Mechanical coupling between myosin molecules causes differences between ensemble and single-molecule measurements

Mechanisms of myosin II force generation: insights from novel experimental techniques and approaches

Myosin II is a molecular motor that converts chemical energy derived from ATP hydrolysis into mechanical work. Myosin II isoforms are responsible for muscle contraction and a range of cell functions relying on the development of force and motion. When the motor attaches to actin, ATP is hydrolyzed and inorganic phosphate (Pi) and ADP are released from its active site. These reactions are coordinated with changes in the structure of myosin, promoting the so-called "power stroke" that causes the sliding of actin filaments. The general features of the myosin-actin interactions are well accepted, but there are critical issues that remain poorly understood, mostly due to technological limitations. In recent years, there has been a significant advance in structural, biochemical, and mechanical methods that have advanced the field considerably. New modeling approaches have also allowed researchers to understand actomyosin interactions at different levels of analysis. This paper reviews recent studies looking into the interaction between myosin II and actin filaments, which leads to power stroke and force generation. It reviews studies conducted with single myosin molecules, myosins working in filaments, muscle sarcomeres, myofibrils, and fibers. It also reviews the mathematical models that have been used to understand the mechanics of myosin II in approaches focusing on single molecules to ensembles. Finally, it includes brief sections on translational aspects, how changes in the myosin motor by mutations and/or posttranslational modifications may cause detrimental effects in diseases and aging, among other conditions, and how myosin II has become an emerging drug target.

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.

Deciphering Mechanochemical Influences of Emergent Actomyosin Crosstalk using QCM-D

Cytoskeletal protein ensembles exhibit emergent mechanics where behavior exhibited in teams is not necessarily the sum of the components' single molecule properties. In addition, filaments may act as force sensors that distribute feedback and influence motor protein behavior. To understand the design principles of such emergent mechanics, we developed an approach utilizing QCM-D to measure how actomyosin bundles respond mechanically to environmental variables that alter constituent myosin II motor behavior. We demonstrate that QCM-D can detect changes in actomyosin viscoelasticity due to molecular-level alterations, such as motor concentration and nucleotide state, thus providing evidence for actin's role as a mechanical force-feedback sensor and a new approach for deciphering the fundamental mechanisms of emergent cytoskeletal ensemble crosstalk.

Justification

Cytoskeletal ensembles exhibit mechanics that are not necessarily the sum of the components' single molecule properties, and this emergent behavior is not well understood. Cytoskeletal filaments may also act as force sensors that influence constituent motor protein behavior. To understand the elusive design principles of such emergent mechanics, we innovated an approach using QCM-D to measure how actomyosin bundles sense and respond mechanically to environmental variables. We demonstrate for the first time that QCM-D can detect changes in actomyosin viscoelasticity due to molecular-level alterations, thus providing evidence for actin's role as a mechanical force-feedback sensor and a new approach for deciphering the fundamentals of emergent cytoskeletal ensemble crosstalk.

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.

Wave-like oscillations of clamped microtubules driven by collective dynein transport

Microtubules (MTs) are observed to move and buckle driven by ATP-dependent molecular motors in both mitotic and interphasic eukaryotic cells as well as in specialized structures such as flagella and cilia with a stereotypical geometry. In previous work, clamped MTs driven by a few kinesin motors were seen to buckle and occasionally flap in what was referred to as flagella-like motion. Theoretical models of active-filament dynamics and a following force have predicted that, with sufficient force and binding-unbinding, such clamped filaments should spontaneously undergo periodic buckling oscillations. However, a systematic experimental test of the theory and reconciliation to a model was lacking. Here, we have engineered a minimal system of MTs clamped at their plus ends and transported by a sheet of dynein motors that demonstrate the emergence of spontaneous traveling-wave oscillations along single filaments. The frequencies of tip oscillations are in the millihertz range and are statistically indistinguishable in the onset and recovery phases. We develop a 2D computational model of clamped MTs binding and unbinding stochastically to motors in a "gliding-assay" geometry. The simulated MTs oscillate with a frequency comparable to experiment. The model predicts the effect of MT length and motor density on qualitative transitions between distinct phases of flapping, regular oscillations, and looping. We develop an effective "order parameter" based on the relative deflection along the filament and orthogonal to it. The transitions predicted in simulations are validated by experimental data. These results demonstrate a role for geometry, MT buckling, and collective molecular motor activity in the emergence of oscillatory dynamics.

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.

FIM: A fatigued-injured muscle model based on the sliding filament theory

Skeletal muscle modeling has a vital role in movement studies and the development of therapeutic approaches. In the current study, a Huxley-based model for skeletal muscle is proposed, which demonstrates the impact of impairments in muscle characteristics. This model focuses on three identified ions: H+, inorganic phosphate Pi, and Ca2+. Modifications are made to actin-myosin attachment and detachment rates to study the effects of H+ and Pi. Additionally, an activation coefficient is included to represent the role of calcium ions interacting with troponin, highlighting the importance of Ca2+. It is found that maximum isometric muscle force decreases by 9.5% due to a reduction in pH from 7.4 to 6.5 and by 47.5% in case of the combination of a reduction in pH and an increase of Pi concentration up to 30 mM, respectively. Then the force decline caused by a fall in the active calcium ions is studied. When only 15% of the total calcium in the myofibrillar space is able to interact with troponin, up to 80% force drop is anticipated by the model. The proposed fatigued-injured muscle model is useful to study the effect of various shortening velocities and initial muscle-tendon lengths on muscle force; in addition, the benefits of the model go beyond predicting the force in different conditions as it can also predict muscle stiffness and power. The power and stiffness decrease by 40% and 6.5%, respectively, due to the pH reduction, and the simultaneous accumulation of H+ and Pi leads to a 50% and 18% drop in power and stiffness.

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.

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.

Virus-free transfection, transient expression, and purification of human cardiac myosin in mammalian muscle cells for biochemical and biophysical assays

Myosin expression and purification is important for mechanistic insights into normal function and mutation induced changes. The latter is particularly important for striated muscle myosin II where mutations cause several debilitating diseases. However, the heavy chain of this myosin is challenging to express and the standard protocol, using C2C12 cells, relies on viral infection. This is time and work intensive and associated with infrastructural demands and biological hazards, limiting widespread use and hampering fast generation of a wide range of mutations. We here develop a virus-free method to overcome these challenges. We use this system to transfect C2C12 cells with the motor domain of the human cardiac myosin heavy chain. After optimizing cell transfection, cultivation and harvesting conditions, we functionally characterized the expressed protein, co-purified with murine essential and regulatory light chains. The gliding velocity (1.5-1.7 µm/s; 25 °C) in the in vitro motility assay as well as maximum actin activated catalytic activity (kcat; 8-9 s-1) and actin concentration for half maximal activity (KATPase; 70-80 µM) were similar to those found previously using virus based infection. The results should allow new types of studies, e.g., screening of a wide range of mutations to be selected for further characterization.

Insights into Muscle Contraction Derived from the Effects of Small-Molecular Actomyosin-Modulating Compounds

Bottom-up mechanokinetic models predict ensemble function of actin and myosin based on parameter values derived from studies using isolated proteins. To be generally useful, e.g., to analyze disease effects, such models must also be able to predict ensemble function when actomyosin interaction kinetics are modified differently from normal. Here, we test this capability for a model recently shown to predict several physiological phenomena along with the effects of the small molecular compound blebbistatin. We demonstrate that this model also qualitatively predicts effects of other well-characterized drugs as well as varied concentrations of MgATP. However, the effects of one compound, amrinone, are not well accounted for quantitatively. We therefore systematically varied key model parameters to address this issue, leading to the increased amplitude of the second sub-stroke of the power stroke from 1 nm to 2.2 nm, an unchanged first sub-stroke (5.3−5.5 nm), and an effective cross-bridge attachment rate that more than doubled. In addition to better accounting for the effects of amrinone, the modified model also accounts well for normal physiological ensemble function. Moreover, a Monte Carlo simulation-based version of the model was used to evaluate force−velocity data from small myosin ensembles. We discuss our findings in relation to key aspects of actin−myosin operation mechanisms causing a non-hyperbolic shape of the force−velocity relationship at high loads. We also discuss remaining limitations of the model, including uncertainty of whether the cross-bridge elasticity is linear or not, the capability to account for contractile properties of very small actomyosin ensembles (<20 myosin heads), and the mechanism for requirements of a higher cross-bridge attachment rate during shortening compared to during isometric contraction.

Myosin II Adjusts Motility Properties and Regulates Force Production Based on Motor Environment

Introduction

Myosin II has been investigated with optical trapping, but single motor-filament assay arrangements are not reflective of the complex cellular environment. To understand how myosin interactions propagate up in scale to accomplish system force generation, we devised a novel actomyosin ensemble optical trapping assay that reflects the hierarchy and compliancy of a physiological environment and is modular for interrogating force effectors.

Methods

Hierarchical actomyosin bundles were formed in vitro. Fluorescent template and cargo actin filaments (AF) were assembled in a flow cell and bundled by myosin. Beads were added in the presence of ATP to bind the cargo AF and activate myosin force generation to be measured by optical tweezers.

Results

Three force profiles resulted across a range of myosin concentrations: high force with a ramp-plateau, moderate force with sawtooth movement, and baseline. The three force profiles, as well as high force output, were recovered even at low solution concentration, suggesting that myosins self-optimize within AFs. Individual myosin steps were detected in the ensemble traces, indicating motors are taking one step at a time while others remain engaged in order to sustain productive force generation.

Conclusions

Motor communication and system compliancy are significant contributors to force output. Environmental conditions, motors taking individual steps to sustain force, the ability to backslip, and non-linear concentration dependence of force indicate that the actomyosin system contains a force-feedback mechanism that senses the local cytoskeletal environment and communicates to the individual motors whether to be in a high or low duty ratio mode.

Supplementary Information

The online version contains supplementary material available at 10.1007/s12195-022-00731-1.

Motility resilience of molecular shuttles against defective motors

Myosin and kinesin are biomolecular motors found in living cells. By propelling their associated cytoskeletal filaments, these biomolecular motors facilitate force generation and material transport in the cells. When extracted, the biomolecular motors are promising candidates for in vitro applications such as biosensor devices, on account of their high operating efficiency and nanoscale size. However, during integration into these devices, some of the motors become defective due to unfavorable adhesion to the substrate surface. These defective motors inhibit the motility of the cytoskeletal filaments which make up the molecular shuttles used in the devices. Difficulties in controlling the fraction of active and defective motors in experiments discourage systematic studies concerning the resilience of the molecular shuttle motility against the impedance of defective motors. Here, we used mathematical modelling to systematically examine the resilience of the propulsion by these molecular shuttles against the impedance of the defective motors. The model showed that the fraction of active motors on the substrate is the essential factor determining the resilience of the molecular shuttle motility. Approximately 40% of active kinesin or 80% of active myosin motors are required to constitute continuous gliding of molecular shuttles in their respective substrates. The simplicity of the mathematical model in describing motility behavior offers utility in elucidating the mechanisms of the motility resilience of molecular shuttles.

Iron Supplementation Improves Skeletal Muscle Contractile Properties in Mice with CKD

Background

Patients with chronic kidney disease (CKD) frequently have compromised physical performance, which increases their mortality; however, their skeletal muscle dysfunction has not been characterized at the single-fiber and molecular levels. Notably, interventions to mitigate CKD myopathy are scarce.

Methods

The effect of CKD in the absence and presence of iron supplementation on the contractile function of individual skeletal muscle fibers from the soleus and extensor digitorum longus muscles was evaluated in 16-week-old mice. CKD was induced by the adenine diet, and iron supplementation was by weekly iron dextran injections.

Results

Maximally activated and fatigued fiber force production was decreased 24%-52% in untreated CKD, independent of size, by reducing strongly bound myosin/actin cross-bridges and/or decreasing myofilament stiffness in myosin heavy chain (MHC) I, IIA, and IIB fibers. Additionally, myosin/actin interactions in untreated CKD were slower for MHC I and IIA fibers and unchanged or faster in MHC IIB fibers. Iron supplementation improved anemia and did not change overall muscle mass in CKD mice. Iron supplementation ameliorated CKD-induced myopathy by increasing strongly bound cross-bridges, leading to improved specific tension, and/or returning the rate of myosin/actin interactions toward or equivalent to control values in MHC IIA and IIB fibers.

Conclusions

Skeletal muscle force production was significantly reduced in untreated CKD, independent of fiber size, indicating that compromised physical function in patients is not solely due to muscle mass loss. Iron supplementation improved multiple aspects of CKD-induced myopathy, suggesting that timely correction of iron imbalance may aid in ameliorating contractile deficits in CKD patients.

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.

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.

A reverse stroke characterizes the force generation of cardiac myofilaments, leading to an understanding of heart function

Changes in the molecular properties of cardiac myosin strongly affect the interactions of myosin with actin that result in cardiac contraction and relaxation. However, it remains unclear how myosin molecules work together in cardiac myofilaments and which properties of the individual myosin molecules impact force production to drive cardiac contractility. Here, we measured the force production of cardiac myofilaments using optical tweezers. The measurements revealed that stepwise force generation was associated with a higher frequency of backward steps at lower loads and higher stall forces than those of fast skeletal myofilaments. To understand these unique collective behaviors of cardiac myosin, the dynamic responses of single cardiac and fast skeletal myosin molecules, interacting with actin filaments, were evaluated under load. The cardiac myosin molecules switched among three distinct conformational positions, ranging from pre- to post-power stroke positions, in 1 mM ADP and 0 to 10 mM phosphate solution. In contrast to cardiac myosin, fast skeletal myosin stayed primarily in the post-power stroke position, suggesting that cardiac myosin executes the reverse stroke more frequently than fast skeletal myosin. To elucidate how the reverse stroke affects the force production of myofilaments and possibly heart function, a simulation model was developed that combines the results from the single-molecule and myofilament experiments. The results of this model suggest that the reversal of the cardiac myosin power stroke may be key to characterizing the force output of cardiac myosin ensembles and possibly to facilitating heart contractions.

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.

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.

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.

Myosin and gelsolin cooperate in actin filament severing and actomyosin motor activity

Actin is a major intracellular protein with key functions in cellular motility, signaling, and structural rearrangements. Its dynamic behavior, such as polymerization and depolymerization of actin filaments in response to intracellular and extracellular cues, is regulated by an abundance of actin binding proteins. Out of these, gelsolin is one of the most potent for filament severing. However, myosin motor activity also fragments actin filaments through motor-induced forces, suggesting that these two proteins could cooperate to regulate filament dynamics and motility. To test this idea, we used an in vitro motility assay, where actin filaments are propelled by surface-adsorbed heavy meromyosin (HMM) motor fragments. This allows studies of both motility and filament dynamics using isolated proteins. Gelsolin, at both nanomolar and micromolar Ca²⁺ concentration, appreciably enhanced actin filament severing caused by HMM-induced forces at 1 mM MgATP, an effect that was increased at higher HMM motor density. This finding is consistent with cooperativity between actin filament severing by myosin-induced forces and by gelsolin. We also observed reduced sliding velocity of the HMM-propelled filaments in the presence of gelsolin, providing further support of myosin-gelsolin cooperativity. Total internal reflection fluorescence microscopy–based single molecule studies corroborated that the velocity reduction was a direct effect of gelsolin binding to the filament and revealed different filament severing pattern of stationary and HMM propelled filaments. Overall, the results corroborate cooperative effects between gelsolin-induced alterations in the actin filaments and changes due to myosin motor activity leading to enhanced F-actin severing of possible physiological relevance.

Hypothesis: Single Actomyosin Properties Account for Ensemble Behavior in Active Muscle Shortening and Isometric Contraction

Muscle contraction results from cyclic interactions between myosin II motors and actin with two sets of proteins organized in overlapping thick and thin filaments, respectively, in a nearly crystalline lattice in a muscle sarcomere. However, a sarcomere contains a huge number of other proteins, some with important roles in muscle contraction. In particular, these include thin filament proteins, troponin and tropomyosin; thick filament proteins, myosin binding protein C; and the elastic protein, titin, that connects the thin and thick filaments. Furthermore, the order and 3D organization of the myofilament lattice may be important per se for contractile function. It is possible to model muscle contraction based on actin and myosin alone with properties derived in studies using single molecules and biochemical solution kinetics. It is also possible to reproduce several features of muscle contraction in experiments using only isolated actin and myosin, arguing against the importance of order and accessory proteins. Therefore, in this paper, it is hypothesized that “single molecule actomyosin properties account for the contractile properties of a half sarcomere during shortening and isometric contraction at almost saturating Ca concentrations”. In this paper, existing evidence for and against this hypothesis is reviewed and new modeling results to support the arguments are presented. Finally, further experimental tests are proposed, which if they corroborate, at least approximately, the hypothesis, should significantly benefit future effective analysis of a range of experimental studies, as well as drug discovery efforts.

A thermophoresis-based biosensor for real-time detection of inorganic phosphate during enzymatic reactions

Inorganic phosphate (P_i)-sensing is a key application in many disciplines, and biosensors emerged as powerful analytic tools for use in environmental P_i monitoring, food quality control, basic research, and medical diagnosis. Current sensing techniques exploit either electrochemical or optical detection approaches for P_i quantification. Here, by combining the advantages of a biological P_i-receptor based on the bacterial phosphate binding protein with the principle of thermophoresis, i.e. the diffusional motion of particles in response to a temperature gradient, we developed a continuous, sensitive, and versatile method for detecting and quantifying free P_i in the subnanomolar to micromolar range in sample volumes ≤10 μL. By recording entropy-driven changes in the directed net diffusional flux of the P_i-sensor in a temperature gradient at defined time intervals, we validate the method for analyzing steady-state enzymatic reactions associated with P_i liberation in real-time for adenosine triphosphate (ATP) turnover by myosin, the actomyosin system and for insoluble, high molecular weight enzyme-protein assemblies in biopsy derived myofibrils. Particular features of the method are: (1) high P_i-sensitivity and selectivity, (2) uncoupling of the read-out signal from potential chemical and spectroscopic interferences, (3) minimal sample volumes and nanogram protein amounts, (4) possibility to run several experiments in parallel, and (5) straightforward data analysis. The present work establishes thermophoresis as powerful sensing method in microscale format for a wide range of applications, augmenting the current set of detection principles in biosensor technology.

Strategies for targeting the cardiac sarcomere: avenues for novel drug discovery

Introduction: Heart failure remains one of the largest clinical challenges in the United States. Researchers have continually searched for more effective heart failure treatments that target the cardiac sarcomere but have found few successes despite numerous expensive cardiovascular clinical trials. Among many reasons, the high failure rate of cardiovascular clinical trials may be partly due to incomplete characterization of a drug candidate's complex interaction with cardiac physiology.Areas covered: In this review, the authors address the issue of preclinical cardiovascular studies of sarcomere-targeting heart failure therapies. The authors consider inherent tradeoffs made between mechanistic transparency and physiological fidelity for several relevant preclinical techniques at the atomic, molecular, heart muscle fiber, whole heart, and whole-organism levels. Thus, the authors suggest a comprehensive, bottom-up approach to preclinical cardiovascular studies that fosters scientific rigor and hypothesis-driven drug discovery.Expert opinion: In the authors' opinion, the implementation of hypothesis-driven drug discovery practices, such as the bottom-up approach to preclinical cardiovascular studies, will be imperative for the successful development of novel heart failure treatments. However, additional changes to clinical definitions of heart failure and current drug discovery culture must accompany the bottom-up approach to maximize the effectiveness of hypothesis-driven drug discovery.

A new twist on tropomyosin binding to actin filaments: perspectives on thin filament function, assembly and biomechanics

Tropomyosin, best known for its role in the steric regulation of muscle contraction, polymerizes head-to-tail to form cables localized along the length of both muscle and non-muscle actin-based thin filaments. In skeletal and cardiac muscles, tropomyosin, under the control of troponin and myosin, moves in a cooperative manner between blocked, closed and open positions on filaments, thereby masking and exposing actin-binding sites necessary for myosin crossbridge head interactions. While the coiled-coil signature of tropomyosin appears to be simple, closer inspection reveals surprising structural complexity required to perform its role in steric regulation. For example, component α-helices of coiled coils are typically zippered together along a continuous core hydrophobic stripe. Tropomyosin, however, contains a number of anomalous, functionally controversial, core amino acid residues. We argue that the atypical residues at this interface, including clusters of alanines and a charged aspartate, are required for preshaping tropomyosin to readily fit to the surface of the actin filament, but do so without compromising tropomyosin rigidity once the filament is assembled. Indeed, persistence length measurements of tropomyosin are characteristic of a semi-rigid cable, in this case conducive to cooperative movement on thin filaments. In addition, we also maintain that tropomyosin displays largely unrecognized and residue-specific torsional variance, which is involved in optimizing contacts between actin and tropomyosin on the assembled thin filament. Corresponding twist-induced stiffness may also enhance cooperative translocation of tropomyosin across actin filaments. We conclude that anomalous core residues of tropomyosin facilitate thin filament regulatory behavior in a multifaceted way.

Collective Force Generation by Molecular Motors Is Determined by Strain-Induced Unbinding

In the living cell, we encounter a large variety of motile processes such as organelle transport and cytoskeleton remodeling. These processes are driven by motor proteins that generate force by transducing chemical free energy into mechanical work. In many cases, the molecular motors work in teams to collectively generate larger forces. Recent optical trapping experiments on small teams of cytoskeletal motors indicated that the collectively generated force increases with the size of the motor team but that this increase depends on the motor type and on whether the motors are studied in vitro or in vivo. Here, we use the theory of stochastic processes to describe the motion of N motors in a stationary optical trap and to compute the N-dependence of the collectively generated forces. We consider six distinct motor types, two kinesins, two dyneins, and two myosins. We show that the force increases always linearly with N but with a prefactor that depends on the performance of the single motor. Surprisingly, this prefactor increases for weaker motors with a lower stall force. This counter-intuitive behavior reflects the increased probability with which stronger motors detach from the filament during strain generation. Our theoretical results are in quantitative agreement with experimental data on small teams of kinesin-1 motors.

Blebbistatin Effects Expose Hidden Secrets in the Force-Generating Cycle of Actin and Myosin

Cyclic interactions between myosin II motors and actin filaments driven by ATP turnover underlie muscle contraction and have key roles in the motility of nonmuscle cells. A remaining enigma in the understanding of this interaction is the relationship between the force-generating structural change and the release of the ATP-hydrolysis product, inorganic phosphate (Pi), from the active site of myosin. Here, we use the small molecular compound blebbistatin to probe otherwise hidden states and transitions in this process. Different hypotheses for the Pi release mechanism are tested by interpreting experimental results from in vitro motility assays and isolated muscle fibers in terms of mechanokinetic actomyosin models. The data fit with ideas that actomyosin force generation is preceded by Pi release, which in turn is preceded by two serial transitions after/coincident with cross-bridge attachment. Blebbistatin changes the rate limitation of the cycle from the first to the second of these transitions, uncovering functional roles of an otherwise short-lived pre-power stroke state that has been implicated by structural data.

Spreading of perturbations in myosin group kinetics along actin filaments

Global changes in the state of spatially distributed systems can often be traced back to perturbations that arise locally. Whether such local perturbations grow into global changes depends on the system geometry and the spatial spreading of these perturbations. Here, we investigate how different spreading behaviors of local perturbations determine their global impact in 1-dimensional systems of different size. Specifically, we assessed sliding arrest events in in vitro motility assays where myosins propel actin, and simulated the underlying mechanochemistry of myosins that bind along the actin filament. We observed spontaneous sliding arrest events that occurred more frequently for shorter actin filaments. This observation could be explained by spontaneous local arrest of myosin kinetics that stabilizes once it spreads throughout an entire actin filament. When we introduced intermediate concentrations of the actin cross-linker filamin, longer actin was arrested more frequently. This observation was reproduced by simulations where filamin binding induces persistent local arrest of myosin kinetics, which subsequently spreads throughout the actin filament. A spin chain model with nearest-neighbor coupling reproduced key features of our experiments and simulations, thus extending to other linear systems with nearest-neighbor coupling the following conclusions: 1) perturbations that are persistent only once they spread throughout the system are more effective in smaller systems, and 2) perturbations that are persistent upon their establishment are more effective in larger systems. Beyond these general conclusions, our work also provides a theoretical model of collective myosin kinetics with a finite range of mechanical coupling along the actin filament.

The load dependence of muscle's force-velocity curve is modulated by alternative myosin converter domains

The hyperbolic shape of the muscle force-velocity relationship (FVR) is characteristic of all muscle fiber types. The degree of curvature of the hyperbola varies between muscle fiber types and is thought to be set by force-dependent properties of different myosin isoforms. However, the structural elements in myosin and the mechanism that determines force dependence are unresolved. We tested our hypothesis that the myosin converter domain plays a critical role in the force-velocity relationship (FVR) mechanism. Drosophila contains a single myosin heavy chain gene with five converters encoded by alternative exons. We measured FVR properties of Drosophila jump muscle fibers from five transgenic lines each expressing a single converter. Consistent with our hypothesis, we observed up to 2.4-fold alterations in FVR curvature. Maximum shortening velocity (v0) and optimal velocity for maximum power generation were also altered, but isometric tension and maximum power generation were unaltered. Converter 11a, normally found in the indirect flight muscle (IFM), imparted the highest FVR curvature and v0, whereas converter 11d, found in larval body wall muscle, imparted the most linear FVR and slowest v0. Jump distance strongly correlated with increasing FVR curvature and v0, meaning flies expressing the converter from the IFM jumped farther than flies expressing the native jump muscle converter. Fitting our data with Huxley's two-state model and a biophysically based four-state model suggest a testable hypothesis that the converter sets muscle type FVR curvature by influencing the detachment rate of negatively strained myosin via changes in the force dependence of product release.

Comparing models with one versus multiple myosin-binding sites per actin target zone: The power of simplicity

Mechanokinetic statistical models describe the mechanisms of muscle contraction on the basis of the average behavior of a large ensemble of actin-myosin motors. Such models often assume that myosin II motor domains bind to regularly spaced, discrete target zones along the actin-based thin filaments and develop force in a series of strain-dependent transitions under the turnover of ATP. The simplest models assume that there is just one myosin-binding site per target zone and a uniform spatial distribution of the myosin motor domains in relation to each site. However, most of the recently developed models assume three myosin-binding sites per target zone, and some models include a spatially explicit 3-D treatment of the myofilament lattice and thereby of the geometry of the actin-myosin contact points. Here, I show that the predictions for steady-state contractile behavior of muscle are very similar whether one or three myosin-binding sites per target zone is assumed, provided that the model responses are appropriately scaled to the number of sites. Comparison of the model predictions for isometrically contracting mammalian muscle cells suggests that each target zone contains three or more myosin-binding sites. Finally, I discuss the strengths and weaknesses of one-site spatially inexplicit models in relation to three-site models, including those that take into account the detailed 3-D geometry of the myofilament lattice. The results of this study suggest that single-site models, with reduced computational cost compared with multisite models, are useful for several purposes, e.g., facilitated molecular mechanistic insights.

Engineering Synthetic Myosin Filaments Using DNA Nanotubes

Throughout the cell, motor proteins work together to drive numerous molecular processes and functions. For example, ensembles of myosin motors collectively transport vesicles and organelles, maintain membrane homeostasis, and drive muscle contraction. Studying these motors in groups has become increasingly important with work demonstrating the emergence of ensemble behavior distinct from individual motor behavior. One powerful technique that has been used in the last decade is DNA nanotechnology, which provides precise control over spacing and organization of patterned motor proteins. Until recently, however, most studies combining DNA nanostructures and molecular motors have been confined to discrete DNA structures with limited attachment points for motor proteins. In this chapter, we describe a new approach for making synthetic motor filaments using DNA nanotubes. We present methods for preparing myosin VI-labeled nanotubes and testing these nanotubes using a general in vitro motility setup. Overall, these nanotubes can easily be used to study other large ensembles of molecular motors, such as muscle myosin or ciliary dynein, both proteins that work in large motor ensembles to drive key cellular functions.

Collective effects of yeast cytoplasmic dynein based microtubule transport

Teams of cortically anchored dyneins pulling at microtubules (MTs) are known to be essential for aster, spindle and nuclear positioning during cell division and fertilization. While the single-molecule basis of dynein processivity is now better understood, the effect of increasing numbers of motors on transport is not clear. Here, we examine the collective transport properties of a Saccharomyces cerevisiae cytoplasmic dynein fragment, widely used as a minimal model, by a combination of quantitative MT gliding assays and stochastic simulations. We find both MT lengths and motor densities qualitatively affect the degree of randomness of MT transport. However, the directionality and velocity of MTs increase above a threshold number of motors (N) interacting with a filament. To better understand this behavior, we simulate a gliding assay based on a model of uniformly distributed immobilized motors transporting semi-flexible MTs. Each dynein dimer is modeled as an effective stochastic stepper with asymmetric force dependent detachment dynamics, based on single-molecule experiments. Simulations predict increasing numbers of motors (N) result in a threshold dependent transition in directionality and transport velocity and a monotonic decrease in effective diffusivity. Thus both experiment and theory show qualitative agreement in the emergence of coordination in transport above a threshold number of motor heads. We hypothesize that the phase-transition like property of this dynein could play a role in vivo during yeast mitosis, when this dynein localizes to the cortex and pulls astral MTs of increasing length, resulting in correct positioning and orientation of the nucleus at the bud-neck.

Nonlinear Actomyosin Elasticity in Muscle?

Cyclic interactions between myosin II motor domains and actin filaments that are powered by turnover of ATP underlie muscle contraction and have key roles in motility of nonmuscle cells. The elastic characteristics of actin-myosin cross-bridges are central in the force-generating process, and disturbances in these properties may lead to disease. Although the prevailing paradigm is that the cross-bridge elasticity is linear (Hookean), recent single-molecule studies suggest otherwise. Despite convincing evidence for substantial nonlinearity of the cross-bridge elasticity in the single-molecule work, this finding has had limited influence on muscle physiology and physiology of other ordered cellular actin-myosin ensembles. Here, we use a biophysical modeling approach to close the gap between single molecules and physiology. The model is used for analysis of available experimental results in the light of possible nonlinearity of the cross-bridge elasticity. We consider results obtained both under rigor conditions (in the absence of ATP) and during active muscle contraction. Our results suggest that a wide range of experimental findings from mechanical experiments on muscle cells are consistent with nonlinear actin-myosin elasticity similar to that previously found in single molecules. Indeed, the introduction of nonlinear cross-bridge elasticity into the model improves the reproduction of key experimental results and eliminates the need for force dependence of the ATP-induced detachment rate, consistent with observations in other single-molecule studies. The findings have significant implications for the understanding of key features of actin-myosin-based production of force and motion in living cells, particularly in muscle, and for the interpretation of experimental results that rely on stiffness measurements on cells or myofibrils.

Acidosis affects muscle contraction by slowing the rates myosin attaches to and detaches from actin

The loss of muscle force and power during fatigue from intense contractile activity is associated with, and likely caused by, elevated levels of phosphate ([Formula: see text]) and hydrogen ions (decreased pH). To understand how these deficits in muscle performance occur at the molecular level, we used direct measurements of mini-ensembles of myosin generating force in the laser trap assay at pH 7.4 and 6.5. The data are consistent with a mechanochemical model in which a decrease in pH reduces myosin's detachment from actin (by slowing ADP release), increases non-productive myosin binding (by detached myosin rebinding without a powerstroke), and reduces myosin's attachment to actin (by slowing the weak-to-strong binding transition). Additional support of this mechanism is found by incorporating it into a branched pathway model for the effects of [Formula: see text] on myosin's interaction with actin. Including pH-dependence in one additional parameter (acceleration of [Formula: see text]-induced detachment), the model reproduces experimental measurements at high and low pH, and variable [Formula: see text], from the single molecule to large ensemble levels. Furthermore, when scaled up, the model predicts force-velocity relationships that are consistent with muscle fiber measurements. The model suggests that reducing pH has two opposing effects, a decrease in attachment favoring a decrease in muscle force and a decrease in detachment favoring an increase in muscle force. Depending on experimental details, the addition of [Formula: see text] can strengthen one or the other effect, resulting in either synergistic or antagonistic effects. This detailed molecular description suggests a molecular basis for contractile failure during muscle fatigue.

Do Actomyosin Single-Molecule Mechanics Data Predict Mechanics of Contracting Muscle?

In muscle, but not in single-molecule mechanics studies, actin, myosin and accessory proteins are incorporated into a highly ordered myofilament lattice. In view of this difference we compare results from single-molecule studies and muscle mechanics and analyze to what degree data from the two types of studies agree with each other. There is reasonable correspondence in estimates of the cross-bridge power-stroke distance (7–13 nm), cross-bridge stiffness (~2 pN/nm) and average isometric force per cross-bridge (6–9 pN). Furthermore, models defined on the basis of single-molecule mechanics and solution biochemistry give good fits to experimental data from muscle. This suggests that the ordered myofilament lattice, accessory proteins and emergent effects of the sarcomere organization have only minor modulatory roles. However, such factors may be of greater importance under e.g., disease conditions. We also identify areas where single-molecule and muscle data are conflicting: (1) whether force generation is an Eyring or Kramers process with just one major power-stroke or several sub-strokes; (2) whether the myofilaments and the cross-bridges have Hookean or non-linear elasticity; (3) if individual myosin heads slip between actin sites under certain conditions, e.g., in lengthening; or (4) if the two heads of myosin cooperate.

Controlling load-dependent kinetics of β-cardiac myosin at the single-molecule level

Concepts in molecular tension sensing in biology are growing and have their origins in studies of muscle contraction. In the heart muscle, a key parameter of contractility is the detachment rate of myosin from actin, which determines the time that myosin is bound to actin in a force-producing state and, importantly, depends on the load (force) against which myosin works. Here we measure the detachment rate of single molecules of human β-cardiac myosin and its load dependence. We find that both can be modulated by both small-molecule compounds and cardiomyopathy-causing mutations. Furthermore, effects of mutations can be reversed by introducing appropriate compounds. Our results suggest that activating versus inhibitory perturbations of cardiac myosin are discriminated by the aggregate result on duty ratio, average force, and ultimately average power output and suggest that cardiac contractility can be controlled by tuning the load-dependent kinetics of single myosin molecules.

No Difference in Myosin Kinetics and Spatial Distribution of the Lever Arm in the Left and Right Ventricles of Human Hearts

The systemic circulation offers larger resistance to the blood flow than the pulmonary system. Consequently, the left ventricle (LV) must pump blood with more force than the right ventricle (RV). The question arises whether the stronger pumping action of the LV is due to a more efficient action of left ventricular myosin, or whether it is due to the morphological differences between ventricles. Such a question cannot be answered by studying the entire ventricles or myocytes because any observed differences would be wiped out by averaging the information obtained from trillions of myosin molecules present in a ventricle or myocyte. We therefore searched for the differences between single myosin molecules of the LV and RV of failing hearts In-situ. We show that the parameters that define the mechanical characteristics of working myosin (kinetic rates and the distribution of spatial orientation of myosin lever arm) were the same in both ventricles. These results suggest that there is no difference in the way myosin interacts with thin filaments in myocytes of failing hearts, and suggests that the difference in pumping efficiencies are caused by interactions between muscle proteins other than myosin or that they are purely morphological.

Robust mechanobiological behavior emerges in heterogeneous myosin systems

Biological complexity presents challenges for understanding natural phenomenon and engineering new technologies, particularly in systems with molecular heterogeneity. Such complexity is present in myosin motor protein systems, and computational modeling is essential for determining how collective myosin interactions produce emergent system behavior. We develop a computational approach for altering myosin isoform parameters and their collective organization, and support predictions with in vitro experiments of motility assays with α-actinins as molecular force sensors. The computational approach models variations in single myosin molecular structure, system organization, and force stimuli to predict system behavior for filament velocity, energy consumption, and robustness. Robustness is the range of forces where a filament is expected to have continuous velocity and depends on used myosin system energy. Myosin systems are shown to have highly nonlinear behavior across force conditions that may be exploited at a systems level by combining slow and fast myosin isoforms heterogeneously. Results suggest some heterogeneous systems have lower energy use near stall conditions and greater energy consumption when unloaded, therefore promoting robustness. These heterogeneous system capabilities are unique in comparison with homogenous systems and potentially advantageous for high performance bionanotechnologies. Findings open doors at the intersections of mechanics and biology, particularly for understanding and treating myosin-related diseases and developing approaches for motor molecule-based technologies.

A Versatile Framework for Simulating the Dynamic Mechanical Structure of Cytoskeletal Networks

Computer simulations can aid in understanding how collective materials properties emerge from interactions between simple constituents. Here, we introduce a coarse-grained model that enables simulation of networks of actin filaments, myosin motors, and cross-linking proteins at biologically relevant time and length scales. We demonstrate that the model qualitatively and quantitatively captures a suite of trends observed experimentally, including the statistics of filament fluctuations, and mechanical responses to shear, motor motilities, and network rearrangements. We use the simulation to predict the viscoelastic scaling behavior of cross-linked actin networks, characterize the trajectories of actin in a myosin motility assay, and develop order parameters to measure contractility of a simulated actin network. The model can thus serve as a platform for interpretation and design of cytoskeletal materials experiments, as well as for further development of simulations incorporating active elements.

Coordinated force generation of skeletal myosins in myofilaments through motor coupling

In contrast to processive molecular motors, skeletal myosins form a large motor ensemble for contraction of muscles against high loads. Despite numerous information on the molecular properties of skeletal myosin, its ensemble effects on collective force generation have not been rigorously clarified. Here we show 4 nm stepwise actin displacements generated by synthetic myofilaments beyond a load of 30 pN, implying that steps cannot be driven exclusively by single myosins, but potentially by coordinated force generations among multiple myosins. The simulation model shows that stepwise actin displacements are primarily caused by coordinated force generation among myosin molecules. Moreover, the probability of coordinated force generation can be enhanced against high loads by utilizing three factors: strain-dependent kinetics between force-generating states; multiple power stroke steps; and high ATP concentrations. Compared with other molecular motors, our findings reveal how the properties of skeletal myosin are tuned to perform cooperative force generation for efficient muscle contraction.

Skeletal muscle myosin forms large ensembles to generate force against high loads. Using optical tweezers and simulation Kaya et al. provide experimental evidence for cooperative force generation, and describe how the molecular properties of skeletal myosins are tuned for coordinated power strokes.

Chemomechanical regulation of myosin Ic cross-bridges: Deducing the elastic properties of an ensemble from single-molecule mechanisms

Myosin Ic is thought to be the principal constituent of the motor that adjusts mechanical responsiveness during adaptation to prolonged stimuli by hair cells, the sensory receptors of the inner ear. In this context myosin molecules operate neither as filaments, as occurs in muscles, nor as single or few molecules, as characterizes intracellular transport. Instead, myosin Ic molecules occur in a complex cluster in which they may exhibit cooperative properties. To better understand the motor’s remarkable function, we introduce a theoretical description of myosin Ic’s chemomechanical cycle based on experimental data from recent single-molecule studies. The cycle consists of distinct chemical states that the myosin molecule stochastically occupies. We explicitly calculate the probabilities of the occupancy of these states and show their dependence on the external force, the availability of actin, and the nucleotide concentrations as required by thermodynamic constraints. This analysis highlights that the strong binding of myosin Ic to actin is dominated by the ADP state for small external forces and by the ATP state for large forces. Our approach shows how specific parameter values of the chemomechanical cycle for myosin Ic result in behaviors distinct from those of other members of the myosin family. Integrating this single-molecule cycle into a simplified ensemble description, we predict that the average number of bound myosin heads is regulated by the external force and nucleotide concentrations. The elastic properties of such an ensemble are determined by the average number of myosin cross-bridges. Changing the binding probabilities and myosin’s stiffness under a constant force results in a mechanical relaxation which is large enough to account for fast adaptation in hair cells.

Myosin molecules are biological nanomachines that transduce chemical energy into mechanical work and thus produce directed motion in living cells. These molecules proceed through cyclic reactions in which they change their conformational states upon the binding and release of nucleotides while attaching to and detaching from filaments. The myosin family consists of many distinct members with diverse functions such as muscle contraction, cargo transport, cell migration, and sensory adaptation. How these functions emerge from the biophysical properties of the individual molecules is an open question. We present an approach that integrates recent findings from single-molecule experiments into a thermodynamically consistent description of myosin Ic and demonstrate how the specific parameter values of the cycle result in a distinct function. The free variables of our description are the chemical input and external force, both of which are experimentally accessible and define the cellular environment in which these proteins function. We use this description to predict the elastic properties of an ensemble of molecules and discuss the implications for myosin Ic’s function in the inner ear as a tension regulator mediating adaptation, a hallmark of biological sensory systems. In this situation myosin molecules cooperate in an intermediate regime, neither as a large ensemble as in muscle nor as a single or a few molecules as in intracellular transport.

The molecular basis of thin filament activation: from single molecule to muscle

For muscles to effectively power locomotion, trillions of myosin molecules must rapidly attach and detach from the actin thin filament. This is accomplished by precise regulation of the availability of the myosin binding sites on actin (i.e. activation). Both calcium (Ca⁺⁺) and myosin binding contribute to activation, but both mechanisms are simultaneously active during contraction, making their relative contributions difficult to determine. Further complicating the process, myosin binding accelerates the attachment rate of neighboring myosin molecules, adding a cooperative element to the activation process. To de-convolve these two effects, we directly determined the effect of Ca⁺⁺ on the rate of attachment of a single myosin molecule to a single regulated actin thin filament, and separately determined the distance over which myosin binding increases the attachment rate of neighboring molecules. Ca⁺⁺ alone increases myosin’s attachment rate ~50-fold, while myosin binding accelerates attachment of neighboring molecules 400 nm along the actin thin filament.

Modulation of Skeletal Muscle Contraction by Myosin Phosphorylation

The striated muscle sarcomere is a highly organized and complex enzymatic and structural organelle. Evolutionary pressures have played a vital role in determining the structure-function relationship of each protein within the sarcomere. A key part of this multimeric assembly is the light chain-binding domain (LCBD) of the myosin II motor molecule. This elongated "beam" functions as a biological lever, amplifying small interdomain movements within the myosin head into piconewton forces and nanometer displacements against the thin filament during the cross-bridge cycle. The LCBD contains two subunits known as the essential and regulatory myosin light chains (ELC and RLC, respectively). Isoformic differences in these respective species provide molecular diversity and, in addition, sites for phosphorylation of serine residues, a highly conserved feature of striated muscle systems. Work on permeabilized skeletal fibers and thick filament systems shows that the skeletal myosin light chain kinase catalyzed phosphorylation of the RLC alters the "interacting head motif" of myosin motor heads on the thick filament surface, with myriad consequences for muscle biology. At rest, structure-function changes may upregulate actomyosin ATPase activity of phosphorylated cross-bridges. During activation, these same changes may increase the Ca2+ sensitivity of force development to enhance force, work, and power output, outcomes known as "potentiation." Thus, although other mechanisms may contribute, RLC phosphorylation may represent a form of thick filament activation that provides a "molecular memory" of contraction. The clinical significance of these RLC phosphorylation mediated alterations to contractile performance of various striated muscle systems are just beginning to be understood. © 2017 American Physiological Society. Compr Physiol 7:171-212, 2017.

Actomyosin based contraction: one mechanokinetic model from single molecules to muscle?

Bridging the gaps between experimental systems on different hierarchical scales is needed to overcome remaining challenges in the understanding of muscle contraction. Here, a mathematical model with well-characterized structural and biochemical actomyosin states is developed to that end. We hypothesize that this model accounts for generation of force and motion from single motor molecules to the large ensembles of muscle. In partial support of this idea, a wide range of contractile phenomena are reproduced without the need to invoke cooperative interactions or ad hoc states/transitions. However, remaining limitations exist, associated with ambiguities in available data for model definition e.g.: (1) the affinity of weakly bound cross-bridges, (2) the characteristics of the cross-bridge elasticity and (3) the exact mechanistic relationship between the force-generating transition and phosphate release in the actomyosin ATPase. Further, the simulated number of attached myosin heads in the in vitro motility assay differs several-fold from duty ratios, (fraction of strongly attached ATPase cycle times) derived in standard analysis. After addressing the mentioned issues the model should be useful in fundamental studies, for engineering of myosin motors as well as for studies of muscle disease and drug development.

Sensitivity of small myosin II ensembles from different isoforms to mechanical load and ATP concentration

Based on a detailed crossbridge model for individual myosin II motors, we systematically study the influence of mechanical load and adenosine triphosphate (ATP) concentration on small myosin II ensembles made from different isoforms. For skeletal and smooth muscle myosin II, which are often used in actomyosin gels that reconstitute cell contractility, fast forward movement is restricted to a small region of phase space with low mechanical load and high ATP concentration, which is also characterized by frequent ensemble detachment. At high load, these ensembles are stalled or move backwards, but forward motion can be restored by decreasing ATP concentration. In contrast, small ensembles of nonmuscle myosin II isoforms, which are found in the cytoskeleton of nonmuscle cells, are hardly affected by ATP concentration due to the slow kinetics of the bound states. For all isoforms, the thermodynamic efficiency of ensemble movement increases with decreasing ATP concentration, but this effect is weaker for the nonmuscle myosin II isoforms.

Maximum limit to the number of myosin II motors participating in processive sliding of actin

In this work, we analysed processive sliding and breakage of actin filaments at various heavy meromyosin (HMM) densities and ATP concentrations in IVMA. We observed that with addition of ATP solution, the actin filaments fragmented stochastically; we then determined mean length and velocity of surviving actin filaments post breakage. Average filament length decreased with increase in HMM density at constant ATP, and increased with increase in ATP concentration at constant HMM density. Using density of HMM molecules and length of actin, we estimated the number of HMM molecules per actin filament (N) that participate in processive sliding of actin. N is solely a function of ATP concentration: 88 ± 24 and 54 ± 22 HMM molecules (mean ± S.D.) at 2 mM and 0.1 mM ATP respectively. Processive sliding of actin filament was observed only when N lay within a minimum lower limit (Nmin) and a maximum upper limit (Nmax) to the number of HMM molecules. When N < Nmin the actin filament diffused away from the surface and processivity was lost and when N > Nmax the filament underwent breakage eventually and could not sustain processive sliding. We postulate this maximum upper limit arises due to increased number of strongly bound myosin heads.