The “Roll and Lock” Mechanism of Force Generation in Muscle

Resolving the kinetics of an ensemble of muscle myosin motors via a temperature-dependent fitting procedure

A data fitting procedure is devised and thoroughly tested to provide self-consistent estimates of the relevant mechanokinetic parameters involved in a plausible scheme underpinning the output of an ensemble of myosin II molecular motors mimicking the contraction of skeletal muscle. The method builds on a stochastic model accounting for the force exerted by the motor ensemble operated both in the low and high force-generating regimes corresponding to different temperature ranges. The proposed interpretative framework is successfully challenged against simulated data, meant to mimic the experimental output of a one-dimensional synthetic nanomachine powered by pure muscle myosin isoforms.

The Mechanism of Modulation of Cardiac Force by Temperature

In maximally Ca2+-activated demembranated fibres from the mammalian skeletal muscle, the depression of the force by lowering the temperature below the physiological level (~35 °C) is explained by the reduction of force in the myosin motor. Instead, cooling is reported to not affect the force per motor in Ca2+-activated cardiac trabeculae from the rat ventricle. Here, the mechanism of the cardiac performance depression by cooling is reinvestigated with fast sarcomere-level mechanics. We determine the changes in the half-sarcomere compliance of maximally Ca2+-activated demembranated rat trabeculae in the range of temperatures of 10-30 °C and analyse the data in terms of a simplified mechanical model of the half-sarcomere to extract the contribution of myofilaments and myosin motors. We find that the changes in the ensemble force are due to changes in the force per motor, while the fraction of actin-attached motors remains constant independent of temperature. The results demonstrate that in the cardiac myosin, as in the skeletal muscle myosin, the force-generating transition is endothermic. The underlying large heat absorption indicates the interaction of extended hydrophobic surfaces within the myosin motor, like those suggested by the crystallographic model of the working stroke.

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

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

Effects of Hydrostatic-Pressure on Muscle Contraction: A Look Back on Some Experimental Findings

Findings from experiments that used hydrostatic pressure changes to analyse the process of skeletal muscle contraction are re-examined. The force in resting muscle is insensitive to an increase in hydrostatic pressure from 0.1 MPa (atmospheric) to 10 MPa, as also found for force in rubber-like elastic filaments. The force in rigour muscle rises with increased pressure, as shown experimentally for normal elastic fibres (e.g., glass, collagen, keratin, etc.). In submaximal active contractions, high pressure leads to tension potentiation. The force in maximally activated muscle decreases with increased pressure: the extent of this force decrease in maximal active muscle is sensitive to the concentration of products of ATP hydrolysis (Pi-inorganic phosphate and ADP-adenosine diphosphate) in the medium. When the increased hydrostatic pressure is rapidly decreased, the force recovered to the atmospheric level in all cases. Thus, the resting muscle force remained the same: the force in the rigour muscle decreased in one phase and that in active muscle increased in two phases. The rate of rise of active force on rapid pressure release increased with the concentration of Pi in the medium, indicating that it is coupled to the Pi release step in the ATPase-driven crossbridge cycle in muscle. Pressure experiments on intact muscle illustrate possible underlying mechanisms of tension potentiation and causes of muscle fatigue.

The force of the myosin motor sets cooperativity in thin filament activation of skeletal muscles

Contraction of striated muscle is regulated by a dual mechanism involving both thin, actin-containing filament and thick, myosin-containing filament. Thin filament is activated by Ca2+ binding to troponin, leading to tropomyosin displacement that exposes actin sites for interaction with myosin motors, extending from the neighbouring stress-activated thick filaments. Motor attachment to actin contributes to spreading activation along the thin filament, through a cooperative mechanism, still unclear, that determines the slope of the sigmoidal relation between isometric force and pCa (−log[Ca2+]), estimated by Hill coefficient nH. We use sarcomere-level mechanics in demembranated fibres of rabbit skeletal muscle activated by Ca2+ at different temperatures (12–35 °C) to show that nH depends on the motor force at constant number of attached motors. The definition of the role of motor force provides fundamental constraints for modelling the dynamics of thin filament activation and defining the action of small molecules as possible therapeutic tools.

Actomyosin Complex

Formation of cross-bridges between actin and myosin occurs ubiquitously in eukaryotic cells and mediates muscle contraction, intracellular cargo transport, and cytoskeletal remodeling. Myosin motors repeatedly bind to and dissociate from actin filaments in a cycle that transduces the chemical energy from ATP hydrolysis into mechanical force generation. While the general layout of surface elements within the actin-binding interface is conserved among myosin classes, sequence divergence within these motifs alters the specific contacts involved in the actomyosin interaction as well as the kinetics of mechanochemical cycle phases. Additionally, diverse lever arm structures influence the motility and force production of myosin molecules during their actin interactions. The structural differences generated by myosin's molecular evolution have fine-tuned the kinetics of its isoforms and adapted them for their individual cellular roles. In this chapter, we will characterize the structural and biochemical basis of the actin-myosin interaction and explain its relationship with myosin's cellular roles, with emphasis on the structural variation among myosin isoforms that enables their functional specialization. We will also discuss the impact of accessory proteins, such as the troponin-tropomyosin complex and myosin-binding protein C, on the formation and regulation of actomyosin cross-bridges.

Analysis methods and quality criteria for investigating muscle physiology using x-ray diffraction

X-ray diffraction studies of muscle have been tremendously powerful in providing fundamental insights into the structures of, for example, the myosin and actin filaments in a variety of muscles and the physiology of the cross-bridge mechanism during the contractile cycle. However, interpretation of x-ray diffraction patterns is far from trivial, and if modeling of the observed diffraction intensities is required it needs to be performed carefully with full knowledge of the possible pitfalls. Here, we discuss (1) how x-ray diffraction can be used as a tool to monitor various specific muscle properties and (2) how to get the most out of the rest of the observed muscle x-ray diffraction patterns by modeling where the reliability of the modeling conclusions can be objectively tested. In other x-ray diffraction methods, such as protein crystallography, the reliability of every step of the process is estimated and quoted in published papers. In this way, the quality of the structure determination can be properly assessed. To be honest with ourselves in the muscle field, we need to do as near to the same as we can, within the limitations of the techniques that we are using. We discuss how this can be done. We also use test cases to reveal the dos and don’ts of using x-ray diffraction to study muscle physiology.

Dependence of thick filament structure in relaxed mammalian skeletal muscle on temperature and interfilament spacing

Contraction of skeletal muscle is regulated by structural changes in both actin-containing thin filaments and myosin-containing thick filaments, but myosin-based regulation is unlikely to be preserved after thick filament isolation, and its structural basis remains poorly characterized. Here, we describe the periodic features of the thick filament structure in situ by high-resolution small-angle x-ray diffraction and interference. We used both relaxed demembranated fibers and resting intact muscle preparations to assess whether thick filament regulation is preserved in demembranated fibers, which have been widely used for previous studies. We show that the thick filaments in both preparations exhibit two closely spaced axial periodicities, 43.1 nm and 45.5 nm, at near-physiological temperature. The shorter periodicity matches that of the myosin helix, and x-ray interference between the two arrays of myosin in the bipolar filament shows that all zones of the filament follow this periodicity. The 45.5-nm repeat has no helical component and originates from myosin layers closer to the filament midpoint associated with the titin super-repeat in that region. Cooling relaxed or resting muscle, which partially mimics the effects of calcium activation on thick filament structure, disrupts the helical order of the myosin motors, and they move out from the filament backbone. Compression of the filament lattice of demembranated fibers by 5% Dextran, which restores interfilament spacing to that in intact muscle, stabilizes the higher-temperature structure. The axial periodicity of the filament backbone increases on cooling, but in lattice-compressed fibers the periodicity of the myosin heads does not follow the extension of the backbone. Thick filament structure in lattice-compressed demembranated fibers at near-physiological temperature is similar to that in intact resting muscle, suggesting that the native structure of the thick filament is largely preserved after demembranation in these conditions, although not in the conditions used for most previous studies with this preparation.

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.

Monitoring the myosin crossbridge cycle in contracting muscle: steps towards 'Muscle-the Movie'

Some vertebrate muscles (e.g. those in bony fish) have a simple lattice A-band which is so well ordered that low-angle X-ray diffraction patterns are sampled in a simple way amenable to crystallographic techniques. Time-resolved X-ray diffraction through the contractile cycle should provide a movie of the molecular movements involved in muscle contraction. Generation of 'Muscle-The Movie' was suggested in the 1990s and since then efforts have been made to work out how to achieve it. Here we discuss how a movie can be generated, we discuss the problems and opportunities, and present some new observations. Low angle X-ray diffraction patterns from bony fish muscles show myosin layer lines that are well sampled on row-lines expected from the simple hexagonal A-band lattice. The 1st, 2nd and 3rd myosin layer lines at d-spacings of around 42.9 nm, 21.5 nm and 14.3 nm respectively, get weaker in patterns from active muscle, but there is a well-sampled intensity remnant along the layer lines. We show here that the pattern from the tetanus plateau is not a residual resting pattern from fibres that have not been fully activated, but is a different well-sampled pattern showing the presence of a second, myosin-centred, arrangement of crossbridges within the active crossbridge population. We also show that the meridional M3 peak from active muscle has two components of different radial widths consistent with (i) active myosin-centred (probably weak-binding) heads giving a narrow peak and (ii) heads on actin in strong states giving a broad peak.

Myosin Head Configurations in Resting and Contracting Murine Skeletal Muscle

Transgenic mouse models have been important tools for studying the relationship of genotype to phenotype for human diseases, including those of skeletal muscle. We show that mouse skeletal muscle can produce high quality X-ray diffraction patterns establishing the mouse intact skeletal muscle X-ray preparation as a potentially powerful tool to test structural hypotheses in health and disease. A notable feature of the mouse model system is the presence of residual myosin layer line intensities in contracting mouse muscle patterns. This provides an additional tool, along with the I1,1/I1,0 intensity ratio, for estimating the proportions of active versus relaxed myosin heads under a given set of conditions that can be used to characterize a given physiological condition or mutant muscle type. We also show that analysis of the myosin layer line intensity distribution, including derivation of the myosin head radius, Rm, may be used to study the role of the super-relaxed state in myosin regulation. When the myosin inhibitor blebbistatin is used to inhibit force production, there is a shift towards a highly quasi-helically ordered configuration that is distinct from the normal resting state, indicating there are more than one helically ordered configuration for resting crossbridges.

A new myofilament contraction model with ATP consumption for ventricular cell model

A new contraction model of cardiac muscle was developed by combining previously described biochemical and biophysical models. The biochemical component of the new contraction model represents events in the presence of Ca2+-crossbridge attachment and power stroke following inorganic phosphate release, detachment evoked by the replacement of ADP by ATP, ATP hydrolysis, and recovery stroke. The biophysical component focuses on Ca2+ activation and force (F b) development assuming an equivalent crossbridge. The new model faithfully incorporates the major characteristics of the biochemical and biophysical models, such as F b activation by transient Ca2+ ([Ca2+]-F b), [Ca2+]-ATP hydrolysis relations, sarcomere length-F b, and F b recovery after jumps in length under the isometric mode and upon sarcomere shortening after a rapid release of mechanical load under the isotonic mode together with the load-velocity relationship. ATP consumption was obtained for all responses. When incorporated in a ventricular cell model, the contraction model was found to share approximately 60% of the total ATP usage in the cell model.

Different Myosin Head Conformations in Bony Fish Muscles Put into Rigor at Different Sarcomere Lengths

At a resting sarcomere length of approximately 2.2 µm bony fish muscles put into rigor in the presence of BDM (2,3-butanedione monoxime) to reduce rigor tension generation show the normal arrangement of myosin head interactions with actin filaments as monitored by low-angle X-ray diffraction. However, if the muscles are put into rigor using the same protocol but stretched to 2.5 µm sarcomere length, a markedly different structure is observed. The X-ray diffraction pattern is not just a weaker version of the pattern at full overlap, as might be expected, but it is quite different. It is compatible with the actin-attached myosin heads being in a different conformation on actin, with the average centre of cross-bridge mass at a higher radius than in normal rigor and the myosin lever arms conforming less to the actin filament geometry, probably pointing back to their origins on their parent myosin filaments. The possible nature of this new rigor cross-bridge conformation is discussed in terms of other well-known states such as the weak binding state and the 'roll and lock' mechanism; we speculate that we may have trapped most myosin heads in an early attached strong actin-binding state in the cross-bridge cycle on actin.

Temperature Effects on Force and Actin⁻Myosin Interaction in Muscle: A Look Back on Some Experimental Findings

Observations made in temperature studies on mammalian muscle during force development, shortening, and lengthening, are re-examined. The isometric force in active muscle goes up substantially on warming from less than 10 °C to temperatures closer to physiological (>30 °C), and the sigmoidal temperature dependence of this force has a half-maximum at ~10 °C. During steady shortening, when force is decreased to a steady level, the sigmoidal curve is more pronounced and shifted to higher temperatures, whereas, in lengthening muscle, the curve is shifted to lower temperatures, and there is a less marked increase with temperature. Even with a small rapid temperature-jump (T-jump), force in active muscle rises in a definitive way. The rate of tension rise is slower with adenosine diphosphate (ADP) and faster with increased phosphate. Analysis showed that a T-jump enhances an early, pre-phosphate release step in the acto-myosin (crossbridge) ATPase cycle, thus inducing a force-rise. The sigmoidal dependence of steady force on temperature is due to this endothermic nature of crossbridge force generation. During shortening, the force-generating step and the ATPase cycle are accelerated, whereas during lengthening, they are inhibited. The endothermic force generation is seen in different muscle types (fast, slow, and cardiac). The underlying mechanism may involve a structural change in attached myosin heads and/or their attachments on heat absorption.

The force-generation process in active muscle is strain sensitive and endothermic: a temperature-perturbation study

In experiments on active muscle, we examined the tension decline and its temperature sensitivity at the onset of ramp shortening and at a range of velocities. A segment (∼1.5 mm long) of a skinned muscle fibre isolated from rabbit psoas muscle was held isometrically (sarcomere length ∼2.5 µm) at 8-9°C, maximally Ca²⁺-activated and a ramp shortening applied. The tension decline with a ramp shortening showed an early decrease of slope (the P₁ transition) followed by a slower decrease in slope (the P₂ transition) to the steady (isotonic) force. The tension level at the initial P₁ transition and the time to that transition decreased as the velocity was increased; the length change to this transition increased with shortening velocity to a steady value of ∼8 nm half-sarcomere^-1 A small, rapid, temperature jump (T-jump) (3-4°C, <0.2 ms) applied coincident with the onset of ramp shortening showed force enhancement by T-jump and changed the tension decline markedly. Analyses showed that the rate of T-jump-induced force rise increased linearly with increase of shortening velocity. These results provide crucial evidence that the strain-sensitive cross-bridge force generation, or a step closely coupled to it, is endothermic.

The Closed State of the Thin Filament Is Not Occupied in Fully Activated Skeletal Muscle

Muscle contraction is powered by actin-myosin interaction controlled by Ca²⁺ via the regulatory proteins troponin (Tn) and tropomyosin (Tpm), which are associated with actin filaments. Tpm forms coiled-coil dimers, which assemble into a helical strand that runs along the whole ∼1 μm length of a thin filament. In the absence of Ca²⁺, Tn that is tightly bound to Tpm binds actin and holds the Tpm strand in the blocked, or B, state, where Tpm shields actin from the binding of myosin heads. Ca²⁺ binding to Tn releases the Tpm from actin so that it moves azimuthally around the filament axis to a closed, or C, state, where actin is partially available for weak binding of myosin heads. Upon transition of the weak actin-myosin bond into a strong, stereo-specific complex, the myosin heads push Tpm strand to the open, or O, state allowing myosin binding sites on several neighboring actin monomers to become open for myosin binding. We used low-angle x-ray diffraction at the European Synchrotron Radiation Facility to check whether the O- to C-state transition in fully activated fibers of fast skeletal muscle of the rabbit occurs during transition from isometric contraction to shortening under low load. No decrease in the intensity of the second actin layer line at reciprocal radii in the range of 0.15-0.275 nm^-1 was observed during shortening suggesting that an azimuthal Tpm movement from the O- to C-state does not occur, although during shortening muscle stiffness is reduced compared to the isometric state, and the intensities of other actin layer lines demonstrate a ∼2-fold decrease in the fraction of myosin heads strongly bound to actin. The data show that a small fraction of actin-bound myosin heads is sufficient for supporting the O-state and, therefore the C-state is not occupied in fully activated skeletal muscle that produces mechanical work at low load.

X-ray Diffraction Evidence for Low Force Actin-Attached and Rigor-Like Cross-Bridges in the Contractile Cycle

Defining the structural changes involved in the myosin cross-bridge cycle on actin in active muscle by X-ray diffraction will involve recording of the whole two dimensional (2D) X-ray diffraction pattern from active muscle in a time-resolved manner. Bony fish muscle is the most highly ordered vertebrate striated muscle to study. With partial sarcomere length (SL) control we show that changes in the fish muscle equatorial A-band (10) and (11) reflections, along with (10)/(11) intensity ratio and the tension, are much more rapid than without such control. Times to 50% change with SL control were 19.5 (±2.0) ms, 17.0 (±1.1) ms, 13.9 (±0.4) ms and 22.5 (±0.8) ms, respectively, compared to 25.0 (±3.4) ms, 20.5 (±2.6) ms, 15.4 (±0.6) ms and 33.8 (±0.6) ms without control. The (11) intensity and the (10)/(11) intensity ratio both still change ahead of tension, supporting the likelihood of the presence of a head population close to or on actin, but producing little or no force, in the early stages of the contractile cycle. Higher order equatorials (e.g., (30), (31), and (32)), more sensitive to crossbridge conformation and distribution, also change very rapidly and overshoot their tension plateau values by a factor of around two, well before the tension plateau has been reached, once again indicating an early low-force cross-bridge state in the contractile cycle. Modelling of these intensity changes suggests the presence of probably two different actin-attached myosin head structural states (mainly low-force attached and rigor-like). No more than two main attached structural states are necessary and sufficient to explain the observations. We find that 48% of the heads are off actin giving a resting diffraction pattern, 20% of heads are in the weak binding conformation and 32% of the heads are in the strong (rigor-like) state. The strong states account for 96% of the tension at the tetanus plateau.

Myosin S2 origins track evolution of strong binding on actin by azimuthal rolling of motor domain

Myosin crystal structures have given rise to the swinging lever arm hypothesis, which predicts a large axial tilt of the lever arm domain during the actin-attached working stroke. Previous work imaging the working stroke in actively contracting, fast-frozen Lethocerus muscle confirmed the axial tilt; but strongly bound myosin heads also showed an unexpected azimuthal slew of the lever arm around the thin filament axis, which was not predicted from known crystal structures. We hypothesized that an azimuthal reorientation of the myosin motor domain on actin during the weak-binding to strong-binding transition could explain the lever arm slew provided that myosin's α-helical coiled-coil subfragment 2 (S2) domain emerged from the thick filament backbone at a particular location. However, previous studies did not adequately resolve the S2 domain. Here we used electron tomography of rigor muscle swollen by low ionic strength to pull S2 clear of the thick filament backbone, thereby revealing the azimuth of its point of origin. The results show that the azimuth of S2 origins of those rigor myosin heads, bound to the actin target zone of actively contracting muscle, originate from a restricted region of the thick filament. This requires an azimuthal reorientation of the motor domain on actin during the weak to strong transition.

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.

The endothermic ATP hydrolysis and crossbridge attachment steps drive the increase of force with temperature in isometric and shortening muscle

The isometric tetanic tension of skeletal muscle increases with temperature because attached crossbridge states bearing a relatively low force convert to those bearing a higher force. It was previously proposed that the tension-generating step(s) in the crossbridge cycle was highly endothermic and was therefore itself directly targeted by changes in temperature. However, this did not explain why a rapid rise in temperature (a temperature jump) caused a much slower rate of rise of tension than a rapid length step. This led to suggestions that the step targeted by a temperature rise is not the tension-generating step but is an extra step in the attached pathway of the crossbridge cycle, perhaps located on a parallel pathway. This enigma has been a major obstacle to a full understanding of the operation of the crossbridge cycle. We have now used a previously developed mechano-kinetic model of the crossbridge cycle in frog muscle to simulate the temperature dependence of isometric tension and shortening velocity. We allowed all five steps in the cycle to be temperature-sensitive. Models with different starting combinations of enthalpy changes and activation enthalpies for the five steps were refined by downhill simplex runs and scored by their ability to fit experimental data on the temperature dependence of isometric tension and the relationship between force and shortening velocity in frog muscle. We conclude that the first tension-generating step may be weakly endothermic and that the rise of tension with temperature is largely driven by the preceding two strongly endothermic steps of ATP hydrolysis and attachment of M.ADP.Pi to actin. The refined model gave a reasonable fit to the available experimental data and after a temperature jump the overall rate of tension rise was much slower than after a length step as observed experimentally. The findings aid our understanding of the crossbridge cycle by showing that it may not be necessary to include an additional temperature-sensitive step.

The spatial distribution of actin and mechanical cycle of myosin are different in right and left ventricles of healthy mouse hearts

The contraction of the right ventricle (RV) expels blood into the pulmonary circulation, and the contraction of the left ventricle (LV) pumps blood into the systemic circulation through the aorta. The respective afterloads imposed on the LV and RV by aortic and pulmonary artery pressures create very different mechanical requirements for the two ventricles. Indeed, differences have been observed in the contractile performance between left and right ventricular myocytes in dilated cardiomyopathy, in congestive heart failure, and in energy usage and speed of contraction at light loads in healthy hearts. In spite of these functional differences, it is commonly believed that the right and left ventricular muscles are identical because there were no differences in stress development, twitch duration, work performance, or power among the RV and LV in dogs. This report shows that on a mesoscopic scale [when only a few molecules are studied (here three to six molecules of actin) in ex vivo ventricular myofibrils], the two ventricles in rigor differ in the degree of orientational disorder of actin within in filaments and during contraction in the kinetics of the cross-bridge cycle.

Structural and functional effects of two stabilizing substitutions, D137L and G126R, in the middle part of α-tropomyosin molecule

Tropomyosin (Tm) is an α-helical coiled-coil protein that binds along the length of actin filament and plays an essential role in the regulation of muscle contraction. There are two highly conserved non-canonical residues in the middle part of the Tm molecule, Asp137 and Gly126, which are thought to impart conformational instability (flexibility) to this region of Tm which is considered crucial for its regulatory functions. It was shown previously that replacement of these residues by canonical ones (Leu substitution for Asp137 and Arg substitution for Gly126) results in stabilization of the coiled-coil in the middle of Tm and affects its regulatory function. Here we employed various methods to compare structural and functional features of Tm mutants carrying stabilizing substitutions Arg137Leu and Gly126Arg. Moreover, we for the first time analyzed the properties of Tm carrying both these substitutions within the same molecule. The results show that both substitutions similarly stabilize the Tm coiled-coil structure, and their combined action leads to further significant stabilization of the Tm molecule. This stabilization not only enhances maximal sliding velocity of regulated actin filaments in the in vitro motility assay at high Ca(2+) concentrations but also increases Ca(2+) sensitivity of the actin-myosin interaction underlying this sliding. We propose that the effects of these substitutions on the Ca(2+)-regulated actin-myosin interaction can be accounted for not only by decreased flexibility of actin-bound Tm but also by their influence on the interactions between the middle part of Tm and certain sites of the myosin head.

Why muscle is an efficient shock absorber

Skeletal muscles power body movement by converting free energy of ATP hydrolysis into mechanical work. During the landing phase of running or jumping some activated skeletal muscles are subjected to stretch. Upon stretch they absorb body energy quickly and effectively thus protecting joints and bones from impact damage. This is achieved because during lengthening, skeletal muscle bears higher force and has higher instantaneous stiffness than during isometric contraction, and yet consumes very little ATP. We wish to understand how the actomyosin molecules change their structure and interaction to implement these physiologically useful mechanical and thermodynamical properties. We monitored changes in the low angle x-ray diffraction pattern of rabbit skeletal muscle fibers during ramp stretch compared to those during isometric contraction at physiological temperature using synchrotron radiation. The intensities of the off-meridional layer lines and fine interference structure of the meridional M3 myosin x-ray reflection were resolved. Mechanical and structural data show that upon stretch the fraction of actin-bound myosin heads is higher than during isometric contraction. On the other hand, the intensities of the actin layer lines are lower than during isometric contraction. Taken together, these results suggest that during stretch, a significant fraction of actin-bound heads is bound non-stereo-specifically, i.e. they are disordered azimuthally although stiff axially. As the strong or stereo-specific myosin binding to actin is necessary for actin activation of the myosin ATPase, this finding explains the low metabolic cost of energy absorption by muscle during the landing phase of locomotion.

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.

Molecular mechanism of actin-myosin motor in muscle

The interaction of actin and myosin powers striated and smooth muscles and some other types of cell motility. Due to its highly ordered structure, skeletal muscle is a very convenient object for studying the general mechanism of the actin-myosin molecular motor. The history of investigation of the actin-myosin motor is briefly described. Modern concepts and data obtained with different techniques including protein crystallography, electron microscopy, biochemistry, and protein engineering are reviewed. Particular attention is given to X-ray diffraction studies of intact muscles and single muscle fibers with permeabilized membrane as they give insight into structural changes that underlie force generation and work production by the motor. Time-resolved low-angle X-ray diffraction on contracting muscle fibers using modern synchrotron radiation sources is used to follow movement of myosin heads with unique time and spatial resolution under near physiological conditions.

Along the road not taken: how many myosin heads act on a single actin filament at any instant in working muscle?

We reconsider the use of stiffness measurements to estimate N, the number of myosin heads acting (working at any instant to produce tension) on a single actin filament in vertebrate striated muscle, and give reasons for our rejection of numbers produced from such measurements. We go on to present a different approach to the problem, citing and extending a model bearing on the value of N which is derived from other physiological and biochemical data and which offers insight into the fundamental actin-myosin contractile event as an impulsive force. New experimental data accumulating over the past decade support this model, in which the myosin heads act sequentially along the actin filament (this is an example of Conformational Spread). In this model only a single myosin head acts on a single actin filament to produce an impulse at any given instant in normally-contracting muscle, either in the isometric or the isotonic mode, so N = 1. However, extra impulses occur within the same time frame after quick release of length or tension. The predictions of this sequential model are in striking agreement with a large body of recent detailed biophysical and biochemical evidence. We suggest that this warrants further in-depth experimental work, specifically to explore and test the sequential model and its implications.

The fraction of myosin motors that participate in isometric contraction of rabbit muscle fibers at near-physiological temperature

The duty ratio, or the part of the working cycle in which a myosin molecule is strongly attached to actin, determines motor processivity and is required to evaluate the force generated by each molecule. In muscle, it is equal to the fraction of myosin heads that are strongly, or stereospecifically, bound to the thin filaments. Estimates of this fraction during isometric contraction based on stiffness measurements or the intensities of the equatorial or meridional x-ray reflections vary significantly. Here, we determined this value using the intensity of the first actin layer line, A1, in the low-angle x-ray diffraction patterns of permeable fibers from rabbit skeletal muscle. We calibrated the A1 intensity by considering that the intensity in the relaxed and rigor states corresponds to 0% and 100% of myosin heads bound to actin, respectively. The fibers maximally activated with Ca(2+) at 4°C were heated to 31-34°C with a Joule temperature jump (T-jump). Rigor and relaxed-state measurements were obtained on the same fibers. The intensity of the inner part of A1 during isometric contraction compared with that in rigor corresponds to 41-43% stereospecifically bound myosin heads at near-physiological temperature, or an average force produced by a head of ~6.3 pN.

An electrostatic model with weak actin-myosin attachment resolves problems with the lattice stability of skeletal muscle

The stability of the filament lattice in relaxed striated muscle can be viewed as a balance of electrostatic and van der Waals forces. The simplest electrostatic model, where actin and myosin filaments are treated as charged cylinders, generates reasonable lattice spacings for skinned fibers. However, this model predicts excessive radial stiffness under osmotic pressure and cannot account for the initial pressure (∼1 kPa) required for significant compression. Good agreement with frog compression data is obtained with an extended model, in which S1 heads are weakly attached to actin when the lattice spacing is reduced below a critical value; further compression moves fixed negative charges on the heads closer to the myofilament backbone as they attach at a more acute angle to actin. The model predicts pH data in which the lattice shrinks as pH is lowered and protons bind to filaments. Electrostatic screening implies that the lattice shrinks with increasing ionic strength, but the observed expansion of the frog lattice at ionic strengths above 0.1 M with KCl might be explained if Cl(-) binds to sites on the motor domain of S1. With myosin-myosin and actin-actin interactions, the predicted lattice spacing decreases slightly with sarcomere length, with a more rapid decrease when actin-myosin filament overlap is very small.

Cross-bridge kinetics in myofibrils containing familial hypertrophic cardiomyopathy R58Q mutation in the regulatory light chain of myosin

Familial hypertrophic cardiomyopathy (FHC) is a heritable form of cardiac hypertrophy caused by single-point mutations in genes encoding sarcomeric proteins including ventricular myosin regulatory light chain (RLC). FHC often leads to malignant outcomes and sudden cardiac death. The FHC mutations are believed to alter the kinetics of the interaction between actin and myosin resulting in inefficient energy utilization and compromised function of the heart. We studied the effect of the FHC-linked R58Q-RLC mutation on the kinetics of transgenic (Tg)-R58Q cardiac myofibrils. Kinetics was determined from the rate of change of orientation of actin monomers during muscle contraction. Actin monomers change orientation because myosin cross-bridges deliver periodic force impulses to it. An individual impulse (but not time average of impulses) carries the information about the kinetics of actomyosin interaction. To observe individual impulses it was necessary to scale down the experiments to the level of a few molecules. A small population (∼4 molecules) was selected by using (deliberately) inefficient fluorescence labeling and observing fluorescent molecules by a confocal microscope. We show that the kinetic rates are significantly smaller in the contracting cardiac myofibrils from Tg-R58Q mice then in control Tg-wild type (WT). We also demonstrate a lower force per cross-section of muscle fiber in Tg-R58Q versus Tg-WT mice. We conclude that the R58Q mutation-induced decrease in cross-bridge kinetics underlines the mechanism by which Tg-R58Q fibers develop low force and thus compromise the ability of the mutated heart to efficiently pump blood.

Evidence for pre- and post-power stroke of cross-bridges of contracting skeletal myofibrils

We examined the orientational fluctuations of a small number of myosin molecules (approximately three) in working skeletal muscle myofibrils. Myosin light chain 1 (LC1) was labeled with a fluorescent dye and exchanged with the native LC1 of skeletal muscle myofibrils cross-linked with 1-ethyl-3-[3(dimethylamino) propyl] carbodiimide to prevent shortening. We observed a small volume within the A-band (∼10(-15) L) by confocal microscopy, and measured cyclic fluctuations in the orientation of the myosin neck (containing LC1) by recording the parallel and perpendicular components of fluorescent light emitted by the fluorescently labeled myosin LC1. Histograms of orientational fluctuations from fluorescent molecules in rigor were represented by a single Gaussian distribution. In contrast, histograms from contracting muscles were best fit by at least two Gaussians. These results provide direct evidence that cross-bridges in working skeletal muscle assume two distinct conformations, presumably corresponding to the pre- and post-power-stroke states.

Myosin heads contribute to the maintenance of filament order in relaxed rabbit muscle

Raising the temperature of rabbit skeletal muscle from ∼0°C to ∼20°C has been shown to enhance the helical organization of the myosin heads and to change the intensities of the 10 and 11 equatorial reflections. We show here by time-resolved x-ray diffraction combined with temperature jump that the movement of the heads to enhance the organized myosin helix occurs at the same fast rate as the change in the intensities of the equatorial reflections. However, model calculations indicate that the change in the equatorials cannot be explained simply in terms of the movement of myosin heads. Analysis of electron micrographs of transverse sections of relaxed muscle fibers cryofixed at ∼5°C and ∼35°C shows that in addition to the reorganization of the heads the thin and thick filaments are less constrained to their positions in the hexagonal filament lattice in the warm muscle than in the cold. Incorporating the changes in filament order in model calculations reconciles these with the observed changes in equatorial reflections. We suggest the thin filaments in the cold muscle are boxed into their positions by the thermal movement of the disordered myosin heads. In the warmer muscle, the packed-down heads leave the thin filaments more room to diffuse laterally.

Emerging complex pathways of the actomyosin powerstroke

Actomyosin powers muscle contraction and various cellular activities, including cell division, differentiation, intracellular transport and sensory functions. Despite their crucial roles, key aspects of force generation have remained elusive. To perform efficient force generation, the powerstroke must occur while myosin is bound to actin. Paradoxically, this process must be initiated when myosin is in a very low actin-affinity state. Recent results shed light on a kinetic pathway selection mechanism whereby the actin-induced activation of the swing of myosin's lever enables efficient mechanical functioning. Structural elements and biochemical principles involved in this mechanism are conserved among various NTPase-effector (e.g. kinesin-microtubule, G protein exchange factor and kinase-scaffold protein) systems that perform chemomechanical or signal transduction.

Crossbridge mechanism(s) examined by temperature perturbation studies on muscle

An overall view of the contractile process that has emerged from -temperature-studies on active muscle is outlined. In isometric muscle, a small rapid temperature-jump (T-jump) enhances an early, pre-phosphate release, step in the acto-myosin (crossbridge) ATPase cycle and induces a characteristic rise in force indicating that crossbridge force generation is endothermic (force rises when heat is absorbed). Sigmoidal temperature dependence of steady force is largely due to the endothermic nature of force generation. During shortening, when muscle force is decreased, the T-jump force generation is enhanced; conversely, when a muscle is lengthening and its force increased, the T-jump force generation is inhibited. Taking T-jump force generation as a signature of the crossbridge - ATPase cycle, the results suggest that during lengthening the ATPase cycle is truncated before endothermic force generation, whereas during shortening this step and the ATPase cycle, are accelerated; this readily provides a molecular basis for the Fenn effect.

Force and power generating mechanism(s) in active muscle as revealed from temperature perturbation studies

The basic characteristics of the process of force and power generation in active muscle that have emerged from temperature studies are examined. This is done by reviewing complementary findings from temperature-dependence studies and rapid temperature-jump (T-jump) experiments and from intact and skinned fast mammalian muscle fibres. In isometric muscle, a small T-jump leads to a characteristic rise in force showing that crossbridge force generation is endothermic (heat absorbed) and associated with increased entropy (disorder). The sensitivity of the T-jump force generation to added inorganic phosphate (Pi) indicates that a T-jump enhances an early step in the actomyosin (crossbridge) ATPase cycle before Pi-release. During muscle lengthening when steady force is increased, the T-jump force generation is inhibited. Conversely, during shortening when steady force is decreased, the T-jump force generation is enhanced in a velocity-dependent manner, showing that T-jump force generation is strain sensitive. Within the temperature range of ∼5–35◦C, the temperature dependence of steady active force is sigmoidal both in isometric and in shortening muscle. However, in shortening muscle, the endothermic character of force generation becomes more pronounced with increased velocity and this can, at least partly, account for the marked increase with warming of the mechanical power output of active muscle.

Electron tomography of cryofixed, isometrically contracting insect flight muscle reveals novel actin-myosin interactions

Background

Isometric muscle contraction, where force is generated without muscle shortening, is a molecular traffic jam in which the number of actin-attached motors is maximized and all states of motor action are trapped with consequently high heterogeneity. This heterogeneity is a major limitation to deciphering myosin conformational changes in situ.

Methodology

We used multivariate data analysis to group repeat segments in electron tomograms of isometrically contracting insect flight muscle, mechanically monitored, rapidly frozen, freeze substituted, and thin sectioned. Improved resolution reveals the helical arrangement of F-actin subunits in the thin filament enabling an atomic model to be built into the thin filament density independent of the myosin. Actin-myosin attachments can now be assigned as weak or strong by their motor domain orientation relative to actin. Myosin attachments were quantified everywhere along the thin filament including troponin. Strong binding myosin attachments are found on only four F-actin subunits, the “target zone”, situated exactly midway between successive troponin complexes. They show an axial lever arm range of 77°/12.9 nm. The lever arm azimuthal range of strong binding attachments has a highly skewed, 127° range compared with X-ray crystallographic structures. Two types of weak actin attachments are described. One type, found exclusively in the target zone, appears to represent pre-working-stroke intermediates. The other, which contacts tropomyosin rather than actin, is positioned M-ward of the target zone, i.e. the position toward which thin filaments slide during shortening.

Conclusion

We present a model for the weak to strong transition in the myosin ATPase cycle that incorporates azimuthal movements of the motor domain on actin. Stress/strain in the S2 domain may explain azimuthal lever arm changes in the strong binding attachments. The results support previous conclusions that the weak attachments preceding force generation are very different from strong binding attachments.

FRET characterisation for cross-bridge dynamics in single-skinned rigor muscle fibres

In this work we demonstrate for the first time the use of Förster resonance energy transfer (FRET) as an assay to monitor the dynamics of cross-bridge conformational changes directly in single muscle fibres. The advantage of FRET imaging is its ability to measure distances in the nanometre range, relevant for structural changes in actomyosin cross-bridges. To reach this goal we have used several FRET couples to investigate different locations in the actomyosin complex. We exchanged the native essential light chain of myosin with a recombinant essential light chain labelled with various thiol-reactive chromophores. The second fluorophore of the FRET couple was introduced by three approaches: labelling actin, labelling SH1 cysteine and binding an adenosine triphosphate (ATP) analogue. We characterise FRET in rigor cross-bridges: in this condition muscle fibres are well described by a single FRET population model which allows us to evaluate the true FRET efficiency for a single couple and the consequent donor–acceptor distance. The results obtained are in good agreement with the distances expected from crystallographic data. The FRET characterisation presented herein is essential before moving onto dynamic measurements, as the FRET efficiency differences to be detected in an active muscle fibre are on the order of 10–15% of the FRET efficiencies evaluated here. This means that, to obtain reliable results to monitor the dynamics of cross-bridge conformational changes, we had to fully characterise the system in a steady-state condition, demonstrating firstly the possibility to detect FRET and secondly the viability of the present approach to distinguish small FRET variations.

Multiscale modeling of structural dynamics underlying force generation and product release in actomyosin complex

To decrypt the mechanistic basis of myosin motor function, it is essential to probe the conformational changes in actomyosin with high spatial and temporal resolutions. In a computational effort to meet this challenge, we have performed a multiscale modeling of the allosteric couplings and transition pathway of actomyosin complex by combining coarse-grained modeling of the entire complex with all-atom molecular dynamics simulations of the active site. Our modeling of allosteric couplings at the pre-powerstroke state has pinpointed key actin-activated couplings to distant myosin parts which are critical to force generation and the sequential release of phosphate and ADP. At the post-powerstroke state, we have identified isoform-dependent couplings which underlie the reciprocal coupling between actin binding and nucleotide binding in fast Myosin II, and load-dependent ADP release in Myosin V. Our modeling of transition pathway during powerstroke has outlined a clear sequence of structural events triggered by actin binding, which lead to subsequent force generation, twisting of central beta-sheet, and the sequential release of phosphate and ADP. Finally we have performed atomistic simulations of active-site dynamics based on an on-path "transition-state" myosin conformation, which has revealed significantly weakened coordination of phosphate by Switch II, and a disrupted key salt bridge between Switch I and II. Meanwhile, the coordination of MgADP by Switch I and P loop is less perturbed. As a result, the phosphate can be released prior to MgADP. This study has shed new lights on the controversy over the structural mechanism of actin-activated phosphate release and force generation in myosin motor.

Probing muscle myosin motor action: x-ray (m3 and m6) interference measurements report motor domain not lever arm movement

The key question in understanding how force and movement are produced in muscle concerns the nature of the cyclic interaction of myosin molecules with actin filaments. The lever arm of the globular head of each myosin molecule is thought in some way to swing axially on the actin-attached motor domain, thus propelling the actin filament past the myosin filament. Recent X-ray diffraction studies of vertebrate muscle, especially those involving the analysis of interference effects between myosin head arrays in the two halves of the thick filaments, have been claimed to prove that the lever arm moves at the same time as the sliding of actin and myosin filaments in response to muscle length or force steps. It was suggested that the sliding of myosin and actin filaments, the level of force produced and the lever arm angle are all directly coupled and that other models of lever arm movement will not fit the X-ray data. Here, we show that, in addition to interference across the A-band, which must be occurring, the observed meridional M3 and M6 X-ray intensity changes can all be explained very well by the changing diffraction effects during filament sliding caused by heads stereospecifically attached to actin moving axially relative to a population of detached or non-stereospecifically attached heads that remain fixed in position relative to the myosin filament backbone. Crucially, and contrary to previous interpretations, the X-ray interference results provide little direct information about the position of the myosin head lever arm; they are, in fact, reporting relative motor domain movements. The implications of the new interpretation are briefly assessed.

Time course and strain dependence of ADP release during contraction of permeabilized skeletal muscle fibers

A phosphorylated, single cysteine mutant of nucleoside diphosphate kinase, labeled with N-[2-(iodoacetamido)ethyl]-7-diethylaminocoumarin-3-carboxamide (P approximately NDPK-IDCC), was used as a fluorescence probe for time-resolved measurement of changes in [MgADP] during contraction of single permeabilized rabbit psoas fibers. The dephosphorylation of the phosphorylated protein by MgADP occurs within the lattice environment of permeabilized fibers with a second-order rate constant at 12 degrees C of 10(5) M(-1) s(-1). This dephosphorylation is accompanied by a change in coumarin fluorescence. We report the time course of P approximately NDPK-IDCC dephosphorylation during the period of active isometric force redevelopment after quick release of fiber strain at pCa(2+) of 4.5. After a rapid length decrease of 0.5% was applied to the fiber, the extra NDPK-IDCC produced during force recovery, above the value during the approximately steady state of isometric contraction, was 2.7 +/- 0.6 microM and 4.7 +/- 1.5 microM at 12 and 20 degrees C, respectively. The rates of P approximately NDPK-IDCC dephosphorylation during force recovery were 28 and 50 s(-1) at 12 and 20 degrees C, respectively. The time courses of isometric force and P approximately NDPK-IDCC dephosphorylation were simulated using a seven-state reaction scheme. Relative isometric force was modeled by changes in the occupancy of strongly bound A.M.ADP.P(i) and A.M.ADP states. A strain-sensitive A.M.ADP isomerization step was rate-limiting (3-6 s(-1)) in the cross-bridge turnover during isometric contraction. At 12 degrees C, the A.M.ADP.P(i) and the pre- and postisomerization A.M.ADP states comprised 56%, 38%, and 7% of the isometric force-bearing AM states, respectively. At 20 degrees C, the force-bearing A.M.ADP.P(i) state was a lower proportion of the total force-bearing states (37%), whereas the proportion of postisomerization A.M.ADP states was higher (19%). The simulations suggested that release of cross-bridge strain caused rapid depopulation of the preisomerization A.M.ADP state and transient accumulation of MgADP in the postisomerization A.M.ADP state. Hence, the strain-sensitive isomerization of A.M.ADP seems to explain the rate of change of P approximately NDPK-IDCC dephosphorylation during force recovery. The temperature-dependent isometric distribution of myosin states is consistent with the previous observation of a small decrease in amplitude of the P(i) transient during force recovery at 20 degrees C and the current observation of an increase in amplitude of the ADP-sensitive NDPK-IDCC transient.

Mechanistic role of movement and strain sensitivity in muscle contraction

Tension generation can be studied by applying step perturbations to contracting muscle fibers and subdividing the mechanical response into exponential phases. The de novo tension-generating isomerization is associated with one of these phases. Earlier work has shown that a temperature jump perturbs the equilibrium constant directly to increase tension. Here, we show that a length jump functions quite differently. A step release (relative movement of thick and thin filaments) appears to release a steric constraint on an ensemble of noncompetent postphosphate release actomyosin cross-bridges, enabling them to generate tension, a concentration jump in effect. Structural studies [Taylor KA, et al. (1999) Tomographic 3D reconstruction of quick-frozen, Ca(2+)-activated contracting insect flight muscle. Cell 99:421-431] that map to these kinetics indicate that both catalytic and lever arm domains of noncompetent myosin heads change angle on actin, whereas lever arm movement alone mediates the power stroke. Together, these kinetic and structural observations show a 13-nm overall interaction distance of myosin with actin, including a final 4- to 6-nm power stroke when the catalytic domain is fixed on actin. Raising fiber temperature with both perturbation techniques accelerates the forward, but slows the reverse rate constant of tension generation, kinetics akin to the unfolding/folding of small proteins. Decreasing strain, however, causes both forward and reverse rate constants to increase. Despite these changes in rate, the equilibrium constant is strain-insensitive. Activation enthalpy and entropy data show this invariance to be the result of enthalpy-entropy compensation. Reaction amplitudes confirm a strain-invariant equilibrium constant and thus a strain-insensitive ratio of pretension- to tension-generating states as work is done.

Force-generating cross-bridges during ramp-shaped releases: evidence for a new structural state

Mechanical and two-dimensional (2D) x-ray diffraction studies suggest that during isometric steady-state contraction, strongly bound cross-bridges mostly occupy early states in the power stroke, whereas rigor or rigor-like cross-bridges could not be detected. However, it remained unclear whether cross-bridges accumulate, at least transiently, in rigor or rigor-like states in response to rapid-length releases. We addressed this question using time-resolved recording of 2D x-ray diffraction patterns of permeabilized fibers from rabbit psoas muscles during isometric contraction and when small, ramp-shaped length-releases were applied to these fibers. This maneuver allows a transient accumulation of cross-bridges in states near the end of their power stroke. By lowering the temperature to 5 degrees C, force transients were slowed sufficiently to record diffraction patterns in several 2-4-ms time frames before and during such releases, using the RAPID detector (Refined ADC Per Input Detector) at beam line ID02 of the European Synchrotron Radiation Facility (Grenoble, France). The same sequence of frames was recorded in relaxation and rigor. Comparisons of 2D patterns recorded during isometric contraction, with patterns recorded at different [MgATPgammaS] and at 1 degrees C, showed that changes in intensity profiles along the first and sixth actin layer lines (ALL1 and ALL6, respectively) allowed for discernment of the formation of rigor or rigor-like cross-bridges. During ramp-shaped releases of activated fibers, intensity profiles along ALL1 and ALL6 did not reveal evidence for the accumulation of rigor-like cross-bridges. Instead, changes in the ALL6-profile suggest that during ramp-shaped releases, cross-bridges transiently accumulate in a structural state that, to our knowledge, was not previously seen, but that could well be a strongly bound state with the light-chain binding domain in a conformation between a near prepower-stroke (isometric) orientation and the orientation in rigor.

Direct modeling of X-ray diffraction pattern from contracting skeletal muscle

A direct modeling approach was used to quantitatively interpret the two-dimensional x-ray diffraction patterns obtained from contracting mammalian skeletal muscle. The dependence of the calculated layer line intensities on the number of myosin heads bound to the thin filaments, on the conformation of these heads and on their mode of attachment to actin, was studied systematically. Results of modeling are compared to experimental data collected from permeabilized fibers from rabbit skeletal muscle contracting at 5 degrees C and 30 degrees C and developing low and high isometric tension, respectively. The results of the modeling show that: i), the intensity of the first actin layer line is independent of the tilt of the light chain domains of myosin heads and can be used as a measure of the fraction of myosin heads stereospecifically attached to actin; ii), during isometric contraction at near physiological temperature, the fraction of these heads is approximately 40% and the light chain domains of the majority of them are more perpendicular to the filament axis than in rigor; and iii), at low temperature, when isometric tension is low, a majority of the attached myosin heads are bound to actin nonstereospecifically whereas at high temperature and tension they are bound stereospecifically.

Towards a unified theory of muscle contraction. I: foundations

Molecular models of contractility in striated muscle require an integrated description of the action of myosin motors, firstly in the filament lattice of the half-sarcomere. Existing models do not adequately reflect the biochemistry of the myosin motor and its sarcomeric environment. The biochemical actin-myosin-ATP cycle is reviewed, and we propose a model cycle with two 4- to 5-nm working strokes, where phosphate is released slowly after the first stroke. A smaller third stroke is associated with ATP-induced detachment from actin. A comprehensive model is defined by applying such a cycle to all myosin-S1 heads in the half-sarcomere, subject to generic constraints as follows: (a) all strain-dependent kinetics required for actin-myosin interactions are derived from reaction-energy landscapes and applied to dimeric myosin, (b) actin-myosin interactions in the half-sarcomere are controlled by matching rules derived from the structure of the filaments, so that each dimer may be associated with a target zone of three actin sites, and (c) the myosin and actin filaments are treated as elastically extensible. Numerical predictions for such a model are presented in the following paper.

An analysis of the temperature dependence of force, during steady shortening at different velocities, in (mammalian) fast muscle fibres

We examined, over a wide range of temperatures (10–35°C), the isometric tension and tension during ramp shortening at different velocities (0.2–4 L₀/s) in tetanized intact fibre bundles from a rat fast (flexor hallucis brevis) muscle; fibre length (L₀) was 2.2 mm and sarcomere length ~2.5 μm. During a ramp shortening, the tension change showed an initial inflection of small amplitude (P₁), followed by a larger exponential decline towards an approximate steady level; the tension continued to decline slowly afterwards and the approximate steady tension at a given velocity was estimated as the tension (P₂) at the point of intersection between two linear slopes, as previously described (Roots et al. 2007). At a given temperature, the tension P₂ declined to a lower level and at a faster rate (from an exponential curve fit) as the shortening velocity was increased; the temperature sensitivity of the rate of tension decline during ramp shortening at different velocities was low (Q₁₀ 0.9–1.5). The isometric tension and the P₂ tension at a given shortening velocity increased with warming so that the relation between tension and (reciprocal) temperature was sigmoidal in both. In isometric muscle, the temperature T_0.5 for half-maximal tension was ~10°C, activation enthalpy change (∆H) was ~100 kJ mol⁻¹ and entropy change (∆S) ~350 J mol⁻¹ K⁻¹. In shortening, these were increased with increase of velocity so that at a shortening velocity (~4 L₀/s) producing maximal power at 35°C, T_0.5 was ~28°C, ∆H was ~200 kJ mol⁻¹ and ∆S ~ 700 J mol⁻¹ K⁻¹; the same trends were seen in the tension data from isotonic release experiments on intact muscle and in ramp shortening experiments on maximally Ca-activated skinned fibres. In general, our findings show that the sigmoidal relation between force and temperature can be extended from isometric to shortening muscle; the implications of the findings are discussed in relation to the crossbridge cycle. The data indicate that the endothermic, entropy driven process that underlies crossbridge force generation in isometric muscle (Zhao and Kawai 1994; Davis, 1998) is even more pronounced in shortening muscle, i.e. when doing external work.

Force generation examined by laser temperature-jumps in shortening and lengthening mammalian (rabbit psoas) muscle fibres

We examined the tension change induced by a rapid temperature jump (T-jump) in shortening and lengthening active muscle fibres. Experiments were done on segments of permeabilized single fibres (length (L0) approximately 2 mm, sarcomere length 2.5 microm) from rabbit psoas muscle; [MgATP] was 4.6 mm, pH 7.1, ionic strength 200 mm and temperature approximately 9 degrees C. A fibre was maximally Ca2+-activated in the isometric state and a approximately 3 degrees C, rapid (< 0.2 ms), laser T-jump applied when the tension was approximately steady in the isometric state, or during ramp shortening or ramp lengthening at a limited range of velocities (0-0.2 L0 s(-1)). The tension increased to 2- to 3 x P0 (isometric force) during ramp lengthening at velocities > 0.05 L0 s(-1), whereas the tension decreased to about < 0.5 x P0 during shortening at 0.1-0.2 L0 s(-1); the unloaded shortening velocity was approximately 1 L0 s(-1) and the curvature of the force-shortening velocity relation was high (a/P0 ratio from Hill's equation of approximately 0.05). In isometric state, a T-jump induced a tension rise of 15-20% to a new steady state; by curve fitting, the tension rise could be resolved into a fast (phase 2b, 40-50 s(-1)) and a slow (phase 3, 5-10 s(-1)) exponential component (as previously reported). During steady lengthening, a T-jump induced a small instantaneous drop in tension, followed by recovery, so that the final tension recorded with and without a T-jump was not significantly different; thus, a T-jump did not lead to a net increase of tension. During steady shortening, the T-jump induced a pronounced tension rise and both its amplitude and the rate (from a single exponential fit) increased with shortening velocity; at 0.1-0.2 L0 s(-1), the extent of fibre shortening during the T-jump tension rise was estimated to be approximately 1.2% L(0) and it was shorter at lower velocities. At a given shortening velocity and over the temperature range of 8-30 degrees C, the rate of T-jump tension rise increased with warming (Q10 approximately 2.7), similar to phase 2b (endothermic force generation) in isometric muscle. Results are discussed in relation to the previous findings in isometric muscle fibres which showed that a T-jump promotes an early step in the crossbridge-ATPase cycle that generates force. In general, the finding that the T-jump effect on active muscle tension is pronounced during shortening, but is depressed/inhibited during lengthening, is consistent with the expectations from the Fenn effect that energy liberation (and acto-myosin ATPase rate) in muscle are increased during shortening and depressed/inhibited during lengthening.