A force-similarity model of the activated muscle is able to predict primary locomotor functions

Biomechanical macroscopic models of the muscle organ as whole are conceptually limited in explaining muscle function in relation to structure. The examples are Hill-type and rheological muscle models where elastic properties of the muscle's contractible element are approached by a spring arranged in series and parallel, respectively. A new scaling model of the activated muscle powering a particular function is proposed. This model is based on the physical similarity suggested between the action-production muscle force and resulting reaction elastic muscle forces. Considered at a macroscopic scale, this force similarity provides four patterns of constraints in development of muscle architecture in different-sized animals. As the result, the analytical modeling predicts the primary motor, brake, strut and spring functions of individual muscles revealed earlier in work-loop experiments and now provided in terms of the scaling exponents for muscle cross-sectional area and fiber length. The model reliability is tested via literature available from muscle allometric data. The conceptual outcome of the study is that the architecture design of skeletal muscles is likely effected by the powering contractions of last fibers known as having higher myofibril volume than slow fibers.     

Modelling concentric contraction of muscle using an improved cross-bridge model.

Despite its overwhelming acceptance in muscle research, the cross-bridge theory does not account for all phenomena observed during muscular contractions. A phenomenon which has received much attention in the biomechanics literature, but has evaded convincing explanation and is not accounted for in the formulation of the classic cross-bridge theory, is the persistent aftereffects of muscular length changes on force production. For example, following muscle shortening, the isometric force of a muscle is depressed for a long time period ( > 5 s) compared to the corresponding isometric force following no length change. In the present study, the classic cross-bridge model was modified in two ways in an attempt to account for the force depressions following muscle shortening. First, the steady-state force depressions following shortening were described by a single scalar variable: the work performed by the muscle during shortening; and second, the dynamic, history-dependent cross-bridge properties were described using a fading memory function. The proposed model was developed and tested for shortening of the cat soleus at constant speeds ranging from 4 to 32 mm/s, for shortening at changing speeds, and for shortening of different magnitudes ranging from 2 to 10 mm. The history-dependent forces during shortening and the steady-state force depressions following shortening were well captured with the modified cross-bridge model. The present model contains two mathematically simple adaptations to the classic cross-bridge model, and is the first such model to account for the long-lasting force depressions following muscle shortening using a single scalar variable.     

The sliding filament model of muscle contraction. II. The energetic and dynamical predictions of a quantum mechanical transducer model

A theoretical model of a molecular energy transducing unit designed for the production of mechanical work is constructed and its consequences examined and compared with the experimentally determined myothermal and dynamic properties of vertebrate striated muscle. The model rests on a number of independent assumptions which include: the almost instantaneous generation of mechanical force by the occurrence of a radiationless transition between vibronic states of the transducer (crossbridge) at a point of potential energy surface crossing; transmission of this force to the load via the active sites on the thin filament by means of non-bonding repulsive forces, no energy being required for detachment; “detachment” consists of a second radiationless transition at a lower energy point than the first force generating transition, the energy difference appearing largely as work. The method of force generation completely avoids problems such as the “force-rate dilemma” which occur repeatedly in any discussion where state populations are near-Boltzmann and also leads without further arbitrary assumptions to such concepts as “attached but non force-producing states” and strongly position dependent “attachment” and “detachment” rate constants since these can only be appreciable near potential energy surface crossings. The kinetics and energetics of a transducer of this type operating cyclically and converting ATP → ADP + P_i are considered and shown to lead to length-tension and energetic behaviour very similar to that exhibited by vertebrate striated muscle, both for contraction and stretching. The existence of a limiting tension for stretching is predicted by the model as is the decrease of the rate of enthalpy release rate below the isometric value. At the limiting tension the rate of enthalpy release by the transducers is virtually zero, as observed. However, the stretching only inhibits the ATP hydrolysis, the cyclic synthesis from ADP and work being impossible with this model. The response to rapid length step changes automatically contains the asymmetry observed experimentally (with respect to lengthening and shortening) and arbitrary assumptions over and above those giving adequate explanation of the steady-state properties are not required. The asymmetry arises mainly as a consequence of the non-bonded pushing action of the crossbridges. This same assumption predicts the occurrence of an asymmetric thermoelastic ratio for active muscle with respect to stretching and contraction. The quantitative aspects of the model are satisfactory as it simultaneously reconciles the numerical magnitudes of macroscopic quantities such as isometric tension, maximum contraction velocity, limiting tension sustainable on stretching, isometric heat rate and resting heat rate with molecular parameters such as the filament and crossbridge periodicities, molecular vibrational relaxation rates, recurrence times for the radiationless transitions occurring, etc. This is achieved without any parameter optimization and only a very much smaller number of unknown parameters than the number of observed results accounted for. Many of the entities occurring in the model cycle (vibronic states of crossbridges, ATP, etc.) appear to be in one-to-one correspondence with many of the kinetic entities postulated to account for the biochemical kinetic results obtained for the actomyosin ATPase system in vitro. Finally, the rigor state has to be viewed in a different way from the conventional one; on the basis that the present model states which are part of the contraction cycle but sparsely populated during the latter (and hence are of chemical kinetic but not dynamical importance) are heavily populated during the rigor state. The mechanical properties of the rigor state would then be determined by these molecular states which would be very short-lived during the contraction cycle. If this is correct the rigor state could yield much more information about inaccessible parts of the contraction cycle than is presently supposed. The model leads one to expect a rather different response to quick length step changes in the rigor state from that of the active state, in contrast to current interpretations in terms of a large number of attached crossbridges, unable to detach due to the absence of ATP.     

Earliest mechanical evidence of cross-bridge activity after stimulation of single skeletal muscle fibers.

The stiffness of single fibers from frog skeletal muscle was measured by the application of small 2-kHz sinusoidal length oscillations during twitch and tetanic contractions at a range of initial sarcomere lengths. The earliest mechanical signs of activation were a fall in tension (latency relaxation) and a rise in stiffness. The earliest stiffness increase and the earliest tension fall occurred simultaneously at all sarcomere lengths. This suggests a cross-bridge origin for the latency relaxation. The lead of stiffness over tension seen during the rise of tension was substantially established during the latent period. Reducing the size of the twitch by reducing calcium release with D-600 (methoxyverapamil) reduced the latency relaxation and the stiffness development during latency much less than it reduced the twitch tension. For very small twitches the peak of the stiffness response occurred during the latent period and the times of onset of both latency relaxation and stiffness rise were delayed, but remained coincident. This suggests a strong connection between the latency relaxation and the rise of stiffness during the latent period, whereas the connection between these events and positive tension generation appears to be less strong.     

An energetic model of muscle contraction

Initial energy utilization in the twitch is visualized as the result of the activity of two distinct processes. The first is the calcium-pumping activity of the sarcoplasmic reticulum, which has a constant energy requirement under normal conditions. The second is the chemomechanical transduction process consisting of a variable number of quantal contractile events, each with a fixed enthalpy equal to the molecular enthalpy of adenosine triphosphate (ATP) hydrolysis in vivo. This enthalpy appears either as heat or as contractile element work. Total enthalpy varies according to the number of quantal contractile events that occur in the twitch cycle. The basis of the variation is suggested to be velocity-dependent activity of the actomyosin ATPase, allowing more quantal events to occur in a contraction cycle when shortening occurs. The classical designation “activation heat” is held to be appropriate for the first process. The partition of the enthalpy of the second process that is currently in vogue is held to be misleading and a new formulation is suggested in which the properties of the quantal contractile event are reflected in general terms. The formulation of the proposed transduction model represents a conceptual return to the viscoelastic theory, but at a quantal level. The model can explain the results of the preceding paper and is adaptable to different muscles without having to postulate fundamental differences in energy utilization.     

The cross-bridge cycle and skeletal muscle fatigue.

The functional correlates of fatigue observed in both animals and humans during exercise include a decline in peak force (P0), maximal velocity, and peak power. Establishing the extent to which these deleterious functional changes result from direct effects on the myofilaments is facilitated through understanding the molecular mechanisms of the cross-bridge cycle. With actin-myosin binding, the cross-bridge transitions from a weakly bound low-force state to a strongly bound high-force state. Low pH reduces the number of high-force cross bridges in fast fibers, and the force per cross bridge in both fast and slow fibers. The former is thought to involve a direct inhibition of the forward rate constant for transition to the strong cross-bridge state. In contrast, inorganic phosphate (Pi) is thought to reduce P0 by accelerating the reversal of this step. Both H+ and Pi decrease myofibrillar Ca2+ sensitivity. This effect is particularly important as the amplitude of the Ca2+ transient falls with fatigue. The inhibitory effects of low pH and high Pi on P0 are reduced as temperature increases from 10 to 30 degrees C. However, the H+-induced depression of peak power in the slow fiber type, and Pi inhibition of myofibrillar Ca2+ sensitivity in slow and fast fibers, are greater at high compared with low temperature. Thus the depressive effects of H+ and Pi at in vivo temperatures cannot easily be predicted from data collected below 25 degrees C. In vitro, reactive oxygen species reduce myofibrillar Ca2+ sensitivity; however, the importance of this mechanism during in vivo exercise is unknown.     

Tissue elastance influences airway smooth muscle shortening: comparison of mechanical properties among different species

We have observed striking differences in the mechanical properties of airway smooth muscle preparations among different species. In this study, we provide a novel analysis on the influence of tissue elastance on smooth muscle shortening using previously published data from our laboratory. We have found that isolated human airways exhibit substantial passive tension in contrast to airways from the dog and pig, which exhibit little passive tension (<5% of maximal active force versus approximately 60% for human bronchi). In the dog and pig, airway preparations shorten up to 70% from Lmax (the length at which maximal active force occurs), whereas human airways shorten by only approximately 12% from Lmax. Isolated airways from the rabbit exhibit relatively low passive tension (approximately 22% Fmax) and shorten by 60% from Lmax. Morphologic evaluation of airway cross sections revealed that 25-35% of the airway wall is muscle in canine, porcine, and rabbit airways in contrast to approximately 9% in human airway preparations. We postulate that the large passive tension needed to stretch the muscle to Lmax reflects the high connective tissue content surrounding the smooth muscle, which limits shortening during smooth muscle contraction by imposing an elastic load, as well as by causing radial constraint.     

Evidence for increased low force cross-bridge population in shortening skinned skeletal muscle fibers: implications for actomyosin kinetics.

The dynamic characteristics of the low force myosin cross-bridges were determined in fully calcium-activated skinned rabbit psoas muscle fibers shortening under constant loads (0.04-0.7 x full isometric tension Po). The shortening was interrupted at various times by a ramp stretch (duration, 10 ms; amplitude, up to 1.8% fiber length) and the resulting tension response was recorded. Except for the earlier period of velocity transients, the tension response showed nonlinear dependence on stretch amplitude; i.e., the magnitude of the tension response started to rise disproportionately as the stretch exceeded a critical amplitude, as in the presence of inorganic phosphate (Pi). This result, as well as the result of stiffness measurement, suggests that the low force cross-bridges similar to those observed in the presence of Pi (presumably A.M.ADP.Pi) are significantly populated during shortening. The critical amplitude of the shortening fibers was greater than that of isometrically contracting fibers, suggesting that the low force cross-bridges are more negatively strained during shortening. As the load was reduced from 0.3 to 0.04 P0, the shortening velocity increased more than twofold, but the amount of the negative strain stayed remarkably constant (approximately 3 nm). This This insensitiveness of the negative strain to velocity is best explained if the dissociation of the low force cross-bridges is accelerated approximately in proportion to velocity. Along with previous reports, the results suggest that the actomyosin ATPase cycle in muscle fibers has at least two key reaction steps in which rate constants are sensitively regulated by shortening velocity and that one of them is the dissociation of the low force A.M.ADP.Pi cross-bridges. This step may virtually limit the rate of actomyosin ATPase turnover and help increase efficiency in fibers shortening at high velocities.     

Effect of temperature on cross-bridge properties in intact frog muscle fibers

It is well known that the force developed by skeletal muscles increases with temperature. Despite the work done on this subject, the mechanism of force potentiation is still debated. Most of the published papers suggest that force enhancement is due to the increase of the individual cross-bridge force. However, reports on skinned fibers and single-molecule experiments suggest that cross-bridge force is temperature independent. The effects of temperature on cross-bridge properties in intact frog fibers were investigated in this study by applying fast stretches at various tension levels (P) on the tetanus rise at 5 degrees C and 14 degrees C to induce cross-bridge detachment. Cross-bridge number was measured from the force (critical force, P(c)) needed to detach the cross-bridge ensemble, and the average cross-bridge strain was calculated from the sarcomere elongation needed to reach P(c) (critical length, L(c)). Our results show that P(c) increased linearly with the force developed at both temperatures, but the P(c)/P ratio was considerably smaller at 14 degrees C. This means that the average force per cross bridge is greater at high temperature. This mechanism accounts for all the tetanic force enhancement. The critical length L(c) was independent of the tension developed at both temperatures but was significantly lower at high temperature suggesting that cross bridges at 14 degrees C are more strained. The increased cross-bridge strain accounts for the greater average force developed.     

The effect of cross-bridge clustering and head-head competition on the mechanical response of skeletal muscle under equilibrium conditions.

The effect of cross-bridge clustering and head-head competition on the mechanical response of skeletal muscle under equilibrium conditions is considered. For this purpose, the recent multiple site equilibrium cross-bridge model of Schoenberg (Schoenberg, M., 1985, Biophys. J., 48:467-475) is extended in accordance with the formalism of T.L. Hill (1974, Prog. Biophys, Mol. Biol., 28:267-340) to consider the case where groups of independent cross-bridge heads compete with each other for binding to multiple actin sites. Cooperative behavior between heads is not allowed. Computations indicate that for the double-headed cross-bridge with two independent equivalent heads, the time course of force decay after a stretch is similar to that for the single-headed cross-bridge; that is, the rate constant for force decay is approximately equal to the cross-bridge head detachment rate constant. The results also show that the force decay after a stretch becomes slower than the detachment rate constant of a single head when cross-bridge heads bind adjacently in clusters so that competition between heads for binding to the available actin sites increases. However, if one assumes that the detachment rate constant of an unstrained head in a fiber is comparable to that of an S1 molecule in solution, this effect is not large enough to explain why some of the rate constants for force decay after a stretch in rigor, or in the presence of ATP analogues such as adenyl-5'-yl imidodiphosphate, appear to be significantly slower than the detachment rate constant of S1 from actin in solution.     

A mono-2-ethylhexyl phthalate hydrolase from a Gordonia sp. that is able to dissimilate di-2-ethylhexyl phthalate

Gordonia sp. strain P8219, a strain able to decompose di-2-ethylhexyl phthalate, was isolated from machine oil-contaminated soil. Mono-2-ethylhexyl phthalate hydrolase was purified from cell extracts of this strain. This enzyme was a 32,164-Da homodimeric protein, and it effectively hydrolyzed monophthalate esters, such as monoethyl, monobutyl, monohexyl, and mono-2-ethylhexyl phthalate. The K(m) and V(max) values for mono-2-ethylhexyl phthalate were 26.9 +/- 4.3 microM and 18.1 +/- 0.9 micromol/min . mg protein, respectively. The deduced amino acid sequence of the enzyme exhibited less than 30% homology with those of meta-cleavage hydrolases which are serine hydrolases but exhibited no significant homology with the sequences of serine esterases. The pentapeptide motif GXSXG, which is conserved in serine hydrolases, was present in the sequence. The enzymatic properties and features of the primary structure suggested that this enzyme is a novel enzyme belonging to an independent group of serine hydrolases.     

The mechanical response of the active human triceps brachii muscle to very rapid stretch and shortening

Very rapid, small amplitude, ramp-and-hold rotations were imposed on the braced forearms of three normal adult male subjects who were isometrically contracting their elbow extensors. By carefully accounting for inertial and viscoelastic coupling effects in the experimental system it was possible to compute the time course of the muscle-moment evoked by these mechanical perturbations. The muscle-moment responses, and their dependence on rotation amplitude and direction, as well as tonic contraction level, are described. These responses are also compared to the predictions of a simple muscle model which we have proposed previously on the basis of frequency-response tests. The results indicate that: at a given tonic contraction level, triceps may be stiffer in an isometric state than in an oscillatory steady state, and high frequency fluctuations in the myoelectric activity are very ineffective in generating corresponding muscle-force fluctuations.     

Extra calcium on shortening in barnacle muscle. Is the decrease in calcium binding related to decreased cross-bridge attachment,force, or length?

Barnacle single muscle fibers were microinjected with the calcium-specific photoprotein aequorin. We have previously shown (Ridgway, E. B., and A. M. Gordon, 1984, Journal of General Physiology, 83:75-104) that when barnacle fibers are stimulated under voltage clamp and length control and allowed to shorten during the declining phase of the calcium transient, extra myoplasmic calcium is observed. The time course of the extra calcium for shortening steps at different times during the calcium transient is intermediate between those of free calcium and muscle force. Furthermore, the amplitude increases with an increased stimulus, calcium transient, and force. Therefore, the extra calcium probably comes from the activating sites on the myofilaments, possibly as a result of changes in calcium binding by the activating sites. The change in calcium binding may be due, in turn, to the change in muscle length and/or muscle force and/or cross-bridge attachment per se. In the present article, we show that the amount of the extra calcium depends on the initial muscle length, declining at shorter lengths. This suggests length-dependent calcium binding. The relation between initial length and extra calcium, however, parallels that between initial length and peak active force. The ratio of extra calcium to active force is therefore virtually independent of initial length. These data do not distinguish between a direct effect of length on calcium binding and an indirect effect owing to changes in cross-bridge attachment and force through some geometrical factor. The amount of extra calcium increases with the size of the shortening step, tending toward saturation for steps of greater than or equal to 10%. This experiment suggests that calcium binding depends on muscle force or cross-bridge attachment, not just length (if at all). There is much less extra calcium seen with shortening steps at high force when the high force results from stretch of the active muscle than when it results from increased stimulation of muscle.(ABSTRACT TRUNCATED AT 400 WORDS)