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

Cardiac length-dependent activation driven by force-dependent thick-filament dynamics

The length-dependent activation (LDA) of maximum force and calcium sensitivity are established features of cardiac muscle contraction but the dominant underlying mechanisms remain to be fully clarified. Alongside the well-documented regulation of contraction via the thin filaments, experiments have identified an additional force-dependent thick-filament activation, whereby myosin heads parked in a so-called off state become available to generate force. This process produces a feedback effect that may potentially drive LDA. Using biomechanical modeling of a human left-ventricular myocyte, this study investigates the extent to which the off-state dynamics could, by itself, plausibly account for LDA, depending on the specific mathematical formulation of the feedback. We hypothesized four different models of the off-state regulatory feedback based on (A) total force, (B) active force, (C) sarcomere strain, and (D) passive force. We tested if these models could reproduce the isometric steady-state and dynamic LDA features predicted by an earlier published model of a human left-ventricle myocyte featuring purely phenomenological length dependences. The results suggest that only total-force feedback (A) is capable of reproducing the expected behaviors, but that passive tension could provide a length-dependent signal on which to initiate the feedback. Furthermore, by attributing LDA to off-state dynamics, our proposed model also qualitatively reproduces experimentally observed effects of the off-state-stabilizing drug mavacamten. Taken together, these results support off-state dynamics as a plausible primary mechanism underlying LDA.

Proposing a Caputo-Land System for active tension. Capturing variable viscoelasticity

Accurate cell-level active tension modeling for cardiomyocytes is critical to understanding cardiac functionality on a subject-specific basis. However, cell-level models in the literature fail to account for viscoelasticity and inter-subject variations in active tension, which are relevant to disease diagnostics and drug screening, e.g., for cardiotoxicity. Thus, we propose a fractional order system to model cell-level active tension by extending Land's state-of-the-art model of cardiac contraction. Our approach features the (left) Caputo derivative of six state variables that identify the mechanistic origins of viscoelasticity in a myocardial cell in terms of the thin filament, thick filament, and length-dependent interactions. This proposed CLS is the first of its kind for active tension modeling in cells and demonstrates notable subject-specificity, with smaller mean square errors than the reference model relative to cell-level experiments across subjects, promising greater clinical relevance than its counterparts in the literature by highlighting the contribution of different cellular mechanisms to apparent viscoelastic cell behavior, and how it could vary with disease.

Personalized biomechanical insights in atrial fibrillation: opportunities & challenges

INTRODUCTION

Atrial fibrillation (AF) is an increasingly prevalent and significant worldwide health problem. Manifested as an irregular atrial electrophysiological activation, it is associated with many serious health complications. AF affects the biomechanical function of the heart as contraction follows the electrical activation, subsequently leading to reduced blood flow. The underlying mechanisms behind AF are not fully understood, but it is known that AF is highly correlated with the presence of atrial fibrosis, and with a manifold increase in risk of stroke.

AREAS COVERED

In this review, we focus on biomechanical aspects in atrial fibrillation, current and emerging use of clinical images, and personalized computational models. We also discuss how these can be used to provide patient-specific care.

EXPERT OPINION

Understanding the connection betweenatrial fibrillation and atrial remodeling might lead to valuable understanding of stroke and heart failure pathophysiology. Established and emerging imaging modalities can bring us closer to this understanding, especially with continued advancements in processing accuracy, reproducibility, and clinical relevance of the associated technologies. Computational models of cardiac electromechanics can be used to glean additional insights on the roles of AF and remodeling in heart function.

Small Molecule RPI-194 Stabilizes Activated Troponin to Increase the Calcium Sensitivity of Striated Muscle Contraction

Small molecule cardiac troponin activators could potentially enhance cardiac muscle contraction in the treatment of systolic heart failure. We designed a small molecule, RPI-194, to bind cardiac/slow skeletal muscle troponin (Cardiac muscle and slow skeletal muscle share a common isoform of the troponin C subunit.) Using solution NMR and stopped flow fluorescence spectroscopy, we determined that RPI-194 binds to cardiac troponin with a dissociation constant K_D of 6-24 μM, stabilizing the activated complex between troponin C and the switch region of troponin I. The interaction between RPI-194 and troponin C is weak (K_D 311 μM) in the absence of the switch region. RPI-194 acts as a calcium sensitizer, shifting the pCa₅₀ of isometric contraction from 6.28 to 6.99 in mouse slow skeletal muscle fibers and from 5.68 to 5.96 in skinned cardiac trabeculae at 100 μM concentration. There is also some cross-reactivity with fast skeletal muscle fibers (pCa₅₀ increases from 6.27 to 6.52). In the slack test performed on the same skinned skeletal muscle fibers, RPI-194 slowed the velocity of unloaded shortening at saturating calcium concentrations, suggesting that it slows the rate of actin-myosin cross-bridge cycling under these conditions. However, RPI-194 had no effect on the ATPase activity of purified actin-myosin. In isolated unloaded mouse cardiomyocytes, RPI-194 markedly decreased the velocity and amplitude of contractions. In contrast, cardiac function was preserved in mouse isolated perfused working hearts. In summary, the novel troponin activator RPI-194 acts as a calcium sensitizer in all striated muscle types. Surprisingly, it also slows the velocity of unloaded contraction, but the cause and significance of this is uncertain at this time. RPI-194 represents a new class of non-specific troponin activator that could potentially be used either to enhance cardiac muscle contractility in the setting of systolic heart failure or to enhance skeletal muscle contraction in neuromuscular disorders.

Quantitative mapping of force-pCa curves to whole heart contraction and relaxation

Abstract

The force–pCa (F–pCa) curve is used to characterize steady‐state contractile properties of cardiac muscle cells in different physiological, pathological and pharmacological conditions. This provides a reduced preparation in which to isolate sarcomere mechanisms. However, it is unclear how changes in the F–pCa curve impact emergent whole‐heart mechanics quantitatively. We study the link between sarcomere and whole‐heart function using a multiscale mathematical model of rat biventricular mechanics that describes sarcomere, tissue, anatomy, preload and afterload properties quantitatively. We first map individual cell‐level changes in sarcomere‐regulating parameters to organ‐level changes in the left ventricular function described by pressure–volume loop characteristics (e.g. end‐diastolic and end‐systolic volumes, ejection fraction and isovolumetric relaxation time). We next map changes in the sarcomere‐regulating parameters to changes in the F–pCa curve. We demonstrate that a change in the F–pCa curve can be caused by multiple different changes in sarcomere properties. We demonstrate that changes in sarcomere properties cause non‐linear and, importantly, non‐monotonic changes in left ventricular function. As a result, a change in sarcomere properties yielding changes in the F–pCa curve that improve contractility does not guarantee an improvement in whole‐heart function. Likewise, a desired change in whole‐heart function (i.e. ejection fraction or relaxation time) is not caused by a unique shift in the F–pCa curve. Changes in the F–pCa curve alone cannot be used to predict the impact of a compound on whole‐heart function.

Key points

The force–pCa (F–pCa) curve is used to assess myofilament calcium sensitivity after pharmacological modulation and to infer pharmacological effects on whole‐heart function.

We demonstrate that there is a non‐unique mapping from changes in F–pCa curves to changes in left ventricular (LV) function.

The effect of changes in F–pCa on LV function depend on the state of the heart and could be different for different pathological conditions.

Screening of compounds to impact whole‐heart function by F–pCa should be combined with active tension and calcium transient measurements to predict better how changes in muscle function will impact whole‐heart physiology.

Heart-on-Chip for Combined Cellular Dynamics Measurements and Computational Modeling Towards Clinical Applications

Organ-on-chip or micro-engineered three-dimensional cellular or tissue models are increasingly implemented in the study of cardiovascular pathophysiology as alternatives to traditional in vitro cell culture. Drug induced cardiotoxicity is a key issue in drug development pipelines, but the current in vitro and in vivo studies suffer from inter-species differences, high costs, and lack of reliability and accuracy in predicting cardiotoxicity. Microfluidic heart-on-chip devices can impose a paradigm shift to the current tools. They can not only recapitulate cardiac tissue level functionality and the communication between cells and extracellular matrices but also allow higher throughput studies conducive to drug screening especially with their added functionalities or sensors that extract disease-specific phenotypic, genotypic, and electrophysiological information in real-time. Such electrical and mechanical components can tailor the electrophysiology and mechanobiology of the experiment to better mimic the in vivo condition as well. Recent advancements and challenges are reviewed in the fabrication, functionalization and sensor assisted mechanical and electrophysiological measurements, numerical and computational modeling of cardiomyocytes' behavior, and the clinical applications in drug screening and disease modeling. This review concludes with the current challenges and perspectives on the future of such organ-on-chip platforms.

A mathematical model of hiPSC cardiomyocytes electromechanics

Human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) are becoming instrumental in cardiac research, human-based cell level cardiotoxicity tests, and developing patient-specific care. As one of the principal functional readouts is contractility, we propose a novel electromechanical hiPSC-CM computational model named the hiPSC-CM-CE. This model comprises a reparametrized version of contractile element (CE) by Rice et al., 2008, with a new passive force formulation, integrated into a hiPSC-CM electrophysiology formalism by Paci et al. in 2020. Our simulated results were validated against in vitro data reported for hiPSC-CMs at matching conditions from different labs. Specifically, key action potential (AP) and calcium transient (CaT) biomarkers simulated by the hiPSC-CM-CE model were within the experimental ranges. On the mechanical side, simulated cell shortening, contraction-relaxation kinetic indices (RT50 and RT25 ), and the amplitude of tension fell within the experimental intervals. Markedly, as an inter-scale analysis, correct classification of the inotropic effects due to non-cardiomyocytes in hiPSC-CM tissues was predicted on account of the passive force expression introduced to the CE. Finally, the physiological inotropic effects caused by Verapamil and Bay-K 8644 and the aftercontractions due to the early afterdepolarizations (EADs) were simulated and validated against experimental data. In the future, the presented model can be readily expanded to take in pharmacological trials and genetic mutations, such as those involved in hypertrophic cardiomyopathy, and study arrhythmia trigger mechanisms.

Generative adversarial networks for construction of virtual populations of mechanistic models: simulations to study Omecamtiv Mecarbil action

Biophysical models are increasingly used to gain mechanistic insights by fitting and reproducing experimental and clinical data. The inherent variability in the recorded datasets, however, presents a key challenge. In this study, we present a novel approach, which integrates mechanistic modeling and machine learning to analyze in vitro cardiac mechanics data and solve the inverse problem of model parameter inference. We designed a novel generative adversarial network (GAN) and employed it to construct virtual populations of cardiac ventricular myocyte models in order to study the action of Omecamtiv Mecarbil (OM), a positive cardiac inotrope. Populations of models were calibrated from mechanically unloaded myocyte shortening recordings obtained in experiments on rat myocytes in the presence and absence of OM. The GAN was able to infer model parameters while incorporating prior information about which model parameters OM targets. The generated populations of models reproduced variations in myocyte contraction recorded during in vitro experiments and provided improved understanding of OM’s mechanism of action. Inverse mapping of the experimental data using our approach suggests a novel action of OM, whereby it modifies interactions between myosin and tropomyosin proteins. To validate our approach, the inferred model parameters were used to replicate other in vitro experimental protocols, such as skinned preparations demonstrating an increase in calcium sensitivity and a decrease in the Hill coefficient of the force–calcium (F–Ca) curve under OM action. Our approach thereby facilitated the identification of the mechanistic underpinnings of experimental observations and the exploration of different hypotheses regarding variability in this complex biological system.

Passive myocardial mechanical properties: meaning, measurement, models

Passive mechanical tissue properties are major determinants of myocardial contraction and relaxation and, thus, shape cardiac function. Tightly regulated, dynamically adapting throughout life, and affecting a host of cellular functions, passive tissue mechanics also contribute to cardiac dysfunction. Development of treatments and early identification of diseases requires better spatio-temporal characterisation of tissue mechanical properties and their underlying mechanisms. With this understanding, key regulators may be identified, providing pathways with potential to control and limit pathological development. Methodologies and models used to assess and mimic tissue mechanical properties are diverse, and available data are in part mutually contradictory. In this review, we define important concepts useful for characterising passive mechanical tissue properties, and compare a variety of in vitro and in vivo techniques that allow one to assess tissue mechanics. We give definitions of key terms, and summarise insight into determinants of myocardial stiffness in situ. We then provide an overview of common experimental models utilised to assess the role of environmental stiffness and composition, and its effects on cardiac cell and tissue function. Finally, promising future directions are outlined.

Loss of crossbridge inhibition drives pathological cardiac hypertrophy in patients harboring the TPM1 E192K mutation

Hypertrophic cardiomyopathy (HCM) is an inherited disorder caused primarily by mutations to thick and thinfilament proteins. Although thin filament mutations are less prevalent than their oft-studied thick filament counterparts, they are frequently associated with severe patient phenotypes and can offer important insight into fundamental disease mechanisms. We have performed a detailed study of tropomyosin (TPM1) E192K, a variant of uncertain significance associated with HCM. Molecular dynamics revealed that E192K results in a more flexible TPM1 molecule, which could affect its ability to regulate crossbridges. In vitro motility assays of regulated actin filaments containing TPM1 E192K showed an overall loss of Ca2+ sensitivity. To understand these effects, we used multiscale computational models that suggested a subtle phenotype in which E192K leads to an inability to completely inhibit actin-myosin crossbridge activity at low Ca2+. To assess the physiological impact of the mutation, we generated patient-derived engineered heart tissues expressing E192K. These tissues showed disease features similar to those of the patients, including cellular hypertrophy, hypercontractility, and diastolic dysfunction. We hypothesized that excess residual crossbridge activity could be triggering cellular hypertrophy, even if the overall Ca2+ sensitivity was reduced by E192K. To test this hypothesis, the cardiac myosin-specific inhibitor mavacamten was applied to patient-derived engineered heart tissues for 4 d followed by 24 h of washout. Chronic mavacamten treatment abolished contractile differences between control and TPM1 E192K engineered heart tissues and reversed hypertrophy in cardiomyocytes. These results suggest that the TPM1 E192K mutation triggers cardiomyocyte hypertrophy by permitting excess residual crossbridge activity. These studies also provide direct evidence that myosin inhibition by mavacamten can counteract the hypertrophic effects of mutant tropomyosin.

The spatial distribution of thin filament activation influences force development and myosin activity in computational models of muscle contraction

Striated muscle contraction is initiated by Ca²⁺ binding to, and activating, thin filament regulatory units (RU) within the sarcomere, which then allows myosin cross-bridges from the opposing thick filament to bind actin and generate force. The amount of overlap between the filaments dictates how many potential cross-bridges are capable of binding, and thus how force is generated by the sarcomere. Myopathies and atrophy can impair muscle function by limiting cross-bridge interactions between the filaments, which can occur when the length of the thin filament is reduced or when RU function is disrupted. To investigate how variations in thin filament length and RU density affect ensemble cross-bridge behavior and force production, we simulated muscle contraction using a spatially explicit computational model of the half-sarcomere. Thin filament RUs were disabled either uniformly from the pointed end of the filament (to model shorter thin filament length) or randomly throughout the length of the half-sarcomere. Both uniform and random RU 'knockout' schemes decreased overall force generation during maximal and submaximal activation. The random knockout scheme also led to decreased calcium sensitivity and cooperativity of the force-pCa relationship. We also found that the rate of force development slowed with the random RU knockout, compared to the uniform RU knockout or conditions of normal RU activation. These findings imply that the relationship between RU density and force production within the sarcomere involves more complex coordination than simply the raw number of RUs available for myosin cross-bridge binding, and that the spatial pattern in which activatable RU are distributed throughout the sarcomere influences the dynamics of force production.

Biophysically detailed mathematical models of multiscale cardiac active mechanics

We propose four novel mathematical models, describing the microscopic mechanisms of force generation in the cardiac muscle tissue, which are suitable for multiscale numerical simulations of cardiac electromechanics. Such models are based on a biophysically accurate representation of the regulatory and contractile proteins in the sarcomeres. Our models, unlike most of the sarcomere dynamics models that are available in the literature and that feature a comparable richness of detail, do not require the time-consuming Monte Carlo method for their numerical approximation. Conversely, the models that we propose only require the solution of a system of PDEs and/or ODEs (the most reduced of the four only involving 20 ODEs), thus entailing a significant computational efficiency. By focusing on the two models that feature the best trade-off between detail of description and identifiability of parameters, we propose a pipeline to calibrate such parameters starting from experimental measurements available in literature. Thanks to this pipeline, we calibrate these models for room-temperature rat and for body-temperature human cells. We show, by means of numerical simulations, that the proposed models correctly predict the main features of force generation, including the steady-state force-calcium and force-length relationships, the length-dependent prolongation of twitches and increase of peak force, the force-velocity relationship. Moreover, they correctly reproduce the Frank-Starling effect, when employed in multiscale 3D numerical simulation of cardiac electromechanics.

Predicting the effects of dATP on cardiac contraction using multiscale modeling of the sarcomere

2'-deoxy-ATP (dATP) is a naturally occurring small molecule that has shown promise as a therapeutic because it significantly increases cardiac myocyte force development even at low dATP/ATP ratios. To investigate mechanisms by which dATP alters myosin crossbridge dynamics, we used Brownian dynamics simulations to calculate association rates between actin and ADP- or dADP-bound myosin. These rates were then directly incorporated in a mechanistic Monte Carlo Markov Chain model of cooperative sarcomere contraction. A unique combination of increased powerstroke and detachment rates was required to match experimental steady-state and kinetic data for dATP force production in rat cardiac myocytes when the myosin attachment rate in the model was constrained by the results of a Brownian dynamics simulation. Nearest-neighbor cooperativity was seen to contribute to, but not fully explain, the steep relationship between dATP/ATP ratio and steady-state force-development observed at lower dATP concentrations. Dynamic twitch simulations performed using measured calcium transients as inputs showed that the effects of dATP on the crossbridge alone were not sufficient to explain experimentally observed enhancement of relaxation kinetics by dATP treatment. Hence, dATP may also affect calcium handling even at low concentrations. By enabling the effects of dATP on sarcomere mechanics to be predicted, this multi-scale modeling framework may elucidate the molecular mechanisms by which dATP can have therapeutic effects on cardiac contractile dysfunction.

KBTBD13 and the ever-expanding sarcomeric universe

KBTBD13 is a protein expressed in striated muscle whose precise function is unknown. Work by de Winter et al. in this issue of the JCI provides evidence that KBTBD13 localizes to the sarcomere and can directly bind actin. A mutation in KBTBD13 that is associated with nemaline myopathy alters the protein's effects on actin, apparently increasing thin-filament stiffness and ultimately depressing contractile force and relaxation rate. We discuss here the implications of this new sarcomeric protein, some alternate explanations for the effects of KBTBD13R408C, and the advantages of using computational models to interpret functional data from muscle.

Cardiac muscle regulatory units are predicted to interact stronger than neighboring cross-bridges

Strong interactions between cross-bridges (XB) and regulatory units (RU) lead to a steep response of cardiac muscle to an increase in intracellular calcium. We developed a model to quantitatively assess the influence of different types of interactions within the sarcomere on the properties of cardiac muscle. In the model, the ensembles consisting of cross-bridge groups connected by elastic tropomyosin are introduced, and their dynamics is described by a set of partial differential equations. Through large scans in the free energy landscape, we demonstrate the different influence of RU-RU, XB-XB, and XB-RU interactions on the cooperativity coefficient of calcium binding, developed maximal force, and calcium sensitivity. The model solution was fitted to reproduce experimental data on force development during isometric contraction, shortening in physiological contraction, and ATP consumption by acto-myosin. On the basis of the fits, we quantified the free energy change introduced through RU-RU and XB-XB interactions and showed that RU-RU interaction leads to ~ 5 times larger change in the free energy profile of the reaction than XB-XB interaction. Due to the deterministic description of muscle contraction and its thermodynamic consistency, we envision that the developed model can be used to study heart muscle biophysics on tissue and organ levels.

Computational models in cardiology

The treatment of individual patients in cardiology practice increasingly relies on advanced imaging, genetic screening and devices. As the amount of imaging and other diagnostic data increases, paralleled by the greater capacity to personalize treatment, the difficulty of using the full array of measurements of a patient to determine an optimal treatment seems also to be paradoxically increasing. Computational models are progressively addressing this issue by providing a common framework for integrating multiple data sets from individual patients. These models, which are based on physiology and physics rather than on population statistics, enable computational simulations to reveal diagnostic information that would have otherwise remained concealed and to predict treatment outcomes for individual patients. The inherent need for patient-specific models in cardiology is clear and is driving the rapid development of tools and techniques for creating personalized methods to guide pharmaceutical therapy, deployment of devices and surgical interventions.

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.

Functional significance of C-terminal mobile domain of cardiac troponin I

Ca²⁺-regulation of cardiac contractility is mediated through the troponin complex, which comprises three subunits: cTnC, cTnI, and cTnT. As intracellular [Ca²⁺] increases, cTnI reduces its binding interactions with actin to primarily interact with cTnC, thereby enabling contraction. A portion of this regulatory switching involves the mobile domain of cTnI (cTnI-MD), the role of which in muscle contractility is still elusive. To study the functional significance of cTnI-MD, we engineered two cTnI constructs in which the MD was truncated to various extents: cTnI(1-167) and cTnI(1-193). These truncations were exchanged for endogenous cTnI in skinned rat papillary muscle fibers, and their influence on Ca²⁺-activated contraction and cross-bridge cycling kinetics was assessed at short (1.9 μm) and long (2.2 μm) sarcomere lengths (SLs). Our results show that the cTnI(1-167) truncation diminished the SL-induced increase in Ca²⁺-sensitivity of contraction, but not the SL-dependent increase in maximal tension, suggesting an uncoupling between the thin and thick filament contributions to length dependent activation. Compared to cTnI(WT), both truncations displayed greater Ca²⁺-sensitivity and faster cross-bridge attachment rates at both SLs. Furthermore, cTnI(1-167) slowed MgADP release rate and enhanced cross-bridge binding. Our findings imply that cTnI-MD truncations affect the blocked-to closed-state transition(s) and destabilize the closed-state position of tropomyosin.

A model of cardiac contraction based on novel measurements of tension development in human cardiomyocytes

Experimental data from human cardiac myocytes at body temperature is crucial for a quantitative understanding of clinically relevant cardiac function and development of whole-organ computational models. However, such experimental data is currently very limited. Specifically, important measurements to characterize changes in tension development in human cardiomyocytes that occur with perturbations in cell length are not available. To address this deficiency, in this study we present an experimental data set collected from skinned human cardiac myocytes, including the passive and viscoelastic properties of isolated myocytes, the steady-state force calcium relationship at different sarcomere lengths, and changes in tension following a rapid increase or decrease in length, and after constant velocity shortening. This data set is, to our knowledge, the first characterization of length and velocity-dependence of tension generation in human skinned cardiac myocytes at body temperature. We use this data to develop a computational model of contraction and passive viscoelasticity in human myocytes. Our model includes troponin C kinetics, tropomyosin kinetics, a three-state crossbridge model that accounts for the distortion of crossbridges, and the cellular viscoelastic response. Each component is parametrized using our experimental data collected in human cardiomyocytes at body temperature. Furthermore we are able to confirm that properties of length-dependent activation at 37°C are similar to other species, with a shift in calcium sensitivity and increase in maximum tension. We revise our model of tension generation in the skinned isolated myocyte to replicate reported tension traces generated in intact muscle during isometric tension, to provide a model of human tension generation for multi-scale simulations. This process requires changes to calcium sensitivity, cooperativity, and crossbridge transition rates. We apply this model within multi-scale simulations of biventricular cardiac function and further refine the parametrization within the whole organ context, based on obtaining a healthy ejection fraction. This process reveals that crossbridge cycling rates differ between skinned myocytes and intact myocytes.

A simple model of cardiac muscle for multiscale simulation: Passive mechanics, crossbridge kinetics and calcium regulation

A simple model of cardiac muscle was designed for multiscale simulation of heart mechanics. Relaxed cardiac muscle was described as a transversally isotropic hyperelastic material. Active tension caused by actin-myosin crossbridges depends on the ensemble averaged strain of myosin heads bound to actin. Calcium activation was modeled by Ca²⁺ binding to troponin-C. To account for the dependence of troponin affinity for Ca²⁺ on myosin heads strongly bound to actin, the kinetics of troponin binding to Ca²⁺ in the overlap zone of the thin and thick filaments and outside it were separated. The changes in the length of these zones during muscle shortening or lengthening were accounted for explicitly. Simplified version of the model contains only 5 ordinary differential equations (ODE). Model parameters were estimated from a limited set of experiments with skeletal and cardiac muscle. Simulations have shown that model reproduces qualitatively a number of experimental observations: steady-state force-velocity and stiffness-velocity relations; mechanical responses to step changes in muscle length or load; steep Ca²⁺-tension relationship and its dependence on sarcomere length tension (the Frank-Starling mechanism); tension, shortening and Ca²⁺-transients in twitch isometric and isotonic contractions, tension development and redevelopment upon fast change in Ca²⁺ concentration or muscle release followed by re-stretch. We believe that the model can be effectively used for modeling contraction and relaxation of the heart.

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.

Mechano-chemical Interactions in Cardiac Sarcomere Contraction: A Computational Modeling Study

We developed a model of cardiac sarcomere contraction to study the calcium-tension relationship in cardiac muscle. Calcium mediates cardiac contraction through its interactions with troponin (Tn) and subsequently tropomyosin molecules. Experimental studies have shown that a slight increase in intracellular calcium concentration leads to a rapid increase in sarcomeric tension. Though it is widely accepted that the rapid increase is not possible without the concept of cooperativity, the mechanism is debated. We use the hypothesis that there exists a base level of cooperativity intrinsic to the thin filament that is boosted by mechanical tension, i.e. a high level of mechanical tension in the thin filament impedes the unbinding of calcium from Tn. To test these hypotheses, we developed a computational model in which a set of three parameters and inputs of calcium concentration and sarcomere length result in output tension. Tension as simulated appeared in good agreement with experimentally measured tension. Our results support the hypothesis that high tension in the thin filament impedes Tn deactivation by increasing the energy required to detach calcium from the Tn. Given this hypothesis, the model predicted that the areas with highest tension, i.e. closest to the Z-disk end of the single overlap region, show the largest concentration of active Tn's.

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.

Modeling calcium regulation of contraction, energetics, signaling, and transcription in the cardiac myocyte

Calcium (Ca(2+)) plays many important regulatory roles in cardiac muscle cells. In the initial phase of the action potential, influx of Ca(2+) through sarcolemmal voltage-gated L-type Ca(2+) channels (LCCs) acts as a feed-forward signal that triggers a large release of Ca(2+) from the junctional sarcoplasmic reticulum (SR). This Ca(2+) drives heart muscle contraction and pumping of blood in a process known as excitation-contraction coupling (ECC). Triggered and released Ca(2+) also feed back to inactivate LCCs, attenuating the triggered Ca(2+) signal once release has been achieved. The process of ECC consumes large amounts of ATP. It is now clear that in a process known as excitation-energetics coupling, Ca(2+) signals exert beat-to-beat regulation of mitochondrial ATP production that closely couples energy production with demand. This occurs through transport of Ca(2+) into mitochondria, where it regulates enzymes of the tricarboxylic acid cycle. In excitation-signaling coupling, Ca(2+) activates a number of signaling pathways in a feed-forward manner. Through effects on their target proteins, these interconnected pathways regulate Ca(2+) signals in complex ways to control electrical excitability and contractility of heart muscle. In a process known as excitation-transcription coupling, Ca(2+) acting primarily through signal transduction pathways also regulates the process of gene transcription. Because of these diverse and complex roles, experimentally based mechanistic computational models are proving to be very useful for understanding Ca(2+) signaling in the cardiac myocyte.