Monitoring the structural behavior of troponin and myoplasmic free Ca2+ concentration during twitch of frog skeletal muscle

The Transient Mechanics of Muscle Require Only a Single Force-Producing Cross-Bridge State and a 100 Å Working Stroke

Simple Summary

With modern increased computational power, newly developed computer programs can be used to simulate how muscle contracts. Here, we created, in silico, a “virtual” muscle that includes modelled myosin cross-bridges, and, using statistical mechanical methods, we calculated the macroscopic response of the muscle during contraction and as a result of applied transients. Good fits to many experimental observations were obtained with this simple model with one attached force-producing state and using a single cross-bridge step size of 100 Å.

Abstract

An informative probe of myosin cross-bridge behaviour in active muscle is a mechanical transient experiment where, for example, a fully active muscle initially held at constant length is suddenly shortened to a new fixed length, providing a force transient, or has its load suddenly reduced, providing a length transient. We describe the simplest cross-bridge mechanical cycle we could find to model these transients. We show using the statistical mechanics of 50,000 cross-bridges that a simple cycle with two actin-attached cross-bridge states, one producing no force and the other producing force, will explain much of what has been observed experimentally, and we discuss the implications of this modelling for our understanding of how muscle works. We show that this same simple model will explain, reasonably well, the isotonic mechanical and X-ray transients under different loads observed by Reconditi et al. (2004, Nature 428, 578) and that there is no need to invoke different cross-bridge step sizes under these different conditions; a step size of 100 Å works well for all loads. We do not claim that this model provides a total mechanical explanation of how muscle works. However, we do suggest that only if there are other observations that cannot be explained by this simple model should something more complicated be considered.

MODELING AND SIMULATION OF SKELETAL MUSCLE BASED ON METABOLISM PHYSIOLOGY

Skeletal muscle energy metabolism plays a very important role in controlling movement of the whole body and has important theoretical guidance for making exercise training plans and losing weight. In this paper, we developed a mathematical model of skeletal muscle excitation–contraction pathway based on the energy metabolism that links excitation to contraction to explore the effects of different metabolic energy systems on calcium ion changes and the force during skeletal muscle contraction. In this paper, a membrane potential model, a calcium cycle model, a cross-bridge dynamics model and an energy metabolism model were established. Finally, the physiological phenomenon of calcium ion transport and calcium ion concentration change of the sarcoplasm was simulated. The results show that the phosphagen system has the fastest metabolic rate and the phosphagen system has the largest impact on the explosive power of skeletal muscle exercise. The specific characteristics of the three metabolic energy systems supporting skeletal muscle movement in vivo were also analyzed in detail.

Crossbridge Recruitment Capacity of Wild-Type and Hypertrophic Cardiomyopathy-Related Mutant Troponin-T Evaluated by X-ray Diffraction and Mechanical Study of Cardiac Skinned Fibers

X-ray diffraction and tension measurement experiments were conducted on rat left ventricular skinned fibers with or without “troponin-T treatment,” which exchanges the endogenous troponin T/I/C complex with exogenous troponin-T. These experiments were performed to observe the structural changes in troponin-T within a fiber elicited by contractile crossbridge formation and investigate the abnormality of hypertrophic cardiomyopathy-related troponin-T mutants. The intensity of the troponin reflection at 1/38.5 nm⁻¹ was decreased significantly by ATP addition after treatment with wild-type or mutant troponin-T, indicating that crossbridge formation affected the conformation of troponin-T. In experiments on cardiac fibers treated with the hypertrophic cardiomyopathy-related mutants E244D- and K247R-troponin-T, treatment with K247R-troponin-T did not recruit contracting actomyosin to a greater extent than wild-type-troponin-T, although a similar drop in the intensity of the troponin reflection occurred. Therefore, the conformational change in K247R-troponin-T was suggested to be unable to fully recruit actomyosin interaction, which may be the cause of cardiomyopathy.

Synchrotron radiation X-ray diffraction studies on muscle: past, present, and future

X-ray diffraction is a technique to study the structure of materials at spatial resolutions up to an atomic scale. In the field of life science, the X-ray diffraction technique is especially suited to study materials having periodical structures, such as protein crystals, nucleic acids, and muscle. Among others, muscle is a dynamic structure and the molecular events occurring during muscle contraction have been the main interest among muscle researchers. In early days, the laboratory X-ray generators were unable to deliver X-ray flux strong enough to resolve the dynamic molecular events in muscle. This situation has dramatically been changed by the advent of intense synchrotron radiation X-rays and advanced detectors, and today X-ray diffraction patterns can be recorded from muscle at sub-millisecond time resolutions. In this review, we shed light mainly on the technical aspects of the history and the current status of the X-ray diffraction studies on muscle and discuss what will be made possible for muscle studies by the advance of new techniques.

Regulation of Contraction by the Thick Filaments in Skeletal Muscle

Contraction of skeletal muscle cells is initiated by a well-known signaling pathway. An action potential in a motor nerve triggers an action potential in a muscle cell membrane, a transient increase of intracellular calcium concentration, binding of calcium to troponin in the actin-containing thin filaments, and a structural change in the thin filaments that allows myosin motors from the thick filaments to bind to actin and generate force. This calcium/thin filament mediated pathway provides the "START" signal for contraction, but it is argued that the functional response of the muscle cell, including the speed of its contraction and relaxation, adaptation to the external load, and the metabolic cost of contraction is largely determined by additional mechanisms. This review considers the role of the thick filaments in those mechanisms, and puts forward a paradigm for the control of contraction in skeletal muscle in which both the thick and thin filaments have a regulatory function. The OFF state of the thick filament is characterized by helical packing of most of the myosin head or motor domains on the thick filament surface in a conformation that makes them unavailable for actin binding or ATP hydrolysis, although a small fraction of the myosin heads are constitutively ON. The availability of the majority fraction of the myosin heads for contraction is controlled in part by the external load on the muscle, so that these heads only attach to actin and hydrolyze ATP when they are required. This phenomenon seems to be the major determinant of the well-known force-velocity relationship of muscle, and controls the metabolic cost of contraction. The regulatory state of the thick filament also seems to control the dynamics of both muscle activation and relaxation.

Modeling Ca2+-Bound Troponin in Excitation Contraction Coupling

To explain disparate decay rates of cytosolic Ca²⁺ and structural changes in the thin filaments during a twitch, we model the time course of Ca²⁺-bound troponin (Tn) resulting from the free Ca²⁺ transient of fast skeletal muscle. In fibers stretched beyond overlap, the decay of Ca²⁺ as measured by a change in fluo-3 fluorescence is significantly slower than the intensity decay of the meridional 1/38.5 nm⁻¹ reflection of Tn; this is not simply explained by considering only the Ca²⁺ binding properties of Tn alone (Matsuo et al., 2010). We apply a comprehensive model that includes the known Ca²⁺ binding properties of Tn in the context of the thin filament with and without cycling crossbridges. Calculations based on the model predict that the transient of Ca²⁺-bound Tn correlates with either the fluo-3 time course in muscle with overlapping thin and thick filaments or the intensity of the meridional 1/38.5 nm⁻¹ reflection in overstretched muscle. Hence, cycling crossbridges delay the dissociation of Ca²⁺ from Tn. Correlation with the fluo-3 fluorescence change is not causal given that the transient of Ca²⁺-bound Tn depends on sarcomere length, whereas the fluo-3 fluorescence change does not. Transient positions of tropomyosin calculated from the time course of Ca²⁺-bound Tn are in reasonable agreement with the transient of measured perturbations of the Tn repeat in overlap and non-overlap muscle preparations.

Structural dynamics of troponin during activation of skeletal muscle

Time-resolved changes in the conformation of troponin in the thin filaments of skeletal muscle were followed during activation in situ by photolysis of caged calcium using bifunctional fluorescent probes in the regulatory and the coiled-coil (IT arm) domains of troponin. Three sequential steps in the activation mechanism were identified. The fastest step (1,100 s(-1)) matches the rate of Ca(2+) binding to the regulatory domain but also dominates the motion of the IT arm. The second step (120 s(-1)) coincides with the azimuthal motion of tropomyosin around the thin filament. The third step (15 s(-1)) was shown by three independent approaches to track myosin head binding to the thin filament, but is absent in the regulatory head. The results lead to a four-state structural kinetic model that describes the molecular mechanism of muscle activation in the thin filament-myosin head complex under physiological conditions.

Clusters of bound Ca(2+) initiate contraction in fast skeletal muscle

Ca(2+)-binding to troponin C ultimately controls force in muscle leading to the expectation that the two curves, pCa/force and pCa/Ca(2+) binding, will coincide. Using an improved fluorescence apparatus to measure Ca(2+)-binding, we confirm a displacement between the position and shape of the pCa/Ca(2+)-binding and pCa/force curves. This displacement may be part of a mechanism that reduces the noise inherent in the control process. There must always be some Ca(2+)-binding events even at 10 or 100nM, well below threshold for muscle contraction. To minimize the response to such random binding events we suggest that clusters of adjacent Ca(2+)-binding sites must be filled before contraction is initiated. Clusters promote the reconfiguration of the thin filament to the "On" state; this simultaneously increases thin filaments' affinity for myosin heads and of troponin C for Ca(2+) producing the highly cooperative pCa/force curve. The cluster requirement displaces the Ca(2+)-binding from the force curve as observed. The thin filament conformational changes and the accompanying affinity increases introduce a discontinuity in the pCa/Ca(2+)-binding curve. The curve, therefore, is most appropriately fit by two separate Hill equations, a simple non-cooperative one (midpoint, pK1, n1∼1) for the foot and a second cooperative one (pK2, n2∼2.5) for the upper part. With this fit pK2 is larger than pK1 as our argument requires, in contrast to fitting to the sum of two Hill equations. It also expresses the idea that there may be three states of the thin filament.

Sarcomere-length dependence of myosin filament structure in skeletal muscle fibres of the frog

X-ray diffraction patterns were recorded at beamline ID02 of the European Synchrotron Radiation Facility from small bundles of skeletal muscle fibres from Rana esculenta at sarcomere lengths between 2.1 and 3.5 μm at 4°C. The intensities of the X-ray reflections from resting fibres associated with the quasi-helical order of the myosin heads and myosin binding protein C (MyBP-C) decreased in the sarcomere length range 2.6-3.0 μm but were constant outside it, suggesting that an OFF conformation of the thick filament is maintained by an interaction between MyBP-C and the thin filaments. During active isometric contraction the intensity of the M3 reflection from the regular repeat of the myosin heads along the filaments decreased in proportion to the overlap between thick and thin filaments, with no change in its interference fine structure. Thus, myosin heads in the regions of the thick filaments that do not overlap with thin filaments are highly disordered during isometric contraction, in contrast to their quasi-helical order at rest. Heads in the overlap region that belong to two-headed myosin molecules that are fully detached from actin are also highly disordered, in contrast to the detached partners of actin-attached heads. These results provide strong support for the concept of a regulatory structural transition in the thick filament involving changes in both the organisation of the myosin heads on its surface and the axial periodicity of the myosin tails in its backbone, mediated by an interaction between MyBP-C and the thin filaments.

High-speed detector for time-resolved diffraction studies

There are a growing number of high brightness synchrotron sources that require high-frame-rate detectors to provide the time-scales required for performing time-resolved diffraction experiments. We report on the development of a very high frame rate CMOS X-ray detector for time-resolved muscle diffraction and time-resolved solution scattering experiments. The detector is based on a low-afterglow scintillator, provides a megapixel resolution with frame rates of up to 120,000 frames per second, an effective pixel size of 64 µm, and can be adapted for various X-ray energies. The paper describes the detector design and initial results of time-resolved diffraction experiments on a synchrotron beamline.

Motion of myosin head domains during activation and force development in skeletal muscle

Muscle contraction is driven by a change in the structure of the head domain of myosin, the "working stroke" that pulls the actin filaments toward the midpoint of the myosin filaments. This movement of the myosin heads can be measured very precisely in intact muscle cells by X-ray interference, but until now this technique has not been applied to physiological activation and force generation following electrical stimulation of muscle cells. By using this approach, we show that the long axes of the myosin head domains are roughly parallel to the filaments in resting muscle, with their center of mass offset by approximately 7 nm from the C terminus of the head domain. The observed mass distribution matches that seen in electron micrographs of isolated myosin filaments in which the heads are folded back toward the filament midpoint. Following electrical stimulation, the heads move by approximately 10 nm away from the filament midpoint, in the opposite direction to the working stroke. The time course of this motion matches that of force generation, but is slower than the other structural changes in the myosin filaments on activation, including the loss of helical and axial order of the myosin heads and the change in periodicity of the filament backbone. The rate of force development is limited by that of attachment of myosin heads to actin in a conformation that is the same as that during steady-state isometric contraction; force generation in the actin-attached head is fast compared with the attachment step.

Mechanism of latency relaxation in frog skeletal muscle

The latency relaxation is a small drop of tension before skeletal muscle begins to develop active tension. This phenomenon was found nearly one century ago but its origin has not been clarified. In this review, the hypotheses for its mechanism are discussed in terms of the recent experimental results using X-ray diffraction. The latency relaxation takes place almost simultaneously as the structural change of the regulatory protein troponin, an unspecified structural change of the thick filament, and increase in stiffness. It seems difficult to associate all of these with the latency relaxation by assuming a simple mechanism.

X-ray fiber diffraction modeling of structural changes of the thin filament upon activation of live vertebrate skeletal muscles

In order to clarify the structural changes of the thin filaments related to the regulation mechanism in skeletal muscle contraction, the intensities of thin filament-based reflections in the X-ray fiber diffraction patterns from live frog skeletal muscles at non-filament overlap length were investigated in the relaxed state and upon activation. Modeling the structural changes of the whole thin filament due to Ca²⁺-activation was systematically performed using the crystallographic data of constituent molecules (actin, tropomyosin and troponin core domain) as starting points in order to determine the structural changes of the regulatory proteins and actin. The results showed that the globular core domain of troponin moved toward the filament axis by ∼6 Å and rotated by ∼16° anticlockwise (viewed from the pointed end) around the filament axis by Ca²⁺-binding to troponin C, and that tropomyosin together with the tail of troponin T moved azimuthally toward the inner domains of actin by ∼12° and radially by ∼7 Å from the relaxed position possibly to partially open the myosin binding region of actin. The domain structure of the actin molecule in F-actin we obtained for frog muscle thin filament was slightly different from that of the Holmes F-actin model in the relaxed state, and upon activation, all subdomains of actin moved in the direction to closing the nucleotide-binding pocket, making the actin molecule more compact. We suggest that the troponin movements and the structural changes within actin molecule upon activation are also crucial components of the regulation mechanism in addition to the steric blocking movement of tropomyosin.