Mechanokinetics of rapid tension recovery in muscle: the Myosin working stroke is followed by a slower release of phosphate

Unraveling a Force-Generating Allosteric Pathway of Actomyosin Communication Associated with ADP and Pi Release

The actomyosin system generates mechanical work with the execution of the power stroke, an ATP-driven, two-step rotational swing of the myosin-neck that occurs post ATP hydrolysis during the transition from weakly to strongly actin-bound myosin states concomitant with P_i release and prior to ADP dissociation. The activating role of actin on product release and force generation is well documented; however, the communication paths associated with weak-to-strong transitions are poorly characterized. With the aid of mutant analyses based on kinetic investigations and simulations, we identified the W-helix as an important hub coupling the structural changes of switch elements during ATP hydrolysis to temporally controlled interactions with actin that are passed to the central transducer and converter. Disturbing the W-helix/transducer pathway increased actin-activated ATP turnover and reduced motor performance as a consequence of prolonged duration of the strongly actin-attached states. Actin-triggered P_i release was accelerated, while ADP release considerably decelerated, both limiting maximum ATPase, thus transforming myosin-2 into a high-duty-ratio motor. This kinetic signature of the mutant allowed us to define the fractional occupancies of intermediate states during the ATPase cycle providing evidence that myosin populates a cleft-closure state of strong actin interaction during the weak-to-strong transition with bound hydrolysis products before accomplishing 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.

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.

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.

Reinterpretation of the Tension Response of Muscle to Stretches and Releases

We have reexamined the experimental time courses of tension in frog muscle after rapid length steps. The early tension recoveries are biexponential. After 3 nm/hs stretches and releases, the rates of the immediate rapid tension changes are similar but the subsequent tension fall after a stretch is much slower than the rise after a release. After 1.5 nm/hs length steps, the entire tension responses are more nearly mirror images. To identify the underlying processes, we used a model of the muscle cross-bridge cycle with two tension-generating (tensing) steps. Analysis of the time course of the tension, the rates of the steps in the cycle, and their contributions to tension provided insights into previously puzzling features of the experimental response. After a stretch, the initial rapid tension fall in the model is caused principally by the reversal of the first tensing step, but after a few milliseconds the tensing step resumes its forward direction. We conclude that the remaining response should not be included in phase 2, the period of early tension recovery. With this exclusion, T₂, the tension at the end of this period, rises with an increase of stretch. The rate of early tension recovery also increases with stretch size, showing that the reversal of the first tensing step is strain sensitive. After small length steps, the fast and slow components of the early tension recovery are both caused mainly by the first tensing step. The fast component is triggered by the initial sliding of the filaments, and the slow component is due to further sliding that occurs as the tension recovers. With small length steps (<0.5 nm/hs), the time course of the response to a stretch is the reverse of that to a release.

Force Responses and Sarcomere Dynamics of Cardiac Myofibrils Induced by Rapid Changes in [Pi]

The second phase of the biphasic force decay upon release of phosphate from caged phosphate was previously interpreted as a signature of kinetics of the force-generating step in the cross-bridge cycle. To test this hypothesis without using caged compounds, force responses and individual sarcomere dynamics upon rapid increases or decreases in concentration of inorganic phosphate [P_i] were investigated in calcium-activated cardiac myofibrils. Rapid increases in [P_i] induced a biphasic force decay with an initial slow decline (phase 1) and a subsequent 3-5-fold faster major decay (phase 2). Phase 2 started with the distinct elongation of a single sarcomere, the so-called sarcomere "give". "Give" then propagated from sarcomere to sarcomere along the myofibril. Propagation speed and rate constant of phase 2 (k_+Pi(2)) had a similar [P_i]-dependence, indicating that the kinetics of the major force decay (phase 2) upon rapid increase in [P_i] is determined by sarcomere dynamics. In contrast, no "give" was observed during phase 1 after rapid [P_i]-increase (rate constant k_+Pi(1)) and during the single-exponential force rise (rate constant k_-Pi) after rapid [P_i]-decrease. The values of k_+Pi(1) and k_-Pi were similar to the rate constant of mechanically induced force redevelopment (k_TR) and Ca²⁺-induced force development (k_ACT) measured at same [P_i]. These results indicate that the major phase 2 of force decay upon a P_i-jump does not reflect kinetics of the force-generating step but results from sarcomere "give". The other phases of P_i-induced force kinetics that occur in the absence of "give" yield the same information as mechanically and Ca²⁺-induced force kinetics (k_+Pi(1) ∼ k_-Pi ∼ k_TR ∼ k_ACT). Model simulations indicate that P_i-induced force kinetics neither enable the separation of P_i-release from the rate-limiting transition f into force states nor differentiate whether the "force-generating step" occurs before, along, or after the P_i-release.

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.

A new mechanokinetic model for muscle contraction, where force and movement are triggered by phosphate release

The atomic structure of myosin-S1 suggests that its working stroke, which generates tension and shortening in muscle, is triggered by the release of inorganic phosphate from the active site. This mechanism is the basis of a new mechanokinetic model for contractility, using the biochemical actomyosin ATPase cycle, strain-dependent kinetics and dimeric myosins on buckling rods. In this model, phosphate-dependent aspects of contractility arise from a rapid reversible release of phosphate from the initial bound state (A.M.ADP.Pi), which triggers the stroke. Added phosphate drives bound myosin towards this initial state, and the transient tension response to a phosphate jump reflects the rate at which it detaches from actin. Predictions for the tensile and energetic properties of striated muscle as a function of phosphate level, including the tension responses to length steps and Pi-jumps, are compared with experimental data from rabbit psoas fibres at 10 °C. The phosphate sensitivity of isometric tension is maximal when the actin affinity of M.ADP.Pi is near unity. Hence variations in actin affinity modulate the phosphate dependence of isometric tension, and may explain why phosphate sensitivity is temperature-dependent or absent in different muscles.

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

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

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.

Three distinct actin-attached structural states of myosin in muscle fibers

We have used thiol cross-linking and electron paramagnetic resonance (EPR) to resolve structural transitions of myosin's light chain domain (LCD) and catalytic domain (CD) that are associated with force generation. Spin labels were incorporated into the LCD of muscle fibers by exchanging spin-labeled regulatory light chain for endogenous regulatory light chain, with full retention of function. To trap myosin in a structural state analogous to the elusive posthydrolysis ternary complex A.M'.D.P, we used pPDM to cross-link SH1 (Cys(707)) to SH2 (Cys(697)) on the CD. LCD orientation and dynamics were measured in three biochemical states: relaxation (A.M.T), SH1-SH2 cross-linked (A.M'.D.P analog), and rigor (A.M.D). EPR showed that the LCD of cross-linked fibers has an orientational distribution intermediate between relaxation and rigor, and saturation transfer EPR revealed slow rotational dynamics indistinguishable from that of rigor. Similar results were obtained for the CD using a bifunctional spin label to cross-link SH1-SH2, but the CD was more disordered than the LCD. We conclude that SH1-SH2 cross-linking traps a state in which both the CD and LCD are intermediate between relaxation (highly disordered and microsecond dynamics) and rigor (highly ordered and rigid), supporting the hypothesis that the cross-linked state is an A.M'D.P analog on the force generation pathway.

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.

Predicting order of conformational changes during protein conformational transitions using an interpolated elastic network model

The decryption of sequence of structural events during protein conformational transitions is essential to a detailed understanding of molecular functions of various biological nanomachines. Coarse-grained models have proven useful by allowing highly efficient simulations of protein conformational dynamics. By combining two coarse-grained elastic network models constructed based on the beginning and end conformations of a transition, we have developed an interpolated elastic network model to generate a transition pathway between the two protein conformations. For validation, we have predicted the order of local and global conformational changes during key ATP-driven transitions in three important biological nanomachines (myosin, F(1) ATPase and chaperonin GroEL). We have found that the local conformational change associated with the closing of active site precedes the global conformational change leading to mechanical motions. Our finding is in good agreement with the distribution of intermediate experimental structures, and it supports the importance of local motions at active site to drive or gate various conformational transitions underlying the workings of a diverse range of biological nanomachines.

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.

A model for processive movement of single-headed myosin-IX

It is puzzling that in spite of its single-headed structure, myosin-IX can move processively along actin. Here, based on the experimental evidence that the strong binding of myosin to actin in rigor state induces structural changes to several local actin monomers, a Brownian ratchet model is proposed to describe this processive movement. In the model, the actin plays an active role in the motility of single-headed myosin, in contrast to the common belief that the actin acts only as a passive track for the motility of the myosin. The unidirectional movement is due to both the asymmetric periodic potential of the myosin interacting with actin and the forward Stokes force induced by the relative rotation of the neck domain to the motor domain, while the processivity is determined by the binding affinity of the myosin for actin in ATP state. This gives a good explanation to the high processivity of myosin-IX, which results from its high binding affinity for actin in ATP state due to the presence of unique loop 2 insertion or N-terminal extension. The experimental results on the motility of myosin-IX such as the step size, large forward/backward stepping ratio, run length, stall force, etc, are explained well.

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.

Temperature jump induced force generation in rabbit muscle fibres gets faster with shortening and shows a biphasic dependence on velocity

We examined the tension responses to ramp shortening and rapid temperature jump (<0.2 ms, 3-4 degrees C T-jump) in maximally Ca(2+)-activated rabbit psoas muscle fibres at 8-9 degrees C (the fibre length (L(0)) was approximately 1.5 mm and sarcomere length 2.5 microm). The aim was to investigate the strain sensitivity of crossbridge force generation in muscle. The T-jump induced tension rise was examined during steady shortening over a wide range of velocities (V) approaching the V(max) (V range approximately 0.01 to approximately 1.5 L(0) s(1)). In the isometric state, a T-jump induced a biphasic tension rise consisting of a fast (approximately 50 s(1), phase 2b) and a slow (approximately 10 s(1), phase 3) component, but if treated as monophasic the rate was approximately 20 s(1). During steady shortening the T-jump tension rise was monophasic; the rate of tension rise increased linearly with shortening velocity, and near V(max) it was approximately 200 s(1), approximately 10x faster than in the isometric state. Relative to the tension reached after the T-jump, the amplitude increased with shortening velocity, and near V(max) it was 4x larger than in the isometric state. Thus, the temperature sensitivity of muscle force is markedly increased with velocity during steady shortening, as found in steady state experiments. The rate of tension decline during ramp shortening also increased markedly with increase of velocity. The absolute amplitude of T-jump tension rise was larger than that in the isometric state at the low velocities (<0.5 L(0) s(1)) but decreased to below that of the isometric state at the higher velocities. Such a biphasic velocity dependence of the absolute amplitude of T-jump tension rise implies interplay between, at least, two processes that have opposing effects on the tension output as the shortening velocity is increased, probably enhancement of crossbridge force generation and faster (post-stroke) crossbridge detachment by negative strain. Overall, our results show that T-jump force generation is strain sensitive and becomes considerably faster when exposed to negative strain. Thus the crossbridge force generation step in muscle is both temperature sensitive (endothermic) and strain sensitive.

Effect of phosphate and temperature on force exerted by white muscle fibres from dogfish

Effects of Pi (inorganic phosphate) are relevant to the in vivo function of muscle because Pi is one of the products of ATP hydrolysis by actomyosin and by the sarcoplasmic reticulum Ca²⁺ pump. We have measured the Pi sensitivity of force produced by permeabilized muscle fibres from dogfish (Scyliorhinus canicula) and rabbit. The activation conditions for dogfish fibres were crucial: fibres activated from the relaxed state at 5, 12, and 20°C were sensitive to Pi, whereas fibres activated from rigor at 12°C were insensitive to Pi in the range 5–25 mmol l⁻¹. Rabbit fibres activated from rigor were sensitive to Pi. Pi sensitivity of force produced by dogfish fibres activated from the relaxed state was greater below normal body temperature (12°C for dogfish) in agreement with what is known for other species. The force-temperature relationship for dogfish fibres (intact and permeabilized fibres activated from relaxed) showed that at 12°C, normal body temperature, the force was near to its maximum value.

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.

Temperature change as a probe of muscle crossbridge kinetics: a review and discussion

Following the ideas introduced by Huxley (Huxley 1957, Prog. Biophys. Biophys. Chem. 7, 255-318), it is generally supposed that muscle contraction is produced by temporary links, called crossbridges, between myosin and actin filaments, which form and break in a cyclic process driven by ATP splitting. Here we consider the interaction of the energy in the crossbridge, in its various states, and the force exerted. We discuss experiments in which the mechanical state of the crossbridge is changed by imposed movement and the energetic consequence observed as heat output and the converse experiments in which the energy content is changed by altering temperature and the mechanical consequences are observed. The thermodynamic relationship between the experiments is explained and, at the first sight, the relationship between the results of these two types of experiment appears paradoxical. However, we describe here how both of them can be explained by a model in which mechanical and energetic changes in the crossbridges occur in separate steps in a branching cycle.

Effect of inorganic phosphate on the force and number of myosin cross-bridges during the isometric contraction of permeabilized muscle fibers from rabbit psoas

The relation between the chemical and mechanical steps of the myosin-actin ATPase reaction that leads to generation of isometric force in fast skeletal muscle was investigated in demembranated fibers of rabbit psoas muscle by determining the effect of the concentration of inorganic phosphate (Pi) on the stiffness of the half-sarcomere (hs) during transient and steady-state conditions of the isometric contraction (temperature 12 degrees C, sarcomere length 2.5 mum). Changes in the hs strain were measured by imposing length steps or small 4 kHz oscillations on the fibers in control solution (without added Pi) and in solution with 3-20 mM added Pi. At the plateau of the isometric contraction in control solution, the hs stiffness is 22.8 +/- 1.1 kPa nm(-1). Taking the filament compliance into account, the total stiffness of the array of myosin cross-bridges in the hs (e) is 40.7 +/- 3.7 kPa nm(-1). An increase in [Pi] decreases the stiffness of the cross-bridge array in proportion to the isometric force, indicating that the force of the cross-bridge remains constant independently of [Pi]. The rate constant of isometric force development after a period of unloaded shortening (r(F)) is 23.5 +/- 1.0 s(-1) in control solution and increases monotonically with [Pi], attaining a maximum value of 48.6 +/- 0.9 s(-1) at 20 mM [Pi], in agreement with the idea that Pi release is a relatively fast step after force generation by the myosin cross-bridge. During isometric force development at any [Pi], e and thus the number of attached cross-bridges increase in proportion to the force, indicating that, independently of the speed of the process that leads to myosin attachment to actin, there is no significant (>1 ms) delay between generation of stiffness and generation of force by the cross-bridges.

Structural dynamics of the actomyosin complex probed by a bifunctional spin label that cross-links SH1 and SH2

We have used a bifunctional spin label (BSL) to cross-link Cys(707) (SH1) and Cys(697) (SH2) in the catalytic domain of myosin subfragment 1 (S1). BSL induces the same weakened ATPase activity and actin-binding affinity that is observed when SH1 and SH2 are cross-linked with pPDM, which traps an analog of the post-hydrolysis state A.M.ADP.P. Electron paramagnetic resonance showed that BSL reports the global orientation and dynamics of S1. When bound to actin in oriented muscle fibers in the absence of ATP, BSL-S1 showed almost complete orientational disorder, as reported previously for the weakly bound A.M.ADP. In contrast, helical order is observed for the strongly bound state A.M. Saturation transfer electron paramagnetic resonance showed that the disorder of cross-linked S1 on actin is nearly static on the microsecond timescale, at least 30 times slower than that of A.M.ADP. We conclude that cross-linked S1 exhibits rotational disorder comparable to that of A.M.ADP, slow rotational mobility comparable to that of A.M, and intermediate actin affinity. These results support the hypothesis that the catalytic domain of myosin is orientationally disordered on actin in a post-hydrolysis state in the early stages of force generation.

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.

Characterization of the pre-force-generation state in the actomyosin cross-bridge cycle

Myosin is an actin-based motor protein that generates force by cycling between actin-attached (strong binding: ADP or rigor) and actin-detached (weak binding: ATP or ADP.P(i)) states during its ATPase cycle. However, it remains unclear what specific conformational changes in the actin binding site take place on binding to actin, and how these structural changes lead to product release and the production of force and motion. We studied the dynamics of the actin binding region of myosin V by using fluorescence resonance energy transfer (FRET) to monitor conformational changes in the upper-50-kDa domain of the actin binding cleft in the weak and strong actin binding states. Steady-state and lifetime data monitoring the FRET signal suggest that the cleft is in a more open conformation in the weak actin binding states. Transient kinetic experiments suggest that a rapid conformational change occurs, which is consistent with cleft closure before actin-activated phosphate release. Our results have identified a pre-force-generation actomyosin ADP.P(i) state, and suggest force generation may occur from a state not yet seen by crystallography in which the actin binding cleft and the nucleotide binding pocket are closed. Computational modeling uncovers dramatic changes in the rigidity of the upper-50-kDa domain in different nucleotide states, which suggests that the intrinsic flexibility of this domain allows myosin motors to accomplish simultaneous tight nucleotide binding (closed nucleotide binding pocket) and high-affinity actin binding (closed actin binding cleft).

The mechanism of the reverse recovery step, phosphate release, and actin activation of Dictyostelium myosin II

The rate-limiting step of the myosin basal ATPase (i.e. in absence of actin) is assumed to be a post-hydrolysis swinging of the lever arm (reverse recovery step), that limits the subsequent rapid product release steps. However, direct experimental evidence for this assignment is lacking. To investigate the binding and the release of ADP and phosphate independently from the lever arm motion, two single tryptophan-containing motor domains of Dictyostelium myosin II were used. The single tryptophans of the W129+ and W501+ constructs are located at the entrance of the nucleotide binding pocket and near the lever arm, respectively. Kinetic experiments show that the rate-limiting step in the basal ATPase cycle is indeed the reverse recovery step, which is a slow equilibrium step (k(forward) = 0.05 s(-1), k(reverse) = 0.15 s(-1)) that precedes the phosphate release step. Actin directly activates the reverse recovery step, which becomes practically irreversible in the actin-bound form, triggering the power stroke. Even at low actin concentrations the power stroke occurs in the actin-attached states despite the low actin affinity of myosin in the pre-power stroke conformation.

Myosin V movement: lessons from molecular dynamics studies of IQ peptides in the lever arm

Myosin V moves along actin filaments by an arm-over-arm motion, known as the lever mechanism. Each of its arms is composed of six consecutive IQ peptides that bind light chain proteins, such as calmodulin or calmodulin-like proteins. We have employed a multistage approach in order to investigate the mechanochemical structural basis of the movement of myosin V from the budding yeast Saccharomyces cerevisiae. For that purpose, we previously carried out molecular dynamics simulations of the Mlc1p-IQ2 and the Mlc1p-IQ4 protein-peptide complexes, and the present study deals with the structures of the IQ peptides when stripped from the Mlc1p protein. We have found that the crystalline structure of the IQ2 peptide retains a stable rodlike configuration in solution, whereas that of the IQ4 peptide grossly deviates from its X-ray conformation exhibiting an intrinsic tendency to curve and bend. The refolding process of the IQ4 peptide is initially driven by electrostatic interactions followed by nonpolar stabilization. Its bending appears to be affected by the ionic strength, when ionic strength higher than approximately 300 mM suppresses it from flexing. Considering that a poly-IQ sequence is the lever arm of myosin V, we suggest that the arm may harbor a joint, localized within the IQ4 sequence, enabling the elasticity of the neck of myosin V. Given that a poly-IQ sequence is present at the entire class of myosin V and the possibility that the yeast's myosin V molecule can exist either as a nonprocessive monomer or as a processive dimer depending on conditions (Krementsova, E. B., Hodges, A. R., Lu, H., and Trybus, K. M. (2006) J. Biol. Chem. 281, 6079-6086), our observations may account for a general structural feature for the myosins' arm embedded flexibility.

Kinetics of ADP dissociation from the trail and lead heads of actomyosin V following the power stroke

Myosin V is a cellular motor protein, which transports cargos along actin filaments. It moves processively by 36-nm steps that require at least one of the two heads to be tightly bound to actin throughout the catalytic cycle. To elucidate the kinetic mechanism of processivity, we measured the rate of product release from the double-headed myosin V-HMM using a new ATP analogue, 3'-(7-diethylaminocoumarin-3-carbonylamino)-3'-deoxy-ATP (deac-aminoATP), which undergoes a 20-fold increase in fluorescence emission intensity when bound to the active site of myosin V (Forgacs, E., Cartwright, S., Kovács, M., Sakamoto, T., Sellers, J. R., Corrie, J. E. T., Webb, M. R., and White, H. D. (2006) Biochemistry 45, 13035-13045). The kinetics of ADP and deac-aminoADP dissociation from actomyosin V-HMM, following the power stroke, were determined using double-mixing stopped-flow fluorescence. These used either deac-aminoATP as the substrate with ADP or ATP chase or alternatively ATP as the substrate with either a deac-aminoADP or deac-aminoATP chase. Both sets of experiments show that the observed rate of ADP or deac-aminoADP dissociation from the trail head of actomyosin V-HMM is the same as from actomyosin V-S1. The dissociation of ADP from the lead head is decreased by up to 250-fold.

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.

Strain-dependent kinetics of the myosin working stroke, and how they could be probed with optical-trap experiments

The strain-dependent kinetics of the myosin working stroke under load is derived from a flat-energy-landscape model for its untethered lever-arm, and compared with other scenarios in the literature. The "flat landscape" scenario is compatible with muscle-fiber experiments, but is more critically relevant to single-myosin experiments with an optically trapped actin filament. In such experiments, the strain dependence of stroke kinetics may be explored by comparing event-averaged and time-averaged displacements of the filament. With a specific kinetic model of the cross-bridge cycle, we have previously shown that the event-averaged displacement underestimates the working stroke. Here we predict that the two kinds of averaging give diverging estimates of the working stroke as the resolving time of the event detector is decreased to 1 ms or less, the discrepancy being critically dependent on the strain dependence of the stroke rate. Such analysis of trap displacement data offers the possibility of testing the strain-dependent stroke rate predicted by the flat-landscape model.

Effect of strain on actomyosin kinetics in isometric muscle fibers

Investigations were conducted into the biochemical and mechanical states of cross-bridges during isometric muscle contraction. Rapid length steps (3 or 6 nm hs(-1)) were applied to rabbit psoas fibers, permeabilized and isometric, at either 12 degrees C or 20 degrees C. Fibers were activated by photolysis of P(3)-1-(2-nitrophenyl)-ethyl ester of ATP infused into rigor fibers at saturating Ca(2+). Sarcomere length, tension, and phosphate release were recorded-the latter using the MDCC-PBP fluorescent probe. A reduction in strain, induced by a rapid release step, produced a short-lived acceleration of phosphate release. Rates of the phosphate transient and that of phases 3 and 4 of tension recovery were unaffected by step size but were elevated at higher temperatures. In contrast the amplitude of the phosphate transient was smaller at 20 degrees C than 12 degrees C. The presence of 0.5 or 1.0 mM added ADP during a release step reduced both the rate of tension recovery and the poststep isometric tension. A kinetic scheme is presented to simulate the observed data and to precisely determine the rate constants for the elementary steps of the ATPase cycle.

Reconciling the working strokes of a single head of skeletal muscle myosin estimated from laser-trap experiments and crystal structures

Myosin generates force by a rotation of its lever arm. Crystal structures of myosin II indicate an unloaded working stroke of 10-12 nm, a range confirmed by recent x-ray interference experiments. However, when an actin filament, held between two weakly, optically trapped beads is made to interact with a single head of skeletal myosin, the bead displacements have often been reported as having a mean value of 5-6 nm, a value that is commonly interpreted as the working stroke. In general, the observed displacement is not expected to be equal to the working stroke because the kinetics of the stroke is necessarily strain-dependent: this effect biases the frequency of binding events to different actin sites so that displacements smaller than the working stroke are preferentially selected. Our analysis is tailored to current trap experiments, in which the time resolution is insufficient to detect pre-rigor states. If the preceding transitions are in equilibrium, the mean displacement is zero, contrary to observations in the presence of ATP. However, under ATP-cycling conditions, we find that the mean displacement is deflated to 0.3-0.7 of the true working stroke, depending on the equilibrium constant of the stroke and the rate at which the first myosin product state can detach from actin. The primary working stroke of processive myosin motors as measured by optical trapping is similarly uncertain.

Initiation of the power stroke in muscle: insights from the phosphate analog AlF4

Motile forces in muscle are generated by the so-called "power stroke," a series of structural changes in the actomyosin cross-bridge driven by hydrolysis of ATP. The initiation of this power stroke is closely related to phosphate release after ATP cleavage and to the change of the myosin head from weak, nonstereospecific actin attachment to strong, stereospecific binding. The exact sequence of events, however, is highly controversial but crucial for the mechanism of how ATP hydrolysis drives structural changes in the head domain of myosins and related NTPases like kinesins and small G proteins. Here, we show that the phosphate analogue AlF4 can form two ADP.phosphate analog states, one with weak binding of myosin to actin and the other with strong binding of myosin to actin. Thus, change from weak to strong binding (i.e., the initiation of the power stroke) can occur before phosphate is released from the active site.

Endothermic force generation, temperature-jump experiments and effects of increased [MgADP] in rabbit psoas muscle fibres

We studied, by experiment and by kinetic modelling, the characteristics of the force increase on heating (endothermic force) in muscle. Experiments were done on maximally Ca2+-activated, permeabilized, single fibres (length approximately 2 mm; sarcomere length, 2.5 microm) from rabbit psoas muscle; [MgATP] was 4.6 mM, pH 7.1 and ionic strength was 200 mM. A small-amplitude (approximately 3 degrees C) rapid laser temperature-jump (0.2 ms T-jump) at 8-9 degrees C induced a tension rise to a new steady state and it consisted of two (fast and slow) exponential components. The T-jump-induced tension rise became slower as [MgADP] was increased, with half-maximal effect at 0.5 mM [MgADP]; the pre- and post-T-jump tension increased approximately 20% with 4 mM added [MgADP]. As determined by the tension change to small, rapid length steps (<1.4%L0 complete in <0.5 ms), the increase of force by [MgADP] was not associated with a concomitant increase of stiffness; the quick tension recovery after length steps (Huxley-Simmons phase 2) was slower with added MgADP. In steady-state experiments, the tension was larger at higher temperatures and the plot of tension versus reciprocal absolute temperature was sigmoidal, with a half-maximal tension at 10-12 degrees C; the relation with added 4 mM MgADP was shifted upwards on the tension axis and towards lower temperatures. The potentiation of tension with 4 mM added MgADP was 20-25% at low temperatures (approximately 5-10 degrees C), but approximately 10% at the physiological temperatures (approximately 30 degrees C). The shortening velocity was decreased with increased [MgADP] at low and high temperatures. The sigmoidal relation between tension and reciprocal temperature, and the basic effects of increased [MgADP] on endothermic force, can be qualitatively simulated using a five-step kinetic scheme for the crossbridge/A-MATPase cycle where the force generating conformational change occurs in a reversible step before the release of inorganic phosphate (P(i)), it is temperature sensitive (Q10 of approximately 4) and the release of MgADP occurs by a subsequent, slower, two-step mechanism. Modelling shows that the sigmoidal relation between force and reciprocal temperature arises from conversion of preforce-generating (A-M.ADP.P(i)) states to force-bearing (A-M.ADP) states as the temperature is raised. A tension response to a simulated T-jump consists of three (one fast and two slow) components, but, by combining the two slow components, they could be reduced to two; their relative amplitudes vary with temperature. The model can qualitatively simulate features of the tension responses induced by large-T-jumps from low starting temperatures, and those induced by small-T-jumps from different starting temperatures and, also, the interactive effects of P(i) and temperature on force in muscle fibres.

Effects of a myosin-II inhibitor (N-benzyl-p-toluene sulphonamide, BTS) on contractile characteristics of intact fast-twitch mammalian muscle fibres

We have examined the effects of N-benzyl-p-toluene sulphonamide (BTS), a potent and specific inhibitor of fast muscle myosin-II, using small bundles of intact fibres or single fibres from rat foot muscle. BTS decreased tetanic tension reversibly in a concentration-dependent manner with half-maximal inhibition at approximately approximately 2 microM at 20 degrees C. The inhibition of tension with 10 microM BTS was marked at the three temperatures examined (10, 20 and 30 degrees C), but greatest at 10 degrees C. BTS decreased active muscle stiffness to a lesser extent than tetanic tension indicating that not all of the tension inhibition was due to a reduced number of attached cross-bridges. BTS-induced inhibition of active tension was not accompanied by any change in the free myoplasmic Ca2+ transients. The potency and specificity of BTS make it a very suitable myosin inhibitor for intact mammalian fast muscle and should be a useful tool for the examination of outstanding questions in muscle contraction.

Adenosine diphosphate and strain sensitivity in myosin motors

The release of adenosine diphosphate (ADP) from the actomyosin cross-bridge plays an important role in the adenosine-triphosphate-driven cross-bridge cycle. In fast contracting muscle fibres, the rate at which ADP is released from the cross-bridge correlates with the maximum shortening velocity of the muscle fibre, and in some models the rate of ADP release defines the maximum shortening velocity. In addition, it has long been thought that the rate of ADP release could be sensitive to the load on the cross-bridge and thereby provide a molecular explanation of the Fenn effect. However, direct evidence of a strain-sensitive ADP-release mechanism has been hard to come by for fast muscle myosins. The recently published evidence for a strain-sensing mechanism involving ADP release for slower muscle myosins, and in particular non-muscle myosins, is more compelling and can provide the mechanism of processivity for motors such as myosin V. It is therefore timely to examine the evidence for this strain-sensing mechanism. The evidence presented here will argue that a strain-sensitive mechanism of ADP release is universal for all myosins but the basic mechanism has evolved in different ways for different types of myosin. Furthermore, this strain-sensing mechanism provides a way of coordinating the action of multiple myosin motor domains in a single myosin molecule, or in complex assemblies of myosins over long distances without invoking a classic direct allosteric or cooperative communication between motors.

Coupling between phosphate release and force generation in muscle actomyosin

Energetic, kinetic and oxygen exchange experiments in the mid-1980s and early 1990s suggested that phosphate (Pi) release from actomyosin-adenosine diphosphate Pi (AM.ADP.Pi) in muscle fibres is linked to force generation and that Pi release is reversible. The transition leading to the force-generating state and subsequent Pi release were hypothesized to be separate, but closely linked steps. Pi shortens single force-generating actomyosin interactions in an isometric optical clamp only if the conditions enable them to last 20-40 ms, enough time for Pi to dissociate. Until 2003, the available crystal forms of myosin suggested a rigid coupling between movement of switch II and tilting of the lever arm to generate force, but they did not explain the reciprocal affinity myosin has for actin and nucleotides. Newer crystal forms and other structural data suggest that closing of the actin-binding cleft opens switch I (presumably decreasing nucleotide affinity). These data are all consistent with the order of events suggested before: myosin.ADP.Pi binds weakly, then strongly to actin, generating force. Then Pi dissociates, possibly further increasing force or sliding.

Using optical tweezers to relate the chemical and mechanical cross-bridge cycles

In most current models of muscle contraction there are two translational steps, the working stroke, whereby an attached myosin cross-bridge moves relative to the actin filament, and the repriming step, in which the cross-bridge returns to its original orientation. The development of single molecule methods has allowed a more detailed investigation of the relationship of these mechanical steps to the underlying biochemistry. In the normal adenosine triphosphate cycle, myosin.adenosine diphosphate.phosphate (M.ADP.Pi) binds to actin and moves it by ca. 5 nm on average before the formation of the end product, the rigor actomyosin state. All the other product-like intermediate states tested were found to give no net movement indicating that M.ADP.Pi alone binds in a pre-force state. Myosin states with bound, unhydrolysed nucleoside triphosphates also give no net movement, indicating that these must also bind in a post-force conformation and that the repriming, post- to pre-transition during the forward cycle must take place while the myosin is dissociated from actin. These observations fit in well with the structural model in which the working stroke is aligned to the opening of the switch 2 element of the ATPase site.