biological processes. Although much is known about how individual motors generate force and movement, surprisingly, little is known about the mechanisms underlying the macroscopic mechanics generated by multiple motors. For example, the observation that a saturating number, N, of myosin heads move an actin filament at a rate that is influenced by actin–myosin attachment and detachment kinetics is accounted for neither experimentally nor theoretically. To better understand the emergent mechanics of actin–myosin mechanochemistry, we use an in vitro motility assay to measure and correlate the N-dependence of actin sliding velocities, actin-activated ATPase activity, force generation against a mechanical load, and the calcium sensitivity of thin filament velocities. Our results show that both velocity and ATPase activity are strain dependent and that velocity becomes maximized with the saturation of myosin-binding sites on actin at a value that is 40% dependent on attachment kinetics and 60% dependent on detachment kinetics. These results support a chemical thermodynamic model for ensemble motor mechanochemistry and imply molecularly explicit mechanisms within this framework, challenging the assumption of independent force generation.

Myosin's powerstroke occurs prior to the release of phosphate from the active site

Myosins are a family of motor proteins responsible for various forms of cellular motility, including muscle contraction and vesicular transport. The most fundamental aspect of myosin is its ability to transduce the chemical energy from the hydrolysis of ATP into mechanical work, in the form of force and/or motion. A key unanswered question of the transduction process is the timing of the force-generating powerstroke relative to the release of phosphate (P_i ) from the active site. We examined the ability of single-headed myosin Va to generate a powerstroke in a single molecule laser trap assay while maintaining P_i in its active site, by either elevating P_i in solution or by introducing a mutation in myosin's active site (S217A) to slow P_i -release from the active site. Upon binding to the actin filament, WT myosin generated a powerstoke rapidly (≥500 s^-1 ) and without a detectable delay, both in the absence and presence of 30 mM P_i . The elevated levels of P_i did, however, affect event lifetime, eliminating the longest 25% of binding events, confirming that P_i rebound to myosin's active site and accelerated detachment. The S217A construct also generated a powerstroke similar in size and rate upon binding to actin despite the slower P_i release rate. These findings provide direct evidence that myosin Va generates a powerstroke with P_i still in its active site. Therefore, the findings are most consistent with a model in which the powerstroke occurs prior to the release of P_i from the active site.

Measuring force generation within reconstituted microtubule bundle assemblies using optical tweezers

Kinesins and microtubule associated proteins (MAPs) are critical to sustain life, facilitating cargo transport, cell division, and motility. To interrogate the mechanistic underpinnings of their function, these microtubule-based motors and proteins have been studied extensively at the single molecule level. However, a long-standing issue in the single molecule biophysics field has been how to investigate motors and associated proteins within a physiologically relevant environment in vitro. While the one motor/one filament orientation of a traditional optical trapping assay has revolutionized our knowledge of motor protein mechanics, this reductionist geometry does not reflect the structural hierarchy in which many motors work within the cellular environment. Here, we review approaches that combine the precision of optical tweezers with reconstituted ensemble systems of microtubules, MAPs, and kinesins to understand how each of these unique elements work together to perform large scale cellular tasks, such as but not limited to building the mitotic spindle. Not only did these studies develop novel techniques for investigating motor proteins in vitro, but they also illuminate ensemble filament and motor synergy that helps bridge the mechanistic knowledge gap between previous single molecule and cell level studies.

Evolution of mechanical cooperativity among myosin II motors

Myosin II is a biomolecular machine that is responsible for muscle contraction. Myosin II motors act cooperatively: during muscle contraction, multiple motors bind to a single actin filament and pull it against an external load, like people pulling on a rope in a tug-of-war. We model the dynamics of actomyosin filaments in order to study the evolution of motor-motor cooperativity. We find that filament backsliding-the distance an actin slides backward when a motor at the end of its cycle releases-is central to the speed and efficiency of muscle contraction. Our model predicts that this backsliding has been reduced through evolutionary adaptations to the motor's binding propensity, the strength of the motor's power stroke, and the force dependence of the motor's release from actin. These properties optimize the collective action of myosin II motors, which is not a simple sum of individual motor actions. The model also shows that these evolutionary variables can explain the speed-efficiency trade-off observed across different muscle tissues. This is an example of how evolution can tune the microscopic properties of individual proteins in order to optimize complex biological functions.

Mechanosensitive myosin II but not cofilin primarily contributes to cyclic cell stretch-induced selective disassembly of actin stress fibers

Cells adapt to applied cyclic stretch (CS) to circumvent chronic activation of proinflammatory signaling. Currently, the molecular mechanism of the selective disassembly of actin stress fibers (SFs) in the stretch direction, which occurs at the early stage of the cellular response to CS, remains controversial. Here, we suggest that the mechanosensitive behavior of myosin II, a major cross-linker of SFs, primarily contributes to the directional disassembly of the actomyosin complex SFs in bovine vascular smooth muscle cells and human U2OS osteosarcoma cells. First, we identified that CS with a shortening phase that exceeds in speed the inherent contractile rate of individual SFs leads to the disassembly. To understand the biological basis, we investigated the effect of expressing myosin regulatory light-chain mutants and found that SFs with less actomyosin activities disassemble more promptly upon CS. We consequently created a minimal mathematical model that recapitulates the salient features of the direction-selective and threshold-triggered disassembly of SFs to show that disassembly or, more specifically, unbundling of the actomyosin bundle SFs is enhanced with sufficiently fast cell shortening. We further demonstrated that similar disassembly of SFs is inducible in the presence of an active LIM-kinase-1 mutant that deactivates cofilin, suggesting that cofilin is dispensable as opposed to a previously proposed mechanism.

Force-velocity and tension transient measurements from Drosophila jump muscle reveal the necessity of both weakly-bound cross-bridges and series elasticity in models of muscle contraction

Muscle contraction is a fundamental biological process where molecular interactions between the myosin molecular motor and actin filaments result in contraction of a whole muscle, a process spanning size scales differing in eight orders of magnitude. Since unique behavior is observed at every scale in between these two extremes, to fully understand muscle function it is vital to develop multi-scale models. Based on simulations of classic measurements of muscle heat generation as a function of work, and shortening rate as a function of applied force, we hypothesize that a model based on molecular measurements must be modified to include a weakly-bound interaction between myosin and actin in order to fit measurements at the muscle fiber or whole muscle scales. This hypothesis is further supported by the model's need for a weakly-bound state in order to qualitatively reproduce the force response that occurs when a muscle fiber is rapidly stretched a small distance. We tested this hypothesis by measuring steady-state force as a function of shortening velocity, and the force transient caused by a rapid length step in Drosophila jump muscle fibers. Then, by performing global parameter optimization, we quantitatively compared the predictions of two mathematical models, one lacking a weakly-bound state and one with a weakly-bound state, to these measurements. Both models could reproduce our force-velocity measurements, but only the model with a weakly-bound state could reproduce our force transient measurements. However, neither model could concurrently fit both measurements. We find that only a model that includes weakly-bound cross-bridges with force-dependent detachment and an elastic element in series with the cross-bridges is able to fit both of our measurements. This result suggests that the force response after stretch is not a reflection of distinct steps in the cross-bridge cycle, but rather arises from the interaction of cross-bridges with a series elastic element. Additionally, the model suggests that the curvature of the force-velocity relationship arises from a combination of the force-dependence of weakly- and strongly-bound cross-bridges. Overall, this work presents a minimal cross-bridge model that has predictive power at the fiber level.

FRET and optical trapping reveal mechanisms of actin activation of the power stroke and phosphate release in myosin V

Myosins generate force and motion by precisely coordinating their mechanical and chemical cycles, but the nature and timing of this coordination remains controversial. We utilized a FRET approach to examine the kinetics of structural changes in the force-generating lever arm in myosin V. We directly compared the FRET results with single-molecule mechanical events examined by optical trapping. We introduced a mutation (S217A) in the conserved switch I region of the active site to examine how myosin couples structural changes in the actin- and nucleotide-binding regions with force generation. Specifically, S217A enhanced the maximum rate of lever arm priming (recovery stroke) while slowing ATP hydrolysis, demonstrating that it uncouples these two steps. We determined that the mutation dramatically slows both actin-induced rotation of the lever arm (power stroke) and phosphate release (≥10-fold), whereas our simulations suggest that the maximum rate of both steps is unchanged by the mutation. Time-resolved FRET revealed that the structure of the pre- and post-power stroke conformations and mole fractions of these conformations were not altered by the mutation. Optical trapping results demonstrated that S217A does not dramatically alter unitary displacements or slow the working stroke rate constant, consistent with the mutation disrupting an actin-induced conformational change prior to the power stroke. We propose that communication between the actin- and nucleotide-binding regions of myosin assures a proper actin-binding interface and active site have formed before producing a power stroke. Variability in this coupling is likely crucial for mediating motor-based functions such as muscle contraction and intracellular transport.

Actin bundle architecture and mechanics regulate myosin II force generation

The actin cytoskeleton is a soft, structural material that underlies biological processes such as cell division, motility, and cargo transport. The cross-linked actin filaments self-organize into a myriad of architectures, from disordered meshworks to ordered bundles, which are hypothesized to control the actomyosin force generation that regulates cell migration, shape, and adhesion. Here, we use fluorescence microscopy and simulations to investigate how actin bundle architectures with varying polarity, spacing, and rigidity impact myosin II dynamics and force generation. Microscopy reveals that mixed-polarity bundles formed by rigid cross-linkers support slow, bidirectional myosin II filament motion, punctuated by periods of stalled motion. Simulations reveal that these locations of stalled myosin motion correspond to sustained, high forces in regions of balanced actin filament polarity. By contrast, mixed-polarity bundles formed by compliant, large cross-linkers support fast, bidirectional motion with no traps. Simulations indicate that trap duration is directly related to force magnitude and that the observed increased velocity corresponds to lower forces resulting from both the increased bundle compliance and filament spacing. Our results indicate that the microstructures of actin assemblies regulate the dynamics and magnitude of myosin II forces, highlighting the importance of architecture and mechanics in regulating forces in biological materials.

Detailed Balance Broken by Catch Bond Kinetics Enables Mechanical-Adaptation in Active Materials

Unlike nearly all engineered materials which contain bonds that weaken under load, biological materials contain "catch" bonds which are reinforced under load. Consequently, materials, such as the cell cytoskeleton, can adapt their mechanical properties in response to their state of internal, non-equilibrium (active) stress. However, how large-scale material properties vary with the distance from equilibrium is unknown, as are the relative roles of active stress and binding kinetics in establishing this distance. Through course-grained molecular dynamics simulations, the effect of breaking of detailed balance by catch bonds on the accumulation and dissipation of energy within a model of the actomyosin cytoskeleton is explored. It is found that the extent to which detailed balance is broken uniquely determines a large-scale fluid-solid transition with characteristic time-reversal symmetries. The transition depends critically on the strength of the catch bond, suggesting that active stress is necessary but insufficient to mount an adaptive mechanical response.

Millisecond Conformational Dynamics of Skeletal Myosin II Power Stroke Studied by High-Speed Atomic Force Microscopy

Myosin-based molecular motors are responsible for a variety of functions in the cells. Myosin II is ultimately responsible for muscle contraction and can be affected by multiple mutations, that may lead to myopathies. Therefore, it is essential to understand the nanomechanical properties of myosin II. Due to the lack of technical capabilities to visualize rapid changes in nonprocessive molecular motors, there are several mechanistic details in the force-generating steps produced by myosin II that are poorly understood. In this study, high-speed atomic force microscopy was used to visualize the actin-myosin complex at high temporal and spatial resolutions, providing further details about the myosin mechanism of force generation. A two-step motion of the double-headed heavy meromyosin (HMM) lever arm, coupled to an 8.4 nm working stroke was observed in the presence of ATP. HMM heads attached to an actin filament worked independently, exhibiting different lever arm configurations in given time during experiments. A lever arm rotation was associated with several non-stereospecific long-lived and stereospecific short-lived (∼1 ms) HMM conformations. The presence of free P_i increased the short-lived stereospecific binding events in which the power stroke occurred, followed by release of P_i after the power stroke.

Myosin with hypertrophic cardiac mutation R712L has a decreased working stroke which is rescued by omecamtiv mecarbil

Hypertrophic cardiomyopathies (HCMs) are the leading cause of acute cardiac failure in young individuals. Over 300 mutations throughout β-cardiac myosin, including in the motor domain, are associated with HCM. A β-cardiac myosin motor mutation (R712L) leads to a severe form of HCM. Actin-gliding motility of R712L-myosin is inhibited, despite near-normal ATPase kinetics. By optical trapping, the working stroke of R712L-myosin was decreased 4-fold, but actin-attachment durations were normal. A prevalent hypothesis that HCM mutants are hypercontractile is thus not universal. R712 is adjacent to the binding site of the heart failure drug omecamtiv mecarbil (OM). OM suppresses the working stroke of normal β-cardiac myosin, but remarkably, OM rescues the R712L-myosin working stroke. Using a flow chamber to interrogate a single molecule during buffer exchange, we found OM rescue to be reversible. Thus, the R712L mutation uncouples lever arm rotation from ATPase activity and this inhibition is rescued by OM.

Mechanosensitive self-assembly of myosin II minifilaments

Self-assembly and force generation are two central processes in biological systems that usually are considered in separation. However, the signals that activate nonmuscle myosin II molecular motors simultaneously lead to self-assembly into myosin II minifilaments as well as progression of the motor heads through the cross-bridge cycle. Here we investigate theoretically the possible effects of coupling these two processes. Our assembly model, which builds on a consensus architecture of the minifilament, predicts a critical aggregation concentration at which the assembly kinetics slows down dramatically. The combined model predicts that increasing actin filament concentration and force both lead to a decrease in the critical aggregation concentration. We suggest that due to these effects, myosin II minifilaments in a filamentous context might be in a critical state that reacts faster to varying conditions than in solution. We finally compare our model to experiments by simulating fluorescence recovery after photobleaching.

The ATPase mechanism of myosin 15, the molecular motor mutated in DFNB3 human deafness

Cochlear hair cells each possess an exquisite bundle of actin-based stereocilia that detect sound. Unconventional myosin 15 (MYO15) traffics and delivers critical molecules required for stereocilia development and thus is essential for building the mechanosensory hair bundle. Mutations in the human MYO15A gene interfere with stereocilia trafficking and cause hereditary hearing loss, DFNB3, but the impact of these mutations is not known, as MYO15 itself is poorly characterized. To learn more, we performed a kinetic study of the ATPase motor domain to characterize its mechanochemical cycle. Using the baculovirus-Sf9 system, we purified a recombinant minimal motor domain (S1) by coexpressing the mouse MYO15 ATPase, essential and regulatory light chains that bind its IQ domains, and UNC45 and HSP90A chaperones required for correct folding of the ATPase. MYO15 purified with either UNC45A or UNC45B coexpression had similar ATPase activities (kcat = ∼ 6 s-1 at 20 °C). Using stopped-flow and quenched-flow transient kinetic analyses, we measured the major rate constants describing the ATPase cycle, including ATP, ADP, and actin binding; hydrolysis; and phosphate release. Actin-attached ADP release was the slowest measured transition (∼12 s-1 at 20 °C), although this did not rate-limit the ATPase cycle. The kinetic analysis shows the MYO15 motor domain has a moderate duty ratio (∼0.5) and weak thermodynamic coupling between ADP and actin binding. These findings are consistent with MYO15 being kinetically adapted for processive motility when oligomerized. Our kinetic characterization enables future studies into how deafness-causing mutations affect MYO15 and disrupt stereocilia trafficking necessary for hearing.

Acto-Myosin Cross-Bridge Stiffness Depends on the Nucleotide State of Myosin II

How various myosin isoforms fulfill the diverse physiological requirements of distinct muscle types remain unclear. Myosin II isoforms expressed in skeletal muscles determine the mechanical performance of the specific muscles. Here, we employed a single-molecule optical trapping method and compared the chemomechanical properties of slow and fast muscle myosin II isoforms. Stiffness of the myosin motor is key to its force-generating ability during muscle contraction. We found that acto-myosin (AM) cross-bridge stiffness depends on its nucleotide state as the myosin progresses through the ATPase cycle. The strong actin bound "AM.ADP" state exhibited >2 fold lower stiffness than "AM rigor" state. The two myosin isoforms displayed similar "rigor" stiffness. We conclude that the time-averaged stiffness of the slow myosin is lower due to prolonged duration of the AM.ADP state, which determines the force-generating potential and contraction speed of the muscle, elucidating the basis for functional diversity among myosins.

Mechanical stimulation of single cells by reversible host-guest interactions in 3D microscaffolds

Many essential cellular processes are regulated by mechanical properties of their microenvironment. Here, we introduce stimuli-responsive composite scaffolds fabricated by three-dimensional (3D) laser lithography to simultaneously stretch large numbers of single cells in tailored 3D microenvironments. The key material is a stimuli-responsive photoresist containing cross-links formed by noncovalent, directional interactions between β-cyclodextrin (host) and adamantane (guest). This allows reversible actuation under physiological conditions by application of soluble competitive guests. Cells adhering in these scaffolds build up initial traction forces of ~80 nN. After application of an equibiaxial stretch of up to 25%, cells remodel their actin cytoskeleton, double their traction forces, and equilibrate at a new dynamic set point within 30 min. When the stretch is released, traction forces gradually decrease until the initial set point is retrieved. Pharmacological inhibition or knockout of nonmuscle myosin 2A prevents these adjustments, suggesting that cellular tensional homeostasis strongly depends on functional myosin motors.

What factors determine the number of nonmuscle myosin II in the sarcomeric unit of stress fibers?

Actin stress fibers (SFs), a contractile apparatus in nonmuscle cells, possess a contractile unit that is apparently similar to the sarcomere of myofibrils in muscles. The function of SFs has thus often been addressed based on well-characterized properties of muscles. However, unlike the fixed number of myosin molecules in myofibrils, the number of nonmuscle myosin II (NMII) within the contractile sarcomeric unit in SFs is quite low and variable for some reason. Here we address what factors may determine the specific number of NMII in SFs. We suggest with a theoretical model that the number lies just in between the function of SFs for bearing cellular tension under static conditions and for promptly disintegrating upon forced cell shortening. We monitored shortening-induced disintegration of SFs in human osteosarcoma U2OS cells expressing mutants of myosin regulatory light chain that virtually regulates the interaction of NMII with actin filaments, and the behaviors observed were indeed consistent with the theoretical consequences. This situation-specific nature of SFs may allow nonmuscle cells to respond adaptively to mechanical stress to circumvent activation of pro-inflammatory signals as previously indicated, i.e., a behavior distinct from that of muscles that are basically specialized for exhibiting contractile activity.

Does protein unfolding play a functional role in vivo?

Unfolding and refolding of multidomain proteins under force have yet to be recognized as a major mechanism of function for proteins in vivo. In this review, we discuss the inherent properties of multidomain proteins under a force vector from a structural and functional perspective. We then characterize three main systems where multidomain proteins could play major roles through mechanical unfolding: muscular contraction, cellular mechanotransduction, and bacterial adhesion. We analyze how key multidomain proteins for each system can produce a gain-of-function from the perspective of a fine-tuned quantized response, a molecular battery, delivery of mechanical work through refolding, elasticity tuning, protection and exposure of cryptic sites, and binding-induced mechanical changes. Understanding how mechanical unfolding and refolding affect function will have important implications in designing mechano-active drugs against conditions such as muscular dystrophy, cancer, or novel antibiotics.

Positional Isomers of a Non-Nucleoside Substrate Differentially Affect Myosin Function

Molecular motors have evolved to transduce chemical energy from ATP into mechanical work to drive essential cellular processes, from muscle contraction to vesicular transport. Dysfunction of these motors is a root cause of many pathologies necessitating the need for intrinsic control over molecular motor function. Herein, we demonstrate that positional isomerism can be used as a simple and powerful tool to control the molecular motor of muscle, myosin. Using three isomers of a synthetic non-nucleoside triphosphate, we demonstrate that myosin's force- and motion-generating capacity can be dramatically altered at both the ensemble and single-molecule levels. By correlating our experimental results with computation, we show that each isomer exerts intrinsic control by affecting distinct steps in myosin's mechanochemical cycle. Our studies demonstrate that subtle variations in the structure of an abiotic energy source can be used to control the force and motility of myosin without altering myosin's structure.

Single-molecule analysis reveals that regulatory light chains fine-tune skeletal myosin II function

Myosin II is the main force-generating motor during muscle contraction. Myosin II exists as different isoforms that are involved in diverse physiological functions. One outstanding question is whether the myosin heavy chain (MHC) isoforms alone account for these distinct physiological properties. Unique sets of essential and regulatory light chains (RLCs) are known to assemble with specific MHCs, raising the intriguing possibility that light chains contribute to specialized myosin functions. Here, we asked whether different RLCs contribute to this functional diversification. To this end, we generated chimeric motors by reconstituting the MHC fast isoform (MyHC-IId) and slow isoform (MHC-I) with different light-chain variants. As a result of the RLC swapping, actin filament sliding velocity increased by ∼10-fold for the slow myosin and decreased by >3-fold for the fast myosin. Results from ensemble molecule solution kinetics and single-molecule optical trapping measurements provided in-depth insights into altered chemo-mechanical properties of the myosin motors that affect the sliding speed. Notably, we found that the mechanical output of both slow and fast myosins is sensitive to the RLC isoform. We therefore propose that RLCs are crucial for fine-tuning the myosin function.

A biomechanical model for the transendothelial migration of cancer cells

We propose a biomechanical model for the extravasation of a tumor cell (TC) through the endothelium of a blood vessel. Based on prior in vitro observations, we assume that the TC extends a protrusion between adjacent endothelial cells (ECs) that adheres to the basement membrane via focal adhesions (FAs). As the protrusion grows in size and branches out, the actomyosin contraction along the stress fibers (SFs) inside the protrusion pulls the relatively rigid nucleus through the endothelial opening. We model the chemo-mechanics of the SFs and the FAs by following the kinetics of the active myosin motors and high-affinity integrins, subject to mechanical feedback. This is incorporated into a finite-element simulation of the extravasation process, with the contractile force pulling the nucleus of the TC against elastic resistance of the ECs. To account for the interaction between the TC nucleus and the endothelium, we consider two scenarios: solid-solid contact and lubrication by cytosol. The former gives a lower bound for the required contractile force to realize transmigration, while the latter provides a more realistic representation of the process. Using physiologically reasonable parameters, our model shows that the SF and FA ensemble can produce a contractile force on the order of 70 nN, which is sufficient to deform the ECs and enable transmigration. Furthermore, we use an atomic force microscope to measure the resistant force on a human bladder cancer cell that is pushed through an endothelium cultured in vitro. The magnitude of the required force turns out to be in the range of 70-100 nN, comparable to the model predictions.

Straightening Out the Elasticity of Myosin Cross-Bridges

In a contracting muscle, myosin cross-bridges extending from thick filaments pull the interdigitating thin (actin-containing) filaments during cyclical ATP-driven interactions toward the center of the sarcomere, the structural unit of striated muscle. Cross-bridge attachments in the sarcomere have been reported to exhibit a similar stiffness under both positive and negative forces. However, in vitro measurements on filaments with a sparse complement of heads detected a decrease of the cross-bridge stiffness at negative forces attributed to the buckling of the subfragment 2 tail portion. Here, we review some old and new data that confirm that cross-bridge stiffness is nearly linear in the muscle filament lattice. The implications of high myosin stiffness at positive and negative strains are considered in muscle fibers and in nonmuscle intracellular cargo transport.

The load dependence and the force-velocity relation in intact myosin filaments from skeletal and smooth muscles

In the present study we evaluated the load dependence of force produced by isolated muscle myosin filaments interacting with fluorescently labeled actin filaments, using for the first time whole native myosin filaments. We used a newly developed approach that allowed the use of physiological levels of ATP. Single filaments composed of either skeletal or smooth muscle myosin and single filaments of actin were attached between pairs of nano-fabricated cantilevers of known stiffness. The filaments were brought into contact to produce force, which caused sliding of the actin filaments over the myosin filaments. We applied load to the system by either pushing or pulling the filaments during interactions and observed that increasing the load increased the force produced by myosin and decreasing the load decreased the force. We also performed additional experiments in which we clamped the filaments at predetermined levels of force, which caused the filaments to slide to adjust the different loads, allowing us to measure the velocity of length changes to construct a force-velocity relation. Force values were in the range observed previously with myosin filaments and molecules. The force-velocity curves for skeletal and smooth muscle myosins resembled the relations observed for muscle fibers. The technique can be used to investigate many issues of interest and debate in the field of muscle biophysics.

Direct visualization of human myosin II force generation using DNA origami-based thick filaments

The sarcomere, the minimal mechanical unit of muscle, is composed of myosins, which self-assemble into thick filaments that interact with actin-based thin filaments in a highly-structured lattice. This complex imposes a geometric restriction on myosin in force generation. However, how single myosins generate force within the restriction remains elusive and conventional synthetic filaments do not recapitulate the symmetric bipolar filaments in sarcomeres. Here we engineered thick filaments using DNA origami that incorporate human muscle myosin to directly visualize the motion of the heads during force generation in a restricted space. We found that when the head diffuses, it weakly interacts with actin filaments and then strongly binds preferentially to the forward region as a Brownian ratchet. Upon strong binding, the two-step lever-arm swing dominantly halts at the first step and occasionally reverses direction. Our results illustrate the usefulness of our DNA origami-based assay system to dissect the mechanistic details of motor proteins.