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The cAMP/PKA pathway is a fundamental regulator of excitation-contraction coupling in cardiomyocytes. Activation of cAMP has a variety of downstream effects on cardiac function including enhanced contraction, accelerated relaxation, adaptive stress response, mitochondrial regulation, and gene transcription. Experimental advances have shed light on the compartmentation of cAMP and PKA, which allow for control over the varied targets of these second messengers and is disrupted in heart failure conditions. Computational modeling is an important tool for understanding the spatial and temporal complexities of this system. In this review article, we outline the advances in computational modeling that have allowed for deeper understanding of cAMP/PKA dynamics in the cardiomyocyte in health and disease, and explore new modeling frameworks that may bring us closer to a more complete understanding of this system. We outline various compartmental and spatial signaling models that have been used to understand how β-adrenergic signaling pathways function in a variety of simulation conditions. We also discuss newer subcellular models of cardiovascular function that may be used as templates for the next phase of computational study of cAMP and PKA in the heart, and outline open challenges which are important to consider in future models.

2-deoxy-ATP (dATP) is a myosin activator known to improve cardiac contractile force [1]. In vitro studies have shown that dATP alters the calcium transient profile in addition to the kinetics of the cross-bridge cycle [2]. Furthermore, in vivo studies of transgenic mice with increased production of dATP show elevated left ventricular systolic function [3]. Pulmonary arterial hypertension (PAH) is a rare disease of the pulmonary vasculature in which pressure overload in the right ventricle results in reduced contractile function and right heart failure [4]. We hypothesize that dATP may have a therapeutic effect on PAH-induced heart failure, by improving contractile function and restoring cardiac output and ejection fraction. However, because the effects of dATP cannot easily be assessed experimentally, we propose using a computational multiscale modeling approach to predict cardiac function. By altering parameters in an existing multiscale biventricular cardiac model [5], we were able to reproduce end-systolic and end-diastolic pressures and volumes that reflect the PAH condition, as well as healthy hearts. dATP was simulated by adjusting parameters in the model at the molecular and cellular levels based on experimental data [1], allowing us to predict the effects of dATP on PAH at the organ level. Our results show that the molecular effects of dATP can increase cardiac output and restore ejection fraction in PAH conditions, though at the cost of elevated mean arterial pressure, and may provide a new approach to treating this disease. Our multiscale modeling approach paves the way for further studies mapping out cardiovascular mechanics. As novel therapeutics continue to be discovered, their application and mechanism can be further explored through these computational models.

Myocardial hypertrophy is the result of sustained perturbations to the mechanical and/or neurohormonal homeostasis of cardiac cells and is driven by integrated, multiscale biophysical and biochemical processes that are currently not well defined. In this brief review, we highlight recent computational and experimental models of cardiac hypertrophy that span mechanisms from the molecular level to the tissue level. Specifically, we focus on: (i) molecular-level models of the structural dynamics of sarcomere proteins in hypertrophic hearts, (ii) cellular-level models of excitation-contraction coupling and mechanosensitive signaling in disease-state myocytes, and (iii) organ-level models of myocardial growth kinematics and predictors thereof. Finally, we discuss how spanning these scales and combining multiple experimental/computational models will provide new information about the processes governing hypertrophy and potential methods to prevent or reverse them.

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 naturally occurring nucleotide 2-deoxy-adenosine 5'-triphosphate (dATP) can be used by cardiac muscle as an alternative energy substrate for myosin chemomechanical activity. We and others have previously shown that dATP increases contractile force in normal hearts and models of depressed systolic function, but the structural basis of these effects has remained unresolved. In this work, we combine multiple techniques to provide structural and functional information at the angstrom-nanometer and millisecond time scales, demonstrating the ability to make both structural measurements and quantitative kinetic estimates of weak actin-myosin interactions that underpin sarcomere dynamics. Exploiting dATP as a molecular probe, we assess how small changes in myosin structure translate to electrostatic-based changes in sarcomere function to augment contractility in cardiac muscle. Through Brownian dynamics simulation and computational structural analysis, we found that deoxy-hydrolysis products [2-deoxy-adenosine 5'-diphosphate (dADP) and inorganic phosphate (Pi)] bound to prepowerstroke myosin induce an allosteric restructuring of the actin-binding surface on myosin to increase the rate of cross-bridge formation. We then show experimentally that this predicted effect translates into increased electrostatic interactions between actin and cardiac myosin in vitro. Finally, using small-angle X-ray diffraction analysis of sarcomere structure, we demonstrate that the proposed increased electrostatic affinity of myosin for actin causes a disruption of the resting conformation of myosin motors, resulting in their repositioning toward the thin filament before activation. The dATP-mediated structural alterations in myosin reported here may provide insight into an improved criterion for the design or selection of small molecules to be developed as therapeutic agents to treat systolic dysfunction.

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 modelling framework may elucidate the molecular mechanisms by which dATP can have therapeutic effects on cardiac contractile dysfunction.

Mutations in cardiac troponin C (D75Y, E59D, and G159D), a key regulatory protein of myofilament contraction, have been associated with dilated cardiomyopathy (DCM). Despite reports of altered myofilament function in these mutants, the underlying molecular alterations caused by these mutations remain elusive. Here we investigate in silico the intramolecular mechanisms by which these mutations affect myofilament contraction. On the basis of the location of cardiac troponin C (cTnC) mutations, we tested the hypothesis that intramolecular effects can explain the altered myofilament calcium sensitivity of force development for D75Y and E59D cTnC, whereas altered cardiac troponin C-troponin I (cTnC-cTnI) interaction contributes to the reported contractile effects of the G159D mutation. We employed a multiscale approach combining molecular dynamics (MD) and Brownian dynamics (BD) simulations to estimate cTnC calcium association and hydrophobic patch opening. We then integrated these parameters into a Markov model of myofilament activation to compute the steady-state force-pCa relationship. The analysis showed that myofilament calcium sensitivity with D75Y and E59D can be explained by changes in calcium binding affinity of cTnC and the rate of hydrophobic patch opening, if a partial cTnC interhelical opening angle (110°) is sufficient for cTnI switch peptide association to cTnC. In contrast, interactions between cTnC and cTnI within the cardiac troponin complex must also be accounted for to explain contractile alterations due to G159D. In conclusion, this is the first multiscale in silico study to elucidate how direct molecular effects of genetic mutations in cTnC translate to altered myofilament contractile function.

Although Ca^(2+) 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 Ca^(2+)-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 ΔG_(CIA), the energy barrier for activating a thin filament regulatory unit in the absence of Ca^(2+). Using this estimate of ΔG_(CIA) 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 Ca^(2+) 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 Ca^(2+) 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 ΔG_(CIA) 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.

Dilated Cardiomyopathy (DCM) is a leading cause of sudden cardiac death characterized by impaired pump function and dilatation of cardiac ventricles. In this review we discuss various in silico approaches to elucidating the mechanisms of genetic mutations leading to DCM. The approaches covered in this review focus on bridging the spatial and temporal gaps that exist between molecular and cellular processes. Mutations in sarcomeric regulatory thin filament proteins such as the troponin complex (cTn) and Tropomyosin (Tm) have been associated with DCM. Despite the experimentally-observed myofilament measures of contractility in the case of these mutations, the mechanisms by which the underlying molecular changes and protein interactions scale up to organ failure by these mutations remains elusive. The review highlights multi-scale modeling approaches and their applicability to study the effects of sarcomeric gene mutations in-silico. We discuss some of the insights that can be gained from computational models of cardiac biomechanics when scaling from molecular states to cellular level.

Conceptual and computational models have generally assumed that each regulatory unit (RU) of the thin filament remains in the blocked state until Ca2+ binds to troponin C. This includes our previous model (Campbell et al., Biophys J 98:2254, 2010), which simultaneously recapitulated key attributes of myofilament activation. However, the model failed to fully reproduce exchange experiments in which some fraction of myofilament troponin C is replaced with a non-Ca2+ binding mutant (xTnC). In simulations, xTnC caused much greater reductions in tension than were shown experimentally (Gillis et al., J Physiol 580:561, 2007). This effect was caused by the assumption of strong cooperative inhibition among nearest-neighbor RUs, which was required to produce basic myofilament activation behavior. We hypothesized that permitting some Ca2+-independent RU activation while maintaining cooperative inhibition would reconcile this discrepancy. In a new model, blocked-to-closed RU transitions were allowed without bound Ca2+ but at greater energetic cost (ΔG). Monte Carlo simulations showed that reducing ΔG to a finite value of 4.7 kJ/mol maintained cooperative myofilament activation while reproducing xTnC experiments (Figure). These results suggest that thin filament function does not require perfect Ca2+ switch fidelity.View Large Image | View Hi-Res Image | Download PowerPoint Slide