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.

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.

Cells solved the Gibbs paradox by learning to contain entropic forces.

As Nature's version of machine learning, evolution has solved many extraordinarily complex problems, none perhaps more remarkable than learning to harness an increase in chemical entropy (disorder) to generate directed chemical forces (order). Using muscle as a model system, here I describe the basic mechanism by which life creates order from disorder. In short, evolution tuned the physical properties of certain proteins to contain changes in chemical entropy. As it happens these are the "sensible" properties Gibbs postulated were needed to solve a paradox that has intrigued and challenged scientists and philosophers for over 100 years.

Cells Solved the Gibbs Paradox by Learning to Contain Entropic Forces.

As Nature's version of machine learning, evolution has solved many extraordinarily complex problems, none perhaps more remarkable than learning to harness an increase in chemical entropy (disorder) to generate directed chemical forces (order). Using muscle as a model system, here I unpack the basic mechanism by which life creates order from disorder. In short, evolution tuned the physical properties of certain proteins to contain changes in chemical entropy. As it happens, these are the "sensible" properties Gibbs postulated were needed to solve his paradox.

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.

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/ton), where d equals step size and ton 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/ton, 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 light chain kinase steady-state kinetics: comparison of smooth muscle myosin II and nonmuscle myosin IIB as substrates.

Myosin light chain kinase (MLCK) phosphorylates S19 of the myosin regulatory light chain (RLC), which is required to activate myosin's ATPase activity and contraction. Smooth muscles are known to display plasticity in response to factors such as inflammation, developmental stage, or stress, which lead to differential expression of nonmuscle and smooth muscle isoforms. Here, we compare steady-state kinetics parameters for phosphorylation of different MLCK substrates: (1) nonmuscle RLC, (2) smooth muscle RLC, and heavy meromyosin subfragments of (3) nonmuscle myosin IIB, and (4) smooth muscle myosin II. We show that MLCK has a ~2-fold higher kcat for both smooth muscle myosin II substrates compared with nonmuscle myosin IIB substrates, whereas Km values were very similar. Myosin light chain kinase has a 1.6-fold and 1.5-fold higher specificity (kcat /Km ) for smooth versus nonmuscle-free RLC and heavy meromyosin, respectively, suggesting that differences in specificity are dictated by RLC sequences. Of the 10 non-identical RLC residues, we ruled out 7 as possible underlying causes of different MLCK kinetics. The remaining 3 residues were found to be surface exposed in the N-terminal half of the RLC, consistent with their importance in substrate recognition. These data are consistent with prior deletion/chimera studies and significantly add to understanding of MLCK myosin interactions. SIGNIFICANCE OF THE STUDY: Phosphorylation of nonmuscle and smooth muscle myosin by myosin light chain kinase (MLCK) is required for activation of myosin's ATPase activity. In smooth muscles, nonmuscle myosin coexists with smooth muscle myosin, but the two myosins have very different chemo-mechanical properties relating to their ability to maintain force. Differences in specificity of MLCK for different myosin isoforms had not been previously investigated. We show that the MLCK prefers smooth muscle myosin by a significant factor. These data suggest that nonmuscle myosin is phosphorylated more slowly than smooth muscle myosin during a contraction cycle.

Diffusion of myosin light chain kinase on actin: A mechanism to enhance myosin phosphorylation rates in smooth muscle.

Smooth muscle myosin (SMM) light chain kinase (MLCK) phosphorylates SMM, thereby activating the ATPase activity required for muscle contraction. The abundance of active MLCK, which is tightly associated with the contractile apparatus, is low relative to that of SMM. SMM phosphorylation is rapid despite the low ratio of MLCK to SMM, raising the question of how one MLCK rapidly phosphorylates many SMM molecules. We used total internal reflection fluorescence microscopy to monitor single molecules of streptavidin-coated quantum dot-labeled MLCK interacting with purified actin, actin bundles, and stress fibers of smooth muscle cells. Surprisingly, MLCK and the N-terminal 75 residues of MLCK (N75) moved on actin bundles and stress fibers of smooth muscle cell cytoskeletons by a random one-dimensional (1-D) diffusion mechanism. Although diffusion of proteins along microtubules and oligonucleotides has been observed previously, this is the first characterization to our knowledge of a protein diffusing in a sustained manner along actin. By measuring the frequency of motion, we found that MLCK motion is permitted only if acto-myosin and MLCK-myosin interactions are weak. From these data, diffusion coefficients, and other kinetic and geometric considerations relating to the contractile apparatus, we suggest that 1-D diffusion of MLCK along actin (a) ensures that diffusion is not rate limiting for phosphorylation, (b) allows MLCK to locate to areas in which myosin is not yet phosphorylated, and (c) allows MLCK to avoid getting "stuck" on myosins that have already been phosphorylated. Diffusion of MLCK along actin filaments may be an important mechanism for enhancing the rate of SMM phosphorylation in smooth muscle.

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.

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.

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 (Ca²âºCaM)-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.

The myosin duty ratio tunes the calcium sensitivity and cooperative activation of the thin filament.

In striated muscle, calcium binding to the thin filament (TF) regulatory complex activates actin-myosin ATPase activity, and actin-myosin kinetics in turn regulates TF activation. However, a quantitative description of the effects of actin-myosin kinetics on the calcium sensitivity (pCa50) and cooperativity (nH) of TF activation is lacking. With the assumption that TF structural transitions and TF-myosin binding transitions are inextricably coupled, we advanced the principles established by Kad et al. [Kad, N., et al. (2005) Proc. Natl. Acad. Sci. U.S.A. 102, 16990-16995] and Sich et al. [Sich, N. M., et al. (2011) J. Biol. Chem. 285, 39150-39159] to develop a simple model of TF regulation, which predicts that pCa50 varies linearly with duty ratio and that nH is maximal near physiological duty ratios. Using in vitro motility to determine the calcium sensitivity of TF sliding velocities, we measured pCa50 and nH at different myosin densities and in the presence of ATPase inhibitors. The observed effects of myosin density and actin-myosin duty ratio on pCa50 and nH are consistent with our model predictions. In striated muscle, pCa50 must match cytosolic calcium concentrations and a maximal nH optimizes calcium responsiveness. Our results indicate that pCa50 and nH can be predictably tuned through TF-myosin ATPase kinetics and that drugs and disease states that alter ATPase kinetics can, through their effects on calcium sensitivity, alter the efficiency of muscle contraction.

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.

Modification of interface between regulatory and essential light chains hampers phosphorylation-dependent activation of smooth muscle myosin.

We examined the regulatory importance of interactions between regulatory light chain (RLC), essential light chain (ELC), and adjacent heavy chain (HC) in the regulatory domain of smooth muscle heavy meromyosin. After mutating the HC, RLC, and/or ELC to disrupt their predicted interactions (using scallop myosin coordinates), we measured basal ATPase, V(max), and K(ATPase) of actin-activated ATPase, actin-sliding velocities, rigor binding to actin, and kinetics of ATP binding and ADP release. If unphosphorylated, all mutants were similar to wild type showing turned-off behaviors. In contrast, if phosphorylated, mutation of RLC residues smM129Q and smG130C in the F-G helix linker, which interact with the ELC (Ca(2+) binding in scallop), was sufficient to abolish motility and diminish ATPase activity, without altering other parameters. ELC mutations within this interacting ELC loop (smR20M and smK25A) were normal, but smM129Q/G130C-R20M or -K25A showed a partially recovered phenotype suggesting that interaction between the RLC and ELC is important. A molecular dynamics study suggested that breaking the RLC/ELC interface leads to increased flexibility at the interface and ELC-binding site of the HC. We hypothesize that this leads to hampered activation by allowing a pre-existing equilibrium between activated and inhibited structural distributions (Vileno, B., Chamoun, J., Liang, H., Brewer, P., Haldeman, B. D., Facemyer, K. C., Salzameda, B., Song, L., Li, H. C., Cremo, C. R., and Fajer, P. G. (2011) Broad disorder and the allosteric mechanism of myosin II regulation by phosphorylation. Proc. Natl. Acad. Sci. U.S.A. 108, 8218-8223) to be biased strongly toward the inhibited distribution even when the RLC is phosphorylated. We propose that an important structural function of RLC phosphorylation is to promote or assist in the maintenance of an intact RLC/ELC interface. If the RLC/ELC interface is broken, the off-state structures are no longer destabilized by phosphorylation.

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 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.