A Mechanistic Model of Ca Regulation of Thin Filaments in Cardiac Muscle

We present a model of Ca-regulated thin filaments in cardiac muscle where tropomyosin is treated as a continuous elastic chain confined in the closed position on the actin helix by electrostatic forces. The main distinction from previous works is that the intrinsic stress-free helical shape of the tropomyosin chain was taken into account explicitly. This results in the appearance of a new, to our knowledge, tension-like term in the energy functional and the equilibrium equation. The competitive binding of calcium and the mobile segment of troponin-I to troponin-C were described by a simple kinetic scheme. The values of dimensionless model parameters were estimated from published data. A stochastic Monte Carlo simulation of calcium curves has been performed and its results were compared to published data. The model explains the high cooperativity of calcium response of the regulated thin filaments even in the absence of myosin heads. The binding of myosin heads to actin increases the calcium sensitivity while not affecting its cooperativity significantly. When the presence of calcium-insensitive troponin-C was simulated in the model, both calcium sensitivity and cooperativity decreased. All these features were previously observed experimentally.     

A new model of cooperative myosin-thin filament binding

Cooperative myosin binding to the thin filament is critical to regulation of cardiac and skeletal muscle contraction. This report delineates and fits to experimental data a new model of this process, in which specific tropomyosin-actin interactions are important, the tropomyosin-tropomyosin polymer is continuous rather than disjointed, and tropomyosin affects myosin-actin binding by shifting among three positions as in recent structural studies. A myosin- and tropomyosin-induced conformational change in actin is proposed, rationalizing the approximately 10,000-fold strengthening effect of myosin on tropomyosin-actin binding. Also, myosin S1 binding to regulated filaments containing mutant tropomyosins with internal deletions exhibited exaggerated cooperativity, implying an allosteric effect of tropomyosin on actin and allowing the effect's measurement. Comparisons among the mutants suggest the change in actin is promoted much more strongly by the middle of tropomyosin than by its ends. Regardless of calcium binding to troponin, this change in actin facilitates the shift in tropomyosin position to the actin inner domain, which is required for tight myosin-actin association. It also increases myosin-actin affinity 7-fold compared with the absence of troponin-tropomyosin. Finally, initiation of a shift in tropomyosin position is 100-fold more difficult than is its extension from one actin to the next, producing the myosin binding cooperativity that underlies cooperative activation of muscle contraction.     

Crossbridge and tropomyosin positions observed in native, interacting thick and thin filaments

Tropomyosin movements on thin filaments are thought to sterically regulate muscle contraction, but have not been visualized during active filament sliding. In addition, although 3-D visualization of myosin crossbridges has been possible in rigor, it has been difficult for thick filaments actively interacting with thin filaments. In the current study, using three-dimensional reconstruction of electron micrographs of interacting filaments, we have been able to resolve not only tropomyosin, but also the docking sites for weak and strongly bound crossbridges on thin filaments. In relaxing conditions, tropomyosin was observed on the outer domain of actin, and thin filament interactions with thick filaments were rare. In contracting conditions, tropomyosin had moved to the inner domain of actin, and extra density, reflecting weakly bound, cycling myosin heads, was also detected, on the extreme periphery of actin. In rigor conditions, tropomyosin had moved further on to the inner domain of actin, and strongly bound myosin heads were now observed over the junction of the inner and outer domains. We conclude (1) that tropomyosin movements consistent with the steric model of muscle contraction occur in interacting thick and thin filaments, (2) that myosin-induced movement of tropomyosin in activated filaments requires strongly bound crossbridges, and (3) that crossbridges are bound to the periphery of actin, at a site distinct from the strong myosin binding site, at an early stage of the crossbridge cycle.     

Kinetic model of regulation of muscle protein activity.

The widely accepted steric model of calcium regulation of actin-myosin interactions in vertebrate muscles has to be completed to fit the kinetic data. It should be supposed that: (1) the thin filaments consist of functionally independent units, containing seven actin sites regulated by one troponin-tropomyosin complex; (2) actin sites become available for myosin heads only due to fluctuations of tropomyosin position; (3) binding of calcium to troponin results either in the shift of the tropomyosin equilibrium position or in the weakening of its interactions with actin strand so that the probability of effective fluctuations increases; (4) link formation between myosin head and some of the available actin site fixates the tropomyosin in such a position that the other six actin sites of the same functional unit become available for myosin too.The model gives linear kinetic scheme for the transitions of a functional unit between nine states (a “turned off” state, and eight “turned on” ones with different occupancy by myosin heads). The dependences of the apparent rate constants of actomyosin formation and dissociation upon the myosin head and substrate concentrations are obtained from the Lymn-Taylor scheme. The frequency of the actomyosin complexes dissociation is assumed to give the ATPase rate.The model fits the kinetic data on the ATP hydrolysis by myosin subfragment-1 with regulated or unregulated actin as a cofactor under various conditions. It shows a sharp dependence of activation upon the apparent affinity of the actin and myosin sites. Therefore, the model appears to be applicable to myosin controlled systems.     

Striated Muscle Regulation of Isometric Tension by Multiple Equilibria

Cooperative activation of striated muscle by calcium is based on the movement of tropomyosin described by the steric blocking theory of muscle contraction. Presently, the Hill model stands alone in reproducing both myosin binding data and a sigmoidal-shaped curve characteristic of calcium activation (Hill TL (1983) Two elementary models for the regulation of skeletal muscle contraction by calcium. Biophys J 44: 383–396.). However, the free myosin is assumed to be fixed by the muscle lattice and the cooperative mechanism is based on calcium-dependent interactions between nearest neighbor tropomyosin subunits, which has yet to be validated. As a result, no comprehensive model has been shown capable of fitting actual tension data from striated muscle. We show how variable free myosin is a selective advantage for activating the muscle and describe a mechanism by which a conformational change in tropomyosin propagates free myosin given constant total myosin. This mechanism requires actin, tropomyosin, and filamentous myosin but is independent of troponin. Hence, it will work equally well with striated, smooth and non-muscle contractile systems. Results of simulations with and without data are consistent with a strand of tropomyosin composed of ∼20 subunits being moved by the concerted action of 3–5 myosin heads, which compares favorably with the predicted length of tropomyosin in the overlap region of thick and thin filaments. We demonstrate that our model fits both equilibrium myosin binding data and steady-state calcium-dependent tension data and show how both the steepness of the response and the sensitivity to calcium can be regulated by the actin-troponin interaction. The model simulates non-cooperative calcium binding both in the presence and absence of strong binding myosin as has been observed. Thus, a comprehensive model based on three well-described interactions with actin, namely, actin-troponin, actin-tropomyosin, and actin-myosin can explain the cooperative calcium activation of striated muscle.     

Direct Measurements of Local Coupling between Myosin Molecules Are Consistent with a Model of Muscle Activation

Muscle contracts due to ATP-dependent interactions of myosin motors with thin filaments composed of the proteins actin, troponin, and tropomyosin. Contraction is initiated when calcium binds to troponin, which changes conformation and displaces tropomyosin, a filamentous protein that wraps around the actin filament, thereby exposing myosin binding sites on actin. Myosin motors interact with each other indirectly via tropomyosin, since myosin binding to actin locally displaces tropomyosin and thereby facilitates binding of nearby myosin. Defining and modeling this local coupling between myosin motors is an open problem in muscle modeling and, more broadly, a requirement to understanding the connection between muscle contraction at the molecular and macro scale. It is challenging to directly observe this coupling, and such measurements have only recently been made. Analysis of these data suggests that two myosin heads are required to activate the thin filament. This result contrasts with a theoretical model, which reproduces several indirect measurements of coupling between myosin, that assumes a single myosin head can activate the thin filament. To understand this apparent discrepancy, we incorporated the model into stochastic simulations of the experiments, which generated simulated data that were then analyzed identically to the experimental measurements. By varying a single parameter, good agreement between simulation and experiment was established. The conclusion that two myosin molecules are required to activate the thin filament arises from an assumption, made during data analysis, that the intensity of the fluorescent tags attached to myosin varies depending on experimental condition. We provide an alternative explanation that reconciles theory and experiment without assuming that the intensity of the fluorescent tags varies.     

Actin and myosin-linked calcium regulation in the nematode Caenorhabditis elegans. Biochemical and structural properties of native filaments and purified proteins.

Calcium regulation of actomyosin activity in the nematode, Caenorhabditis elegans, has been studied with purified proteins and crude thin filaments. Actin and tropomyosin have been purified from C. elegans and shown to be similar in most respects to actin and tropomyosin from rabbit skeletal muscle. The actin comigrates with rabbit actin on polyacrylamide-sodium dodecyl sulfate gel electrophoresis, forms similar filaments and paracrystals, and activates the Mg2+-ATPase of rabbit myosin heads as efficiently as rabbit actin. Nematode tropomyosin has a greater apparent molecular weight (estimated by mobility on polyacrylamide-sodium dodecyl sulfate gels) than the rabbit protein, yet it forms Mg2+-paracrystals with a slightly shorter periodicity. Native thin filaments extracted from nematodes activate rabbit myosin subfragment 1 Mg2+-ATPase in a calcium sensitive manner; the extent of activation is threefold greater in 0.2 mM CaCl2 than in the absence of calcium. This observation suggests that the thin filaments contain components which are functionally equivalent to vertebrate troponins. Calcium is also required for maximal activation of the Mg2+-ATPase of purified nematode myosin by pure rabbit F-actin. C. elegans therefore has both myosin and thin filament-linked calcium regulatory systems. The origin of the actin, tropomyosin, and myosin from different tissues and the use of genetic analysis to answer questions about assembly and function in vivo are discussed.     

Effects of deletion of tropomyosin overlap on regulated actomyosin subfragment 1 ATPase.

The role of the overlap region at the ends of tropomyosin molecules in the properties of regulated thin filaments has been investigated by substituting nonpolymerizable tropomyosin for tropomyosin in a reconstituted troponin-tropomyosin-actomyosin subfragment 1 ATPase assay system. A previous study [Heeley, Golosinka & Smillie (1987) J. Biol. Chem. 262, 9971-9978] has shown that at an ionic strength of 70 mM, troponin will induce full binding of nonpolymerizable tropomyosin to F-actin both in the presence and absence of calcium. At a myosin subfragment 1-to-actin ratio of 2:1 ([actin] = 4 microM) and an ionic strength of 50 mM, comparable levels of ATPase inhibition were observed with increasing levels of tropomyosin or the truncated derivative in the presence of troponin (-Ca2+). Large differences were noted, however, in the activation by Ca2+. Significantly lower ATPase activities were observed with nonpolymerizable tropomyosin and troponin (+Ca2+) over a range of subfragment 1-to-actin ratios from 0.25 to 2.5. The concentration of subfragment 1 required to generate ATPase activities exceeding those seen with actomyosin subfragment 1 alone under these conditions was 3-4-fold greater when nonpolymerizable tropomyosin was used. Similar effects were seen at the much lower ionic strength of 13 mM and are consistent with the reduced ATPase activity with nonpolymerizable tropomyosin observed previously [Walsh, Trueblood, Evans & Weber (1985) J. Mol. Biol. 182, 265-269] at low ionic strength and a subfragment 1-to-actin ratio of 1:100. Little cooperativity in activity as a function of subfragment 1 concentration with either intact tropomyosin or its truncated derivative was observed under the present conditions. Further studies are directed towards an understanding of these effects in terms of the two-state binding model for the attachment of myosin heads to regulated thin filaments.     

Caldesmon restricts the movement of both C- and N-termini of tropomyosin on F-actin in ghost fibers during the actomyosin ATPase cycle

New data on the movements of tropomyosin singly labeled at alpha- or beta-chain during the ATP hydrolysis cycle in reconstituted ghost fibers have been obtained by using the polarized fluorescence technique which allowed us following the azimuthal movements of tropomyosin on actin filaments. Pronounced structural changes in tropomyosin evoked by myosin heads suggested the "rolling" of the tropomyosin molecule on F-actin surface during the ATP hydrolysis cycle. The movements of actin-bound tropomyosin correlated to the strength of S1 to actin binding. Weak binding of myosin to actin led to an increase in the affinity of the tropomyosin N-terminus to actin with simultaneous decrease in the affinity of the C-terminus. On the contrary, strong binding of myosin to actin resulted in the opposite changes of the affinity to actin of both ends of the tropomyosin molecule. Caldesmon inhibited the "rolling" of tropomyosin on the surface of the thin filament during the ATP hydrolysis cycle, drastically decreased the affinity of the whole tropomyosin molecule to actin, and "freezed" tropomyosin in the position characteristic of the weak binding of myosin to actin.     

The effect of caldesmon on actin-myosin interaction in skeletal muscle fibers

The effects of caldesmon on structural and dynamic properties of phalloidin-rhodamine-labeled F-actin in single skeletal muscle fibers were investigated by polarized microphotometry. The binding of caldesmon to F-actin in glycerinated fibers reduced the alterations of thin filaments structure and dynamics that occur upon the transition of the fibers from rigor to relaxing conditions. In fibers devoid of myosin and regulatory proteins (ghost fibers) the binding of caldesmon to F-actin precluded structural changes in actin filaments induced by skeletal muscle myosin subfragment 1 and smooth muscle tropomyosin. These results suggest that the restraint for the alteration of actin structure and dynamics upon binding of myosin heads and/or tropomyosin evoked by caldesmon can be related to its inhibitory effect on actin-myosin interaction.     

An actin subdomain 2 mutation that impairs thin filament regulation by troponin and tropomyosin

Striated muscle thin filaments adopt different quaternary structures, depending upon calcium binding to troponin and myosin binding to actin. Modification of actin subdomain 2 alters troponin-tropomyosin-mediated regulation, suggesting that this region of actin may contain important protein-protein interaction sites. We used yeast actin mutant D56A/E57A to examine this issue. The mutation increased the affinity of tropomyosin for actin 3-fold. The addition of Ca(2+) to mutant actin filaments containing troponin-tropomyosin produced little increase in the thin filament-myosin S1 MgATPase rate. Despite this, three-dimensional reconstruction of electron microscope images of filaments in the presence of troponin and Ca(2+) showed tropomyosin to be in a position similar to that found for muscle actin filaments, where most of the myosin binding site is exposed. Troponin-tropomyosin bound with comparable affinity to mutant and wild type actin in the absence and presence of calcium, and in the presence of myosin S1, tropomyosin bound very tightly to both types of actin. The mutation decreased actin-myosin S1 affinity 13-fold in the presence of troponin-tropomyosin and 2.6-fold in the absence of the regulatory proteins. The results suggest the importance of negatively charged actin subdomain 2 residues 56 and 57 for myosin binding to actin, for tropomyosin-actin interactions, and for regulatory conformational changes in the actin-troponin-tropomyosin complex.     

Modulation of myosin function by isoform-specific properties of Saccharomyces cerevisiae and muscle tropomyosins.

Tropomyosin is an extended coiled-coil protein that influences actin function by binding longitudinally along thin filaments. The present work compares cardiac tropomyosin and the two tropomyosins from Saccharomyces cerevisiae, TPM1 and TPM2, that are much shorter than vertebrate tropomyosins. Unlike cardiac tropomyosin, the phase of the coiled-coil-forming heptad repeat of TPM2 is discontinuous; it is interrupted by a 4-residue deletion. TPM1 has two such deletions, which flank the 38-residue partial gene duplication that causes TPM1 to span five actins instead of the four of TPM2. Each of the three tropomyosin isoforms modulates actin-myosin interactions, with isoform-specific effects on cooperativity and strength of myosin binding. These different properties can be explained by a model that combines opposite effects, steric hindrance between myosin and tropomyosin when the latter is bound to a subset of its sites on actin, and also indirect, favorable interactions between tropomyosin and myosin, mediated by mutually promoted changes in actin. Both of these effects are influenced by which tropomyosin isoform is present. Finally, the tropomyosins have isoform-specific effects on in vitro sliding speed and on the myosin concentration dependence of this movement, suggesting that non-muscle tropomyosin isoforms exist, at least in part, to modulate myosin function.     

Movement of smooth muscle tropomyosin by myosin heads.

It has been proposed that during the activation of muscle contraction the initial binding of myosin heads to the actin thin filament contributes to switching on the thin filament and that this might involve the movement of actin-bound tropomyosin. The movement of smooth muscle tropomyosin on actin was investigated in this work by measuring the change in distance between specific residues on tropomyosin and actin by fluorescence resonance energy transfer (FRET) as a function of myosin head binding to actin. An energy transfer acceptor was attached to Cys374 of actin and a donor to the tropomyosin heterodimer at either Cys36 of the beta-chain or Cys190 of the alpha-chain. FRET changed for the donor at both positions of tropomyosin upon addition of skeletal or smooth muscle myosin heads, indicating a movement of the whole tropomyosin molecule. The changes in FRET were hyperbolic and saturated at about one head per seven actin subunits, indicating that each head cooperatively affects several tropomyosin molecules, presumably via tropomyosin's end-to-end interaction. ATP, which dissociates myosin from actin, completely reversed the changes in FRET induced by heads, whereas in the presence of ADP the effect of heads was the same as in its absence. The results indicate that myosin with and without ADP, intermediates in the myosin ATPase hydrolytic pathway, are effective regulators of tropomyosin position, which might play a role in the regulation of smooth muscle contraction.     

Cooperative [Ca²+]-dependent regulation of the rate of myosin binding to actin: solution data and the tropomyosin chain model

The regulation of muscle contraction by calcium involves interactions among actin filaments, myosin-S1, tropomyosin (Tm), and troponin (Tn). We have extended our previous model in which the TmTn regulatory units are treated as a continuous flexible chain, and applied it to transient kinetic data. We have measured the time course of myosin-S1 binding to actin-Tm-Tn filaments in solution at various calcium levels with [actin]/[myosin] ratios of 10 and 0.1, which exhibit modest slowing as [Ca(2+)] is reduced and a lag phase at low calcium. These observations can be explained if myosin binds to actin in two steps, where the first step is rate-limiting and blocked by TmTnI at low calcium, and the second step is fast, reversible, and controlled by the neighboring configuration of coupled tropomyosin-troponin units. The model can describe the calcium dependence of the observed myosin binding reactions and predicts cooperative calcium binding to TnC with competition between actin and Ca-TnC for the binding of TnI. Implications for theories of thin-filament regulation in muscle are discussed.     

Linear dichroism of acrylodan-labeled tropomyosin and myosin subfragment 1 bound to actin in myofibrils.

Muscle contraction can be activated by the binding of myosin heads to the thin filament, which appears to result in thin filament structural changes. In vitro studies of reconstituted muscle thin filaments have shown changes in tropomyosin-actin geometry associated with the binding of myosin subfragment 1 to actin. Further information about these structural changes was obtained with fluorescence-detected linear dichroism of tropomyosin, which was labeled at Cys 190 with acrylodan and incorporated into oriented ghost myofibrils. The fluorescence from three sarcomeres of the fibril was collected with the high numerical aperture objective of a microscope and the dichroic ratio, R (0/90 degrees), for excitation parallel/perpendicular to the fibril, was obtained, which gave the average probe dipole polar angle, Theta. For both acrylodan-labeled tropomyosin bound to actin in fibrils and in Mg2+ paracrystals, Theta congruent to 52 degrees +/- 1.0 degrees, allowing for a small degree of orientational disorder. Binding of myosin subfragment 1 to actin in fibrils did not change Theta; i.e., the orientation of the rigidly bound probe on tropomyosin did not change relative to the actin axis. These data indicate that myosin subfragment 1 binding to actin does not appreciably perturb the structure of tropomyosin near the probe and suggest that the geometry changes are such as to maintain the parallel orientation of the tropomyosin and actin axes, a finding consistent with models of muscle regulation. Data are also presented for effects of MgADP on the orientation of labeled myosin subfragment 1 bound to actin in myofibrils.     

Cooperative [Ca]-Dependent Regulation of the Rate of Myosin Binding to Actin: Solution Data and the Tropomyosin Chain Model

The regulation of muscle contraction by calcium involves interactions among actin filaments, myosin-S1, tropomyosin (Tm), and troponin (Tn). We have extended our previous model in which the TmTn regulatory units are treated as a continuous flexible chain, and applied it to transient kinetic data. We have measured the time course of myosin-S1 binding to actin-Tm-Tn filaments in solution at various calcium levels with [actin]/[myosin] ratios of 10 and 0.1, which exhibit modest slowing as [Ca²⁺] is reduced and a lag phase at low calcium. These observations can be explained if myosin binds to actin in two steps, where the first step is rate-limiting and blocked by TmTnI at low calcium, and the second step is fast, reversible, and controlled by the neighboring configuration of coupled tropomyosin-troponin units. The model can describe the calcium dependence of the observed myosin binding reactions and predicts cooperative calcium binding to TnC with competition between actin and Ca-TnC for the binding of TnI. Implications for theories of thin-filament regulation in muscle are discussed.     

Effects of actin-myosin kinetics on the calcium sensitivity of regulated thin filaments

Activation of thin filaments in striated muscle occurs when tropomyosin exposes myosin binding sites on actin either through calcium-troponin (Ca-Tn) binding or by actin-myosin (A-M) strong binding. However, the extent to which these binding events contributes to thin filament activation remains unclear. Here we propose a simple analytical model in which strong A-M binding and Ca-Tn binding independently activates the rate of A-M weak-to-strong binding. The model predicts how the level of activation varies with pCa as well as A-M attachment, N·k(att), and detachment, k(det), kinetics. To test the model, we use an in vitro motility assay to measure the myosin-based sliding velocities of thin filaments at different pCa, N·k(att), and k(det) values. We observe that the combined effects of varying pCa, N·k(att), and k(det) are accurately fit by the analytical model. The model and supporting data imply that changes in attachment and detachment kinetics predictably affect the calcium sensitivity of striated muscle mechanics, providing a novel A-M kinetic-based interpretation for perturbations (e.g. disease-related mutations) that alter calcium sensitivity.     

Activation of smooth muscle myosin Mg2+-ATPase by native thin filaments and actin/tropomyosin

Application of the myosin competition test (Lehman, W., and Szent-Gy?rgyi, A. G. (1975) J. Gen. Physiol. 66, 1-30) to chicken gizzard actomyosin indicated that this smooth muscle contains a thin filament-linked regulatory mechanism. Chicken gizzard thin filaments, isolated as described previously (Marston, S. B., and Lehman, W. (1985) Biochem. J. 231, 517-522), consisted almost exclusively of actin, tropomyosin, caldesmon, and an unidentified 32-kilodalton polypeptide in molar ratios of 1:1/6:1/26:1/17, respectively. When reconstituted with phosphorylated gizzard myosin, these thin filaments conferred Ca2+ sensitivity (67.8 +/- 2.1%; n = 5) on the myosin Mg2+-ATPase. On the other hand, no Ca2+ sensitivity of the myosin Mg2+-ATPase was observed when purified gizzard actin or actin plus tropomyosin was reconstituted with phosphorylated gizzard myosin. Native thin filaments were rendered essentially free of caldesmon and the 32-kilodalton polypeptide by extraction with 25 mM MgCl2. When reconstituted with phosphorylated gizzard myosin, caldesmon-free thin filaments and native thin filaments exhibited approximately the same Ca2+ sensitivity (45.1 and 42.7%, respectively). The observed Ca2+ sensitivity appears, therefore, not to be due to caldesmon. Only trace amounts of two Ca2+-binding proteins could be detected in native thin filaments. These were identified as calmodulin (present at a molar ratio to actin of 1:733) and the 20-kilodalton light chain of myosin (present at a molar ratio to actin of 1:270). The Ca2+ sensitivity observed in an in vitro system reconstituted from gizzard thin filaments and either skeletal myosin or phosphorylated gizzard myosin is due, therefore, to calmodulin and/or an unidentified minor protein component of the thin filaments which may be an actin-binding protein involved in regulating actin filament structure in a Ca2+-dependent manner.     

Cooperative regulation of myosin-actin interactions by a continuous flexible chain I: actin-tropomyosin systems

We present a model for cooperative myosin binding to the regulated actin filament, where tropomyosins are treated as a weakly-confined continuous flexible chain covering myosin binding sites. Thermal fluctuations in chain orientation are initially required for myosin binding, leaving kinked regions under which subsequent myosins may bind without further distortion of the chain. Statistical mechanics predicts the fraction of sites with bound myosin-S1 as a function of their affinities. Published S1 binding curves to regulated filaments with different tropomyosin isoforms are fitted by varying the binding constant, chain persistence length nu (in actin monomers), and chain kink energy A from a single bound S1. With skeletal tropomyosin, we find an S1 actin-binding constant of 2.2 x 10(7) M(-1), A = 1.6 k(B)T and nu = 2.7. Similar persistence lengths are found with yeast tropomyosin. Larger values are found for tropomyosin-troponin in the presence of calcium (nu = 3.7) and tropomyosins from smooth muscle and fibroblasts (nu = 4.5). The relationship of these results to structural information and the rigid-unit model of McKillop and Geeves is discussed.