Measurement of rate constants for the contractile cycle of intact mammalian muscle fibers

Measuring myosin cross-bridge attachment time in activated muscle fibers using stochastic vs. sinusoidal length perturbation analysis

The average time myosin cross bridges remain bound to actin (t(on)) can be measured by sinusoidal length perturbations (sinusoidal analysis) of striated muscle fibers using recently developed analytic methods. This approach allows measurements of t(on) in preparations possessing a physiologically relevant myofilament lattice. In this study, we developed an approach to measure t(on) in 5-10% of the time required for sinusoidal analysis by using stochastic length perturbations (white noise analysis). To compare these methods, we measured the influence of MgATP concentration ([MgATP]) on t(on) in demembranated myocardial strips from mice, sampling muscle behavior from 0.125 to 200 Hz with a 20-s burst of white noise vs. a 300-s series of sinusoids. Both methods detected a similar >300% increase in t(on) as [MgATP] decreased from 5 to 0.25 mM, differing by only 3-14% at any [MgATP]. Additional experiments with Drosophila indirect flight muscle fibers demonstrated that faster cross-bridge cycling kinetics permit further reducing of the perturbation time required to measure t(on). This reduced sampling time allowed strain-dependent measurements of t(on) in flight muscle fibers by combining 10-s bursts of white noise during periods of linear shortening and lengthening. Analyses revealed longer t(on) values during shortening and shorter t(on) values during lengthening. This asymmetry may provide a mechanism that contributes to oscillatory energy transfer between the flight muscles and thoracic cuticle to power flight. This study demonstrates that white noise analysis can detect underlying molecular processes associated with dynamic muscle contraction comparable to sinusoidal analysis, but in a fraction of the time.

Two-state model of acto-myosin attachment-detachment predicts C-process of sinusoidal analysis

The force response of activated striated muscle to length perturbations includes the so-called C-process, which has been considered the frequency domain representation of the fast single-exponential force decay after a length step (phases 1 and 2). The underlying molecular mechanisms of this phenomenon, however, are still the subject of various hypotheses. In this study, we derived analytical expressions and created a corresponding computer model to describe the consequences of independent acto-myosin cross-bridges characterized solely by 1), intermittent periods of attachment (t(att)) and detachment (t(det)), whose values are stochastically governed by independent probability density functions; and 2), a finite Hookian stiffness (k(stiff)) effective only during periods of attachment. The computer-simulated force response of 20,000 (N) cross-bridges making up a half-sarcomere (F(hs)(t)) to sinusoidal length perturbations (L(hs)(t)) was predicted by the analytical expression in the frequency domain, (F(hs)(omega)/L(hs)(omega))=(t(att)/t(cycle))Nk(stiff)(iomega/(t(att)(-1)+iomega)), where t(att) = mean value of t(att), t(cycle) = mean value of t(att) + t(det), k(stiff) = mean stiffness, and omega = 2pi x frequency of perturbation. The simulated force response due to a length step (L(hs)) was furthermore predicted by the analytical expression in the time domain, F(hs)(t)=(t(att)/t(cycle))Nk(stiff)L(hs)e(-t/t(att)). The forms of these analytically derived expressions are consistent with expressions historically used to describe these specific characteristics of a force response and suggest that the cycling of acto-myosin cross-bridges and their associated stiffnesses are responsible for the C-process and for phases 1 and 2. The rate constant 2pic, i.e., the frequency parameter of the historically defined C-process, is shown here to be equal to t(att)(-1). Experimental results from activated cardiac muscle examined at different temperatures and containing predominately alpha- or beta-myosin heavy chain isoforms were found to be consistent with the above interpretation.

Viscous properties of human muscle during contraction

The purpose of this study was to determine viscous properties of human muscle during plantarflexion efforts. Experiments were performed on 17 subjects with an ankle ergometer allowing sinusoidal oscillations during isometric contractions and isokinetic movements. Sinusoidal oscillations led to the expression of (i) Bode diagrams of the musculo-articular system allowing the determination of a damping coefficient (Bbode); and (ii) a viscous coefficient (Bsin) using an adaptation of Hill's equation to sinusoidal oscillations. Isokinetic movements led to torque-velocity relationships. They showed a fall in torque associated to an increase in angular velocity what was quantified by calculating a damping coefficient (Biso). Both experiments gave consistent results indicating that Bbode was the lowest viscous parameter. This difference is discussed in terms of (i) "analog" viscosity originating from muscle cross-bridges; and (ii) real mechanical damping of passive structures.

Contractile behaviour in skeletal muscle-tendon unit during small amplitude sine wave perturbations

The effects of sinusoidal vibrations (0.2 mm) on contractile behaviour of the medial gastrocnemius muscle of the rat (N = 6) were determined over a wide range of frequencies (10-210 Hz). The performance of the contractile element (CE) during maximal tetanic contractions and vibrations was calculated by correcting muscle performance for series elasticity. For one experimental muscle the contractions were simulated using a computer model based on mechanical characteristics of that particular muscle. It was found that 10 Hz movements increased the slope of the CE force-velocity curve, compared to its isokinetically determined characteristics. At higher frequencies (30 Hz and above) this slope decreased. It is hypothesised that these two changes in CE behaviour are based on the same phenomena in CE behaviour: force enhancement by active stretch and depression by shortening. The time constants of the decay of these processes may cause the different impact on CE force-velocity behaviour. It is concluded that CE performance is affected at all frequencies, but its impact on muscle-tendon performance shows at low frequencies only. At high-frequencies series elastic characteristics play a dominant role.

Frequency response to rat gastrocnemius medialis in small amplitude vibrations

The effect of vibration frequency during small amplitude (approximately 0.25% of muscle-tendon complex length) vibrations on muscle stiffness and phase angle of the rat gastrocnemius medialis muscle (n = 7) was investigated at four different force levels. Frequencies varying from 5 to 180 Hz were studied. Furthermore, series elastic stiffness was determined as a function of muscle force. The experiments were also simulated, using a Hill-type muscle model representing the fundamental characteristics of the experimental muscles. The frequency response found in the experiments deviated from the simulation results: stiffness and phase were lowest at about 30 Hz, whereas the simulations showed a rapid asymptotic increase of stiffness and decrease of phase angle with increasing frequency. The values levelled off at about 60 Hz. The discrepancy between experimental and simulation results is thought to be due to changes of the contractile properties of muscle, especially at low movement frequencies, where the contractile machinery has a significant influence on muscle stiffness. At frequencies of 120 Hz and above, the muscle stiffness resembled series elastic stiffness in both experimental muscles and simulations. This suggests that the contractile element contracts approximately isometrically. Functional implications of the frequency response are discussed.

Muscle stiffness during transient and continuous movements of cat muscle: perturbation characteristics and physiological relevance

Continuous stochastic position perturbations are an attractive alternative to transient perturbations in muscle and reflex studies because they allow efficient characterization of system properties. However, the relevance of the results obtained from stochastic perturbations remains unclear because they may induce a state change in muscle properties. We addressed this concern by comparing the force and stiffness responses of isolated muscles of the decerebrate cat elicited by stochastic perturbations to those evoked by "step" stretches of similar amplitudes. Muscle stiffness during stochastic perturbations was found to be predominantly linear and elastic in nature for a given operating point, showing no evidence of instantaneous amplitude-dependent nonlinearities, even during large movements. In contrast, force responses evoked by step stretches were found to be mainly viscous in nature and nonlinear for larger stretches, with only a small maintained (elastic) component. Stiffness magnitude decreased with displacement amplitude for both stochastic and step perturbations. Our results are largely consistent with the crossbridge theory of muscle contraction, indicating that transient and continuous displacements evoke different, although functionally relevant, aspects of muscle behavior. These differences have several implications for the neural control of posture and movement, and for the design of perturbations appropriate for its study.

Gel electrophoresis of reacting macromolecules. Rate-limited self-association

Prompted by experimental sodium dodecyl sulfate-gradient polyacrylamide gel electrophoresis (PAGE) patterns of an oligomerizing 73-residue peptide, PAGE and gradient PAGE patterns were simulated numerically for two rate-limited, reversible self-associating systems, viz., monomer-dimer and monomer-dimer-tetramer interactions. A wide range of values for rate constants and other relevant parameters was examined. The cardinal result for interactions with half-times comparable to the time of electrophoresis is that the number of peaks in the pattern can exceed the number of interacting species. Since peaks of intermediate migration velocities are composed of interconverting monomer and oligomers, molecular weights corresponding to individual species cannot be assigned to them.

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.

Force development and relaxation in single motor units of adult cats during a standard fatigue test

1. The purpose of this study was to investigate tetanic force development and relaxation in single motor units that were subjected to a standard fatigue test. 2. Motor units of tibialis posterior, a hindlimb muscle in the adult cat, were assigned to four categories (i.e. types S, FR, FI, FF) using conventional criteria. 3. Based on the first tetanus of the fatigue test, type S units took significantly longer to develop force and to relax than the fast-twitch units. Within the fast-twitch subpopulations, type FR and FI units were significantly slower to develop force and to relax than were type FF units, but there were no significant differences between type FR and FI units. 4. After 120 s of the fatigue test, the rates of force development were faster than initial values in type S and FR units, but were largely unchanged for the type FI and FF units. Most relaxation parameters were unaffected by stimulation in type S and FR units, but all parameters became significantly slower in type FI and FF units. 5. The average time courses of force development and relaxation showed that during 240 s of the fatigue test, type S units exhibited either a progressive increase in a parameter or no change at all. In contrast, fast-twitch units displayed profiles that included initial increases in a force development or relaxation parameter followed by variable amounts of decline that corresponded to fatigability. 6. It is concluded that repetitive activation affects the development and relaxation of tetanic force in all motor-unit types. Average changes in these parameters tended to parallel the conventional classification of motor units into four categories.

RecA protein self-assembly. Multiple discrete aggregation states

Light scattering, sedimentation and electron microscopy have been used to investigate the aggregation states of highly purified RecA protein in solution. We show that RecA protein will self-assemble into a discrete series of quaternary structures depending upon protein concentration, ionic environment, and nucleotide cofactors. In a stock solution at moderate concentration (10 to 50 microM) RecA protein exists as small particles approximately 4 nm in diameter, larger particles approximately 12 nm in diameter (most probably rings of RecA protein), 10 nm diameter rods varying from 50 to 200 nm in length, and finally as much larger bundles of rods. The addition of monovalent salt shifts the distribution of RecA protein between its various oligomeric states. Increasing protein concentration favors more highly aggregated structures. At a given protein concentration, addition of mM levels of MgCl2 promotes the rapid formation of rods and slow formation of bundles. Under conditions typical of in vitro strand exchange reactions, RecA protein was found to exist as a mixture of rods and 12 nm particles with relatively few monomers.

The kinetics relating calcium and force in skeletal muscle

The kinetics relating Ca2+ transients and muscle force were examined using data obtained with the photoprotein aequorin in skeletal muscles of the rat, barnacle, and frog. These data were fitted by various models using nonlinear methods for minimizing the least mean square errors. Models in which Ca2+ binding to troponin was rate limiting for force production did not produce good agreement with the observed data, except for a small twitch of the barnacle muscle. Models in which cross-bridge kinetics were rate limiting also did not produce good agreement with the observed data, unless the detachment rate constant was allowed to increase sharply on the falling phase of tension production. Increasing the number of cross-bridge states did not dramatically improve the agreement between predicted and observed force. We conclude that the dynamic relationship between Ca2+ transients and force production in intact muscle fibers under physiological conditions can be approximated by a model in which (a) two Ca2+ ions bind rapidly to each troponin molecule, (b) force production is limited by the rate of formation of tightly bound cross-bridges, and (c) the rate of cross-bridge detachment increases rapidly once tension begins to decline and free Ca2+ levels have fallen to low values after the last stimulus. Such a model can account not only for the pattern of force production during a twitch and tetanus, but also the complex, nonlinear pattern of summation which is observed during an unfused tetanus at intermediate rates of stimulation.

Comparison of force and stiffness in normal and dystrophic mouse muscles

Isometric force and stiffness of fast- and slow-twitch muscles of affected and normal mice of the 129/ReJ dy/dy strain were studied at rest and during active contraction at a variety of lengths. Dystrophic muscles developed less force in response to stimulation, but the resting stiffness was not reduced as much, particularly at long muscle lengths. This is consistent with the replacement of muscle fibers by connective tissue that is considerably less elastic. When second and third stimuli are superimposed on the rising phase of a twitch in a normal muscle, a less-than-linear summation of force and stiffness generation (early depression) is followed by a more-than-linear summation (later facilitation). Dystrophic muscles showed a smaller early depression and a greater later facilitation of force and active muscle stiffness. Many of these phenomena can be predicted from a simple model of Ca2+ release and binding to troponin.