Multiscale modeling of twitch contractions in cardiac trabeculae

Mechanisms of myosin II force generation: insights from novel experimental techniques and approaches

Myosin II is a molecular motor that converts chemical energy derived from ATP hydrolysis into mechanical work. Myosin II isoforms are responsible for muscle contraction and a range of cell functions relying on the development of force and motion. When the motor attaches to actin, ATP is hydrolyzed and inorganic phosphate (Pi) and ADP are released from its active site. These reactions are coordinated with changes in the structure of myosin, promoting the so-called "power stroke" that causes the sliding of actin filaments. The general features of the myosin-actin interactions are well accepted, but there are critical issues that remain poorly understood, mostly due to technological limitations. In recent years, there has been a significant advance in structural, biochemical, and mechanical methods that have advanced the field considerably. New modeling approaches have also allowed researchers to understand actomyosin interactions at different levels of analysis. This paper reviews recent studies looking into the interaction between myosin II and actin filaments, which leads to power stroke and force generation. It reviews studies conducted with single myosin molecules, myosins working in filaments, muscle sarcomeres, myofibrils, and fibers. It also reviews the mathematical models that have been used to understand the mechanics of myosin II in approaches focusing on single molecules to ensembles. Finally, it includes brief sections on translational aspects, how changes in the myosin motor by mutations and/or posttranslational modifications may cause detrimental effects in diseases and aging, among other conditions, and how myosin II has become an emerging drug target.

Identifying mechanisms and therapeutic targets in muscle using Bayesian parameter estimation with conditional variational autoencoders

Machine learning techniques have potential to accelerate discoveries in biologically complex systems. However, they require large data sets and can be challenging in high dimensional systems such as cardiac muscle. In this study, we combined experimental measures of cardiac muscle twitch forces with mechanistic simulations and a newly developed mixture of Bayesian inference with neural networks (in autoencoders) to solve the inverse problem of determining the underlying kinetics for observed force generation by cardiac muscle. The autoencoders are trained on millions of simulations spanning parameter spaces that correspond to the mechanochemistry of cardiac sarcomeres. We apply the trained model to experimental data in order to infer parameters that can explain a diseased twitch and ways to recover it.

A novel kinetic model to demonstrate the independent effects of ATP and ADP/Pi concentrations on sarcomere function

Understanding muscle contraction mechanisms is a standing challenge, and one of the approaches has been to create models of the sarcomere-the basic contractile unit of striated muscle. While these models have been successful in elucidating many aspects of muscle contraction, they fall short in explaining the energetics of functional phenomena, such as rigor, and in particular, their dependence on the concentrations of the biomolecules involved in the cross-bridge cycle. Our hypothesis posits that the stochastic time delay between ATP adsorption and ADP/Pi release in the cross-bridge cycle necessitates a modeling approach where the rates of these two reaction steps are controlled by two independent parts of the total free energy change of the hydrolysis reaction. To test this hypothesis, we built a two-filament, stochastic-mechanical half-sarcomere model that separates the energetic roles of ATP and ADP/Pi in the cross-bridge cycle's free energy landscape. Our results clearly demonstrate that there is a nontrivial dependence of the cross-bridge cycle's kinetics on the independent concentrations of ATP, ADP, and Pi. The simplicity of the proposed model allows for analytical solutions of the more basic systems, which provide novel insight into the dominant mechanisms driving some of the experimentally observed contractile phenomena.

Functional control of myosin motors in the cardiac cycle

Contraction of the heart is driven by cyclical interactions between myosin and actin filaments powered by ATP hydrolysis. The modular structure of heart muscle and the organ-level synchrony of the heartbeat ensure tight reciprocal coupling between this myosin ATPase cycle and the macroscopic cardiac cycle. The myosin motors respond to the cyclical activation of the actin and myosin filaments to drive the pressure changes that control the inflow and outflow valves of the heart chambers. Opening and closing of the valves in turn switches the myosin motors between roughly isometric and roughly isotonic contraction modes. Peak filament stress in the heart is much smaller than in fully activated skeletal muscle, although the myosin filaments in the two muscle types have the same number of myosin motors. Calculations indicate that only ~5% of the myosin motors in the heart are needed to generate peak systolic pressure, although many more motors are needed to drive ejection. Tight regulation of the number of active motors is essential for the efficient functioning of the healthy heart - this control is commonly disrupted by gene variants associated with inherited heart disease, and its restoration might be a useful end point in the development of novel therapies.

Modeling thick filament activation suggests a molecular basis for force depression

Multiscale models aiming to connect muscle's molecular and cellular function have been difficult to develop, in part due to a lack of self-consistent multiscale data. To address this gap, we measured the force response from single, skinned rabbit psoas muscle fibers to ramp shortenings and step stretches performed on the plateau region of the force-length relationship. We isolated myosin from the same muscles and, under similar conditions, performed single-molecule and ensemble measurements of myosin's ATP-dependent interaction with actin using laser trapping and in vitro motility assays. We fit the fiber data by developing a partial differential equation model that includes thick filament activation, whereby an increase in force on the thick filament pulls myosin out of an inhibited state. The model also includes a series elastic element and a parallel elastic element. This parallel elastic element models a titin-actin interaction proposed to account for the increase in isometric force after stretch (residual force enhancement). By optimizing the model fit to a subset of our fiber measurements, we specified seven unknown parameters. The model then successfully predicted the remainder of our fiber measurements and also our molecular measurements from the laser trap and in vitro motility. The success of the model suggests that our multiscale data are self-consistent and can serve as a testbed for other multiscale models. Moreover, the model captures the decrease in isometric force observed in our muscle fibers after active shortening (force depression), suggesting a molecular mechanism for force depression, whereby a parallel elastic element combines with thick filament activation to decrease the number of cycling cross-bridges.

Assessing Cardiac Contractility From Single Molecules to Whole Hearts

Fundamentally, the heart needs to generate sufficient force and power output to dynamically meet the needs of the body. Cardiomyocytes contain specialized structures referred to as sarcomeres that power and regulate contraction. Disruption of sarcomeric function or regulation impairs contractility and leads to cardiomyopathies and heart failure. Basic, translational, and clinical studies have adapted numerous methods to assess cardiac contraction in a variety of pathophysiological contexts. These tools measure aspects of cardiac contraction at different scales ranging from single molecules to whole organisms. Moreover, these studies have revealed new pathogenic mechanisms of heart disease leading to the development of novel therapies targeting contractility. In this review, the authors explore the breadth of tools available for studying cardiac contractile function across scales, discuss their strengths and limitations, highlight new insights into cardiac physiology and pathophysiology, and describe how these insights can be harnessed for therapeutic candidate development and translational.

Myosin in autoinhibited off state(s), stabilized by mavacamten, can be recruited in response to inotropic interventions

Mavacamten is a FDA-approved small-molecule therapeutic designed to regulate cardiac function at the sarcomere level by selectively but reversibly inhibiting the enzymatic activity of myosin. It shifts myosin toward ordered off states close to the thick filament backbone. It remains elusive whether these myosin heads in the off state(s) can be recruited in response to physiological stimuli when required to boost cardiac output. We show that cardiac myosins stabilized in these off state(s) by mavacamten are recruitable by 1) Ca2+, 2) increased chronotropy [heart rate (HR)], 3) stretch, and 4) β-adrenergic (β-AR) stimulation, all known physiological inotropic interventions. At the molecular level, we show that Ca2+ increases myosin ATPase activity by shifting mavacamten-stabilized myosin heads from the inactive super-relaxed state to the active disordered relaxed state. At the myofilament level, both Ca2+ and passive lengthening can shift mavacamten-ordered off myosin heads from positions close to the thick filament backbone to disordered on states closer to the thin filaments. In isolated rat cardiomyocytes, increased stimulation rates enhanced shortening fraction in mavacamten-treated cells. This observation was confirmed in vivo in telemetered rats, where left-ventricular dP/dtmax, an index of inotropy, increased with HR in mavacamten-treated animals. Finally, we show that β-AR stimulation in vivo increases left-ventricular function and stroke volume in the setting of mavacamten. Our data demonstrate that the mavacamten-promoted off states of myosin in the thick filament are at least partially activable, thus preserving cardiac reserve mechanisms.

Regulating Striated Muscle Contraction: Through Thick and Thin

Force generation in striated muscle is primarily controlled by structural changes in the actin-containing thin filaments triggered by an increase in intracellular calcium concentration. However, recent studies have elucidated a new class of regulatory mechanisms, based on the myosin-containing thick filament, that control the strength and speed of contraction by modulating the availability of myosin motors for the interaction with actin. This review summarizes the mechanisms of thin and thick filament activation that regulate the contractility of skeletal and cardiac muscle. A novel dual-filament paradigm of muscle regulation is emerging, in which the dynamics of force generation depends on the coordinated activation of thin and thick filaments. We highlight the interfilament signaling pathways based on titin and myosin-binding protein-C that couple thin and thick filament regulatory mechanisms. This dual-filament regulation mediates the length-dependent activation of cardiac muscle that underlies the control of the cardiac output in each heartbeat.

Design Principles and Benefits of Spatially Explicit Models of Myofilament Function

Spatially explicit models of muscle contraction include fine-scale details about the spatial, kinetic, and/or mechanical properties of the biological processes being represented within the model network. Over the past 25 years, this has primarily consisted of a set of mathematical and computational algorithms representing myosin cross-bridge activity, Ca2+-activation of contraction, and ensemble force production within a half-sarcomere representation of the myofilament network. Herein we discuss basic design principles associated with creating spatially explicit models of myofilament function, as well as model assumptions underlying model development. A brief overview of computational approaches is introduced. Opportunities for new model directions that could investigate coupled regulatory pathways between the thick-filament and thin-filaments are also presented. Given the modular design and flexibility associated with spatially explicit models, we highlight some advantages of this approach compared to other model formulations.

Advancing clinical translation of cardiac biomechanics models: a comprehensive review, applications and future pathways

Cardiac mechanics models are developed to represent a high level of detail, including refined anatomies, accurate cell mechanics models, and platforms to link microscale physiology to whole-organ function. However, cardiac biomechanics models still have limited clinical translation. In this review, we provide a picture of cardiac mechanics models, focusing on their clinical translation. We review the main experimental and clinical data used in cardiac models, as well as the steps followed in the literature to generate anatomical meshes ready for simulations. We describe the main models in active and passive mechanics and the different lumped parameter models to represent the circulatory system. Lastly, we provide a summary of the state-of-the-art in terms of ventricular, atrial, and four-chamber cardiac biomechanics models. We discuss the steps that may facilitate clinical translation of the biomechanics models we describe. A well-established software to simulate cardiac biomechanics is lacking, with all available platforms involving different levels of documentation, learning curves, accessibility, and cost. Furthermore, there is no regulatory framework that clearly outlines the verification and validation requirements a model has to satisfy in order to be reliably used in applications. Finally, better integration with increasingly rich clinical and/or experimental datasets as well as machine learning techniques to reduce computational costs might increase model reliability at feasible resources. Cardiac biomechanics models provide excellent opportunities to be integrated into clinical workflows, but more refinement and careful validation against clinical data are needed to improve their credibility. In addition, in each context of use, model complexity must be balanced with the associated high computational cost of running these models.

Cooperative mechanisms underlie differences in myocardial contractile dynamics between large and small mammals

Ca2+ binding to troponin C (TnC) and myosin cross-bridge binding to actin act in a synergistic cooperative manner to modulate myocardial contraction and relaxation. The responsiveness of the myocardial thin filament to the activating effects of Ca2+ and myosin cross-bridge binding has been well-characterized in small mammals (e.g., mice). Given the nearly 10-fold difference in resting heart rates and twitch kinetics between small and large mammals, it is unlikely that the cooperative mechanisms underlying thin filament activation are identical in these two species. To test this idea, we measured the Ca2+ dependencies of steady-state force and the rate constant of force redevelopment (ktr) in murine and porcine permeabilized ventricular myocardium. While murine myocardium exhibited a steep activation-dependence of ktr, the activation-dependent profile of ktr was significantly reduced in porcine ventricular myocardium. Further insight was attained by examining force-pCa and ktr-pCa relationships. In the murine myocardium, the pCa50 for ktr was right-shifted compared with the pCa50 for force, meaning that increases in steady-state force occurred well before increases in the rate of force redevelopment were observed. In the porcine myocardium, we observed a tighter coupling of the force-pCa and ktr-pCa relationships, as evidenced by near-maximal rates of force redevelopment at low levels of Ca2+ activation. These results demonstrate that the molecular mechanisms underlying the cooperative activation of force are a dynamic property of the mammalian heart, involving, at least in part, the species- and tissue-specific expression of cardiac myosin heavy chain isoforms.

Modeling Thick Filament Activation Suggests a Molecular Basis for Force Depression

Multiscale models aiming to connect muscle's molecular and cellular function have been difficult to develop, in part, due to a lack of self-consistent multiscale data. To address this gap, we measured the force response from single skinned rabbit psoas muscle fibers to ramp shortenings and step stretches performed on the plateau region of the force-length relationship. We isolated myosin from the same muscles and, under similar conditions, performed single molecule and ensemble measurements of myosin's ATP-dependent interaction with actin using laser trapping and in vitro motility assays. We fit the fiber data by developing a partial differential equation model that includes thick filament activation, whereby an increase in force on the thick filament pulls myosin out of an inhibited state. The model also includes a series elastic element and a parallel elastic element. This parallel elastic element models a titin-actin interaction proposed to account for the increase in isometric force following stretch (residual force enhancement). By optimizing the model fit to a subset of our fiber measurements, we specified seven unknown parameters. The model then successfully predicted the remainder of our fiber measurements and also our molecular measurements from the laser trap and in vitro motility. The success of the model suggests that our multiscale data are self-consistent and can serve as a testbed for other multiscale models. Moreover, the model captures the decrease in isometric force observed in our muscle fibers after active shortening (force depression), suggesting a molecular mechanism for force depression, whereby a parallel elastic element combines with thick filament activation to decrease the number of cycling cross-bridges.

Mathematical modeling of active contraction of the human cardiac myocyte: A review

Background and objective

In this present research paper, a mathematical model has been developed to study myocyte contraction in the human cardiac muscle, using the Land model. Different parts of the human heart with a focus on the composition of the myocyte cells have been explored numerically to enabling us to determine the interaction of various parameters in the heart muscle. The main objective of the work is to direct the study of the Land model, which has been exploited to simulate the contraction of real human myocytes.

Methods

Mathematical models has been developed based on the Hill model and Huxley model. Myocyte contraction for different scenarios, such as in isometric tension and isotonic tension have been studied.

Results

It is found that increase in stretch, the peak active tension increases, in line with well-established length-dependent tension generation. Five parameters are selected: [Ca2+]T50, Tref, TRPN50, β0, and β1, which have been varied in between the range of -50%-100%, to examine the isometric effects of each parameter on the behavior of the tension developed in the intact myocyte cells, with the most sensitive parameter being [Ca2+]T50.

Conclusion

In conclusion, it is found that the Land model provides a good platform for the analysis of the active contraction of the human cardiac myocyte.

Myosin in autoinhibited off state(s), stabilized by mavacamten, can be recruited via inotropic effectors

Mavacamten is a novel, FDA-approved, small molecule therapeutic designed to regulate cardiac function by selectively but reversibly inhibiting the enzymatic activity of myosin. It shifts myosin towards ordered off states close to the thick filament backbone. It remains unresolved whether mavacamten permanently sequesters these myosin heads in the off state(s) or whether these heads can be recruited in response to physiological stimuli when required to boost cardiac output. We show that cardiac myosins stabilized in these off state(s) by mavacamten are recruitable by Ca2+, increased heart rate, stretch, and β-adrenergic (β-AR) stimulation, all known physiological inotropic effectors. At the molecular level, we show that, in presence of mavacamten, Ca2+ increases myosin ATPase activity by shifting myosin heads from the reserve super-relaxed (SRX) state to the active disordered relaxed (DRX) state. At the myofilament level, both Ca2+ and passive lengthening can shift ordered off myosin heads from positions close to the thick filament backbone to disordered on states closer to the thin filaments in the presence of mavacamten. In isolated rat cardiomyocytes, increased stimulation rates enhanced shortening fraction in mavacamten-treated cells. This observation was confirmed in vivo in telemetered rats, where left-ventricular dP/dtmax, an index of inotropy, increased with heart rate in mavacamten treated animals. Finally, we show that β-AR stimulation in vivo increases left-ventricular function and stroke volume in the setting of mavacamten. Our data demonstrate that the mavacamten-promoted off states of myosin in the thick filament are activable, at least partially, thus leading to preservation of cardiac reserve mechanisms.

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.

Machine learning meets Monte Carlo methods for models of muscle's molecular machinery to classify mutations

The timing and magnitude of force generation by a muscle depend on complex interactions in a compliant, contractile filament lattice. Perturbations in these interactions can result in cardiac muscle diseases. In this study, we address the fundamental challenge of connecting the temporal features of cardiac twitches to underlying rate constants and their perturbations associated with genetic cardiomyopathies. Current state-of-the-art metrics for characterizing the mechanical consequence of cardiac muscle disease do not utilize information embedded in the complete time course of twitch force. We pair dimension reduction techniques and machine learning methods to classify underlying perturbations that shape the timing of twitch force. To do this, we created a large twitch dataset using a spatially explicit Monte Carlo model of muscle contraction. Uniquely, we modified the rate constants of this model in line with mouse models of cardiac muscle disease and varied mutation penetrance. Ultimately, the results of this study show that machine learning models combined with biologically informed dimension reduction techniques can yield excellent classification accuracy of underlying muscle perturbations.

Computational Modeling on Drugs Effects for Left Ventricle in Cardiomyopathy Disease

Cardiomyopathy is associated with structural and functional abnormalities of the ventricular myocardium and can be classified in two major groups: hypertrophic (HCM) and dilated (DCM) cardiomyopathy. Computational modeling and drug design approaches can speed up the drug discovery and significantly reduce expenses aiming to improve the treatment of cardiomyopathy. In the SILICOFCM project, a multiscale platform is developed using coupled macro- and microsimulation through finite element (FE) modeling of fluid-structure interactions (FSI) and molecular drug interactions with the cardiac cells. FSI was used for modeling the left ventricle (LV) with a nonlinear material model of the heart wall. Simulations of the drugs' influence on the electro-mechanics LV coupling were separated in two scenarios, defined by the principal action of specific drugs. We examined the effects of Disopyramide and Dygoxin which modulate Ca2+ transients (first scenario), and Mavacamten and 2-deoxy adenosine triphosphate (dATP) which affect changes of kinetic parameters (second scenario). Changes of pressures, displacements, and velocity distributions, as well as pressure-volume (P-V) loops in the LV models of HCM and DCM patients were presented. Additionally, the results obtained from the SILICOFCM Risk Stratification Tool and PAK software for high-risk HCM patients closely followed the clinical observations. This approach can give much more information on risk prediction of cardiac disease to specific patients and better insight into estimated effects of drug therapy, leading to improved patient monitoring and treatment.

Cardiac myosin filaments are directly regulated by calcium

Classically, striated muscle contraction is initiated by calcium (Ca2+)-dependent structural changes in regulatory proteins on actin-containing thin filaments, which allow the binding of myosin motors to generate force. Additionally, dynamic switching between resting off and active on myosin states has been shown to regulate muscle contractility, a recently validated mechanism by novel myosin-targeted therapeutics. The molecular nature of this switching, however, is not understood. Here, using a combination of small-angle x-ray fiber diffraction and biochemical assays with reconstituted systems, we show that cardiac thick filaments are directly Ca2+-regulated. We find that Ca2+ induces a structural transition of myosin heads from ordered off states close to the thick filament to disordered on states closer to the thin filaments. Biochemical assays show a Ca2+-induced transition from an inactive super-relaxed (SRX) state(s) to an active disordered-relaxed (DRX) state(s) in synthetic thick filaments. We show that these transitions are an intrinsic property of cardiac myosin only when assembled into thick filaments and provide a fresh perspective on nature's two orthogonal mechanisms to regulate muscle contraction through the thin and the thick filaments.

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.

SILICOFCM platform, multiscale modeling of left ventricle from echocardiographic images and drug influence for cardiomyopathy disease

BACKGROUND AND OBJECTIVE

In silico clinical trials are the future of medicine and virtual testing and simulation are the future of medical engineering. The use of a computational platform can reduce costs and time required for developing new models of medical devices and drugs. The computational platform, which is one of the main results of the SILICOFCM project, was developed using state-of-the-art finite element modeling for macro simulation of fluid-structure interaction with micro modeling at the molecular level for drug interaction with the cardiac cells. SILICOFCM platform is using for risk prediction and optimal drug therapy of familial cardiomyopathy in a specific patient.

METHODS

In order to obtain 3D image reconstruction, the U-net architecture was used to determine geometric parameters for the left ventricle which were extracted from the echocardiographic apical and M-mode views. A micro-mechanics cellular model which includes three kinetic processes of sarcomeric proteins interactions was developed. It allows simulation of the drugs which are divided into three major groups defined by the principal action of each drug. Fluid-solid coupling for the left ventricle was presented. A nonlinear material model of the heart wall that was developed by using constitutive curves which include the stress-strain relationship was used.

RESULTS

The results obtained with the parametric model of the left ventricle where pressure-volume (PV) diagrams depend on the change of Ca2+ were presented. It directly affects the ejection fraction. The presented approach with the variation of the left ventricle (LV) geometry and simulations which include the influence of different parameters on the PV diagrams are directly interlinked with drug effects on the heart function. It includes different drugs such as Entresto and Digoxin that directly affect the cardiac PV diagrams and ejection fraction.

CONCLUSIONS

Computational platforms such as the SILICOFCM platform are novel tools for risk prediction of cardiac disease in a specific patient that will certainly open a new avenue for in silico clinical trials in the future.

Functional and structural differences between skinned and intact muscle preparations

Myofilaments and their associated proteins, which together constitute the sarcomeres, provide the molecular-level basis for contractile function in all muscle types. In intact muscle, sarcomere-level contraction is strongly coupled to other cellular subsystems, in particular the sarcolemmal membrane. Skinned muscle preparations (where the sarcolemma has been removed or permeabilized) are an experimental system designed to probe contractile mechanisms independently of the sarcolemma. Over the last few decades, experiments performed using permeabilized preparations have been invaluable for clarifying the understanding of contractile mechanisms in both skeletal and cardiac muscle. Today, the technique is increasingly harnessed for preclinical and/or pharmacological studies that seek to understand how interventions will impact intact muscle contraction. In this context, intrinsic functional and structural differences between skinned and intact muscle pose a major interpretational challenge. This review first surveys measurements that highlight these differences in terms of the sarcomere structure, passive and active tension generation, and calcium dependence. We then highlight the main practical challenges and caveats faced by experimentalists seeking to emulate the physiological conditions of intact muscle. Gaining an awareness of these complexities is essential for putting experiments in due perspective.

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.

FiberSim: A flexible open-source model of myofilament-level contraction

FiberSim is a flexible open-source model of myofilament-level contraction. The code uses a spatially explicit technique, meaning that it tracks the position and status of each contractile molecule within the lattice framework. This allows the model to simulate some of the mechanical effects modulated by myosin-binding protein C, as well as the dose dependence of myotropes and the effects of varying isoform expression levels. This paper provides a short introduction to FiberSim and presents simulations of tension-pCa curves with and without regulation of thick and thin filament activation by myosin-binding protein C. A myotrope dose-dependent response as well as slack/re-stretch maneuvers to assess rates of tension recovery are also presented. The software was designed to be flexible (the user can define their own model and/or protocol) and computationally efficient (simulations can be performed on a regular laptop). We hope that other investigators will use FiberSim to explore myofilament level mechanisms and to accelerate research focusing on the contractile properties of sarcomeres.

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.