Cooperative regulation of myosin-actin interactions by a continuous flexible chain II: actin-tropomyosin-troponin and regulation by calcium

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.

Cooperativity of myosin II motors in the non-regulated and regulated thin filaments investigated with high-speed AFM

Skeletal myosins II are non-processive molecular motors that work in ensembles to produce muscle contraction while binding to the actin filament. Although the molecular properties of myosin II are well known, there is still debate about the collective work of the motors: is there cooperativity between myosin motors while binding to the actin filaments? In this study, we use high-speed AFM to evaluate this issue. We observed that the initial binding of small arrays of myosin heads to the non-regulated actin filaments did not affect the cooperative probability of subsequent bindings and did not lead to an increase in the fractional occupancy of the actin binding sites. These results suggest that myosin motors are independent force generators when connected in small arrays, and that the binding of one myosin does not alter the kinetics of other myosins. In contrast, the probability of binding of myosin heads to regulated thin filaments under activating conditions (at high Ca2+ concentration in the presence of 2 μM ATP) was increased with the initial binding of one myosin, leading to a larger occupancy of available binding sites at the next half-helical pitch of the filament. The result suggests that myosin cooperativity is observed over five pseudo-repeats and defined by the activation status of the thin filaments.

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.

Potential impacts of the cardiac troponin I mobile domain on myofilament activation and relaxation

The cardiac thin filament is regulated in a Ca²⁺-dependent manner through conformational changes of troponin and tropomyosin (Tm). It has been generally understood that under conditions of low Ca²⁺ the inhibitory peptide domain (IP) of troponin I (TnI) binds to actin and holds Tm over the myosin binding sites on actin to prevent crossbridge formation. More recently, evidence that the C-terminal mobile domain (MD) of TnI also binds actin has made for a more complex scenario. This study uses a computational model to investigate the consequences of assuming that TnI regulates Tm movement via two actin-binding domains rather than one. First, a 16-state model of the cardiac thin filament regulatory unit was created with TnI-IP as the sole regulatory domain. Expansion of this to include TnI-MD formed a 24-state model. Comparison of these models showed that assumption of a second actin-binding site allows the individual domains to have a lower affinity for actin than would be required for IP acting alone. Indeed, setting actin affinities of the IP and MD to 25% of that assumed for the IP in the single-site model was sufficient to achieve precisely the same degree of Ca²⁺ regulation. We also tested the 24-state model's ability to represent steady-state experimental data in the case of disruption of either the IP or MD. We were able to capture qualitative changes in several properties that matched what was seen in the experimental data. Lastly, simulations were run to examine the effect of disruption of the IP or MD on twitch dynamics. Our results suggest that both domains are required to keep diastolic cross-bridge activity to a minimum and accelerate myofilament relaxation. Overall, our analyses support a paradigm in which two domains of TnI bind with moderate affinity to actin, working in tandem to complete Ca²⁺-dependent regulation of the thin filament.

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.

Spectrum of MYO7A Mutations in an Indigenous South African Population Further Elucidates the Nonsyndromic Autosomal Recessive Phenotype of DFNB2 to Include Both Homozygous and Compound Heterozygous Mutations

MYO7A gene encodes unconventional myosin VIIA, which, when mutated, causes a phenotypic spectrum ranging from recessive hearing loss DFNB2 to deaf-blindness, Usher Type 1B (USH1B). MYO7A mutations are reported in nine DFNB2 families to date, none from sub-Saharan Africa.In DNA, from a cohort of 94 individuals representing 92 families from the Limpopo province of South Africa, eight MYO7A variations were detected among 10 individuals. Family studies identified homozygous and compound heterozygous mutations in 17 individuals out of 32 available family members. Four mutations were novel, p.Gly329Asp, p.Arg373His, p.Tyr1780Ser, and p.Pro2126Leufs*5. Two variations, p.Ser617Pro and p.Thr381Met, previously listed as of uncertain significance (ClinVar), were confirmed to be pathogenic. The identified mutations are predicted to interfere with the conformational properties of myosin VIIA through interruption or abrogation of multiple interactions between the mutant and neighbouring residues. Specifically, p.Pro2126Leufs*5, is predicted to abolish the critical site for the interactions between the tail and the motor domain essential for the autoregulation, leaving a non-functional, unregulated protein that causes hearing loss. We have identified MYO7A as a possible key deafness gene among indigenous sub-Saharan Africans. The spectrum of MYO7A mutations in this South African population points to DFNB2 as a specific entity that may occur in a homozygous or in a compound heterozygous state.

Mechanical contribution to muscle thin filament activation

Vertebrate striated muscle thin filaments are thought to be thermodynamically activated in response to an increase in Ca²⁺ concentration. We tested this hypothesis by measuring time intervals for gliding runs and pauses of individual skeletal muscle thin filaments in cycling myosin motility assays. A classic thermodynamic mechanism predicts that if chemical potential is constant, transitions between runs and pauses of gliding thin filaments will occur at constant rate as given by a Poisson distribution. In this scenario, rate is given by the odds of a pause, and hence, run times between pauses fit an exponential distribution that slopes negatively for all observable run times. However, we determined that relative density of observed run times fits an exponential only at low Ca²⁺ levels that activate filament gliding. Further titration with Ca²⁺, or adding excess regulatory proteins tropomyosin and troponin, shifted the relative density of short run times to fit the positive slope of a gamma distribution, which derives from waiting times between Poisson events. Events that arise during a run and prevent the chance of ending a run for a random interval of time account for the observed run time distributions, suggesting that the events originate with cycling myosin. We propose that regulatory proteins of the thin filament require the mechanical force of cycling myosin to achieve the transition state for activation. During activation, combinations of cycling myosin that contribute insufficient activation energy delay deactivation.

Age-Onset Phosphorylation of a Minor Actin Variant Promotes Intestinal Barrier Dysfunction

Age-associated decay of intercellular interactions impairs the cells' capacity to tightly associate within tissues and form a functional barrier. This barrier dysfunction compromises organ physiology and contributes to systemic failure. The actin cytoskeleton represents a key determinant in maintaining tissue architecture. Yet, it is unclear how age disrupts the actin cytoskeleton and how this, in turn, promotes mortality. Here, we show that an uncharacterized phosphorylation of a low-abundant actin variant, ACT-5, compromises integrity of the C. elegans intestinal barrier and accelerates pathogenesis. Age-related loss of the heat-shock transcription factor, HSF-1, disrupts the JUN kinase and protein phosphatase I equilibrium which increases ACT-5 phosphorylation within its troponin binding site. Phosphorylated ACT-5 accelerates decay of the intestinal subapical terminal web and impairs its interactions with cell junctions. This compromises barrier integrity, promotes pathogenesis, and drives mortality. Thus, we provide the molecular mechanism by which age-associated loss of specialized actin networks impacts tissue integrity.

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.

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.

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.

High-speed AFM reveals subsecond dynamics of cardiac thin filaments upon Ca2+ activation and heavy meromyosin binding

High-speed atomic force microscopy (HS-AFM) can be used to study dynamic processes with real-time imaging of molecules within 1- to 5-nm spatial resolution. In the current study, we evaluated the 3-state model of activation of cardiac thin filaments (cTFs) isolated as a complex and deposited on a mica-supported lipid bilayer. We studied this complex for dynamic conformational changes 1) at low and high [Ca2+] (pCa 9.0 and 4.5), and 2) upon myosin binding to the cTF in the nucleotide-free state or in the presence of ATP. HS-AFM was used to directly visualize the tropomyosin-troponin complex and Ca2+-induced tropomyosin movements accompanied by structural transitions of actin monomers within cTFs. Our data show that cTFs at relaxing or activating conditions are not ultimately in a blocked or activated state, respectively, but rather the combination of states with a prevalence that is dependent on the [Ca2+] and the presence of weakly or strongly bound myosin. The weakly and strongly bound myosin induce similar changes in the structure of cTFs as confirmed by the local dynamical displacement of individual tropomyosin strands in the center of a regulatory unit of cTF at the relaxed and activation conditions. The displacement of tropomyosin at the relaxed conditions had never been visualized directly and explains the ability of myosin binding to TF at the relaxed conditions. Based on the ratios of nonactivated and activated segments within cTFs, we proposed a mechanism of tropomyosin switching from different states that includes both weakly and strongly bound myosin.

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.

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 short history of the development of mathematical models of cardiac mechanics

Cardiac mechanics plays a crucial role in atrial and ventricular function, in the regulation of growth and remodelling, in the progression of disease, and the response to treatment. The spatial scale of the critical mechanisms ranges from nm (molecules) to cm (hearts) with the fastest events occurring in milliseconds (molecular events) and the slowest requiring months (growth and remodelling). Due to its complexity and importance, cardiac mechanics has been studied extensively both experimentally and through mathematical models and simulation. Models of cardiac mechanics evolved from seminal studies in skeletal muscle, and developed into cardiac specific, species specific, human specific and finally patient specific calculations. These models provide a formal framework to link multiple experimental assays recorded over nearly 100 years into a single unified representation of cardiac function. This review first provides a summary of the proteins, physiology and anatomy involved in the generation of cardiac pump function. We then describe the evolution of models of cardiac mechanics starting with the early theoretical frameworks describing the link between sarcomeres and muscle contraction, transitioning through myosin-level models to calcium-driven systems, and ending with whole heart patient-specific models.

Effects of an Interchain Disulfide Bond on Tropomyosin Structure: A Molecular Dynamics Study

Tropomyosin (Tpm) is a coiled-coil actin-binding dimer protein that participates in the regulation of muscle contraction. Both Tpm chains contain Cys190 residues which are normally in the reduced state, but form an interchain disulfide bond in failing heart. Changes in structural and functional properties of Tpm and its complexes with actin upon disulfide cross-linking were studied using various experimental methods. To understand the molecular mechanism underlying these changes and to reveal the possible mechanism of the involvement of the cross-linking in heart failure, molecular dynamics (MD) simulations of the middle part of Tpm were performed in cross-linked and reduced states. The cross-linking increased bending stiffness of Tpm assessed from MD trajectories at 27 °C in agreement with previous experimental observations. However, at 40 °C, the cross-linking caused a decrease in Tpm stiffness and a significant reduction in the number of main chain hydrogen bonds in the vicinity of residues 133 and 134. These data are in line with observations showing enhanced thermal unfolding of the least stable part of Tpm at 30–40 °C and accelerated trypsin cleavage at residue 133 at 40 °C (but not at 27 °C) upon cross-linking. These results allow us to speculate about the possible mechanism of involvement of Tpm cross-linking to heart failure pathogenesis.

Stepwise C-Terminal Truncation of Cardiac Troponin T Alters Function at Low and Saturating Ca2

Activation of striated muscle contraction occurs in response to Ca²⁺ binding to troponin C. The resulting reorganization of troponin repositions tropomyosin on actin and permits activation of myosin-catalyzed ATP hydrolysis. It now appears that the C-terminal 14 amino acids of cardiac troponin T (TnT) control the level of activity at both low and high Ca²⁺. We made a series of C-terminal truncation mutants of human cardiac troponin T, isoform 2, to determine if the same residues of TnT are involved in the low and high Ca²⁺ effects. We measured the effect of these mutations on the normalized ATPase activity at saturating Ca²⁺. Changes in acrylodan tropomyosin fluorescence and the degree of Ca²⁺ stimulation of the rate of binding of rigor myosin subfragment 1 to pyrene-labeled actin-tropomyosin-troponin were measured at low Ca²⁺. These measurements define the distribution of actin-tropomyosin-troponin among the three regulatory states. Residues SKTR and GRWK of TnT were required for the functioning of TnT at both low and high Ca²⁺. Thus, the effects on forming the inactive B-state and in retarding formation of the active M-state require the same regions of TnT. We also observed that the rate of binding of rigor subfragment 1 to pyrene-labeled regulated actin at saturating Ca²⁺ was higher for the truncation mutants than for wild-type TnT. This violated an assumption necessary for determining the B-state population by this kinetic method.

Myosin MgADP Release Rate Decreases as Sarcomere Length Increases in Skinned Rat Soleus Muscle Fibers

Actin-myosin cross-bridges use chemical energy from MgATP hydrolysis to generate force and shortening in striated muscle. Previous studies show that increases in sarcomere length can reduce thick-to-thin filament spacing in skinned muscle fibers, thereby increasing force production at longer sarcomere lengths. However, it is unclear how changes in sarcomere length and lattice spacing affect cross-bridge kinetics at fundamental steps of the cross-bridge cycle, such as the MgADP release rate. We hypothesize that decreased lattice spacing, achieved through increased sarcomere length or osmotic compression of the fiber via dextran T-500, could slow MgADP release rate and increase cross-bridge attachment duration. To test this, we measured cross-bridge cycling and MgADP release rates in skinned soleus fibers using stochastic length-perturbation analysis at 2.5 and 2.0 μm sarcomere lengths as pCa and [MgATP] varied. In the absence of dextran, the force-pCa relationship showed greater Ca²⁺ sensitivity for 2.5 vs. 2.0 μm sarcomere length fibers (pCa₅₀ = 5.68 ± 0.01 vs. 5.60 ± 0.01). When fibers were compressed with 4% dextran, the length-dependent increase in Ca²⁺ sensitivity of force was attenuated, though the Ca²⁺ sensitivity of the force-pCa relationship at both sarcomere lengths was greater with osmotic compression via 4% dextran compared to no osmotic compression. Without dextran, the cross-bridge detachment rate slowed by ∼15% as sarcomere length increased, due to a slower MgADP release rate (11.2 ± 0.5 vs. 13.5 ± 0.7 s^-1). In the presence of dextran, cross-bridge detachment was ∼20% slower at 2.5 vs. 2.0 μm sarcomere length due to a slower MgADP release rate (10.1 ± 0.6 vs. 12.9 ± 0.5 s^-1). However, osmotic compression of fibers at either 2.5 or 2.0 μm sarcomere length produced only slight (and statistically insignificant) slowing in the rate of MgADP release. These data suggest that skeletal muscle exhibits sarcomere-length-dependent changes in cross-bridge kinetics and MgADP release that are separate from, or complementary to, changes in lattice spacing.

Switching Muscles On and Off in Steps: The McKillop-Geeves Three-State Model of Muscle Regulation

BJ Classic highlighting the article "Regulation of the interaction between actin and myosin subfragment 1: evidence for three states of the thin filament."

Cooperativity of myosin interaction with thin filaments is enhanced by stabilizing substitutions in tropomyosin

Muscle contraction is powered by myosin interaction with actin-based thin filaments containing Ca²⁺-regulatory proteins, tropomyosin and troponin. Coiled-coil tropomyosin molecules form a long helical strand that winds around actin filament and either shields actin from myosin binding or opens it. Non-canonical residues G126 and D137 in the central part of tropomyosin destabilize its coiled-coil structure. Their substitutions for canonical ones, G126R and D137L, increase structural stability and the velocity of sliding of reconstructed thin filaments along myosin coated surface. The effect of these stabilizing mutations on force of the actin-myosin interaction is unknown. It also remains unclear whether the stabilization affects single actin-myosin interactions or it modifies the cooperativity of the binding of myosin molecules to actin. We used an optical trap to measure the effects of the stabilization on step size, unitary force and duration of the interactions at low and high load and compared the results with those obtained in an in vitro motility assay. We found that significant prolongation of lifetime of the actin-myosin complex under high load observed at high extent of tropomyosin stabilization, i.e. with double mutant, G126R/D137L, correlates with higher force in the motility assay. Also, the higher the extent of stabilization of tropomyosin, the fewer myosin molecules are needed to propel the thin filaments. The data suggest that the effects of the stabilizing mutations in tropomyosin on the myosin interaction with regulated thin filaments are mainly realized via cooperative mechanisms by increasing the size of cooperative unit.

The molecular basis of thin filament activation: from single molecule to muscle

For muscles to effectively power locomotion, trillions of myosin molecules must rapidly attach and detach from the actin thin filament. This is accomplished by precise regulation of the availability of the myosin binding sites on actin (i.e. activation). Both calcium (Ca⁺⁺) and myosin binding contribute to activation, but both mechanisms are simultaneously active during contraction, making their relative contributions difficult to determine. Further complicating the process, myosin binding accelerates the attachment rate of neighboring myosin molecules, adding a cooperative element to the activation process. To de-convolve these two effects, we directly determined the effect of Ca⁺⁺ on the rate of attachment of a single myosin molecule to a single regulated actin thin filament, and separately determined the distance over which myosin binding increases the attachment rate of neighboring molecules. Ca⁺⁺ alone increases myosin’s attachment rate ~50-fold, while myosin binding accelerates attachment of neighboring molecules 400 nm along the actin thin filament.

The Closed State of the Thin Filament Is Not Occupied in Fully Activated Skeletal Muscle

Muscle contraction is powered by actin-myosin interaction controlled by Ca²⁺ via the regulatory proteins troponin (Tn) and tropomyosin (Tpm), which are associated with actin filaments. Tpm forms coiled-coil dimers, which assemble into a helical strand that runs along the whole ∼1 μm length of a thin filament. In the absence of Ca²⁺, Tn that is tightly bound to Tpm binds actin and holds the Tpm strand in the blocked, or B, state, where Tpm shields actin from the binding of myosin heads. Ca²⁺ binding to Tn releases the Tpm from actin so that it moves azimuthally around the filament axis to a closed, or C, state, where actin is partially available for weak binding of myosin heads. Upon transition of the weak actin-myosin bond into a strong, stereo-specific complex, the myosin heads push Tpm strand to the open, or O, state allowing myosin binding sites on several neighboring actin monomers to become open for myosin binding. We used low-angle x-ray diffraction at the European Synchrotron Radiation Facility to check whether the O- to C-state transition in fully activated fibers of fast skeletal muscle of the rabbit occurs during transition from isometric contraction to shortening under low load. No decrease in the intensity of the second actin layer line at reciprocal radii in the range of 0.15-0.275 nm^-1 was observed during shortening suggesting that an azimuthal Tpm movement from the O- to C-state does not occur, although during shortening muscle stiffness is reduced compared to the isometric state, and the intensities of other actin layer lines demonstrate a ∼2-fold decrease in the fraction of myosin heads strongly bound to actin. The data show that a small fraction of actin-bound myosin heads is sufficient for supporting the O-state and, therefore the C-state is not occupied in fully activated skeletal muscle that produces mechanical work at low load.

Molecular mechanisms of deregulation of the thin filament associated with the R167H and K168E substitutions in tropomyosin Tpm1.1

Point mutations R167H and K168E in tropomyosin Tpm1.1 (TM) disturb Ca²⁺-dependent regulation of the actomyosin ATPase. To understand mechanisms of this defect we studied multistep changes in mobility and spatial arrangement of tropomyosin, actin and myosin heads during the ATPase cycle in reconstituted ghost fibres using the polarized fluorescence microscopy. It was found that both mutations disturbed the mode of troponin operation in the fibres. At high Ca²⁺, troponin increased the fraction of actin monomers that were in the "switched on" state, but both mutant tropomyosins were shifted toward the outer actin domains, which decreased the fraction of strongly bound myosin heads throughout the ATPase cycle. At low Ca²⁺, the R167H-TM was located close to the outer actin domains, which reduced the number of strongly-bound myosin heads. However, under these conditions troponin increased the number of actin monomers that were switched on. The K168E-TM was displaced far to the outer actin domains and troponin binding decreased the fraction of switched on actin monomers, but the proportion of the strongly bound myosin heads was abnormally high. Thus, the mutations differently disturbed transmission of conformational changes between troponin, tropomyosin and actin, which is essential for the Са²⁺-dependent regulation of the thin filament.

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.

Contributions of Ca2+-Independent Thin Filament Activation to Cardiac Muscle Function

Although Ca2+ is the principal regulator of contraction in striated muscle, in vitro evidence suggests that some actin-myosin interaction is still possible even in its absence. Whether this Ca2+-independent activation (CIA) occurs under physiological conditions remains unclear, as does its potential impact on the function of intact cardiac muscle. The purpose of this study was to investigate CIA using computational analysis. We added a structurally motivated representation of this phenomenon to an existing myofilament model, which allowed predictions of CIA-dependent muscle behavior. We found that a certain amount of CIA was essential for the model to reproduce reported effects of nonfunctional troponin C on myofilament force generation. Consequently, those data enabled estimation of ΔGCIA, the energy barrier for activating a thin filament regulatory unit in the absence of Ca2+. Using this estimate of ΔGCIA as a point of reference (∼7 kJ mol(-1)), we examined its impact on various aspects of muscle function through additional simulations. CIA decreased the Hill coefficient of steady-state force while increasing myofilament Ca2+ sensitivity. At the same time, CIA had minimal effect on the rate of force redevelopment after slack/restretch. Simulations of twitch tension show that the presence of CIA increases peak tension while profoundly delaying relaxation. We tested the model's ability to represent perturbations to the Ca2+ regulatory mechanism by analyzing twitch records measured in transgenic mice expressing a cardiac troponin I mutation (R145G). The effects of the mutation on twitch dynamics were fully reproduced by a single parameter change, namely lowering ΔGCIA by 2.3 kJ mol(-1) relative to its wild-type value. Our analyses suggest that CIA is present in cardiac muscle under normal conditions and that its modulation by gene mutations or other factors can alter both systolic and diastolic function.

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.

Cross-Bridge Group Ensembles Describing Cooperativity in Thermodynamically Consistent Way

The aim of this work is to incorporate cooperativity into Huxley-type cross-bridge model in thermodynamically consistent way. While the Huxley-type models assume that cross-bridges act independently from each other, we take into account that each cross-bridge is influenced by its neighbors and cooperativity is induced by tropomyosin movement. For that, we introduce ensembles of cross-bridge groups connected by elastic tropomyosin. By taking into account that the mechanical displacement of tropomyosin induces free energy change of the cross-bridge group ensemble, we develop the formalism for thermodynamically consistent description of the cooperativity in muscle contraction. An example model was composed to test the approach. The model parameters were found by optimization from the linear relation between oxygen consumption and stress-strain area as well as experimentally measured stress dynamics of rat trabecula. We have found a good agreement between the optimized model solution and experimental data. Simulations also showed that it is possible to study cooperativity with the approach developed in this work.

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.

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.

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.

Structural and functional effects of two stabilizing substitutions, D137L and G126R, in the middle part of α-tropomyosin molecule

Tropomyosin (Tm) is an α-helical coiled-coil protein that binds along the length of actin filament and plays an essential role in the regulation of muscle contraction. There are two highly conserved non-canonical residues in the middle part of the Tm molecule, Asp137 and Gly126, which are thought to impart conformational instability (flexibility) to this region of Tm which is considered crucial for its regulatory functions. It was shown previously that replacement of these residues by canonical ones (Leu substitution for Asp137 and Arg substitution for Gly126) results in stabilization of the coiled-coil in the middle of Tm and affects its regulatory function. Here we employed various methods to compare structural and functional features of Tm mutants carrying stabilizing substitutions Arg137Leu and Gly126Arg. Moreover, we for the first time analyzed the properties of Tm carrying both these substitutions within the same molecule. The results show that both substitutions similarly stabilize the Tm coiled-coil structure, and their combined action leads to further significant stabilization of the Tm molecule. This stabilization not only enhances maximal sliding velocity of regulated actin filaments in the in vitro motility assay at high Ca(2+) concentrations but also increases Ca(2+) sensitivity of the actin-myosin interaction underlying this sliding. We propose that the effects of these substitutions on the Ca(2+)-regulated actin-myosin interaction can be accounted for not only by decreased flexibility of actin-bound Tm but also by their influence on the interactions between the middle part of Tm and certain sites of the myosin head.

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.

The myosin duty ratio tunes the calcium sensitivity and cooperative activation of the thin filament

In striated muscle, calcium binding to the thin filament (TF) regulatory complex activates actin-myosin ATPase activity, and actin-myosin kinetics in turn regulates TF activation. However, a quantitative description of the effects of actin-myosin kinetics on the calcium sensitivity (pCa50) and cooperativity (nH) of TF activation is lacking. With the assumption that TF structural transitions and TF-myosin binding transitions are inextricably coupled, we advanced the principles established by Kad et al. [Kad, N., et al. (2005) Proc. Natl. Acad. Sci. U.S.A. 102, 16990-16995] and Sich et al. [Sich, N. M., et al. (2011) J. Biol. Chem. 285, 39150-39159] to develop a simple model of TF regulation, which predicts that pCa50 varies linearly with duty ratio and that nH is maximal near physiological duty ratios. Using in vitro motility to determine the calcium sensitivity of TF sliding velocities, we measured pCa50 and nH at different myosin densities and in the presence of ATPase inhibitors. The observed effects of myosin density and actin-myosin duty ratio on pCa50 and nH are consistent with our model predictions. In striated muscle, pCa50 must match cytosolic calcium concentrations and a maximal nH optimizes calcium responsiveness. Our results indicate that pCa50 and nH can be predictably tuned through TF-myosin ATPase kinetics and that drugs and disease states that alter ATPase kinetics can, through their effects on calcium sensitivity, alter the efficiency of muscle contraction.

Interplay between the overlapping ends of tropomyosin and the N terminus of cardiac troponin T affects tropomyosin states on actin

The functional significance of the molecular swivel at the head-to-tail overlapping ends of contiguous tropomyosin (Tm) dimers in striated muscle is unknown. Contractile measurements were made in muscle fibers from transgenic (TG) mouse hearts that expressed a mutant α-Tm (Tm(H276N)). We also reconstituted mouse cardiac troponin T (McTnT) N-terminal deletion mutants, McTnT(1-44Δ) and McTnT(45-74Δ), into muscle fibers from Tm(H276N). For controls, we used the wild-type (WT) McTnT because altered effects could be correlated with the mutant forms of McTnT. Tm(H276N) slowed crossbridge (XB) detachment rate (g) by 19%. McTnT(1-44Δ) attenuated Ca(2+)-activated maximal tension against Tm(WT) (36%) and Tm(H276N) (38%), but sped g only against Tm(H276N) by 35%. The rate of tension redevelopment decreased (17%) only in McTnT(1-44Δ) + Tm(H276N) fibers. McTnT(45-74Δ) attenuated tension (19%) and myofilament Ca(2+) sensitivity (pCa50=5.93 vs. 6.00 in the control fibers) against Tm(H276N), but not against Tm(WT) background. Thus, altered XB cycling kinetics decreased the fraction of strongly bound XBs in McTnT(1-44Δ) + Tm(H276N) fibers, whereas diminished thin-filament cooperativity attenuated tension in McTnT(45-74Δ) + Tm(H276N) fibers. In summary, our study is the first to show that the interplay between the N terminus of cTnT and the overlapping ends of contiguous Tm effectuates different states of Tm on the actin filament.

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.

The troponin I: inhibitory peptide uncouples force generation and the cooperativity of contractile activation in mammalian skeletal muscle

Hodges and his colleagues identified a 12 amino acid fragment of troponin I (TnI-ip) that inhibits Ca(2+)-activated force and reduces the effectiveness Ca(2+) as an activator. To understand the role of troponin C (TnC) in the extended cooperative interactions of thin filament activation, we compared the effect of TnI-ip with that of partial troponin TnC extraction. Both methods reduce maximal Ca(2+)-activated force and increase [Ca(2+)] required for activation. In contrast to TnC extraction, TnI-ip does not reduce the extended cooperative interactions between adjacent thin filament regulatory units as assessed by the slope of the pCa/force relationship. Additional evidence that TnI-ip does not interfere with extended cooperativity comes from studies that activate muscle by rigor crossbridges (RXBs). TnI-ip increases both the cooperativity of activation and the concentration of RXBs needed for maximal force. This shows that TnI-ip binding to TnC increases the stability of the relaxed state of the thin filament. TnI-ip, therefore, uncouples force generation from extended cooperativity in both Ca(2+) and RXB activated muscle contraction. Because maximum force can be reduced with no change-or even an increase-in cooperativity, force-generating crossbridges do not appear to be the primary activators of cooperativity between thin filament regulatory units of skeletal muscle.

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

The regulation of striated muscle contraction involves cooperative interactions between actin filaments, myosin-S1 (S1), tropomyosin (Tm), troponin (Tn), and calcium. These interactions are modeled by treating overlapping tropomyosins as a continuous flexible chain (CFC), weakly confined by electrostatic interactions with actin. The CFC is displaced locally in opposite directions on the actin surface by the binding of either S1 or Troponin I (TnI) to actin. The apparent rate constants for myosin and TnI binding to and detachment from actin are then intrinsically coupled via the CFC model to the presence of neighboring bound S1s and TnIs. Monte Carlo simulations at prescribed values of the CFC stiffness, the CFC’s degree of azimuthal confinement, and the angular displacements caused by the bound proteins were able to predict the stopped-flow transients of S1 binding to regulated F-actin. The transients collected over a large range of calcium concentrations could be well described by adjusting a single calcium-dependent parameter, the rate constant of TnI detachment from actin, k_−I. The resulting equilibrium constant \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ K_{\text{B}} \equiv 1/K_{\text{I}} $$\end{document} varied sigmoidally with the free calcium, increasing from 0.12 at low calcium (pCa >7) to 12 at high calcium (pCa <5.5) with a Hill coefficient of ~2.15. The similarity of the curves for excess-actin and excess-myosin data confirms their allosteric relationship. The spatially explicit calculations confirmed variable sizes for the cooperative units and clustering of bound myosins at low calcium concentrations. Moreover, inclusion of negative cooperativity between myosin units predicted the observed slowing of myosin binding at excess-myosin concentrations.

A kinetic model of troponin dissociation in relation to thin filament regulation in striated muscle

The apparent rate of troponin (Tn) dissociation from myofibrils has been used as a method to study thin filament regulation in striated muscle. The rate is dependent upon calcium and strong crossbridges and supports the three-state model for thin filament regulation. The dissociation rate of Tn is extremely low so it is not intuitively clear that such a slow process would probe thin filament regulation. We have investigated this issue by developing a simple kinetic model to explain the Tn dissociation rate measured by labeled Tn exchange in the myofibrils. Tn is composed of three interacting subunits, TnC, TnI and TnT. In our model, TnI's regulatory domain switches from actin-tropomyosin to TnC followed by TnT dissociation from actin-tropomyosin. This TnI regulatory domain switching is linked to the transition of the thin filament from the blocked state to the closed state. It is calcium dependent and several orders of magnitude faster than TnT dissociation from actin-tropomyosin. By integrating the dimensionless rate equations of this model, we have computed the time course of each of the various components. In our numerical simulations, the rate constant for TnI switching from actin-tropomyosin to TnC was varied from 10 s⁻¹ to 1000 s⁻¹ to simulate the low calcium, blocked state to high calcium, closed state. The computed progress curves for labeled Tn exchange into the myofibrils and the derived intensity ratio between the non-overlap and overlap regions well explains the intensity ratio progress curves observed experimentally. These numerical simulations and experimental observations reveal that the apparent rate of Tn dissociation probes the blocked state to closed state equilibrium of the myofibrillar thin filament.

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.

Multi-scale computational models of familial hypertrophic cardiomyopathy: genotype to phenotype

Familial hypertrophic cardiomyopathy (FHC) is an inherited disorder affecting roughly one in 500 people. Its hallmark is abnormal thickening of the ventricular wall, leading to serious complications that include heart failure and sudden cardiac death. Treatment is complicated by variation in the severity, symptoms and risks for sudden death within the patient population. Nearly all of the genetic lesions associated with FHC occur in genes encoding sarcomeric proteins, indicating that defects in cardiac muscle contraction underlie the condition. Detailed biophysical data are increasingly available for computational analyses that could be used to predict heart phenotypes based on genotype. These models must integrate the dynamic processes occurring in cardiac cells with properties of myocardial tissue, heart geometry and haemodynamic load in order to predict strain and stress in the ventricular walls and overall pump function. Recent advances have increased the biophysical detail in these models at the myofilament level, which will allow properties of FHC-linked mutant proteins to be accurately represented in simulations of whole heart function. The short-term impact of these models will be detailed descriptions of contractile dysfunction and altered myocardial strain patterns at the earliest stages of the disease-predictions that could be validated in genetically modified animals. Long term, these multi-scale models have the potential to improve clinical management of FHC through genotype-based risk stratification and personalized therapy.

Coupling of adjacent tropomyosins enhances cross-bridge-mediated cooperative activation in a markov model of the cardiac thin filament

We developed a Markov model of cardiac thin filament activation that accounts for interactions among nearest-neighbor regulatory units (RUs) in a spatially explicit manner. Interactions were assumed to arise from structural coupling of adjacent tropomyosins (Tms), such that Tm shifting within each RU was influenced by the Tm status of its neighbors. Simulations using the model demonstrate that this coupling is sufficient to produce observed cooperativity in both steady-state and dynamic force-Ca(2+) relationships. The model was further validated by comparison with reported responses under various conditions including inhibition of myosin binding and the addition of strong-binding, non-force-producing myosin fragments. The model also reproduced the effects of 2.5 mM added P(i) on Ca(2+)-activated force and the rate of force redevelopment measured in skinned rat myocardial preparations. Model analysis suggests that Tm-Tm coupling potentiates the activating effects of strongly-bound cross-bridges and contributes to force-Ca(2+) dynamics of intact cardiac muscle. The model further predicts that activation at low Ca(2+) concentrations is cooperatively inhibited by nearest neighbors, requiring Ca(2+) binding to >25% of RUs to produce appreciable levels of force. Without excluding other putative cooperative mechanisms, these findings suggest that structural coupling of adjacent Tm molecules contributes to several properties of cardiac myofilament activation.

Resolution and uniqueness of estimated parameters of a model of thin filament regulation in solution

The estimation of chemical kinetic rate constants for any non-trivial model is complex due to the nonlinear effects of second order chemical reactions. We developed an algorithm to accomplish this goal based on the Damped Least Squares (DLS) inversion method and then tested the effectiveness of this method on the McKillop-Geeves (MG) model of thin filament regulation. The kinetics of MG model is defined by a set of nonlinear ordinary differential equations (ODEs) that predict the evolution of troponin-tropomyosin-actin and actin-myosin states. The values of the rate constants are estimated by integrating these ODEs numerically and fitting them to a series of stopped-flow pyrene fluorescence transients of myosin-S1 fragment binding to regulated actin in solution. The accuracy and robustness of the estimated rate constants are evaluated for DLS and two other methods, namely quasi-Newton (QN) and simulated annealing (SA). The comparison of these methods revealed that SA provides the best estimates of the model parameters because of its global optimization scheme. However it converges slowly and does quantify the uniqueness of the estimated parameters. On the other hand the QN method converges rapidly but only if the initial guess of the parameters is close to the optimum values, otherwise it diverges. Overall, the DLS method proves to be the most convenient method. It converges fast and was able to provide excellent estimates of kinetic parameters. Furthermore, DLS provides the model resolution matrix, which quantifies the interdependence of model parameters thereby evaluating the uniqueness of their estimated values. This property is essential for estimating of the dependence of the model parameters on experimental conditions (e.g. Ca(2+) concentration) when it is assessed from noisy experimental data such as pyrene fluorescence from stopped-flow transients. The advantages of the DLS method observed in this study should be further examined in other physicochemical systems to firmly establish the observed effectiveness of DSL vs. the other parameter estimation methods.

New insights into the regulation of the actin cytoskeleton by tropomyosin

The actin cytoskeleton is regulated by a variety of actin-binding proteins including those constituting the tropomyosin family. Tropomyosins are coiled-coil dimers that bind along the length of actin filaments. In muscles, tropomyosin regulates the interaction of actin-containing thin filaments with myosin-containing thick filaments to allow contraction. In nonmuscle cells where multiple tropomyosin isoforms are expressed, tropomyosins participate in a number of cellular events involving the cytoskeleton. This chapter reviews the current state of the literature regarding tropomyosin structure and function and discusses the evidence that tropomyosins play a role in regulating actin assembly.

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.