Contractile system of muscle as an auto-oscillator

It is widely known that the contractile system of muscle takes on either the state of contraction (force-generating) or the state of relaxation (non-force-generating), which is known as the "all-or-nothing" principle. However, it is important to note that under intermediate activation conditions there exists a third state, which demonstrates auto-oscillatory properties and is termed SPOC (SPontaneous Oscillatory Contraction) state. We present a phase diagram, in which the states of the contractile system of muscle are divided into three regions consisting of contraction, relaxation and SPOC states. In the present review, experimental data related to the characteristics of SPOC are summarized and the mechanism of SPOC is described. We propose that the bio-motile system itself is an auto-oscillator, even in a membrane-less supra-molecular structure composed of an assembly of molecular motors and cytoskeletons (actin filaments and microtubules). Finally, the physiological significance of SPOC is discussed.     

SPontaneous Oscillatory Contraction (SPOC): auto-oscillations observed in striated muscle at partial activation

Striated muscle is well known to exist in either of two states—contraction or relaxation—under the regulation of Ca²⁺ concentration. Described here is a less well-known third, intermediate state induced under conditions of partial activation, known as SPOC (SPontaneous Oscillatory Contraction). This state is characterised by auto-oscillation between rapid-lengthening and slow-shortening phases. Notably, SPOC occurs in skinned muscle fibres and is therefore not the result of fluctuating Ca²⁺ levels, but is rather an intrinsic and fundamental phenomenon of the actomyosin motor. Summarised in this review are the experimental data on SPOC and its fundamental mechanism. SPOC presents a novel technique for studying independent communication and coordination between sarcomeres. In cardiac muscle, this auto-oscillatory property may work in concert with electro-chemical signalling to coordinate the heartbeat. Further, SPOC may represent a new way of demonstrating functional defects of sarcomeres in human heart failure.     

Myofilament length-dependent activation develops within 5 ms in guinea-pig myocardium

Myofilament length-dependent activation is a universal property of striated muscle, yet the molecular mechanisms that underlie this phenomenon are incompletely understood. Additionally, the rate by which sarcomere length (SL) is sensed and then transduced to form length-dependent activation is unknown. Here, using isolated guinea-pig myocardium, we employed a rapid solution-switch single myofibril technique that allows for the study of contractile action/relaxation dynamics in the virtual absence of diffusion delays. We compared contraction kinetics obtained at submaximal activation at steady-state SL with contractions observed after rapid SL ramps to that same SL just before activation. Neither the activation and relaxation kinetics nor the final submaximal force development differed significantly between the two contraction modes for SL ramps as fast as 5 ms. We conclude that the transduction of the length signal by the cardiac sarcomere to modulate thin filament activation levels occurs virtually instantaneously, possibly resulting from structural rearrangements of the contractile proteins.     

Synchronous behavior of spontaneous oscillations of sarcomeres in skeletal myofibrils under isotonic conditions.

An isotonic control system for studying dynamic properties of single myofibrils was developed to evaluate the change of sarcomere lengths in glycerinated skeletal myofibrils under conditions of spontaneous oscillatory contraction (SPOC) in the presence of inorganic phosphate and a high ADP-to-ATP ratio. Sarcomere length oscillated spontaneously with a peak-to-peak amplitude of about 0.5 microns under isotonic conditions in which the external loads were maintained constant at values between 1.5 x 10(4) and 3.5 x 10(4) N/m2. The shortening and yielding of sarcomeres occurred in concert, in contrast to the previously reported conditions (isomeric or auxotonic) under which the myofibrillar tension is allowed to oscillate. This synchronous SPOC appears to be at a higher level of synchrony than in the organized state of SPOC previously observed under auxotonic conditions. The period of sarcomere length oscillation did not largely depend on external load. The active tension under SPOC conditions increased as the sarcomere length increased from 2.1 to 3.2 microns, although it was still smaller than the tension under normal Ca2+ contraction (which is on the order of 10(5) N/m2). The synchronous SPOC implies that there is a mechanism for transmitting information between sarcomeres such that the state of activation of sarcomeres is affected by the state of adjacent sarcomeres. We conclude that the change of myofibrillar tension is not responsible for the SPOC of each sarcomere but that it affects the level of synchrony of sarcomere oscillations.     

Myosin filament sliding through the Z-disc relates striated muscle fibre structure to function

Striated muscle contraction requires intricate interactions of microstructures. The classic textbook assumption that myosin filaments are compressed at the meshed Z-disc during striated muscle fibre contraction conflicts with experimental evidence. For example, myosin filaments are too stiff to be compressed sufficiently by the muscular force, and, unlike compressed springs, the muscle fibres do not restore their resting length after contractions to short lengths. Further, the dependence of a fibre''s maximum contraction velocity on sarcomere length is unexplained to date. In this paper, we present a structurally consistent model of sarcomere contraction that reconciles these findings with the well-accepted sliding filament and crossbridge theories. The few required model parameters are taken from the literature or obtained from reasoning based on structural arguments. In our model, the transition from hexagonal to tetragonal actin filament arrangement near the Z-disc together with a thoughtful titin arrangement enables myosin filament sliding through the Z-disc. This sliding leads to swivelled crossbridges in the adjacent half-sarcomere that dampen contraction. With no fitting of parameters required, the model predicts straightforwardly the fibre''s entire force–length behaviour and the dependence of the maximum contraction velocity on sarcomere length. Our model enables a structurally and functionally consistent view of the contractile machinery of the striated fibre with possible implications for muscle diseases and evolution.     

Differences in the Charge Distribution of Glycerol-Extracted Muscle Fibers in Rigor, Relaxation, and Contraction

Glycerol-extracted rabbit psoas muscle fibers were impaled with KCl-filled glass microelectrodes. For fibers at rest-length, the potentials were significantly more negative in solutions producing relaxation than in solutions producing either rigor or contraction; further the potentials in the latter two cases were not significantly different. For stretched fibers, with no overlap between thick and thin filaments, the potentials did not differ in the rigor, the relaxation, or the contraction solutions. The potentials measured from fibers in rigor did not vary significantly with the sarcomere length. For relaxed fibers, however, the potential magnitude decreased with increasing sarcomere length. The difference between the potentials measured for rigor and relaxed fibers exhibited a nonlinear relationship with sarcomere length. The potentials from calcium-insensitive fibers were less negative in both the rigor and the relaxation solutions than those from normal fibers. When calcium-insensitive fibers had been incubated in Hasselbach and Schneider's solution plus MgCl₂ or Guba-Straub's solution plus MgATP the potentials recorded upon impalement were similar in the rigor and the relaxation solution to those obtained from normal fibers in the relaxed state. It is concluded that the increase in the negative potential as the glycerinated fiber goes from rigor to relaxation may be due to an alteration in the conformation of the contractile proteins in the relaxed state.     

Distribution of calcium during contraction and relaxation of crayfish skeletal muscle fibre.

A model of activation of muscle contraction has been applied to the crayfish isolated skeletal muscle fibre. The model is based on calcium diffusion and binding to specific regulatory sites in a sarcomere. Calcium ions activate interactions of contractile proteins and thus the generation of force. The model quantifies the relation between calcium released from intracellular stores and force elicited. Experimental tension records from isolated crayfish skeletal muscle fibres under voltage clamp conditions are analyzed. Model parameters were determined either via approximation of the onset of tension by the model solution or from the model based relations between the tension maximum, and depolarizing pulse length and amplitude. This allowed to determine time changes of free and bound calcium distribution in the sarcomere and the calcium release from terminal cisternae. The steady state calcium concentration at terminal cisternae showed S-shaped voltage dependence with saturation below approx. 10 mumol/l at positive membrane potentials.     

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.     

Sarcomere Length Nonuniformity and Force Regulation in Myofibrils and Sarcomeres

The smallest contractile unit in striated muscles is the sarcomere. Although some of the classic features of contraction assume a uniform behavior of sarcomeres within myofibrils, the occurrence of sarcomere length nonuniformities has been well recognized for years, but it is yet not well understood. In the past years, there has been a great advance in experiments using isolated myofibrils and sarcomeres that has allowed scientists to directly evaluate sarcomere length nonuniformity. This review will focus on studies conducted with these preparations to develop the hypotheses that 1) force production in myofibrils is largely altered and regulated by intersarcomere dynamics and that 2) the mechanical work of one sarcomere in a myofibril is transmitted to other sarcomeres in series. We evaluated studies looking into myofibril activation, relaxation, and force changes produced during activation. We conclude that force production in myofibrils is largely regulated by intersarcomere dynamics, which arises from the cooperative work of the contractile and elastic elements within a myofibril.     

Rheology of myocardium. The relation between force, velocity, sarcomere length and activation in rat cardiac muscle

The relations between force, shortening velocity and sarcomere length (F-V-SL) during cardiac contraction, underlie Starling's Law of the Heart. F-V-SL were investigated in isolated, intact and skinned trabeculae and myocytes from rat heart. SL and V were measured with laser diffraction techniques; F was measured with a silicon strain gauge. The "ascending" F-SL relation appeared to result from both length dependent sensitivity of the contractile system to activator calcium ions and the presence of restoring forces (Fr), residing in the collagen skeleton of the muscle. Fr increased exponentially with decreasing SL below slack length to 25% of maximal twitch force (Ft) at SL = 1.60 microns. V was inversely proportional to the load and attained a maximum at zero load (Vo). Vo increased with factors that increased F: [Ca++], SL, and time during the twitch. Vo reached a maximum and remained constant (13.5 microns/s) when F attained or exceeded 50% of its maximum value. Viscous force in the passive muscle increased with V to a maximum of 4% of Ft at V = 40 microns/s. The relation between Vo and these factors could be predicted by a model of contraction in which the measured visco-elastic properties of myocardium were incorporated, while the truly unloaded maximal velocity of sarcomere shortening was assumed to be independent of the level of activation of the contractile filaments. A model of the cardiac cycle which explains the relation between Frank's and Starling's laws is presented.     

Real-time measurement of the length of a single sarcomere in rat ventricular myocytes: a novel analysis with quantum dots

As the dynamic properties of cardiac sarcomeres are markedly changed in response to a length change of even ～0.1 μm, it is imperative to quantitatively measure sarcomere length (SL). Here we show a novel system using quantum dots (QDs) that enables a real-time measurement of the length of a single sarcomere in cardiomyocytes. First, QDs were conjugated with anti-α-actinin antibody and applied to the sarcomeric Z disks in isolated skinned cardiomyocytes of the rat. At partial activation, spontaneous sarcomeric oscillations (SPOC) occurred, and QDs provided a quantitative measurement of the length of a single sarcomere over the broad range (i.e., from ～1.7 to ～2.3 μm). It was found that the SPOC amplitude was inversely related to SL, but the period showed no correlation with SL. We then treated intact cardiomyocytes with the mixture of the antibody-QDs and FuGENE HD, and visualized the movement of the Z lines/T tubules. At a low frequency of 1 Hz, the cycle of the motion of a single sarcomere consisted of fast shortening followed by slow relengthening. However, an increase in stimulation frequency to 3-5 Hz caused a phase shift of shortening and relengthening due to acceleration of relengthening, and the waveform became similar to that observed during SPOC. Finally, the anti-α-actinin antibody-QDs were transfected from the surface of the beating heart in vivo. The striated patterns with ～1.96-μm intervals were observed after perfusion under fluorescence microscopy, and an electron microscopic observation confirmed the presence of QDs in and around the T tubules and Z disks, but primarily in the T tubules, within the first layer of cardiomyocytes of the left ventricular wall. Therefore, QDs are a useful tool to quantitatively analyze the movement of single sarcomeres in cardiomyocytes, under various experimental settings.     

Use of motor cortex stimulation to measure simultaneously the changes in dynamic muscle properties and voluntary activation in human muscles.

Force responses to transcranial magnetic stimulation of motor cortex (TMS) during exercise provide information about voluntary activation and contractile properties of the muscle. Here, TMS-generated twitches and muscle relaxation during the TMS-evoked silent period were measured in fresh, heated, and fatigued muscle. Subjects performed isometric contractions of elbow flexors in two studies. Torque and EMG were recorded from elbow flexor and extensor muscles. One study (n = 6) measured muscle contraction times and relaxation rates during brief maximal and submaximal contractions in fresh and fatigued muscle. Another study (n = 7) aimed to 1) assess the reproducibility of muscle contractile properties during brief voluntary contractions in fresh muscle, 2) validate the technique for contractile properties in passively heated muscle, and 3) apply the technique to study contractile properties during sustained maximal voluntary contractions. In both studies, muscle contractile properties during voluntary contractions were compared with the resting twitch evoked by motor nerve stimulation. Measurement of muscle contractile properties during voluntary contractions is reproducible in fresh muscle and reveals faster and slower muscle relaxation rates in heated and fatigued muscle, respectively. The technique is more sensitive to altered muscle state than the traditional motor nerve resting twitch. Use of TMS during sustained maximal contractions reveals slowing of muscle contraction and relaxation with different time courses and a decline in voluntary activation. Voluntary output from the motor cortex becomes insufficient to maintain complete activation of muscle, although slowing of muscle contraction and relaxation indicates that lower motor unit firing rates are required for fusion of force.     

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.     

Half-sarcomere dynamics in myofibrils during activation and relaxation studied by tracking fluorescent markers

To study the dynamics of individual half-sarcomeres in striated muscle contraction, myofibrils prepared from rabbit psoas muscle and left ventricles of guinea pig were immunostained with two conjugated antibody complexes consisting of a primary antibody against either alpha-actinin or myomesin and a secondary fluorescently labeled Fab-fragment. We simultaneously measured force kinetics and determined the positions of the Z-line and M-band signals by fluorescence video microscopy and sophisticated computer vision (tracking) algorithms. Upon calcium activation, sarcomeres and half-sarcomeres shortened nonuniformly. Shortening occurred first rapidly and exponentially during the force rise and then slowly during the force plateau. In psoas myofibrils, time-resolved displacements of the A-band in sarcomeres were observed, i.e., the two halves of individual sarcomeres behaved nonuniformly. Nonuniformity in length changes between the two halves of sarcomeres was comparable to that between two adjacent half-sarcomeres of neighboring sarcomeres. Sequential lengthening of half-sarcomeres was observed in cardiac myofibrils during the rapid phase of force relaxation. The independent dynamics of the halves in a sarcomere reveals the half-sarcomere as the functional unit rather than the structural unit, the sarcomere. The technique will facilitate the study of filament sliding within individual half-sarcomeres and the mechanics of intersegmental chemomechanical coupling in multisegmental striated muscles.     

Role of the Z band in the mechanical properties of the heart

In striated muscle the mechanism of contraction involves the cooperative movement of contractile and elastic components. This review emphasizes a structural approach that describes the cellular and extracellular components with known anatomical, biochemical, and physical properties that make them candidates for these contractile and elastic components. Classical models of contractile and elastic elements and their underlying assumptions are presented. Mechanical properties of cardiac and skeletal muscle are compared and contrasted and then related to ultrastructure. Information from these approaches leads to the conclusion that the Z band is essential for muscle contraction. Our review of Z band structure shows the Z band at the interface where extracellular components meet the cell surface. The Z band is also the interface from cell surface to myofibril, from extra-myofibrillar to myofibril, and finally from sarcomere to sarcomere. Our studies of Z band in defined physiologic states show that this lattice is an integral part of the contractile elements and can function as an elastic component. The Z band is a complex dynamic lattice uniquely suited to play several roles in muscle contraction.     

Mechanical control of the rising phase of contraction of frog skeletal and cardiac muscle

The effect of shortening on contractile activity was studied in experiments in which shortening during the rising phase of an isotonic contraction was suddenly stopped. At the same muscle length and the same time after stimulation the rise in tension was much faster, if preceded by shortening, than during an isometric contraction, demonstrating an increase in contractile activity. In this experiment the rate of tension rise determined in various phases of contraction was proportional to the rate of isotonic shortening at the same time after stimulation. Therefore, the time course of the isotonic rising phase could be derived from the tension rise after shortening. The rate of isotonic shortening was found to be unrelated to the tension generated at various lengths and to correspond closely to the activation process induced by shortening. The length response explains differences between isotonic and isometric contractions with regard to energy release (Fenn effect) and time relations. These results extend previous work which showed that shortening during later phases of a twitch prolongs, while lengthening abbreviates contraction. Thus the length responses, which have been called shortening activation and lengthening deactivation, control activity throughout an isotonic twitch.     

Multiscale modeling of twitch contractions in cardiac trabeculae

Understanding the dynamics of a cardiac muscle twitch contraction is complex because it requires a detailed understanding of the kinetic processes of the Ca²⁺ transient, thin-filament activation, and the myosin–actin cross-bridge chemomechanical cycle. Each of these steps has been well defined individually, but understanding how all three of the processes operate in combination is a far more complex problem. Computational modeling has the potential to provide detailed insight into each of these processes, how the dynamics of each process affect the complexity of contractile behavior, and how perturbations such as mutations in sarcomere proteins affect the complex interactions of all of these processes. The mechanisms involved in relaxation of tension during a cardiac twitch have been particularly difficult to discern due to nonhomogeneous sarcomere lengthening during relaxation. Here we use the multiscale MUSICO platform to model rat trabecular twitches. Validation of computational models is dependent on being able to simulate different experimental datasets, but there has been a paucity of data that can provide all of the required parameters in a single experiment, such as simultaneous measurements of force, intracellular Ca²⁺ transients, and sarcomere length dynamics. In this study, we used data from different studies collected under similar experimental conditions to provide information for all the required parameters. Our simulations established that twitches either in an isometric sarcomere or in fixed-length, multiple-sarcomere trabeculae replicate the experimental observations if models incorporate a length–tension relationship for the nonlinear series elasticity of muscle preparations and a scheme for thick-filament regulation. The thick-filament regulation assumes an off state in which myosin heads are parked onto the thick-filament backbone and are unable to interact with actin, a state analogous to the super-relaxed state. Including these two mechanisms provided simulations that accurately predict twitch contractions over a range of different conditions.     

Evaluation of Muscle Function of the Extensor Digitorum Longus Muscle Ex vivo and Tibialis Anterior Muscle In situ in Mice

Body movements are mainly provided by mechanical function of skeletal muscle. Skeletal muscle is composed of numerous bundles of myofibers that are sheathed by intramuscular connective tissues. Each myofiber contains many myofibrils that run longitudinally along the length of the myofiber. Myofibrils are the contractile apparatus of muscle and they are composed of repeated contractile units known as sarcomeres. A sarcomere unit contains actin and myosin filaments that are spaced by the Z discs and titin protein. Mechanical function of skeletal muscle is defined by the contractile and passive properties of muscle. The contractile properties are used to characterize the amount of force generated during muscle contraction, time of force generation and time of muscle relaxation. Any factor that affects muscle contraction (such as interaction between actin and myosin filaments, homeostasis of calcium, ATP/ADP ratio, etc.) influences the contractile properties. The passive properties refer to the elastic and viscous properties (stiffness and viscosity) of the muscle in the absence of contraction. These properties are determined by the extracellular and the intracellular structural components (such as titin) and connective tissues (mainly collagen) ^1-2. The contractile and passive properties are two inseparable aspects of muscle function. For example, elbow flexion is accomplished by contraction of muscles in the anterior compartment of the upper arm and passive stretch of muscles in the posterior compartment of the upper arm. To truly understand muscle function, both contractile and passive properties should be studied.The contractile and/or passive mechanical properties of muscle are often compromised in muscle diseases. A good example is Duchenne muscular dystrophy (DMD), a severe muscle wasting disease caused by dystrophin deficiency ³. Dystrophin is a cytoskeletal protein that stabilizes the muscle cell membrane (sarcolemma) during muscle contraction ⁴. In the absence of dystrophin, the sarcolemma is damaged by the shearing force generated during force transmission. This membrane tearing initiates a chain reaction which leads to muscle cell death and loss of contractile machinery. As a consequence, muscle force is reduced and dead myofibers are replaced by fibrotic tissues ⁵. This later change increases muscle stiffness ⁶. Accurate measurement of these changes provides important guide to evaluate disease progression and to determine therapeutic efficacy of novel gene/cell/pharmacological interventions. Here, we present two methods to evaluate both contractile and passive mechanical properties of the extensor digitorum longus (EDL) muscle and the contractile properties of the tibialis anterior (TA) muscle.     

Residual force enhancement in myofibrils and sarcomeres

Residual force enhancement has been observed following active stretch of skeletal muscles and single fibres. However, there has been intense debate whether force enhancement is a sarcomeric property, or is associated with sarcomere length instability and the associated development of non-uniformities. Here, we studied force enhancement for the first time in isolated myofibrils (n=18) that, owing to the strict in series arrangement, allowed for evaluation of this property in individual sarcomeres (n=79). We found consistent force enhancement following stretch in all myofibrils and each sarcomere, and forces in the enhanced state typically exceeded the isometric forces on the plateau of the force-length relationship. Measurements were made on the plateau and the descending limb of the force-length relationship and revealed gross sarcomere length non-uniformities prior to and following active myofibril stretching, but in contrast to previous accounts, revealed that sarcomere lengths were perfectly stable under these experimental conditions. We conclude that force enhancement is a sarcomeric property that does not depend on sarcomere length instability, that force enhancement varies greatly for different sarcomeres within the same myofibril and that sarcomeres with vastly different amounts of actin-myosin overlap produce the same isometric steady-state forces. This last finding was not explained by differences in the amount of contractile proteins within sarcomeres, vastly different passive properties of individual sarcomeres or (half-) sarcomere length instabilities, suggesting that the basic mechanical properties of muscles, such as force enhancement, force depression and creep, which have traditionally been associated with sarcomere instabilities and the corresponding dynamic redistribution of sarcomere lengths, are not caused by such instabilities, but rather seem to be inherent properties of the mechanisms of contraction.     

The sliding filament model of muscle contraction. III. Stability analysis and sinusoidal perturbations

A theoretical model of the energy transducing part of a single sarcomere, which has previously accounted for most of the steady state energetic and dynamical properties of striated muscle, is subjected to stability analysis. The steady states of isotonic and isometric contraction turn out to be stable and the magnitudes of the characteristic roots allow accurate reduction of the original seven state theory to a four state theory. Both versions possess a complex pair of roots giving a damped oscillatory character to the contraction velocity, the tension generated and the populations of the crossbridge states.