Cooperative regulation of myosin-S1 binding to actin filaments by a continuous flexible Tm-Tn chain

Changing face of contractile activation in striated muscle at physiological temperature

Calcium binding to troponin, with subsequent displacement of its linked tropomyosin molecule on the thin filament surface, cooperates with myosin binding to actin in the contractile regulation of striated muscle. The intertwined role of these systems is studied in the present issue of JGP by Ishii et al. (https://doi.org/10.1085/jgp.202313414). A particularly interesting feature of the paper, except for studying both skeletal and cardiac muscle proteins, is that the experiments unlike most other similar studies are performed at physiological temperature (35-40°C).

Using Multiscale Simulations as a Tool to Interpret Equatorial X-ray Fiber Diffraction Patterns from Skeletal Muscle

Synchrotron small-angle X-ray diffraction is the method of choice for nm-scale structural studies of striated muscle under physiological conditions and on millisecond time scales. The lack of generally applicable computational tools for modeling X-ray diffraction patterns from intact muscles has been a significant barrier to exploiting the full potential of this technique. Here, we report a novel "forward problem" approach using the spatially explicit computational simulation platform MUSICO to predict equatorial small-angle X-ray diffraction patterns and the force output simultaneously from resting and isometrically contracting rat skeletal muscle that can be compared to experimental data. The simulation generates families of thick-thin filament repeating units, each with their individually predicted occupancies of different populations of active and inactive myosin heads that can be used to generate 2D-projected electron density models based on known Protein Data Bank structures. We show how, by adjusting only a few selected parameters, we can achieve a good correspondence between experimental and predicted X-ray intensities. The developments presented here demonstrate the feasibility of combining X-ray diffraction and spatially explicit modeling to form a powerful hypothesis-generating tool that can be used to motivate experiments that can reveal emergent properties of muscle.

Varying thin filament activation in the framework of the Huxley'57 model

Muscle contraction is triggered by the activation of the actin sites of the thin filament by calcium ions. It results that the thin filament activation level varies over time. Moreover, this activation process is also used as a regulation mechanism of the developed force. Our objective is to build a model of varying actin site activation level within the classical Huxley'57 two-state framework. This new model is obtained as an enhancement of a previously proposed formulation of the varying thick filament activation within the same framework. We assume that the state of an actin site depends on whether it is activated and whether it forms a cross-bridge with the associated myosin head, which results in four possible states. The transitions between the actin site states are controlled by the global actin sites activation level and the dynamics of these transitions is coupled with the attachment-detachment process. A preliminary calibration of the model with experimental twitch contraction data obtained at varying sarcomere lengths is performed.

Effect of Myosin Isoforms on Cardiac Muscle Twitch of Mice, Rats and Humans

To understand how pathology-induced changes in contractile protein isoforms modulate cardiac muscle function, it is necessary to quantify the temporal-mechanical properties of contractions that occur under various conditions. Pathological responses are much easier to study in animal model systems than in humans, but extrapolation between species presents numerous challenges. Employing computational approaches can help elucidate relationships that are difficult to test experimentally by translating the observations from rats and mice, as model organisms, to the human heart. Here, we use the spatially explicit MUSICO platform to model twitch contractions from rodent and human trabeculae collected in a single laboratory. This approach allowed us to identify the variations in kinetic characteristics of α- and β-myosin isoforms across species and to quantify their effect on cardiac muscle contractile responses. The simulations showed how the twitch transient varied with the ratio of the two myosin isoforms. Particularly, the rate of tension rise was proportional to the fraction of α-myosin present, while the β-isoform dominated the rate of relaxation unless α-myosin was >50%. Moreover, both the myosin isoform and the Ca2+ transient contributed to the twitch tension transient, allowing two levels of regulation of twitch contraction.

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.

The effect of variable troponin C mutation thin filament incorporation on cardiac muscle twitch contractions

One of the complexities of understanding the pathology of familial forms of cardiac diseases is the level of mutation incorporation in sarcomeres. Computational models of the sarcomere that are spatially explicit offer an approach to study aspects of mutational incorporation into myofilaments that are more challenging to get at experimentally. We studied two well characterized mutations of cardiac TnC, L48Q and I61Q, that decrease or increase the release rate of Ca²⁺ from cTnC, k_-Ca, resulting in HCM and DCM respectively [1]. Expression of these mutations in transgenic mice was used to provide experimental data for incorporation of 30 and 50% (respectively) into sarcomeres. Here we demonstrate that fixed length twitch contractions of trabeculae from mice containing mutant differ from WT; L48Q trabeculae have slower relaxation while I61Q trabeculae have markedly reduced peak tension. Using our multiscale modelling approach [2] we were able to describe the tension transients of WT mouse myocardium. Tension transients for the mutant cTnCs were simulated with changes in k_-Ca, measured experimentally for each cTnC mutant in whole troponin complex, a change in the affinity of cTnC for cTnI, and a reduction in the number of detached crossbridges available for binding. A major advantage of the multiscale explicit 3-D model is that it predicts the effects of variable mutation incorporation, and the effects of variations in mutation distribution within thin filaments in sarcomeres. Such effects are currently impossible to explore experimentally. We explored random and clustered distributions of mutant cTnCs in thin filaments, as well as distributions of individual thin filaments with only WT or mutant cTnCs present. The effects of variable amounts of incorporation and non-random distribution of mutant cTnCs are more marked for I61Q than L48Q cTnC. We conclude that this approach can be effective for study on mutations in multiple proteins of the sarcomere. SUMMARY: A challenge in experimental studies of diseases is accounting for the effect of variable mutation incorporation into myofilaments. Here we use a spatially explicit computational approach, informed by experimental data from transgenic mice expressing one of two mutations in cardiac Troponin C that increase or decrease calcium sensitivity. We demonstrate that the model can accurately describe twitch contractions for the data and go on to explore the effect of variable mutant incorporation and localization on simulated cardiac muscle twitches.

Troponin Revealed: Uncovering the Structure of the Thin Filament On-Off Switch in Striated Muscle

Recently, our understanding of the structural basis of troponin-tropomyosin's Ca2+-triggered regulation of striated muscle contraction has advanced greatly, particularly via cryo-electron microscopy data. Compelling atomic models of troponin-tropomyosin-actin were published for both apo- and Ca2+-saturated states of the cardiac thin filament. Subsequent electron microscopy and computational analyses have supported and further elaborated the findings. Per cryo-electron microscopy, each troponin is highly extended and contacts both tropomyosin strands, which lie on opposite sides of the actin filament. In the apo-state characteristic of relaxed muscle, troponin and tropomyosin hinder strong myosin-actin binding in several different ways, apparently barricading the actin more substantially than does tropomyosin alone. The troponin core domain, the C-terminal third of TnI, and tropomyosin under the influence of a 64-residue helix of TnT located at the overlap of adjacent tropomyosins are all in positions that would hinder strong myosin binding to actin. In the Ca2+-saturated state, the TnI C-terminus dissociates from actin and binds in part to TnC; the core domain pivots significantly; the N-lobe of TnC binds specifically to actin and tropomyosin; and tropomyosin rotates partially away from myosin's binding site on actin. At the overlap domain, Ca2+ causes much less tropomyosin movement, so a more inhibitory orientation persists. In the myosin-saturated state of the thin filament, there is a large additional shift in tropomyosin, with molecular interactions now identified between tropomyosin and both actin and myosin. A new era has arrived for investigation of the thin filament and for functional understandings that increasingly accommodate the recent structural results.

The mechanism of thin filament regulation: Models in conflict?

Evidence on two- and three-state models of the calcium regulation models of muscle contractions remain in favor of three-state models.

In a recent JGP article, Heeley et al. (2019. J. Gen. Physiol. https://doi.org/10.1085/jgp.201812198) reopened the debate about two- versus three-state models of thin filament regulation. The authors review their work, which measures the rate constant of P_i release from myosin.ADP.Pi activated by actin or thin filaments under a variety of conditions. They conclude that their data can be described by a two-state model and raise doubts about the generally accepted three-state model as originally formulated by McKillop and Geeves (1993. Biophys. J.https://doi.org/10.1016/S0006-3495(93)81110-X). However, in the following article, we follow Plato’s dictum that “twice and thrice over, as they say, good it is to repeat and review what is good.” We have therefore reviewed the evidence for the three- and two-state models and present our view that the evidence is overwhelmingly in favor of three structural states of the thin filament, which regulate access of myosin to its binding sites on actin and, hence, muscle contractility.

A Stochastic Multiscale Model of Cardiac Thin Filament Activation Using Brownian-Langevin Dynamics

We use Brownian-Langevin dynamics principles to derive a coarse-graining multiscale myofilament model that can describe the thin-filament activation process during contraction. The model links atomistic molecular simulations of protein-protein interactions in the thin-filament regulatory unit to sarcomere-level activation dynamics. We first calculate the molecular interaction energy between tropomyosin and actin surface using Brownian dynamics simulations. This energy profile is then generalized to account for the observed tropomyosin transitions between its regulatory stable states. The generalized energy landscape then served as a basis for developing a filament-scale model using Langevin dynamics. This integrated analysis, spanning molecular to thin-filament scales, is capable of tracking the events of the tropomyosin conformational changes as it moves over the actin surface. The tropomyosin coil with flexible overlap regions between adjacent tropomyosins is represented in the model as a system of coupled stochastic ordinary differential equations. The proposed multiscale approach provides a more detailed molecular connection between tropomyosin dynamics, the trompomyosin-actin interaction-energy landscape, and the generated force by the sarcomere.

Tropomyosin dynamics during cardiac muscle contraction as governed by a multi-well energy landscape

The dynamic oscillations of tropomyosin molecules in the azimuthal direction over the surface of the actin filament during thin filament activation are studied here from an energy landscape perspective. A mathematical model based on principles from nonlinear dynamics and chaos theory is derived to describe these dynamical motions. In particular, an energy potential with three wells is proposed to govern the tropomyosin oscillations between the observed regulatory positions observed during muscle contraction, namely the blocked "B", closed "C" and open "M" states. Based on the variations in both the frequency and amplitude of the environmental (surrounding the thin filament system) driving tractions, such as the electrostatic, hydrophobic, and Ca2+-dependent forces, the tropomyosin movements are shown to be complex; they can change from being simple harmonic oscillations to being fully chaotic. Three cases (periodic, period-2, and chaotic patterns) are presented to showcase the different possible dynamic responses of tropomyosin sliding over the actin filament. A probability density function is used as a statistical measure to calculate the average residence time spanned out by the tropomyosin molecule when visiting each (B, C, M) equilibrium state. The results were found to depend strongly on the energy landscape profile and its featured barriers, which normally govern the transitions between the B-C-M states during striated muscle activation.

Computational Tool to Study Perturbations in Muscle Regulation and Its Application to Heart Disease

Striated muscle contraction occurs when myosin thick filaments bind to thin filaments in the sarcomere and generate pulling forces. This process is regulated by calcium, and it can be perturbed by pathological conditions (e.g., myopathies), physiological adaptations (e.g., β-adrenergic stimulation), and pharmacological interventions. Therefore, it is important to have a methodology to robustly determine the impact of these perturbations and statistically evaluate their effects. Here, we present an approach to measure the equilibrium constants that govern muscle activation, estimate uncertainty in these parameters, and statistically test the effects of perturbations. We provide a MATLAB-based computational tool for these analyses, along with easy-to-follow tutorials that make this approach accessible. The hypothesis testing and error estimation approaches described here are broadly applicable, and the provided tools work with other types of data, including cellular measurements. To demonstrate the utility of the approach, we apply it to elucidate the biophysical mechanism of a mutation that causes familial hypertrophic cardiomyopathy. This approach is generally useful for studying muscle diseases and therapeutic interventions that target muscle contraction.

Microscopic heat pulses activate cardiac thin filaments

During the excitation-contraction coupling of the heart, sarcomeres are activated via thin filament structural changes (i.e., from the "off" state to the "on" state) in response to a release of Ca2+ from the sarcoplasmic reticulum. This process involves chemical reactions that are highly dependent on ambient temperature; for example, catalytic activity of the actomyosin ATPase rises with increasing temperature. Here, we investigate the effects of rapid heating by focused infrared (IR) laser irradiation on the sliding of thin filaments reconstituted with human α-tropomyosin and bovine ventricular troponin in an in vitro motility assay. We perform high-precision analyses measuring temperature by the fluorescence intensity of rhodamine-phalloidin-labeled F-actin coupled with a fluorescent thermosensor sheet containing the temperature-sensitive dye Europium (III) thenoyltrifluoroacetonate trihydrate. This approach enables a shift in temperature from 25°C to ∼46°C within 0.2 s. We find that in the absence of Ca2+ and presence of ATP, IR laser irradiation elicits sliding movements of reconstituted thin filaments with a sliding velocity that increases as a function of temperature. The heating-induced acceleration of thin filament sliding likewise occurs in the presence of Ca2+ and ATP; however, the temperature dependence is more than twofold less pronounced. These findings could indicate that in the mammalian heart, the on-off equilibrium of the cardiac thin filament state is partially shifted toward the on state in diastole at physiological body temperature, enabling rapid and efficient myocardial dynamics in systole.

Nebulin and titin modulate cross-bridge cycling and length-dependent calcium sensitivity

Various mutations in the structural proteins nebulin and titin that are present in human disease are known to affect the contractility of striated muscle. Loss of nebulin is associated with reduced actin filament length and impairment of myosin binding to actin, whereas titin is thought to regulate muscle passive elasticity and is likely involved in length-dependent activation. Here, we sought to assess the modulation of muscle function by these sarcomeric proteins by using the computational platform muscle simulation code (MUSICO) to quantitatively separate the effects of structural changes, kinetics of cross-bridge cycling, and calcium sensitivity of the thin filaments. The simulations show that variation in thin filament length cannot by itself account for experimental observations of the contractility in nebulin-deficient muscle, but instead must be accompanied by a decreased myosin binding rate. Additionally, to match the observed calcium sensitivity, the rate of TnI detachment from actin needed to be increased. Simulations for cardiac muscle provided quantitative estimates of the effects of different titin-based passive elasticities on muscle force and activation in response to changes in sarcomere length and interfilament lattice spacing. Predicted force-pCa relations showed a decrease in both active tension and sensitivity to calcium with a decrease in passive tension and sarcomere length. We conclude that this behavior is caused by partial redistribution of the muscle load between active muscle force and titin-dependent passive force, and also by redistribution of stretch along the thin filament, which together modulate the release of TnI from actin. These data help advance understanding of how nebulin and titin mutations affect muscle function.

A new twist on tropomyosin binding to actin filaments: perspectives on thin filament function, assembly and biomechanics

Tropomyosin, best known for its role in the steric regulation of muscle contraction, polymerizes head-to-tail to form cables localized along the length of both muscle and non-muscle actin-based thin filaments. In skeletal and cardiac muscles, tropomyosin, under the control of troponin and myosin, moves in a cooperative manner between blocked, closed and open positions on filaments, thereby masking and exposing actin-binding sites necessary for myosin crossbridge head interactions. While the coiled-coil signature of tropomyosin appears to be simple, closer inspection reveals surprising structural complexity required to perform its role in steric regulation. For example, component α-helices of coiled coils are typically zippered together along a continuous core hydrophobic stripe. Tropomyosin, however, contains a number of anomalous, functionally controversial, core amino acid residues. We argue that the atypical residues at this interface, including clusters of alanines and a charged aspartate, are required for preshaping tropomyosin to readily fit to the surface of the actin filament, but do so without compromising tropomyosin rigidity once the filament is assembled. Indeed, persistence length measurements of tropomyosin are characteristic of a semi-rigid cable, in this case conducive to cooperative movement on thin filaments. In addition, we also maintain that tropomyosin displays largely unrecognized and residue-specific torsional variance, which is involved in optimizing contacts between actin and tropomyosin on the assembled thin filament. Corresponding twist-induced stiffness may also enhance cooperative translocation of tropomyosin across actin filaments. We conclude that anomalous core residues of tropomyosin facilitate thin filament regulatory behavior in a multifaceted way.

Modeling the Actin.myosin ATPase Cross-Bridge Cycle for Skeletal and Cardiac Muscle Myosin Isoforms

Modeling the complete actin.myosin ATPase cycle has always been limited by the lack of experimental data concerning key steps of the cycle, because these steps can only be defined at very low ionic strength. Here, using human β-cardiac myosin-S1, we combine published data from transient and steady-state kinetics to model a minimal eight-state ATPase cycle. The model illustrates the occupancy of each intermediate around the cycle and how the occupancy is altered by changes in actin concentration for [actin] = 1-20K_m. The cycle can be used to predict the maximal velocity of contraction (by motility assay or sarcomeric shortening) at different actin concentrations (which is consistent with experimental velocity data) and predict the effect of a 5 pN load on a single motor. The same exercise was repeated for human α-cardiac myosin S1 and rabbit fast skeletal muscle S1. The data illustrates how the motor domain properties can alter the ATPase cycle and hence the occupancy of the key states in the cycle. These in turn alter the predicted mechanical response of the myosin independent of other factors present in a sarcomere, such as filament stiffness and regulatory proteins. We also explore the potential of this modeling approach for the study of mutations in human β-cardiac myosin using the hypertrophic myopathy mutation R453C. Our modeling, using the transient kinetic data, predicts mechanical properties of the motor that are compatible with the single-molecule study. The modeling approach may therefore be of wide use for predicting the properties of myosin mutations.

Modulation of Skeletal Muscle Contraction by Myosin Phosphorylation

The striated muscle sarcomere is a highly organized and complex enzymatic and structural organelle. Evolutionary pressures have played a vital role in determining the structure-function relationship of each protein within the sarcomere. A key part of this multimeric assembly is the light chain-binding domain (LCBD) of the myosin II motor molecule. This elongated "beam" functions as a biological lever, amplifying small interdomain movements within the myosin head into piconewton forces and nanometer displacements against the thin filament during the cross-bridge cycle. The LCBD contains two subunits known as the essential and regulatory myosin light chains (ELC and RLC, respectively). Isoformic differences in these respective species provide molecular diversity and, in addition, sites for phosphorylation of serine residues, a highly conserved feature of striated muscle systems. Work on permeabilized skeletal fibers and thick filament systems shows that the skeletal myosin light chain kinase catalyzed phosphorylation of the RLC alters the "interacting head motif" of myosin motor heads on the thick filament surface, with myriad consequences for muscle biology. At rest, structure-function changes may upregulate actomyosin ATPase activity of phosphorylated cross-bridges. During activation, these same changes may increase the Ca2+ sensitivity of force development to enhance force, work, and power output, outcomes known as "potentiation." Thus, although other mechanisms may contribute, RLC phosphorylation may represent a form of thick filament activation that provides a "molecular memory" of contraction. The clinical significance of these RLC phosphorylation mediated alterations to contractile performance of various striated muscle systems are just beginning to be understood. © 2017 American Physiological Society. Compr Physiol 7:171-212, 2017.

Actomyosin based contraction: one mechanokinetic model from single molecules to muscle?

Bridging the gaps between experimental systems on different hierarchical scales is needed to overcome remaining challenges in the understanding of muscle contraction. Here, a mathematical model with well-characterized structural and biochemical actomyosin states is developed to that end. We hypothesize that this model accounts for generation of force and motion from single motor molecules to the large ensembles of muscle. In partial support of this idea, a wide range of contractile phenomena are reproduced without the need to invoke cooperative interactions or ad hoc states/transitions. However, remaining limitations exist, associated with ambiguities in available data for model definition e.g.: (1) the affinity of weakly bound cross-bridges, (2) the characteristics of the cross-bridge elasticity and (3) the exact mechanistic relationship between the force-generating transition and phosphate release in the actomyosin ATPase. Further, the simulated number of attached myosin heads in the in vitro motility assay differs several-fold from duty ratios, (fraction of strongly attached ATPase cycle times) derived in standard analysis. After addressing the mentioned issues the model should be useful in fundamental studies, for engineering of myosin motors as well as for studies of muscle disease and drug development.

Predicting Effects of Tropomyosin Mutations on Cardiac Muscle Contraction through Myofilament Modeling

Point mutations to the human gene TPM1 have been implicated in the development of both hypertrophic and dilated cardiomyopathies. Such observations have led to studies investigating the link between single residue changes and the biophysical behavior of the tropomyosin molecule. However, the degree to which these molecular perturbations explain the performance of intact sarcomeres containing mutant tropomyosin remains uncertain. Here, we present a modeling approach that integrates various aspects of tropomyosin's molecular properties into a cohesive paradigm representing their impact on muscle function. In particular, we considered the effects of tropomyosin mutations on (1) persistence length, (2) equilibrium between thin filament blocked and closed regulatory states, and (3) the crossbridge duty cycle. After demonstrating the ability of the new model to capture Ca-dependent myofilament responses during both dynamic and steady-state activation, we used it to capture the effects of hypertrophic cardiomyopathy (HCM) related E180G and D175N mutations on skinned myofiber mechanics. Our analysis indicates that the fiber-level effects of the two mutations can be accurately described by a combination of changes to the three tropomyosin properties represented in the model. Subsequently, we used the model to predict mutation effects on muscle twitch. Both mutations led to increased twitch contractility as a consequence of diminished cooperative inhibition between thin filament regulatory units. Overall, simulations suggest that a common twitch phenotype for HCM-linked tropomyosin mutations includes both increased contractility and elevated diastolic tension.

Thin Filament Structure and the Steric Blocking Model

By interacting with the troponin-tropomyosin complex on myofibrillar thin filaments, Ca2+ and myosin govern the regulatory switching processes influencing contractile activity of mammalian cardiac and skeletal muscles. A possible explanation of the roles played by Ca2+ and myosin emerged in the early 1970s when a compelling "steric model" began to gain traction as a likely mechanism accounting for muscle regulation. In its most simple form, the model holds that, under the control of Ca2+ binding to troponin and myosin binding to actin, tropomyosin strands running along thin filaments either block myosin-binding sites on actin when muscles are relaxed or move away from them when muscles are activated. Evidence for the steric model was initially based on interpretation of subtle changes observed in X-ray fiber diffraction patterns of intact skeletal muscle preparations. Over the past 25 years, electron microscopy coupled with three-dimensional reconstruction directly resolved thin filament organization under many experimental conditions and at increasingly higher resolution. At low-Ca2+, tropomyosin was shown to occupy a "blocked-state" position on the filament, and switched-on in a two-step process, involving first a movement of tropomyosin away from the majority of the myosin-binding site as Ca2+ binds to troponin and then a further movement to fully expose the site when small numbers of myosin heads bind to actin. In this contribution, basic information on Ca2+-regulation of muscle contraction is provided. A description is then given relating the voyage of discovery taken to arrive at the present understanding of the steric regulatory model.

Structural determinants of muscle thin filament cooperativity

End-to-end connections between adjacent tropomyosin molecules along the muscle thin filament allow long-range conformational rearrangement of the multicomponent filament structure. This process is influenced by Ca(2+) and the troponin regulatory complexes, as well as by myosin crossbridge heads that bind to and activate the filament. Access of myosin crossbridges onto actin is gated by tropomyosin, and in the case of striated muscle filaments, troponin acts as a gatekeeper. The resulting tropomyosin-troponin-myosin on-off switching mechanism that controls muscle contractility is a complex cooperative and dynamic system with highly nonlinear behavior. Here, we review key information that leads us to view tropomyosin as central to the communication pathway that coordinates the multifaceted effectors that modulate and tune striated muscle contraction. We posit that an understanding of this communication pathway provides a framework for more in-depth mechanistic characterization of myopathy-associated mutational perturbations currently under investigation by many research groups.

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.

Despite decades of study, there is no clear connection between muscle contraction at the molecular and the macroscopic scale. For example, we cannot yet predict how a genetic defect in a muscle protein will result in a physiological change in the heart. This multi-scale understanding is difficult, in part, because molecules cooperate during muscle contraction; that is, one molecule’s behavior is influenced by the behavior of its neighbors. It is difficult to make direct measurements from such coupled molecular systems and also difficult to describe them quantitatively. Despite these obstacles, we recently published experimental measurements and theoretical models of this coupling, but there were apparent discrepancies between the two. Here, we use detailed computer simulations of these experiments to show that, in fact, the measurements agree with the model to a remarkable extent. This agreement suggests that the model captures the essential molecular events that underlie the coupling between muscle molecules. This removes a major obstacle to a multi-scale understanding of muscle contraction and, while more work is necessary, suggests that a connection between the molecular and macroscopic scale is within reach.

Citrullination of myofilament proteins in heart failure

AIMS

Citrullination, the post-translational conversion of arginine to citrulline by the enzyme family of peptidylarginine deiminases (PADs), is associated with several diseases, and specific citrullinated proteins have been shown to alter function while others act as auto-antigens. In this study, we identified citrullinated proteins in human myocardial samples, from healthy and heart failure patients, and determined several potential functional consequences. Further we investigated PAD isoform cell-specific expression in the heart.

METHODS AND RESULTS

A citrullination-targeted proteomic strategy using data-independent (SWATH) acquisition method was used to identify the modified cardiac proteins. Citrullinated-induced sarcomeric proteins were validated using two-dimensional gel electrophoresis and investigated using biochemical and functional assays. Myocardial PAD isoforms were confirmed by RT-PCR with PAD2 being the major isoform in myocytes. In total, 304 citrullinated sites were identified that map to 145 proteins among the three study groups: normal, ischaemia, and dilated cardiomyopathy. Citrullination of myosin (using HMM fragment) decreased its intrinsic ATPase activity and inhibited the acto-HMM-ATPase activity. Citrullinated TM resulted in stronger F-actin binding and inhibited the acto-HMM-ATPase activity. Citrullinated TnI did not alter the binding to F-actin or acto-HMM-ATPase activity. Overall, citrullination of sarcomeric proteins caused a decrease in Ca(2+) sensitivity in skinned cardiomyocytes, with no change in maximal calcium-activated force or hill coefficient.

CONCLUSION

Citrullination unique to the cardiac proteome was identified. Our data indicate important structural and functional alterations to the cardiac sarcomere and the contribution of protein citrullination to this process.

A Spatially Detailed Model of Isometric Contraction Based on Competitive Binding of Troponin I Explains Cooperative Interactions between Tropomyosin and Crossbridges

Biophysical models of cardiac tension development provide a succinct representation of our understanding of force generation in the heart. The link between protein kinetics and interactions that gives rise to high cooperativity is not yet fully explained from experiments or previous biophysical models. We propose a biophysical ODE-based representation of cross-bridge (XB), tropomyosin and troponin within a contractile regulatory unit (RU) to investigate the mechanisms behind cooperative activation, as well as the role of cooperativity in dynamic tension generation across different species. The model includes cooperative interactions between regulatory units (RU-RU), between crossbridges (XB-XB), as well more complex interactions between crossbridges and regulatory units (XB-RU interactions). For the steady-state force-calcium relationship, our framework predicts that: (1) XB-RU effects are key in shifting the half-activation value of the force-calcium relationship towards lower [Ca²⁺], but have only small effects on cooperativity. (2) XB-XB effects approximately double the duty ratio of myosin, but do not significantly affect cooperativity. (3) RU-RU effects derived from the long-range action of tropomyosin are a major factor in cooperative activation, with each additional unblocked RU increasing the rate of additional RU’s unblocking. (4) Myosin affinity for short (1–4 RU) unblocked stretches of actin of is very low, and the resulting suppression of force at low [Ca²⁺] is a major contributor in the biphasic force-calcium relationship. We also reproduce isometric tension development across mouse, rat and human at physiological temperature and pacing rate, and conclude that species differences require only changes in myosin affinity and troponin I/troponin C affinity. Furthermore, we show that the calcium dependence of the rate of tension redevelopment k_tr is explained by transient blocking of RU’s by a temporary decrease in XB-RU effects.

Force generation in cardiac muscle cells is driven by changes in calcium concentration. Relatively small changes in the calcium concentration over the course of a heart beat lead to the large changes in force required to fully contract and relax the heart. This is known as ‘cooperative activation’, and involves a complex interaction of several proteins involved in contraction. Current computer models which reproduce force generation often do not represent these processes explicitly, and stochastic approaches that do tend to require large amounts of computational power to solve, which limit the range of investigations in which they can be used. We have created an new computational model that captures the underlying physiological processes in more detail, and is more efficient than stochastic approaches, while still being able to run a large range of simulations. The model is able to explain the biological processes leading to the cooperative activation of muscle. In addition, the model reproduces how this cooperative activation translates to normal muscle function to generate force from changes in calcium across three different species.

The force dependence of isometric and concentric potentiation in mouse muscle with and without skeletal myosin light chain kinase

The isometric potentiation associated with myosin phosphorylation is force dependent. The purpose of this study was to assess the influence of a pre-existing period of isometric force on the concentric force potentiation displayed by mouse muscles with and without the ability to phosphorylate myosin. We tested isometric (ISO) and concentric (CON) potentiation, as well as concentric potentiation after isometric force (ISO-CON), in muscles from wild-type (WT) and skeletal myosin light chain kinase-deficient (skMLCK−/−) mice. A conditioning stimulus increased (i.e., potentiated) mean concentric force in the ISO-CON and CON conditions to 1.31 ± 0.02 and 1.35 ± 0.02 (WT) and to 1.19 ± 0.02 and 1.21 ± 0.01 (skMLCK−/−) of prestimulus levels, respectively (data n = 6–8, p < 0.05). No potentiation of mean isometric force was observed in either genotype. The potentiation of mean concentric force was inversely related to relative tetanic force level (P/Po) in both genotypes. Moreover, concentric potentiation varied greatly within each contraction type and was negatively correlated with unpotentiated force in both genotypes. Thus, although no effect of pre-existing force was observed, strong and inverse relationships between concentric force potentiation and unpotentiated concentric force may suggest an influence of attached and force-generating crossbridges on potentiation magnitude in both WT and skMLCK−/− muscles.

Using fluorescent myosin to directly visualize cooperative activation of thin filaments

Contraction of striated muscle is tightly regulated by the release and sequestration of calcium within myocytes. At the molecular level, calcium modulates myosin's access to the thin filament. Once bound, myosin is hypothesized to potentiate the binding of further myosins. Here, we directly image single molecules of myosin binding to and activating thin filaments. Using this approach, the cooperative binding of myosin along thin filaments has been quantified. We have found that two myosin heads are required to laterally activate a regulatory unit of thin filament. The regulatory unit is found to be capable of accommodating 11 additional myosins. Three thin filament activation states possessing differential myosin binding capacities are also visible. To describe this system, we have formulated a simple chemical kinetic model of cooperative activation that holds across a wide range of solution conditions. The stochastic nature of activation is strongly highlighted by data obtained in sub-optimal activation conditions where the generation of activation waves and their catastrophic collapse can be observed. This suggests that the thin filament has the potential to be turned fully on or off in a binary fashion.

Use of pyrene-labelled actin to probe actin-myosin interactions: kinetic and equilibrium studies

Studying the dynamics of the interaction between actin and myosin and how this is modulated by ATP and other nucleotides is fundamental to any understanding of myosin motor protein activity. The fluorescent label pyrene, covalently attached to actin (at Cys 374), has been one of the most useful optical probes to report myosin binding to actin. The unique spectral features of pyrene make it sensitive to changes in the microenvironment of the probe and allow to monitor processes such as conformational changes and protein-protein interactions. Here we describe how to make and use pyrene-labelled actin and describe a set of fluorescence stopped-flow measurements that allow the actin-myosin interaction to be explored at protein concentrations from μM to nM for many of the known myosin motors.

Muscle activation described with a differential equation model for large ensembles of locally coupled molecular motors

Molecular motors, by turning chemical energy into mechanical work, are responsible for active cellular processes. Often groups of these motors work together to perform their biological role. Motors in an ensemble are coupled and exhibit complex emergent behavior. Although large motor ensembles can be modeled with partial differential equations (PDEs) by assuming that molecules function independently of their neighbors, this assumption is violated when motors are coupled locally. It is therefore unclear how to describe the ensemble behavior of the locally coupled motors responsible for biological processes such as calcium-dependent skeletal muscle activation. Here we develop a theory to describe locally coupled motor ensembles and apply the theory to skeletal muscle activation. The central idea is that a muscle filament can be divided into two phases: an active and an inactive phase. Dynamic changes in the relative size of these phases are described by a set of linear ordinary differential equations (ODEs). As the dynamics of the active phase are described by PDEs, muscle activation is governed by a set of coupled ODEs and PDEs, building on previous PDE models. With comparison to Monte Carlo simulations, we demonstrate that the theory captures the behavior of locally coupled ensembles. The theory also plausibly describes and predicts muscle experiments from molecular to whole muscle scales, suggesting that a micro- to macroscale muscle model is within reach.

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.

Dynamic coupling of regulated binding sites and cycling myosin heads in striated muscle

Myosim, a computer model of muscle contraction, includes molecular-level effects and incorporates dynamic coupling of myosin heads and binding sites.

In an activated muscle, binding sites on the thin filament and myosin heads switch frequently between different states. Because the status of the binding sites influences the status of the heads, and vice versa, the binding sites and myosin heads are dynamically coupled. The functional consequences of this coupling were investigated using MyoSim, a new computer model of muscle. MyoSim extends existing models based on Huxley-type distribution techniques by incorporating Ca²⁺ activation and cooperative effects. It can also simulate arbitrary cross-bridge schemes set by the researcher. Initial calculations investigated the effects of altering the relative speeds of binding-site and cross-bridge kinetics, and of manipulating cooperative processes. Subsequent tests fitted simulated force records to experimental data recorded using permeabilized myocardial preparations. These calculations suggest that the rate of force development at maximum activation is limited by myosin cycling kinetics, whereas the rate at lower levels of activation is limited by how quickly binding sites become available. Additional tests investigated the behavior of transiently activated cells by driving simulations with experimentally recorded Ca²⁺ signals. The unloaded shortening profile of a twitching myocyte could be reproduced using a model with two myosin states, cooperative activation, and strain-dependent kinetics. Collectively, these results demonstrate that dynamic coupling of binding sites and myosin heads is important for contractile function.

Tropomyosin dynamics

Tropomyosin is a two chained α-helical coiled coil protein that binds actin filaments and interacts with various actin binding proteins. Tropomyosin function depends on its ability to move to distinct locations on the surface of actin in response to the binding of different thin filament effectors. Tropomyosin dynamics plays an important role in these fluctuating interactions with actin and is thought to be fundamental to many of its biological activities. For example tropomyosin concerted movement on the surface of actin triggered by Ca(2+) binding to troponin or myosin head binding to actin has been argued to be key to the cooperative allosteric regulation of muscle contraction. These large-scale motions are affected by tropomyosin internal dynamics and mechanical properties. Tropomyosin internal dynamics corresponding to smaller and more localised structural fluctuations are increasingly recognised to play an important role in its function. A thorough understanding of the coupling between local and global structural fluctuations in tropomyosin is required to understand how time dependent structural fluctuations in tropomyosin contribute to the overall thin filament dynamics and dictate their various biological activities.

Cardiac muscle activation blunted by a mutation to the regulatory component, troponin T

The striated muscle thin filament comprises actin, tropomyosin, and troponin. The Tn complex consists of three subunits, troponin C (TnC), troponin I (TnI), and troponin T (TnT). TnT may serve as a bridge between the Ca(2+) sensor (TnC) and the actin filament. In the short helix preceding the IT-arm region, H1(T2), there are known dilated cardiomyopathy-linked mutations (among them R205L). Thus we hypothesized that there is an element in this short helix that plays an important role in regulating the muscle contraction, especially in Ca(2+) activation. We mutated Arg-205 and several other amino acid residues within and near the H1(T2) helix. Utilizing an alanine replacement method to compare the effects of the mutations, the biochemical and mechanical impact on the actomyosin interaction was assessed by solution ATPase activity assay, an in vitro motility assay, and Ca(2+) binding measurements. Ca(2+) activation was markedly impaired by a point mutation of the highly conserved basic residue R205A, residing in the short helix H1(T2) of cTnT, whereas the mutations to nearby residues exhibited little effect on function. Interestingly, rigor activation was unchanged between the wild type and R205A TnT. In addition to the reduction in Ca(2+) sensitivity observed in Ca(2+) binding to the thin filament, myosin S1-ADP binding to the thin filament was significantly affected by the same mutation, which was also supported by a series of S1 concentration-dependent ATPase assays. These suggest that the R205A mutation alters function through reduction in the nature of cooperative binding of S1.

Gestalt-binding of tropomyosin on actin during thin filament activation

Our thesis is that thin filament function can only be fully understood and muscle regulation then elucidated if atomic structures of the thin filament are available to reveal the positions of tropomyosin on actin in all physiological states. After all, it is tropomyosin influenced by troponin that regulates myosin-crossbridge cycling on actin and therefore controls contraction in all muscles. In addition, we maintain that a complete appreciation of thin filament activation also requires that the mechanical properties of tropomyosin itself are recognized and then related to the effect of myosin-association on actin. Taking the Gestalt-binding of tropomyosin into account, coupled with our electron microscopy structures and computational chemistry, we propose a comprehensive mechanism for tropomyosin regulatory movement over the actin filament surface that explains the cooperative muscle activation process. In fact, well-known point mutations of critical amino acids on the actin-tropomyosin binding interface disrupt Gestalt-binding and are associated with a number of inherited myopathies. Moreover, dysregulation of tropomyosin may also be a factor that interferes with the gatekeeping operation of non-muscle tropomyosin in the controlling interactions of a wide variety of cellular actin-binding proteins. The clinical relevance of Gestalt-binding is discussed in articles by the Marston and the Gunning groups in this special journal issue devoted to the impact of tropomyosin on biological systems.