Cross-bridge model of muscle contraction. Quantitative analysis

We recently presented, in a qualitative manner, a cross-bridge model of muscle contraction which was based on a biochemical kinetic cycle for the actomyosin ATPase activity. This cross-bridge model consisted of two cross-bridge states detached from actin and two cross-bridge states attached to actin. In the present paper, we attempt to fit this model quantitatively to both biochemical and physiological data. We find that the resulting complete cross-bridge model is able to account reasonably well for both the isometric transient data observed when a muscle is subjected to a sudden change in length and for the relationship between the velocity of muscle contraction in vivo and the actomyosin ATPase activity in vitro. This model also illustrates the interrelationship between biochemical and physiological data necessary for the development of a complete cross-bridge model of muscle contraction.     

Actomyosin ATPase activity of middle ear muscles in the cat

Summary When incubated for histochemical demonstration of actomyosin ATPase both the tensor tympani and the stapedius were found to contain two types of muscle fibres, one with high actomyosin ATPase activity, indicating a high speed of contraction, and one with low actomyosin ATPase activity, indicating a low speed of contraction. In the tensor tympani 59% and 41% of the muscle fibres had a high and low ATPase activity, respectively. The corresponding numbers in the stapedius muscle were 82% and 18%. These findings are discussed with reference to previous physiological and morphological studies.     

Myosin from fast and slow skeletal and cardiac muscles of mammals of different size.

The ATPase activity of myosin and contraction time in extensor digitorum longus muscle, soleus muscle and cardiac muscle was compared in mammals differing in size. It was shown that the myosin ATPase activity of homologous muscles decreases and contraction time increases with increasing size of animals. The rate of tryptic digestion of myosin, the electrophoretic pattern of light chains of myosin and the effect of p-chloromercuribenzoate on ATPase activity of myosin were also studied. All these three myosin properties are very characteristic when the myosin from a fast muscle is compared with the myosin from a slow muscle of the same animal, but no relationship between these three myosin properties and ATPase activity of myosin was found, when homologous muscles of various mammals were compared.     

A kinetic model that explains the effect of inorganic phosphate on the mechanics and energetics of isometric contraction of fast skeletal muscle

A conventional five-step chemo-mechanical cycle of the myosin–actin ATPase reaction, which implies myosin detachment from actin upon release of hydrolysis products (ADP and phosphate, Pi) and binding of a new ATP molecule, is able to fit the [Pi] dependence of the force and number of myosin motors during isometric contraction of skeletal muscle. However, this scheme is not able to explain why the isometric ATPase rate of fast skeletal muscle is decreased by an increase in [Pi] much less than the number of motors. The question can be solved assuming the presence of a branch in the cycle: in isometric contraction, when the force generation process by the myosin motor is biased at the start of the working stroke, the motor can detach at an early stage of the ATPase cycle, with Pi still bound to its catalytic site, and then rapidly release the hydrolysis products and bind another ATP. In this way, the model predicts that in fast skeletal muscle the energetic cost of isometric contraction increases with [Pi]. The large dissociation constant of the product release in the branched pathway allows the isometric myosin–actin reaction to fit the equilibrium constant of the ATPase.     

Thymol: a classical small-molecule compound that has a dual effect (potentiating and inhibitory) on myosin

The effect of thymol on the ATPase activity of myosin subfragment-1 (S1) and on the contractile properties of skinned skeletal muscle fibers was studied. At concentrations of 1.5-2 mM, thymol activated the S1 ATPase substantially and the actin-activated S1 ATPase modestly. At the same concentrations, the isometric force of skinned skeletal muscle fibers was modestly suppressed (11% at 2 mM). However, the kinetic parameters of contraction were suppressed more: the velocity of shortening and the rate of force redevelopment after shortening were suppressed by 43% and 31% at 2 mM, respectively. Thus, among other small-molecule inhibitors, thymol is unique in that it has opposite effects on the enzymatic activity and kinetic parameters of contraction. Thymol may serve as a potent tool for studying the mechanism of coupling between the ATPase reaction and contraction in muscle.     

The control of energy release in extracted muscle fibers

Tension and P liberation were determined at the same time in glycerol-extracted muscle fibers suspended in ATP solutions. In the relaxed state, produced by ATP in rather fresh preparations, P liberation was low, but somewhat higher than in normal resting muscle. On addition of small amounts of CaCl₂ the fibers gave a strong contraction during which P liberation was on the average about 5 times higher than in the relaxed condition. In aged muscle fibers ATP always produced a strong contraction associated with a high ATPase activity which was not influenced by Ca. The P liberation during a sustained contraction was much smaller in extracted fibers than in normal muscle, but the former maintained tension much more economically than the latter, resembling smooth muscle in this respect. Also the removal of Mg caused a contraction associated with high ATPase activity. Mg, therefore, is inhibitory in relaxed fibers. In fibers activated by Ca or by aging, however, it caused enhancement. The effects of ions on ATPase activity of relaxed fibers are similar to those on myosin and dissociated actomyosin, whereas activated fibers resemble actomyosin at low salt concentration.     

肌肉收缩Hill特性式的理论研究

从肌球蛋白工作循环的机械化学偶联模型出发,利用化学动力学方法和生物化学热力学原理,结合肌球蛋白单分子实验结果,从能量转化的观点给出了肌肉收缩的Hill特性式,加深了对Hill特性式及肌肉收缩过程中能量转化的理解,在整合肌球蛋白单分子性质与肌肉收缩宏观性质的信息方面做了尝试。     

A metabolic control analysis of kinetic controls in ATP free energy metabolism in contracting skeletal muscle

A system analysis ofATP free energy metabolism in skeletal muscle was made using theprinciples of metabolic control theory. We developed a network model ofATP free energy metabolism in muscle consisting of actomyosin ATPase,sarcoplasmic reticulum (SR) Ca²⁺-ATPase, and mitochondria.These components were sufficient to capture the major aspects of theregulation of the cytosolic ATP-to-ADP concentration ratio (ATP/ADP) inmuscle contraction and had inherent homeostatic properties regulatingthis free energy potential. As input for the analysis, we used ATPmetabolic flux and the cytosolic ATP/ADP at steady state at sixcontraction frequencies between 0 and 2 Hz measured in human forearmflexor muscle by ³¹P-NMR spectroscopy. We used themathematical formalism of metabolic control theory to analyze thedistribution of fractional kinetic control of ATPase flux and theATP/ADP in the network at steady state among the components over thisexperimental range and an extrapolated range of stimulation frequencies(up to 10 Hz). The control analysis showed that the contractileactomyosin ATPase has dominant kinetic control of ATP flux in forearmflexor muscle over the 0- to 1.6-Hz range of contraction frequenciesthat resulted in steady states, as determined by ³¹P-NMR.However, flux control begins to shift toward mitochondria at >1 Hz.This inversion of flux control from ATP demand to ATP supply controlhierarchy progressed as the contraction frequency increased past 2 Hzand was nearly complete at 10 Hz. The functional significance of thisresult is that, at steady state, ATP free energy consumption cannotoutstrip the ATP free energy supply. Therefore, this reduced,three-component muscle ATPase system is inherently homeostatic.

     

肌肉收缩Hill特性式的理论研究

从肌球蛋白工作循环的机械化学偶联模型出发,利用化学动力学方法和生化热力学原理,结合肌球蛋白单分子实验结果,从能量转化的角度,研究了肌肉收缩过程中的力与速度关系,发现结果与Hill特性式基本一致。     

An expanded latch-bridge model of protein kinase C-mediated smooth muscle contraction.

A thin-filament-regulated latch-bridge model of smooth muscle contraction is proposed to integrate thin-filament-based inhibition of actomyosin ATPase activity with myosin phosphorylation in the regulation of smooth muscle mechanics. The model included two latch-bridge cycles, one of which was identical to the four-state model as proposed by Hai and Murphy (Am J Physiol Cell Physiol 255: C86-C94, 1988), whereas the ultraslow cross-bridge cycle has lower cross-bridge cycling rates. The model-fitted phorbol ester induced slow contractions at constant myosin phosphorylation and predicted steeper dependence of force on myosin phosphorylation in phorbol ester-stimulated smooth muscle. By shifting cross bridges between the two latch-bridge cycles, the model predicts that a smooth muscle cell can either maintain force at extremely low-energy cost or change its contractile state rapidly, if necessary. Depending on the fraction of cross bridges engaged in the ultraslow latch-bridge cycle, the model predicted biphasic kinetics of smooth muscle mechanics and variable steady-state dependencies of force and shortening velocity on myosin phosphorylation. These results suggest that thin-filament-based regulatory proteins may function as tuners of actomyosin ATPase activity, thus allowing a smooth muscle cell to have two discrete cross-bridge cycles with different cross-bridge cycling rates.     

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.     

Co-operative regulation mechanism of muscle contraction: Inter-tropomyosin co-operation model

A new model is presented on the basis of our experimental data and the “tropomyosin-blocking theory” of muscle relaxation to explain the regulation of certain characteristics of muscle contraction, namely that the relation of contraction to pCa is co-operative while calcium-binding is essentially non-cooperative. Our experiments show that end-to-end interactions between adjacent tropomyosin molecules in the groove of the actin helix are essential for the co-operative regulation. The blocking theory says that the tropomyosin molecule in relaxed muscle sterically blocks the myosin attachment site on actin, whereas in contracting muscle it moves to a position away from the attachment site. In this model a concerted movement of tropomyosin molecules, brought about by their end-to-end interactions, is considered to be the essential mechanism of co-operative regulation, and it is assumed that the positional changes of tropomyosin occur primarily when the four calcium binding sites of troponin on the tropomyosin are saturated with calcium. Theoretical analysis of the model, based upon the two-state allosteric model, leads to a Michaelis-Menten equation for the Ca-binding function together with a co-operative equation for the state function, proportional to the contraction or ATPase activity. These two functions fit well the experimental data. With cardiac muscle the slope of the contraction versus pCa curve is slightly less steep than that obtained with skeletal muscle. This difference can be explained by the difference in the number of Ca-binding sites of troponins.     

The role of troponins in muscle contraction

Troponin (Tn) is the sarcomeric Ca2+ regulator for striated (skeletal and cardiac) muscle contraction. On binding Ca2+ Tn transmits information via structural changes throughout the actin-tropomyosin filaments, activating myosin ATPase activity and muscle contraction. Although the Tn-mediated regulation of striated muscle contraction is now well understood, the role of different Tn isoforms in these processes is the subject of intensive investigations. This review addresses the physiological significance of the multiple Tn isoforms in skeletal and cardiac muscles as well as their role in the regulation of contraction.     

ATPase Activity of Myosin Correlated with Speed of Muscle Shortening

Myosin was isolated from 14 different muscles (mammals, lower vertebrates, and invertebrates) of known maximal speed of shortening. These myosin preparations were homogeneous in the analytical ultracentrifuge or, in a few cases, showed, in addition to the main myosin peak, part of the myosin in aggregated form. Actin- and Ca⁺⁺-activated ATPase activities of the myosins were generally proportional to the speed of shortening of their respective muscles; i.e. the greater the intrinsic speed, the higher the ATPase activity. This relation was found when the speed of shortening ranged from 0.1 to 24 muscle lengths/sec. The temperature coefficient of the Ca⁺⁺-activated myosin ATPase was the same as that of the speed of shortening, Q₁₀ about 2. Higher Q₁₀ values were found for the actin-activated myosin ATPase, especially below 10°C. By using myofibrils instead of reconstituted actomyosin, Q₁₀ values close to 2 could be obtained for the Mg⁺⁺-activated myofibrillar ATPase at ionic strength of 0.014. In another series of experiments, myosin was isolated from 11 different muscles of known isometric twitch contraction time. The ATPase activity of these myosins was inversely proportional to the contraction time of the muscles. These results suggest a role for the ATPase activity of myosin in determining the speed of muscle contraction. In contrast to the ATPase activity of myosin, which varied according to the speed of contraction, the F-actin-binding ability of myosin from various muscles was rather constant.     

Regulation of the actin-activated ATPase of aorta smooth muscle myosin

Phosphorylation of the 20,000-Da light chains, LC20, of vertebrate smooth muscle myosins is thought to be the primary mechanism for regulating the actin-activated ATPase activities of these myosins and consequently smooth muscle contraction. While actin stimulates the MgATPase activities of phosphorylated smooth muscle myosins, it is generally believed that the MgATPase activities of the unphosphorylated myosins are not stimulated by actin. However, under conditions where both unphosphorylated (5% phosphorylated LC20) and phosphorylated calf aorta myosins are mostly filamentous, the maximum rate, Vmax, of the actin-activated ATPase of the unphosphorylated myosin is one-half that of the phosphorylated myosin. While LC20 phosphorylation causes only a modest increase in Vmax, in the presence of tropomyosin, this phosphorylation does cause up to a 10-fold decrease in Kapp, the actin concentration required to achieve 1/2 Vmax. In the presence of low concentrations of tropomyosin/actin, a linear relationship is obtained between the fraction of LC20 phosphorylated and stimulation of the actin-activated ATPase. The relatively high actin-activated ATPase activity of unphosphorylated aorta myosin suggests that other proteins may be involved in the regulation of smooth muscle contraction. In contrast to the results presented here for aorta myosin, it has been reported that actin does not activate the MgATPase activity of unphosphorylated gizzard myosin and that the actin-activated ATPase of gizzard myosin increases more slowly than LC20 phosphorylation.     

Butanedione monoxime suppresses contraction and ATPase activity of rabbit skeletal muscle

The effects of 2,3-butanedione 2-monoxime (BDM) on mechanical responses of glycerinated fibers and the ATPase activity of heavy meromyosin (HMM) and myofibrils have been studied using rabbit skeletal muscle. The mechanical responses and the ATPase activity were measured in similar conditions (ionic strength 0.06-0.2 M, 0.4-4 mM MgATP, 0-20 mM BDM, 2-20 degrees C and pH 7.0). BDM reversibly reduced the isometric tension, shortening speed, and instantaneous stiffness of the fibers. BDM also inhibited myofibrillar and HMM ATPase activities. The inhibitory effect on the relative ATPase activity of HMM was not influenced by the addition of actin or troponin-tropomyosin-actin. High temperature and low ionic strength weakened BDM's suppression of contraction of the fibers and the ATPase activity of contracting myofibrils, but not of the HMM, acto-HMM and relaxed myofibrillar ATPase activity. The size of the initial phosphate burst at 20 degrees C was independent of the concentration of BDM. These results suggest that the suppression of contraction of muscle fibers is due mainly to direct action of BDM on the myosin molecules.     

Mutation of the high affinity calcium binding sites in cardiac troponin C.

Fast skeletal and cardiac troponin C (TnC) contain two high affinity Ca2+/Mg2+ binding sites within the C-terminal domain that are thought to be important for association of TnC with the troponin complex of the thin filament. To test directly the function of these high affinity sites in cardiac TnC they were systematically altered by mutagenesis to generate proteins with a single inactive site III or IV (CBM-III and CBM-IV, respectively), or with both sites III and IV inactive (CBM-III-IV). Equilibrium dialysis indicated that the mutated sites did not bind Ca2+ at pCa 4. Both CBM-III and CBM-IV were similar to the wild type protein in their ability to regulate Ca(2+)-dependent contraction in slow skeletal muscle fibers, and Ca(2+)-dependent ATPase activity in fast skeletal and cardiac muscle myofibrils. The mutant CBM-III-IV is capable of regulating contraction in permeabilized slow muscle fibers but only if the fibers are maintained in a contraction solution containing a high concentration of the mutant protein. CBM-III-IV also regulates myofibril ATPase activity in fast skeletal and cardiac myofibrils but only at concentrations 10-100-fold greater than the normal protein. The pCa50 and Hill coefficient values for Ca(2+)-dependent activation of fast skeletal muscle myofibril ATPase activity by the normal protein and all three mutants are essentially the same. Competition between active and inactive forms of cardiac and slow TnC in a functional assay demonstrates that mutation of both sites III and IV greatly reduces the affinity of cardiac and slow TnC for its functionally relevant binding site in the myofibrils. The data indicate that although neither high affinity site is absolutely essential for regulation of muscle contraction in vitro, at least one active C-terminal site is required for tight association of cardiac troponin C with myofibrils. This requirement can be satisfied by either site III or IV.     

肌肉收缩的理论研究

基于肌球蛋白工作循环模型,从物理学的角度出发,利用化学动力学方法,给出肌动蛋白丝的动力学方程,讨论肌球蛋白的运力学行为,发现肌动蛋白运动呈锯齿状,并得到振动周期约为3.0s,与实验结果基本吻合。结论是宏观的肌肉运动是单分子运动的集体协同行为,为肌肉的运动训练和治疗提供理论参考。     

平滑肌肌球蛋白磷酸化与肌动球蛋白功能调节

在有Ｃａ２＋和钙调蛋白存在时,肌球蛋白轻链激酶催化肌球蛋白磷酸化,促使肌动蛋白激活的肌球蛋白（肌动球蛋白）Ｍｇ２＋－ＡＴＰ酶活性显著增加．然而,肌球蛋白磷酸化水平与Ｍｇ２＋－ＡＴＰ酶之间的关系是非线性的,原肌球蛋白可以进一步增加Ｍｇ２＋－ＡＴＰ酶的活性,但仍不改变它们之间的非线性关系．肌球蛋白轻链激酶的合成肽抑制剂抑制了肌球蛋白磷酸化和Ｍｇ２＋－ＡＴＰ酶活性,并导致平滑肌去膜肌纤维的等长收缩张力与速度的降低．结果提示肌球蛋白轻链激酶参与脊椎动物平滑肌收缩的调节过程,肌球蛋白轻链磷酸化作用会引起平滑肌收缩     

碱性调宁蛋白的研究进展

碱性调宁蛋白是一个首先从鸡砂囊和牛主动脉中分离出的相对分子质量为34×103的碱性蛋白。它在平滑肌中特异表达,结合钙调蛋白,肌动蛋白,肌球蛋白,抑制肌球蛋白的ATP酶活性,参与平滑肌收缩、细胞信号转导、维持细胞骨架、抑制细胞增生等。