A simple model with myofilament compliance predicts activation-dependent crossbridge kinetics in skinned skeletal fibers

Disruption of Z-Disc Function Promotes Mechanical Dysfunction in Human Myocardium: Evidence for a Dual Myofilament Modulatory Role by Alpha-Actinin 2

The ACTN2 gene encodes α-actinin 2, located in the Z-disc of the sarcomeres in striated muscle. In this study, we sought to investigate the effects of an ACTN2 missense variant of unknown significance (p.A868T) on cardiac muscle structure and function. Left ventricular free wall samples were obtained at the time of cardiac transplantation from a heart failure patient with the ACTN2 A868T heterozygous variant. This variant is in the EF 3-4 domain known to interact with titin and α-actinin. At the ultrastructural level, ACTN2 A868T cardiac samples presented small structural changes in cardiomyocytes when compared to healthy donor samples. However, contractile mechanics of permeabilized ACTN2 A868T variant cardiac tissue displayed higher myofilament Ca2+ sensitivity of isometric force, reduced sinusoidal stiffness, and faster rates of tension redevelopment at all Ca2+ levels. Small-angle X-ray diffraction indicated increased separation between thick and thin filaments, possibly contributing to changes in muscle kinetics. Molecular dynamics simulations indicated that while the mutation does not significantly impact the structure of α-actinin on its own, it likely alters the conformation associated with titin binding. Our results can be explained by two Z-disc mediated communication pathways: one pathway that involves α-actinin's interaction with actin, affecting thin filament regulation, and the other pathway that involves α-actinin's interaction with titin, affecting thick filament activation. This work establishes the role of α-actinin 2 in modulating cross-bridge kinetics and force development in the human myocardium as well as how it can be involved in the development of cardiac disease.

Mechanical contribution to muscle thin filament activation

Vertebrate striated muscle thin filaments are thought to be thermodynamically activated in response to an increase in Ca²⁺ concentration. We tested this hypothesis by measuring time intervals for gliding runs and pauses of individual skeletal muscle thin filaments in cycling myosin motility assays. A classic thermodynamic mechanism predicts that if chemical potential is constant, transitions between runs and pauses of gliding thin filaments will occur at constant rate as given by a Poisson distribution. In this scenario, rate is given by the odds of a pause, and hence, run times between pauses fit an exponential distribution that slopes negatively for all observable run times. However, we determined that relative density of observed run times fits an exponential only at low Ca²⁺ levels that activate filament gliding. Further titration with Ca²⁺, or adding excess regulatory proteins tropomyosin and troponin, shifted the relative density of short run times to fit the positive slope of a gamma distribution, which derives from waiting times between Poisson events. Events that arise during a run and prevent the chance of ending a run for a random interval of time account for the observed run time distributions, suggesting that the events originate with cycling myosin. We propose that regulatory proteins of the thin filament require the mechanical force of cycling myosin to achieve the transition state for activation. During activation, combinations of cycling myosin that contribute insufficient activation energy delay deactivation.

A myosin-based mechanism for stretch activation and its possible role revealed by varying phosphate concentration in fast and slow mouse skeletal muscle fibers

Stretch activation (SA) is a delayed increase in force following a rapid muscle length increase. SA is best known for its role in asynchronous insect flight muscle, where it has replaced calcium's typical role of modulating muscle force levels during a contraction cycle. SA also occurs in mammalian skeletal muscle but has previously been thought to be too low in magnitude, relative to calcium-activated (CA) force, to be a significant contributor to force generation during locomotion. To test this supposition, we compared SA and CA force at different P_i concentrations (0-16 mM) in skinned mouse soleus (slow-twitch) and extensor digitorum longus (EDL; fast-twitch) muscle fibers. CA isometric force decreased similarly in both muscles with increasing P_i, as expected. SA force decreased with P_i in EDL (40%), leaving the SA to CA force ratio relatively constant across P_i concentrations (17-25%). In contrast, SA force increased in soleus (42%), causing a quadrupling of the SA to CA force ratio, from 11% at 0 mM P_i to 43% at 16 mM P_i, showing that SA is a significant force modulator in slow-twitch mammalian fibers. This modulation would be most prominent during prolonged muscle use, which increases P_i concentration and impairs calcium cycling. Based upon our previous Drosophila myosin isoform studies and this work, we propose that in slow-twitch fibers a rapid stretch in the presence of P_i reverses myosin's power stroke, enabling quick rebinding to actin and enhanced force production, while in fast-twitch fibers, stretch and P_i cause myosin to detach from actin.

Elastic domains of giant proteins in striated muscle: Modeling compliance with rulers

Chase examines a study using the MUSICO model of striated muscle to evaluate the function of giant elastic proteins titin and nebulin.

A stochastic simulation of skeletal muscle calcium transients in a structurally realistic sarcomere model using MCell

Skeletal muscle contraction is initiated when an action potential triggers the release of Ca2+ into the sarcomere in a process referred to as excitation-contraction coupling. The speed and scale of this process makes direct observation very challenging and invasive. To determine how the concentration of Ca2+ changes within the myofibril during a single activation, several simulation models have been developed. These models follow a common pattern; divide the half sarcomere into a series of compartments, then use ordinary differential equations to solve reactions occurring within and between the compartments. To further develop this type of simulation, we have created a realistic structural model of a skeletal muscle myofibrillar half-sarcomere using MCell software that incorporates the myofilament lattice structure. Using this simulation model, we were successful in reproducing the averaged calcium transient during a single activation consistent with both the experimental and previous simulation results. In addition, our simulation demonstrated that the inclusion of the myofilament lattice within our model produced an asymmetric distribution of Ca2+, with more Ca2+ accumulating near the Z-disk and less Ca2+ reaching the m-line. This asymmetric distribution of Ca2+ is also apparent when we examine how the Ca2+ are bound to the troponin-C proteins along the actin filaments. Our simulation model also allowed us to produce advanced visualizations of this process, including two simulation animations, allowing us to view Ca2+ release, diffusion, binding and uptake within the myofibrillar half-sarcomere.

Nebulin increases thin filament stiffness and force per cross-bridge in slow-twitch soleus muscle fibers

Nebulin stabilizes the thin filament and regulates force generation in skeletal muscle, but its precise role is not understood. Using conditional knockout mice, Kawai et al. demonstrate that nebulin functions to increase the force per cross-bridge in skinned slow-twitch soleus muscle fibers.

Nebulin (Neb) is associated with the thin filament in skeletal muscle cells, but its functions are not well understood. For this goal, we study skinned slow-twitch soleus muscle fibers from wild-type (Neb⁺) and conditional Neb knockout (Neb⁻) mice. We characterize cross-bridge (CB) kinetics and the elementary steps of the CB cycle by sinusoidal analysis during full Ca²⁺ activation and observe that Neb increases active tension 1.9-fold, active stiffness 2.7-fold, and rigor stiffness 3.0-fold. The ratio of stiffness during activation and rigor states is 62% in Neb⁺ fibers and 68% in Neb⁻ fibers. These are approximately proportionate to the number of strongly attached CBs during activation. Because the thin filament length is 15% shorter in Neb⁻ fibers than in Neb⁺ fibers, the increase in force per CB in the presence of Neb is ∼1.5 fold. The equilibrium constant of the CB detachment step (K₂), its rate (k₂), and the rate of the reverse force generation step (k₋₄) are larger in Neb⁺ fibers than in Neb⁻ fibers. The rates of the force generation step (k₄) and the reversal detachment step (k₋₂) change in the opposite direction. These effects can be explained by Le Chatelier’s principle: Increased CB strain promotes less force-generating state(s) and/or detached state(s). Further, when CB distributions among the six states are calculated, there is no significant difference in the number of strongly attached CBs between fibers with and without Neb. These results demonstrate that Neb increases force per CB. We also confirm that force is generated by isomerization of actomyosin (AM) from the AM.ADP.Pi state (ADP, adenosine diphophate; Pi, phosphate) to the AM*ADP.Pi state, where the same force is maintained after Pi release to result in the AM*ADP state. We propose that Neb changes the actin (and myosin) conformation for better ionic and hydrophobic/stereospecific AM interaction, and that the effect of Neb is similar to that of tropomyosin.

Structural and functional impact of troponin C-mediated Ca2+ sensitization on myofilament lattice spacing and cross-bridge mechanics in mouse cardiac muscle

Acto-myosin cross-bridge kinetics are important for beat-to-beat regulation of cardiac contractility; however, physiological and pathophysiological mechanisms for regulation of contractile kinetics are incompletely understood. Here we explored whether thin filament-mediated Ca²⁺ sensitization influences cross-bridge kinetics in permeabilized, osmotically compressed cardiac muscle preparations. We used a murine model of hypertrophic cardiomyopathy (HCM) harboring a cardiac troponin C (cTnC) Ca²⁺-sensitizing mutation, Ala8Val in the regulatory N-domain. We also treated wild-type murine muscle with bepridil, a cTnC-targeting Ca²⁺ sensitizer. Our findings suggest that both methods of increasing myofilament Ca²⁺ sensitivity increase cross-bridge cycling rate measured by the rate of tension redevelopment (k_TR); force per cross-bridge was also enhanced as measured by sinusoidal stiffness and I_1,1/I_1,0 ratio from X-ray diffraction. Computational modeling suggests that Ca²⁺ sensitization through this cTnC mutation or bepridil accelerates k_TR primarily by promoting faster cross-bridge detachment. To elucidate if myofilament structural rearrangements are associated with changes in k_TR, we used small angle X-ray diffraction to simultaneously measure myofilament lattice spacing and isometric force during steady-state Ca²⁺ activations. Within in vivo lattice dimensions, lattice spacing and steady-state isometric force increased significantly at submaximal activation. We conclude that the cTnC N-domain controls force by modulating both the number and rate of cycling cross-bridges, and that the both methods of Ca²⁺ sensitization may act through stabilization of cTnC's D-helix. Furthermore, we propose that the transient expansion of the myofilament lattice during Ca²⁺ activation may be an additional factor that could increase the rate of cross-bridge cycling in cardiac muscle. These findings may have implications for the pathophysiology of HCM.

Titin-mediated thick filament activation stabilizes myofibrils on the descending limb of their force-length relationship

PURPOSE

The aim of this study was to extend current half-sarcomere models by involving a recently found force-mediated activation of the thick filament and analyze the effect of this mechanosensing regulation on the length stability of half-sarcomeres arranged in series.

METHODS

We included a super-relaxed state of myosin motors and its force-dependent activation in a conventional cross-bridge model. We simulated active stretches of a sarcomere consisting of 2 non-uniform half-sarcomeres on the descending limb of the force-length relationship.

RESULTS

The mechanosensing model predicts that, in a passive sarcomere on the descending limb of the force-length relationship, the longer half-sarcomere has a higher fraction of myosin motors in the on-state than the shorter half-sarcomere. The difference in the number of myosin motors in the on-state ensures that upon calcium-mediated thin filament activation, the force-dependent thick filament activation keeps differences in active force within 20% during an active stretch. In the classical cross-bridge model, the corresponding difference exceeds 80%, leading to great length instabilities.

CONCLUSION

Our simulations suggest that, in contrast to the classical cross-bridge model, the mechanosensing regulation is able to stabilize a system of non-uniform half-sarcomeres arranged in series on the descending limb of the force-length relationship.

Mechanical parameters of the molecular motor myosin II determined in permeabilised fibres from slow and fast skeletal muscles of the rabbit

KEY POINTS

The different performance of slow and fast muscles is mainly attributed to diversity of the myosin heavy chain (MHC) isoform expressed within them. In this study fast sarcomere-level mechanics has been applied to Ca²⁺ -activated single permeabilised fibres isolated from soleus (containing the slow myosin isoform) and psoas (containing the fast myosin isoform) muscles of rabbit for a comparative definition of the mechano-kinetics of force generation by slow and fast myosin isoforms in situ. The stiffness and the force of the slow myosin isoform are three times smaller than those of the fast isoform, suggesting that the stiffness of the myosin motor is a determinant of the isoform-dependent functional diversity between skeletal muscles. These results open the question of the mechanism that can reconcile the reduced performance of the slow MHC with the higher efficiency of the slow muscle.

ABSTRACT

The skeletal muscle exhibits large functional differences depending on the myosin heavy chain (MHC) isoform expressed in its molecular motor, myosin II. The differences in the mechanical features of force generation by myosin isoforms were investigated in situ by using fast sarcomere-level mechanical methods in permeabilised fibres (sarcomere length 2.4 μm, temperature 12°C, 4% dextran T-500) from slow (soleus, containing the MHC-1 isoform) and fast (psoas, containing the MHC-2X isoform) skeletal muscle of the rabbit. The stiffness of the half-sarcomere was determined at the plateau of Ca²⁺ -activated isometric contractions and in rigor and analysed with a model that accounted for the filament compliance to estimate the stiffness of the myosin motor (ε). ε was 0.56 ± 0.04 and 1.70 ± 0.37 pN nm^-1 for the slow and fast isoform, respectively, while the average strain per attached motor (s₀ ) was similar (∼3.3 nm) in both isoforms. Consequently the force per motor (F₀  = εs₀ ) was three times smaller in the slow isoform than in the fast isoform (1.89 ± 0.43 versus 5.35 ± 1.51 pN). The fraction of actin-attached motors responsible for maximum isometric force at saturating Ca²⁺ (T_0,4.5 ) was 0.47 ± 0.09 in soleus fibres, 70% larger than that in psoas fibres (0.29 ± 0.08), so that F₀ in slow fibres was decreased by only 53%. The lower stiffness and force of the slow myosin isoform open the question of the molecular basis of the higher efficiency of slow muscle with respect to fast muscle.

L71F mutation in rat cardiac troponin T augments crossbridge recruitment and detachment dynamics against α-myosin heavy chain, but not against β-myosin heavy chain

The N-terminal extension of human cardiac troponin T (TnT), which modulates myofilament Ca²⁺ sensitivity, contains several hypertrophic cardiomyopathy (HCM)-causing mutations including S69F. However, the functional consequence of S69F mutation is unknown. The human analog of S69F in rat TnT is L71F (TnT_L71F). Because the functional consequences due to structural changes in the N-terminal extension are influenced by the type of myosin heavy chain (MHC) isoform, we hypothesized that the TnT_L71F-mediated effect would be differently modulated by α- and β-MHC isoforms. TnT_L71F and wild-type rat TnT were reconstituted into de-membranated muscle fibers from normal (α-MHC) and propylthiouracil-treated rat hearts (β-MHC) to measure steady-state and dynamic contractile parameters. The magnitude of the TnT_L71F-mediated attenuation of Ca²⁺-activated maximal tension was greater in α- than in β-MHC fibers. For example, TnT_L71F attenuated maximal tension by 31% in α-MHC fibers but only by 10% in β-MHC fibers. Furthermore, TnT_L71F reduced myofilament Ca²⁺ sensitivity by 0.11 pCa units in α-MHC fibers but only by 0.05 pCa units in β-MHC fibers. TnT_L71F augmented rate constants of crossbridge recruitment and crossbridge detachment dynamics in α-MHC fibers but not in β-MHC fibers. Collectively, our data demonstrate that TnT_L71F induces greater contractile deficits against α-MHC than against β-MHC background.

Modulation of Skeletal Muscle Contraction by Myosin Phosphorylation

The striated muscle sarcomere is a highly organized and complex enzymatic and structural organelle. Evolutionary pressures have played a vital role in determining the structure-function relationship of each protein within the sarcomere. A key part of this multimeric assembly is the light chain-binding domain (LCBD) of the myosin II motor molecule. This elongated "beam" functions as a biological lever, amplifying small interdomain movements within the myosin head into piconewton forces and nanometer displacements against the thin filament during the cross-bridge cycle. The LCBD contains two subunits known as the essential and regulatory myosin light chains (ELC and RLC, respectively). Isoformic differences in these respective species provide molecular diversity and, in addition, sites for phosphorylation of serine residues, a highly conserved feature of striated muscle systems. Work on permeabilized skeletal fibers and thick filament systems shows that the skeletal myosin light chain kinase catalyzed phosphorylation of the RLC alters the "interacting head motif" of myosin motor heads on the thick filament surface, with myriad consequences for muscle biology. At rest, structure-function changes may upregulate actomyosin ATPase activity of phosphorylated cross-bridges. During activation, these same changes may increase the Ca2+ sensitivity of force development to enhance force, work, and power output, outcomes known as "potentiation." Thus, although other mechanisms may contribute, RLC phosphorylation may represent a form of thick filament activation that provides a "molecular memory" of contraction. The clinical significance of these RLC phosphorylation mediated alterations to contractile performance of various striated muscle systems are just beginning to be understood. © 2017 American Physiological Society. Compr Physiol 7:171-212, 2017.

Increased Titin Compliance Reduced Length-Dependent Contraction and Slowed Cross-Bridge Kinetics in Skinned Myocardial Strips from Rbm (20ΔRRM) Mice

Titin is a giant protein spanning from the Z-disk to the M-band of the cardiac sarcomere. In the I-band titin acts as a molecular spring, contributing to passive mechanical characteristics of the myocardium throughout a heartbeat. RNA Binding Motif Protein 20 (RBM20) is required for normal titin splicing, and its absence or altered function leads to greater expression of a very large, more compliant N2BA titin isoform in Rbm20 homozygous mice (Rbm20^ΔRRM) compared to wild-type mice (WT) that almost exclusively express the stiffer N2B titin isoform. Prior studies using Rbm20^ΔRRM animals have shown that increased titin compliance compromises muscle ultrastructure and attenuates the Frank-Starling relationship. Although previous computational simulations of muscle contraction suggested that increasing compliance of the sarcomere slows the rate of tension development and prolongs cross-bridge attachment, none of the reported effects of Rbm20^ΔRRM on myocardial function have been attributed to changes in cross-bridge cycling kinetics. To test the relationship between increased sarcomere compliance and cross-bridge kinetics, we used stochastic length-perturbation analysis in Ca²⁺-activated, skinned papillary muscle strips from Rbm20^ΔRRM and WT mice. We found increasing titin compliance depressed maximal tension, decreased Ca²⁺-sensitivity of the tension-pCa relationship, and slowed myosin detachment rate in myocardium from Rbm20^ΔRRM vs. WT mice. As sarcomere length increased from 1.9 to 2.2 μm, length-dependent activation of contraction was eliminated in the Rbm20^ΔRRM myocardium, even though myosin MgADP release rate decreased ~20% to prolong strong cross-bridge binding at longer sarcomere length. These data suggest that increasing N2BA expression may alter cardiac performance in a length-dependent manner, showing greater deficits in tension production and slower cross-bridge kinetics at longer sarcomere length. This study also supports the idea that passive mechanical characteristics of the myocardium influence ensemble cross-bridge behavior and maintenance of tension generation throughout the sarcomere.

Contractile properties of developing human fetal cardiac muscle

KEY POINTS

The contractile properties of human fetal cardiac muscle have not been previously studied. Small-scale approaches such as isolated myofibril and isolated contractile protein biomechanical assays allow study of activation and relaxation kinetics of human fetal cardiac muscle under well-controlled conditions. We have examined the contractile properties of human fetal cardiac myofibrils and myosin across gestational age 59-134 days. Human fetal cardiac myofibrils have low force and slow kinetics of activation and relaxation that increase during the time period studied, and kinetic changes may result from structural maturation and changes in protein isoform expression. Understanding the time course of human fetal cardiac muscle structure and contractile maturation can provide a framework to study development of contractile dysfunction with disease and evaluate the maturation state of cultured stem cell-derived cardiomyocytes.

ABSTRACT

Little is known about the contractile properties of human fetal cardiac muscle during development. Understanding these contractile properties, and how they change throughout development, can provide valuable insight into human heart development, and provide a framework to study the early stages of cardiac diseases that develop in utero. We characterized the contractile properties of isolated human fetal cardiac myofibrils across 8-19 weeks of gestation. Mechanical measurements revealed that in early stages of gestation there is low specific force and slow rates of force development and relaxation, with increases in force and the rates of activation and relaxation as gestation progresses. The duration and slope of the initial, slow phase of relaxation, related to myosin detachment and thin filament deactivation rates, decreased with gestation age. F-actin sliding on human fetal cardiac myosin-coated surfaces slowed significantly from 108 to 130 days of gestation. Electron micrographs showed human fetal muscle myofibrils elongate and widen with age, but features such as the M-line and Z-band are apparent even as early as day 52. Protein isoform analysis revealed that β-myosin is predominantly expressed even at the earliest time point studied, but there is a progressive increase in expression of cardiac troponin I (TnI), with a concurrent decrease in slow skeletal TnI. Together, our results suggest that cardiac myofibril force production and kinetics of activation and relaxation change significantly with gestation age and are influenced by the structural maturation of the sarcomere and changes in contractile filament protein isoforms.

Flight capacity of Bactrocera dorsalis (Diptera: Tephritidae) adult females based on flight mill studies and flight muscle ultrastructure

The oriental fruit fly, Bactrocera dorsalis (Hendel) (Diptera: Tephritidae), is considered a major economic threat in many regions worldwide. To better comprehend flight capacity of B. dorsalis and its physiological basis, a computer-monitored flight mill was used to study flight capacity of B. dorsalis adult females of various ages, and the changes of its flight muscle ultrastructures were studied by transmission electron microscopy. The flight capacity (both speed and distance) changed significantly with age of B. dorsalis female adults, peaking at about 15 d; the myofibril diameter of the flight muscle of test insects at 15-d old was the longest, up to 1.56 µm, the sarcomere length at 15-d old was the shortest, averaging at 1.37 µm, volume content of mitochondria of flight muscle at 15-d old reached the peak, it was 32.64%. This study provides the important scientific data for better revealing long-distance movement mechanism of B. dorsalis.

Significant role of female sex hormones in cardiac myofilament activation in angiotensin II-mediated hypertensive rats

Ovariectomy leads to suppression of cardiac myofilament activation in healthy rats implicating the physiological essence of female sex hormones on myocardial contraction. However, the possible function of these hormones during pathologically induced myofilament adaptation is not known. In this study, sham-operated and ovariectomized female rats were chronically exposed to angiotensin II (AII), which has been shown to cause myocardial adaptation. In the shams, AII induced cardiac adaptation by increasing myofilament Ca(2+) sensitivity. Interestingly, this hypersensitivity was further enhanced in AII-infused ovariectomized rats. Ovariectomy increased the phosphorylation levels of cardiac tropomyosin, which may underlie the mechanism of hypersensitivity. On the other hand, AII infusion did not alter maximal tension that was suppressed after ovariectomy. This finding coincided with a comparable increase in β-isoform of myosin heavy chains in both ovariectomized groups. Together, it is conceivable that female sex hormones serve as predominant factors that regulate cardiac myofilament activation. Furthermore, they may prevent stress-induced myofilament maladaptation.

Effect of muscle length on cross-bridge kinetics in intact cardiac trabeculae at body temperature

Dynamic force generation in cardiac muscle, which determines cardiac pumping activity, depends on both the number of sarcomeric cross-bridges and on their cycling kinetics. The Frank–Starling mechanism dictates that cardiac force development increases with increasing cardiac muscle length (corresponding to increased ventricular volume). It is, however, unclear to what extent this increase in cardiac muscle length affects the rate of cross-bridge cycling. Previous studies using permeabilized cardiac preparations, sub-physiological temperatures, or both have obtained conflicting results. Here, we developed a protocol that allowed us to reliably and reproducibly measure the rate of tension redevelopment (k_tr; which depends on the rate of cross-bridge cycling) in intact trabeculae at body temperature. Using K⁺ contractures to induce a tonic level of force, we showed the k_tr was slower in rabbit muscle (which contains predominantly β myosin) than in rat muscle (which contains predominantly α myosin). Analyses of k_tr in rat muscle at optimal length (L_opt) and 90% of optimal length (L₉₀) revealed that k_tr was significantly slower at L_opt (27.7 ± 3.3 and 27.8 ± 3.0 s⁻¹ in duplicate analyses) than at L₉₀ (45.1 ± 7.6 and 47.5 ± 9.2 s⁻¹). We therefore show that k_tr can be measured in intact rat and rabbit cardiac trabeculae, and that the k_tr decreases when muscles are stretched to their optimal length under near-physiological conditions, indicating that the Frank–Starling mechanism not only increases force but also affects cross-bridge cycling kinetics.

A study of tropomyosin's role in cardiac function and disease using thin-filament reconstituted myocardium

Tropomyosin (Tm) is the key regulatory component of the thin-filament and plays a central role in the cardiac muscle's cooperative activation mechanism. Many mutations of cardiac Tm are related to hypertrophic cardiomyopathy (HCM), dilated cardiomyopathy (DCM), and left ventricular noncompaction (LVNC). Using the thin-filament extraction/reconstitution technique, we are able to incorporate various Tm mutants and protein isoforms into a muscle fiber environment to study their roles in Ca(2+) regulation, cross-bridge kinetics, and force generation. The thin-filament reconstitution technique poses several advantages compared to other in vitro and in vivo methods: (1) Tm mutants and isoforms are placed into the real muscle fiber environment to exhibit their effect on a level much higher than simple protein complexes; (2) only the primary and immediate effects of Tm mutants are studied in the thin-filament reconstituted myocardium; (3) lethal mutants of Tm can be studied without causing a problem; and (4) inexpensive. In transgenic models, various secondary effects (myocyte disarray, ECM fibrosis, altered protein phosphorylation levels, etc.) also affect the performance of the myocardium, making it very difficult to isolate the primary effect of the mutation. Our studies on Tm have demonstrated that: (1) Tm positively enhances the hydrophobic interaction between actin and myosin in the "closed state", which in turn enhances the isometric tension; (2) Tm's seven periodical repeats carry distinct functions, with the 3rd period being essential for the tension enhancement; (3) Tm mutants lead to HCM by impairing the relaxation on one hand, and lead to DCM by over inhibition of the AM interaction on the other hand. Ca(2+) sensitivity is affected by inorganic phosphate, ionic strength, and phosphorylation of constituent proteins; hence it may not be the primary cause of the pathogenesis. Here, we review our current knowledge regarding Tm's effect on the actomyosin interaction and the early molecular pathogenesis of Tm mutation related to HCM, DCM, and LVNC.

DCM-related tropomyosin mutants E40K/E54K over-inhibit the actomyosin interaction and lead to a decrease in the number of cycling cross-bridges

Two DCM mutants (E40K and E54K) of tropomyosin (Tm) were examined using the thin-filament extraction/reconstitu­tion technique. The effects of the Ca²⁺, ATP, phos­phate (Pi), and ADP concentrations on isometric tension and its transients were studied at 25°C, and the results were com­pared to those for the WT protein. Our results indicate that both E40K and E54K have a significantly lower T_HC (high Ca²⁺ ten­sion at pCa 4.66) (E40K: 1.21±0.06 T_a, ±SEM, N = 34; E54K: 1.24±0.07 T_a, N = 28), a significantly lower T_LC (low- Ca²⁺ tension at pCa 7.0) (E40K: 0.07±0.02 T_a, N = 34; E54K: 0.06±0.02 T_a, N = 28), and a significantly lower T_act (Ca²⁺ activatable tension) (T_act = T_HC–T_LC, E40K: 1.15±0.08 T_a, N = 34; E54K: 1.18±0.06 T_a, N = 28) than WT (T_HC = 1.53±0.07 T_a, T_LC = 0.12±0.01 T_a, T_act = 1.40±0.07 T_a, N = 25). All tensions were normalized to T_a ( = 13.9±0.8 kPa, N = 57), the ten­sion of actin-filament reconstituted cardiac fibers (myocardium) under the standard activating conditions. The Ca²⁺ sensitivity (pCa₅₀) of E40K (5.23±0.02, N = 34) and E54K (5.24±0.03, N = 28) was similar to that of the WT protein (5.26±0.03, N = 25). The cooper­a­tivity increased significantly in E54K (3.73±0.25, N = 28) compared to WT (2.80±0.17, N = 25). Seven kinetic constants were deduced using sinusoidal analysis at pCa 4.66. These results enabled us to calculate the cross-bridge distribution in the strongly attached states, and thereby deduce the force/cross-bridge. The results indicate that the force/cross-bridge is ∼15% less in E54K than WT, but remains similar to that of the WT protein in the case of E40K. We conclude that over-inhibition of the actomyosin interaction by E40K and E54K Tm mutants leads to a decreased force-generating ability at systole, which is the main mechanism underlying the early pathogenesis of DCM.

Familial hypertrophic cardiomyopathy related E180G mutation increases flexibility of human cardiac α-tropomyosin

α-Tropomyosin (αTm) is central to Ca(2+)-regulation of cardiac muscle contraction. The familial hypertrophic cardiomyopathy mutation αTm E180G enhances Ca(2+)-sensitivity in functional assays. To investigate the molecular basis, we imaged single molecules of human cardiac αTm E180G by direct probe atomic force microscopy. Analyses of tangent angles along molecular contours yielded persistence length corresponding to ~35% increase in flexibility compared to wild-type. Increased flexibility of the mutant was confirmed by fitting end-to-end length distributions to the worm-like chain model. This marked increase in flexibility can significantly impact systolic and possibly diastolic phases of cardiac contraction, ultimately leading to hypertrophy.

Persistence length of human cardiac α-tropomyosin measured by single molecule direct probe microscopy

α-Tropomyosin (αTm) is the predominant tropomyosin isoform in adult human heart and constitutes a major component in Ca²+-regulated systolic contraction of cardiac muscle. We present here the first direct probe images of WT human cardiac αTm by atomic force microscopy, and quantify its mechanical flexibility with three independent analysis methods. Single molecules of bacterially-expressed human cardiac αTm were imaged on poly-lysine coated mica and their contours were analyzed. Analysis of tangent-angle (θ(s)) correlation along molecular contours, second moment of tangent angles (<θ²(s)>), and end-to-end length (L(e-e)) distributions respectively yielded values of persistence length (L(p)) of 41-46 nm, 40-45 nm, and 42-52 nm, corresponding to 1-1.3 molecular contour lengths (L(c)). We also demonstrate that a sufficiently large population, with at least 100 molecules, is required for a reliable L(p) measurement of αTm in single molecule studies. Our estimate that L(p) for αTm is only slightly longer than L(c) is consistent with a previous study showing there is little spread of cooperative activation into near-neighbor regulatory units of cardiac thin filaments. The L(p) determined here for human cardiac αTm perhaps represents an evolutionarily tuned optimum between Ca²+ sensitivity and cooperativity in cardiac thin filaments and likely constitutes an essential parameter for normal function in the human heart.

Facilitated cross-bridge interactions with thin filaments by familial hypertrophic cardiomyopathy mutations in α-tropomyosin

Familial hypertrophic cardiomyopathy (FHC) is a disease of cardiac sarcomeres. To identify molecular mechanisms underlying FHC pathology, functional and structural differences in three FHC-related mutations in recombinant α-Tm (V95A, D175N, and E180G) were characterized using both conventional and modified in vitro motility assays and circular dichroism spectroscopy. Mutant Tm's exhibited reduced α-helical structure and increased unordered structure. When thin filaments were fully occupied by regulatory proteins, little or no motion was detected at pCa 9, and maximum speed (pCa 5) was similar for all tropomyosins. Ca²⁺-responsiveness of filament sliding speed was increased either by increased pCa₅₀ (V95A), reduced cooperativity n (D175N), or both (E180G). When temperature was increased, thin filaments with E180G exhibited dysregulation at temperatures ~10°C lower, and much closer to body temperature, than WT. When HMM density was reduced, thin filaments with D175N required fewer motors to initiate sliding or achieve maximum sliding speed.

Enhanced active cross-bridges during diastole: molecular pathogenesis of tropomyosin's HCM mutations

Three HCM-causing tropomyosin (Tm) mutants (V95A, D175N, and E180G) were examined using the thin-filament extraction and reconstitution technique. The effects of Ca(2+), ATP, phosphate, and ADP concentrations on cross-bridge kinetics in myocardium reconstituted with each of these mutants were studied at 25°C, and compared to wild-type (WT) Tm at physiological ionic strength (200 mM). All three mutants showed significantly higher (2-3.5 fold) low Ca(2+) tension (T(LC)) and stiffness than WT at pCa 8.0. High Ca(2+) tension (T(HC)) was significantly higher for E180G than that for WT, whereas T(HC) of V95A and D175N was similar to WT; high Ca(2+) stiffness (Y(HC)) had the same trend. The Ca(2+) sensitivity of isometric force was significantly greater for V95A and E180G than for WT, whereas that of D175N remained the same as for WT; for all mutants, cooperativity was lower than for WT. Nine kinetic constants and the cross-bridge distribution were deduced using sinusoidal analysis. The number of force-generating cross bridges was similar among the D175N, E180G, and WT Tm forms, but it was significantly larger in the case of V95A than WT. We conclude that the increased number of actively cycling cross bridges at pCa 8 is the major cause of Tm mutation-related HCM pathogenesis, which may result in diastolic dysfunction. Decreased contractility (T(act)) in V95A and D175N may further contribute to the severity of myocyte hypertrophy and related prognosis of the disease.

The role of thin filament cooperativity in cardiac length-dependent calcium activation

Length-dependent activation (LDA) is a prominent feature of cardiac muscle characterized by decreases in the Ca(2+) levels required to generate force (i.e., increases in Ca(2+) sensitivity) when muscle is stretched. Previous studies have concluded that LDA originates from the increased ability of (strong) cross-bridges to attach when muscle is lengthened, which in turn enhances Ca(2+) binding to the troponin C (TnC) subunit of the troponin complex. However, our results demonstrate that inhibition of strong cross-bridge attachment with blebbistatin had no effect on the length-dependent modulation of Ca(2+) sensitivity (i.e., EC(50)) or Ca(2+) cooperativity, suggesting that LDA originates upstream of cross-bridge attachment. To test whether LDA arises from length dependence of thin-filament activation, we replaced native cTnC with a mutant cTnC (DM-TnC) that is incapable of binding Ca(2+). Although progressive replacement of native cTnC with DM-TnC caused an expected monotonic decrease in the maximal force (F(max)), DM-TnC incorporation induced much larger increases in EC(50) and decreases in Ca(2+) cooperativity at short lengths than at long lengths. These findings support the conclusion that LDA arises primarily from the influence of length on the modulation of the Ca(2+) cooperativity arising from interaction between adjacent troponin-tropomyosin complexes on the thin filament.

Flightin is necessary for length determination, structural integrity, and large bending stiffness of insect flight muscle thick filaments

Despite the fundamental role of thick filaments in muscle contraction, little is known about the mechanical behavior of these filaments and how myosin-associated proteins dictate differences between muscle types. In this study, we used atomic force microscopy to study the morphological and mechanical properties of fully hydrated native thick filaments isolated from indirect flight muscle (IFM) of normal and mutant Drosophila lacking flightin (fln(0)). IFM thick filaments from newly eclosed (0-1 h old) wild-type flies have a mean length of 3.04+/-0.05 microm. In contrast, IFM thick filaments from newly eclosed fln(0) flies are more variable in length and, on average, are significantly longer (3.90+/-1.33 microm) than wild-type filaments from flies of the same age. In the absence of flightin, thick filaments can attain lengths >300% of wild-type filaments, indicating that flightin is required for setting the proper filament length in vivo. Filaments lacking flightin are structurally compromised, and filament preparations from fully matured 3- to 5-day-old adult fln(0) IFM yielded fragments of variable length much shorter than 3.20+/-0.04 microm, the length obtained from wild-type flies of similar age. The persistence length, an index of bending stiffness, was calculated from measurements of filament end-to-end length and contour length. We show that the presence of flightin increases persistence length by more than 40% and that wild-type filaments increase in stiffness with age. These results indicate that flightin fulfills an essential role in defining the structural and mechanical properties of IFM thick filaments.

Non-linear myofilament elasticity in frog intact muscle fibres

The aim of the present investigation was to elucidate the elastic properties of the myofilaments during tetanic activity in striated muscle. The study was carried out on intact single muscle fibres from the anterior tibialis muscle of Rana temporaria (2.0-2.5 degrees C). The instantaneous stiffness was measured as the change in force that occurred in response to a high-frequency (2-4 kHz) length oscillation while the fibre was released to shorten against a pre-set constant load that ranged between 40 and 70% of maximum tetanic force in different experiments. Measurements of fibre stiffness were carried out, at a given load, both at 2.20 microm sarcomere length (S(2.20)), i.e. at full overlap between the thick and thin filaments, and at 2.60 microm sarcomere length (S(2.60)). The fact that the load on the fibre was constant during the stiffness measurements at the two sarcomere lengths implies that the stiffness of elastic elements, acting in series with the myofilaments, was constant at the two sarcomere lengths. The fibre stiffness was consistently lower at the extended sarcomere length, the S(2.60)/S(2.20) ratio ranging from 0.83 to 0.97 at the different loads investigated. Based on the S(2.60)/S(2.20) ratio, the compliance of the free portions of the thick and thin filaments could be calculated. The myofilament stiffness was found to increase progressively as the load was raised from 40 to 70% of maximum tetanic force. At 2.20 microm sarcomere length and at 40% of maximum load on the fibre, the calculated myofilament stiffness was approximately 2.5 times the maximum cross-bridge stiffness.

Insights into the kinetics of Ca2+-regulated contraction and relaxation from myofibril studies

Muscle contraction results from force-generating interactions between myosin cross-bridges on the thick filament and actin on the thin filament. The force-generating interactions are regulated by Ca(2+) via specialised proteins of the thin filament. It is controversial how the contractile and regulatory systems dynamically interact to determine the time course of muscle contraction and relaxation. Whereas kinetics of Ca(2+)-induced thin-filament regulation is often investigated with isolated proteins, force kinetics is usually studied in muscle fibres. The gap between studies on isolated proteins and structured fibres is now bridged by recent techniques that analyse the chemical and mechanical kinetics of small components of a muscle fibre, subcellular myofibrils isolated from skeletal and cardiac muscle. Formed of serially arranged repeating units called sarcomeres, myofibrils have a complete fully structured ensemble of contractile and Ca(2+) regulatory proteins. The small diameter of myofibrils (few micrometres) facilitates analysis of the kinetics of sarcomere contraction and relaxation induced by rapid changes of [ATP] or [Ca(2+)]. Among the processes studied on myofibrils are: (1) the Ca(2+)-regulated switch on/off of the troponin complex, (2) the chemical steps in the cross-bridge adenosine triphosphatase cycle, (3) the mechanics of force generation and (4) the length dynamics of individual sarcomeres. These studies give new insights into the kinetics of thin-filament regulation and of cross-bridge turnover, how cross-bridges transform chemical energy into mechanical work, and suggest that the cross-bridge ensembles of each half-sarcomere cooperate with each other across the half-sarcomere borders. Additionally, we now have a better understanding of muscle relaxation and its impairment in certain muscle diseases.

Towards a unified theory of muscle contraction. I: foundations

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

Thin filament Ca2+ binding properties and regulatory unit interactions alter kinetics of tension development and relaxation in rabbit skeletal muscle

The influence of Ca(2+) binding properties of individual troponin versus cooperative regulatory unit interactions along thin filaments on the rate tension develops and declines was examined in demembranated rabbit psoas fibres and isolated myofibrils. Native skeletal troponin C (sTnC) was replaced with sTnC mutants having altered Ca(2+) dissociation rates (k(off)) or with mixtures of sTnC and D28A, D64A sTnC, that does not bind Ca(2+) at sites I and II (xxsTnC), to reduce near-neighbour regulatory unit (RU) interactions. At saturating Ca(2+), the rate of tension redevelopment (k(TR)) was not altered for fibres containing sTnC mutants with decreased k(off) or mixtures of sTnC:xxsTnC. We examined the influence of k(off) on maximal activation and relaxation in myofibrils because they allow rapid and large changes in [Ca(2+)]. In myofibrils with M80Q sTnC(F27W) (decreased k(off)), maximal tension, activation rate (k(ACT)), k(TR) and rates of relaxation were not altered. With I60Q sTnC(F27W) (increased k(off)), maximal tension, k(ACT) and k(TR) decreased, with no change in relaxation rates. Surprisingly, the duration of the slow phase of relaxation increased or decreased with decreased or increased k(off), respectively. For all sTnC reconstitution conditions, Ca(2+) dependence of k(TR) in fibres showed Ca(2+) sensitivity of k(TR) (pCa(50)) shifted parallel to tension and low-Ca(2+) k(TR) was elevated. Together the data suggest the Ca(2+)-dependent rate of tension development and the duration (but not rate) of relaxation can be greatly influenced by k(off) of sTnC. This influence of sTnC binding kinetics occurs primarily within individual RUs, with only minor contributions of RU interactions at low Ca(2+).

The effects of force inhibition by sodium vanadate on cross-bridge binding, force redevelopment, and Ca2+ activation in cardiac muscle

Strongly bound, force-generating myosin cross-bridges play an important role as allosteric activators of cardiac thin filaments. Sodium vanadate (Vi) is a phosphate analog that inhibits force by preventing cross-bridge transition into force-producing states. This study characterizes the mechanical state of cross-bridges with bound Vi as a tool to examine the contribution of cross-bridges to cardiac contractile activation. The K(i) of force inhibition by Vi was approximately 40 microM. Sinusoidal stiffness was inhibited with Vi, although to a lesser extent than force. We used chord stiffness measurements to monitor Vi-induced changes in cross-bridge attachment/detachment kinetics at saturating [Ca(2+)]. Vi decreased chord stiffness at the fastest rates of stretch, whereas at slow rates chord stiffness actually increased. This suggests a shift in cross-bridge population toward low force states with very slow attachment/detachment kinetics. Low angle x-ray diffraction measurements indicate that with Vi cross-bridge mass shifted away from thin filaments, implying decreased cross-bridge/thin filament interaction. The combined x-ray and mechanical data suggest at least two cross-bridge populations with Vi; one characteristic of normal cycling cross-bridges, and a population of weak-binding cross-bridges with bound Vi and slow attachment/detachment kinetics. The Ca(2+) sensitivity of force (pCa(50)) and force redevelopment kinetics (k(TR)) were measured to study the effects of Vi on contractile activation. When maximal force was inhibited by 40% with Vi pCa(50) decreased, but greater force inhibition at higher [Vi] did not further alter pCa(50). In contrast, the Ca(2+) sensitivity of k(TR) was unaffected by Vi. Interestingly, when force was inhibited by Vi k(TR) increased at submaximal levels of Ca(2+)-activated force. Additionally, k(TR) is faster at saturating Ca(2+) at [Vi] that inhibit force by > approximately 70%. The effects of Vi on k(TR) imply that k(TR) is determined not only by the intrinsic properties of the cross-bridge cycle, but also by cross-bridge contribution to thin filament activation.

Single Skeletal Muscle Fiber Elastic and Contractile Characteristics in Young and Older Men

The current investigation was designed to: (a) assess the impact of aging on elastic characteristics of single skeletal muscle fibers from young (N = 6) and older men (N = 6); and (b) correlate the potential changes, with the fiber contractile properties. Chemically skinned single muscle fibers (n = 235) from vastus lateralis muscle were maximally activated. Maximal force and cross-sectional area were measured, and specific force calculated. The slack test was used to measure maximal unloaded shortening velocity. A quick release of 0.15% of fiber length was applied to determine instantaneous stiffness. The myosin heavy chain isoform composition of each single fiber was determined by sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE). Aging induces changes in both fiber elasticity (i.e., increased instantaneous stiffness) and contractility (i.e., reduced specific force and unloaded shortening velocity) in type I and IIa fibers. However, the changes in fiber stiffness may not directly influence contractile characteristics alterations.

Mechanism of tension generation in muscle: an analysis of the forward and reverse rate constants

Tension generation in muscle occurs during the attached phase of the ATP-powered cyclic interaction of myosin heads with thin filaments. The transient nature of tension-generating intermediates and the complexity of the mechanochemical cross-bridge cycle have impeded a quantitative description of tension generation. Recent experiments performed under special conditions yielded a sigmoidal dependence of fiber tension on temperature--a unique case that simplifies the system to a two-state transition. We have applied this two-state analysis to kinetic data obtained from biexponential laser temperature-jump tension transients. Here we present the forward and reverse rate constants for de novo tension generation derived from analysis of the kinetics of the fast laser temperature-jump phase tau(2) (equivalent of the length-jump phase 2(slow)). The slow phase tau(3) is temperature-independent indicating coupling to rather than a direct role in, de novo tension generation. Increasing temperature accelerates the forward, and slows the reverse, rate constant for the creation of the tension-generating state. Arrhenius behavior of the forward and anti-Arrhenius behavior of the reverse rate constant is a kinetic signature of multistate multipathway protein-folding reactions. We conclude that locally unfolded tertiary and/or secondary structure of the actomyosin cross-bridge mediates the power stroke.

Stiffness and fraction of Myosin motors responsible for active force in permeabilized muscle fibers from rabbit psoas

The stiffness of the single myosin motor (epsilon) is determined in skinned fibers from rabbit psoas muscle by both mechanical and thermodynamic approaches. Changes in the elastic strain of the half-sarcomere (hs) are measured by fast mechanics both in rigor, when all myosin heads are attached, and during active contraction, with the isometric force (T0) modulated by changing either [Ca2+] or temperature. The hs compliance is 43.0+/-0.8 nm MPa-1 in isometric contraction at saturating [Ca2+], whereas in rigor it is 28.2+/-1.1 nm MPa-1. The equivalent compliance of myofilaments is 21.0+/-3.3 nm MPa-1. Accordingly, the stiffness of the ensemble of myosin heads attached in the hs is 45.5+/-1.7 kPa nm-1 in isometric contraction at saturating [Ca2+] (e0), and in rigor (er) it rises to 138.9+/-21.2 kPa nm-1. Epsilon, calculated from er and the lattice molecular dimensions, is 1.21+/-0.18 pN nm-1. epsilon estimated, using a thermodynamic approach, from the relation of T0 at saturating [Ca2+] versus the reciprocal of absolute temperature is 1.25+/-0.14 pN nm-1, similar to that estimated for fibers in rigor. Consequently, the ratio e0/er (0.33+/-0.05) can be used to estimate the fraction of attached heads during isometric contraction at saturating [Ca2+]. If the osmotic agent dextran T-500 (4 g/100 ml) is used to reduce the lateral filament spacing of the relaxed fiber to the value before skinning, both e0 and er increase by approximately 40%. Epsilon becomes approximately 1.7 pN nm-1 and the fraction and the force of myosin heads attached in the isometric contraction remain the same as before dextran application. The finding that the fraction of myosin heads attached to actin in an isometric contraction is 0.33 rules out the hypothesis of multiple mechanical cycles per ATP hydrolyzed.

Effects of Physical Training and Detraining, Immobilisation, Growth and Aging on Human Fascicle Geometry

In addition to its size and the extent of its neural activation, a muscle's geometry (the angles and lengths of its fibres or fascicles) strongly influences its force production characteristics. As with many other tissues within the body, muscle displays significant plasticity in its geometry. This review summarises geometric differences between various athlete populations and describes research examining the plasticity of muscle geometry with physical training, immobilisation/detraining, growth and aging. Typically, heavy resistance training in young adults has been shown to cause significant increases in fascicle angle of vastus lateralis and triceps brachii as measured by ultrasonography, while high-speed/plyometrics training in the absence of weight training has been associated with increases in fascicle length and a reduction in angles of vastus lateralis fascicles. These changes indicate that differences in geometry between various athletic populations might be at least partly attributable to their differing training regimes. Despite some inter-muscular differences, detraining/unloading is associated with decreases in fascicle angle, although little change was shown in muscles such as vastus lateralis and triceps brachii in studies examining the effects of prolonged bed rest. No research has examined the effects of other interventions such as endurance or chronic stretching training. Few data exist describing geometric adaptation during growth and maturation, although increases in gastrocnemius fascicle angle and length seem to occur until maturation in late adolescence. Although some evidence suggests that a decrease in both fascicle angle and length accompanies the normal aging process, there is a paucity of data examining the issue; heavy weight training might attenuate the decline, at least in fascicle length. A significant research effort is required to more fully understand geometric adaptation in response to physical training, immobilisation/detraining, growth and aging.

Multi-scale modelling and the IUPS physiome project

We review the development of models of cellular and tissue function and in particular address issues of multi-scale modelling, including the transition from stochastic models to continuum models and the incorporation of cell and tissue structure. The heart is used as an example of linking models at the molecular level to cell, tissue and organ level function.

The efficiency of muscle contraction

When a muscle contracts and shortens against a load, it performs work. The performance of work is fuelled by the expenditure of metabolic energy, more properly quantified as enthalpy (i.e., heat plus work). The ratio of work performed to enthalpy produced provides one measure of efficiency. However, if the primary interest is in the efficiency of the actomyosin cross-bridges, then the metabolic overheads associated with basal metabolism and excitation-contraction coupling, together with those of subsequent metabolic recovery process, must be subtracted from the total heat and work observed. By comparing the cross-bridge work component of the remainder to the Gibbs free energy of hydrolysis of ATP, a measure of thermodynamic efficiency is achieved. We describe and quantify this partitioning process, providing estimates of the efficiencies of selected steps, while discussing the errors that can arise in the process of quantification. The dependence of efficiency on animal species, fibre-type, temperature, and contractile velocity is considered. The effect of contractile velocity on energetics is further examined using a two-state, Huxley-style, mathematical model of cross-bridge cycling that incorporates filament compliance. Simulations suggest only a modest effect of filament compliance on peak efficiency, but progressively larger gains (vis-à-vis the rigid filament case) as contractile velocity approaches Vmax. This effect is attributed primarily to a reduction in the component of energy loss arising from detachment of cross-bridge heads at non-zero strain.

Force recovery after activated shortening in whole skeletal muscle: transient and steady-state aspects of force depression

The depression of isometric force after active shortening is a well-accepted characteristic of skeletal muscle, yet its mechanisms remain unknown. Although traditionally analyzed at steady state, transient phenomena caused, at least in part, by cross-bridge kinetics may provide novel insight into the mechanisms associated with force depression (FD). To identify the transient aspects of FD and its relation to shortening speed, shortening amplitude, and muscle mechanical work, in situ experiments were conducted in soleus muscle-tendon units of anesthetized cats. The period immediately after shortening, in which force recovers toward steady state, was fit by using an exponential recovery function (R2 > 0.99). Statistical analyses revealed that steady-state FD (FD(ss)) increased with shortening amplitude and mechanical work. This FD(ss) increase was always accompanied by a significant decrease in force recovery rate. Furthermore, a significant reduction in stiffness was observed after all activated shortenings, presumably because of a reduced proportion of attached cross bridges. These results were interpreted with respect to the two most prominent proposed mechanisms of force depression: sarcomere length nonuniformity theory (7, 32) and a stress-induced inhibition of cross-bridge binding in the newly formed actin-myosin overlap zone (14, 28). We hypothesized that the latter could describe both steady-state and transient aspects of FD using a single scalar variable, the mechanical work done during shortening. As either excursion (overlap) or force (stress) is increased, mechanical work increases, and cross-bridge attachment would become more inhibited, as supported by this study in which an increase in mechanical work resulted in a slower recovery to a more depressed steady-state force.

Cross-bridge versus thin filament contributions to the level and rate of force development in cardiac muscle

In striated muscle thin filament activation is initiated by Ca(2+) binding to troponin C and augmented by strong myosin binding to actin (cross-bridge formation). Several lines of evidence have led us to hypothesize that thin filament properties may limit the level and rate of force development in cardiac muscle at all levels of Ca(2+) activation. As a test of this hypothesis we varied the cross-bridge contribution to thin filament activation by substituting 2 deoxy-ATP (dATP; a strong cross-bridge augmenter) for ATP as the contractile substrate and compared steady-state force and stiffness, and the rate of force redevelopment (k(tr)) in demembranated rat cardiac trabeculae as [Ca(2+)] was varied. We also tested whether thin filament dynamics limits force development kinetics during maximal Ca(2+) activation by comparing the rate of force development (k(Ca)) after a step increase in [Ca(2+)] with photorelease of Ca(2+) from NP-EGTA to maximal k(tr), where Ca(2+) binding to thin filaments should be in (near) equilibrium during force redevelopment. dATP enhanced steady-state force and stiffness at all levels of Ca(2+) activation. At similar submaximal levels of steady-state force there was no increase in k(tr) with dATP, but k(tr) was enhanced at higher Ca(2+) concentrations, resulting in an extension (not elevation) of the k(tr)-force relationship. Interestingly, we found that maximal k(tr) was faster than k(Ca), and that dATP increased both by a similar amount. Our data suggest the dynamics of Ca(2+)-mediated thin filament activation limits the rate that force develops in rat cardiac muscle, even at saturating levels of Ca(2+).

Approaches to modeling crossbridges and calcium-dependent activation in cardiac muscle

While the primary function of the heart is a pump, ironically, the development of myofilament models that predict developed force have generally lagged behind the modeling of the electrophysiological and Ca2+-handling aspects of heart cells. A major impediment is that the basic events in force generating actin-myosin interactions are still not well understood and quantified despite advanced techniques that can probe molecular levels events and identify numerous energetic states. As a result, the modeler must decide how to best abstract the many identified states into useful models with an essential tradeoff in the level of complexity. Namely, complex models map more directly to biophysical states but experimental data does not yet exist to well constrain the rate constants and parameters. In contrast, parameters can be better constrained in simpler, lumped models, but the simplicity may preclude versatility and extensibility to other applications. Other controversies exist as to why the activation of the actin-myosin is so steeply dependent on activator Ca2+. More specifically steady-state force-[Ca2+] (F-Ca) relationships are similar to Hill functions, presumably as the result of cooperative interactions between neighboring crossbridges and/or regulatory proteins. We postulate that mathematical models must contain explicit representation of nearest-neighbor cooperative interactions to reproduce F-Ca relationships similar to experimental measures, whereas spatially compressing, mean-field approximation used in most models cannot. Finally, a related controversy is why F-Ca relationships show increased Ca2+ sensitivity as sarcomere length (SL) increases. We propose a model that suggests that the length-dependent effects can result from an interaction of explicit nearest-neighbor cooperative mechanisms and the number of recruitable crossbridges as a function of SL.

The mechanism of the force response to stretch in human skinned muscle fibres with different myosin isoforms

Force enhancement during lengthening of an active muscle, a condition that normally occurs during locomotion in vivo, is attributed to recruitment of myosin heads that exhibit fast attachment to and detachment from actin in a cycle that does not imply ATP splitting. We investigated the kinetic and mechanical features of this cycle in Ca(2+) activated single skinned fibres from human skeletal muscles containing different myosin heavy chain (MHC) isoforms, identified with single-fibre gel electrophoresis. Fibres were activated by using a new set-up that allows development of most of the tension following a temperature jump from 0-1 degrees C to the test temperature (approximately 12 degrees C). In this way we could prevent the development of sarcomere non-uniformity and record sarcomere length changes with a striation follower in any phase of the mechanical protocol. We found that: (i) fibres with fast MHC isoforms develop 40-70% larger isometric forces than those with slow isoforms, as a result of both a larger fraction of force-generating myosin heads and a higher force per head; (ii) in both slow and fast fibres, force enhancement by stretch is due to recruitment of myosin head attachments, without increase in strain per head above the value generated by the isometric heads; and (iii) the extent of recruitment is larger in slow fibres than in fast fibres, so that the steady force and power output elicited by lengthening become similar, indicating that mechanical and kinetic properties of the actin-myosin interactions under stretch become independent of the MHC isoform.