Cross-bridge Dynamics Research Articles

Concentration and Elongation of Attached Cross-bridges as Pressure Determinants in a Ventricular Model

A ventricular model based on a muscle model relating sarcomere dynamics to Ca2+kinetics was used to establish the relative contribution to pressure development of the two components of cross-bridge dynamics: attached cross-bridge concentration and elongation of its elastic structure. The model was tested by reproduction of experiments reflecting myofibrillar behavior at the ventricular level as well as chamber mechanical properties. It was then used to study cross-bridge behavior independently of Ca2+activation, by simulation of flow-clamp experiments at constant Ca2+concentration. During the volume ramp, both reduced cross-bridge elongation and decreased concentration by cross-bridge detachment caused a fall of pressure; at end-ejection there was a fast partial increase of pressure by recovery of cross-bridge elongation, and during post-ejection there was a slower pressure change towards the value corresponding to end-ejection volume by cross-bridge reattachment according to the rate of constants of Ca2+kinetics. Likewise, during a physiological normal ejection, results showed that a maximal decrease in cross-bridge elongation (Δh) produced a maximal reduction of ejecting pressure with respect to that at constant cross-bridge elongation (ΔP), both in simulated beats (ΔP=20%, Δh=17%), and in experimentally fitted pressure–volume data from open-chest dogs (ΔP=43.7±3.8%, Δh=30.7±8.3%), Δh being dependent of peak flow (Δh=0.1471 peak flow+6.0788,r=0.72). We conclude that normal ejecting pressure depends not only on cross-bridge concentration, but also on the elongation of its elastic structure, which reduces pressure according to flow.

Measured and modeled properties of mammalian skeletal muscle. I. The effects of post-activation potentiation on the time course and velocity dependencies of force production.

Activation of mammalian fast-twitch skeletal muscle induces a persistent effect known as post-activation potentiation (PAP), classically defined as an increase in force production at sub-maximal levels of activation. The underlying mechanism is thought to be phosphorylation of the myosin regulatory light chain (MRLC), which leads to an increase in the rate constant for cross-bridge attachment (Sweeney et al., 1993). If true, this suggests the hypothesis that other contractile properties should be affected during PAP. Using a feline fast-twitch whole-muscle preparation (caudofemoralis) at 37 degrees C, we observed that PAP greatly increased tetanic forces during active lengthening decreased isometric tetanic rise times and delayed isometric tetanic force relaxation. The first two of these effects were length dependent with a greater effect occurring at shorter lengths. These findings confirmed that PAP has other functionally important effects beyond a simple increase in sub-maximal isometric forces. Furthermore, length was found to have an effect independent of PAP on the shortening half of the FV relationship (less force was produced at longer lengths) and on the rate of force relaxation during the later stages of isometric tetanic force decay (slower relaxation at longer lengths). All of these findings can be explained with a simplified, two-state model of cross-bridge dynamics that accounts for the interaction of both interfilament spacing and MRLC phosphorylation on the apparent rate constants for cross-bridge attachment and detachment. These findings are largely consistent with data collected previously from reduced preparations such as skinned fibers at cold, unphysiological temperatures (e.g. 5 degrees C). One finding that could not be explained by our model was that twitch fall times in the dispotentiated state were parabolically correlated with length, whereas in the potentiated state the relationship was linear. The time course of decay of this effect did not follow the time course of force dispotentiation, suggesting that there are other activation-dependent processes occurring in parallel with MRLC phosphorylation.

Human muscle modelling from a user's perspective

Methods for developing mathematical models representing entire human muscles are briefly reviewed, with special emphasis on aspects of modelling velocity dependence using cross-bridge dynamics, and isometric force–length properties from myofilament lengths and muscle architecture. For each of these components, mechanistic (using basic contraction mechanisms) and phenomenological (“black-box”) models are available. Experiments on constant-velocity lengthening at different velocities were simulated using (a) a cross-bridge based model and (b) a Hill-based model. The Hill model was superior in its ability to predict muscle forces under different conditions with the same model parameters. Regarding force–length properties, myofilament overlap and muscle architecture did not correctly predict maximal isometric joint moments over the entire functional range of motion. The width of the force–length relationship of all contractile elements in a lower extremity model may be optimized to fit measured isometric moment–angle relationships. The resulting increase in width suggests that for some short-fibered muscles with complex architecture, the “effective” muscle fibre length is increased because muscle fibres may be partly connected in series as well as in parallel. It is concluded that a hybrid phenomenological/mechanistic muscle model is most likely to be practical (i.e. parameters can be estimated for human muscle) as well as accurate (i.e. correct forces are predicted for a wide range of conditions).

Rectified Brownian movement in molecular and cell biology

A unified model is presented for rectified Brownian movement as the mechanism for a variety of putatively chemomechanical energy conversions in molecular and cell biology. The model is established by a detailed analysis of ubiquinone transport in electron transport chains and of allosteric conformation changes in proteins. It is applied to P-type ATPase ion transporters and to a variety of rotary arm enzyme complexes. It provides a basis for the dynamics of actin-myosin cross-bridges in muscle fibers. In this model, metabolic free energy does no work directly, but instead biases boundary conditions for thermal diffusion. All work is done by thermal energy, which is harnessed at the expense of metabolic free energy through the establishment of the asymmetric boundary conditions. @S1063-651X~98!13502-X#

Cross-bridge dynamics in the contracting heart.

The mechanical characteristics of the myosin motor is one of the key determinants of ventricular function. In small mammals there are two myosin isoforms, V1 and V3, with profoundly different performance characteristics. We used myothermal and mechanical analysis of intact papillary muscles from thryoxine (V1) and popylthiouracil (V3) treated rabbit hearts to assess the mechanical attributes of the myosin cross-bridge cycle. The average cross-bridge force time integral for V1 papillary muscles is 0.15 +/- 0.02 pNs for the entire isometric twitch and 0.19 +/- 0.03 pNs for the portion of the isometric twitch between 0.9 peak isometric force for the rising and declining portions of the twitch. The ratio of V1/V3 for the cross-bridge force time integral for the entire twitch and at the peak of the twitch is 0.5 (p < 0.05) and 0.4 (p < 0.05), respectively. Since the peak of the twitch measurements minimize internal shortening only these will be presented below. The average unitary force and attachment time during the peak of the twitch for V1 hearts was 1.55 +/- 0.37 pN and 140 +/- 20 msec, respectively. The ratios of V1/V3 for these parameters were 0.6 (p < 0.05) and 0.8 (ns). The cycling rate and duty cycle for V1 were 4.37 +/- 0.81 cycles per head-second and 0.66 +/- 0.22. The ratios of V1/V3 for cycling rate and duty cycle were 2.8 (p < 0.05) and 2.7 (ns). These measurements are consistent with and help explain the energetic and mechanical function of the intact heart.

Phosphorylation-dependent power output of transgenic flies: an integrated study

We examine how the structure and function of indirect flight muscle (IFM) and the entire flight system of Drosophila melanogaster are affected by phosphorylation of the myosin regulatory light chain (MLC2). This integrated study uses site-directed mutagenesis to examine the relationship between removal of the myosin light chain kinase (MLCK) phosphorylation site, in vivo function of the flight system (flight tests, wing kinematics, metabolism, power output), isolated IFM fiber mechanics, MLC2 isoform pattern, and sarcomeric ultrastructure. The MLC2 mutants exhibit graded impairment of flight ability that correlates with a reduction in both IFM and flight system power output and a reduction in the constitutive level of MLC2 phosphorylation. The MLC2 mutants have wild-type IFM sarcomere and cross-bridge structures, ruling out obvious changes in the ultrastructure as the cause of the reduced performance. We describe a viscoelastic model of cross-bridge dynamics based on sinusoidal length perturbation analysis (Nyquist plots) of skinned IFM fibers. The sinusoidal analysis suggests the high power output of Drosophila IFM required for flight results from a phosphorylation-dependent recruitment of power-generating cross-bridges rather than a change in kinetics of the power generating step. The reduction in cross-bridge number appears to affect the way mutant flies generate flight forces of sufficient magnitude to keep them airborne. In two MLC2 mutant strains that exhibit a reduced IFM power output, flies appear to compensate by lowering wingbeat frequency and by elevating wingstroke amplitude (and presumably muscle strain). This behavioral alteration is not seen in another mutant strain in which the power output and estimated number of recruited cross-bridges is similar to that of wild type.

A re-examination of calcium activation in the Huxley cross-bridge model.

This paper investigates mathematical relations between models of calcium activation kinetics and Huxley-type models of cross-bridge dynamics in muscle. It is found that different calcium-activation schemes lead to the same form of generalized Huxley rate equation with calcium activation. [formula: see text] if it is assumed that calcium-troponin interaction rates are fast compared to the rates of transition associated with force-generating cross-bridge states. Calcium affects cross-bridge dynamics by modifying the bonding rate f, but does not affect the number of interacting cross bridges a or the unbonding rate g; this occurs through the appearance in the equation of an activation factor, r, which is a pure function of sarcoplasmic free calcium concentration. In particular, it is shown that both the "tight-coupling" and "loose-coupling" calcium-activation schemes introduced by Zahalak and Ma [1] lead to the same rate equation with the same activation factor; the difference between them appears in the calcium mass-balance equation. While both of these activation models can be made to fit simple twitch and force-velocity data equally well, experimentally observed load-dependent shifts in the free calcium concentration are compatible with the right-coupling scheme, but not with loose coupling.

Economy of contraction of cardiomyocytes as influenced by different positive inotropic interventions.

In the present study the effects of the novel cardiotonic agent EMD-57033 on contraction and energetic demand of isolated, electrically stimulated cardiomyocytes were investigated and compared with the effects of enhancement of extracellular calcium and of the beta-mimetic isoproterenol. In a specially designed setup [H. Rose, K.H. Strotmann, S. Pöpping, Y. Fischer, D. Kulsch, and H. Kammermeier. Am. J. Physiol. 261 (Heart Circ. Physiol. 30): H1329-H1334, 1991] parameters of contractile behavior and metabolic demand (O2 consumption) of isolated cardiac myocytes were measured. For a given enhancement of contractile performance (cell shortening) the increase in energetic demand (VO2) after application of EMD-57033 were markedly lower than on treatment with elevated extracellular Ca2+ concentration or with isoproterenol. This economization of positive inotropic effects was proposed to be due to two factors. First, stimulation-related ion cycling was only slightly enhanced with marked increase in contraction amplitude after application of EMD-57033. Second, calcium sensitization reflected in a leftward shift of the calcium concentration needed for half-maximum force development could be interpreted to be mediated by modulation of the cross-bridge dynamics of the myofilaments, where reduction of the switch-off rate of the cross bridges and prolongation of their force-generating states were presumed to be involved. Lowered pH (7.0) decreased economy of contraction. EMD-57033 restored contraction amplitude and economy of contraction at lowered pH.

Crossbridge Dynamics under Various Inotropic States in Cardiac Muscle: Evaluation by Perturbation Analyses.

As is evident in this review, significant advances have been made in the analysis of crossbridge cycling in cardiac muscle. It becomes apparent that the myocardial crossbridge cycling rate is altered by various factors such as: 1) changes in the intracellular constituents (Ca2+, MgATP, MgADP, Pi, and H+), 2) difference in the type of myosin isozyme, and 3) probably, troponin I, C-protein, and MLC2 phosphorylation. The physiological consequences of an altered crossbridge cycling rate may give rise to the changes in the contraction profile during twitch, tension cost (the ratio of ATPase activity to tension), and the thermal economy (the ratio of heat liberated to tension) of cardiac muscle. These findings and implications should be kept in mind when interpreting cardiac performance under different inotropic states.

Metabolic correlates of fatigue from different types of exercise in man.

It is well established that muscle fatigue, defined as a decline in maximal force generating capacity, is a common response to muscular activity. To what extent metabolic factors contribute to the reduced muscle function is still debated. Metabolic effects can affect muscle through different processes, either through a reduced ATP supply or by effects on EC-coupling or crossbridge dynamics. Observations from in vitro experiments are often extrapolated to interpret fatigue mechanisms from measurements performed in vivo, without recognizing that the biochemical reactions involved can be quite different depending on such factors as activation pattern, mode and duration of exercise. During repeated submaximal contractions, there is a negligible accumulation of H+ and inorganic phosphate, and hence fatigue must be ascribed to other factors. Substrate depletion might contribute to exhaustion, but cannot explain the gradual loss of maximal force. Curiously, the energetic cost of contraction increases progressively during repeated isometric but not during concentric contractions. With contractions involving high-force or high power output, fatigue is better related to H2PO4- than to pH, but still other factors seem to play a role.

Orientation and dynamics of myosin heads in aluminum fluoride induced pre-power stroke states: an EPR study.

We have determined the orientation and dynamics of the putative pre-power stroke crossbridges in skinned muscle fibers labeled with maleimide spin-label at Cys-707 of myosin. Orientation was measured using electron paramagnetic resonance (EPR) and mobility by saturation transfer EPR. The crossbridges are trapped in the pre-power stroke conformation in the presence of aluminum fluoride, Ca, and ATP. In agreement with data published for unlabeled fibers (Chase et al., 1994), spin-labeled muscle fibers display 42.5% of rigor stiffness, without the generation of force. The trapped crossbridges are as disordered as the relaxed heads, but their microsecond dynamics are significantly restricted. Modeling of the immobile fraction (35%), in terms of attached heads as estimated from stiffness, suggests that the bound heads rotate with a correlation time tau r = 150-400 microseconds, as compared to tau r = 3 microseconds for the heads in relaxed fibers. These "strongly" attached myosin heads, at orientations other than in rigor, are a candidate for the state from which head rotation generates force, as postulated by H. E. Huxley (1969). Ordering of the heads may well be the structural event driving the generation of force.

A model of stress relaxation in cross-bridge systems: effect of a series elastic element

Many experimental protocols employed in the study of muscle mechanics use tension transients as a probe of the magnitudes of the kinetic rates in the underlying cross-bridge dynamics. These transients could potentially be modified by the elastic elements that exist both within the fiber and at the points of attachment to the experimental apparatus. To better understand the magnitude of such modifications, we have used computer simulation to investigate the transients that would be expected for cross bridges acting on an actin filament attached to an elastic element. The original model of cross-bridge mechanics by A.F. Huxley was used (Prog. Biophys. 7: 255-318, 1957). After an isometric equilibrium is achieved, a tension transient is produced by changing the dissociation rate constant, g1, while holding the attachment rate constant, f1, fixed. This decreases the number of attached, force-producing cross bridges. We find that the tension transients are markedly slowed by the presence of even a few (> or = 2) nanometers of series elastic strain per half-sarcomere. Thus some rate constants inferred from mechanical transients (e.g., those induced by caged ligands) may underestimate the actual kinetic rates of the cross-bridge processes.

Cross-bridge dynamics in human ventricular myocardium. Regulation of contractility in the failing heart.

To investigate whether altered cross-bridge kinetics contribute to the contractile abnormalities observed in heart failure, we determined the mechanical properties of cardiac muscles from control and myopathic hearts. Muscle fibers from normal (n = 5) and dilated cardiomyopathy (n = 6) hearts were obtained and chemically skinned with saponin. The muscles were then maximally activated at saturating calcium concentrations. Unloaded shortening velocities (V0) were determined in both groups. V0 in control was 0.72 +/- 0.09 Lmax/sec, whereas in myopathic muscles, V0 was 0.41 +/- 0.06 Lmax/sec at 22 degrees C. The muscles were also sinusoidally oscillated at frequencies ranging between 0.01 and 100 Hz. The dynamic stiffness of the muscles was calculated from the ratio of force response amplitude to length oscillation amplitude. At low frequencies (< 0.2 Hz) the stiffness was constant but was larger in myopathic muscles. In the range of 0.2-1 Hz, there was a drop in the magnitude of dynamic stiffness to approximately one quarter of the low-frequency baseline. This range reflects cross-bridge turnover kinetics. In control muscles, the frequency of minimum stiffness was 0.78 +/- 0.06 Hz, whereas it was 0.42 +/- 0.07 Hz in myopathic muscles. At higher frequencies, the dynamic stiffness increased and reached a plateau at 30 Hz. There were no differences in the plateau reached between control and myopathic muscles. Because myopathic hearts have a markedly diminished energy reserve, the slowing of the cross-bridge cycling rate plays an important adaptational role in the observed contractility changes in human heart failure. Although the potential to generate maximal Ca(2+)-activated force is similar in normal and myopathic hearts, alterations in contractile protein composition could explain the diminished cross-bridge cycling rate in failing hearts.

Comparison of crossbridge dynamics between intact and skinned myocardium from ferret right ventricles.

This study compares the crossbridge kinetics of intact and skinned preparations from ferret cardiac muscles at 20 degrees C to determine whether skinning causes any alteration in the crossbridge response to an imposed length change. A papillary or trabecular muscle was isolated from the right ventricle, the muscle length adjusted to give the maximum twitch tension (Lmax), and the preparation was subjected to Ba2+ contracture. When steady tension developed, the length of the preparation was perturbed sinusoidally in 19 discrete frequencies, ranging from 0.13 to 135 Hz, and at a small peak-to-peak amplitude (0.25% Lmax). We identified three exponential processes in the sinusodial force-response to the imposed length oscillation, and these were labeled processes B, C, and D in order of increasing speed. A slow process, A, normally present in fast-twitch skeletal muscles, is very small or absent in cardiac muscles. Process B is an exponential delay, and the muscle produces oscillatory work on the forcing apparatus; processes C and D are exponential advances in which the muscle absorbs work. The preparation was chemically skinned and activated in the presence of (mM) CaEGTA 6 (pCa 4.55), MgATP 5, magnesium propionate 1, and phosphate 1, pH 7.0, with ionic strength adjusted to 200 mM with potassium propionate. We found that the crossbridge kinetics were not altered by the skinning procedure. The apparent rate constants extracted from the sinusoidal analysis were nearly identical in Ba2+ contracture (intact preparation) and in Ca2+ activation (skinned preparation), and the Nyquist plots were similar. Because the rate constants changed sensitively with the substrate (MgATP) concentrations, we concluded that the substrate is adequately supplied during Ba2+ contracture in the intact preparation. Our study demonstrates the compatibility of results obtained from an intact and from a skinned preparation.

A purely mechanical theory of muscular contraction

A simple mathematic model is constructed for the cross-bridge dynamics that govern muscular contraction, based on ideas introduced by Huxley and Simmons. The model differs from earlier ones in that it is based on distributions over time rather than displacement and uses a sharp disengagement rule. The constitutive functions of the model are set using classical experimental results and its predictions for the length-step experiment of Ford, Huxley, and Simmons are examined.

Adrenaline increases the rate of cross-bridge cycling in rat cardiac muscle

To characterize the myocardial cross-bridge dynamics in catecholamine-induced positive inotropic state, we studied the effects of adrenaline (6 × 10 −6 m) on the transient central segment length (SL) response to step decrease in tension in rat right ventricular papillary muscle in barium contracture. The time course of this response is thought to reflect the kinetics of actin-myosin interaction. The muscle was released stepwise from the steady contracture tension ( T c ) to new steady tension levels ( T r ) of varying magnitudes at 22°C. When the tension decrease was < 0.7 T c , the SL transient responses comprised, in most cases, four phases. The first phase was a rapid and minute shortening during tension reduction; the second was a slow further shortening; the third, a slow lengthening; and the fourth, an extremely slow shortening toward a new steady length under the new tension. Adrenaline showed almost no effect on Tc and the amplitude of SL transients, but markedly reduced the duration of the second (D 2) and third (D 3) phases of SL transient regardless of the amplitude of tension reduction. The reduction of duration was 14 ± 3% in D 2 and 26 ± 5% in D 3 at T r T c of 0.84 ± 0.03 on the average (mean ± s.d.) in nine preparations. The velocity measured from the quasi-steady SL shortening in the second phase increased with the addition of adrenaline, regardless of the amplitude of tension reduction. The increase in the shortening velocity was 16 ± 6% (mean ± s.d., n = 9) at T r T c of 0.18 ± 0.04. These results suggest that adrenaline increases the rate of cross-bridge cycling in cardiac muscle independent of activation level.

Photon correlation spectroscopy of the polarization signal from single muscle fibres

Measurements of crossbridge dynamics have been obtained from the spectrum of diffracted light derived from single, skinned fibres of skeletal muscle. This technique combines optical ellipsometry with photon correlation spectroscopy of the intrinsic reporters from the muscle cell. The difference in the intensities of the two linearly polarized electric field components of diffracted light is autocorrelated in time, and the dynamics of optical anisotropy from the contributing units of the sarcomere are measured. In focusing on the fast-time dynamics, we detected two principal features: a rapidly relaxing temporal signal with a relaxation time of approximately 5 microseconds, and an oscillatory component which transforms into a broad but spectrally defined signal centred at around 370 kHz. Experiments were conducted to measure changes of these two signals upon relax-rigor transition and alpha-chymotrypsin degradation. These studies strongly suggest that the relaxational component of the signal is primarily due to myosin crossbridge motion; the 370 kHz spectral signal has as its likely source the myosin thick filament.

Form birefringence of muscle

We investigate the sensitivity of measurements of muscle birefringence to cross-bridge dynamics in the resting, active, and rigor states. The theory of form birefringence is reviewed, and an optical model is constructed for the form birefringence of muscle. Values for the parameters in the model are selected or deduced from the literature. As an illustration of the use of the model, plausible distributions for the orientations of cross-bridges in the resting, active, and rigor states are constructed using a model for cross-bridge dynamics suggested by Huxley and Kress (1985). The general magnitude of the predictions of our model is comparable with that of published measurements of muscle birefringence. However, the precise values of the predicted birefringence for the resting, active, and rigor states are sensitive to the assumed orientations of cross-bridges. We also investigate the dependence of muscle birefringence on sarcomere length and on disorder in the orientation of the myofilament array. We conclude that measurements of muscle birefringence can play a useful role in distinguishing between proposed models of cross-bridge dynamics.

Microsecond rotational dynamics of phosphorescent-labeled muscle cross-bridges

We have measured the microsecond rotational motions of myosin heads in muscle cross-bridges under physiological ionic conditions at 4 degrees C, by detecting the time-resolved phosphorescence of eosin-maleimide covalently attached to heads in skeletal muscle myofibrils. The anisotropy decay of heads in rigor (no ATP) is constant over the time range from 0.5 to 200 microsecond, indicating that they do not undergo rotational motion in this time range. In the presence of 5 mM MgATP, however, heads undergo complex rotational motion with correlation times of about 5 and 40 microsecond. The motion of heads in relaxed myofibrils is restricted out to 1 ms, as indicated by a nonzero value of the residual anisotropy. The anisotropy decay of eosin-labeled myosin, extracted from labeled myofibrils, also exhibits complex decay on the 200-microsecond time scale when assembled into synthetic thick filaments. The correlation times and amplitudes of heads in filaments (under the same ionic conditions as the myofibril experiments) are unaffected by MgATP and very similar to the values for heads in relaxed myofibrils. The larger residual anisotropy and longer correlation times seen in myofibrils are consistent with a restriction of rotational motion in the confines of the myofibril protein lattice. These are the first time-resolved measurements under physiological conditions of the rotational motions of cross-bridges in the microsecond time range.

Skeletal muscle adaptations for maximizing exercise performance

A description of the skeletal muscle adaptations responsible for the large variations in exercise performance between and within species are outlined. These variations arise from phenotypic expression, muscle mass, and fiber quality. Specific adaptations in cross-bridge dynamics, contractile and regulatory protein isoforms, amounts of Ca2+ releasing and sequestering structures, metabolic capacity, and design inherent in the different fiber types are discussed. The alterations associated with physical stimuli generally involve changes in the rates of protein degradation and synthesis, whereas nonphysiological stimuli are normally required to induce changes in the kinds of proteins produced.