A multiscale computational model of spatially resolved calcium cycling in cardiac myocytes: from detailed cleft dynamics to the whole cell concentration profiles

T cell Ca2+ microdomains through the lens of computational modeling

Cellular Ca2+ signaling is highly organized in time and space. Locally restricted and short-lived regions of Ca2+ increase, called Ca2+ microdomains, constitute building blocks that are differentially arranged to create cellular Ca2+ signatures controlling physiological responses. Here, we focus on Ca2+ microdomains occurring in restricted cytosolic spaces between the plasma membrane and the endoplasmic reticulum, called endoplasmic reticulum-plasma membrane junctions. In T cells, these microdomains have been finely characterized. Enough quantitative data are thus available to develop detailed computational models of junctional Ca2+ dynamics. Simulations are able to predict the characteristics of Ca2+ increases at the level of single channels and in junctions of different spatial configurations, in response to various signaling molecules. Thanks to the synergy between experimental observations and computational modeling, a unified description of the molecular mechanisms that create Ca2+ microdomains in the first seconds of T cell stimulation is emerging.

The ryanodine receptor microdomain in cardiomyocytes

The ryanodine receptor type 2 (RyR) is a key player in Ca2+ handling during excitation-contraction coupling. During each heartbeat, RyR channels are responsible for linking the action potential with the contractile machinery of the cardiomyocyte by releasing Ca2+ from the sarcoplasmic reticulum. RyR function is fine-tuned by associated signalling molecules, arrangement in clusters and subcellular localization. These parameters together define RyR function within microdomains and are subject to disease remodelling. This review describes the latest findings on RyR microdomain organization, the alterations with disease which result in increased subcellular heterogeneity and emergence of microdomains with enhanced arrhythmogenic potential, and presents novel technologies that guide future research to study and target RyR channels within specific microdomains.

IP3R activity increases propensity of RyR-mediated sparks by elevating dyadic [Ca2＋]

Calcium (Ca^2＋) plays a critical role in the excitation contraction coupling (ECC) process that mediates the contraction of cardiomyocytes during each heartbeat. While ryanodine receptors (RyRs) are the primary Ca^2＋ channels responsible for generating the cell-wide Ca^2＋ transients during ECC, Ca^2＋ release, via inositol 1,4,5-trisphosphate (IP₃) receptors (IP₃Rs) are also reported in cardiomyocytes to elicit ECC-modulating effects. Recent studies suggest that the localization of IP₃Rs at dyads grant their ability to modify the occurrence of Ca^2＋ sparks (elementary Ca^2＋ release events that constitute cell wide Ca^2＋ releases associated with ECC) which may underlie their modulatory influence on ECC. Here, we aim to uncover the mechanism by which dyad-localized IP₃Rs influence Ca^2＋ spark dynamics. To this end, we developed a mathematical model of the dyad that incorporates the behaviour of IP₃Rs, in addition to RyRs, to reveal the impact of their activity on local Ca^2＋ handling and consequent Ca^2＋ spark occurrence and its properties. Consistent with published experimental data, our model predicts that the propensity for Ca^2＋ spark formation increases in the presence of IP₃R activity. Our simulations support the hypothesis that IP₃Rs elevate Ca^2＋ in the dyad, sensitizing proximal RyRs towards activation and hence Ca^2＋ spark formation. The stochasticity of IP₃R gating is an important aspect of this mechanism. However, dyadic IP₃R activity lowers the Ca^2＋ available in the junctional sarcoplasmic reticulum (JSR) for release, thus resulting in Ca^2＋ sparks with similar durations but lower amplitudes.

Ca2+ Release via IP3 Receptors Shapes the Cardiac Ca2+ Transient for Hypertrophic Signaling

Calcium (Ca²⁺) plays a central role in mediating both contractile function and hypertrophic signaling in ventricular cardiomyocytes. L-type Ca²⁺ channels trigger release of Ca²⁺ from ryanodine receptors for cellular contraction, whereas signaling downstream of G-protein-coupled receptors stimulates Ca²⁺ release via inositol 1,4,5-trisphosphate receptors (IP₃Rs), engaging hypertrophic signaling pathways. Modulation of the amplitude, duration, and duty cycle of the cytosolic Ca²⁺ contraction signal and spatial localization have all been proposed to encode this hypertrophic signal. Given current knowledge of IP₃Rs, we develop a model describing the effect of functional interaction (cross talk) between ryanodine receptor and IP₃R channels on the Ca²⁺ transient and examine the sensitivity of the Ca²⁺ transient shape to properties of IP₃R activation. A key result of our study is that IP₃R activation increases Ca²⁺ transient duration for a broad range of IP₃R properties, but the effect of IP₃R activation on Ca²⁺ transient amplitude is dependent on IP₃ concentration. Furthermore we demonstrate that IP₃-mediated Ca²⁺ release in the cytosol increases the duty cycle of the Ca²⁺ transient, the fraction of the cycle for which [Ca²⁺] is elevated, across a broad range of parameter values and IP₃ concentrations. When coupled to a model of downstream transcription factor (NFAT) activation, we demonstrate that there is a high correspondence between the Ca²⁺ transient duty cycle and the proportion of activated NFAT in the nucleus. These findings suggest increased cytosolic Ca²⁺ duty cycle as a plausible mechanism for IP₃-dependent hypertrophic signaling via Ca²⁺-sensitive transcription factors such as NFAT in ventricular cardiomyocytes.

Multi-scale approaches for the simulation of cardiac electrophysiology: I - Sub-cellular and stochastic calcium dynamics from cell to organ

Computational models of the heart at multiple spatial scales, from sub-cellular nanodomains to the whole-organ, are a powerful tool for the simulation of cardiac electrophysiology. Application of these models has provided remarkable insight into the normal and pathological functioning of the heart. In these two articles, we present methods for modelling cardiac electrophysiology at all of these spatial scales. In part one, presented here, we discuss methods and approaches for modelling sub-cellular calcium dynamics at the whole-cell and organ scales, valuable for modelling excitation-contraction coupling and mechanisms of arrhythmia triggers.

Multiscale Modeling of Dyadic Structure-Function Relation in Ventricular Cardiac Myocytes

Cardiovascular disease is often related to defects of subcellular components in cardiac myocytes, specifically in the dyadic cleft, which include changes in cleft geometry and channel placement. Modeling of these pathological changes requires both spatially resolved cleft as well as whole cell level descriptions. We use a multiscale model to create dyadic structure-function relationships to explore the impact of molecular changes on whole cell electrophysiology and calcium cycling. This multiscale model incorporates stochastic simulation of individual L-type calcium channels and ryanodine receptor channels, spatially detailed concentration dynamics in dyadic clefts, rabbit membrane potential dynamics, and a system of partial differential equations for myoplasmic and lumenal free Ca²⁺ and Ca²⁺-binding molecules in the bulk of the cell. We found action potential duration, systolic, and diastolic [Ca²⁺] to respond most sensitively to changes in L-type calcium channel current. The ryanodine receptor channel cluster structure inside dyadic clefts was found to affect all biomarkers investigated. The shape of clusters observed in experiments by Jayasinghe et al. and channel density within the cluster (characterized by mean occupancy) showed the strongest correlation to the effects on biomarkers.

NCX-Mediated Subcellular Ca2+ Dynamics Underlying Early Afterdepolarizations in LQT2 Cardiomyocytes

Long QT syndrome type 2 (LQT2) is a congenital disease characterized by loss of function mutations in hERG potassium channels (I_Kr). LQT2 is associated with fatal ventricular arrhythmias promoted by triggered activity in the form of early afterdepolarizations (EADs). We previously demonstrated that intracellular Ca²⁺ handling is remodeled in LQT2 myocytes. Remodeling leads to aberrant late RyR-mediated Ca²⁺ releases that drive forward-mode Na⁺-Ca²⁺ exchanger (NCX) current and slow repolarization to promote reopening of L-type calcium channels and EADs. Forward-mode NCX was found to be enhanced despite the fact that these late releases do not significantly alter the whole-cell cytosolic calcium concentration during a vulnerable period of phase 2 of the action potential corresponding to the onset of EADs. Here, we use a multiscale ventricular myocyte model to explain this finding. We show that because the local NCX current is a saturating nonlinear function of the local submembrane calcium concentration, a larger number of smaller-amplitude discrete Ca²⁺ release events can produce a large increase in whole-cell forward-mode NCX current without increasing significantly the whole-cell cytosolic calcium concentration. Furthermore, we develop novel insights, to our knowledge, into how alterations of stochastic RyR activity at the single-channel level cause late aberrant Ca²⁺ release events. Experimental measurements in transgenic LTQ2 rabbits confirm the critical arrhythmogenic role of NCX and identify this current as a potential target for antiarrhythmic therapies in LQT2.

Human T cells in silico: Modelling dynamic intracellular calcium and its influence on cellular electrophysiology

A network of ion currents influences basic cellular T cell functions. After T cell receptor activation, changes in highly regulated calcium levels play a central role in triggering effector functions and cell differentiation. A dysregulation of these processes might be involved in the pathogenesis of several diseases. We present a mathematical model based on the NEURON simulation environment that computes dynamic calcium levels in combination with the current output of diverse ion channels (K_V1.3, K_Ca3.1, K_2P channels (TASK1-3, TRESK), VRAC, TRPM7, CRAC). In line with experimental data, the simulation shows a strong increase in intracellular calcium after T cell receptor stimulation before reaching a new, elevated calcium plateau in the T cell's activated state. Deactivation of single ion channel modules, mimicking the application of channel blockers, reveals that two types of potassium channels are the main regulators of intracellular calcium level: calcium-dependent potassium (K_Ca3.1) and two-pore-domain potassium (K_2P) channels.

Studying dyadic structure-function relationships: a review of current modeling approaches and new insights into Ca2+ (mis)handling

Excitation–contraction coupling in cardiac myocytes requires calcium influx through L-type calcium channels in the sarcolemma, which gates calcium release through sarcoplasmic reticulum ryanodine receptors in a process known as calcium-induced calcium release, producing a myoplasmic calcium transient and enabling cardiomyocyte contraction. The spatio-temporal dynamics of calcium release, buffering, and reuptake into the sarcoplasmic reticulum play a central role in excitation–contraction coupling in both normal and diseased cardiac myocytes. However, further quantitative understanding of these cells’ calcium machinery and the study of mechanisms that underlie both normal cardiac function and calcium-dependent etiologies in heart disease requires accurate knowledge of cardiac ultrastructure, protein distribution and subcellular function. As current imaging techniques are limited in spatial resolution, limiting insight into changes in calcium handling, computational models of excitation–contraction coupling have been increasingly employed to probe these structure–function relationships. This review will focus on the development of structural models of cardiac calcium dynamics at the subcellular level, orienting the reader broadly towards the development of models of subcellular calcium handling in cardiomyocytes. Specific focus will be given to progress in recent years in terms of multi-scale modeling employing resolved spatial models of subcellular calcium machinery. A review of the state-of-the-art will be followed by a review of emergent insights into calcium-dependent etiologies in heart disease and, finally, we will offer a perspective on future directions for related computational modeling and simulation efforts.

Stochastic initiation and termination of calcium-mediated triggered activity in cardiac myocytes

Cardiac myocytes normally initiate action potentials in response to a current stimulus that depolarizes the membrane above an excitation threshold. Aberrant excitation can also occur due to spontaneous calcium (Ca²⁺) release (SCR) from intracellular stores after the end of a preceding action potential. SCR drives the Na⁺/Ca²⁺ exchange current inducing a "delayed afterdepolarization" that can in turn trigger an action potential if the excitation threshold is reached. This "triggered activity" is known to cause arrhythmias, but how it is initiated and terminated is not understood. Using computer simulations of a ventricular myocyte model, we show that initiation and termination are inherently random events. We determine the probability of those events from statistical measurements of the number of beats before initiation and before termination, respectively, which follow geometric distributions. Moreover, we elucidate the origin of randomness by a statistical analysis of SCR events, which do not follow a Poisson process observed in other eukaryotic cells. Due to synchronization of Ca²⁺ releases during the action potential upstroke, waiting times of SCR events after the upstroke are narrowly distributed, whereas SCR amplitudes follow a broad normal distribution with a width determined by fluctuations in the number of independent Ca²⁺ wave foci. This distribution enables us to compute the probabilities of initiation and termination of bursts of triggered activity that are maintained by a positive feedback between the action potential upstroke and SCR. Our results establish a theoretical framework for interpreting complex and varied manifestations of triggered activity relevant to cardiac arrhythmias.

Computational cardiology and risk stratification for sudden cardiac death: one of the grand challenges for cardiology in the 21st century

Risk stratification in the context of sudden cardiac death has been acknowledged as one of the major challenges facing cardiology for the past four decades. In recent years, the advent of high performance computing has facilitated organ-level simulation of the heart, meaning we can now examine the causes, mechanisms and impact of cardiac dysfunction in silico. As a result, computational cardiology, largely driven by the Physiome project, now stands at the threshold of clinical utility in regards to risk stratification and treatment of patients at risk of sudden cardiac death. In this white paper, we outline a roadmap of what needs to be done to make this translational step, using the relatively well-developed case of acquired or drug-induced long QT syndrome as an exemplar case.