Direct observation of phosphate inhibiting the force-generating capacity of a miniensemble of Myosin molecules

Effect of rest duration between sets on fatigue and recovery after short intense plyometric exercise

Plyometric training is characterized by high-intensity exercise which is performed in short term efforts divided into sets. The purpose of the present study was twofold: first, to investigate the effects of three distinct plyometric exercise protocols, each with varying work-to-rest ratios, on muscle fatigue and recovery using an incline-plane training machine; and second, to assess the relationship between changes in lower limb muscle strength and power and the biochemical response to the three exercise variants employed. Forty-five adult males were randomly divided into 3 groups (n = 15) performing an exercise of 60 rebounds on an incline-plane training machine. The G0 group performed continuous exercise, while the G45 and G90 groups completed 4 sets of 15 repetitions, each set lasting 45 s with 45 s rest in G45 (work-to-rest ratio of 1:1) and 90 s rest in G90 (1:2 ratio). Changes in muscle torques of knee extensors and flexors, as well as blood lactate (LA) and ammonia levels, were assessed before and every 5 min for 30 min after completing the workout. The results showed significantly higher (p < 0.001) average power across all jumps generated during intermittent compared to continuous exercise. The greatest decrease in knee extensor strength immediately post-exercise was recorded in group G0 and the least in G90. The post-exercise time course of LA changes followed a similar pattern in all groups, while the longer the interval between sets, the faster LA returned to baseline. Intermittent exercise had a more favourable effect on muscle energy metabolism and recovery than continuous exercise, and the work-to-rest ratio of 1:2 in plyometric exercises was sufficient rest time to allow the continuation of exercise in subsequent sets at similar intensity.

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.

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.

New paradigms in actomyosin energy transduction: Critical evaluation of non-traditional models for orthophosphate release

Release of the ATP hydrolysis product ortophosphate (Pi) from the active site of myosin is central in chemo-mechanical energy transduction and closely associated with the main force-generating structural change, the power-stroke. Despite intense investigations, the relative timing between Pi-release and the power-stroke remains poorly understood. This hampers in depth understanding of force production by myosin in health and disease and our understanding of myosin-active drugs. Since the 1990s and up to today, models that incorporate the Pi-release either distinctly before or after the power-stroke, in unbranched kinetic schemes, have dominated the literature. However, in recent years, alternative models have emerged to explain apparently contradictory findings. Here, we first compare and critically analyze three influential alternative models proposed previously. These are either characterized by a branched kinetic scheme or by partial uncoupling of Pi-release and the power-stroke. Finally, we suggest critical tests of the models aiming for a unified picture.

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

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

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

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

Effects of hydroxyurea on skeletal muscle energetics and force production in a sickle cell disease murine model

Hydroxyurea (HU) is commonly used as a treatment for patients with sickle cell disease (SCD) to enhance fetal hemoglobin production. This increased production is expected to reduce anemia (which depresses oxygen transport) and abnormal Hb content alleviating clinical symptoms such as vaso-occlusive crisis and acute chest syndrome. The effects of HU on skeletal muscle bioenergetics in vivo are still unknown. Due to the beneficial effects of HU upon oxygen delivery, improved skeletal muscle energetics and function in response to a HU treatment have been hypothesized. Muscle energetics and function were analyzed during a standardized rest-exercise-recovery protocol, using ³¹P-magnetic resonance spectroscopy in Townes SCD mice. Measurements were performed in three groups of mice: one group of 2-mo-old mice (SCD_2m, n = 8), another one of 4-mo-old mice (SCD_4m, n = 8), and a last group of 4-mo-old mice that have been treated from 2 mo of age with HU at 50 mg/kg/day (SCD_4m-HU, n = 8). As compared with SCD_2m mice, SCD_4m mice were heavier and displayed a lower acidosis. As lower specific forces were developed by SCD_4m compared with SCD_2m, greater force-normalized phosphocreatine consumption and oxidative and nonoxidative costs of contraction were also reported. HU-treated mice (SCD_4m-HU) displayed a significantly higher specific force production as compared with untreated mice (SCD_4m), whereas muscle energetics was unchanged. Overall, our results support a beneficial effect of HU on muscle function.NEW & NOTEWORTHY Our results highlighted that force production decreases between 2 and 4 mo of age in SCD mice thereby indicating a decrease of muscle function during this period. Of interest, HU treatment seemed to blunt the observed age effect given that SCD_4m-HU mice displayed a higher specific force production as compared with SCD_4m mice. In that respect, HU treatment would help to maintain a higher capacity of force production during aging in SCD.

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.

Inorganic phosphate accelerates cardiac myofilament relaxation in response to lengthening

Myocardial relaxation in late systole is enhanced by increasing velocities of lengthening. Given that inorganic phosphate (Pi) can rebind to the force-producing myosin enzyme prior to MgADP release and hasten crossbridge detachment, we hypothesized that myocardial relaxation in late systole would be further enhanced by lengthening in the presence of Pi. Wistar rat left ventricular papillary muscles were attached to platinum clips, placed between a force transducer and a length motor at room temperature, and bathed in Krebs solution with 1.8 mM Ca²⁺ and varying Pi of 0, 1, 2, and 5 mM. Tension transients were elicited by electrical stimulation at 1 Hz. Peak tension was significantly enhanced by Pi: 0.593 ± 0.088 mN mm⁻² at 0 mM Pi and 0.817 ± 0.159 mN mm⁻² at 5 mM Pi (mean ± SEM, p < 0.01 by ANCOVA). All temporal characteristics of the force transient were significantly shortened with increasing Pi, e.g., time-to-50% recovery was shortened from 305 ± 14 ms at 0 mM Pi to 256 ± 10 ms at 5 mM Pi (p < 0.01). A 1% lengthening stretch with varying duration of 10–200 ms was applied at time-to-50% recovery during the descending phase of the force transient. Matching lengthening stretches were also applied when the muscle was not stimulated, thus providing a control for the passive viscoelastic response. After subtracting the passive from the active force response, the resulting myofilament response demonstrated features of faster myofilament relaxation in response to the stretch. For example, time-to-70% relaxation with 100 ms lengthening duration was shortened by 8.8 ± 6.8 ms at 0 Pi, 19.6 ± 4.8* ms at 1 mM Pi, 31.0 ± 5.6* ms at 2 Pi, and 25.6 ± 5.3* ms at 5 mM Pi (*p < 0.01 compared to no change). Using skinned myocardium, half maximally calcium-activated myofilaments underwent a 1% quick stretch, and the tension response was subjected to analysis for sensitivity of myosin detachment rate to stretch, g₁, at various Pi concentrations. The parameter g₁ was enhanced from 15.39 ± 0.35 at 0 Pi to 22.74 ± 1.31 s⁻¹/nm at 8 Pi (p < 0.01). Our findings suggest that increasing Pi at the myofilaments enhances lengthening-induced relaxation by elevating the sensitivity of myosin crossbridge detachment due to lengthening and thus speed the transition from late-systole to early-diastole.

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.

On the role of skeletal muscle acidosis and inorganic phosphates as determinants of central and peripheral fatigue: A 31 P-MRS study

Intramuscular hydrogen ion (H⁺ ) and inorganic phosphate (Pi) concentrations were dissociated during exercise to challenge their relationships with peripheral and central fatigue in vivo. Ten recreationally active, healthy men (27 ± 5 years; 180 ± 4 cm; 76 ± 10 kg) performed two consecutive intermittent isometric single-leg knee-extensor trials (60 maximal voluntary contractions; 3 s contraction, 2 s relaxation) interspersed with 5 min of rest. Phosphorus magnetic resonance spectroscopy (³¹ P-MRS) was used to continuously quantify intramuscular [H⁺ ] and [Pi] during both trials. Using electrical femoral nerve stimulation, quadriceps twitch force (Q_tw ) and voluntary activation (VA) were quantified at rest and throughout both trials. Decreases in Q_tw and VA from baseline were used to determine peripheral and central fatigue, respectively. Q_tw was strongly related to both [H⁺ ] (β coefficient: -0.9, P < 0.0001) and [Pi] (-1.1, P < 0.0001) across trials. There was an effect of trial on the relationship between Q_tw and [H⁺ ] (-0.5, P < 0.0001), but not Q_tw and [Pi] (0.0, P = 0.976). This suggests that, unlike the unaltered association with [Pi], a given level of peripheral fatigue was associated with a different [H⁺ ] in Trial 1 vs. Trial 2. VA was related to [H⁺ ] (-0.3, P < 0.0001), but not [Pi] (-0.2, P = 0.243), across trials and there was no effect of trial (-0.1, P = 0.483). Taken together, these results support intramuscular Pi as a primary cause of peripheral fatigue, and muscle acidosis, probably acting on group III/IV muscle afferents in the interstitial space, as a contributor to central fatigue during exercise. KEY POINTS: We investigated the relationship between intramuscular metabolites and neuromuscular function in humans performing two maximal, intermittent, knee-extension trials interspersed with 5 min of rest. Concomitant measurements of intramuscular hydrogen (H⁺ ) and inorganic phosphate (Pi) concentrations, as well as quadriceps twitch-force (Q_tw ) and voluntary activation (VA), were made throughout each trial using phosphorus magnetic resonance spectroscopy (³¹ P-MRS) and electrical femoral nerve stimulations. Although [Pi] fully recovered prior to the onset of the second trial, [H⁺ ] did not. Q_tw was strongly related to both [H⁺ ] and [Pi] across both trials. However, the relationship between Q_tw and [H⁺ ] shifted leftward from the first to the second trial, whereas the relationship between Q_tw and [Pi] remained unaltered. VA was related to [H⁺ ], but not [Pi], across both trials. These in vivo findings support the hypotheses of intramuscular Pi as a primary cause of peripheral fatigue, and muscle acidosis, probably acting on group III/IV muscle afferents, as a contributor to central fatigue.

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

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

Enhancing diastolic function by strain-dependent detachment of cardiac myosin crossbridges

The force response of cardiac muscle undergoing a quick stretch is conventionally interpreted to represent stretching of attached myosin crossbridges (phase 1) and detachment of these stretched crossbridges at an exponential rate (phase 2), followed by crossbridges reattaching in increased numbers due to an enhanced activation of the thin filament (phases 3 and 4). We propose that, at least in mammalian cardiac muscle, phase 2 instead represents an enhanced detachment rate of myosin crossbridges due to stretch, phase 3 represents the reattachment of those same crossbridges, and phase 4 is a passive-like viscoelastic response with power-law relaxation. To test this idea, we developed a two-state model of crossbridge attachment and detachment. Unitary force was assigned when a crossbridge was attached, and an elastic force was generated when an attached crossbridge was displaced. Attachment rate, f(x), was spatially distributed with a total magnitude f₀. Detachment rate was modeled as g(x) = g₀+ g₁x, where g₀ is a constant and g₁ indicates sensitivity to displacement. The analytical solution suggested that the exponential decay rate of phase 2 represents (f₀ + g₀) and the exponential rise rate of phase 3 represents g₀. The depth of the nadir between phases 2 and 3 is proportional to g₁. We prepared skinned mouse myocardium and applied a 1% stretch under varying concentrations of inorganic phosphate (Pi). The resulting force responses fitted the analytical solution well. The interpretations of phases 2 and 3 were consistent with lower f₀ and higher g₀ with increasing Pi. This novel scheme of interpreting the force response to a quick stretch does not require enhanced thin-filament activation and suggests that the myosin detachment rate is sensitive to stretch. Furthermore, the enhanced detachment rate is likely not due to the typical detachment mechanism following MgATP binding, but rather before MgADP release, and may involve reversal of the myosin power stroke.

Cardiac myosin binding protein-C phosphorylation accelerates β-cardiac myosin detachment rate in mouse myocardium

Cardiac myosin binding protein-C (cMyBP-C) is a thick filament protein that influences sarcomere stiffness and modulates cardiac contraction-relaxation through its phosphorylation. Phosphorylation of cMyBP-C and ablation of cMyBP-C have been shown to increase the rate of MgADP release in the acto-myosin cross-bridge cycle in the intact sarcomere. The influence of cMyBP-C on Pi-dependent myosin kinetics has not yet been examined. We investigated the effect of cMyBP-C, and its phosphorylation, on myosin kinetics in demembranated papillary muscle strips bearing the β-cardiac myosin isoform from nontransgenic and homozygous transgenic mice lacking cMyBP-C. We used quick stretch and stochastic length-perturbation analysis to characterize rates of myosin detachment and force development over 0-12 mM Pi and at maximal (pCa 4.8) and near-half maximal (pCa 5.75) Ca2+ activation. Protein kinase A (PKA) treatment was applied to half the strips to probe the effect of cMyBP-C phosphorylation on Pi sensitivity of myosin kinetics. Increasing Pi increased myosin cross-bridge detachment rate similarly for muscles with and without cMyBP-C, although these rates were higher in muscle without cMyBP-C. Treating myocardial strips with PKA accelerated detachment rate when cMyBP-C was present over all Pi, but not when cMyBP-C was absent. The rate of force development increased with Pi in all muscles. However, Pi sensitivity of the rate force development was reduced when cMyBP-C was present versus absent, suggesting that cMyBP-C inhibits Pi-dependent reversal of the power stroke or stabilizes cross-bridge attachment to enhance the probability of completing the power stroke. These results support a functional role for cMyBP-C in slowing myosin detachment rate, possibly through a direct interaction with myosin or by altering strain-dependent myosin detachment via cMyBP-C-dependent stiffness of the thick filament and myofilament lattice. PKA treatment reduces the role for cMyBP-C to slow myosin detachment and thus effectively accelerates β-myosin detachment in the intact myofilament lattice.NEW & NOTEWORTHY Length perturbation analysis was used to demonstrate that β-cardiac myosin characteristic rates of detachment and recruitment in the intact myofilament lattice are accelerated by Pi, phosphorylation of cMyBP-C, and the absence of cMyBP-C. The results suggest that cMyBP-C normally slows myosin detachment, including Pi-dependent detachment, and that this inhibition is released with phosphorylation or absence of cMyBP-C.

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

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

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

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

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

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

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

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

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.

A myosin-based mechanism for stretch activation and its possible role revealed by varying phosphate concentration in fast and slow mouse skeletal muscle fibers

Stretch activation (SA) is a delayed increase in force following a rapid muscle length increase. SA is best known for its role in asynchronous insect flight muscle, where it has replaced calcium's typical role of modulating muscle force levels during a contraction cycle. SA also occurs in mammalian skeletal muscle but has previously been thought to be too low in magnitude, relative to calcium-activated (CA) force, to be a significant contributor to force generation during locomotion. To test this supposition, we compared SA and CA force at different P_i concentrations (0-16 mM) in skinned mouse soleus (slow-twitch) and extensor digitorum longus (EDL; fast-twitch) muscle fibers. CA isometric force decreased similarly in both muscles with increasing P_i, as expected. SA force decreased with P_i in EDL (40%), leaving the SA to CA force ratio relatively constant across P_i concentrations (17-25%). In contrast, SA force increased in soleus (42%), causing a quadrupling of the SA to CA force ratio, from 11% at 0 mM P_i to 43% at 16 mM P_i, showing that SA is a significant force modulator in slow-twitch mammalian fibers. This modulation would be most prominent during prolonged muscle use, which increases P_i concentration and impairs calcium cycling. Based upon our previous Drosophila myosin isoform studies and this work, we propose that in slow-twitch fibers a rapid stretch in the presence of P_i reverses myosin's power stroke, enabling quick rebinding to actin and enhanced force production, while in fast-twitch fibers, stretch and P_i cause myosin to detach from actin.

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.

Acidosis decreases the Ca2+ sensitivity of thin filaments by preventing the first actomyosin interaction

Intracellular acidosis is a putative agent of skeletal muscle fatigue, in part, because it depresses the calcium (Ca²⁺) sensitivity of the myofilaments. However, the molecular mechanism behind this depression in Ca²⁺ sensitivity is unknown, providing a significant challenge to a complete understanding of the fatigue process. To elucidate this mechanism, we directly determined the effect of acidosis on the ability of a single myosin molecule to bind to a regulated actin filament in a laser trap assay. Decreasing pH from 7.4 to 6.5 significantly (P < 0.05) reduced the frequency of single actomyosin-binding events at submaximal (pCa 8-pCa 6) but not at maximal Ca²⁺ concentration (pCa 5-pCa 4). To delineate whether this was due to a direct effect on myosin versus an indirect effect on the regulatory proteins troponin (Tn) and tropomyosin (Tm), binding frequency was also quantified in the absence of Tn and Tm. This revealed that acidosis did not significantly alter the frequency of actomyosin binding events in the absence of regulatory proteins (1.4 ± 0.15 vs. 1.4 ± 0.15 events/s for pH 7.4 and 6.5, respectively). Acidosis also did not significantly affect the size of myosin's powerstroke or the duration of binding events in the presence of regulatory proteins, at every [Ca²⁺]. These data suggest acidosis impedes activation of the thin filament by competitively inhibiting Ca²⁺ binding to TnC. This slows the rate at which myosin initially attaches to actin; therefore, less cross bridges will be bound and generating force at any given submaximal [Ca²⁺]. These data provide a molecular explanation for the acidosis-induced decrease in force observed at the submaximal Ca²⁺ concentrations that might contribute to the loss of force during muscle fatigue.

Bioenergetic basis for the increased fatigability with ageing

KEY POINTS

The mechanisms for the age-related increase in fatigability during dynamic exercise remain elusive. We tested whether age-related impairments in muscle oxidative capacity would result in a greater accumulation of fatigue causing metabolites, inorganic phosphate (P_i ), hydrogen (H⁺ ) and diprotonated phosphate (H₂ PO₄ ^- ), in the muscle of old compared to young adults during a dynamic knee extension exercise. The age-related increase in fatigability (reduction in mechanical power) of the knee extensors was closely associated with a greater accumulation of metabolites within the working muscle but could not be explained by age-related differences in muscle oxidative capacity. These data suggest that the increased fatigability in old adults during dynamic exercise is primarily determined by age-related impairments in skeletal muscle bioenergetics that result in a greater accumulation of metabolites.

ABSTRACT

The present study aimed to determine whether the increased fatigability in old adults during dynamic exercise is associated with age-related differences in skeletal muscle bioenergetics. Phosphorus nuclear magnetic resonance spectroscopy was used to quantify concentrations of high-energy phosphates and pH in the knee extensors of seven young (22.7 ± 1.2 years; six women) and eight old adults (76.4 ± 6.0 years; seven women). Muscle oxidative capacity was measured from the phosphocreatine (PCr) recovery kinetics following a 24 s maximal voluntary isometric contraction. The fatiguing exercise consisted of 120 maximal velocity contractions (one contraction per 2 s) against a load equivalent to 20% of the maximal voluntary isometric contraction. The PCr recovery kinetics did not differ between young and old adults (0.023 ± 0.007 s^-1  vs. 0.019 ± 0.004 s^-1 , respectively). Fatigability (reductions in mechanical power) of the knee extensors was ∼1.8-fold greater with age and was accompanied by a greater decrease in pH (young = 6.73 ± 0.09, old = 6.61 ± 0.04) and increases in concentrations of inorganic phosphate, [P_i ], (young = 22.7 ± 4.8 mm, old = 32.3 ± 3.6 mm) and diprotonated phosphate, [H₂ PO₄ ^- ], (young = 11.7 ± 3.6 mm, old = 18.6 ± 2.1 mm) at the end of the exercise in old compared to young adults. The age-related increase in power loss during the fatiguing exercise was strongly associated with intracellular pH (r = -0.837), [P_i ] (r = 0.917) and [H₂ PO₄ ^- ] (r = 0.930) at the end of the exercise. These data suggest that the age-related increase in fatigability during dynamic exercise has a bioenergetic basis and is explained by an increased accumulation of metabolites within the muscle.

Bioenergetic basis of skeletal muscle fatigue

Energetic demand from high-intensity exercise can easily exceed ATP synthesis rates of mitochondria leading to a reliance on anaerobic metabolism. The reliance on anaerobic metabolism results in the accumulation of intracellular metabolites, namely inorganic phosphate (P_i) and hydrogen (H⁺), that are closely associated with exercise-induced reductions in power. Cellular and molecular studies have revealed several steps where these metabolites impair contractile function demonstrating a causal role in fatigue. Elevated P_i or H⁺ directly inhibits force and power of the cross-bridge and decreases myofibrillar Ca²⁺ sensitivity, whereas P_i also inhibits Ca²⁺ release from the sarcoplasmic reticulum (SR). When both metabolites are elevated, they act synergistically to cause marked reductions in power, indicating that fatigue during high-intensity exercise has a bioenergetic basis.

Monitoring Exercise-Induced Muscle Fatigue and Adaptations: Making Sense of Popular or Emerging Indices and Biomarkers

Regular exercise with the appropriate intensity and duration may improve an athlete’s physical capacities by targeting different performance determinants across the endurance–strength spectrum aiming to delay fatigue. The mechanisms of muscle fatigue depend on exercise intensity and duration and may range from substrate depletion to acidosis and product inhibition of adenosinetriphosphatase (ATPase) and glycolysis. Fatigue mechanisms have been studied in isolated muscles; single muscle fibers (intact or skinned) or at the level of filamentous or isolated motor proteins; with each approach contributing to our understanding of the fatigue phenomenon. In vivo methods for monitoring fatigue include the assessment of various functional indices supported by the use of biochemical markers including blood lactate levels and more recently redox markers. Blood lactate measurements; as an accompaniment of functional assessment; are extensively used for estimating the contribution of the anaerobic metabolism to energy expenditure and to help interpret an athlete’s resistance to fatigue during high intensity exercise. Monitoring of redox indices is gaining popularity in the applied sports performance setting; as oxidative stress is not only a fatigue agent which may play a role in the pathophysiology of overtraining syndrome; but also constitutes an important signaling pathway for training adaptations; thus reflecting training status. Careful planning of sampling and interpretation of blood biomarkers should be applied; especially given that their levels can fluctuate according to an athlete’s lifestyle and training histories.

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

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

Acidosis and Phosphate Directly Reduce Myosin's Force-Generating Capacity Through Distinct Molecular Mechanisms

Elevated levels of the metabolic by-products, including acidosis (i.e., high [H⁺]) and phosphate (P_i) are putative agents of muscle fatigue; however, the mechanism through which they affect myosin’s function remain unclear. To elucidate these mechanisms, we directly examined the effect of acidosis (pH 6.5 vs. 7.4), alone and in combination with elevated levels of P_i on the force-generating capacity of a mini-ensemble of myosin using a laser trap assay. Acidosis decreased myosin’s average force-generating capacity by 20% (p < 0.05). The reduction was due to both a decrease in the force generated during each actomyosin interaction, as well as an increase in the number of binding events generating negative forces. Adding P_i to the acidic condition resulted in a quantitatively similar decrease in force but was solely due to an elimination of all high force-generating events (>2 pN), resulting from an acceleration of the myosin’s rate of detachment from actin. Acidosis and P_i also had distinct effects on myosin’s steady state ATPase rate with acidosis slowing it by ∼90% (p > 0.05), while the addition of P_i under acidic conditions caused a significant recovery in the ATPase rate. These data suggest that these two fatigue agents have distinct effects on myosin’s cross-bridge cycle that may underlie the synergistic effect that they have muscle force. Thus these data provide novel molecular insight into the mechanisms underlying the depressive effects of P_i and H⁺ on muscle contraction during fatigue.

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

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

Modulators of actin-myosin dissociation: basis for muscle type functional differences during fatigue

The muscle types present with variable fatigue tolerance, in part due to the myosin isoform expressed. However, the critical steps that define “fatigability” in vivo of fast vs. slow myosin isoforms, at the molecular level, are not yet fully understood. We examined the modulation of the ATP-induced myosin subfragment 1 (S1) dissociation from pyrene-actin by inorganic phosphate (P_i), pH, and temperature using a specially modified stopped-flow system that allowed fast kinetics measurements at physiological temperature. We contrasted the properties of rabbit psoas (fast) and bovine masseter (slow) myosins (obtained from samples collected from New Zealand rabbits and from a licensed abattoir, respectively, according to institutional and national ethics permits). To identify ATP cycling biochemical intermediates, we assessed ATP binding to a preequilibrated mixture of actomyosin and variable [ADP], pH (pH 7 vs. pH 6.2), and P_i (zero, 15, or 30 added mM P_i) in a range of temperatures (5 to 45°C). Temperature and pH variations had little, if any, effect on the ADP dissociation constant (K_ADP) for fast S1, but for slow S1, K_ADP was weakened with increasing temperature or low pH. In the absence of ADP, the dissociation constant for phosphate (K_Pi) was weakened with increasing temperature for fast S1. In the presence of ADP, myosin type differences were revealed at the apparent phosphate affinity, depending on pH and temperature. Overall, the newly revealed kinetic differences between myosin types could help explain the in vivo observed muscle type functional differences at rest and during fatigue.

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

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

Can inorganic phosphate explain sag during unfused tetanic contractions of skeletal muscle?

We test the hypothesis that cytosolic inorganic phosphate (P_i) can account for the contraction‐induced reductions in twitch duration which impair summation and cause force to decline (sag) during unfused tetanic contractions of fast‐twitch muscle. A five‐state model of crossbridge cycling was used to simulate twitch and unfused tetanic contractions. As P_i concentration ([P_i]) was increased from 0 to 30 mmol·L⁻¹, twitch duration decreased, with progressive reductions in sensitivity to P_i as [P_i] was increased. When unfused tetani were simulated with rising [P_i], sag was most pronounced when initial [P_i] was low, and when the magnitude of [P_i] increase was large. Fast‐twitch extensor digitorum longus (EDL) muscles (sag‐prone, typically low basal [P_i]) and slow‐twitch soleus muscles (sag‐resistant, typically high basal [P_i]) were isolated from 14 female C57BL/6 mice. Muscles were sequentially incubated in solutions containing either glucose or pyruvate to create typical and low P_i environments, respectively. Twitch duration was greater (P < 0.05) in pyruvate than glucose in both muscles. Stimuli applied at intervals approximately three times the time to peak twitch tension resulted in sag of 35.0 ± 3.7% in glucose and 50.5 ± 1.4% in pyruvate in the EDL (pyruvate > glucose; P < 0.05), and 3.9 ± 0.3% in glucose and 37.8 ± 2.7% in pyruvate in the soleus (pyruvate > glucose; P < 0.05). The influence of P_i on crossbridge cycling provides a tenable mechanism for sag. Moreover, the low basal [P_i] in fast‐twitch relative to slow‐twitch muscle has promise as an explanation for the fiber‐type dependency of sag.

Sequence-dependent nanometer-scale conformational dynamics of individual RecBCD-DNA complexes

RecBCD is a multifunctional enzyme that possesses both helicase and nuclease activities. To gain insight into the mechanism of its helicase function, RecBCD unwinding at low adenosine triphosphate (ATP) (2-4 μM) was measured using an optical-trapping assay featuring 1 base-pair (bp) precision. Instead of uniformly sized steps, we observed forward motion convolved with rapid, large-scale (∼4 bp) variations in DNA length. We interpret this motion as conformational dynamics of the RecBCD-DNA complex in an unwinding-competent state, arising, in part, by an enzyme-induced, back-and-forth motion relative to the dsDNA that opens and closes the duplex. Five observations support this interpretation. First, these dynamics were present in the absence of ATP. Second, the onset of the dynamics was coupled to RecBCD entering into an unwinding-competent state that required a sufficiently long 5' strand to engage the RecD helicase. Third, the dynamics were modulated by the GC-content of the dsDNA. Fourth, the dynamics were suppressed by an engineered interstrand cross-link in the dsDNA that prevented unwinding. Finally, these dynamics were suppressed by binding of a specific non-hydrolyzable ATP analog. Collectively, these observations show that during unwinding, RecBCD binds to DNA in a dynamic mode that is modulated by the nucleotide state of the ATP-binding pocket.

Inherent force-dependent properties of β-cardiac myosin contribute to the force-velocity relationship of cardiac muscle

The heart adjusts its power output to meet specific physiological needs through the coordination of several mechanisms, including force-induced changes in contractility of the molecular motor, the β-cardiac myosin (βCM). Despite its importance in driving and regulating cardiac power output, the effect of force on the contractility of a single βCM has not been measured. Using single molecule optical-trapping techniques, we found that βCM has a two-step working stroke. Forces that resist the power stroke slow the myosin-driven contraction by slowing the rate of ADP release, which is the kinetic step that limits fiber shortening. The kinetic properties of βCM are affected by load, suggesting that the properties of myosin contribute to the force-velocity relationship in intact muscle and play an important role in the regulation of cardiac power output.

Mechanisms of in vivo muscle fatigue in humans: investigating age-related fatigue resistance with a computational model

KEY POINTS

Muscle fatigue can be defined as the transient decrease in maximal force that occurs in response to muscle use. Fatigue develops because of a complex set of changes within the neuromuscular system that are difficult to evaluate simultaneously in humans. The skeletal muscle of older adults fatigues less than that of young adults during static contractions. The potential sources of this difference are multiple and intertwined. To evaluate the individual mechanisms of fatigue, we developed an integrative computational model based on neural, biochemical, morphological and physiological properties of human skeletal muscle. Our results indicate first that the model provides accurate predictions of fatigue and second that the age-related resistance to fatigue is due largely to a lower reliance on glycolytic metabolism during contraction. This model should prove useful for generating hypotheses for future experimental studies into the mechanisms of muscle fatigue.

ABSTRACT

During repeated or sustained muscle activation, force-generating capacity becomes limited in a process referred to as fatigue. Multiple factors, including motor unit activation patterns, muscle fibre contractile properties and bioenergetic function, can impact force-generating capacity and thus the potential to resist fatigue. Given that neuromuscular fatigue depends on interrelated factors, quantifying their independent effects on force-generating capacity is not possible in vivo. Computational models can provide insight into complex systems in which multiple inputs determine discrete outputs. However, few computational models to date have investigated neuromuscular fatigue by incorporating the multiple levels of neuromuscular function known to impact human in vivo function. To address this limitation, we present a computational model that predicts neural activation, biomechanical forces, intracellular metabolic perturbations and, ultimately, fatigue during repeated isometric contractions. This model was compared with metabolic and contractile responses to repeated activation using values reported in the literature. Once validated in this way, the model was modified to reflect age-related changes in neuromuscular function. Comparisons between initial and age-modified simulations indicated that the age-modified model predicted less fatigue during repeated isometric contractions, consistent with reports in the literature. Together, our simulations suggest that reduced glycolytic flux is the greatest contributor to the phenomenon of age-related fatigue resistance. In contrast, oxidative resynthesis of phosphocreatine between intermittent contractions and inherent buffering capacity had minimal impact on predicted fatigue during isometric contractions. The insights gained from these simulations cannot be achieved through traditional in vivo or in vitro experimentation alone.

Direct measurements of the coordination of lever arm swing and the catalytic cycle in myosin V

Myosins use a conserved structural mechanism to convert the energy from ATP hydrolysis into a large swing of the force-generating lever arm. The precise timing of the lever arm movement with respect to the steps in the actomyosin ATPase cycle has not been determined. We have developed a FRET system in myosin V that uses three donor-acceptor pairs to examine the kinetics of lever arm swing during the recovery and power stroke phases of the ATPase cycle. During the recovery stroke the lever arm swing is tightly coupled to priming the active site for ATP hydrolysis. The lever arm swing during the power stroke occurs in two steps, a fast step that occurs before phosphate release and a slow step that occurs before ADP release. Time-resolved FRET demonstrates a 20-Å change in distance between the pre- and postpower stroke states and shows that the lever arm is more dynamic in the postpower stroke state. Our results suggest myosin binding to actin in the ADP.Pi complex triggers a rapid power stroke that gates the release of phosphate, whereas a second slower power stroke may be important for mediating strain sensitivity.

Phosphate and ADP differently inhibit coordinated smooth muscle myosin groups

Actin filaments propelled in vitro by groups of skeletal muscle myosin motors exhibit distinct phases of active sliding or arrest, whose occurrence depends on actin length (L) within a range of up to 1.0 μm. Smooth muscle myosin filaments are exponentially distributed with ≈150 nm average length in vivo--suggesting relevance of the L-dependence of myosin group kinetics. Here, we found L-dependent actin arrest and sliding in in vitro motility assays of smooth muscle myosin. We perturbed individual myosin kinetics with varying, physiological concentrations of phosphate (Pi, release associated with main power stroke) and adenosine diphosphate (ADP, release associated with minor mechanical step). Adenosine triphosphate was kept constant at physiological concentration. Increasing [Pi] lowered the fraction of time for which actin was actively sliding, reflected in reduced average sliding velocity (ν) and motile fraction (fmot, fraction of time that filaments are moving); increasing [ADP] increased the fraction of time actively sliding and reduced the velocity while sliding, reflected in reduced ν and increased fmot. We introduced specific Pi and ADP effects on individual myosin kinetics into our recently developed mathematical model of actin propulsion by myosin groups. Simulations matched our experimental observations and described the inhibition of myosin group kinetics. At low [Pi] and [ADP], actin arrest and sliding were reflected by two distinct chemical states of the myosin group. Upon [Pi] increase, the probability of the active state decreased; upon [ADP] increase, the probability of the active state increased, but the active state became increasingly similar to the arrested state.

A microfluidic chamber to study the dynamics of muscle-contraction-specific molecular interactions

In vitro motility and laser trap assays are commonly used for molecular mechanics measurements. However, chemicals cannot be added during these measurements, because they create flows that alter the molecular mechanics. Thus, we designed a microfluidic device that allows the addition of chemicals without creating bulk flows. Biocompatibility of the components of this device was tested. A microchannel chamber was created by photolithography with the patterns transferred to polydimethylsiloxane (PDMS). The PDMS chamber was bound to a polycarbonate membrane, which itself was bound to a molecular mechanics chamber. The microchannels ensured rapid distribution of the chemicals over the membrane, whereas the membrane ensured efficient delivery to the mechanics chamber while preventing bulk flow. The biocompatibility of the materials was tested by comparing the velocity (ν(max)) of propulsion by myosin of fluorescently labeled actin filaments to that of the conventional assay; no difference in ν(max) was observed. To estimate total chemical delivery time, labeled bovine serum albumin was injected in the channel chamber and TIRF was used to determine the time to reach the assay surface (2.7 ± 0.1 s). Furthermore, the standard distance of a trapped microsphere calculated during buffer diffusion using the microfluidic device (14.9 ± 3.2 nm) was not different from that calculated using the conventional assay (15.6 ± 5.3 nm, p = 0.922). Finally, ν(max) obtained by injecting adenosine triphosphate (ATP) in the microchannel chamber (2.37 ± 0.48 μm/s) was not different from that obtained when ATP was delivered directly to the mechanics chamber (2.52 ± 0.42 μm/s, p = 0.822). This microfluidic prototype validates the design for molecular mechanics measurements.

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.