Quantitative systems modeling aims to integrate knowledge in different research areas with models describing biological mechanisms and dynamics to gain a better understanding of complex clinical syndromes. Heart failure (HF) is a chronic complex cardiac disease that results from structural or functional disorders impairing the ability of the ventricle to fill with or eject blood. Highly interactive and dynamic changes in mechanical, structural, neurohumoral, metabolic, and electrophysiological properties collectively predispose the failing heart to cardiac arrhythmias, which are responsible for about a half of HF deaths. Multiscale cardiac modeling and simulation integrate structural and functional data from HF experimental models and patients to improve our mechanistic understanding of this complex arrhythmia syndrome. In particular, they allow investigating how disease-induced remodeling alters the coupling of electrophysiology, Ca²⁺ and Na⁺ handling, contraction, and energetics that lead to rhythm derangements. The Ca²⁺ /calmodulin-dependent protein kinase II, which expression and activity are enhanced in HF, emerges as a critical hub that modulates the feedbacks between these various subsystems and promotes arrhythmogenesis. This article is categorized under: Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Mechanistic Models Models of Systems Properties and Processes > Cellular Models Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models.

Population-based computational approaches have been developed in recent years and helped to gain insight into arrhythmia mechanisms, and intra- and inter-patient variability (e.g., in drug responses). Here, we illustrate the use of multivariable logistic regression to analyze the factors that enhance or reduce the susceptibility to cellular arrhythmogenic events. As an example, we generate 1000 model variants by randomly modifying ionic conductances and maximal rates of ion transports in our atrial myocyte model and simulate an arrhythmia-provoking protocol that enhances early afterdepolarization (EAD) proclivity. We then treat EAD occurrence as a categorical, yes or no variable, and perform logistic regression to relate perturbations in model parameters to the presence/absence of EADs. We find that EAD formation is sensitive to the conductance of the voltage-gated Na⁺, the acetylcholine-sensitive and ultra-rapid K⁺ channels, and the Na⁺/Ca²⁺ exchange current, which matches our mechanistic understanding of the process and preliminary sensitivity analysis. The described technique: •allows investigating the factors underlying dichotomous outcomes, and is therefore a useful tool improve our understanding of arrhythmic risk;•is valid for analyzing both deterministic and stochastic models, and various phenomena (e.g., delayed afterdepolarizations and Ca²⁺ sparks);•is computationally more efficient than one-at-a-time parameter sensitivity analysis.

The cardiac voltage gated Ca(2+) current (ICa) is critical to the electrophysiological properties, excitation-contraction coupling, mitochondrial energetics, and transcriptional regulation in heart. Thus, it is not surprising that cardiac ICa is regulated by numerous pathways. This review will focus on changes in ICa that occur during the cardiac action potential (AP), with particular attention to Ca(2+)-dependent inactivation (CDI), Ca(2+)-dependent facilitation (CDF) and how calmodulin (CaM) and Ca(2+)-CaM dependent protein kinase (CaMKII) participate in the regulation of Ca(2+) current during the cardiac AP. CDI depends on CaM pre-bound to the C-terminal of the L-type Ca(2+) channel, such that Ca(2+) influx and Ca(2+) released from the sarcoplasmic reticulum bind to that CaM and cause CDI. In cardiac myocytes CDI normally pre-dominates over voltage-dependent inactivation. The decrease in ICa via CDI provides direct negative feedback on the overall Ca(2+) influx during a single beat, when myocyte Ca(2+) loading is high. CDF builds up over several beats, depends on CaMKII-dependent Ca(2+) channel phosphorylation, and results in a staircase of increasing ICa peak, with progressively slower inactivation. CDF and CDI co-exist and in combination may fine-tune the ICa waveform during the cardiac AP. CDF may partially compensate for the tendency for Ca(2+) channel availability to decrease at higher heart rates because of accumulating inactivation. CDF may also allow some reactivation of ICa during long duration cardiac APs, and contribute to early afterdepolarizations, a form of triggered arrhythmias.

In cardiac electrophysiology, there exist many sources of inter- and intra-personal variability. These include variability in conditions and environment, and genotypic and molecular diversity, including differences in expression and behavior of ion channels and transporters, which lead to phenotypic diversity (e.g., variable integrated responses at the cell, tissue, and organ levels). These variabilities play an important role in progression of heart disease and arrhythmia syndromes and outcomes of therapeutic interventions. Yet, the traditional in silico framework for investigating cardiac arrhythmias is built upon a parameter/property-averaging approach that typically overlooks the physiological diversity. Inspired by work done in genetics and neuroscience, new modeling frameworks of cardiac electrophysiology have been recently developed that take advantage of modern computational capabilities and approaches, and account for the variance in the biological data they are intended to illuminate. In this review, we outline the recent advances in statistical and computational techniques that take into account physiological variability, and move beyond the traditional cardiac model-building scheme that involves averaging over samples from many individuals in the construction of a highly tuned composite model. We discuss how these advanced methods have harnessed the power of big (simulated) data to study the mechanisms of cardiac arrhythmias, with a special emphasis on atrial fibrillation, and improve the assessment of proarrhythmic risk and drug response. The challenges of using in silico approaches with variability are also addressed and future directions are proposed.

The K_V1.5 potassium channel, which underlies the ultra-rapid delayed-rectifier current (I_Kur) and is predominantly expressed in atria vs. ventricles, has emerged as a promising target to treat atrial fibrillation (AF). However, while numerous K_V1.5-selective compounds have been screened, characterized, and tested in various animal models of AF, evidence of antiarrhythmic efficacy in humans is still lacking. Moreover, current guidelines for pre-clinical assessment of candidate drugs heavily rely on steady-state concentration-response curves or IC₅₀ values, which can overlook adverse cardiotoxic effects. We sought to investigate the effects of kinetics and state-dependent binding of I_Kur-targeting drugs on atrial electrophysiology in silico and reveal the ideal properties of I_Kur blockers that maximize anti-AF efficacy and minimize pro-arrhythmic risk. To this aim, we developed a new Markov model of I_Kur that describes K_V1.5 gating based on experimental voltage-clamp data in atrial myocytes from patient right-atrial samples in normal sinus rhythm. We extended the I_Kur formulation to account for state-specificity and kinetics of K_V1.5-drug interactions and incorporated it into our human atrial cell model. We simulated 1- and 3-Hz pacing protocols in drug-free conditions and with a [drug] equal to the IC₅₀ value. The effects of binding and unbinding kinetics were determined by examining permutations of the forward (k_on) and reverse (k_off) binding rates to the closed, open, and inactivated states of the K_V1.5 channel. We identified a subset of ideal drugs exhibiting anti-AF electrophysiological parameter changes at fast pacing rates (effective refractory period prolongation), while having little effect on normal sinus rhythm (limited action potential prolongation). Our results highlight that accurately accounting for channel interactions with drugs, including kinetics and state-dependent binding, is critical for developing safer and more effective pharmacological anti-AF options.

Current pharmacological therapy against atrial fibrillation (AF), the most common cardiac arrhythmia, is limited by moderate efficacy and adverse side effects including ventricular proarrhythmia and organ toxicity. One way to circumvent the former is to target ion channels that are predominantly expressed in atria vs. ventricles, such as K_V1.5, carrying the ultra-rapid delayed-rectifier K⁺ current (I_Kur). Recently, we used an in silico strategy to define optimal K_V1.5-targeting drug characteristics, including kinetics and state-dependent binding, that maximize AF-selectivity in human atrial cardiomyocytes in normal sinus rhythm (nSR). However, because of evidence for I_Kur being strongly diminished in long-standing persistent (chronic) AF (cAF), the therapeutic potential of drugs targeting I_Kur may be limited in cAF patients. Here, we sought to simulate the efficacy (and safety) of I_Kur inhibitors in cAF conditions. To this end, we utilized sensitivity analysis of our human atrial cardiomyocyte model to assess the importance of I_Kur for atrial cardiomyocyte electrophysiological properties, simulated hundreds of theoretical drugs to reveal those exhibiting anti-AF selectivity, and compared the results obtained in cAF with those in nSR. We found that despite being downregulated, I_Kur contributes more prominently to action potential (AP) and effective refractory period (ERP) duration in cAF vs. nSR, with ideal drugs improving atrial electrophysiology (e.g., ERP prolongation) more in cAF than in nSR. Notably, the trajectory of the AP during cAF is such that more I_Kur is available during the more depolarized plateau potential. Furthermore, I_Kur block in cAF has less cardiotoxic effects (e.g., AP duration not exceeding nSR values) and can increase Ca²⁺ transient amplitude thereby enhancing atrial contractility. We propose that in silico strategies such as that presented here should be combined with in vitro and in vivo assays to validate model predictions and facilitate the ongoing search for novel agents against AF.

Aims

Atrial fibrillation (AF), the most prevalent clinical arrhythmia, is associated with atrial remodelling manifesting as acute and chronic alterations in expression, function, and regulation of atrial electrophysiological and Ca2+-handling processes. These AF-induced modifications crosstalk and propagate across spatial scales creating a complex pathophysiological network, which renders AF resistant to existing pharmacotherapies that predominantly target transmembrane ion channels. Developing innovative therapeutic strategies requires a systems approach to disentangle quantitatively the pro-arrhythmic contributions of individual AF-induced alterations.

Methods and results

Here, we built a novel computational framework for simulating electrophysiology and Ca2+-handling in human atrial cardiomyocytes and tissues, and their regulation by key upstream signalling pathways [i.e. protein kinase A (PKA), and Ca2+/calmodulin-dependent protein kinase II (CaMKII)] involved in AF-pathogenesis. Populations of atrial cardiomyocyte models were constructed to determine the influence of subcellular ionic processes, signalling components, and regulatory networks on atrial arrhythmogenesis. Our results reveal a novel synergistic crosstalk between PKA and CaMKII that promotes atrial cardiomyocyte electrical instability and arrhythmogenic triggered activity. Simulations of heterogeneous tissue demonstrate that this cellular triggered activity is further amplified by CaMKII- and PKA-dependent alterations of tissue properties, further exacerbating atrial arrhythmogenesis.

Conclusions

Our analysis reveals potential mechanisms by which the stress-associated adaptive changes turn into maladaptive pro-arrhythmic triggers at the cellular and tissue levels and identifies potential anti-AF targets. Collectively, our integrative approach is powerful and instrumental to assemble and reconcile existing knowledge into a systems network for identifying novel anti-AF targets and innovative approaches moving beyond the traditional ion channel-based strategy.

Despite evidence that women are at higher risk of drug-induced torsade de pointes and sudden cardiac death, female sex is vastly underrepresented in cardiovascular research, thus limiting our fundamental understanding of sex-specific arrhythmia mechanisms and our ability to predict arrhythmia propensity. To address this urgent clinical and preclinical need, we developed a quantitative tool that predicts the electrophysiological response to drug administration in female cardiomyocytes starting from data collected in males. We demonstrate the suitability of our translator for sex-specific cardiac safety assessment and include proof-of-concept application of our translator to in vitro and in vivo data.