An accelerated state of myosin-based actin motility

The Problem with Inventing Molecular Mechanisms to Fit Thermodynamic Equations of Muscle

Almost every model of muscle contraction in the literature to date is a molecular power stroke model, even though this corpuscular mechanism is opposed by centuries of science, by 85 years of unrefuted evidence that muscle is a thermodynamic system, and by a quarter century of direct observations that the molecular mechanism of muscle contraction is a molecular switch, not a molecular power stroke. An ensemble of molecular switches is a binary mechanical thermodynamic system from which A.V. Hill's muscle force-velocity relationship is directly derived, where Hill's parameter a is the internal force against which unloaded muscle shortens, and Hill's parameter b is the product of the switch displacement, d, and the actin-myosin ATPase rate. Ignoring this model and the centuries of thermodynamics that preceded it, corpuscularians continue to develop molecular power stroke models, adding to their 65-year jumble of "new", "innovative", and "unconventional" molecular mechanisms for Hill's a and b parameters, none of which resemble the underlying physical chemistry. Remarkably, the corpuscularian community holds the thermodynamicist to account for these discrepancies, which, as outlined here, I have done for 25 years. It is long past time for corpuscularians to be held accountable for their mechanisms, which by all accounts have no foundation in science. The stakes are high. Molecular power stroke models are widely used in research and in clinical decision-making and have, for over half a century, muddied our understanding of the inner workings of one of the most efficient and clean-burning machines on the planet. It is problematic that corpuscularians present these models to stakeholders as science when in fact corpuscularians have been actively defending these models against science for decades. The path forward for scientists is to stop baseless rejections of muscle thermodynamics and to begin testing corpuscular and thermodynamic mechanisms with the goal of disproving one or the other of these hypotheses.

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.

Myosin II Adjusts Motility Properties and Regulates Force Production Based on Motor Environment

Introduction

Myosin II has been investigated with optical trapping, but single motor-filament assay arrangements are not reflective of the complex cellular environment. To understand how myosin interactions propagate up in scale to accomplish system force generation, we devised a novel actomyosin ensemble optical trapping assay that reflects the hierarchy and compliancy of a physiological environment and is modular for interrogating force effectors.

Methods

Hierarchical actomyosin bundles were formed in vitro. Fluorescent template and cargo actin filaments (AF) were assembled in a flow cell and bundled by myosin. Beads were added in the presence of ATP to bind the cargo AF and activate myosin force generation to be measured by optical tweezers.

Results

Three force profiles resulted across a range of myosin concentrations: high force with a ramp-plateau, moderate force with sawtooth movement, and baseline. The three force profiles, as well as high force output, were recovered even at low solution concentration, suggesting that myosins self-optimize within AFs. Individual myosin steps were detected in the ensemble traces, indicating motors are taking one step at a time while others remain engaged in order to sustain productive force generation.

Conclusions

Motor communication and system compliancy are significant contributors to force output. Environmental conditions, motors taking individual steps to sustain force, the ability to backslip, and non-linear concentration dependence of force indicate that the actomyosin system contains a force-feedback mechanism that senses the local cytoskeletal environment and communicates to the individual motors whether to be in a high or low duty ratio mode.

Supplementary Information

The online version contains supplementary material available at 10.1007/s12195-022-00731-1.

Myosin essential light chain 1sa decelerates actin and thin filament gliding on β-myosin molecules

The β-myosin heavy chain expressed in ventricular myocardium and the myosin heavy chain (MyHC) in slow-twitch skeletal Musculus soleus (M. soleus) type-I fibers are both encoded by MYH7. Thus, these myosin molecules are deemed equivalent. However, some reports suggested variations in the light chain composition between M. soleus and ventricular myosin, which could influence functional parameters, such as maximum velocity of shortening. To test for functional differences of the actin gliding velocity on immobilized myosin molecules, we made use of in vitro motility assays. We found that ventricular myosin moved actin filaments with ∼0.9 µm/s significantly faster than M. soleus myosin (0.3 µm/s). Filaments prepared from isolated actin are not the native interaction partner of myosin and are believed to slow down movement. Yet, using native thin filaments purified from M. soleus or ventricular tissue, the gliding velocity of M. soleus and ventricular myosin remained significantly different. When comparing the light chain composition of ventricular and M. soleus β-myosin, a difference became evident. M. soleus myosin contains not only the "ventricular" essential light chain (ELC) MLC1sb/v, but also an additional longer and more positively charged MLC1sa. Moreover, we revealed that on a single muscle fiber level, a higher relative content of MLC1sa was associated with significantly slower actin gliding. We conclude that the ELC MLC1sa decelerates gliding velocity presumably by a decreased dissociation rate from actin associated with a higher actin affinity compared to MLC1sb/v. Such ELC/actin interactions might also be relevant in vivo as differences between M. soleus and ventricular myosin persisted when native thin filaments were used.

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.

Evidence for S2 flexibility by direct visualization of quantum dot-labeled myosin heads and rods within smooth muscle myosin filaments moving on actin in vitro

Myosins in muscle assemble into filaments by interactions between the C-terminal light meromyosin (LMM) subdomains of the coiled-coil rod domain. The two head domains are connected to LMM by the subfragment-2 (S2) subdomain of the rod. Our mixed kinetic model predicts that the flexibility and length of S2 that can be pulled away from the filament affects the maximum distance working heads can move a filament unimpeded by actin-attached heads. It also suggests that it should be possible to observe a head remain stationary relative to the filament backbone while bound to actin (dwell), followed immediately by a measurable jump upon detachment to regain the backbone trajectory. We tested these predictions by observing filaments moving along actin at varying ATP using TIRF microscopy. We simultaneously tracked two different color quantum dots (QDs), one attached to a regulatory light chain on the lever arm and the other attached to an LMM in the filament backbone. We identified events (dwells followed by jumps) by comparing the trajectories of the QDs. The average dwell times were consistent with known kinetics of the actomyosin system, and the distribution of the waiting time between observed events was consistent with a Poisson process and the expected ATPase rate. Geometric constraints suggest a maximum of ∼26 nm of S2 can be unzipped from the filament, presumably involving disruption in the coiled-coil S2, a result consistent with observations by others of S2 protruding from the filament in muscle. We propose that sufficient force is available from the working heads in the filament to overcome the stiffness imposed by filament-S2 interactions.

S-Nitrosoglutathione Reductase Underlies the Dysfunctional Relaxation to Nitric Oxide in Preterm Labor

Tocolytics show limited efficacy to prevent preterm delivery. In uterine smooth muscle cGMP accumulation following addition of nitric oxide (NO) has little effect on relaxation suggesting a role for protein S-nitrosation. In human myometrial tissues from women in labor at term (TL), or spontaneously in labor preterm (sPTL), direct stimulation of soluble guanylyl cyclase (sGC) fails to relax myometrium, while the same treatment relaxes vascular smooth muscle completely. Unlike term myometrium, effects of NO are not only blunted in sPTL, but global protein S-nitrosation is also diminished, suggesting a dysfunctional response to NO-mediated protein S-nitrosation. Examination of the enzymatic regulator of endogenous S-nitrosoglutathione availability, S-nitrosoglutathione reductase, reveals increased expression of the reductase in preterm myometrium associated with decreased total protein S-nitrosation. Blockade of S-nitrosoglutathione reductase relaxes sPTL tissue. Addition of NO donor to the actin motility assay attenuates force. Failure of sGC activation to mediate relaxation in sPTL tissues, together with the ability of NO to relax TL, but not sPTL myometrium, suggests a unique pathway for NO-mediated relaxation in myometrium. Our results suggest that examining the action of S-nitrosation on critical contraction associated proteins central to the regulation of uterine smooth muscle contraction can reveal new tocolytic targets.

A mixed-kinetic model describes unloaded velocities of smooth, skeletal, and cardiac muscle myosin filaments in vitro

In vitro motility assays, where purified myosin and actin move relative to one another, are used to better understand the mechanochemistry of the actomyosin adenosine triphosphatase (ATPase) cycle. We examined the relationship between the relative velocity (V) of actin and myosin and the number of available myosin heads (N) or [ATP] for smooth (SMM), skeletal (SKM), and cardiac (CMM) muscle myosin filaments moving over actin as well as V from actin filaments moving over a bed of monomeric SKM. These data do not fit well to a widely accepted model that predicts that V is limited by myosin detachment from actin (d/t_on), where d equals step size and t_on equals time a myosin head remains attached to actin. To account for these data, we have developed a mixed-kinetic model where V is influenced by both attachment and detachment kinetics. The relative contributions at a given V vary with the probability that a head will remain attached to actin long enough to reach the end of its flexible S2 tether. Detachment kinetics are affected by L/t_on, where L is related to the tether length. We show that L is relatively long for SMM, SKM, and CMM filaments (59 ± 3 nm, 22 ± 9 nm, and 22 ± 2 nm, respectively). In contrast, L is shorter (8 ± 3 nm) when myosin monomers are attached to a surface. This suggests that the behavior of the S2 domain may be an important mechanical feature of myosin filaments that influences unloaded shortening velocities of muscle.

Myosin-Induced Gliding Patterns at Varied [MgATP] Unveil a Dynamic Actin Filament

Actin filaments have key roles in cell motility but are generally claimed to be passive interaction partners in actin-myosin-based motion generation. Here, we present evidence against this static view based on an altered myosin-induced actin filament gliding pattern in an in vitro motility assay at varied [MgATP]. The statistics that characterize the degree of meandering of the actin filament paths suggest that for [MgATP] ≥ 0.25 mM, the flexural rigidity of heavy meromyosin (HMM)-propelled actin filaments is similar (without phalloidin) or slightly lower (with phalloidin) than that of HMM-free filaments observed in solution without surface tethering. When [MgATP] was reduced to ≤0.1 mM, the actin filament paths in the in vitro motility assay became appreciably more winding in both the presence and absence of phalloidin. This effect of lowered [MgATP] was qualitatively different from that seen when HMM was mixed with ATP-insensitive, N-ethylmaleimide-treated HMM (NEM-HMM; 25-30%). In particular, the addition of NEM-HMM increased a non-Gaussian tail in the path curvature distribution as well as the number of events in which different parts of an actin filament followed different paths. These effects were the opposite of those observed with reduced [MgATP]. Theoretical modeling suggests a 30-40% lowered flexural rigidity of the actin filaments at [MgATP] ≤ 0.1 mM and local bending of the filament front upon each myosin head attachment. Overall, the results fit with appreciable structural changes in the actin filament during actomyosin-based motion generation, and modulation of the actin filament mechanical properties by the dominating chemomechanical actomyosin state.

Maximum limit to the number of myosin II motors participating in processive sliding of actin

In this work, we analysed processive sliding and breakage of actin filaments at various heavy meromyosin (HMM) densities and ATP concentrations in IVMA. We observed that with addition of ATP solution, the actin filaments fragmented stochastically; we then determined mean length and velocity of surviving actin filaments post breakage. Average filament length decreased with increase in HMM density at constant ATP, and increased with increase in ATP concentration at constant HMM density. Using density of HMM molecules and length of actin, we estimated the number of HMM molecules per actin filament (N) that participate in processive sliding of actin. N is solely a function of ATP concentration: 88 ± 24 and 54 ± 22 HMM molecules (mean ± S.D.) at 2 mM and 0.1 mM ATP respectively. Processive sliding of actin filament was observed only when N lay within a minimum lower limit (Nmin) and a maximum upper limit (Nmax) to the number of HMM molecules. When N < Nmin the actin filament diffused away from the surface and processivity was lost and when N > Nmax the filament underwent breakage eventually and could not sustain processive sliding. We postulate this maximum upper limit arises due to increased number of strongly bound myosin heads.

Statistical mechanics of the Huxley-Simmons model

The chemomechanical model of Huxley and Simmons (HS) [A. F. Huxley and R. M. Simmons, Nature 233, 533 (1971)NATUAS0028-083610.1038/233533a0] provides a paradigmatic description of mechanically induced collective conformational changes relevant in a variety of biological contexts, from muscles power stroke and hair cell gating to integrin binding and hairpin unzipping. We develop a statistical mechanical perspective on the HS model by exploiting a formal analogy with a paramagnetic Ising model. We first study the equilibrium HS model with a finite number of elements and compute explicitly its mechanical and thermal properties. To model kinetics, we derive a master equation and solve it for several loading protocols. The developed formalism is applicable to a broad range of allosteric systems with mean-field interactions.

Mechanics of Vascular Smooth Muscle

Vascular smooth muscle (VSM; see Table 1 for a list of abbreviations) is a heterogeneous biomaterial comprised of cells and extracellular matrix. By surrounding tubes of endothelial cells, VSM forms a regulated network, the vasculature, through which oxygenated blood supplies specialized organs, permitting the development of large multicellular organisms. VSM cells, the engine of the vasculature, house a set of regulated nanomotors that permit rapid stress-development, sustained stress-maintenance and vessel constriction. Viscoelastic materials within, surrounding and attached to VSM cells, comprised largely of polymeric proteins with complex mechanical characteristics, assist the engine with countering loads imposed by the heart pump, and with control of relengthening after constriction. The complexity of this smart material can be reduced by classical mechanical studies combined with circuit modeling using spring and dashpot elements. Evaluation of the mechanical characteristics of VSM requires a more complete understanding of the mechanics and regulation of its biochemical parts, and ultimately, an understanding of how these parts work together to form the machinery of the vascular tree. Current molecular studies provide detailed mechanical data about single polymeric molecules, revealing viscoelasticity and plasticity at the protein domain level, the unique biological slip-catch bond, and a regulated two-step actomyosin power stroke. At the tissue level, new insight into acutely dynamic stress-strain behavior reveals smooth muscle to exhibit adaptive plasticity. At its core, physiology aims to describe the complex interactions of molecular systems, clarifying structure-function relationships and regulation of biological machines. The intent of this review is to provide a comprehensive presentation of one biomachine, VSM.

Phosphate and ADP differently inhibit coordinated smooth muscle myosin groups

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

Velocities of unloaded muscle filaments are not limited by drag forces imposed by myosin cross-bridges

It is not known which kinetic step in the acto-myosin ATPase cycle limits contraction speed in unloaded muscles (V0). Huxley's 1957 model [Huxley AF (1957) Prog Biophys Biophys Chem 7:255-318] predicts that V0 is limited by the rate that myosin detaches from actin. However, this does not explain why, as observed by Bárány [Bárány M (1967) J Gen Physiol 50(6, Suppl):197-218], V0 is linearly correlated with the maximal actin-activated ATPase rate (vmax), which is limited by the rate that myosin attaches strongly to actin. We have observed smooth muscle myosin filaments of different length and head number (N) moving over surface-attached F-actin in vitro. Fitting filament velocities (V) vs. N to a detachment-limited model using the myosin step size d=8 nm gave an ADP release rate 8.5-fold faster and ton (myosin's attached time) and r (duty ratio) ∼10-fold lower than previously reported. In contrast, these data were accurately fit to an attachment-limited model, V=N·v·d, over the range of N found in all muscle types. At nonphysiologically high N, V=L/ton rather than d/ton, where L is related to the length of myosin's subfragment 2. The attachment-limited model also fit well to the [ATP] dependence of V for myosin-rod cofilaments at three fixed N. Previously published V0 vs. vmax values for 24 different muscles were accurately fit to the attachment-limited model using widely accepted values for r and N, giving d=11.1 nm. Therefore, in contrast with Huxley's model, we conclude that V0 is limited by the actin-myosin attachment rate.

The kinetics underlying the velocity of smooth muscle myosin filament sliding on actin filaments in vitro

Actin-myosin interactions are well studied using soluble myosin fragments, but little is known about effects of myosin filament structure on mechanochemistry. We stabilized unphosphorylated smooth muscle myosin (SMM) and phosphorylated smooth muscle myosin (pSMM) filaments against ATP-induced depolymerization using a cross-linker and attached fluorescent rhodamine (XL-Rh-SMM). Electron micrographs showed that these side polar filaments are very similar to unmodified filaments. They are ~0.63 μm long and contain ~176 molecules. Rate constants for ATP-induced dissociation and ADP release from acto-myosin for filaments and S1 heads were similar. Actin-activated ATPases of SMM and XL-Rh-SMM were similarly regulated. XL-Rh-pSMM filaments moved processively on F-actin that was bound to a PEG brush surface. ATP dependence of filament velocities was similar to that for solution ATPases at high [actin], suggesting that both processes are limited by the same kinetic step (weak to strong transition) and therefore are attachment- limited. This differs from actin sliding over myosin monomers, which is primarily detachment-limited. Fitting filament data to an attachment-limited model showed that approximately half of the heads are available to move the filament, consistent with a side polar structure. We suggest the low stiffness subfragment 2 (S2) domain remains unhindered during filament motion in our assay. Actin-bound negatively displaced heads will impart minimal drag force because of S2 buckling. Given the ADP release rate, the velocity, and the length of S2, these heads will detach from actin before slack is taken up into a backwardly displaced high stiffness position. This mechanism explains the lack of detachment- limited kinetics at physiological [ATP]. These findings address how nonlinear elasticity in assemblies of motors leads to efficient collective force generation.

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

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

Skeletal muscle myofilament adaptations to aging, disease, and disuse and their effects on whole muscle performance in older adult humans

Skeletal muscle contractile function declines with aging, disease, and disuse. In vivo muscle contractile function depends on a variety of factors, but force, contractile velocity and power generating capacity ultimately derive from the summed contribution of single muscle fibers. The contractile performance of these fibers are, in turn, dependent upon the isoform and function of myofilament proteins they express, with myosin protein expression and its mechanical and kinetic characteristics playing a predominant role. Alterations in myofilament protein biology, therefore, may contribute to the development of functional limitations and disability in these conditions. Recent studies suggest that these conditions are associated with altered single fiber performance due to decreased expression of myofilament proteins and/or changes in myosin-actin cross-bridge interactions. Furthermore, cellular and myofilament-level adaptations are related to diminished whole muscle and whole body performance. Notably, the effect of these various conditions on myofilament and single fiber function tends to be larger in older women compared to older men, which may partially contribute to their higher rates of disability. To maintain functionality and provide the most appropriate and effective countermeasures to aging, disease, and disuse in both sexes, a more thorough understanding is needed of the contribution of myofilament adaptations to functional disability in older men and women and their contribution to tissue level function and mobility impairment.

Hypertrophic cardiomyopathy associated Lys104Glu mutation in the myosin regulatory light chain causes diastolic disturbance in mice

We have examined, for the first time, the effects of the familial hypertrophic cardiomyopathy (HCM)-associated Lys104Glu mutation in the myosin regulatory light chain (RLC). Transgenic mice expressing the Lys104Glu substitution (Tg-MUT) were generated and the results were compared to Tg-WT (wild-type human ventricular RLC) mice. Echocardiography with pulse wave Doppler in 6month-old Tg-MUT showed early signs of diastolic disturbance with significantly reduced E/A transmitral velocities ratio. Invasive hemodynamics in 6month-old Tg-MUT mice also demonstrated a borderline significant prolonged isovolumic relaxation time (Tau) and a tendency for slower rate of pressure decline, suggesting alterations in diastolic function in Tg-MUT. Six month-old mutant animals had no LV hypertrophy; however, at >13months they displayed significant hypertrophy and fibrosis. In skinned papillary muscles from 5 to 6month-old mice a mutation induced reduction in maximal tension and slower muscle relaxation rates were observed. Mutated cross-bridges showed increased rates of binding to the thin filaments and a faster rate of the power stroke. In addition, ~2-fold lower level of RLC phosphorylation was observed in the mutant compared to Tg-WT. In line with the higher mitochondrial content seen in Tg-MUT hearts, the MUT-myosin ATPase activity was significantly higher than WT-myosin, indicating increased energy consumption. In the in vitro motility assay, MUT-myosin produced higher actin sliding velocity under zero load, but the velocity drastically decreased with applied load in the MUT vs. WT myosin. Our results suggest that diastolic disturbance (impaired muscle relaxation, lower E/A) and inefficiency of energy use (reduced contractile force and faster ATP consumption) may underlie the Lys104Glu-mediated HCM phenotype.

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

Elevated levels of phosphate (Pi) reduce isometric force, providing support for the notion that the release of Pi from myosin is closely associated with the generation of muscular force. Pi is thought to rebind to actomyosin in an ADP-bound state and reverse the force-generating steps, including the rotation of the lever arm (i.e., the powerstroke). Despite extensive study, this mechanism remains controversial, in part because it fails to explain the effects of Pi on isometric ATPase and unloaded shortening velocity. To gain new insight into this process, we determined the effect of Pi on the force-generating capacity of a small ensemble of myosin (∼12 myosin heads) using a three-bead laser trap assay. In the absence of Pi, myosin pulled the actin filament out of the laser trap an average distance of 54 ± 4 nm, translating into an average peak force of 1.2 pN. By contrast, in the presence of 30 mM Pi, myosin generated only enough force to displace the actin filament by 13 ± 1 nm, generating just 0.2 pN of force. The elevated Pi also caused a >65% reduction in binding-event lifetime, suggesting that Pi induces premature detachment from a strongly bound state. Definitive evidence of a Pi-induced powerstroke reversal was not observed, therefore we determined if a branched kinetic model in which Pi induces detachment from a strongly bound, postpowerstroke state could explain these observations. The model was able to accurately reproduce not only the data presented here, but also the effects of Pi on both isometric ATPase in muscle fibers and actin filament velocity in a motility assay. The ability of the model to capture the findings presented here as well as previous findings suggests that Pi-induced inhibition of force may proceed along a kinetic pathway different from that of force generation.

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.

Loop 2 of myosin is a force-dependent inhibitor of the rigor bond

Myosin's actin-binding loop (loop 2) carries a charge opposite to that of its binding site on actin and is thought to play an important role in ionic interactions between the two molecules during the initial binding step. However, no subsequent role has been identified for loop 2 in actin-myosin binding. We used an optical trap to measure bond formation and bond rupture between actin and rigor heavy meromyosin when loaded perpendicular to the filament axis. We studied HMM with intact or proteolytically cleaved loop 2 at low and physiologic ionic strength. Here we show that the presence of intact loop 2 allows actomyosin bonds to form quickly and that they do so in a short-lived bound state. Increasing tensile load causes the transition to a long-lived state-the distinguishing behavior of a catch bond. When loop 2 was cleaved catch bond behavior was abrogated leaving only a long-lived state. These data suggest that in addition to its role in locating binding sites on actin, loop 2 is also a force-dependent inhibitor of the long-lived actomyosin complex. This may be important for reducing the duty ratio and increasing the shortening velocity of actomyosin at low forces.

Myofilament protein alterations promote physical disability in aging and disease

Skeletal muscle contractile function declines with age and age-associated diseases. Although muscle atrophy undoubtedly contributes to this decrease, recent findings suggest that reduced myofilament protein content and function also may participate. Based on these data, we propose that age- and disease-related alterations in myofilament proteins represent one molecular mechanism contributing to the development of physical disability.

Kinetics of myosin light chain kinase activation of smooth muscle myosin in an in vitro model system

During activation of smooth muscle contraction, one myosin light chain kinase (MLCK) molecule rapidly phosphorylates many smooth muscle myosin (SMM) molecules, suggesting that muscle activation rates are influenced by the kinetics of MLCK-SMM interactions. To determine the rate-limiting step underlying activation of SMM by MLCK, we measured the kinetics of calcium-calmodulin (Ca²⁺CaM)-MLCK-mediated SMM phosphorylation and the corresponding initiation of SMM-based F-actin motility in an in vitro system with SMM attached to a coverslip surface. Fitting the time course of SMM phosphorylation to a kinetic model gave an initial phosphorylation rate, kp(o), of ~1.17 heads s⁻¹ MLCK⁻¹. Also, we measured the dwell time of single streptavidin-coated quantum dot-labeled MLCK molecules interacting with surface-attached SMM and phosphorylated SMM using total internal reflection fluorescence microscopy. From these data, the dissociation rate constant from phosphorylated SMM was 0.80 s⁻¹, which was similar to the kp(o) mentioned above and with rates measured in solution. This dissociation rate was essentially independent of the phosphorylation state of SMM. From calculations using our measured dissociation rates and Kd values, and estimates of SMM and MLCK concentrations in muscle, we predict that the dissociation of MLCK from phosphorylated SMM is rate-limiting and that the rate of the phosphorylation step is faster than this dissociation rate. Also, association with SMM (11-46 s⁻¹) would be much faster than with pSMM (<0.1-0.2 s⁻¹). This suggests that the probability of MLCK interacting with unphosphorylated versus phosphorylated SMM is 55-460 times greater. This would avoid sequestering MLCK to unproductive interactions with previously phosphorylated SMM, potentially leading to faster rates of phosphorylation in muscle.

Kinetics of myosin light chain kinase activation of smooth muscle myosin in an in vitro model system

During activation of smooth muscle contraction, one myosin light chain kinase (MLCK) molecule rapidly phosphorylates many smooth muscle myosin (SMM) molecules, suggesting that muscle activation rates are influenced by the kinetics of MLCK-SMM interactions. To determine the rate-limiting step underlying activation of SMM by MLCK, we measured the kinetics of calcium-calmodulin (Ca²⁺CaM)-MLCK-mediated SMM phosphorylation and the corresponding initiation of SMM-based F-actin motility in an in vitro system with SMM attached to a coverslip surface. Fitting the time course of SMM phosphorylation to a kinetic model gave an initial phosphorylation rate, kp(o), of ~1.17 heads s⁻¹ MLCK⁻¹. Also, we measured the dwell time of single streptavidin-coated quantum dot-labeled MLCK molecules interacting with surface-attached SMM and phosphorylated SMM using total internal reflection fluorescence microscopy. From these data, the dissociation rate constant from phosphorylated SMM was 0.80 s⁻¹, which was similar to the kp(o) mentioned above and with rates measured in solution. This dissociation rate was essentially independent of the phosphorylation state of SMM. From calculations using our measured dissociation rates and Kd values, and estimates of SMM and MLCK concentrations in muscle, we predict that the dissociation of MLCK from phosphorylated SMM is rate-limiting and that the rate of the phosphorylation step is faster than this dissociation rate. Also, association with SMM (11-46 s⁻¹) would be much faster than with pSMM (<0.1-0.2 s⁻¹). This suggests that the probability of MLCK interacting with unphosphorylated versus phosphorylated SMM is 55-460 times greater. This would avoid sequestering MLCK to unproductive interactions with previously phosphorylated SMM, potentially leading to faster rates of phosphorylation in muscle.

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.

Recent insights into the molecular basis of muscular fatigue

The cause of muscle fatigue has been studied for more than 100 yr, yet its molecular basis remains poorly understood. Prevailing theories suggest that much of the fatigue-induced loss in force and velocity can be attributed to the inhibitory action of metabolites, principally phosphate (Pi) and hydrogen ions (H, i.e., acidosis), on the contractile proteins, but the precise detail of how this inhibition occurs has been difficult to visualize at the molecular level. However, recent technological developments in the areas of biophysics, molecular biology, and structural biology are enabling researchers to directly observe the function and dysfunction of muscle contractile proteins at the level of a single molecule. In fact, the first direct evidence that high levels of H and Pi inhibit the function of muscle's molecular motor, myosin, has recently been observed in a single molecule laser trap assay. Likewise, advances in structural biology are taking our understanding further, providing detail at the atomic level of how some metabolites might alter the internal motions of myosin and thereby inhibit its ability to generate force and motion. Finally, new insights are also being gained into the indirect role that muscle regulatory proteins troponin (Tn) and tropomyosin (Tn) play in the fatigue process. In vitro studies, incorporating TnTm, suggest that a significant portion of the decreased force and motion during fatigue may be mediated through a disruption of the molecular motions of specific regions within Tn and Tm. These recent advances are providing unprecedented molecular insight into the structure and function of the contractile proteins and, in the process, are reshaping our understanding of the process of fatigue.

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.

The effects of phosphate and acidosis on regulated thin-filament velocity in an in vitro motility assay

Muscle fatigue from intense contractile activity is thought to result, in large part, from the accumulation of inorganic phosphate (Pi) and hydrogen ions (H+) acting to directly inhibit the function of the contractile proteins; however, the molecular basis of this process remain unclear. We used an in vitro motility assay and determined the effects of elevated H+ and Pi on the ability of myosin to bind to and translocate regulated actin filaments (RTF) to gain novel insights into the molecular basis of fatigue. At saturating Ca++, acidosis depressed regulated filament velocity ( VRTF) by ∼90% (6.2 ± 0.3 vs. 0.5 ± 0.2 μm/s at pH 7.4 and 6.5, respectively). However, the addition of 30 mM Pi caused VRTF to increase fivefold, from 0.5 ± 0.2 to 2.6 ± 0.3 μm/s at pH 6.5. Similarly, at all subsaturating Ca++ levels, acidosis slowed VRTF, but the addition of Pi significantly attenuated this effect. We also manipulated the [ADP] in addition to the [Pi] to probe which specific step(s) of cross-bridge cycle of myosin is affected by elevated H+. The findings are consistent with acidosis slowing the isomerization step between two actomyosin ADP-bound states. Because the state before this isomerization is most vulnerable to Pi rebinding, and the associated detachment from actin, this finding may also explain the Pi-induced enhancement of VRTF at low pH. These results therefore may provide a molecular basis for a significant portion of the loss of shortening velocity and possibly muscular power during fatigue.

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).

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

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

Fluctuations and symmetries in two-dimensional active gels

Motivated by the unique physical properties of biological active matter, e.g., cytoskeletal dynamics in eukaryotic cells, we set up effective two-dimensional (2d) coarse-grained hydrodynamic equations for the dynamics of thin active gels with polar or nematic symmetries. We use the well-known three-dimensional (3d) descriptions (K. Kruse et al., Eur. Phys. J. E 16, 5 (2005); A. Basu et al., Eur. Phys. J. E 27, 149 (2008)) for thin active-gel samples confined between parallel plates with appropriate boundary conditions to derive the effective 2d constitutive relations between appropriate thermodynamic fluxes and generalised forces for small deviations from equilibrium. We consider three distinct cases, characterised by spatial symmetries and boundary conditions, and show how such considerations dictate the structure of the constitutive relations. We use these to study the linear instabilities, calculate the correlation functions and the diffusion constant of a small tagged particle, and elucidate their dependences on the activity or nonequilibrium drive.

Phosphate enhances myosin-powered actin filament velocity under acidic conditions in a motility assay

Elevated levels of inorganic phosphate (P(i)) are believed to inhibit muscular force by reversing myosin's force-generating step. These same levels of P(i) can also affect muscle velocity, but the molecular basis underlying these effects remains unclear. We directly examined the effect of P(i) (30 mM) on skeletal muscle myosin's ability to translocate actin (V(actin)) in an in vitro motility assay. Manipulation of the pH enabled us to probe rebinding of P(i) to myosin's ADP-bound state, while changing the ATP concentration probed rebinding to the rigor state. Surprisingly, the addition of P(i) significantly increased V(actin) at both pH 6.8 and 6.5, causing a doubling of V(actin) at pH 6.5. To probe the mechanisms underlying this increase in speed, we repeated these experiments while varying the ATP concentration. At pH 7.4, the effects of P(i) were highly ATP dependent, with P(i) slowing V(actin) at low ATP (<500 μM), but with a minor increase at 2 mM ATP. The P(i)-induced slowing of V(actin), evident at low ATP (pH 7.4), was minimized at pH 6.8 and completely reversed at pH 6.5. These data were accurately fit with a simple detachment-limited kinetic model of motility that incorporated a P(i)-induced prolongation of the rigor state, which accounted for the slowing of V(actin) at low ATP, and a P(i)-induced detachment from a strongly bound post-power-stroke state, which accounted for the increase in V(actin) at high ATP. These findings suggest that P(i) differentially affects myosin function: enhancing velocity, if it rebinds to the ADP-bound state, while slowing velocity, if it binds to the rigor state.

Force-generating capacity of human myosin isoforms extracted from single muscle fibre segments

Muscle, motor unit and muscle fibre type-specific differences in force-generating capacity have been investigated for many years, but there is still no consensus regarding specific differences between slow- and fast-twitch muscles, motor units or muscle fibres. This is probably related to a number of different confounding factors disguising the function of the molecular motor protein myosin. We have therefore studied the force-generating capacity of specific myosin isoforms or combination of isoforms extracted from short single human muscle fibre segments in a modified single fibre myosin in vitro motility assay, in which an internal load (actin-binding protein) was added in different concentrations to evaluate the force-generating capacity. The force indices were the x-axis intercept and the slope of the relationship between the fraction of moving filaments and the α-actinin concentration. The force-generating capacity of the β/slow myosin isoform (type I) was weaker (P < 0.05) than the fast myosin isoform (type II), but the force-generating capacity of the different human fast myosin isoforms types IIa and IIx or a combination of both (IIax) were indistinguishable. A single fibre in vitro motility assay for both speed and force of specific myosin isoforms is described and used to measure the difference in force-generating capacity between fast and slow human myosin isoforms. The assay is proposed as a useful tool for clinical studies on the effects on muscle function of specific mutations or post-translational modifications of myosin.

Effects of actin-myosin kinetics on the calcium sensitivity of regulated thin filaments

Activation of thin filaments in striated muscle occurs when tropomyosin exposes myosin binding sites on actin either through calcium-troponin (Ca-Tn) binding or by actin-myosin (A-M) strong binding. However, the extent to which these binding events contributes to thin filament activation remains unclear. Here we propose a simple analytical model in which strong A-M binding and Ca-Tn binding independently activates the rate of A-M weak-to-strong binding. The model predicts how the level of activation varies with pCa as well as A-M attachment, N·k(att), and detachment, k(det), kinetics. To test the model, we use an in vitro motility assay to measure the myosin-based sliding velocities of thin filaments at different pCa, N·k(att), and k(det) values. We observe that the combined effects of varying pCa, N·k(att), and k(det) are accurately fit by the analytical model. The model and supporting data imply that changes in attachment and detachment kinetics predictably affect the calcium sensitivity of striated muscle mechanics, providing a novel A-M kinetic-based interpretation for perturbations (e.g. disease-related mutations) that alter calcium sensitivity.

The direct molecular effects of fatigue and myosin regulatory light chain phosphorylation on the actomyosin contractile apparatus

Skeletal muscle, during periods of exertion, experiences several different fatigue-based changes in contractility, including reductions in force, velocity, power output, and energy usage. The fatigue-induced changes in contractility stem from many different factors, including alterations in the levels of metabolites, oxidative damage, and phosphorylation of the myosin regulatory light chain (RLC). Here, we measured the direct molecular effects of fatigue-like conditions on actomyosin's unloaded sliding velocity using the in vitro motility assay. We examined how changes in ATP, ADP, P(i), and pH affect the ability of the myosin to translocate actin and whether the effects of each individual molecular species are additive. We found that the primary causes of the reduction in unloaded sliding velocity are increased [ADP] and lowered pH and that the combined effects of the molecular species are nonadditive. Furthermore, since an increase in RLC phosphorylation is often associated with fatigue, we examined the differential effects of myosin RLC phosphorylation and fatigue on actin filament velocity. We found that phosphorylation of the RLC causes a 22% depression in sliding velocity. On the other hand, RLC phosphorylation ameliorates the slowing of velocity under fatigue-like conditions. We also found that phosphorylation of the myosin RLC increases actomyosin affinity for ADP, suggesting a kinetic role for RLC phosphorylation. Furthermore, we showed that ADP binding to skeletal muscle is load dependent, consistent with the existence of a load-dependent isomerization of the ADP bound state.

Alternative S2 hinge regions of the myosin rod affect myofibrillar structure and myosin kinetics

The subfragment 2/light meromyosin "hinge" region has been proposed to significantly contribute to muscle contraction force and/or speed. Transgenic replacement of the endogenous fast muscle isovariant hinge A (exon 15a) in Drosophila melanogaster indirect flight muscle with the slow muscle hinge B (exon 15b) allows examination of the structural and functional changes when only this region of the myosin molecule is different. Hinge B was previously shown to increase myosin rod length, increase A-band and sarcomere length, and decrease flight performance compared to hinge A. We applied additional measures to these transgenic lines to further evaluate the consequences of modifying this hinge region. Structurally, the longer A-band and sarcomere lengths found in the hinge B myofibrils appear to be due to the longitudinal addition of myosin heads. Functionally, hinge B, although a significant distance from the myosin catalytic domain, alters myosin kinetics in a manner consistent with this region increasing myosin rod length. These structural and functional changes combine to decrease whole fly wing-beat frequency and flight performance. Our results indicate that this hinge region plays an important role in determining myosin kinetics and in regulating thick and thin filament lengths as well as sarcomere length.

Kinetic and motor functions mediated by distinct regions of the regulatory light chain of smooth muscle myosin

To understand the importance of selected regions of the regulatory light chain (RLC) for phosphorylation-dependent regulation of smooth muscle myosin (SMM), we expressed three heavy meromyosins (HMMs) containing the following RLC mutants; K12E in a critical region of the phosphorylation domain, GTDP(95-98)/AAAA in the central hinge, and R160C a putative binding residue for phosphorylated S19. Single-turnover actin-activated Mg(2+)-ATPase (V(max) and K(ATPase)) and in vitro actin-sliding velocities were examined for both unphosphorylated (up-) and phosphorylated (p-) states. Turnover rates for the up-state (0.007-0.030 s(-1)) and velocities (no motion) for all constructs were not significantly different from the up-wild type (WT) indicating that they were completely turned off. The apparent binding constants for actin in the presence of ATP (K(ATPase)) were too weak to measure as expected for fully regulated constructs. For p-HMM containing GTDP/AAAA, we found that both ATPase and motility were normal. The data suggest that the native sequence in the central hinge between the two lobes of the RLC is not required for turning the HMM off and on both kinetically and mechanically. For p-HMM containing R160C, all parameters were normal, suggesting that R160C is not involved in coordination of the phosphorylated S19. For p-HMM containing K12E, the V(max) was 64% and the actin-sliding velocity was approximately 50% of WT, suggesting that K12 is an important residue for the ability to sense or to promote the conformational changes required for kinetic and mechanical activation.

Properties of tug-of-war model for cargo transport by molecular motors

Molecular motors are essential components for the biophysical functions of the cell. Current quantitative understanding of how multiple motors move along a single track is not complete, even though models and theories for a single motor mechanochemistry abound. Recently, Müller et al. have developed a tug-of-war model to describe the bidirectional movement of the cargo [Proc. Natl. Acad. Sci. U.S.A. 105, 4609 (2008)]. They found that the tug-of-war model exhibits several qualitative different motility regimes, which depend on the precise value of single motor parameters, and they suggested that the sensitivity can be used by a cell to regulate its cargo traffic. In the present paper, we will carry out a detailed theoretical analysis of a special case of tug-of-war model: in which the numbers of the two different motor species which bound to the cargo tend to infinite. Through the analysis, all the stable, i.e., biophysically observable, steady states and their stability domains can be obtained. Depending on values of the several parameters, the tug-of-war model exhibits uni-, bi-, or tristability. The steady-state movement of the cargo, which is transported by two different molecular motor species, is determined by the initial numbers of the motors which bound to the track.

Characterization of tightly associated smooth muscle myosin-myosin light-chain kinase-calmodulin complexes

A current popular model to explain phosphorylation of smooth muscle myosin (SMM) by myosin light-chain kinase (MLCK) proposes that MLCK is bound tightly to actin but weakly to SMM. We found that MLCK and calmodulin (CaM) co-purify with unphosphorylated SMM from chicken gizzard, suggesting that they are tightly bound. Although the MLCK:SMM molar ratio in SMM preparations was well below stoichiometric (1:73+/-9), the ratio was approximately 23-37% of that in gizzard tissue. Fifteen to 30% of MLCK was associated with CaM at approximately 1 nM free [Ca(2+)]. There were two MLCK pools that bound unphosphorylated SMM with K(d) approximately 10 and 0.2 microM and phosphorylated SMM with K(d) approximately 20 and 0.2 microM. Using an in vitro motility assay to measure actin sliding velocities, we showed that the co-purifying MLCK-CaM was activated by Ca(2+) and phosphorylation of SMM occurred at a pCa(50) of 6.1 and at a Hill coefficient of 0.9. Similar properties were observed from reconstituted MLCK-CaM-SMM. Using motility assays, co-sedimentation assays, and on-coverslip enzyme-linked immunosorbent assays to quantify proteins on the motility assay coverslip, we provide strong evidence that most of the MLCK is bound directly to SMM through the telokin domain and some may also be bound to both SMM and to co-purifying actin through the N-terminal actin-binding domain. These results suggest that this MLCK may play a role in the initiation of contraction.

The energetics of allosteric regulation of ADP release from myosin heads

Myosin molecules are involved in a wide range of transport and contractile activities in cells. A single myosin head functions through its ATPase reaction as a force generator and as a mechanosensor, and when two or more myosin heads work together in moving along an actin filament, the interplay between these mechanisms contributes to collective myosin behaviors. For example, the interplay between force-generating and force-sensing mechanisms coordinates the two heads of a myosin V molecule in its hand-over-hand processive stepping along an actin filament. In muscle, it contributes to the Fenn effect and smooth muscle latch. In both examples, a key force-sensing mechanism is the regulation of ADP release via interhead forces that are generated upon actin-myosin binding. Here we present a model describing the mechanism of allosteric regulation of ADP release from myosin heads as a change, DeltaDeltaG(-D), in the standard free energy for ADP release that results from the work, Deltamicro(mech), performed by that myosin head upon ADP release, or DeltaDeltaG(-D) = Deltamicro(mech). We show that this model is consistent with previous measurements for strain-dependent kinetics of ADP release in both myosin V and muscle myosin II. The model makes explicit the energetic cost of accelerating ADP release, showing that acceleration of ADP release during myosin V processivity requires approximately 4 kT of energy whereas the energetic cost for accelerating ADP release in a myosin II-based actin motility assay is only approximately 0.4 kT. The model also predicts that the acceleration of ADP release involves a dissipation of interhead forces. To test this prediction, we use an in vitro motility assay to show that the acceleration of ADP release from both smooth and skeletal muscle myosin II correlates with a decrease in interhead force. Our analyses provide clear energetic constraints for models of the allosteric regulation of ADP release and provide novel, testable insights into muscle and myosin V function.

Slowly modulating fluctuations as mesoscopic distortions occurring on an actin filament

An actin filament sliding on myosin molecules exhibits fluctuating or staggered movements as responding to changes in the ATP concentration. We previously observed that fluctuations in the sliding velocity enhanced in a manner being independent of the magnitude of the velocity. The present study focused upon a single actin filament bound to a glass surface through avidin-biotin bonding to examine those fluctuations inherent to the filament in the presence of heavy meromyosin. The auto-correlation analysis revealed that the relaxation time of fluctuations in the filamental displacement obtains its maximum value at about 100microM of the ATP concentration in the ambient, while the magnitude of the fluctuations gradually increased with an increase of the concentration. Furthermore, the measurement of the fluorescence intensity from the markers fixed on the filament demonstrated an enhancement of the negative correlation between the measured peak intensity and the spatial spreading of its intensity over the range of 0-200microM of the ATP concentration, as indicating both development and mitigation of local distortions occurring within the filament.

Regulatory light chain mutations associated with cardiomyopathy affect myosin mechanics and kinetics

The myosin regulatory light chain (RLC) wraps around the alpha-helical neck region of myosin. This neck region has been proposed to act as a lever arm, amplifying small conformational changes in the myosin head to generate motion. The RLC serves an important structural role, supporting the myosin neck region and a modulatory role, tuning the kinetics of the actin myosin interaction. Given the importance of the RLC, it is not surprising that mutations of the RLC can lead to familial hypertrophic cardiomyopathy (FHC), the leading cause of sudden cardiac death in people under 30. Population studies identified two FHC mutations located near the cationic binding site of the RLC, R58Q and N47K. Although these mutations are close in sequence, they differ in clinical presentation and prognosis, with R58Q showing a more severe phenotype. We examined the molecular based changes in myosin that are responsible for the disease phenotype by purifying myosin from transgenic mouse hearts expressing mutant myosins and examining actin filament sliding using the in vitro motility assay. We found that both R58Q and N47K show reductions in force compared to the wild type that could result in compensatory hypertrophy. Furthermore, we observed a higher ATPase rate and an increased activation at submaximal calcium levels for the R58Q myosin that could lead to decreased efficiency and incomplete cardiac relaxation, potentially explaining the more severe phenotype for the R58Q mutation.

Unloaded speed of shortening in voltage-clamped intact skeletal muscle fibers from wt, mdx, and transgenic minidystrophin mice using a novel high-speed acquisition system

Skeletal muscle unloaded shortening has been indirectly determined in the past. Here, we present a novel high-speed optical tracking technique that allows recording of unloaded shortening in single intact, voltage-clamped mammalian skeletal muscle fibers with 2-ms time resolution. L-type Ca(2+) currents were simultaneously recorded. The time course of shortening was biexponential: a fast initial phase, tau(1), and a slower successive phase, tau(2,) with activation energies of 59 kJ/mol and 47 kJ/mol. Maximum unloaded shortening speed, v(u,max), was faster than that derived using other techniques, e.g., approximately 14.0 L(0) s(-1) at 30 degrees C. Our technique also allowed direct determination of shortening acceleration. We applied our technique to single fibers from C57 wild-type, dystrophic mdx, and minidystrophin-expressing mice to test whether unloaded shortening was affected in the pathophysiological mechanism of Duchenne muscular dystrophy. v(u,max) and a(u,max) values were not significantly different in the three strains, whereas tau(1) and tau(2) were increased in mdx fibers. The results were complemented by myosin heavy and light chain (MLC) determinations that showed the same myosin heavy chain IIA profiles in the interossei muscles from the different strains. In mdx muscle, MLC-1f was significantly increased and MLC-2f and MLC-3f somewhat reduced. Fast initial active shortening seems almost unaffected in mdx muscle.

Inorganic phosphate binds to the empty nucleotide binding pocket of conventional myosin II

In muscle inorganic phosphate strongly decreases force generation in the presence of millimolar MgATP, whereas phosphate slows shortening velocity only at micromolar MgATP concentrations. It is still controversial whether reduction in shortening velocity by phosphate results from phosphate binding to the nucleotide-free myosin head or from binding of phosphate to an actomyosin-ADP state as postulated for the inhibition of force generation by phosphate. Because most single-molecule studies are performed at micromolar concentrations of MgATP where phosphate effects on movement are rather prominent, clarification of the mechanisms of phosphate inhibition is essential for interpretation of data in which phosphate is used in single molecule studies to probe molecular events of force generation and movement. In in vitro assays we found that inhibition of filament gliding by inorganic phosphate was associated with increased fragmentation of actin filaments. In addition, phosphate did not extend dwell times of Cy3-EDA-ATP (2'(3')-O-[[2-[[6-[2-[3-(1-ethyl-1,3-dihydro-3,3-dimethyl-5-sulfo-2H-indol-2-ylidene)-1-propenyl]-3,3-dimethyl-5-sulfo-3H-indolio]-1-oxohexyl]amino]ethyl]carbamoyl]ATP) but reduced the number of Cy3-signals per field of view, approaching 50% at phosphate concentrations of 1-2 mM. Apparently, inhibition of movement does not result from binding of phosphate to an actomyosin-ADP intermediate as proposed by Hooft and coworkers (Hooft, A. M., Maki, E. J., Cox, K. K., and Baker, J. E. (2007) Biochemistry 46, 3513-3520) but, rather, from forming a strong-binding actomyosin-phosphate intermediate.