Drug effect unveils inter-head cooperativity and strain-dependent ADP release in fast skeletal actomyosin

Pseudo-phosphorylation of essential light chains affects the functioning of skeletal muscle myosin

The work aimed to investigate how the phosphorylation of the myosin essential light chain of fast skeletal myosin (LC1) affects the functional properties of the myosin molecule. Using mass-spectrometry, we revealed phosphorylated peptides of LC1 in myosin from different fast skeletal muscles. Mutations S193D and T65D that mimic natural phosphorylation of LC1 were produced, and their effects on functional properties of the entire myosin molecule and isolated myosin head (S1) were studied. We have shown that T65D mutation drastically decreased the sliding velocity of thin filaments in an in vitro motility assay and strongly increased the duration of actin-myosin interaction in optical trap experiments. These effects of T65D mutation in LC1 observed only with the whole myosin but not with S1 were prevented by double T65D/S193D mutation. The T65D and T65D/S193D mutations increased actin-activated ATPase activity of S1 and decreased ADP affinity for the actin-S1 complex. The results indicate that pseudo-phosphorylation of LC1 differently affects the properties of the whole myosin molecule and its isolated head. Also, the results show that phosphorylation of LC1 of skeletal myosin could be one more mechanism of regulation of actin-myosin interaction that needs further investigation.

Properties of Cardiac Myosin with Cardiomyopathic Mutations in Essential Light Chains

The effects of cardiomyopathic mutations E56G, M149V, and E177G in the MYL3 gene encoding essential light chain of human ventricular myosin (ELCv), on the functional properties of cardiac myosin and its isolated head (myosin subfragment 1, S1) were investigated. Only the M149V mutation upregulated the actin-activated ATPase activity of S1. All mutations significantly increased the Ca2+-sensitivity of the sliding velocity of thin filaments on the surface with immobilized myosin in the in vitro motility assay, while mutations E56G and M149V (but not E177G) reduced the sliding velocity of regulated thin filaments and F-actin filaments almost twice. Therefore, despite the fact that all studied mutations in ELCv are involved in the development of hypertrophic cardiomyopathy, the mechanisms of their influence on the actin-myosin interaction are different.

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.

Multistep orthophosphate release tunes actomyosin energy transduction

Muscle contraction and a range of critical cellular functions rely on force-producing interactions between myosin motors and actin filaments, powered by turnover of adenosine triphosphate (ATP). The relationship between release of the ATP hydrolysis product ortophosphate (Pi) from the myosin active site and the force-generating structural change, the power-stroke, remains enigmatic despite its central role in energy transduction. Here, we present a model with multistep Pi-release that unifies current conflicting views while also revealing additional complexities of potential functional importance. The model is based on our evidence from kinetics, molecular modelling and single molecule fluorescence studies of Pi binding outside the active site. It is also consistent with high-speed atomic force microscopy movies of single myosin II molecules without Pi at the active site, showing consecutive snapshots of pre- and post-power stroke conformations. In addition to revealing critical features of energy transduction by actomyosin, the results suggest enzymatic mechanisms of potentially general relevance.

Release of the ATP hydrolysis product orthophosphate (Pi) from the myosin active site is central in force generation but is poorly understood. Here, Moretto et al. present evidence for multistep Pi-release reconciling apparently contradictory results.

Molecular Events of the Crossbridge Cycle Reflected in the Force–Velocity Relationship of Activated Muscle

Muscles convert chemical energy to mechanical work. Mechanical performance of a muscle is often assessed by the muscle’s ability to shorten and generate power over a range of loads or forces, characterized by the force–velocity and force–power relationships. The hyperbolic force–velocity relationship of muscle, for a long time, has been regarded as a pure empirical description of the force–velocity data. Connections between mechanical manifestation in terms of force–velocity properties and the kinetics of the crossbridge cycle have only been established recently. In this review, we describe how the model of Huxley’s crossbridge kinetics can be transformed to the hyperbolic Hill equation, and link the changes in force–velocity properties to molecular events within the crossbridge cycle driven by ATP hydrolysis. This allows us to reinterpret some findings from previous studies on experimental interventions that altered the force–velocity relationship and gain further insight into the molecular mechanisms of muscle contraction under physiological and pathophysiological conditions.

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.

Electrostatic interactions in the SH1-SH2 helix of human cardiac myosin modulate the time of strong actomyosin binding

Two single mutations, R694N and E45Q, were introduced in the beta isoform of human cardiac myosin to remove permanent salt bridges E45:R694 and E98:R694 in the SH1-SH2 helix of the myosin head. Beta isoform-specific bridges E45:R694 and E98:R694 were discovered in the molecular dynamics simulations of the alpha and beta myosin isoforms. Alpha and beta isoforms exhibit different kinetics, ADP dissociates slower from actomyosin containing beta myosin isoform, therefore, beta myosin stays strongly bound to actin longer. We hypothesize that the electrostatic interactions in the SH1-SH2 helix modulate the affinity of ADP to actomyosin, and therefore, the time of the strong actomyosin binding. Wild type and the mutants of the myosin head construct (1-843 amino acid residues) were expressed in differentiated C2C12 cells, and the duration of the strongly bound state of actomyosin was characterized using transient kinetics spectrophotometry. All myosin constructs exhibited a fast rate of ATP binding to actomyosin and a slow rate of ADP dissociation, showing that ADP release limits the time of the strongly bound state of actomyosin. The mutant R694N showed a faster rate of ADP release from actomyosin, compared to the wild type and the E45Q mutant, thus indicating that electrostatic interactions within the SH1-SH2 helix region of human cardiac myosin modulate ADP release and thus, the duration of the strongly bound state of actomyosin.

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.

Single molecule turnover of fluorescent ATP by myosin and actomyosin unveil elusive enzymatic mechanisms

Benefits of single molecule studies of biomolecules include the need for minimal amounts of material and the potential to reveal phenomena hidden in ensembles. However, results from recent single molecule studies of fluorescent ATP turnover by myosin are difficult to reconcile with ensemble studies. We found that key reasons are complexities due to dye photophysics and fluorescent contaminants. After eliminating these, through surface cleaning and use of triple state quenchers and redox agents, the distributions of ATP binding dwell times on myosin are best described by 2 to 3 exponential processes, with and without actin, and with and without the inhibitor para-aminoblebbistatin. Two processes are attributable to ATP turnover by myosin and actomyosin respectively, whereas the remaining process (rate constant 0.2–0.5 s⁻¹) is consistent with non-specific ATP binding to myosin, possibly accelerating ATP transport to the active site. Finally, our study of actin-activated myosin ATP turnover without sliding between actin and myosin reveals heterogeneity in the ATP turnover kinetics consistent with models of isometric contraction.

With fluorescence based-TIRF microspectroscopy, Ušaj et al. unveil mechanistic details about the ATP turnover rates by myosin and actomyosin with enzymatic reaction pathways that were not possible to obtain from ensemble studies. This study could be important to the field of molecular motors.

Ex vivo Methods for Measuring Cardiac Muscle Mechanical Properties

Cardiovascular disease continues to be the leading cause of morbidity and mortality in the United States and thousands of manuscripts each year are aimed at elucidating mechanisms underlying cardiac disease. The methods for quantifying cardiac performance are quite varied, with each technique assessing unique features of cardiac muscle mechanical properties. Accordingly, in this review, we discuss current ex vivo methods for quantifying cardiac muscle performance, highlighting what can be learned from each method, and how each technique can be used in conjunction to complement others for a more comprehensive understanding of cardiac function. Importantly, cardiac function can be assessed at several different levels, from the whole organ down to individual protein-protein interactions. Here, we take a reductionist view of methods that are commonly used to measure the distinct aspects of cardiac mechanical function, beginning with whole heart preparations and finishing with the in vitro motility assay. While each of the techniques are individually well-documented in the literature, there is a significant need for a comparison of the techniques, delineating the mechanical parameters that can are best measured with each technique, as well as the strengths and weaknesses inherent to each method. Additionally, we will consider complementary techniques and how these methods can be used in combination to improve our understanding of cardiac mechanical function. By presenting each of these methods, with their strengths and limitations, in a single manuscript, this review will assist cardiovascular biologists in understanding the existing literature on cardiac mechanical function, as well as designing future experiments.

Myosin from the ventricle is more sensitive to omecamtiv mecarbil than myosin from the atrium

Omecamtiv mecarbil (OM), an activator of cardiac myosin, strongly affects contractile characteristics of the ventricles and, to a much lesser extent, the characteristics of atrial contraction. We compared the molecular mechanism of action of OM on the interaction of atrial and ventricular myosin with actin using an optical trap and an in vitro motility assay. In concentrations up to 0.5 μM, OM did not affect the step size of a myosin molecule but reduced it at a higher OM level. OM substantially prolonged the interaction of both isoforms of myosin with actin. However, the interaction characteristics of ventricular myosin with actin were more sensitive to OM than those of atrial myosin. Our results, obtained at the level of isolated proteins, can explain why the impact of OM in therapeutic concentrations on the contractile function of the atrium is less significant as compared to those of the ventricle.

X-ray Diffraction Studies on the Structural Origin of Dynamic Tension Recovery Following Ramp-Shaped Releases in High-Ca Rigor Muscle Fibers

It is generally believed that during muscle contraction, myosin heads (M) extending from myosin filament attaches to actin filaments (A) to perform power stroke, associated with the reaction, A-M-ADP-Pi → A-M + ADP + Pi, so that myosin heads pass through the state of A-M, i.e., rigor A-M complex. We have, however, recently found that: (1) an antibody to myosin head, completely covering actin-binding sites in myosin head, has no effect on Ca²⁺-activated tension in skinned muscle fibers; (2) skinned fibers exhibit distinct tension recovery following ramp-shaped releases (amplitude, 0.5% of Lo; complete in 5 ms); and (3) EDTA, chelating Mg ions, eliminate the tension recovery in low-Ca rigor fibers but not in high-Ca rigor fibers. These results suggest that A-M-ADP myosin heads in high-Ca rigor fibers have dynamic properties to produce the tension recovery following ramp-shaped releases, and that myosin heads do not pass through rigor A-M complex configuration during muscle contraction. To obtain information about the structural changes in A-M-ADP myosin heads during the tension recovery, we performed X-ray diffraction studies on high-Ca rigor skinned fibers subjected to ramp-shaped releases. X-ray diffraction patterns of the fibers were recorded before and after application of ramp-shaped releases. The results obtained indicate that during the initial drop in rigor tension coincident with the applied release, rigor myosin heads take up applied displacement by tilting from oblique to perpendicular configuration to myofilaments, and after the release myosin heads appear to rotate around the helical structure of actin filaments to produce the tension recovery.

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.

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.

Atomistic Models from Orientation and Distance Constraints Using EPR of a Bifunctional Spin Label

We have used high-resolution orientation and distance measurements derived from electron paramagnetic resonance of a bifunctional spin label (BSL) to build and refine atomistic models of protein structure. We demonstrate this approach by investigating the effects of nucleotide binding on the structure of myosin's catalytic domain while myosin is in complex with actin. Constraints for orientation of individual helices were obtained in a previous study from continuous-wave electron paramagnetic resonance of myosin labeled at specific sites with BSLs in oriented muscle fibers. In this study, new distance constraints were derived from double electron-electron resonance on myosin constructs labeled with a BSL specifically at two sites. Using these complementary constraints together, we thoroughly characterize the BSL's rigid, highly stereoselective attachment to protein α-helices, which permits accurate measurements of orientation and distance. We also leverage these measurements to derive a novel, to our knowledge, structural model for myosin-II in complex with actin and MgADP and compare our model to other recent actomyosin structures. The described approach is applicable to any orientable complex (e.g., membranes or filaments) in which site-specific di-Cys mutation is feasible.

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.

Comparative analysis of widely used methods to remove nonfunctional myosin heads for the in vitro motility assay

The in vitro motility assay allows studies of muscle contraction through observation of actin filament propulsion by surface-adsorbed myosin motors or motor fragments isolated from muscle. A possible problem is that motility may be compromised by nonfunctional, “dead”, motors, obtained in the isolation process. Here we investigate the effects on motile function of two approaches designed to eliminate the effects of these dead motors. We first tested the removal of heavy meromyosin (HMM) molecules with ATP-insensitive “dead” heads by pelleting them with actin filaments, using ultracentrifugation in the presence of 1 mM MgATP (“affinity purification”). Alternatively we incubated motility assay flow cells, after HMM surface adsorption, with non-fluorescent “blocking actin” (1 µM) to block the dead heads. Both affinity purification and use of blocking actin increased the fraction of motile filaments compared to control conditions. However, affinity purification significantly reduced the actin sliding speed in five out of seven experiments on silanized surfaces and in one out of four experiments on nitrocellulose surfaces. Similar effects on velocity were not observed with the use of blocking actin. However, a reduced speed was also seen (without affinity purification) if HMM or myosin subfragment 1 was mixed with 1 mM MgATP before and during surface adsorption. We conclude that affinity purification can produce unexpected effects that may complicate the interpretation of in vitro motility assays and other experiments with surface adsorbed HMM, e.g. single molecule mechanics experiments. The presence of MgATP during incubation with myosin motor fragments is critical for the complicating effects.

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.

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.

Omecamtiv Mecarbil Enhances the Duty Ratio of Human β-Cardiac Myosin Resulting in Increased Calcium Sensitivity and Slowed Force Development in Cardiac Muscle

The small molecule drug omecamtiv mecarbil (OM) specifically targets cardiac muscle myosin and is known to enhance cardiac muscle performance, yet its impact on human cardiac myosin motor function is unclear. We expressed and purified human β-cardiac myosin subfragment 1 (M2β-S1) containing a C-terminal Avi tag. We demonstrate that the maximum actin-activated ATPase activity of M2β-S1 is slowed more than 4-fold in the presence of OM, whereas the actin concentration required for half-maximal ATPase was reduced dramatically (30-fold). We find OM does not change the overall actin affinity. Transient kinetic experiments suggest that there are two kinetic pathways in the presence of OM. The dominant pathway results in a slow transition between actomyosin·ADP states and increases the time myosin is strongly bound to actin. However, OM also traps a population of myosin heads in a weak actin affinity state with slow product release. We demonstrate that OM can reduce the actin sliding velocity more than 100-fold in the in vitro motility assay. The ionic strength dependence of in vitro motility suggests the inhibition may be at least partially due to drag forces from weakly attached myosin heads. OM causes an increase in duty ratio examined in the motility assay. Experiments with permeabilized human myocardium demonstrate that OM increases calcium sensitivity and slows force development (k_tr) in a concentration-dependent manner, whereas the maximally activated force is unchanged. We propose that OM increases the myosin duty ratio, which results in enhanced calcium sensitivity but slower force development in human myocardium.

Actomyosin interaction at low ATP concentrations

In vitro motility assay (IVMA) experiments were performed to analyze the movement of actin filaments sliding on a pavement of myosin molecules at different [ATP] and [ADP]. In standard experimental conditions at [ATP] = 2 mM, about 80% of the actin filaments move in unloaded conditions with a constant velocity. However, a fraction of at least 20% static actin filaments is always present. The accepted explanation is the occurrence of damaged "rigor"-like myosin heads that do not undergo the normal ATP-dependent cycling motion. However, in a series of IVMA experiments performed at different [ATP] we observed that the mobility of actin filaments increased with lowering [ATP]. We investigated the influence of [ATP] on the number of mobile actin filaments. IVMA experiments were performed at controlled nucleotide concentrations and the percentage of mobile filaments accurately determined by specific operator-guided software. The value of ΔG _ATP involved was determined. Results showed that the number of mobile actin filaments sliding on type 2B heavy meromyosin isoform (2B HMM) increased at very low [ATP] accompanied by less negative ΔG _ATP values. Similar results were obtained by increasing [ADP]. Performing experiments at the same [ATP] with different myosin types, we found a higher number of mobile actin filaments on slow type 1 HMM with respect to type 2B HMM while the highest number of mobile actin filaments was found on single-head myosin (S1 fraction). We also found that [ATP] did not influence the percentage of mobile actin filaments sliding on S1. Our results reveal novel aspects of actomyosin interaction.

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.

Direct Measurements of Local Coupling between Myosin Molecules Are Consistent with a Model of Muscle Activation

Muscle contracts due to ATP-dependent interactions of myosin motors with thin filaments composed of the proteins actin, troponin, and tropomyosin. Contraction is initiated when calcium binds to troponin, which changes conformation and displaces tropomyosin, a filamentous protein that wraps around the actin filament, thereby exposing myosin binding sites on actin. Myosin motors interact with each other indirectly via tropomyosin, since myosin binding to actin locally displaces tropomyosin and thereby facilitates binding of nearby myosin. Defining and modeling this local coupling between myosin motors is an open problem in muscle modeling and, more broadly, a requirement to understanding the connection between muscle contraction at the molecular and macro scale. It is challenging to directly observe this coupling, and such measurements have only recently been made. Analysis of these data suggests that two myosin heads are required to activate the thin filament. This result contrasts with a theoretical model, which reproduces several indirect measurements of coupling between myosin, that assumes a single myosin head can activate the thin filament. To understand this apparent discrepancy, we incorporated the model into stochastic simulations of the experiments, which generated simulated data that were then analyzed identically to the experimental measurements. By varying a single parameter, good agreement between simulation and experiment was established. The conclusion that two myosin molecules are required to activate the thin filament arises from an assumption, made during data analysis, that the intensity of the fluorescent tags attached to myosin varies depending on experimental condition. We provide an alternative explanation that reconciles theory and experiment without assuming that the intensity of the fluorescent tags varies.

Despite decades of study, there is no clear connection between muscle contraction at the molecular and the macroscopic scale. For example, we cannot yet predict how a genetic defect in a muscle protein will result in a physiological change in the heart. This multi-scale understanding is difficult, in part, because molecules cooperate during muscle contraction; that is, one molecule’s behavior is influenced by the behavior of its neighbors. It is difficult to make direct measurements from such coupled molecular systems and also difficult to describe them quantitatively. Despite these obstacles, we recently published experimental measurements and theoretical models of this coupling, but there were apparent discrepancies between the two. Here, we use detailed computer simulations of these experiments to show that, in fact, the measurements agree with the model to a remarkable extent. This agreement suggests that the model captures the essential molecular events that underlie the coupling between muscle molecules. This removes a major obstacle to a multi-scale understanding of muscle contraction and, while more work is necessary, suggests that a connection between the molecular and macroscopic scale is within reach.

High-resolution helix orientation in actin-bound myosin determined with a bifunctional spin label

Using electron paramagnetic resonance (EPR) of a bifunctional spin label (BSL) bound stereospecifically to Dictyostelium myosin II, we determined with high resolution the orientation of individual structural elements in the catalytic domain while myosin is in complex with actin. BSL was attached to a pair of engineered cysteine side chains four residues apart on known α-helical segments, within a construct of the myosin catalytic domain that lacks other reactive cysteines. EPR spectra of BSL-myosin bound to actin in oriented muscle fibers showed sharp three-line spectra, indicating a well-defined orientation relative to the actin filament axis. Spectral analysis indicated that orientation of the spin label can be determined within <2.1° accuracy, and comparison with existing structural data in the absence of nucleotide indicates that helix orientation can also be determined with <4.2° accuracy. We used this approach to examine the crucial ADP release step in myosin's catalytic cycle and detected reversible rotations of two helices in actin-bound myosin in response to ADP binding and dissociation. One of these rotations has not been observed in myosin-only crystal structures.

Poorly understood aspects of striated muscle contraction

Muscle contraction results from cyclic interactions between the contractile proteins myosin and actin, driven by the turnover of adenosine triphosphate (ATP). Despite intense studies, several molecular events in the contraction process are poorly understood, including the relationship between force-generation and phosphate-release in the ATP-turnover. Different aspects of the force-generating transition are reflected in the changes in tension development by muscle cells, myofibrils and single molecules upon changes in temperature, altered phosphate concentration, or length perturbations. It has been notoriously difficult to explain all these events within a given theoretical framework and to unequivocally correlate observed events with the atomic structures of the myosin motor. Other incompletely understood issues include the role of the two heads of myosin II and structural changes in the actin filaments as well as the importance of the three-dimensional order. We here review these issues in relation to controversies regarding basic physiological properties of striated muscle. We also briefly consider actomyosin mutation effects in cardiac and skeletal muscle function and the possibility to treat these defects by drugs.

Muscle activation described with a differential equation model for large ensembles of locally coupled molecular motors

Molecular motors, by turning chemical energy into mechanical work, are responsible for active cellular processes. Often groups of these motors work together to perform their biological role. Motors in an ensemble are coupled and exhibit complex emergent behavior. Although large motor ensembles can be modeled with partial differential equations (PDEs) by assuming that molecules function independently of their neighbors, this assumption is violated when motors are coupled locally. It is therefore unclear how to describe the ensemble behavior of the locally coupled motors responsible for biological processes such as calcium-dependent skeletal muscle activation. Here we develop a theory to describe locally coupled motor ensembles and apply the theory to skeletal muscle activation. The central idea is that a muscle filament can be divided into two phases: an active and an inactive phase. Dynamic changes in the relative size of these phases are described by a set of linear ordinary differential equations (ODEs). As the dynamics of the active phase are described by PDEs, muscle activation is governed by a set of coupled ODEs and PDEs, building on previous PDE models. With comparison to Monte Carlo simulations, we demonstrate that the theory captures the behavior of locally coupled ensembles. The theory also plausibly describes and predicts muscle experiments from molecular to whole muscle scales, suggesting that a micro- to macroscale muscle model is within reach.

Hypothesis and theory: mechanical instabilities and non-uniformities in hereditary sarcomere myopathies

Familial hypertrophic cardiomyopathy (HCM), due to point mutations in genes for sarcomere proteins such as myosin, occurs in 1/500 people and is the most common cause of sudden death in young individuals. Similar mutations in skeletal muscle, e.g., in the MYH7 gene for slow myosin found in both the cardiac ventricle and slow skeletal muscle, may also cause severe disease but the severity and the morphological changes are often different. In HCM, the modified protein function leads, over years to decades, to secondary remodeling with substantial morphological changes, such as hypertrophy, myofibrillar disarray, and extensive fibrosis associated with severe functional deterioration. Despite intense studies, it is unclear how the moderate mutation-induced changes in protein function cause the long-term effects. In hypertrophy of the heart due to pressure overload (e.g., hypertension), mechanical stress in the myocyte is believed to be major initiating stimulus for activation of relevant cell signaling cascades. Here it is considered how expression of mutated proteins, such as myosin or regulatory proteins, could have similar consequences through one or both of the following mechanisms: (1) contractile instabilities within each sarcomere (with more than one stable velocity for a given load), (2) different tension generating capacities of cells in series. These mechanisms would have the potential to cause increased tension and/or stretch of certain cells during parts of the cardiac cycle. Modeling studies are used to illustrate these ideas and experimental tests are proposed. The applicability of similar ideas to skeletal muscle is also postulated, and differences between heart and skeletal muscle are discussed.

The kinetics of mechanically coupled myosins exhibit group size-dependent regimes

Naturally occurring groups of muscle myosin behave differently from individual myosins or small groups commonly assayed in vitro. Here, we investigate the emergence of myosin group behavior with increasing myosin group size. Assuming the number of myosin binding sites (N) is proportional to actin length (L) (N = L/35.5 nm), we resolve in vitro motility of actin propelled by skeletal muscle myosin for L = 0.2-3 μm. Three distinct regimes were found: L < 0.3 μm, sliding arrest; 0.3 μm ≤ L ≤ 1 μm, alternation between arrest and continuous sliding; L > 1 μm, continuous sliding. We theoretically investigated the myosin group kinetics with mechanical coupling via actin. We find rapid actin sliding steps driven by power-stroke cascades supported by postpower-stroke myosins, and phases without actin sliding caused by prepower-stroke myosin buildup. The three regimes are explained: N = 8, rare cascades; N = 15, cascade bursts; N = 35, continuous cascading. Two saddle-node bifurcations occur for increasing N (mono → bi → mono-stability), with steady states corresponding to arrest and continuous cascading. The experimentally measured dependence of actin sliding statistics on L and myosin concentration is correctly predicted.

Hill's equation of muscle performance and its hidden insight on molecular mechanisms

Muscles shorten faster against light loads than they do against heavy loads. The hyperbolic equation first used by A.V. Hill over seven decades ago to illustrate the relationship between shortening velocity and load is still the predominant method used to characterize muscle performance, even though it has been regarded as purely empirical and lacking precision in predicting velocities at high and low loads. Popularity of the Hill equation has been sustained perhaps because of historical reasons, but its simplicity is certainly attractive. The descriptive nature of the equation does not diminish its role as a useful tool in our quest to understand animal locomotion and optimal design of muscle-powered devices like bicycles. In this Review, an analysis is presented to illustrate the connection between the historic Hill equation and the kinetics of myosin cross-bridge cycle based on the latest findings on myosin motor interaction with actin filaments within the structural confines of a sarcomere. In light of the new data and perspective, some previous studies of force-velocity relations of muscle are revisited to further our understanding of muscle mechanics and the underlying biochemical events, specifically how extracellular and intracellular environment, protein isoform expression, and posttranslational modification of contractile and regulatory proteins change the interaction between myosin and actin that in turn alter muscle force, shortening velocity, and the relationship between them.

Nonlinear cross-bridge elasticity and post-power-stroke events in fast skeletal muscle actomyosin

Generation of force and movement by actomyosin cross-bridges is the molecular basis of muscle contraction, but generally accepted ideas about cross-bridge properties have recently been questioned. Of the utmost significance, evidence for nonlinear cross-bridge elasticity has been presented. We here investigate how this and other newly discovered or postulated phenomena would modify cross-bridge operation, with focus on post-power-stroke events. First, as an experimental basis, we present evidence for a hyperbolic [MgATP]-velocity relationship of heavy-meromyosin-propelled actin filaments in the in vitro motility assay using fast rabbit skeletal muscle myosin (28-29°C). As the hyperbolic [MgATP]-velocity relationship was not consistent with interhead cooperativity, we developed a cross-bridge model with independent myosin heads and strain-dependent interstate transition rates. The model, implemented with inclusion of MgATP-independent detachment from the rigor state, as suggested by previous single-molecule mechanics experiments, accounts well for the [MgATP]-velocity relationship if nonlinear cross-bridge elasticity is assumed, but not if linear cross-bridge elasticity is assumed. In addition, a better fit is obtained with load-independent than with load-dependent MgATP-induced detachment rate. We discuss our results in relation to previous data showing a nonhyperbolic [MgATP]-velocity relationship when actin filaments are propelled by myosin subfragment 1 or full-length myosin. We also consider the implications of our results for characterization of the cross-bridge elasticity in the filament lattice of muscle.

The myosin duty ratio tunes the calcium sensitivity and cooperative activation of the thin filament

In striated muscle, calcium binding to the thin filament (TF) regulatory complex activates actin-myosin ATPase activity, and actin-myosin kinetics in turn regulates TF activation. However, a quantitative description of the effects of actin-myosin kinetics on the calcium sensitivity (pCa50) and cooperativity (nH) of TF activation is lacking. With the assumption that TF structural transitions and TF-myosin binding transitions are inextricably coupled, we advanced the principles established by Kad et al. [Kad, N., et al. (2005) Proc. Natl. Acad. Sci. U.S.A. 102, 16990-16995] and Sich et al. [Sich, N. M., et al. (2011) J. Biol. Chem. 285, 39150-39159] to develop a simple model of TF regulation, which predicts that pCa50 varies linearly with duty ratio and that nH is maximal near physiological duty ratios. Using in vitro motility to determine the calcium sensitivity of TF sliding velocities, we measured pCa50 and nH at different myosin densities and in the presence of ATPase inhibitors. The observed effects of myosin density and actin-myosin duty ratio on pCa50 and nH are consistent with our model predictions. In striated muscle, pCa50 must match cytosolic calcium concentrations and a maximal nH optimizes calcium responsiveness. Our results indicate that pCa50 and nH can be predictably tuned through TF-myosin ATPase kinetics and that drugs and disease states that alter ATPase kinetics can, through their effects on calcium sensitivity, alter the efficiency of muscle contraction.

A cross-bridge cycle with two tension-generating steps simulates skeletal muscle mechanics

We examined whether cross-bridge cycle models with one or two tension-generating steps can account for the force-velocity relation of and tension response to length steps of frog skeletal muscle. Transition-state theory defined the strain dependence of the rate constants. The filament stiffness was non-Hookean. Models were refined against experimental data by simulated annealing and downhill simplex runs. Models with one tension-generating step were rejected, as they had a low efficiency and fitted the experimental data relatively poorly. The best model with two tension-generating steps (stroke distances 5.6 and 4.6 nm) and a cross-bridge stiffness of 1.7 pN/nm gave a good account of the experimental data. The two tensing steps allow an efficiency of up to 38% during shortening. In an isometric contraction, 54.7% of the attached heads were in a pre-tension-generating state, 44.5% of the attached heads had undergone the first tension-generating step, and only 0.8% had undergone both tension-generating steps; they bore 34%, 64%, and 2%, respectively, of the isometric tension. During slow shortening, the second tensing step made a greater contribution. During lengthening, up to 93% of the attached heads were in a pre-tension-generating state yet bore elevated tension by being dragged to high strains before detaching.

1,3-Diethylurea-enhanced Mg-ATPase activity of skeletal muscle myosin with a converse effect on the sliding motility

We investigate the effects of urea and its derivatives on the ATPase activity and on the in vitro motility of chicken skeletal muscle actomyosin. Mg-ATPase rate of myosin subfragment-1 (S1) is increased by 4-fold by 0.3M 1,3-diethylurea (DEU), but it is unaffected by urea, thiourea, and 1,3-dimethylurea at ≤1M concentration. Thus, we further examine the effects of DEU in comparison to those of urea as reference. In in vitro motility assay, we find that in the presence of 0.3M DEU, the sliding speeds of actin filaments driven by myosin and heavy meromyosin (HMM) are significantly decreased to 1/16 and 1/6.6, respectively, compared with the controls. However, the measurement of the actin-activated ATPase activity of HMM shows that the maximal rate, Vmax, is almost unchanged with DEU. Thus, the myosin-driven sliding motility of actin filaments is significantly impeded in the presence of 0.3M DEU, whereas the cyclic interaction of myosin with F-actin occurs during the ATP turnover, the rate of which is close to that without DEU. In contrast to DEU, 0.3M urea exhibits only modest effects on both actin-activated ATPase and sliding motility of actomyosin. Thus, DEU has the effect of uncoupling the sliding motility of actomyosin from its ATP turnover.

Sample solution constraints on motor-driven diagnostic nanodevices

The last decade has seen appreciable advancements in efforts towards increased portability of lab-on-a-chip devices by substituting microfluidics with molecular motor-based transportation. As of now, first proof-of-principle devices have analyzed protein mixtures of low complexity, such as target protein molecules in buffer solutions optimized for molecular motor performance. However, in a diagnostic work-up, lab-on-a-chip devices need to be compatible with complex biological samples. While it has been shown that such samples do not interfere with crucial steps in molecular diagnostics (for example antibody-antigen recognition), their effect on molecular motors is unknown. This critical and long overlooked issue is addressed here. In particular, we studied the effects of blood, cell lysates and solutions containing genomic DNA extracts on actomyosin and kinesin-microtubule-based transport, the two biomolecular motor systems that are most promising for lab-on-a-chip applications. We found that motor function is well preserved at defined dilutions of most of the investigated biological samples and demonstrated a molecular motor-driven label-free blood type test. Our results support the feasibility of molecular-motor driven nanodevices for diagnostic point-of-care applications and also demonstrate important constraints imposed by sample composition and device design that apply both to kinesin-microtubule and actomyosin driven applications.

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

In contracting muscle, individual myosin molecules function as part of a large ensemble, hydrolyzing ATP to power the relative sliding of actin filaments. The technological advances that have enabled direct observation and manipulation of single molecules, including recent experiments that have explored myosin's force-dependent properties, provide detailed insight into the kinetics of myosin's mechanochemical interaction with actin. However, it has been difficult to reconcile these single-molecule observations with the behavior of myosin in an ensemble. Here, using a combination of simulations and theory, we show that the kinetic mechanism derived from single-molecule experiments describes ensemble behavior; but the connection between single molecule and ensemble is complex. In particular, even in the absence of external force, internal forces generated between myosin molecules in a large ensemble accelerate ADP release and increase how far actin moves during a single myosin attachment. These myosin-induced changes in strong binding lifetime and attachment distance cause measurable properties, such as actin speed in the motility assay, to vary depending on the number of myosin molecules interacting with an actin filament. This ensemble-size effect challenges the simple detachment limited model of motility, because even when motility speed is limited by ADP release, increasing attachment rate can increase motility speed.

Actomyosin kinetics of pure fast and slow rat myosin isoforms studied by in vitro motility assay approach

An in vitro motility assay approach was used to investigate the mechanisms of the functional differences between myosin isoforms, by studying the effect of MgATP and MgADP on actin sliding velocity (V(f)) of pure slow and fast rat skeletal myosin at different temperatures. The value of V(f) depended on [MgATP] according to Michaelis-Menten kinetics, with an apparent constant (K(m)) of 54.2, 64.4 and 200 μm for the fast isoform and 18.6, 36.5 and 45.5 μM for the slow isoform at 20, 25 and 35°C, respectively. The presence of 2 mM MgADP decreased V(f) and yielded an inhibition constant (K(i)) of 377, 463 and 533 μM for the fast isoform at 20, 25 and 35°C, respectively, and 120 and 355 μM for the slow isoform at 25 and 35°C, respectively. The analysis of K(m) and K(i) suggested that slow and fast isoforms differ in the kinetics limiting V(f). Moreover, the higher sensitivity of the fast myosin isoform to a drop in [MgATP] is consistent with the higher fatigability of fast fibres than slow fibres. From the Michaelis-Menten relation in the absence of MgADP, we calculated the rate of actomyosin dissociation by MgATP (k(+ATP)) and the rate of MgADP release (k(-ADP)). We found values of k(+ATP) of 4.8 × 10(6), 6.5 × 10(6) and 6.6 × 10(6) M(-1) s(-1) for the fast isoform and 3.3 × 10(6), 2.9 × 10(6) and 6.7 × 10(6) M(-1) s(-1) for the slow isoform and values of k(-ADP) of 263, 420 and 1320 s(-1) for the fast isoform and 62, 107 and 306 s(-1) for the slow isoform at 20, 25 and 35°C, respectively. The results suggest that k(-ADP) could be the major determinant of functional differences between the fast and slow myosin isoforms at physiological temperatures.

Actomyosin-ADP states, interhead cooperativity, and the force-velocity relation of skeletal muscle

Despite intense efforts to elucidate the molecular mechanisms that determine the maximum shortening velocity and the shape of the force-velocity relationship in striated muscle, our understanding of these mechanisms remains incomplete. Here, this issue is addressed by means of a four-state cross-bridge model with significant explanatory power for both shortening and lengthening contractions. Exploration of the parameter space of the model suggests that an actomyosin-ADP state (AM( *)ADP) that is separated from the actual ADP release step by a strain-dependent isomerization is important for determining both the maximum shortening velocity and the shape of the force-velocity relationship. The model requires a velocity-dependent, cross-bridge attachment rate to account for certain experimental findings. Of interest, the velocity dependence for shortening contraction is similar to that for population of the AM( *)ADP state (with a velocity-independent attachment rate). This accords with the idea that attached myosin heads in the AM( *)ADP state position the partner heads for rapid attachment to the next site along actin, corresponding to the apparent increase in attachment rate in the model.

Heavy meromyosin molecules extending more than 50 nm above adsorbing electronegative surfaces

In the in vitro motility assay, actin filaments are propelled by surface-adsorbed myosin motors, or rather, myosin motor fragments such as heavy meromyosin (HMM). Recently, efforts have been made to develop actomyosin powered nanodevices on the basis of this assay but such developments are hampered by limited understanding of the HMM adsorption geometry. Therefore, we here investigate the HMM adsorption geometries on trimethylchlorosilane- [TMCS-] derivatized hydrophobic surfaces and on hydrophilic negatively charged surfaces (SiO(2)). The TMCS surface is of great relevance in fundamental studies of actomyosin and both surface substrates are important for the development of motor powered nanodevices. Whereas both the TMCS and SiO(2) surfaces were nearly saturated with HMM (incubation at 120 microg mL(-1)) there was little actin binding on SiO(2) in the absence of ATP and no filament sliding in the presence of ATP. This contrasts with excellent actin-binding and motility on TMCS. Quartz crystal microbalance with dissipation (QCM-D) studies demonstrate a HMM layer with substantial protein mass up to 40 nm above the TMCS surface, considerably more than observed for myosin subfragment 1 (S1; 6 nm). Together with the excellent actin transportation on TMCS, this strongly suggests that HMM adsorbs to TMCS mainly via its most C-terminal tail part. Consistent with this idea, fluorescence interference contrast (FLIC) microscopy showed that actin filaments are held by HMM 38 +/- 2 nm above the TMCS-surface with the catalytic site, on average, 20-30 nm above the surface. Viewed in a context with FLIC, QCM-D and TIRF results, the lack of actin motility and the limited actin binding on SiO(2) shows that HMM adsorbs largely via the actin-binding region on this surface with the C-terminal coiled-coil tails extending >50 nm into solution. The results and new insights from this study are of value, not only for the development of motor powered nanodevices but also for the interpretation of fundamental biophysical studies of actomyosin function and for the understanding of surface-protein interactions in general.