Effects of the N-terminal domains of myosin binding protein-C in an in vitro motility assay: Evidence for long-lived cross-bridges

Myosin binding protein-C (MyBP-C) is a thick-filament protein whose precise function within the sarcomere is not known. However, recent evidence from cMyBP-C knock-out mice that lack MyBP-C in the heart suggest that cMyBP-C normally slows cross-bridge cycling rates and reduces myocyte power output. To investigate possible mechanisms by which cMyBP-C limits cross-bridge cycling kinetics we assessed effects of recombinant N-terminal domains of MyBP-C on the ability of heavy meromyosin (HMM) to support movement of actin filaments using in vitro motility assays. Here we show that N-terminal domains of cMyBP-C containing the MyBP-C "motif," a sequence of approximately 110 amino acids, which is conserved across all MyBP-C isoforms, reduced actin filament velocity under conditions where filaments are maximally activated (i.e. either in the absence of thin filament regulatory proteins or in the presence of troponin and tropomyosin and high [Ca2+]). By contrast, under conditions where thin filament sliding speed is submaximal (i.e. in the presence of troponin and tropomyosin and low [Ca2+]), proteins containing the motif increased filament speed. Recombinant N-terminal proteins also bound to F-actin and inhibited acto-HMM ATPase rates in solution. The results suggest that N-terminal domains of MyBP-C slow cross-bridge cycling kinetics by reducing rates of cross-bridge detachment.     

Cardiac myofilaments: mechanics and regulation

The mechanical properties of the cardiac myofilament are an important determinant of pump function of the heart. This report is focused on the regulation of myofilament function in cardiac muscle. Calcium ions form the trigger that induces activation of the thin filament which, in turn, allows for cross-bridge formation, ATP hydrolysis, and force development. The structure and protein-protein interactions of the cardiac sarcomere that are responsible for these processes will be reviewed. The molecular mechanism that underlies myofilament activation is incompletely understood. Recent experimental approaches have been employed to unravel the mechanism and regulation of myofilament mechanics and energetics by activator calcium and sarcomere length, as well as contractile protein phosphorylation mediated by protein kinase A. Central to these studies is the question whether such factors impact on muscle function simply by altering thin filament activation state, or whether modulation of cross-bridge cycling also plays a part in the responses of muscle to these stimuli.     

Length dependence of active force production in skeletal muscle.

The sliding filament and cross-bridge theories of muscle contraction provide discrete predictions of the tetanic force-length relationship of skeletal muscle that have been tested experimentally. The active force generated by a maximally activated single fiber (with sarcomere length control) is maximal when the filament overlap is optimized and is proportionally decreased when overlap is diminished. The force-length relationship is a static property of skeletal muscle and, therefore, it does not predict the consequences of dynamic contractions. Changes in sarcomere length during muscle contraction result in modulation of the active force that is not necessarily predicted by the cross-bridge theory. The results of in vivo studies of the force-length relationship suggest that muscles that operate on the ascending limb of the force-length relationship typically function in stretch-shortening cycle contractions, and muscles that operate on the descending limb typically function in shorten-stretch cycle contractions. The joint moments produced by a muscle depend on the moment arm and the sarcomere length of the muscle. Moment arm magnitude also affects the excursion (length change) of a muscle for a given change in joint angle, and the number of sarcomeres arranged in series within a muscle fiber determines the sarcomere length change associated with a given excursion.     

Cardiac mechanoenergetics in silico

The aim of this thesis is to investigate the link between biochemical intracellular processes and mechanical contraction of the cardiac muscle. First, the regulation of intracellular energy fluxes between mitochondria and myofibrils is studied. It is shown, that the experimentally observed metabolic stability of the cardiac muscle is reproducible by a simple feedback regulation mechanism, i.e., ATP consumption in myofibrils and ATP production in mitochondria are balanced by the changes of the high energy phosphate concentrations. Second, an important property of energy transformation from biochemical form to mechanical work in the cardiac muscle, the linear relationship between the oxygen consumption and the stress-strain area, is replicated by a cross-bridge model. Third, by using the developed cross-bridge model, the correlation between ejection fraction of the left ventricle and heterogeneity of sarcomere strain, developed stress and ATP consumption in the left ventricular wall is established. Fourth, an experimentally observed linear relationship between oxygen consumption and the pressure-volume area can be predicted theoretically from a linear relationship between the oxygen consumption and the stress-strain area. Summing up, it is shown how the macrovariables of a cardiac muscle are interwoven with intracellular physiological processes into a whole.     

Analysis of hystereses in force length and force calcium relations

Analysis of the hystereses in the force-length relationship at constant Ca(2+) concentration and in the force-calcium relationship at constant sarcomere length (SL) provides insight into the mechanisms that control cross-bridge (XB) recruitment. The hystereses are related here to two mechanisms that regulate the number of strong XBs: the cooperativity, whereby the number of strong XBs determines calcium affinity, and the mechanical feedback, whereby the shortening velocity determines the duration for which the XBs are in the strong state. The study simulates the phenomena and defines the role of these feedbacks. The model that couples calcium kinetics with XB cycling was built on Simulink software (Matlab). Counterclockwise (CCW) hysteresis, wherein the force response lags behind the SL oscillations, at a constant calcium level, is obtained in the force-length plane when neglecting the mechanical feedback and accounting only for the cooperativity mechanism. Conversely, the force response precedes the SL oscillations, yielding a clockwise (CW) hysteresis when only the mechanical feedback is allowed to exist. In agreement with experimental observations, either CW or CCW hysteresis is obtained when both feedbacks coexist: CCW hystereses are obtained at low frequencies (<3 Hz), and the direction is reversed to CW at higher frequencies (>3 Hz). The cooperativity dominates at low frequencies and allows the muscle to adapt XB recruitment to slow changes in the loading conditions. The changeover frequency from CCW to CW hysteresis defines the velocity limit above which the muscle absorbs rather than generates energy. The hysteresis in the force-calcium relation is conveniently explained by the same cooperativity mechanism. We propose that a single cooperativity mechanism that depends on the number of strong XBs can explain the hystereses in the force-length as well as in the force-calcium relationships.     

On the theory of muscle contraction: filament extensibility and the development of isometric force and stiffness.

The newly discovered extensibility of actin and myosin filaments challenges the foundation of the theory of muscle mechanics. We have reformulated A. F. Huxley's sliding filament theory to explicitly take into account filament extensibility. During isometric force development, growing cross-bridge tractions transfer loads locally between filaments, causing them to extend and, therefore, to slide locally relative to one another. Even slight filament extensibility implies that 1) relative displacement between the two must be nonuniform along the region of filament overlap, 2) cross-bridge strain must vary systematically along the overlap region, and importantly, 3) the local shortening velocities, even at constant overall sarcomere length, reduce force below the level that would have developed if the filaments had been inextensible. The analysis shows that an extensible filament system with only two states (attached and detached) displays three important characteristics: 1) muscle stiffness leads force during force development; 2) cross-bridge stiffness is significantly higher than previously assessed by inextensible filament models; and 3) stiffness is prominently dissociated from the number of attached cross-bridges during force development. The analysis also implies that the local behavior of one myosin head must depend on the state of neighboring attachment sites. This coupling occurs exclusively through local sliding velocities, which can be significant, even during isometric force development. The resulting mechanical cooperativity is grounded in fiber mechanics and follows inevitably from filament extensibility.     

In vitro actin filament sliding velocities produced by mixtures of different types of myosin.

Using in vitro motility assays, we examined the sliding velocity of actin filaments generated by pairwise mixings of six different types of actively cycling myosins. In isolation, the six myosins translocated actin filaments at differing velocities. We found that only small proportions of a more slowly translating myosin type could significantly inhibit the sliding velocity generated by a myosin type that translocated filaments rapidly. In other experiments, the addition of noncycling, unphosphorylated smooth and nonmuscle myosin to actively translating myosin also inhibited the rapid sliding velocity, but to a significantly reduced extent. The data were analyzed in terms of a model derived from the original working cross-bridge model of A.F. Huxley. We found that the inhibition of rapidly translating myosins by slowly cycling was primarily dependent upon only a single parameter, the cross-bridge detachment rate at the end of the working powerstroke. In contrast, the inhibition induced by the presence of noncycling, unphosphorylated myosins required a change in another parameter, the transition rate from the weakly attached actomyosin state to the strongly attached state at the beginning of the cross-bridge power stroke.     

Sarcomere lattice geometry influences cooperative myosin binding in muscle

In muscle, force emerges from myosin binding with actin (forming a cross-bridge). This actomyosin binding depends upon myofilament geometry, kinetics of thin-filament Ca²⁺ activation, and kinetics of cross-bridge cycling. Binding occurs within a compliant network of protein filaments where there is mechanical coupling between myosins along the thick-filament backbone and between actin monomers along the thin filament. Such mechanical coupling precludes using ordinary differential equation models when examining the effects of lattice geometry, kinetics, or compliance on force production. This study uses two stochastically driven, spatially explicit models to predict levels of cross-bridge binding, force, thin-filament Ca²⁺ activation, and ATP utilization. One model incorporates the 2-to-1 ratio of thin to thick filaments of vertebrate striated muscle (multi-filament model), while the other comprises only one thick and one thin filament (two-filament model). Simulations comparing these models show that the multi-filament predictions of force, fractional cross-bridge binding, and cross-bridge turnover are more consistent with published experimental values. Furthermore, the values predicted by the multi-filament model are greater than those values predicted by the two-filament model. These increases are larger than the relative increase of potential inter-filament interactions in the multi-filament model versus the two-filament model. This amplification of coordinated cross-bridge binding and cycling indicates a mechanism of cooperativity that depends on sarcomere lattice geometry, specifically the ratio and arrangement of myofilaments.     

Geometrical restrictions on cross-bridge motion and sliding filament dynamics

To ensure asynchronous motion and continuous force development in a sliding filament mechanism when the cross-bridge configurational cycle is geometrically constant and uniform, the repeat distances of the cross-bridge set and the active site set must be different. When the two sets overlap they will then form an interference pattern—the elements are in phase in some regions, out of phase in others. The geometrical restrictions that this puts on the cross-bridge cycle are discussed. One consequence may be that only a discrete set of modes of motion are possible in active filament sliding, the number of modes being determined by the energy supply rate and the internal friction in the system.     

The first three minutes: smooth muscle contraction, cytoskeletal events, and soft glasses.

Smooth muscle exhibits biophysical characteristics and physiological behaviors that are not readily explained by present paradigms of cytoskeletal and cross-bridge mechanics. There is increasing evidence that contractile activation of the smooth muscle cell involves an array of cytoskeletal processes that extend beyond cross-bridge cycling and the sliding of thick and thin filaments. We review here the evidence suggesting that the biophysical and mechanical properties of the smooth muscle cell reflect the integrated interactions of an array of highly dynamic cytoskeletal processes that both react to and transform the dynamics of cross-bridge interactions over the course of the contraction cycle. The activation of the smooth muscle cell is proposed to trigger dynamic remodeling of the actin filament lattice within cellular microdomains in response to local mechanical and pharmacological events, enabling the cell to adapt to its external environment. As the contraction progresses, the cytoskeletal lattice stabilizes, solidifies, and forms a rigid structure well suited for transmission of tension generated by the interaction of myosin and actin. The integrated molecular transitions that occur within the contractile cycle are interpreted in the context of microscale agitation mechanisms and resulting remodeling events within the intracellular microenvironment. Such an interpretation suggests that the cytoskeleton may behave as a glassy substance whose mechanical function is governed by an effective temperature.     

Models in which many cross-bridges attach simultaneously can explain the filament movement per ATP split during muscle contraction

Contractile filaments in skeletal muscle are moved by less than 2 nm for each ATP used. If just one cross-bridge is attached to each thin filament at any instant then this distance represents the fundamental myosin cross-bridge step size (i.e. the distance one cross-bridge moves a thin filament in one ATP-splitting cycle). However, most contraction models assume many cross-bridges are attached at any instant along each thin filament. The purpose of this study was to establish whether the net filament sliding per ATP used could be explained quantitatively in terms of a cross-bridge model in which multiple cross-bridges are attached along each thin filament. It was found that the relationship between net filament sliding per ATP split and the load against which the muscle shortens is compatible with such a model and furthermore predicts that the cross-bridge step size is between 7.5 and 12.5 nm over most of the range of loads. These values were similar for different muscle fibre types.     

Dynamic analysis of the structure and function of sarcomeres

We attempted to analyze the relationships between the steric structure of the sarcomere and its physiological functions by the use of a sarcomere model of muscle contraction, which includes the geometric arrangement of the thick and thin filaments of the sarcomere, as well as of the cross-bridges and actin sites. Motions of both cross-bridges and myofilaments were considered in terms of our three-state model of the elementary cycle under constraints caused by the steric structure of the sarcomere proposed by Huxley and Brown. Each cross-bridge moves in a molecular potential of our three-state model under the influence of the sliding motions of myofilaments. The sarcomere model described well the tension-velocity relation and isotonic transient processes quantitatively and consistently. In addition, it allowed independence of the no-load shortening velocity upon the overlap of the thick and thin filaments, although the motions of cross-bridges were not independent. Effects of the helical periodicities of the thick and thin filaments and of the number of cross-bridges upon muscle contraction were studied, and the conditions for smooth and efficient contraction of muscle were obtained.     

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.     

Thick-to-Thin Filament Surface Distance Modulates Cross-Bridge Kinetics in Drosophila Flight Muscle

The demembranated (skinned) muscle fiber preparation is widely used to investigate muscle contraction because the intracellular ionic conditions can be precisely controlled. However, plasma membrane removal results in a loss of osmotic regulation, causing abnormal hydration of the myofilament lattice and its proteins. We investigated the structural and functional consequences of varied myofilament lattice spacing and protein hydration on cross-bridge rates of force development and detachment in Drosophila melanogaster indirect flight muscle, using x-ray diffraction to compare the lattice spacing of dissected, osmotically compressed skinned fibers to native muscle fibers in living flies. Osmolytes of different sizes and exclusion properties (Dextran T-500 and T-10) were used to differentially alter lattice spacing and protein hydration. At in vivo lattice spacing, cross-bridge attachment time (t_on) increased with higher osmotic pressures, consistent with a reduced cross-bridge detachment rate as myofilament protein hydration decreased. In contrast, in the swollen lattice, t_on decreased with higher osmotic pressures. These divergent responses were reconciled using a structural model that predicts t_on varies inversely with thick-to-thin filament surface distance, suggesting that cross-bridge rates of force development and detachment are modulated more by myofilament lattice geometry than protein hydration. Generalizing these findings, our results suggest that cross-bridge cycling rates slow as thick-to-thin filament surface distance decreases with sarcomere lengthening, and likewise, cross-bridge cycling rates increase during sarcomere shortening. Together, these structural changes may provide a mechanism for altering cross-bridge performance throughout a contraction-relaxation cycle.     

Effect of rigor and cycling cross-bridges on the structure of troponin C and on the Ca2+ affinity of the Ca2+-specific regulatory sites in skinned rabbit psoas fibers

Intrinsic troponin C (TnC) was extracted from small bundles of rabbit psoas fibers and replaced with TnC labeled with dansylaziridine (5-dimethylaminonaphthalene-1-sulfonyl). The flourescence of incorporated dansylaziridine-labeled TnC was enhanced by the binding of Ca2+ to the Ca2+-specific (regulatory) sites of TnC and was measured simultaneously with force (Zot, H.G., Güth, K., and Potter, J.D. (1986) J. Biol. Chem. 261, 15883-15890). Various myosin cross-bridge states also altered the fluorescence of dansylaziridine-labeled TnC in the filament, with cycling cross-bridges having a greater effect than rigor cross-bridges; and in both cases, there was an additional effect of Ca2+. The paired fluorescence and tension data were used to calculate the apparent Ca2+ affinity of the regulatory sites in the thin filament and were shown to increase at least 10-fold during muscle activation presumably due to the interaction of cycling cross-bridges with the thin filament. The cross-bridge state responsible for this enhanced Ca2+ affinity was shown to be the myosin-ADP state present only when cross-bridges are cycling. The steepness of the pCa force curves (where pCa represents the -log of the free Ca2+ concentration) obtained in the presence of ATP at short and long sarcomere lengths was the same, suggesting that cooperative interactions between adjacent troponin-tropomyosin units may spread along much of the actin filament when cross-bridges are attached to it. In contrast to the cycling cross-bridges, rigor bridges only increased the Ca2+ affinity of the regulatory sites 2-fold. Taken together, the results presented here indicate a strong coupling between the Ca2+ regulatory sites and cross-bridge interactions with the thin filament.     

Link between the enzymatic kinetics and mechanical behavior in an actomyosin motor

We have attempted to link the solution actomyosin ATPase with the mechanical properties of in vitro actin filament sliding over heavy meromyosin. To accomplish this we perturbed the system by altering the substrate with various NTPs and divalent cations, and by altering ionic strength. A wide variety of enzymatic and mechanical measurements were made under very similar solution conditions. Excellent correlations between the mechanical and enzymatic quantities were revealed. Analysis of these correlations based on a force-balance model led us to two fundamental equations, which can be described approximately as follows: the maximum sliding velocity is proportional to square root of V(max)K(m)(A), where K(m)(A) is the actin concentration at which the substrate turnover rate is half of its maximum (V(max)). The active force generated by a cross-bridge under no external load or under a small external load is proportional to square root of V(max)/K(m)(A). The equations successfully accounted for the correlations observed in the present study and observations in other laboratories.     

Geometrical factors influencing muscle force development. I. The effect of filament spacing upon axial forces.

The influence of geometry on the force and stiffness measured during muscle contraction at different sarcomere lengths is examined by using three specific models of muscle cross-bridge geometry which are based upon the double-hinge model of H. E. Huxley (Science [Wash. D.C.]. 1969, 164:1356-1366) extended to three dimensions. The force generated during muscle contraction depends upon the orientation of the individual cross-bridge force vectors and the distribution of the cross-bridges between various states. For the simplest models, in which filament separation has no effect upon cross-bridge distribution, it is shown that changes in force vectors accompanying changes in myofilament separation between sarcomere lengths 2.0 and 3.65 microgram in an intact frog skeletal muscle fiber have only a small effect upon axial force. The simplest models, therefore, produce a total axial force proportional to the overlap between the actin and myosin filaments and independent of filament separation. However, the analysis shows that it is possible to find assumptions that produce a cross-bridge model in which the axial force is not independent of filament spacing. It is also shown that for some modes of attachment of subfragment-1 (S1) to actin the azimuthal location of the actin site is important in determining the axial force. A mode of S1 attachment to actin similar to that deduced by Moore et al. (J. Mol. Biol., 1970, 50:279-294), however, exhibits rather constant cross-bridge behavior over a wide range of actin site location.     

Perturbed equilibria of myosin binding in airway smooth muscle: bond-length distributions, mechanics, and ATP metabolism

We carried out a detailed mathematical analysis of the effects of length fluctuations on the dynamically evolving cross-bridge distributions, simulating those that occur in airway smooth muscle during breathing. We used the latch regulation scheme of Hai and Murphy (Am. J. Physiol. Cell Physiol. 255:C86-C94, 1988) integrated with Huxley's sliding filament theory of muscle contraction. This analysis showed that imposed length fluctuations decrease the mean number of attached bridges, depress muscle force and stiffness, and increase force-length hysteresis. At frequencies >0.1 Hz, the bond-length distribution of slowly cycling latch bridges changed little over the stretch cycle and contributed almost elastically to muscle force, but the rapidly cycling cross-bridge distribution changed substantially and dominated the hysteresis. By contrast, at frequencies <0.033 Hz this behavior was reversed: the rapid cycling cross-bridge distribution changed little, effectively functioning as a constant force generator, while the latch bridge bond distribution changed substantially and dominated the stiffness and hysteresis. The analysis showed the dissociation of force/length hysteresis and cross-bridge cycling rates when strain amplitude exceeds 3%; that is, there is only a weak coupling between net external mechanical work and the ATP consumption required for cycling cross-bridges during the oscillatory steady state. Although these results are specific to airway smooth muscle, the approach generalizes to other smooth muscles subjected to cyclic length fluctuations.     

Compliant realignment of binding sites in muscle: transient behavior and mechanical tuning.

The presence of compliance in the lattice of filaments in muscle raises a number of concerns about how one accounts for force generation in the context of the cross-bridge cycle--binding site motions and coupling between cross-bridges confound more traditional analyses. To explore these issues, we developed a spatially explicit, mechanochemical model of skeletal muscle contraction. With a simple three-state model of the cross-bridge cycle, we used a Monte Carlo simulation to compute the instantaneous balance of forces throughout the filament lattice, accounting for both thin and thick filament distortions in response to cross-bridge forces. This approach is compared to more traditional mass action kinetic models (in the form of coupled partial differential equations) that assume filament inextensibility. We also monitored instantaneous force generation, ATP utilization, and the dynamics of the cross-bridge cycle in simulations of step changes in length and variations in shortening velocity. Three critical results emerge from our analyses: 1) there is a significant realignment of actin-binding sites in response to cross-bridge forces, 2) this realignment recruits additional cross-bridge binding, and 3) we predict mechanical behaviors that are consistent with experimental results for velocity and length transients. Binding site realignment depends on the relative compliance of the filament lattice and cross-bridges, and within the measured range of these parameters, gives rise to a sharply tuned peak for force generation. Such mechanical tuning at the molecular level is the result of mechanical coupling between individual cross-bridges, mediated by thick filament deformations, and the resultant realignment of binding sites on the thin filament.