Nonlinear elasticity and an 8-nm working stroke of single myosin molecules in myofilaments

A novel kinetic model to demonstrate the independent effects of ATP and ADP/Pi concentrations on sarcomere function

Understanding muscle contraction mechanisms is a standing challenge, and one of the approaches has been to create models of the sarcomere-the basic contractile unit of striated muscle. While these models have been successful in elucidating many aspects of muscle contraction, they fall short in explaining the energetics of functional phenomena, such as rigor, and in particular, their dependence on the concentrations of the biomolecules involved in the cross-bridge cycle. Our hypothesis posits that the stochastic time delay between ATP adsorption and ADP/Pi release in the cross-bridge cycle necessitates a modeling approach where the rates of these two reaction steps are controlled by two independent parts of the total free energy change of the hydrolysis reaction. To test this hypothesis, we built a two-filament, stochastic-mechanical half-sarcomere model that separates the energetic roles of ATP and ADP/Pi in the cross-bridge cycle's free energy landscape. Our results clearly demonstrate that there is a nontrivial dependence of the cross-bridge cycle's kinetics on the independent concentrations of ATP, ADP, and Pi. The simplicity of the proposed model allows for analytical solutions of the more basic systems, which provide novel insight into the dominant mechanisms driving some of the experimentally observed contractile phenomena.

Synthesis and Direct Observation of Chiral Supramolecular Polymer of Porphyrin Having Cholesteryl Groups

We report the synthesis and microscopic investigations of two chiral helical porphyrin supramolecular polymers with different coordinating metals that are expected to be capable of serving as synthetic macromolecular motors driven by thermal fluctuations. Furthermore, based on their microscopic images, we propose a stepwise process for the formation of higher-order structures. These porphyrins formed completely different association states, and this was reflected in the marked differences in the shapes of the supramolecular polymers. The Cu-TChOAlaCPP supramolecular polymers formed H-aggregate rods in diisopropyl ether, then grew into superhelices and then into ribbons. On the other hand, Zn-TChOAlaCPP supramolecular polymers formed aggregates based on van der Waals interactions in diethyl ether, then grew into fibers and then grew into multiple-helices and ribbons. In addition, we imaged the interaction between long and short chains of the Cu-TChOAlaCPP supramolecular polymer by fast-scanning atomic force microscopy, and we indicated the availability as a macromolecular motor driven by thermal fluctuations.

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.

Design Principles and Benefits of Spatially Explicit Models of Myofilament Function

Spatially explicit models of muscle contraction include fine-scale details about the spatial, kinetic, and/or mechanical properties of the biological processes being represented within the model network. Over the past 25 years, this has primarily consisted of a set of mathematical and computational algorithms representing myosin cross-bridge activity, Ca2+-activation of contraction, and ensemble force production within a half-sarcomere representation of the myofilament network. Herein we discuss basic design principles associated with creating spatially explicit models of myofilament function, as well as model assumptions underlying model development. A brief overview of computational approaches is introduced. Opportunities for new model directions that could investigate coupled regulatory pathways between the thick-filament and thin-filaments are also presented. Given the modular design and flexibility associated with spatially explicit models, we highlight some advantages of this approach compared to other model formulations.

Effects of muscular endurance and tendon extensibility on endurance of joint stiffness

In some sporting events (e.g., long-distance running), the ability to maintain joint stiffness is considered an essential physical ability. However, the determinants of joint stiffness endurance remain unclear. This study aimed to examine the effects of muscular endurance and tendon extensibility on joint stiffness endurance. Thirteen males performed the fatigue task (5 sets of 50 hopping). Ankle joint stiffness during drop jump was measured before and after fatigue task. The maximum number of repetitions at 30% of one repetition maximum for plantar flexion was measured as muscular endurance. Maximal elongation of the Achilles tendon was measured during ramp (with a low strain rate of tendon) and ballistic (with a high strain rate of tendon) contractions as tendon extensibility. Joint stiffness significantly decreased by 7.5% after the fatigue task (p = 0.033). The maximum number of repetitions at 30% of 1RM (79.6 ± 48.7 repetitions) was not significantly correlated with the relative change in joint stiffness (r = 0.283, p = 0.348). The maximal elongation of the Achilles tendon measured during ramp and ballistic contractions were not significantly associated with the relative change in joint stiffness (r = 0.326, p = 0.277 for ramp contraction; r = 0.438, p = 0.135 for ballistic contraction). These results suggest that muscular endurance and tendon extensibility were unrelated to joint stiffness endurance.

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.

Matching Mechanics and Energetics of Muscle Contraction Suggests Unconventional Chemomechanical Coupling during the Actin-Myosin Interaction

The mechanical performances of the vertebrate skeletal muscle during isometric and isotonic contractions are interfaced with the corresponding energy consumptions to define the coupling between mechanical and biochemical steps in the myosin-actin energy transduction cycle. The analysis is extended to a simplified synthetic nanomachine in which eight HMM molecules purified from fast mammalian skeletal muscle are brought to interact with an actin filament in the presence of 2 mM ATP, to assess the emergent properties of a minimum number of motors working in ensemble without the effects of both the higher hierarchical levels of striated muscle organization and other sarcomeric, regulatory and cytoskeleton proteins. A three-state model of myosin-actin interaction is able to predict the known relationships between energetics and transient and steady-state mechanical properties of fast skeletal muscle either in vivo or in vitro only under the assumption that during shortening a myosin motor can interact with two actin sites during one ATP hydrolysis cycle. Implementation of the molecular details of the model should be achieved by exploiting kinetic and structural constraints present in the transients elicited by stepwise perturbations in length or force superimposed on the isometric contraction.

Theoretical efficiency limits and speed-efficiency trade-off in myosin motors

Muscle myosin is a non-processive molecular motor generates mechanical work when cooperating in large ensembles. During its cyle, each individual motor keeps attaching and detaching from the actin filament. The random nature of attachment and detachment inevitably leads to losses and imposes theoretical limits on the energetic efficiency. Here, we numerically determine the theoretical efficiency limit of a classical myosin model with a given number of mechano-chemical states. All parameters that are not bounded by physical limits (like rate limiting steps) are determined by numerical efficiency optimization. We show that the efficiency is limited by the number of states, the stiffness and the rate-limiting kinetic steps. There is a trade-off between speed and efficiency. Slow motors are optimal when most of the available free energy is allocated to the working stroke and the stiffness of their elastic element is high. Fast motors, on the other hand, work better with a lower and asymmetric stiffness and allocate a larger fraction of free energy to the release of ADP. Overall, many features found in myosins coincide with the findings from the model optimization: there are at least 3 bound states, the largest part of the working stroke takes place during the first transition, the ADP affinity is adapted differently in slow and fast myosins and there is an asymmetry in elastic elements.

Mechanism of elastic energy storage of honey bee abdominal muscles under stress relaxation

Energy storage of passive muscles plays an important part in frequent activities of honey bee abdomens due to the muscle distribution and open circulatory system. However, the elastic energy and mechanical properties of structure in passive muscles remain unclear. In this article, stress relaxation tests on passive muscles from the terga of the honey bee abdomens were performed under different concentrations of blebbistatin and motion parameters. In stress relaxation, the load drop with the rapid and slow stages depending on stretching velocity and stretching length reflects the features of myosin-titin series structure and cross-bridge-actin cyclic connections in muscles. Then a model with 2 parallel modules based on the 2 feature structures in muscles was thus developed. The model described the stress relaxation and stretching of passive muscles from honey bee abdomen well for a good fitting in stress relaxation and verification in loading process. In addition, the stiffness change of cross-bridge under different concentrations of blebbistatin is obtained from the model. We derived the elastic deformation of cross-bridge and the partial derivatives of energy expressions on motion parameters from this model, which accorded the experimental results. This model reveals the mechanism of passive muscles from honey bee abdomens suggesting that the temporary energy storage of cross-bridge in terga muscles under abdomen bending provides potential energy for springback during the periodic abdomen bending of honey bee or other arthropod insects. The finding also provides an experimental and theoretical basis for the novel microstructure and material design of bionic muscle.

Cooperativity of myosin II motors in the non-regulated and regulated thin filaments investigated with high-speed AFM

Skeletal myosins II are non-processive molecular motors that work in ensembles to produce muscle contraction while binding to the actin filament. Although the molecular properties of myosin II are well known, there is still debate about the collective work of the motors: is there cooperativity between myosin motors while binding to the actin filaments? In this study, we use high-speed AFM to evaluate this issue. We observed that the initial binding of small arrays of myosin heads to the non-regulated actin filaments did not affect the cooperative probability of subsequent bindings and did not lead to an increase in the fractional occupancy of the actin binding sites. These results suggest that myosin motors are independent force generators when connected in small arrays, and that the binding of one myosin does not alter the kinetics of other myosins. In contrast, the probability of binding of myosin heads to regulated thin filaments under activating conditions (at high Ca2+ concentration in the presence of 2 μM ATP) was increased with the initial binding of one myosin, leading to a larger occupancy of available binding sites at the next half-helical pitch of the filament. The result suggests that myosin cooperativity is observed over five pseudo-repeats and defined by the activation status of the thin filaments.

Single-Molecule Unidirectional Processive Movement along a Helical Polymer Chain in Non-aqueous Medium

In this work, a molecule "walking" along a single chain of a synthetic helical polymer, which is used as a rail on a substrate in an organic solvent at room temperature, is observed. The walking comprises the unidirectional processive movement of a short-chain molecule along a chiral helical chain in 3 nm steps, driven by Brownian motion and a tapping effect of the atomic force microscopy tip based on a flash ratchet mechanism. Furthermore, the rail consists of a long-chain substituted phenylacetylene polymer with pendant cholesteryl groups, along which the short-chain molecule can walk as a result of van der Waals interactions. The macromolecular motion is videoed using a fast-scanning atomic force microscope, and additionally, this phenomenon is also simulated by all-atom molecular dynamics calculations. On the basis of these results, we propose the principle of a polymer molecular motor. This is the first report of a synthetic walking machine of a chiral helical polymer driven by thermal fluctuation as an artificial life function.

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.

A thermodynamically consistent monte carlo cross-bridge model with a trapping mechanism reveals the role of stretch activation in heart pumping

Changes in intracellular calcium concentrations regulate heart beats. However, the decline in the left ventricular pressure during early diastole is much sharper than that of the Ca²⁺ transient, resulting in a rapid supply of blood to the left ventricle during the diastole. At the tissue level, cardiac muscles have a distinct characteristic, known as stretch activation, similar to the function of insect flight muscles. Stretch activation, which is a delayed increase in force following a rapid muscle length increase, has been thought to be related to autonomous control in these muscles. In this numerical simulation study, we introduced a molecular mechanism of stretch activation and investigated the role of this mechanism in the pumping function of the heart, using the previously developed coupling multiple-step active stiffness integration scheme for a Monte Carlo (MC) cross-bridge model and a bi-ventricular finite element model. In the MC cross-bridge model, we introduced a mechanism for trapping the myosin molecule in its post-power stroke state. We then determined the rate constants of transitions for trapping and escaping in a thermodynamically consistent manner. Based on our numerical analysis, we draw the following conclusions regarding the stretch activation mechanism: (i) the delayed force becomes larger than the original isometric force because the population of trapped myosin molecules and their average force increase after stretching; (ii) the delayed force has a duration of more than a few seconds owing to a fairly small rate constant of escape from the trapped state. For the role of stretch activation in heart pumping, we draw the following conclusions: (iii) for the regions in which the contraction force decreases earlier than the neighboring region in the end-systole phase, the trapped myosin molecules prevent further lengthening of the myocytes, which then prevents further shortening of neighboring myocytes; (iv) as a result, the contraction forces are sustained longer, resulting in a larger blood ejection, and their degeneration is synchronized.

Muscle active force-length curve explained by an electrophysical model of interfilament spacing

The active isometric force-length relation (FLR) of striated muscle sarcomeres is central to understanding and modeling muscle function. The mechanistic basis of the descending arm of the FLR is well explained by the decreasing thin:thick filament overlap that occurs at long sarcomere lengths. The mechanistic basis of the ascending arm of the FLR (the decrease in force that occurs at short sarcomere lengths), alternatively, has never been well explained. Because muscle is a constant-volume system, interfilament lattice distances must increase as sarcomere length shortens. This increase would decrease thin and thick-filament electrostatic interactions independently of thin:thick filament overlap. To examine this effect, we present here a fundamental, physics-based model of the sarcomere that includes filament molecular properties, calcium binding, sarcomere geometry including both thin:thick filament overlap and interfilament radial distance, and electrostatics. The model gives extremely good fits to existing FLR data from a large number of different muscles across their entire range of measured activity levels, with the optimized parameter values in all cases lying within anatomically and physically reasonable ranges. A local first-order sensitivity analysis (varying individual parameters while holding the values of all others constant) shows that model output is most sensitive to a subset of model parameters, most of which are related to sarcomere geometry, with model output being most sensitive to interfilament radial distance. This conclusion is supported by re-running the fits with only this parameter subset being allowed to vary, which increases fit errors only moderately. These results show that the model well reproduces existing experimental data, and indicate that changes in interfilament spacing play as central a role as changes in filament overlap in determining the FLR, particularly on its ascending arm.

Cross-bridge mechanics estimated from skeletal muscles' work-loop responses to impacts in legged locomotion

Legged locomotion has evolved as the most common form of terrestrial locomotion. When the leg makes contact with a solid surface, muscles absorb some of the shock-wave accelerations (impacts) that propagate through the body. We built a custom-made frame to which we fixated a rat (Rattus norvegicus, Wistar) muscle (m. gastrocnemius medialis and lateralis: GAS) for emulating an impact. We found that the fibre material of the muscle dissipates between 3.5 and [Formula: see text] ranging from fresh, fully active to passive muscle material, respectively. Accordingly, the corresponding dissipated energy in a half-sarcomere ranges between 10.4 and [Formula: see text], respectively. At maximum activity, a single cross-bridge would, thus, dissipate 0.6% of the mechanical work available per ATP split per impact, and up to 16% energy in common, submaximal, activities. We also found the cross-bridge stiffness as low as [Formula: see text], which can be explained by the Coulomb-actuating cross-bridge part dominating the sarcomere stiffness. Results of the study provide a deeper understanding of contractile dynamics during early ground contact in bouncy gait.

Semi-Implicit Time Integration with Hessian Eigenvalue Corrections for a Larger Time Step in Molecular Dynamics Simulations

In molecular dynamics simulations, the limited time step size has been a barrier to simulating long-time behaviors. Implicit time integration methods allow markedly larger time steps than the standard explicit time method, although they have major drawbacks such as overheads solving linear systems and instability of Newton iterations. To overcome these issues, we propose a semi-implicit time integration scheme, the semi-implicit Hessian correction (SimHec) scheme, for overdamped Langevin dynamics. The method focuses on the Hessian matrices of bonded and nonbonded interactions, where components with large negative Hessian eigenvalues are cut off in the linear approximation of momentum equations to avoid instability. The narrow band Hessian matrix enables an efficient parallelized linear solution with an overlapping approximation. We tested SimHec for the interdomain fluctuations in adenylate kinase and the powerstroke transition of myosin II using a coarse-grained protein model. SimHec reproduced the same dynamics as the explicit method, although the transition dynamics tended to be accelerated and fluctuations in bonded potentials were slightly reduced. These deviations were corrected using a hybrid method, SimHec-H, which adds explicit time steps after the semi-implicit time step. The proposed scheme allowed us to use time steps 50-200 times larger than those in explicit time integration, which resulted in a speedup factor of 7-30 taking the overhead into account.

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.

The Sliding Filament Theory Since Andrew Huxley: Multiscale and Multidisciplinary Muscle Research

Two groundbreaking papers published in 1954 laid out the theory of the mechanism of muscle contraction based on force-generating interactions between myofilaments in the sarcomere that cause filaments to slide past one another during muscle contraction. The succeeding decades of research in muscle physiology have revealed a unifying interest: to understand the multiscale processes-from atom to organ-that govern muscle function. Such an understanding would have profound consequences for a vast array of applications, from developing new biomimetic technologies to treating heart disease. However, connecting structural and functional properties that are relevant at one spatiotemporal scale to those that are relevant at other scales remains a great challenge. Through a lens of multiscale dynamics, we review in this article current and historical research in muscle physiology sparked by the sliding filament theory.

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.

Evidence for S2 flexibility by direct visualization of quantum dot-labeled myosin heads and rods within smooth muscle myosin filaments moving on actin in vitro

Myosins in muscle assemble into filaments by interactions between the C-terminal light meromyosin (LMM) subdomains of the coiled-coil rod domain. The two head domains are connected to LMM by the subfragment-2 (S2) subdomain of the rod. Our mixed kinetic model predicts that the flexibility and length of S2 that can be pulled away from the filament affects the maximum distance working heads can move a filament unimpeded by actin-attached heads. It also suggests that it should be possible to observe a head remain stationary relative to the filament backbone while bound to actin (dwell), followed immediately by a measurable jump upon detachment to regain the backbone trajectory. We tested these predictions by observing filaments moving along actin at varying ATP using TIRF microscopy. We simultaneously tracked two different color quantum dots (QDs), one attached to a regulatory light chain on the lever arm and the other attached to an LMM in the filament backbone. We identified events (dwells followed by jumps) by comparing the trajectories of the QDs. The average dwell times were consistent with known kinetics of the actomyosin system, and the distribution of the waiting time between observed events was consistent with a Poisson process and the expected ATPase rate. Geometric constraints suggest a maximum of ∼26 nm of S2 can be unzipped from the filament, presumably involving disruption in the coiled-coil S2, a result consistent with observations by others of S2 protruding from the filament in muscle. We propose that sufficient force is available from the working heads in the filament to overcome the stiffness imposed by filament-S2 interactions.

Multiscale modeling of twitch contractions in cardiac trabeculae

Understanding the dynamics of a cardiac muscle twitch contraction is complex because it requires a detailed understanding of the kinetic processes of the Ca2+ transient, thin-filament activation, and the myosin-actin cross-bridge chemomechanical cycle. Each of these steps has been well defined individually, but understanding how all three of the processes operate in combination is a far more complex problem. Computational modeling has the potential to provide detailed insight into each of these processes, how the dynamics of each process affect the complexity of contractile behavior, and how perturbations such as mutations in sarcomere proteins affect the complex interactions of all of these processes. The mechanisms involved in relaxation of tension during a cardiac twitch have been particularly difficult to discern due to nonhomogeneous sarcomere lengthening during relaxation. Here we use the multiscale MUSICO platform to model rat trabecular twitches. Validation of computational models is dependent on being able to simulate different experimental datasets, but there has been a paucity of data that can provide all of the required parameters in a single experiment, such as simultaneous measurements of force, intracellular Ca2+ transients, and sarcomere length dynamics. In this study, we used data from different studies collected under similar experimental conditions to provide information for all the required parameters. Our simulations established that twitches either in an isometric sarcomere or in fixed-length, multiple-sarcomere trabeculae replicate the experimental observations if models incorporate a length-tension relationship for the nonlinear series elasticity of muscle preparations and a scheme for thick-filament regulation. The thick-filament regulation assumes an off state in which myosin heads are parked onto the thick-filament backbone and are unable to interact with actin, a state analogous to the super-relaxed state. Including these two mechanisms provided simulations that accurately predict twitch contractions over a range of different conditions.

Muscle myosin performance measured with a synthetic nanomachine reveals a class-specific Ca2+ -sensitivity of the frog myosin II isoform

KEY POINTS

A nanomachine made of an ensemble of seven heavy-meromyosin (HMM) fragments of muscle myosin interacting with an actin filament is able to mimic the half-sarcomere generating steady force and constant-velocity shortening. To preserve Ca²⁺ as a free parameter, the Ca²⁺ -insensitive gelsolin fragment TL40 is used to attach the correctly oriented actin filament to the laser-trapped bead acting as a force transducer. The new method reveals that the performance of the nanomachine powered by myosin from frog hind-limb muscles depends on [Ca²⁺ ], an effect mediated by a Ca²⁺ -binding site in the regulatory light chain of HMM. The Ca²⁺ -sensitivity is class-specific because the performance of the nanomachine powered by mammalian skeletal muscle myosin is Ca²⁺ independent. A model simulation is able to interface the nanomachine performance with that of the muscle of origin and provides a molecular explanation of the functional diversity of muscles with different orthologue isoforms of myosin.

ABSTRACT

An ensemble of seven heavy-meromyosin (HMM) fragments of myosin-II purified from the hindlimb muscles of the frog (Rana esculenta) is used to drive a synthetic nanomachine that pulls an actin filament in the absence of confounding effects of other sarcomeric proteins. In the present version of the nanomachine the +end of the actin filament is attached to the laser trapped bead via the Ca²⁺ -insensitive gelsolin fragment TL40, making [Ca²⁺ ] a free parameter. Frog myosin performance in 2 mm ATP is affected by Ca²⁺ : in 0.1 mm Ca²⁺ , the isometric steady force (F₀ , 15.25 pN) is increased by 50% (P = 0.004) with respect to that in Ca²⁺ -free solution, the maximum shortening velocity (V₀ , 4.6 μm s^-1 ) is reduced by 27% (P = 0.46) and the maximum power (P_max , 7.6 aW) is increased by 21% (P = 0.17). V₀ reduction is not significant for the paucity of data at low force, although it is solidified by a similar decrease (33%, P < 0.0001) in the velocity of actin sliding as indicated by an in vitro motility assay (V_f ). The rate of ATP-hydrolysis in solution (φ) exhibits a similar calcium dependence. Ca²⁺ titration curves for V_f and φ give K_d values of ∼30 μm. All the above mechanical and kinetic parameters are independent of Ca²⁺ when HMM from rabbit psoas myosin is used, indicating that the Ca²⁺ -sensitivity is a class-specific property of muscle myosin. A unique multiscale model allows interfacing of the nanomachine performance to that of the muscle of origin and identifies the kinetic steps responsible for the Ca²⁺ -sensitivity of frog myosin.

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.

Differences in stretch-shortening cycle and residual force enhancement between muscles

It has been suggested that cross bridge kinetics and residual force enhancement (RFE) affect force in the stretch-shortening cycle (SSC). Because cross bridge kinetics and titin isoforms, which are thought to be related to RFE, differ between muscles, the SSC effect may be also muscle-dependent. Thus, we compared the SSC effect between psoas and soleus muscles, which have a distinct fiber type distribution and different titin isoforms. Four tests (SSC, SSC control, RFE, RFE control) were conducted using isolated, skinned fibers of psoas and soleus. In the SSC tests, fibers were activated at an average sarcomere length of 2.4 μm, stretched to 3.0 μm, and shortened to 2.4 μm. In the SSC control tests, fibers were activated at an average sarcomere length of 3.0 μm and then shortened to 2.4 μm. The relative increase in mechanical work obtained during shortening between tests was defined as the SSC effect. In the RFE tests, fibers were activated at an average sarcomere length of 2.4 μm and then stretched to 3.0 μm, while the RFE control tests consisted of an isometric contraction at 3.0 μm. The difference in steady-state isometric force between tests was defined as RFE. The SSC effect was greater in soleus than in psoas, while the RFE was the same for both muscles. Since the SSC effect was greater in soleus, while the RFE was the same, the observed greater SSC effect is probably not directly caused by RFE, but may be related to differences in cross bridge kinetics.

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 Myosin II-Based Nanomachine Devised for the Study of Ca2+-Dependent Mechanisms of Muscle Regulation

The emergent properties of the array arrangement of the molecular motor myosin II in the sarcomere of the striated muscle, the generation of steady force and shortening, can be studied in vitro with a synthetic nanomachine made of an ensemble of eight heavy-meromyosin (HMM) fragments of myosin from rabbit psoas muscle, carried on a piezoelectric nanopositioner and brought to interact with a properly oriented actin filament attached via gelsolin (a Ca2+-regulated actin binding protein) to a bead trapped by dual laser optical tweezers. However, the application of the original version of the nanomachine to investigate the Ca2+-dependent regulation mechanisms of the other sarcomeric (regulatory or cytoskeleton) proteins, adding them one at a time, was prevented by the impossibility to preserve [Ca2+] as a free parameter. Here, the nanomachine is implemented by assembling the bead-attached actin filament with the Ca2+-insensitive gelsolin fragment TL40. The performance of the nanomachine is determined both in the absence and in the presence of Ca2+ (0.1 mM, the concentration required for actin attachment to the bead with gelsolin). The nanomachine exhibits a maximum power output of 5.4 aW, independently of [Ca2+], opening the possibility for future studies of the Ca2+-dependent function/dysfunction of regulatory and cytoskeletal proteins.

Collagen, stiffness, and adhesion: the evolutionary basis of vertebrate mechanobiology

The emergence of collagen I in vertebrates resulted in a dramatic increase in the stiffness of the extracellular environment, supporting long-range force propagation and the development of low-compliant tissues necessary for the development of vertebrate traits including pressurized circulation and renal filtration. Vertebrates have also evolved integrins that can bind to collagens, resulting in the generation of higher tension and more efficient force transmission in the extracellular matrix. The stiffer environment provides an opportunity for the vertebrates to create new structures such as the stress fibers, new cell types such as endothelial cells, new developmental processes such as neural crest delamination, and new tissue organizations such as the blood-brain barrier. Molecular players found only in vertebrates allow the modification of conserved mechanisms as well as the design of novel strategies that can better serve the physiological needs of the vertebrates. These innovations collectively contribute to novel morphogenetic behaviors and unprecedented increases in the complexities of tissue mechanics and functions.

Cellular contractile forces are nonmechanosensitive

Cells' ability to apply contractile forces to their environment and to sense its mechanical properties (e.g., rigidity) are among their most fundamental features. Yet, the interrelations between contractility and mechanosensing, in particular, whether contractile force generation depends on mechanosensing, are not understood. We use theory and extensive experiments to study the time evolution of cellular contractile forces and show that they are generated by time-dependent actomyosin contractile displacements that are independent of the environment's rigidity. Consequently, contractile forces are nonmechanosensitive. We further show that the force-generating displacements are directly related to the evolution of the actomyosin network, most notably to the time-dependent concentration of F-actin. The emerging picture of force generation and mechanosensitivity offers a unified framework for understanding contractility.

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.

Regulation of pluripotency and reprogramming by RNA binding proteins

Embryonic stem cells have the capacities of self-renewal and pluripotency. Pluripotency establishment (somatic cell reprogramming), maintenance, and execution (differentiation) require orchestrated regulatory mechanisms of a cell's molecular machinery, including signaling pathways, epigenetics, transcription, translation, and protein degradation. RNA binding proteins (RBPs) take part in every process of RNA regulation and recent studies began to address their important functions in the regulation of pluripotency and reprogramming. Here, we discuss the roles of RBPs in key regulatory steps in the control of pluripotency and reprogramming. Among RNA binding proteins are a group of RNA helicases that are responsible for RNA structure remodeling with important functional implications. We highlight the largest family of RNA helicases, DDX (DEAD-box) helicase family and our current understanding of their functions specifically in the regulation of pluripotency and reprogramming.

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.

The problem with skeletal muscle series elasticity

Muscles contain contractile and (visco-) elastic passive components. At the latest since Hill’s classic works in the 1930s, it has been known that these elastic components affect the length and rate of change in length of the contractile component, and thus the active force capability of dynamically working muscles. In an attempt to elucidate functional properties of these muscle elastic components, scientists have introduced the notion of “series” and “parallel” elasticity. Unfortunately, this has led to much confusion and erroneous interpretations of results when the mechanical definitions of parallel and series elasticity were violated.

In this review, I will focus on muscle series elasticity, by first providing the mechanical definition for series elasticity, and then provide theoretical and experimental examples of the concept of series elasticity. Of particular importance is the treatment of aponeuroses. Aponeuroses are not in series with the tendon of a muscle nor the muscle’s contractile elements. The implicit and explicit treatment of aponeuroses as series elastic elements in muscle has led to incorrect conclusions about aponeuroses stiffness and Young’s modulus, and has contributed to vast overestimations of the storage and release of mechanical energy in cyclic muscle contractions.

Series elasticity is a defined mechanical concept that needs to be treated carefully when applied to skeletal muscle mechanics. Measuring aponeuroses mechanical properties in a muscle, and its possible contribution to the storage and release of mechanical energy is not trivial, and to my best knowledge, has not been (correctly) done yet.

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.

The effects of inorganic phosphate on muscle force development and energetics: challenges in modelling related to experimental uncertainties

Muscle force and power are developed by myosin cross-bridges, which cyclically attach to actin, undergo a force-generating transition and detach under turnover of ATP. The force-generating transition is intimately associated with release of inorganic phosphate (Pi) but the exact sequence of events in relation to the actual Pi release step is controversial. Details of this process are reflected in the relationships between [Pi] and the developed force and shortening velocity. In order to account for these relationships, models have proposed branched kinetic pathways or loose coupling between biochemical and force-generating transitions. A key hypothesis underlying the present study is that such complexities are not required to explain changes in the force–velocity relationship and ATP turnover rate with altered [Pi]. We therefore set out to test if models without branched kinetic paths and Pi-release occurring before the main force-generating transition can account for effects of varied [Pi] (0.1–25 mM). The models tested, one assuming either linear or non-linear cross-bridge elasticity, account well for critical aspects of muscle contraction at 0.5 mM Pi but their capacity to account for the maximum power output vary. We find that the models, within experimental uncertainties, account for the relationship between [Pi] and isometric force as well as between [Pi] and the velocity of shortening at low loads. However, in apparent contradiction with available experimental findings, the tested models produce an anomalous force–velocity relationship at elevated [Pi] and high loads with more than one possible velocity for a given load. Nevertheless, considering experimental uncertainties and effects of sarcomere non-uniformities, these discrepancies are insufficient to refute the tested models in favour of more complex alternatives.

Myosin Cross-Bridge Behaviour in Contracting Muscle-The T1 Curve of Huxley and Simmons (1971) Revisited

The stiffness of the myosin cross-bridges is a key factor in analysing possible scenarios to explain myosin head changes during force generation in active muscles. The seminal study of Huxley and Simmons (1971: Nature233: 533) suggested that most of the observed half-sarcomere instantaneous compliance (=1/stiffness) resides in the myosin heads. They showed with a so-called T₁ plot that, after a very fast release, the half-sarcomere tension reduced to zero after a step size of about 60Å (later with improved experiments reduced to 40Å). However, later X-ray diffraction studies showed that myosin and actin filaments themselves stretch slightly under tension, which means that most (at least two-thirds) of the half sarcomere compliance comes from the filaments and not from cross-bridges. Here we have used a different approach, namely to model the compliances in a virtual half sarcomere structure in silico. We confirm that the T₁ curve comes almost entirely from length changes in the myosin and actin filaments, because the calculated cross-bridge stiffness (probably greater than 0.4 pN/Å) is higher than previous studies have suggested. Our model demonstrates that the formulations produced by previous authors give very similar results to our model if the same starting parameters are used. However, we find that it is necessary to model the X-ray diffraction data as well as mechanics data to get a reliable estimate of the cross-bridge stiffness. In the light of the high cross-bridge stiffness found in the present study, we present a plausible modified scenario to describe aspects of the myosin cross-bridge cycle in active muscle. In particular, we suggest that, apart from the filament compliances, most of the cross-bridge contribution to the instantaneous T₁ response may come from weakly-bound myosin heads, not myosin heads in strongly attached states. The strongly attached heads would still contribute to the T₁ curve, but only in a very minor way, with a stiffness that we postulate could be around 0.1 pN/Å, a value which would generate a working stroke close to 100 Å from the hydrolysis of one ATP molecule. The new model can serve as a tool to calculate sarcomere elastic properties for any vertebrate striated muscle once various parameters have been determined (e.g., tension, T₁ intercept, temperature, X-ray diffraction spacing results).

Single molecule mechanics resolves the earliest events in force generation by cardiac myosin

Key steps of cardiac mechanochemistry, including the force-generating working stroke and the release of phosphate (P_i), occur rapidly after myosin-actin attachment. An ultra-high-speed optical trap enabled direct observation of the timing and amplitude of the working stroke, which can occur within <200 μs of actin binding by β-cardiac myosin. The initial actomyosin state can sustain loads of at least 4.5 pN and proceeds directly to the stroke or detaches before releasing ATP hydrolysis products. The rates of these processes depend on the force. The time between binding and stroke is unaffected by 10 mM P_i which, along with other findings, indicates the stroke precedes phosphate release. After P_i release, P_i can rebind enabling reversal of the working stroke. Detecting these rapid events under physiological loads provides definitive indication of the dynamics by which actomyosin converts biochemical energy into mechanical work.

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.

A chemical kinetic model for Ca2+ induced spontaneous oscillatory contraction of myocardium

The Ca²⁺ induced Spontaneous Oscillatory Contraction (Ca-SPOC) of cardiac myofibrils oscillate with a period similar to resting heartbeat of several animal species, and its auto-oscillatory properties set the basic rhythm of cardiac contraction. To explain the dynamics of Ca-SPOC, the present paper constructs a novel chemical kinetical model based upon the cooperative behavior between the two heads of myosin II dimer, also considering the reaction-diffusion effect of ATP inside myocardial fibers. The simulation results show that the concentration of ATP inside myocardial fibers oscillates over time under some special conditions, together with the proportions of myosin II dimers in different states periodically changing with time, which contributes to produce the sustained oscillations of contractive tension. These results indicate that the SPOC of muscles may be partly due to chemical oscillation involved in the actomyosin ATPase cycle, which has been ignored by the previous theoretical studies.

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

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

Effect of myofibril passive elastic properties on the mechanical communication between motor proteins on adjacent sarcomeres

Rapid sarcomere lengthening waves propagate along a single muscle myofibril during spontaneous oscillatory contraction (SPOC). In asynchronous insect flight muscles, SPOC is thought to be almost completely synchronized over the entire myofibril. This phenomenon does not require Ca²⁺ regulation of the dynamics of the motor proteins, and cannot be explained simply by the longitudinal mechanical equilibrium among sarcomeres in the myofibril. In the present study, we rationalize these phenomena by considering the lateral mechanical equilibrium, in which two tensions originating from the inverse relationship between sarcomere length and lattice spacing, along with the lattice alignment, play important roles in the mechanical communication between motor proteins on adjacent filaments via the Z-disc. The proposed model is capable of explaining various SPOC phenomena based on the stochastic power-stroke mechanism of motor proteins, which responds to temporal changes in longitudinal mechanical load.

Emergent spatiotemporal dynamics of the actomyosin network in the presence of chemical gradients

We used particle-based computer simulations to study the emergent properties of the actomyosin cytoskeleton. Our model accounted for biophysical interactions between filamentous actin and non-muscle myosin II and was motivated by recent experiments demonstrating that spatial regulation of myosin activity is required for fibroblasts responding to spatial gradients of platelet derived growth factor (PDGF) to undergo chemotaxis. Our simulations revealed the spontaneous formation of actin asters, consistent with the punctate actin structures observed in chemotacting fibroblasts. We performed a systematic analysis of model parameters to identify biochemical steps in myosin activity that significantly affect aster formation and performed simulations in which model parameter values vary spatially to investigate how the model responds to chemical gradients. Interestingly, spatial variations in motor stiffness generated time-dependent behavior of the actomyosin network, in which actin asters continued to spontaneously form and dissociate in different regions of the gradient. Our results should serve as a guide for future experimental investigations.

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.

Prestrain and cholinergic receptor-dependent differential recruitment of mechanosensitive energy loss and energy release elements in airway smooth muscle

We tested the hypothesis that oscillatory airway smooth muscle (ASM) mechanics is governed by mechanosensitive energy loss and energy release elements that can be recruited by prestrain and cholinergic stimulation. We measured mechanical energy loss and mechanical energy release in unstimulated and carbachol-stimulated bovine ASM held at prestrains ranging from 0.3 to 1.0 L_o (reference length) and subjected to sinusoidal length oscillation at 1 hz with oscillatory strain amplitudes ranging from 0.1 to 1.5% L_o. We found that oscillatory ASM mechanics during sinusoidal length oscillation is governed predominantly by one class of nonlinear mechanosensitive energy loss element and one class of nonlinear mechanosensitive energy release element with differential mechanosensitivities to oscillatory strain amplitude. The greater mechanosensitivity of the energy loss element than energy release element may explain the bronchodilatory effect of deep inspiration. Prestrain, an important determinant of ASM responsiveness, differentially increased energy loss and energy release in unstimulated and carbachol-stimulated ASM. Cholinergic stimulation, an important cause of bronchoconstriction and airway inflammation, also differentially increased energy loss and energy release. When prestrain and cholinergic stimulation were combined, we found that prestrain and cholinergic stimulation synergistically increased energy loss and energy release by ASM. The relationship between recruitment of energy loss elements and recruitment of energy release elements was nonlinear, suggesting that energy loss and energy release elements are not coupled in ASM cells. These findings imply that large lung volume and cholinergic ASM activation would synergistically increase mechanical energy expenditure during inspiration and mechanical recoil of ASM during expiration. NEW & NOTEWORTHY We report for the first time that oscillatory airway smooth muscle mechanics is governed predominantly by one class of nonlinear mechanosensitive energy loss element and one class of nonlinear mechanosensitive energy release element with differential mechanosensitivities to oscillatory strain amplitude. Prestrain and cholinergic stimulation synergistically and differentially recruit energy loss and energy release elements. The greater mechanosensitivity of the energy loss element than the energy release element may explain the bronchodilatory effect of deep inspiration.

Functional significance of HCM mutants of tropomyosin, V95A and D175N, studied with in vitro motility assays

The majority of hypertrophic cardiomyopathy (HCM) is caused by mutations in sarcomere proteins. We examined tropomyosin (Tpm)’s HCM mutants in humans, V95A and D175N, with in vitro motility assay using optical tweezers to evaluate the effects of the Tpm mutations on the actomyosin interaction at the single molecular level. Thin filaments were reconstituted using these Tpm mutants, and their sliding velocity and force were measured at varying Ca²⁺ concentrations. Our results indicate that the sliding velocity at pCa ≥8.0 was significantly increased in mutants, which is expected to cause a diastolic problem. The velocity that can be activated by Ca²⁺ decreased significantly in mutants causing a systolic problem. With sliding force, Ca²⁺ activatable force decreased in V95A and increased in D175N, which may cause a systolic problem. Our results further demonstrate that the duty ratio determined at the steady state of force generation in saturating [Ca²⁺] decreased in V95A and increased in D175N. The Ca²⁺ sensitivity and cooperativity were not significantly affected by the mutations. These results suggest that the two mutants modulate molecular processes of the actomyosin interaction differently, but to result in the same pathology known as HCM.