Behaviour of the crossbridges in stretched or compressed muscle fibres

The maximum chord of the myosin heads is comparable to the closest surface-to-surface spacing between the myofilaments in a muscle at the slack length. Therefore, when the sarcomere length increases or when the fibre is compressed, the surface-to-surface myofilament spacing becomes lower than the head long axis. We conclude that, in stretched or compressed fibres, some crossbridges cannot attach, owing to steric hindrance. When the amount of compression is limited, this hindrance may be overcome by a tilting of the heads in the plane perpendicular to the filament axes; in this case, there is no consequence as concerns the crossbridge properties. In highly compressed fibres, the crossbridges become progressively hindered and all the crossbridges are hindered for an axis-to-axis spacing representing about 60% of the spacing observed under zero external osmotic pressure. In this case, both the isometric tension and the ATPase activity of the fibre are zero. In fibres stretched up to 3.77 microns (sarcomere length corresponding to the disappearance of the overlap between the thick and the thin filaments), the ratio of hindered crossbridges over the functional crossbridges may be estimated at about 55%. In stretched fibres, a noticeable proportion of crossbridges are sterically hindered and the crossbridges performance (e.g. constants of attachment and detachment) depends on filament spacing, i.e. on sarcomere length. Therefore, we think it is probably impossible to consider the crossbridges as independent force converters, since this idea requires that the crossbridge properties are independent of sarcomere length. In this connection, all the experiments performed on osmotically compressed fibres are of major importance for the understanding of the true mechanisms of muscle contraction.     

Expression of titin isoforms in red and white muscle fibres of carp (Cyprinus carpio L.) exposed to different sarcomere strains during swimming

Titin (also known as connectin) is a striated-muscle-specific protein that spans the distance between the Z- and M-lines of the sarcomere. The elastic segment of the titin molecule in the I-band is thought to be responsible for developing passive tension and for maintaining the central position of thick filaments in contracting sarcomeres. Different muscle types express isoforms of titin that differ in their molecular mass. To help to elucidate the relation between the occurrence of titin isoforms and the functional properties of different fibre types, we investigated the presence of different titin isoforms in red and white fibres of the axial muscles of carp. Gel electrophoresis of single fibres revealed that the molecular mass of titin was larger in red than in white fibres. Fibres from anterior and posterior axial muscles were also compared. For both white and red fibres the molecular mass of titin in posterior muscle fibres was larger than in anterior muscle fibres. Thus, the same fibre type can express different titin isoforms depending on its location along the body axis. The contribution of titin to passive tension and stiffness of red anterior and posterior fibres was also determined. Single fibres were skinned and the sarcomere length dependencies of passive tension and passive stiffness were determined. Measurements were made before and after extracting thin and thick filaments using relaxing solutions with 0.6 mol · l⁻¹ KCl and 1 mol · l⁻¹ KI. Tension and stiffness measured before extraction were assumed to result from both titin and intermediate filaments, and tension after extraction from only intermediate filaments. Compared to mammalian skeletal muscle, intermediate filaments developed high levels of tension and stiffness in both posterior and anterior fibres. The passive tension-sarcomere length curve of titin increased more steeply in red anterior fibres than in red posterior fibres and the curve reached a plateau at a shorter sarcomere length. Thus, the smaller titin isoform of anterior fibres results in more passive tension and stiffness for a given sarcomere strain. During continuous swimming, red fibres are exposed to larger changes in sarcomere strain than white fibres, and posterior fibres to larger changes in strain than anterior fibres. We propose that sarcomere strain is one of the functional parameters that modulates the expression of different titin isoforms in axial muscle fibres of carp. Accepted: 7 May 1997     

Cooperative behaviour of the elementary sarcomere units and the cross-bridge step size

We present a model of muscle contraction based on purely physical grounds and modulated by a parameter, k, related to the visco-elastic hindrances of the contractile apparatus. The model predicts a strong cooperation among sarcomere units and proposes that viscous hindrance is a fundamental component of the economy of the contraction. The concept of cross-bridge step size is also discussed and it is concluded that the step size is of various and probably undeterminable length.     

X-ray diffraction studies of the contractile mechanism in single muscle fibres

The molecular mechanism of muscle contraction was investigated in intact muscle fibres by X-ray diffraction. Changes in the intensities of the axial X-ray reflections produced by imposing rapid changes in fibre length establish the average conformation of the myosin heads during active isometric contraction, and show that the heads tilt during the elastic response to a change in fibre length and during the elementary force generating process: the working stroke. X-ray interference between the two arrays of myosin heads in each filament allows the axial motions of the heads following a sudden drop in force from the isometric level to be measured in situ with unprecedented precision. At low load, the average working stroke is 12 nm, which is consistent with crystallographic studies. The working stroke is smaller and slower at a higher load. The compliance of the actin and myosin filaments was also determined from the change in the axial spacings of the X-ray reflections following a force step, and shown to be responsible for most of the sarcomere compliance. The mechanical properties of the sarcomere depend on both the motor actions of the myosin heads and the compliance of the myosin and actin filaments.     

Thermodynamic features of myosin filament suspensions: implications for the modeling of muscle contraction.

The analysis of myosin filament suspensions shows that these solutions are characterized by highly nonideal behavior. From these data a model is constructed that allows us to predict that 1) when subjected to an increasing protein osmotic pressure, myosin filaments experience an elastic deformation, which is not linearly related to the acting force; and 2) at constant protein osmotic pressure, when the cross-bridges of the myosin filaments are subjected to an external, nonosmotic force parallel to the filament axis, they are deformed and the water activity coefficient is altered. As a consequence, in muscle, passive and active shortening of the sarcomere is expected to promote the change of the water-water and of the water-protein interactions. We thus propose to depict muscle contraction as a chemo-osmoelastic transduction, where the analysis of the energy partition during the power stroke requires consideration of the osmotic factor in addition to the chemoelastic ones.     

Passive tension and stiffness of vertebrate skeletal and insect flight muscles: the contribution of weak cross-bridges and elastic filaments.

Tension and dynamic stiffness of passive rabbit psoas, rabbit semitendinosus, and waterbug indirect flight muscles were investigated to study the contribution of weak-binding cross-bridges and elastic filaments (titin and minititin) to the passive mechanical behavior of these muscles. Experimentally, a functional dissection of the relative contribution of actomyosin cross-bridges and titin and minititin was achieved by 1) comparing mechanically skinned muscle fibers before and after selective removal of actin filaments with a noncalcium-requiring gelsolin fragment (FX-45), and 2) studying passive tension and stiffness as a function of sarcomere length, ionic strength, temperature, and the inhibitory effect of a carboxyl-terminal fragment of smooth muscle caldesmon. Our data show that weak bridges exist in both rabbit skeletal muscle and insect flight muscle at physiological ionic strength and room temperature. In rabbit psoas fibers, weak bridge stiffness appears to vary with both thin-thick filament overlap and with the magnitude of passive tension. Plots of passive tension versus passive stiffness are multiphasic and strikingly similar for these three muscles of distinct sarcomere proportions and elastic proteins. The tension-stiffness plot appears to be a powerful tool in discerning changes in the mechanical behavior of the elastic filaments. The stress-strain and stiffness-strain curves of all three muscles can be merged into one, by normalizing strain rate and strain amplitude of the extensible segment of titin and minititin, further supporting the segmental extension model of resting tension development.     

Stiffness of hip adductor myofibrils is decreased in children with spastic cerebral palsy

Cerebral palsy (CP) is the result of a static brain lesion which causes spasticity and muscle contracture. The source of the increased passive stiffness in patients is not understood and while whole muscle down to single muscle fibres have been investigated, the smallest functional unit of muscle (the sarcomere) has not been. Muscle biopsies (adductor longus and gracilis) from pediatric patients were obtained (CP n = 9 and control n = 2) and analyzed for mechanical stiffness, in-vivo sarcomere length and titin isoforms. Adductor longus muscle was the focus of this study and the results for sarcomere length showed a significant increase in length for CP (3.6 µm) compared to controls (2.6 µm). Passive stress at the same sarcomere length for CP compared to control was significantly lower in CP and the elastic modulus for the physiological range of muscle was lower in CP compared to control (98.2 kPa and 166.1 kPa, respectively). Our results show that CP muscle at its most reduced level (the myofibril) is more compliant compared to normal, which is completely opposite to what is observed at higher structural levels (single fibres, muscle fibre bundles and whole muscle). It is noteworthy that at the in vivo sarcomere length in CP, the passive forces are greater than normal, purely as a functional of these more compliant sarcomeres operating at long lengths. Titin isoforms were not different between CP and non-CP adductor longus but titin:nebulin was reduced in CP muscle, which may be due to titin loss or an over-expression of nebulin in CP muscles.     

Strain-induced reorientation of an intramuscular connective tissue network: implications for passive muscle elasticity

The most abundant intramuscular connective tissue component, the perimysium, of bovine M. sternomandibularis muscle was shown to be a crossed-ply arrangement of crimped collagen fibres which reorientate and decrimp on changing muscle fibre sarcomere length. Reorientation of perimysial strands was observed by light microscopy and identification of these strands as collagen fibres was confirmed by high-angle X-ray diffraction. Mean collagen fibre direction with respect to the muscle fibres ranged from approximately 80 degrees at sarcomere length = 1.1 micron to approximately 20 degrees at 3.9 microns. This behaviour was well described by a model of a crimped planar network surrounding a muscle fibre bundle of constant volume but varying length. Modelling of the mechanical properties of the perimysium at different sarcomere lengths produced a load-sarcomere length curve which was in good agreement with the passive elastic properties of the muscle, especially at long sarcomere lengths. It is concluded that the role of the perimysial collagen network is to prevent over-stretching of the muscle fibre bundles.     

The ultrahistochemical picture of the so-called reversed ATPase in the gastrocnemius muscle of the rat.

The ultrahistochemical localization of the "reversed" ATPase activity was investigated. Red muscle fibres showed permanent sarcomere contraction, enzymatic activity in the inner membrane and matrix of mitochondria, and large, osmiophilic, probably calcium-containing structures within mitochondria and on their outside. White muscle fibre sarcomeres were relaxed, and activity within their sarcoplasmic reticulum was marked, but slight in the mitochondria. The relaxed state of the sarcomere in the white muscle fibres is supposed to be connected with inactivation of myofibrillar ATPase by acid preincubation, whereas red muscle contraction indicates that acid preincubation does not inactivate their myofibrillar ATPase. That the product of its activity failed to become visible in the sarcomeres is probably due to imperfection of the method. Two sub-types of red muscle fibres were distinguished: those showing only enzymatic activity in mitochondria, and those containing large intra- and extramitochondrial osmiophilic structures. The origin and composition of these structures is difficult to explain. A relation seems to exist between their presence within mitochondria and outside.     

Optimum power output and structural design of sarcomeres

A model of a "general" sarcomere is presented for the calculation of power output as a function of (i) contraction range, (ii) contraction velocity, (iii) muscle fibre stimulation (active state) and (iv) structural parameters of the sarcomere (i.e. lengths of actin, myosin, and bare zone on myosin, and thickness of the Z-disc). The model is applicable to virtually all types of striated muscle fibres. By computer simulation, particular combinations of actin and myosin lengths were found that maximize the specific power output for particular functional demands, specified in terms of contraction range and contraction velocity. The accuracy of the prediction of the optimum sarcomere design by the model depends on the quality of its input, i.e. the available knowledge of the in vivo spectrum of contraction velocities and sarcomere excursions. Predictions of sarcomere design from model simulations were compared with ultrastructural data from the literature. With the present model, the complete variation in the ratio of myosin length over actin length (from about 1.05 down to 0.65, as observed in insect and vertebrate sarcomeres) can be explained as a series of adaptations for optimum power output from a small to a large contraction range, respectively.     

The positional stability of thick filaments in activated skeletal muscle depends on sarcomere length: evidence for the role of titin filaments

Electron microscopy was used to study the positional stability of thick filaments in isometrically contracting skinned rabbit psoas muscle as a function of sarcomere length at 7 degrees C. After calcium activation at a sarcomere length of 2.6 micron, where resting stiffness is low, sarcomeres become nonuniform in length. The dispersion in sarcomere length is complete by the time maximum tension is reached. A-bands generally move from their central position and continue moving toward one of the Z-discs after tension has reached a plateau at its maximum level. The lengths of the thick and thin filaments remain constant during this movement. The extent of A-band movement during contraction depends on the final length of the individual sarcomere. After prolonged activation, all sarcomeres between 1.9 and 2.5 micron long exhibit A-bands that are adjacent to a Z-disc, with no intervening I-band. Sarcomeres 2.6 or 2.7 micron long exhibit a partial movement of A-bands. At longer sarcomere lengths, where the resting stiffness exceeds the slope of the active tension-length relation, the A-bands remain perfectly centered during contraction. Sarcomere symmetry and length uniformity are restored upon relaxation. These results indicate that the central position of the thick filaments in the resting sarcomere becomes unstable upon activation. In addition, they provide evidence that the elastic titin filaments, which join thick filaments to Z-discs, produce almost all of the resting tension in skinned rabbit psoas fibers and act to resist the movement of thick filaments away from the center of the sarcomere during contraction.     

Theoretical considerations on myofibril stiffness.

A discrete model of the interaction between individual myofilaments was developed to study the stiffness of a sarcomere for the case in which filament compliance is not negligible. Our model retains, in the limit, the characteristics of the previously published model by Ford et al. (Ford, L. E., A. F. Huxley, and R. M. Simmons. 1981. The relation between stiffness and filament overlap in stimulated frog muscle fibres. J. Physiol. 311:219-249). In addition, the model is able to model the interaction in cases in which few cross-bridges are attached, or when the distribution of attached cross-bridges is not uniform. Our results confirm previous indications that it might be impossible to calculate the number of attached cross-bridges by using only stiffness measurements in quick-stretch (or release) experiments.     

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

The contribution of thick and thin filaments to skeletal muscle fiber compliance has been shown to be significant. If similar to the compliance of cycling cross-bridges, myofilament compliance could explain the difference in time course of stiffness and force during the rise of tension in a tetanus as well as the difference in Ca(2+) sensitivity of force and stiffness and more rapid phase 2 tension recovery (r) at low Ca(2+) activation. To characterize the contribution of myofilament compliance to sarcomere compliance and isometric force kinetics, the Ca(2+)-activation dependence of sarcomere compliance in single glycerinated rabbit psoas fibers, in the presence of ATP (5.0 mM), was measured using rapid length steps. At steady sarcomere length, the dependence of sarcomere compliance on the level of Ca(2+)-activated force was similar in form to that observed for fibers in rigor where force was varied by changing length. Additionally, the ratio of stiffness/force was elevated at lower force (low [Ca(2+)]) and r was faster, compared with maximum activation. A simple series mechanical model of myofilament and cross-bridge compliance in which only strong cross-bridge binding was activation dependent was used to describe the data. The model fit the data and predicted that the observed activation dependence of r can be explained if myofilament compliance contributes 60-70% of the total fiber compliance, with no requirement that actomyosin kinetics be [Ca(2+)] dependent or that cooperative interactions contribute to strong cross-bridge binding.     

Passive force generation and titin isoforms in mammalian skeletal muscle.

When relaxed striated muscle cells are stretched, a resting tension is produced which is thought to arise from stretching long, elastic filaments composed of titin (also called connectin). Here, I show that single skinned rabbit soleus muscle fibers produce resting tension that is several-fold lower than that found in rabbit psoas fibers. At sarcomere lengths where the slope of the resting tension-sarcomere length relation is low, electron microscopy of skinned fibers indicates that thick filaments move from the center to the side of the sarcomere during prolonged activation. As sarcomeres are stretched and the resting tension sarcomere length relation becomes steeper, this movement is decreased. The sarcomere length range over which thick filament movement decreases is higher in soleus than in psoas fibers, paralleling the different lengths at which the slope of the resting tension-sarcomere length relations increase. These results indicate that the large differences in resting tension between single psoas and soleus fibers are due to different tensions exerted by the elastic elements linking the end of each thick filament to the nearest Z-disc, i.e., the titin filaments. Quantitative gel electrophoresis of proteins from single muscle fibers excludes the possibility that resting tension is less in soleus than in psoas fibers simply because they have fewer titin filaments. A small difference in the electrophoretic mobility of titin between psoas and soleus fibers suggests the alternate possibility that mammalian muscle cells use at least two titin isoforms with differing elastic properties to produce variations in resting tension.     

Morphology and organization of muscle fibres in the thoracic coxal muscle receptor organ and the associated promotor muscle, in a crayfish, Cherax destructor, and mud crab, Scylla serrata

Using confocal laser scanning and conventional light microscopy, the morphology and organization of the muscle fibres in a proprioceptor, the thoracic coxal muscle receptor organ (TCMRO), and the associated 'extrafusal' promotor muscle were investigated in two species of decapod crustacea, the crayfish Cherax destructor and the mud crab Scylla serrata . The diameter of the TCMROs was shown to increase distally, with an increase up to 350% recorded for the crayfish. The tapered shape of the crayfish TCMRO was demonstrated to amplify movements mechanically at the transducer region where the afferent nerves attach. Serial sectioning of the TCMROs, showed that the fibre number increased in the proximal to distal direction from 14 to 30 fibres in the crayfish and from 7 to 20 in the crab. Optical sectioning with the laser scanning confocal microscope revealed that the increase in fibre numbers was the result of muscle fibres branching in the distal third section of the TCMRO. The percentage of muscle tissue in the cross-sectional area in the TCMRO was found to be only 35.2% and 64.6% in the crayfish and crab, respectively. Longitudinal sectioning using laser scanning confocal microscopy revealed the average sarcomere length of the TCMRO muscle fibres of both species to be in the intermediate range for crustacean muscle fibres (4.1 ± 0.1 µm and 4.55 ± 0.34 µm for the crayfish and crab) compared with the long sarcomere muscle fibres in the associated promotor muscles (7.87 ± 0.2 and 10.6 ± 0.6 µm). The distinct morphology of the TCMRO muscle fibres – smaller diameter, intermediate sarcomere length and branching of fibres compared to the larger, long sarcomere promotor fibre muscle fibres – suggest that the TCMRO muscle fibres are specialized in their role of proprioception.     

Muscle mechanism: The acceleration of the load

The load (force/cross-section) determines the response of muscle power output, force and speed of contraction). The force is the product of the mass by the acceleration, thus the same force is generated by an infinite number of mass and acceleration couples and each one of these couples displays different physical and biological effects. Therefore, the load must be defined both by the mass and by the acceleration. Early muscle investigators were well aware of this situation as it is indicated by the work of Hill on the flexion of the arm against the “heavy fly-wheel”. By making use of a model of sarcomere contraction we show here that the acceleration of the load is the first determinant of the time course of the process of generation of the isometric tension. We also propose that, in order to reproduce the rapid release, it is not necessary to invoke the presence of a distinct elastic element in the contractile machinery. It is sufficient to assume that the stiffness of the same machinery increases with the contractile force.     

Thin filaments of rabbit skeletal muscle are in helical register

Thin sections of rapidly frozen and freeze-substituted rabbit glycerinated muscle fibres loaded with myosin subfragment-1 were used to examine a three-dimensional arrangement of thin filaments in vertebrate skeletal muscle. Clearer images of the "arrowhead" structure were obtained when specimens were freeze-substituted first in a tannic acid solution and then in an OsO4 solution. The images obtained showed that the arrowheads were aligned laterally. This indicates that all the thin filaments have the same rotational orientation in a half sarcomere of rabbit skeletal muscle in the rigor state.     

Interaction between rabbit muscle actin and several chaetoglobosins or cytochalasins.

The mold metabolites chaetoglobosins Ch-A, B, C, E, F, and J exert, as do the cytochalasins CB, CD, CE, and CG, enhancing effects of various strength on the polymerization of rabbit muscle G-actin. The polymers formed differ widely in their viscosity, Ch-B and Ch-J leading to the least viscous actins. Equal states of viscosity are arrived at by interaction of F-actin with the respective drugs. There is no correlation between the ATP hydrolyzing activity of F-actin elicited by the various cytochalasins and their influence on the viscosity.     

Muscle contraction: viscous-like frictional forces and the impulsive model

Apart from a few experimental studies muscle viscosity has not received much recent analytical attention as a determinant of the contractile process. This is surprising, since any muscle cell is 80% water, and may undergo large shape changes during its working cycle. Intuitively one might expect the viscosity of the solvent to be an important determinant of the physiological activity of muscle tissue. This was apparent to pioneers of the study of muscle contraction such as Hill and his contemporaries, whose putative theoretical formulations contained terms related to muscle viscosity. More recently, though, a hydrodynamic calculation by Huxley, using a solvent viscosity close to that of water, has been held to demonstrate that viscous forces are negligible in muscle contraction. We have re-examined the role of viscosity in contraction, postulating impulsive acto-myosin forces that are opposed by a viscous resistance between the filaments. The viscous force required, 10⁴ times the hydrodynamic estimate, is close to recent experimental measurements, themselves 10²–10³ times the hydrodynamic estimate. This also agrees with contemporary measurements of cytoplasmic viscosity in other biological cells using magnetic bead micro-rheometry. These are several orders of magnitude greater than the viscosity of water. In the course of the analysis we have derived the force-velocity equation for an isolated half-sarcomere containing a single actin filament for the first time, and from first principles. We conclude that muscle viscosity is indeed important for the contractile process, and that it has been too readily discounted.     

Reversal of the Myosin Power Stroke Induced by Fast Stretching of Intact Skeletal Muscle Fibers

Force generation and movement in skeletal muscle result from a cyclical interaction of overlapping myosin and actin filaments that permits the free energy of ATP hydrolysis to be converted into mechanical work. The rapid force recovery that occurs after a step release imposed on a muscle is thought to result from a synchronized tilting of myosin lever arms toward a position of lower free energy (the power stroke). We investigated the power stroke mechanism in intact muscle fibers of Rana esculenta using a fast stretch to detach forcibly cross-bridges. Stretches were applied either with or without a conditioning step release. Cross-bridge rupture tension was not significantly influenced by the release, whereas sarcomere elongation at the rupture point increased immediately after the release and returned to the prerelease condition within 15-20 ms, following a slower time course compared to the recovery of tension. These observations suggest that the rupture force of a bridge is unaltered by a conditioning release, but rupture must first be preceded by a power stroke reversal, which restores the prepower stroke state. The sarcomere extension at the rupture point indicates both the extent of this power stroke reversal and the time course of strained bridge replenishment.