Kinetics of the actomyosin ATPase in muscle fibers

Four phases of a force transient emerge from a binary mechanical system

Accurate models of muscle contraction are important for understanding both muscle performance and the therapeutics that enhance physiological function. However, models are only accurate and meaningful if they are consistent with physical laws. A single muscle fiber contains billions of randomly fluctuating atoms that on the spatial scale of a muscle fiber generate unidirectional force and power output. This thermal system is formally constrained by the laws of thermodynamics, and a recently developed thermodynamic model of muscle force generation provides qualitative descriptions of the muscle force-velocity relationship, muscle force generation, muscle force transients, and the thermodynamic work loop of muscle with a thermodynamic (not molecular) power stroke mechanism. To demonstrate the accuracy of this model requires that its outputs be quantitatively compared with experimentally observed muscle function. Here I show that a two-state thermodynamic model accurately describes the experimentally observed four-phase force transient response to both mechanical and chemical perturbations. This is the simplest possible model of one of the most complex characteristic signatures of muscle mechanics.

Elucidating Events within the Black Box of Enzyme Catalysis in Energy Metabolism: Insights into the Molecular Mechanism of ATP Hydrolysis by F1-ATPase

Oxygen exchange reactions occurring at β-catalytic sites of the FOF1-ATP synthase/F1-ATPase imprint a unique record of molecular events during the catalytic cycle of ATP synthesis/hydrolysis. This work presents a new theory of oxygen exchange and tests it on oxygen exchange data recorded on ATP hydrolysis by mitochondrial F1-ATPase (MF1). The apparent rate constant of oxygen exchange governing the intermediate Pi-HOH exchange accompanying ATP hydrolysis is determined by kinetic analysis over a ~50,000-fold range of substrate ATP concentration (0.1-5000 μM) and a corresponding ~200-fold range of reaction velocity (3.5-650 [moles of Pi/{moles of F1-ATPase}-1 s-1]). Isotopomer distributions of [18O]Pi species containing 0, 1, 2, and 3 labeled oxygen atoms predicted by the theory have been quantified and shown to be in perfect agreement with the experimental distributions over the entire range of medium ATP concentrations without employing adjustable parameters. A novel molecular mechanism of steady-state multisite ATP hydrolysis by the F1-ATPase has been proposed. Our results show that steady-state ATP hydrolysis by F1-ATPase occurs with all three sites occupied by Mg-nucleotide. The various implications arising from models of energy coupling in ATP synthesis/hydrolysis by the ATP synthase/F1-ATPase have been discussed. Current models of ATP hydrolysis by F1-ATPase, including those postulated from single-molecule data, are shown to be effectively bisite models that contradict the data. The trisite catalysis formulated by Nath's torsional mechanism of energy transduction and ATP synthesis/hydrolysis since its first appearance 25 years ago is shown to be in better accord with the experimental record. The total biochemical information on ATP hydrolysis is integrated into a consistent model by the torsional mechanism of ATP synthesis/hydrolysis and shown to elucidate the elementary chemical and mechanical events within the black box of enzyme catalysis in energy metabolism by F1-ATPase.

Four Phases of a Force Transient Emerge from a Binary Mechanical System

Models of muscle contraction are important for guiding drug discovery, drug validation, and clinical decision-making with the goal of improving human health. Models of muscle contraction are also key to discovering clean energy technologies from one of the most efficient and clean-burning machines on the planet. However, these important goals can only be met through muscle models that are based on science. Most every model and mechanism (e.g., a molecular power stroke) of muscle contraction described in the literature to date is based on a corpuscular mechanic philosophy that has been challenged by science for over two decades. A thermodynamic model and mechanisms (e.g., a molecular switch) of muscle contraction is supported by science but has not yet been tested against experimental data. Here, I show that following a rapid perturbation to the free energy of a thermodynamic muscle system, a transient force response emerges with four phases, each corresponding to a different clearly-defined thermodynamic (not molecular) process. I compare these four phases to those observed in two classic muscle transient experiments. The observed consistency between model and data implies that the simplest possible model of muscle contraction (a binary mechanical system) accurately describes muscle contraction.

Actin crosslinking by α-actinin averts viscous dissipation of myosin force transmission in stress fibers

Contractile force generated in actomyosin stress fibers (SFs) is transmitted along SFs to the extracellular matrix (ECM), which contributes to cell migration and sensing of ECM rigidity. In this study, we show that efficient force transmission along SFs relies on actin crosslinking by α-actinin. Upon reduction of α-actinin-mediated crosslinks, the myosin II activity induced flows of actin filaments and myosin II along SFs, leading to a decrease in traction force exertion to ECM. The fluidized SFs maintained their cable integrity probably through enhanced actin polymerization throughout SFs. A computational modeling analysis suggested that lowering the density of actin crosslinks caused viscous slippage of actin filaments in SFs and, thereby, dissipated myosin-generated force transmitting along SFs. As a cellular scale outcome, α-actinin depletion attenuated the ECM-rigidity-dependent difference in cell migration speed, which suggested that α-actinin-modulated SF mechanics is involved in the cellular response to ECM rigidity.

Thermodynamics and Kinetics of a Binary Mechanical System: Mechanisms of Muscle Contraction

Biological motors function at the interface of biology, physics, and chemistry, and it remains unsettled what rules from which disciplines account for how these motors work. Myosin motors are enzymes that catalyze the hydrolysis of ATP through a mechanism involving a switch-like myosin structural change (a lever arm rotation) induced by actin binding that generates a small displacement of an actin filament. In muscle, individual myosin motors are widely assumed to function as molecular machines having mechanical properties that resemble those of muscle. In a fundamental departure from this perspective, here, I show that muscle more closely resembles a heat engine with mechanical properties that emerge from the thermodynamics of a myosin motor ensemble. The transformative impact of thermodynamics on our understanding of how a heat engine works guides a parallel transformation in our understanding of how muscle works. I consider the simplest possible model of force generation: a binary mechanical system. I develop the mechanics, energetics, and kinetics of this system and show that a single binding reaction generates force when muscle is held at a fixed length and performs work when muscle is allowed to shorten. This creates a network of thermodynamic binding pathways that resembles many of the characteristic mechanical and energetic behaviors of muscle including the muscle force-velocity relationship, heat output by shortening muscle, four phases of a muscle tension transient, spontaneous oscillatory contractions, and force redevelopment. Analogous to the thermodynamic (Carnot) cycle for a heat engine, isothermal and adiabatic binding and detachment reactions create a thermodynamic cycle for muscle that resembles cardiac pressure-volume loops (i.e., how the heart works). This paper provides an outline for how to re-interpret muscle mechanic data using thermodynamics - an ongoing effort that will continue providing novel insights into how muscle and molecular motors work.

A chemical thermodynamic model of motor enzymes unifies chemical-Fx and powerstroke models

Molecular motors play a central role in many biological processes, ranging from pumping blood and breathing to growth and wound healing. Through motor-catalyzed chemical reactions, these nanomachines convert the chemical free energy from ATP hydrolysis into two different forms of mechanical work. Motor enzymes perform reversible work, wrev, through an intermediate step in their catalyzed reaction cycle referred to as a working step, and they perform Fx work when they move a distance, x, against a force, F. In a powerstroke model, wrev is performed when the working step stretches a spring within a given motor enzyme. In a chemical-Fx model, wrev is performed in generating a conserved Fx potential defined external to the motor enzyme. It is difficult to find any common ground between these models even though both have been shown to account for mechanochemical measurements of motor enzymes with reasonable accuracy. Here, I show that, by changing one simple assumption in each model, the powerstroke and chemical-Fx model can be reconciled through a chemical thermodynamic model. The formal and experimental justifications for changing these assumptions are presented. The result is a unifying model for mechanochemical coupling in motor enzymes first presented by A.V. Hill in 1938 that is consistent with single-molecule structural and mechanical data.

Velocity of myosin-based actin sliding depends on attachment and detachment kinetics and reaches a maximum when myosin-binding sites on actin saturate

Molecular motors such as kinesin and myosin often work in groups to generate the directed movements and forces critical for many biological processes. Although much is known about how individual motors generate force and movement, surprisingly, little is known about the mechanisms underlying the macroscopic mechanics generated by multiple motors. For example, the observation that a saturating number, N, of myosin heads move an actin filament at a rate that is influenced by actin–myosin attachment and detachment kinetics is accounted for neither experimentally nor theoretically. To better understand the emergent mechanics of actin–myosin mechanochemistry, we use an in vitro motility assay to measure and correlate the N-dependence of actin sliding velocities, actin-activated ATPase activity, force generation against a mechanical load, and the calcium sensitivity of thin filament velocities. Our results show that both velocity and ATPase activity are strain dependent and that velocity becomes maximized with the saturation of myosin-binding sites on actin at a value that is 40% dependent on attachment kinetics and 60% dependent on detachment kinetics. These results support a chemical thermodynamic model for ensemble motor mechanochemistry and imply molecularly explicit mechanisms within this framework, challenging the assumption of independent force generation.

Myosin-based regulation of twitch and tetanic contractions in mammalian skeletal muscle

Time-resolved X-ray diffraction of isolated fast-twitch muscles of mice was used to show how structural changes in the myosin-containing thick filaments contribute to the regulation of muscle contraction, extending the previous focus on regulation by the actin-containing thin filaments. This study shows that muscle activation involves the following sequence of structural changes: thin filament activation, disruption of the helical array of myosin motors characteristic of resting muscle, release of myosin motor domains from the folded conformation on the filament backbone, and actin attachment. Physiological force generation in the 'twitch' response of skeletal muscle to single action potential stimulation is limited by incomplete activation of the thick filament and the rapid inactivation of both filaments. Muscle relaxation after repetitive stimulation is accompanied by a complete recovery of the folded motor conformation on the filament backbone but by incomplete reformation of the helical array, revealing a structural basis for post-tetanic potentiation in isolated muscles.

Orthophosphate increases the efficiency of slow muscle-myosin isoform in the presence of omecamtiv mecarbil

Omecamtiv mecarbil (OM) is a putative positive inotropic tool for treatment of systolic heart dysfunction, based on the finding that in vivo it increases the ejection fraction and in vitro it prolongs the actin-bond life time of the cardiac and slow-skeletal muscle isoforms of myosin. OM action in situ, however, is still poorly understood as the enhanced Ca²⁺-sensitivity of the myofilaments is at odds with the reduction of force and rate of force development observed at saturating Ca²⁺. Here we show, by combining fast sarcomere-level mechanics and ATPase measurements in single slow demembranated fibres from rabbit soleus, that the depressant effect of OM on the force per attached motor is reversed, without effect on the ATPase rate, by physiological concentrations of inorganic phosphate (Pi) (1-10 mM). This mechanism could underpin an energetically efficient reduction of systolic tension cost in OM-treated patients, whenever [Pi] increases with heart-beat frequency.

Omecamtiv mecarbil is a small molecule effector under clinical trial for the treatment of systolic heart failure. Here the authors define the molecular mechanisms of its inotropic action and find it can increase the efficiency of contraction in muscle fibres when the orthophosphate concentration rises with the beat frequency.

Omecamtiv Mecarbil Slows Myosin Kinetics in Skinned Rat Myocardium at Physiological Temperature

Heart failure is a life-threatening condition that occurs when the heart muscle becomes weakened and cannot adequately circulate blood and nutrients around the body. Omecamtiv mecarbil (OM) is a compound that has been developed to treat systolic heart failure via targeting the cardiac myosin heavy chain to increase myocardial contractility. Biophysical and biochemical studies have found that OM increases calcium (Ca²⁺) sensitivity of contraction by prolonging the myosin working stroke and increasing the actin-myosin cross-bridge duty ratio. Most in vitro studies probing the effects of OM on cross-bridge kinetics and muscle force production have been conducted at subphysiological temperature, even though temperature plays a critical role in enzyme activity and cross-bridge function. Herein, we used skinned, ventricular papillary muscle strips from rats to investigate the effects of [OM] on Ca²⁺-activated force production, cross-bridge kinetics, and myocardial viscoelasticity at physiological temperature (37°C). We find that OM only increases myocardial contractility at submaximal Ca²⁺ activation levels and not maximal Ca²⁺ activation levels. As [OM] increased, the kinetic rate constants for cross-bridge recruitment and detachment slowed for both submaximal and maximal Ca²⁺-activated conditions. These findings support a mechanism by which OM increases cardiac contractility at physiological temperature via increasing cross-bridge contributions to thin-filament activation as cross-bridge kinetics slow and the duration of cross-bridge attachment increases. Thus, force only increases at submaximal Ca²⁺ activation due to cooperative recruitment of neighboring cross-bridges, because thin-filament activation is not already saturated. In contrast, OM does not increase myocardial force production for maximal Ca²⁺-activated conditions at physiological temperature because cooperative activation of thin filaments may already be saturated.

Piperine's mitigation of obesity and diabetes can be explained by its up-regulation of the metabolic rate of resting muscle

We identify a target for treating obesity and type 2 diabetes, the consumption of calories by an increase in the metabolic rate of resting skeletal muscle. The metabolic rate of skeletal muscle can be increased by shifting myosin heads from the super-relaxed state (SRX), with a low ATPase activity, to a disordered relaxed state (DRX), with a higher ATPase activity. The shift of myosin heads was detected by a change in fluorescent intensity of a probe attached to the myosin regulatory light chain in skinned skeletal fibers, allowing us to perform a high-throughput screen of 2,128 compounds. The screen identified one compound, which destabilized the super-relaxed state, piperine (the main alkaloid component of black pepper). Destabilization of the SRX by piperine was confirmed by single-nucleotide turnover measurements. The effect was only observed in fast twitch skeletal fibers and not in slow twitch fibers or cardiac tissues. Piperine increased ATPase activity of skinned relaxed fibers by 66 ± 15%. The K_d was ∼2 µM. Piperine had little effect on the mechanics of either fully active or resting muscle fibers. Previous work has shown that piperine can mitigate both obesity and type 2 diabetes in rodent models of these conditions. We propose that the increase in resting muscle metabolism contributes to these positive effects. The results described here show that up-regulation of resting muscle metabolism could treat obesity and type 2 diabetes and that piperine would provide a useful lead compound for the development of these therapies.

Functional Impact of Ryanodine Receptor Oxidation on Intracellular Calcium Regulation in the Heart

Type 2 ryanodine receptor (RyR2) serves as the major intracellular Ca²⁺ release channel that drives heart contraction. RyR2 is activated by cytosolic Ca²⁺ via the process of Ca²⁺-induced Ca²⁺ release (CICR). To ensure stability of Ca²⁺ dynamics, the self-reinforcing CICR must be tightly controlled. Defects in this control cause sarcoplasmic reticulum (SR) Ca²⁺ mishandling, which manifests in a variety of cardiac pathologies that include myocardial infarction and heart failure. These pathologies are also associated with oxidative stress. Given that RyR2 contains a large number of cysteine residues, it is no surprise that RyR2 plays a key role in the cellular response to oxidative stress. RyR's many cysteine residues pose an experimental limitation in defining a specific target or mechanism of action for oxidative stress. As a result, the current understanding of redox-mediated RyR2 dysfunction remains incomplete. Several oxidative modifications, including S-glutathionylation and S-nitrosylation, have been suggested playing an important role in the regulation of RyR2 activity. Moreover, oxidative stress can increase RyR2 activity by forming disulfide bonds between two neighboring subunits (intersubunit cross-linking). Since intersubunit interactions within the RyR2 homotetramer complex dictate the channel gating, such posttranslational modification of RyR2 would have a significant impact on RyR2 function and Ca²⁺ regulation. This review summarizes recent findings on oxidative modifications of RyR2 and discusses contributions of these RyR2 modifications to SR Ca²⁺ mishandling during cardiac pathologies.

Sucrose increases the activation energy barrier for actin-myosin strong binding

To determine the mechanism by which sucrose slows in vitro actin sliding velocities, V, we used stopped flow kinetics and a single molecule binding assay, SiMBA. We observed that in the absence of ATP, sucrose (880mM) slowed the rate of actin-myosin (A-M) strong binding by 71±8% with a smaller inhibitory effect observed on spontaneous rigor dissociation (21±3%). Similarly, in the presence of ATP, sucrose slowed strong binding associated with Pi release by 85±9% with a smaller inhibitory effect on ATP-induced A-M dissociation, kT (39±2%). Sucrose had no noticeable effect on any other step in the ATPase reaction. In SiMBA, sucrose had a relatively small effect on the diffusion coefficient for actin fragments (25±2%), and with stopped flow we showed that sucrose increased the activation energy barrier for A-M strong binding by 37±3%, indicating that sucrose inhibits the rate of A-M strong binding by slowing bond formation more than diffusional searching. The inhibitory effects of sucrose on the rate of A-M rigor binding (71%) are comparable in magnitude to sucrose's effects on both V (79±33% decrease) and maximal actin-activated ATPase, kcat, (81±16% decrease), indicating that the rate of A-M strong bond formation significantly influences both kcat and V.

To understand muscle you must take it apart

Striated muscle is an elegant system for study at many levels. Much has been learned about the mechanism of contraction from studying the mechanical properties of intact and permeabilized (or skinned) muscle fibers. Structural studies using electron microscopy, X-ray diffraction or spectroscopic probes attached to various contractile proteins were possible because of the highly ordered sarcomeric arrangement of actin and myosin. However, to understand the mechanism of force generation at a molecular level, it is necessary to take the system apart and study the interaction of myosin with actin using in vitro assays. This reductionist approach has lead to many fundamental insights into how myosin powers muscle contraction. In addition, nature has provided scientists with an array of muscles with different mechanical properties and with a superfamily of myosin molecules. Taking advantage of this diversity in myosin structure and function has lead to additional insights into common properties of force generation. This review will highlight the development of the major assays and methods that have allowed this combined reductionist and comparative approach to be so fruitful. This review highlights the history of biochemical and biophysical studies of myosin and demonstrates how a broad comparative approach combined with reductionist studies have led to a detailed understanding of how myosin interacts with actin and uses chemical energy to generate force and movement in muscle contraction and motility in general.

ATP turnover by individual myosin molecules hints at two conformers of the myosin active site

Coupling of ATP hydrolysis to structural changes in the motor domain is fundamental to the driving of motile functions by myosins. Current understanding of this chemomechanical coupling is primarily based on ensemble average measurements in solution and muscle fibers. Although important, the averaging could potentially mask essential details of the chemomechanical coupling, particularly for mixed populations of molecules. Here, we demonstrate the potential of studying individual myosin molecules, one by one, for unique insights into established systems and to dissect mixed populations of molecules where separation can be particularly challenging. We measured ATP turnover by individual myosin molecules, monitoring appearance and disappearance of fluorescent spots upon binding/dissociation of a fluorescent nucleotide to/from the active site of myosin. Surprisingly, for all myosins tested, we found two populations of fluorescence lifetimes for individual myosin molecules, suggesting that termination of fluorescence occurred by two different paths, unexpected from standard kinetic schemes of myosin ATPase. In addition, molecules of the same myosin isoform showed substantial intermolecular variability in fluorescence lifetimes. From kinetic modeling of our two fluorescence lifetime populations and earlier solution data, we propose two conformers of the active site of myosin, one that allows the complete ATPase cycle and one that dissociates ATP uncleaved. Statistical analysis and Monte Carlo simulations showed that the intermolecular variability in our studies is essentially due to the stochastic behavior of enzyme kinetics and the limited number of ATP binding events detectable from an individual myosin molecule with little room for static variation among individual molecules, previously described for other enzymes.

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.

Actin Sliding Velocities are Influenced by the Driving Forces of Actin-Myosin Binding

Unloaded shortening speeds, V, of muscle are thought to be limited by actin-bound myosin heads that resist shortening, or V = a·d·τon-1 where τon-1 is the rate at which myosin detaches from actin and d is myosin's step size. The a-term describes the efficiency of force transmission between myosin heads, and has been shown to become less than one at low myosin densities in a motility assay. Molecules such as inorganic phosphate, Pi, and blebbistatin inhibit both V and actin-myosin strong binding kinetics suggesting a link between V and attachment kinetics. To determine whether these small molecules slow V by increasing resistance to actin sliding or by decreasing the efficiency of force transmission, a, we determine how inhibition of V by Pi and blebbistatin changes the force exerted on actin filaments during an in vitro sliding assay, measured from changes in the rate, τbreak-1, at which actin filaments break. Upon addition of 30 mM Pi to a low (30 μM) [ATP] motility buffer V decreased from 1.8 to 1.3 μm·sec-1 and τbreak-1 from 0.029 to 0.018 sec-1. Upon addition of 50 μM blebbistatin to a low [ATP] motility buffer, V decreased from 1.0 to 0.7 μm·sec-1 and τbreak-1 from 0.059 to 0.022 sec-1. These results imply that blebbistatin and Pi slow V by decreasing force transmission, a, not by increasing resistive forces, implying that actin-myosin attachment kinetics influence V.

Molecular machines directly observed by high-speed atomic force microscopy

Molecular machines made of proteins are highly dynamic and carry out sophisticated biological functions. The direct and dynamic high-resolution visualization of molecular machines in action is considered to be the most straightforward approach to understanding how they function but this has long been infeasible until recently. High-speed atomic force microscopy has recently been realized, making such visualization possible. The captured images of myosin V, F1-ATPase, and bacteriorhodopsin have enabled their dynamic processes and structure dynamics to be revealed in great detail, giving unique and deep insights into their functional mechanisms.

Temperature dependent measurements reveal similarities between muscle and non-muscle myosin motility

We examined the temperature dependence of muscle and non-muscle myosin (heavy meromyosin, HMM) with in vitro motility and actin-activated ATPase assays. Our results indicate that myosin V (MV) has a temperature dependence that is similar in both ATPase and motility assays. We demonstrate that skeletal muscle myosin (SK), smooth muscle myosin (SM), and non-muscle myosin IIA (NM) have different temperature dependence in ATPase compared to in vitro motility assays. In the class II myosins we examined (SK, SM, and NM) the rate-limiting step in ATPase assays is thought to be attachment to actin or phosphate release, while for in vitro motility assays it is controversial. In MV the rate-limiting step for both in vitro motility and ATPase assays is known to be ADP release. Consequently, in MV the temperature dependence of the ADP release rate constant is similar to the temperature dependence of in vitro motility. Interestingly, the temperature dependence of the ADP release rate constant of SM and NM was shifted toward the in vitro motility temperature dependence. Our results suggest that the rate-limiting step in SK, SM, and NM may shift from attachment-limited in solution to detachment limited in the in vitro motility assay. Internal strain within the myosin molecule or by neighboring myosin motors may slow ADP release which becomes rate-limiting in the in vitro motility assay. Within this small subset of myosins examined, the in vitro sliding velocity correlates reasonably well with actin-activated ATPase activity, which was suggested by the original study by Barany (J Gen Physiol 50:197-218, 1967).

An integrated in vitro and in situ study of kinetics of myosin II from frog skeletal muscle

A new efficient protocol for extraction and conservation of myosin II from frog skeletal muscle made it possible to preserve the myosin functionality for a week and apply single molecule techniques to the molecular motor that has been best characterized for its mechanical, structural and energetic parameters in situ.With the in vitro motility assay, we estimated the sliding velocity of actin on frog myosin II (VF) and its modulation by pH, myosin density, temperature (range 4-30◦C) and substrate concentration. VF was 8.88 ± 0.26 μms⁻¹ at 30.6◦C and decreased to 1.60 ± 0.09 μms⁻¹ at 4.5◦C. The in vitro mechanical and kinetic parameters were integrated with the in situ parameters of frog muscle myosin working in arrays in each half-sarcomere. By comparing VF with the shortening velocities determined in intact frog muscle fibres under different loads and their dependence on temperature, we found that VF is 40-50% less than the fibre unloaded shortening velocity (V0) at the same temperature and we determined the load that explains the reduced value of VF. With this integrated approach we could define fundamental kinetic steps of the acto-myosin ATPase cycle in situ and their relation with mechanical steps. In particular we found that at 5◦C the rate of ADP release calculated using the step size estimated from in situ experiments accounts for the rate of detachment of motors during steady shortening under low loads.

Switch between large hand-over-hand and small inchworm-like steps in myosin VI

Many biological motor molecules move within cells using stepsizes predictable from their structures. Myosin VI, however, has much larger and more broadly distributed stepsizes than those predicted from its short lever arms. We explain the discrepancy by monitoring Qdots and gold nanoparticles attached to the myosin-VI motor domains using high-sensitivity nanoimaging. The large stepsizes were attributed to an extended and relatively rigid lever arm; their variability to two stepsizes, one large (72 nm) and one small (44 nm). These results suggest that there exist two tilt angles during myosin-VI stepping, which correspond to the pre- and postpowerstroke states and regulate the leading head. The large steps are consistent with the previously reported hand-over-hand mechanism, while the small steps follow an inchworm-like mechanism and increase in frequency with ADP. Switching between these two mechanisms in a strain-sensitive, ADP-dependent manner allows myosin VI to fulfill its multiple cellular tasks including vesicle transport and membrane anchoring.

A metabolite-sensitive, thermodynamically constrained model of cardiac cross-bridge cycling: implications for force development during ischemia

We present a metabolically regulated model of cardiac active force generation with which we investigate the effects of ischemia on maximum force production. Our model, based on a model of cross-bridge kinetics that was developed by others, reproduces many of the observed effects of MgATP, MgADP, Pi, and H(+) on force development while retaining the force/length/Ca(2+) properties of the original model. We introduce three new parameters to account for the competitive binding of H(+) to the Ca(2+) binding site on troponin C and the binding of MgADP within the cross-bridge cycle. These parameters, along with the Pi and H(+) regulatory steps within the cross-bridge cycle, were constrained using data from the literature and validated using a range of metabolic and sinusoidal length perturbation protocols. The placement of the MgADP binding step between two strongly-bound and force-generating states leads to the emergence of an unexpected effect on the force-MgADP curve, where the trend of the relationship (positive or negative) depends on the concentrations of the other metabolites and [H(+)]. The model is used to investigate the sensitivity of maximum force production to changes in metabolite concentrations during the development of ischemia.

Force generation in single conventional actomyosin complexes under high dynamic load

The mechanical load borne by a molecular motor affects its force, sliding distance, and its rate of energy transduction. The control of ATPase activity by the mechanical load on a muscle tunes its efficiency to the immediate task, increasing ATP hydrolysis as the power output increases at forces less than isometric (the Fenn effect) and suppressing ATP hydrolysis when the force is greater than isometric. In this work, we used a novel 'isometric' optical clamp to study the mechanics of myosin II molecules to detect the reaction steps that depend on the dynamic properties of the load. An actin filament suspended between two beads and held in separate optical traps is brought close to a surface that is sparsely coated with motor proteins on pedestals of silica beads. A feedback system increases the effective stiffness of the actin by clamping the force on one of the beads and moving the other bead electrooptically. Forces measured during actomyosin interactions are increased at higher effective stiffness. The results indicate that single myosin molecules transduce energy nearly as efficiently as whole muscle and that the mechanical control of the ATP hydrolysis rate is in part exerted by reversal of the force-generating actomyosin transition under high load without net utilization of ATP.

Does phosphate release limit the ATPases of soleus myofibrils? Evidence that (A)M. ADP.Pi states predominate on the cross-bridge cycle

The ATPases (+/-Ca2+) of myofibrils from rabbit soleus (a slow muscle) and psoas (a fast muscle) have different Ea: -Ca2+, 78 and 60 kJ/mol and +Ca2+, 155 and 71 kJ/mol, respectively. At physiological temperatures, the two types of myofibrillar ATPase are very similar and yet the mechanical properties of the muscles are different (Candau et al. (2003) Biophys J 85: 3132-3141). Muscle contraction relies on specific interactions of the different chemical states on the myosin head ATPase pathway with the thin filament. An explanation for the Ea data is that different states populate the pathways of the two types of myofibril because the rate limiting steps are different. Here, we put this to the test by a comparison of the transient kinetics of the initial steps of the ATPases of the two types of myofibril at 4 degrees C. We used two methods: rapid flow quench ('cold ATP chase': titration of active sites, ATP binding kinetics, k(cat); 'Pi burst': ATP cleavage kinetics) and fluorescence stopped-flow (MDCC-phosphate binding protein for free Pi; myofibrillar tryptophan fluorescence for myosin head-thin filament detachment and ATP cleavage kinetics). We find that, as with psoas myofibrils, the most populated state on the cross-bridge cycle of soleus myofibrils, whether relaxed or activated, is (A)M.ADP.Pi. We propose a reaction pathway that includes several (A)M.ADP.Pi sub-states that are either 'weak' or 'strong', depending on the mechanical condition.

Kinetics of structural changes in the relay loop and SH3 domain of myosin

The intrinsic fluorescence of smooth muscle myosin signals conformational changes associated with different catalytic states of the ATPase cycle. To elucidate this relationship, we have examined the pre-steady-state kinetics of nucleotide binding, hydrolysis, and product release in motor domain-essential light chain mutants containing a single endogenous tryptophan, either residue 512 in the rigid relay loop or residue 29 adjacent to the SH3 domain. The intrinsic fluorescence of W512 is sensitive to both nucleotide binding and hydrolysis, and appears to report structural changes at the active site, presumably through a direct connection with switch II. The intrinsic fluorescence of W29 is sensitive to nucleotide binding but not hydrolysis, and does not appear to be tightly linked with structural changes occurring at the active site. We propose that the SH3 domain may be sensitive to conformational changes in the lever arm through contacts with the essential light chain.

Cross-bridge number, position, and angle in target zones of cryofixed isometrically active insect flight muscle

Electron micrographic tomograms of isometrically active insect flight muscle, freeze substituted after rapid freezing, show binding of single myosin heads at varying angles that is largely restricted to actin target zones every 38.7 nm. To quantify the parameters that govern this pattern, we measured the number and position of attached myosin heads by tracing cross-bridges through the three-dimensional tomogram from their origins on 14.5-nm-spaced shelves along the thick filament to their thin filament attachments in the target zones. The relationship between the probability of cross-bridge formation and axial offset between the shelf and target zone center was well fitted by a Gaussian distribution. One head of each myosin whose origin is close to an actin target zone forms a cross-bridge most of the time. The probability of cross-bridge formation remains high for myosin heads originating within 8 nm axially of the target zone center and is low outside 12 nm. We infer that most target zone cross-bridges are nearly perpendicular to the filaments (60% within 11 degrees ). The results suggest that in isometric contraction, most cross-bridges maintain tension near the beginning of their working stroke at angles near perpendicular to the filament axis. Moreover, in the absence of filament sliding, cross-bridges cannot change tilt angle while attached nor reach other target zones while detached, so may cycle repeatedly on and off the same actin target monomer.

Decavanadate as a biochemical tool in the elucidation of muscle contraction regulation

Recently reported decameric vanadate (V(10)) high affinity binding site in myosin S1, suggests that it can be used as a tool in the muscle contraction regulation. In the present article, it is shown that V(10) species induces myosin S1 cleavage, upon irradiation, at the 23 and 74 kDa sites, the latter being prevented by actin and the former blocked by the presence of ATP. Identical cleavage patterns were found for meta- and decavanadate solutions, indicating that V(10) and tetrameric vanadate (V(4)) have the same binding sites in myosin S1. Concentrations as low as 50 muM decavanadate (5 muM V(10) species) induces 30% of protein cleavage, whereas 500 muM metavanadate is needed to attain the same extent of cleavage. After irradiation, V(10) species is rapidly decomposed, upon protein addition, forming vanadyl (V(4+)) species during the process. It was also observed by NMR line broadening experiments that, V(10) competes with V(4) for the myosin S1 binding sites, having a higher affinity. In addition, V(4) interaction with myosin S1 is highly affected by the products release during ATP hydrolysis in the presence or absence of actin, whereas V(10) appears to be affected at a much lower extent. From these results it is proposed that the binding of vanadate oligomers to myosin S1 at the phosphate loop (23 kDa site) is probably the cause of the actin stimulated myosin ATPase inhibition by the prevention of ATP/ADP exchange, and that this interaction is favoured for higher vanadate anions, such as V(10).

The force exerted by a muscle cross-bridge depends directly on the strength of the actomyosin bond

Myosin produces force in a cyclic interaction, which involves alternate tight binding to actin and to ATP. We have investigated the energetics associated with force production by measuring the force generated by skinned muscle fibers as the strength of the actomyosin bond is changed. We varied the strength of the actomyosin bond by addition of a polymer that promotes protein-protein association or by changing temperature or ionic strength. We estimated the free energy available to generate force by measuring isometric tension, as the free energy of the states that precede the working stroke are lowered with increasing phosphate. We found that the free energy available to generate force and the force per attached cross-bridge at low [Pi] were both proportional to the free energy available from the formation of the actomyosin bond. We conclude that the formation of the actomyosin bond is involved in providing the free energy driving the production of isometric tension and mechanical work. Because the binding of myosin to actin is an endothermic, entropically driven reaction, work must be performed by a "thermal ratchet" in which a thermal fluctuation in Brownian motion is captured by formation of the actomyosin bond.

A one-headed class V myosin molecule develops multiple large (approximately 32-nm) steps successively

Class V myosin (myosin-V) was first found as a processive motor that moves along an actin filament with large ( approximately 36-nm) successive steps and plays an important role in cargo transport in cells. Subsequently, several other myosins have also been found to move processively. Because myosin-V has two heads with ATP- and actin-binding sites, the mechanism of successive movement has been generally explained based on the two-headed structure. However, the fundamental problem of whether the two-headed structure is essential for the successive movement has not been solved. Here, we measure motility of engineered myosin-V having only one head by optical trapping nanometry. The results show that a single one-headed myosin-V undergoes multiple successive large (approximately 32-nm) steps, suggesting that a novel mechanism is operating for successive myosin movement.

At physiological temperatures the ATPase rates of shortening soleus and psoas myofibrils are similar

We obtained the temperature dependences of the adenosine triphosphatase (ATPase) activities (calcium-activated and relaxed) of myofibrils from a slow muscle, which we compared with those from a fast muscle. We chose rabbit soleus and psoas because their myosin heavy chains are almost pure: isoforms I and IIX, respectively. The Arrhenius plots of the ATPases are linear (4-35 degrees C) with energies of activation for soleus myofibrils 155 kJ mol(-1) (activated) and 78 kJ mol(-1) (relaxed). With psoas myofibrils, the energies of activation were 71 kJ mol(-1) (activated) and 60 kJ mol(-1) (relaxed). When extrapolated to 42 degrees C the ATPase rates of the two types of myofibril were identical: 50 s(-1) (activated) and 0.23 s(-1) (relaxed). Whereas with psoas myofibrils the K(m) for adenosine triphosphate (activated ATPase) is relatively insensitive to temperature, that for soleus myofibrils increased from 0.3 microM at 4 degrees C to 66.5 microM at 35 degrees C. Our results illustrate the importance of temperature when comparing the mechanochemical coupling in different types of muscle. We discuss the problem of how to reconcile the similarity of the myofibrillar ATPase rates at physiological temperatures with their different mechanical properties.

Crystallographic findings on the internally uncoupled and near-rigor states of myosin: further insights into the mechanics of the motor

Here we report a 2.3-A crystal structure of scallop myosin S1 complexed with ADP.BeF(x), as well as three additional structures (at 2.8-3.8 A resolution) for this S1 complexed with ATP analogs, some of which are cross-linked by para-phenyl dimaleimide, a short intramolecular cross-linker. In all cases, the complexes are characterized by an unwound SH1 helix first seen in an unusual 2.5-A scallop myosin-MgADP structure and described as corresponding to a previously unrecognized actin-detached internally uncoupled state. The unwinding of the SH1 helix effectively uncouples the converter/lever arm module from the motor and allows cross-linking by para-phenyl dimaleimide, which has been shown to occur only in weak actin-binding states of the molecule. Mutations near the metastable SH1 helix that disable the motor can be accounted for by viewing this structural element as a clutch controlling the transmission of torque to the lever arm. We have also determined a 3.2-A nucleotide-free structure of scallop myosin S1, which suggests that in the near-rigor state there are two conformations in the switch I loop, depending on whether nucleotide is present. Analysis of the subdomain motions in the weak actin-binding states revealed by x-ray crystallography, together with recent electron microscopic results, clarify the mechanical roles of the parts of the motor in the course of the contractile cycle and suggest how strong binding to actin triggers both the power stroke and product release.

Force generation, but not myosin ATPase activity, declines with age in rat muscle fibers

We tested the hypothesis that age-associated decline in muscle function is related to a change in myosin ATPase activity. Single, glycerinated semimembranosus fibers from young (8-12 mo) and aged (32-37 mo) Fischer 344 x Brown Norway male rats were analyzed simultaneously for force and myosin ATPase activity over a range of Ca2+ concentrations. Maximal force generation was ~20% lower in fibers from aged animals (P = 0.02), but myosin ATPase activity was not different between fibers from young and aged rats: 686 +/- 46 (n = 30) and 697 +/- 46 microM/s (n = 33) (P = 0.89). The apparent rate constant for the dissociation of strong-binding myosin from actin was calculated to be ~30% greater in fibers from aged animals (P = 0.03), indicating that the lower force produced by fibers from aged animals is due to a greater flux of myosin heads from the strong-binding state to the weak-binding state during contraction. This is in agreement with our previous electron paramagnetic resonance experiments that showed a reduced fraction of myosin heads in the strong-binding state during a maximal isometric contraction in fibers from older rats.

Characterization of the cross-bridge force-generating step using inorganic phosphate and BDM in myofibrils from rabbit skeletal muscles

The inhibitory effects of inorganic phosphate (P(i)) on isometric force in striated muscle suggest that in the ATPase reaction P(i) release is coupled to force generation. Whether P(i) release and the power stroke are synchronous events or force is generated by an isomerization of the quaternary complex of actomyosin and ATPase products (AM.ADP.P(i)) prior to the following release of P(i) is still controversial. Examination of the dependence of isometric force on [P(i)] in rabbit fast (psoas; 5-15 degrees C) and slow (soleus; 15-20 degrees C) myofibrils was used to test the two-step hypothesis of force generation and P(i) release. Hyperbolic fits of force-[P(i)] relations obtained in fast and slow myofibrils at 15 degrees C produced an apparent asymptote as [P(i)]-->infinity of 0.07 and 0.44 maximal isometric force (i.e. force in the absence of P(i)) in psoas and soleus myofibrils, respectively, with an apparent K(d) of 4.3 mM in both. In each muscle type, the force-[P(i)] relation was independent of temperature. However, 2,3-butanedione 2-monoxime (BDM) decreased the apparent asymptote of force in both muscle types, as expected from its inhibition of the force-generating isomerization. These data lend strong support to models of cross-bridge action in which force is produced by an isomerization of the AM.ADP.P(i) complex immediately preceding the P(i) release step.

The biochemical kinetics underlying actin movement generated by one and many skeletal muscle myosin molecules

To better understand how skeletal muscle myosin molecules move actin filaments, we determine the motion-generating biochemistry of a single myosin molecule and study how it scales with the motion-generating biochemistry of an ensemble of myosin molecules. First, by measuring the effects of various ligands (ATP, ADP, and P(i)) on event lifetimes, tau(on), in a laser trap, we determine the biochemical kinetics underlying the stepwise movement of an actin filament generated by a single myosin molecule. Next, by measuring the effects of these same ligands on actin velocities, V, in an in vitro motility assay, we determine the biochemistry underlying the continuous movement of an actin filament generated by an ensemble of myosin molecules. The observed effects of P(i) on single molecule mechanochemistry indicate that motion generation by a single myosin molecule is closely associated with actin-induced P(i) dissociation. We obtain additional evidence for this relationship by measuring changes in single molecule mechanochemistry caused by a smooth muscle HMM mutation that results in a reduced P(i)-release rate. In contrast, we observe that motion generation by an ensemble of myosin molecules is limited by ATP-induced actin dissociation (i.e., V varies as 1/tau(on)) at low [ATP], but deviates from this relationship at high [ATP]. The single-molecule data uniquely provide a direct measure of the fundamental mechanochemistry of the actomyosin ATPase reaction under a minimal load and serve as a clear basis for a model of ensemble motility in which actin-attached myosin molecules impose a load.

The myosin power stroke

Optical trapping technology now allows investigators in the motility field to measure the forces generated by single motor molecules. A handful of research groups have exploited this approach to further develop our understanding of the actin-based motor, myosin, an ATPase that is capable of converting chemical energy into mechanical work during a cyclical interaction with filamentous actin. In this regard, myosin-II from muscle is the most well-characterized myosin superfamily member. By combining the data obtained from optical trap assays with that from ensemble biochemical and mechanical assays, this review discusses the fundamental properties of the myosin-II power stroke and, perhaps more significantly, how these properties are governed by this molecule's atomic structure and the biochemical transitions that define its catalytic cycle.

Multiple structures of thick filaments in resting cardiac muscle and their influence on cross-bridge interactions

Based on two criteria, the tightness of packing of myosin rods within the backbone of the filament and the degree of order of the myosin heads, thick filaments isolated from a control group of rat hearts had three different structures. Two of the structures of thick filaments had ordered myosin heads and were distinguishable from each other by the difference in tightness of packing of the myosin rods. Depending on the packing, their structure has been called loose or tight. The third structure had narrow shafts and disordered myosin heads extending at different angles from the backbone. This structure has been called disordered. After phosphorylation of myosin-binding protein C (MyBP-C) with protein kinase A (PKA), almost all thick filaments exhibited the loose structure. Transitions from one structure to another in quiescent muscles were produced by changing the concentration of extracellular Ca. The probability of interaction between isolated thick and thin filaments in control, PKA-treated preparations, and preparations exposed to different Ca concentrations was estimated by electron microscopy. Interactions were more frequent with phosphorylated thick filaments having the loose structure than with either the tight or disordered structure. In view of the presence of MgATP and the absence of Ca, the interaction between the myosin heads and the thin filaments was most likely the weak attachment that precedes the force-generating steps in the cross-bridge cycle. These results suggest that phosphorylation of MyBP-C in cardiac thick filaments increases the probability of cross-bridges forming weak attachments to thin filaments in the absence of activation. This mechanism may modulate the number of cross-bridges generating force during activation.

Effects of sarcomere length and temperature on the rate of ATP utilisation by rabbit psoas muscle fibres

1. The steady state rate of ATP utilisation by single permeabilised fibres from rabbit psoas muscle immersed in silicone oil was measured using a linked enzyme assay that coupled ADP production to the oxidation of NADH.2. At sarcomere length 2.5 microm, at 10 degrees C, the rate of ATP utilisation in relaxing conditions was 6 +/- 1 microM s-1 (mean +/- S.E.M., n = 8 fibres); during isometric contraction it was 310 +/- 10 microM s-1 (mean +/- S.E.M., n = 11). Assuming a myosin active site concentration of 150 microM, these values correspond to rates of ATP utilisation per active site of about 0.04 and 2.1 s-1, respectively. 3. The rate of ATP utilisation in relaxing conditions was independent of sarcomere length in the range 2.5-4.0 microm. The rate of ATP utilisation during isometric contraction had a dependence on resting sarcomere length similar to that of isometric force in the range 2.5-4.0 microm, but was less strongly dependent on sarcomere length than was isometric force in the range 1.5-2.5 microm. 4. The rate of ATP utilisation in relaxing conditions had a Q10 of 2.5 in the temperature range 7-25 degrees C, but this increased to 9.7 in the range 25-35 degrees C, suggesting that some active force may have been generated in relaxing solution at temperatures above 25 degrees C. 5. The rate of ATP utilisation during isometric contraction had a Q10 of 3.6 throughout the temperature range 7-25 degrees C; this was similar to the Q10 for isometric force at low temperature (3.5 at 7-10 degrees C) but much larger than that for isometric force at higher temperature (1.3 at 20-25 degrees C). 6. Application of the NADH-linked assay to single muscle fibres in oil improves the effective sensitivity and time resolution of the method, and allows continuous measurements of the rate of ADP production during active contraction.

ATP-induced transconformation of myosin revealed by determining three-dimensional positions of fluorophores from fluorescence energy transfer measurements

The method of fluorescence resonance energy transfer (FRET) is one of the most important techniques for measuring the distance between two fluorophores and for detecting the changes in protein structure under physiological conditions. The use of green fluorescent protein is also a powerful technology that has been used to elucidate dynamic molecular events. From these we have developed a novel method to determine the three-dimensional positions of fluorophores by combining the FRET data and other structural information available. Using this method, we could determine the ATP-induced changes of three-dimensional structure of truncated Dictyostelium myosin in solution. The myosin structure with ADP in solution was found to be similar to that of the crystal structure of MgADPBeFx-bound truncated Dictyostelium myosin (type I structure), whereas myosin with ATP in solution was similar to the crystal structure of MgAdPVi-bound one (type II structure). However, the crystal structure of MgADP-bound scallop myosin (type III structure) could not be explained by any of our FRET data under various conditions. This indicates that the type III crystal structure might represent a transient intermediate conformation that could not be detected using fluorescence energy transfer.

ATP consumption and efficiency of human single muscle fibers with different myosin isoform composition

Chemomechanical transduction was studied in single fibers isolated from human skeletal muscle containing different myosin isoforms. Permeabilized fibers were activated by laser-pulse photolytic release of 1.5 mM ATP from p(3)-1-(2-nitrophenyl)ethylester of ATP. The ATP hydrolysis rate in the muscle fibers was determined with a fluorescently labeled phosphate-binding protein. The effects of varying load and shortening velocity during contraction were investigated. The myosin isoform composition was determined in each fiber by sodium dodecyl sulfate-polyacrylamide gel electrophoresis. At 12 degrees C large variations (three- to fourfold) were found between slow and fast (2A and 2A-2B) fibers in their maximum shortening velocity, peak power output, velocity at which peak power is produced, isometric ATPase activity, and tension cost. Isometric tension was similar in all fiber groups. The ATP consumption rate increased during shortening in proportion to shortening velocity. At 12 degrees C the maximum efficiency was similar (0.21-0.27) for all fiber types and was reached at a higher speed of shortening for the faster fibers. In all fibers, peak efficiency increased to approximately 0.4 when the temperature was raised from 12 degrees C to 20 degrees C. The results were simulated with a kinetic scheme describing the ATPase cycle, in which the rate constant controlling ADP release is sensitive to the load on the muscle. The main difference between slow and fast fibers was reproduced by increasing the rate constant for the hydrolysis step, which was rate limiting at low loads. Simulation of the effect of increasing temperature required an increase in the force per cross-bridge and an acceleration of the rate constants in the reaction pathway.

Characterization of single actomyosin rigor bonds: load dependence of lifetime and mechanical properties

Load dependence of the lifetime of the rigor bonds formed between a single myosin molecule (either heavy meromyosin, HMM, or myosin subfragment-1, S1) and actin filament was examined in the absence of nucleotide by pulling the barbed end of the actin filament with optical tweezers. For S1, the relationship between the lifetime (tau) and the externally imposed load (F) at absolute temperature T could be expressed as tau(F) = tau(0).exp(-F.d/k(B)T) with tau(0) of 67 s and an apparent interaction distance d of 2.4 nm (k(B) is the Boltzmann constant). The relationship for HMM was expressed by the sum of two exponentials, with two sets of tau(0) and d being, respectively, 62 s and 2.7 nm, and 950 s and 1.4 nm. The fast component of HMM coincides with tau(F) for S1, suggesting that the fast component corresponds to single-headed binding and the slow component to double-headed binding. These large interaction distances, which may be a common characteristic of motor proteins, are attributed to the geometry for applying an external load. The pulling experiment has also allowed direct estimation of the number of myosin molecules interacting with an actin filament. Actin filaments tethered to a single HMM molecule underwent extensive rotational Brownian motion, indicating a low torsional stiffness for HMM. From these results, we discuss the characteristics of interaction between actin and myosin, with the focus on the manner of binding of myosin.

The effect of inorganic phosphate on force generation in single myofibrils from rabbit skeletal muscle

In striated muscle, force generation and phosphate (P(i)) release are closely related. Alterations in the [P(i)] bathing skinned fibers have been used to probe key transitions of the mechanochemical coupling. Accuracy in this kind of studies is reduced, however, by diffusional barriers. A new perfusion technique is used to study the effect of [P(i)] in single or very thin bundles (1-3 microM in diameter; 5 degrees C) of rabbit psoas myofibrils. With this technique, it is possible to rapidly jump [P(i)] during contraction and observe the transient and steady-state effects on force of both an increase and a decrease in [P(i)]. Steady-state isometric force decreases linearly with an increase in log[P(i)] in the range 500 microM to 10 mM (slope -0.4/decade). Between 5 and 200 microM P(i), the slope of the relation is smaller ( approximately -0.07/decade). The rate constant of force development (k(TR)) increases with an increase in [P(i)] over the same concentration range. After rapid jumps in [P(i)], the kinetics of both the force decrease with an increase in [P(i)] (k(Pi(+))) and the force increase with a decrease in [P(i)] (k(Pi(-))) were measured. As observed in skinned fibers with caged P(i), k(Pi(+)) is about three to four times higher than k(TR), strongly dependent on final [P(i)], and scarcely modulated by the activation level. Unexpectedly, the kinetics of force increase after jumps from high to low [P(i)] is slower: k(Pi(-)) is indistinguishable from k(TR) measured at the same [P(i)] and has the same calcium sensitivity.

Vanadate oligomer interactions with myosin

'Monovanadate' containing a mixture of at least four different vanadate species and 'decavanadate' containing apparently only two vanadate species, mainly decameric species, inhibit myosin and actomyosin ATPase activities. The addition of myosin to 'monovanadate' and 'decavanadate' solutions promotes differential increases on the 51V NMR spectral linewidths of vanadate oligomers. The relative order of line broadening upon myosin addition, reflecting the interaction of the vanadate oligomers with the protein, was V10 > V4 > V1 = 1, whereas no changes were observed for monomeric vanadate species. It is concluded that decameric and tetrameric vanadate species interact quite potently with the protein and affect myosin as well actomyosin ATPase activities.

Variable surface loops and myosin activity: accessories to a motor

The catalytic head of myosin is a globular structure that has historically been divided into three segments of 25, 50, and 20 kDa. The solvent-exposed, proteolytically-sensitive surface loops of myosin that join these three segments are highly variable in their sequences. While surface loops have not traditionally been thought to affect enzymatic activities, these loops lie near the ATP and actin-binding sites and have been implicated in the modulation of myosin's kinetic activities. In this work we review the wealth of data regarding the loops that has accumulated over the years and discuss the roles of the loops in contributing to the different activities displayed by different myosin isoforms.

The effect of polyethylene glycol on the mechanics and ATPase activity of active muscle fibers

We have used polyethylene glycol (PEG) to perturb the actomyosin interaction in active skinned muscle fibers. PEG is known to potentiate protein-protein interactions, including the binding of myosin to actin. The addition of 5% w/v PEG (MW 300 or 4000) to active fibers increased fiber tension and decreased shortening velocity and ATPase activity, all by 25-40%. Variation in [ADP] or [ATP] showed that the addition of PEG had little effect on the dissociation of the cross-bridge at the end of the power stroke. Myosin complexed with ADP and the phosphate analog V(i) or AlF(4) binds weakly to actin and is an analog of a pre-power-stroke state. PEG substantially enhances binding of these states both in active fibers and in solution. Titration of force with increasing [P(i)] showed that PEG increased the free energy available to drive the power stroke by about the same amount as it increased the free energy available from the formation of the actomyosin bond. Thus PEG potentiates the binding of myosin to actin in active fibers, and it provides a method for enhancing populations of some states for structural or mechanical studies, particularly those of the normally weakly bound transient states that precede the power stroke.

X-ray structures of the Dictyostelium discoideum myosin motor domain with six non-nucleotide analogs

The three-dimensional structures of the truncated myosin head from Dictyostelium discoideum myosin II complexed with dinitrophenylaminoethyl-, dinitrophenylaminopropyl-, o-nitrophenylaminoethyl-, m-nitrophenylaminoethyl-, p-nitrophenylaminoethyl-, and o-nitrophenyl-N-methyl-aminoethyl-diphosphate.beryllium fluoride have been determined to better than 2.3-A resolution. The structure of the protein and nucleotide binding pocket in these complexes is very similar to that of S1dC.ADP.BeF(x) (Fisher, A. J., Smith, C. A., Thoden, J., Smith, R., Sutoh, K., Holden, H. M., and Rayment, I. (1995) Biochemistry 34, 8960-8972). The position of the triphosphate-like moiety is essentially identical in all complexes. Furthermore, the alkyl-amino group plays the same role as the ribose by linking the triphosphate to the adenine binding pocket; however, none of the phenyl groups lie in the same position as adenine in S1dC.MgADP.BeF(x), even though several of these nucleotide analogs are functionally equivalent to ATP. Rather the former location of adenine is occupied by water in the nanolog complexes, and the phenyl groups are organized in a manner that attempts to optimize their hydrogen bonding interactions with this constellation of solvent molecules. A comparison of the kinetic and structural properties of the nanologs relative to ATP suggests that the ability of a substrate to sustain tension and to generate movement correlates with a well defined interaction with the active site water structure observed in S1dC.MgADP.BeF(x).