Parameter sensitivity analysis in electrophysiological models using multivariable regression

Creating cell-specific computational models of stem cell-derived cardiomyocytes using optical experiments

Human induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs) have gained traction as a powerful model in cardiac disease and therapeutics research, since iPSCs are self-renewing and can be derived from healthy and diseased patients without invasive surgery. However, current iPSC-CM differentiation methods produce cardiomyocytes with immature, fetal-like electrophysiological phenotypes, and the variety of maturation protocols in the literature results in phenotypic differences between labs. Heterogeneity of iPSC donor genetic backgrounds contributes to additional phenotypic variability. Several mathematical models of iPSC-CM electrophysiology have been developed to help to predict cell responses, but these models individually do not capture the phenotypic variability observed in iPSC-CMs. Here, we tackle these limitations by developing a computational pipeline to calibrate cell preparation-specific iPSC-CM electrophysiological parameters. We used the genetic algorithm (GA), a heuristic parameter calibration method, to tune ion channel parameters in a mathematical model of iPSC-CM physiology. To systematically optimize an experimental protocol that generates sufficient data for parameter calibration, we created in silico datasets by simulating various protocols applied to a population of models with known conductance variations, and then fitted parameters to those datasets. We found that calibrating to voltage and calcium transient data under 3 varied experimental conditions, including electrical pacing combined with ion channel blockade and changing buffer ion concentrations, improved model parameter estimates and model predictions of unseen channel block responses. This observation also held when the fitted data were normalized, suggesting that normalized fluorescence recordings, which are more accessible and higher throughput than patch clamp recordings, could sufficiently inform conductance parameters. Therefore, this computational pipeline can be applied to different iPSC-CM preparations to determine cell line-specific ion channel properties and understand the mechanisms behind variability in perturbation responses.

Sinoatrial node heterogeneity and fibroblasts increase atrial driving capability in a two-dimensional human computational model

Background: Cardiac pacemaking remains an unsolved matter from many perspectives. Extensive experimental and computational studies have been performed to describe the sinoatrial physiology across different scales, from the molecular to clinical levels. Nevertheless, the mechanism by which a heartbeat is generated inside the sinoatrial node and propagated to the working myocardium is not fully understood at present. This work aims to provide quantitative information about this fascinating phenomenon, especially regarding the contributions of cellular heterogeneity and fibroblasts to sinoatrial node automaticity and atrial driving. Methods: We developed a bidimensional computational model of the human right atrial tissue, including the sinoatrial node. State-of-the-art knowledge of the anatomical and physiological aspects was adopted during the design of the baseline tissue model. The novelty of this study is the consideration of cellular heterogeneity and fibroblasts inside the sinoatrial node for investigating the manner by which they tune the robustness of stimulus formation and conduction under different conditions (baseline, ionic current blocks, autonomic modulation, and external high-frequency pacing). Results: The simulations show that both heterogeneity and fibroblasts significantly increase the safety factor for conduction by more than 10% in almost all the conditions tested and shorten the sinus node recovery time after overdrive suppression by up to 60%. In the human model, especially under challenging conditions, the fibroblasts help the heterogeneous myocytes to synchronise their rate (e.g. -82% inσ C L under 25 nM of acetylcholine administration) and capture the atrium (with 25% L-type calcium current block). However, the anatomical and gap junctional coupling aspects remain the most important model parameters that allow effective atrial excitations. Conclusion: Despite the limitations to the proposed model, this work suggests a quantitative explanation to the astonishing overall heterogeneity shown by the sinoatrial node.

Computational modeling of cardiac electrophysiology and arrhythmogenesis: toward clinical translation

The complexity of cardiac electrophysiology, involving dynamic changes in numerous components across multiple spatial (from ion channel to organ) and temporal (from milliseconds to days) scales, makes an intuitive or empirical analysis of cardiac arrhythmogenesis challenging. Multiscale mechanistic computational models of cardiac electrophysiology provide precise control over individual parameters, and their reproducibility enables a thorough assessment of arrhythmia mechanisms. This review provides a comprehensive analysis of models of cardiac electrophysiology and arrhythmias, from the single cell to the organ level, and how they can be leveraged to better understand rhythm disorders in cardiac disease and to improve heart patient care. Key issues related to model development based on experimental data are discussed, and major families of human cardiomyocyte models and their applications are highlighted. An overview of organ-level computational modeling of cardiac electrophysiology and its clinical applications in personalized arrhythmia risk assessment and patient-specific therapy of atrial and ventricular arrhythmias is provided. The advancements presented here highlight how patient-specific computational models of the heart reconstructed from patient data have achieved success in predicting risk of sudden cardiac death and guiding optimal treatments of heart rhythm disorders. Finally, an outlook toward potential future advances, including the combination of mechanistic modeling and machine learning/artificial intelligence, is provided. As the field of cardiology is embarking on a journey toward precision medicine, personalized modeling of the heart is expected to become a key technology to guide pharmaceutical therapy, deployment of devices, and surgical interventions.

Cell-to-cell heterogeneity in ion channel conductance impacts substrate vulnerability to arrhythmia

Determining whether an ectopic depolarization will lead to a self-perpetuating arrhythmia is of critical importance in determining arrhythmia risk, so it is necessary to understand what factors impact substrate vulnerability. This study sought to explore the impact of cell-to-cell heterogeneity in ion channel conductance on substrate vulnerability to arrhythmia by measuring the duration of the vulnerable window in computational models of one-dimensional cables of ventricular cardiomyocytes. We began by using a population of uniform cable models to determine the mechanisms underlying the vulnerable window phenomenon. We found that in addition to the known importance of GNa, the conductances GCa,L and GKr also play a minor role in determining the vulnerable window duration. We also found that a steeper slope of the repolarizing action potential during the vulnerable window correlated with a shorter vulnerable window duration in uniform cables. We applied our understanding from these initial simulations to an investigation of the vulnerable window in heterogeneous cable models. The heterogeneous cables displayed a great deal of intra-cable variation in vulnerable window duration, highly sensitive to the cardiomyocytes in the local environment of the ectopic stimulus. Coupling strength modulated not only the magnitude of the vulnerable window duration but also the extent of intra-tissue variability in vulnerable window duration.NEW & NOTEWORTHY We investigate the impact of cell-to-cell heterogeneity in ion channel conductance on substrate vulnerability to arrhythmia by measuring the vulnerable window duration in computational cardiomyocyte cable models. We demonstrate a wide range of intra-cable variability in vulnerable window duration (VWD) and show how this is changed by ion channel block and coupling strength perturbations.

Development of in-silico drug cardiac toxicity evaluation system with consideration of inter-individual variability

Safety pharmacology examines the potential for new drugs to have unusual, rare side effects such as torsade de pointes (TdP). Recently, as a part of the Comprehensive in vitro Proarrhythmia Assay (CiPA) project, techniques for predicting the development of drug-induced TdP through computer simulations have been proposed and verified. However, CiPA assessment generally does not consider the effect of cardiac cell inter-individual variability, especially related to metabolic status. The study aimed to explore whether rare proarrhythmic effects may be linked to the inter-individual variability of cardiac cells and whether incorporating this variability into computational models could alter the prediction of drugs' TdP risks. This study evaluated the contribution of two biological characteristics to the proarrhythmic effects. The first was spermine concentration, which varies with metabolic status; the second was L-type calcium permeability that could occur due to mutations. Twenty-eight drugs were examined throughout this study, and qNet was analyzed as an essential feature. Even though there were some discrepancies of TdP risk predictions from the baseline model, we found that considering the inter-individual variability might change the TdP risk of drugs. Several drugs in the high-risk drugs group were predicted to affect as intermediate and low-risk drugs in some individuals and vice versa. Also, most intermediate-risk drugs were expected to act as low-risk drugs. When compared, the effects of inter-individual variability of L-type calcium were more significant than spermine in altering the TdP risk of compounds. These results emphasize the importance of considering inter-individual variability to assess drugs.

Inferring Parameters of Pyramidal Neuron Excitability in Mouse Models of Alzheimer's Disease Using Biophysical Modeling and Deep Learning

Alzheimer's disease (AD) is believed to occur when abnormal amounts of the proteins amyloid beta and tau aggregate in the brain, resulting in a progressive loss of neuronal function. Hippocampal neurons in transgenic mice with amyloidopathy or tauopathy exhibit altered intrinsic excitability properties. We used deep hybrid modeling (DeepHM), a recently developed parameter inference technique that combines deep learning with biophysical modeling, to map experimental data recorded from hippocampal CA1 neurons in transgenic AD mice and age-matched wildtype littermate controls to the parameter space of a conductance-based CA1 model. Although mechanistic modeling and machine learning methods are by themselves powerful tools for approximating biological systems and making accurate predictions from data, when used in isolation these approaches suffer from distinct shortcomings: model and parameter uncertainty limit mechanistic modeling, whereas machine learning methods disregard the underlying biophysical mechanisms. DeepHM addresses these shortcomings by using conditional generative adversarial networks to provide an inverse mapping of data to mechanistic models that identifies the distributions of mechanistic modeling parameters coherent to the data. Here, we demonstrated that DeepHM accurately infers parameter distributions of the conductance-based model on several test cases using synthetic data generated with complex underlying parameter structures. We then used DeepHM to estimate parameter distributions corresponding to the experimental data and infer which ion channels are altered in the Alzheimer's mouse models compared to their wildtype controls at 12 and 24 months. We found that the conductances most disrupted by tauopathy, amyloidopathy, and aging are delayed rectifier potassium, transient sodium, and hyperpolarization-activated potassium, respectively.

A computational model predicts sex-specific responses to calcium channel blockers in mammalian mesenteric vascular smooth muscle

The function of the smooth muscle cells lining the walls of mammalian systemic arteries and arterioles is to regulate the diameter of the vessels to control blood flow and blood pressure. Here, we describe an in silico model, which we call the 'Hernandez-Hernandez model', of electrical and Ca2+ signaling in arterial myocytes based on new experimental data indicating sex-specific differences in male and female arterial myocytes from murine resistance arteries. The model suggests the fundamental ionic mechanisms underlying membrane potential and intracellular Ca2+ signaling during the development of myogenic tone in arterial blood vessels. Although experimental data suggest that KV1.5 channel currents have similar amplitudes, kinetics, and voltage dependencies in male and female myocytes, simulations suggest that the KV1.5 current is the dominant current regulating membrane potential in male myocytes. In female cells, which have larger KV2.1 channel expression and longer time constants for activation than male myocytes, predictions from simulated female myocytes suggest that KV2.1 plays a primary role in the control of membrane potential. Over the physiological range of membrane potentials, the gating of a small number of voltage-gated K+ channels and L-type Ca2+ channels are predicted to drive sex-specific differences in intracellular Ca2+ and excitability. We also show that in an idealized computational model of a vessel, female arterial smooth muscle exhibits heightened sensitivity to commonly used Ca2+ channel blockers compared to male. In summary, we present a new model framework to investigate the potential sex-specific impact of antihypertensive drugs.

Creating cell-specific computational models of stem cell-derived cardiomyocytes using optical experiments

Human induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs) have gained traction as a powerful model in cardiac disease and therapeutics research, since iPSCs are self-renewing and can be derived from healthy and diseased patients without invasive surgery. However, current iPSC-CM differentiation methods produce cardiomyocytes with immature, fetal-like electrophysiological phenotypes, and the variety of maturation protocols in the literature results in phenotypic differences between labs. Heterogeneity of iPSC donor genetic backgrounds contributes to additional phenotypic variability. Several mathematical models of iPSC-CM electrophysiology have been developed to help understand the ionic underpinnings of, and to simulate, various cell responses, but these models individually do not capture the phenotypic variability observed in iPSC-CMs. Here, we tackle these limitations by developing a computational pipeline to calibrate cell preparation-specific iPSC-CM electrophysiological parameters. We used the genetic algorithm (GA), a heuristic parameter calibration method, to tune ion channel parameters in a mathematical model of iPSC-CM physiology. To systematically optimize an experimental protocol that generates sufficient data for parameter calibration, we created simulated datasets by applying various protocols to a population of in silico cells with known conductance variations, and we fitted to those datasets. We found that calibrating models to voltage and calcium transient data under 3 varied experimental conditions, including electrical pacing combined with ion channel blockade and changing buffer ion concentrations, improved model parameter estimates and model predictions of unseen channel block responses. This observation held regardless of whether the fitted data were normalized, suggesting that normalized fluorescence recordings, which are more accessible and higher throughput than patch clamp recordings, could sufficiently inform conductance parameters. Therefore, this computational pipeline can be applied to different iPSC-CM preparations to determine cell line-specific ion channel properties and understand the mechanisms behind variability in perturbation responses.

A computational model predicts sex-specific responses to calcium channel blockers in mammalian mesenteric vascular smooth muscle

The function of the smooth muscle cells lining the walls of mammalian systemic arteries and arterioles is to regulate the diameter of the vessels to control blood flow and blood pressure. Here, we describe an in-silico model, which we call the "Hernandez-Hernandez model", of electrical and C a 2+ signaling in arterial myocytes based on new experimental data indicating sex-specific differences in male and female arterial myocytes from murine resistance arteries. The model suggests the fundamental ionic mechanisms underlying membrane potential and intracellular C a 2+ signaling during the development of myogenic tone in arterial blood vessels. Although experimental data suggest that KV1.5 channel currents have similar amplitudes, kinetics, and voltage dependencies in male and female myocytes, simulations suggest that the KV1.5 current is the dominant current regulating membrane potential in male myocytes. In female cells, which have larger KV2.1 channel expression and longer time constants for activation than male myocytes, predictions from simulated female myocytes suggest that KV2.1 plays a primary role in the control of membrane potential. Over the physiological range of membrane potentials, the gating of a small number of voltage-gated K+ channels and L-type C a 2+ channels are predicted to drive sex-specific differences in intracellular C a 2+ and excitability. We also show that in an idealized computational model of a vessel, female arterial smooth muscle exhibits heightened sensitivity to commonly used C a 2+ channel blockers compared to male. In summary, we present a new model framework to investigate the potential sex-specific impact of anti-hypertensive drugs.

Computational Modeling of Cardiac Electrophysiology

Mathematical modeling and simulation are well-established and powerful tools to integrate experimental data of individual components of cardiac electrophysiology, excitation-contraction coupling, and regulatory signaling pathways, to gain quantitative and mechanistic insight into pathophysiological processes and guide therapeutic strategies. Here, we briefly describe the processes governing cardiac myocyte electrophysiology and Ca2+ handling and their regulation, as well as action potential propagation in tissue. We discuss the models and methods used to describe these phenomena, including procedures for model parameterization and validation, in addition to protocols for model interrogation and analysis and techniques that account for phenotypic variability and parameter uncertainty. Our objective is to provide a summary of basic concepts and approaches as a resource for scientists training in this discipline and for all researchers aiming to gain an understanding of cardiac modeling studies.

Assessing drug safety by identifying the axis of arrhythmia in cardiomyocyte electrophysiology

Many classes of drugs can induce fatal cardiac arrhythmias by disrupting the electrophysiology of cardiomyocytes. Safety guidelines thus require all new drugs to be assessed for pro-arrhythmic risk prior to conducting human trials. The standard safety protocols primarily focus on drug blockade of the delayed-rectifier potassium current (IKr). Yet the risk is better assessed using four key ion currents (IKr, ICaL, INaL, IKs). We simulated 100,000 phenotypically diverse cardiomyocytes to identify the underlying relationship between the blockade of those currents and the emergence of ectopic beats in the action potential. We call that relationship the axis of arrhythmia. It serves as a yardstick for quantifying the arrhythmogenic risk of any drug from its profile of multi-channel block alone. We tested it on 109 drugs and found that it predicted the clinical risk labels with an accuracy of 88.1-90.8%. Pharmacologists can use our method to assess the safety of novel drugs without resorting to animal testing or unwieldy computer simulations.

Predictive Male-to-Female Translation of Cardiac Electrophysiological Response to Drugs

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.

Integrative human atrial modelling unravels interactive protein kinase A and Ca2+/calmodulin-dependent protein kinase II signalling as key determinants of atrial arrhythmogenesis

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.

Dual effects of the small-conductance Ca2+-activated K+ current on human atrial electrophysiology and Ca2+-driven arrhythmogenesis: an in silico study

By sensing changes in intracellular Ca2+, small-conductance Ca2+-activated K+ (SK) channels dynamically regulate the dynamics of the cardiac action potential (AP) on a beat-to-beat basis. Given their predominance in atria versus ventricles, SK channels are considered a promising atrial-selective pharmacological target against atrial fibrillation (AF), the most common cardiac arrhythmia. However, the precise contribution of SK current (ISK) to atrial arrhythmogenesis is poorly understood, and may potentially involve different mechanisms that depend on species, heart rates, and degree of AF-induced atrial remodeling. Both reduced and enhanced ISK have been linked to AF. Similarly, both SK channel up- and downregulation have been reported in chronic AF (cAF) versus normal sinus rhythm (nSR) patient samples. Here, we use our multiscale modeling framework to obtain mechanistic insights into the contribution of ISK in human atrial cardiomyocyte electrophysiology. We simulate several protocols to quantify how ISK modulation affects the regulation of AP duration (APD), Ca2+ transient, refractoriness, and occurrence of alternans and delayed afterdepolarizations (DADs). Our simulations show that ISK activation shortens the APD and atrial effective refractory period, limits Ca2+ cycling, and slightly increases the propensity for alternans in both nSR and cAF conditions. We also show that increasing ISK counteracts DAD development by enhancing the repolarization force that opposes the Ca2+-dependent depolarization. Taken together, our results suggest that increasing ISK in human atrial cardiomyocytes could promote reentry while protecting against triggered activity. Depending on the leading arrhythmogenic mechanism, ISK inhibition may thus be a beneficial or detrimental anti-AF strategy.NEW & NOTEWORTHY Using our established framework for human atrial myocyte simulations, we investigated the role of the small-conductance Ca2+-activated K+ current (ISK) in the regulation of cell function and the development of Ca2+-driven arrhythmias. We found that ISK inhibition, a promising atrial-selective pharmacological strategy against atrial fibrillation, counteracts the reentry-promoting abbreviation of atrial refractoriness, but renders human atrial myocytes more vulnerable to delayed afterdepolarizations, thus potentially increasing the propensity for ectopic (triggered) activity.

Uncertainty assessment of proarrhythmia predictions derived from multi-level in silico models

In silico methods can be used for an early assessment of arrhythmogenic properties of drug candidates. However, their use for decision-making is conditioned by the possibility to estimate the predictions' uncertainty. This work describes our efforts to develop uncertainty quantification methods for the predictions produced by multi-level proarrhythmia models. In silico models used in this field usually start with experimental or predicted IC50 values that describe drug-induced ion channel blockade. Using such inputs, an electrophysiological model computes how the ion channel inhibition, exerted by a drug in a certain concentration, translates to an altered shape and duration of the action potential in cardiac cells, which can be represented as arrhythmogenic risk biomarkers such as the APD90. Using this framework, we identify the main sources of aleatory and epistemic uncertainties and propose a method based on probabilistic simulations that replaces single-point estimates predicted using multiple input values, including the IC50s and the electrophysiological parameters, by distributions of values. Two selected variability types associated with these inputs are then propagated through the multi-level model to estimate their impact on the uncertainty levels in the output, expressed by means of intervals. The proposed approach yields single predictions of arrhythmogenic risk biomarkers together with value intervals, providing a more comprehensive and realistic description of drug effects on a human population. The methodology was tested by predicting arrhythmogenic biomarkers on a series of twelve well-characterised marketed drugs, belonging to different arrhythmogenic risk classes.

Multiplatform modeling of atrial fibrillation identifies phospholamban as a central regulator of cardiac rhythm

Atrial fibrillation (AF) is a common and genetically inheritable form of cardiac arrhythmia; however, it is currently not known how these genetic predispositions contribute to the initiation and/or maintenance of AF-associated phenotypes. One major barrier to progress is the lack of experimental systems to investigate the effects of gene function on rhythm parameters in models with human atrial and whole-organ relevance. Here, we assembled a multi-model platform enabling high-throughput characterization of the effects of gene function on action potential duration and rhythm parameters using human induced pluripotent stem cell-derived atrial-like cardiomyocytes and a Drosophila heart model, and validation of the findings using computational models of human adult atrial myocytes and tissue. As proof of concept, we screened 20 AF-associated genes and identified phospholamban loss of function as a top conserved hit that shortens action potential duration and increases the incidence of arrhythmia phenotypes upon stress. Mechanistically, our study reveals that phospholamban regulates rhythm homeostasis by functionally interacting with L-type Ca2+ channels and NCX. In summary, our study illustrates how a multi-model system approach paves the way for the discovery and molecular delineation of gene regulatory networks controlling atrial rhythm with application to AF.

In silico analysis of the dynamic regulation of cardiac electrophysiology by Kv 11.1 ion-channel trafficking

Cardiac electrophysiology is regulated by continuous trafficking and internalization of ion channels occurring over minutes to hours. Kv 11.1 (also known as hERG) underlies the rapidly activating delayed-rectifier K+ current (IKr ), which plays a major role in cardiac ventricular repolarization. Experimental characterization of the distinct temporal effects of genetic and acquired modulators on channel trafficking and gating is challenging. Computer models are instrumental in elucidating these effects, but no currently available model incorporates ion-channel trafficking. Here, we present a novel computational model that reproduces the experimentally observed production, forward trafficking, internalization, recycling and degradation of Kv 11.1 channels, as well as their modulation by temperature, pentamidine, dofetilide and extracellular K+ . The acute effects of these modulators on channel gating were also incorporated and integrated with the trafficking model in the O'Hara-Rudy human ventricular cardiomyocyte model. Supraphysiological dofetilide concentrations substantially increased Kv 11.1 membrane levels while also producing a significant channel block. However, clinically relevant concentrations did not affect trafficking. Similarly, severe hypokalaemia reduced Kv 11.1 membrane levels based on long-term culture data, but had limited effect based on short-term data. By contrast, clinically relevant elevations in temperature acutely increased IKr due to faster kinetics, while after 24 h, IKr was decreased due to reduced Kv 11.1 membrane levels. The opposite was true for lower temperatures. Taken together, our model reveals a complex temporal regulation of cardiac electrophysiology by temperature, hypokalaemia, and dofetilide through competing effects on channel gating and trafficking, and provides a framework for future studies assessing the role of impaired trafficking in cardiac arrhythmias. KEY POINTS: Kv 11.1 channels underlying the rapidly activating delayed-rectifier K+ current are important for ventricular repolarization and are continuously shuttled from the cytoplasm to the plasma membrane and back over minutes to hours. Kv 11.1 gating and trafficking are modulated by temperature, drugs and extracellular K+ concentration but experimental characterization of their combined effects is challenging. Computer models may facilitate these analyses, but no currently available model incorporates ion-channel trafficking. We introduce a new two-state ion-channel trafficking model able to reproduce a wide range of experimental data, along with the effects of modulators of Kv 11.1 channel functioning and trafficking. The model reveals complex dynamic regulation of ventricular repolarization by temperature, extracellular K+ concentration and dofetilide through opposing acute (millisecond) effects on Kv 11.1 gating and long-term (hours) modulation of Kv 11.1 trafficking. This in silico trafficking framework provides a tool to investigate the roles of acute and long-term processes on arrhythmia promotion and maintenance.

Gating of homeostatic regulation of intrinsic excitability produces cryptic long-term storage of prior perturbations

Neurons and neuronal circuits must maintain their function throughout the life of the organism despite changing environments. Previous theoretical and experimental work suggests that neurons monitor their activity using intracellular calcium concentrations to regulate their intrinsic excitability. Models with multiple sensors can distinguish among different patterns of activity, but previous work using models with multiple sensors produced instabilities that lead the models' conductances to oscillate and then to grow without bound and diverge. We now introduce a nonlinear degradation term that explicitly prevents the maximal conductances to grow beyond a bound. We combine the sensors' signals into a master feedback signal that can be used to modulate the timescale of conductance evolution. Effectively, this means that the negative feedback can be gated on and off according to how far the neuron is from its target. The modified model recovers from multiple perturbations. Interestingly, depolarizing the models to the same membrane potential with current injection or with simulated high extracellular K+ produces different changes in conductances, arguing that caution must be used in interpreting manipulations that serve as a proxy for increased neuronal activity. Finally, these models accrue traces of prior perturbations that are not visible in their control activity after perturbation but that shape their responses to subsequent perturbations. These cryptic or hidden changes may provide insight into disorders such as posttraumatic stress disorder that only become visible in response to specific perturbations.

Enhanced Ca2+-Dependent SK-Channel Gating and Membrane Trafficking in Human Atrial Fibrillation

BACKGROUND

Small-conductance Ca2+-activated K+ (SK)-channel inhibitors have antiarrhythmic effects in animal models of atrial fibrillation (AF), presenting a potential novel antiarrhythmic option. However, the regulation of SK-channels in human atrial cardiomyocytes and its modification in patients with AF are poorly understood and were the object of this study.

METHODS

Apamin-sensitive SK-channel current (ISK) and action potentials were recorded in human right-atrial cardiomyocytes from sinus rhythm control (Ctl) patients or patients with (long-standing persistent) chronic AF (cAF).

RESULTS

ISK was significantly higher, and apamin caused larger action potential prolongation in cAF- versus Ctl-cardiomyocytes. Sensitivity analyses in an in silico human atrial cardiomyocyte model identified IK1 and ISK as major regulators of repolarization. Increased ISK in cAF was not associated with increases in mRNA/protein levels of SK-channel subunits in either right- or left-atrial tissue homogenates or right-atrial cardiomyocytes, but the abundance of SK2 at the sarcolemma was larger in cAF versus Ctl in both tissue-slices and cardiomyocytes. Latrunculin-A and primaquine (anterograde and retrograde protein-trafficking inhibitors) eliminated the differences in SK2 membrane levels and ISK between Ctl- and cAF-cardiomyocytes. In addition, the phosphatase-inhibitor okadaic acid reduced ISK amplitude and abolished the difference between Ctl- and cAF-cardiomyocytes, indicating that reduced calmodulin-Thr80 phosphorylation due to increased protein phosphatase-2A levels in the SK-channel complex likely contribute to the greater ISK in cAF-cardiomyocytes. Finally, rapid electrical activation (5 Hz, 10 minutes) of Ctl-cardiomyocytes promoted SK2 membrane-localization, increased ISK and reduced action potential duration, effects greatly attenuated by apamin. Latrunculin-A or primaquine prevented the 5-Hz-induced ISK-upregulation.

CONCLUSIONS

ISK is upregulated in patients with cAF due to enhanced channel function, mediated by phosphatase-2A-dependent calmodulin-Thr80 dephosphorylation and tachycardia-dependent enhanced trafficking and targeting of SK-channel subunits to the sarcolemma. The observed AF-associated increases in ISK, which promote reentry-stabilizing action potential duration shortening, suggest an important role for SK-channels in AF auto-promotion and provide a rationale for pursuing the antiarrhythmic effects of SK-channel inhibition in humans.

A compartmentalized mathematical model of the β1- and β2-adrenergic signaling systems in ventricular myocytes from mouse in heart failure

Mouse models of heart failure are extensively used to research human cardiovascular diseases. In particular, one of the most common is the mouse model of heart failure resulting from transverse aortic constriction (TAC). Despite this, there are no comprehensive compartmentalized mathematical models that describe the complex behavior of the action potential, [Ca²⁺]_i transients, and their regulation by β₁- and β₂-adrenergic signaling systems in failing mouse myocytes. In this paper, we develop a novel compartmentalized mathematical model of failing mouse ventricular myocytes after TAC procedure. The model describes well the cell geometry, action potentials, [Ca²⁺]_i transients, and β₁- and β₂-adrenergic signaling in the failing cells. Simulation results obtained with the failing cell model are compared with those from the normal ventricular myocytes. Exploration of the model reveals the sarcoplasmic reticulum Ca²⁺ load mechanisms in failing ventricular myocytes. We also show a larger susceptibility of the failing myocytes to early and delayed afterdepolarizations and to a proarrhythmic behavior of Ca²⁺ dynamics upon stimulation with isoproterenol. The mechanisms of the proarrhythmic behavior suppression are investigated and sensitivity analysis is performed. The developed model can explain the existing experimental data on failing mouse ventricular myocytes and make experimentally testable predictions of a failing myocyte's behavior.

Electrophysiological heterogeneity in large populations of rabbit ventricular cardiomyocytes

AIMS

Cardiac electrophysiological heterogeneity includes: (i) regional differences in action potential (AP) waveform, (ii) AP waveform differences in cells isolated from a single region, (iii) variability of the contribution of individual ion currents in cells with similar AP durations (APDs). The aim of this study is to assess intra-regional AP waveform differences, to quantify the contribution of specific ion channels to the APD via drug responses and to generate a population of mathematical models to investigate the mechanisms underlying heterogeneity in rabbit ventricular cells.

METHODS AND RESULTS

APD in ∼50 isolated cells from subregions of the LV free wall of rabbit hearts were measured using a voltage-sensitive dye. When stimulated at 2 Hz, average APD90 value in cells from the basal epicardial region was 254 ± 25 ms (mean ± standard deviation) in 17 hearts with a mean interquartile range (IQR) of 53 ± 17 ms. Endo-epicardial and apical-basal APD90 differences accounted for ∼10% of the IQR value. Highly variable changes in APD occurred after IK(r) or ICa(L) block that included a sub-population of cells (HR) with an exaggerated (hyper) response to IK(r) inhibition. A set of 4471 AP models matching the experimental APD90 distribution was generated from a larger population of models created by random variation of the maximum conductances (Gmax) of 8 key ion channels/exchangers/pumps. This set reproduced the pattern of cell-specific responses to ICa(L) and IK(r) block, including the HR sub-population. The models exhibited a wide range of Gmax values with constrained relationships linking ICa(L) with IK(r), ICl, INCX, and INaK.

CONCLUSION

Modelling the measured range of inter-cell APDs required a larger range of key Gmax values indicating that ventricular tissue has considerable inter-cell variation in channel/pump/exchanger activity. AP morphology is retained by relationships linking specific ionic conductances. These interrelationships are necessary for stable repolarization despite large inter-cell variation of individual conductances and this explains the variable sensitivity to ion channel block.

Machine learning provides insight into models of heterogeneous electrical activity in human beta-cells

Understanding how heterogeneous cellular responses emerge from cell-to-cell variations in expression and function of subcellular components is of general interest. Here, we focus on human insulin-secreting beta-cells, which are believed to constitute a population in which heterogeneity is of physiological importance. We exploit recent single-cell electrophysiological data that allow biologically realistic population modeling of human beta-cells that accounts for cellular heterogeneity and correlation between ion channel parameters. To investigate how ion channels influence the dynamics of our updated mathematical model of human pancreatic beta-cells, we explore several machine learning techniques to determine which model parameters are important for determining the qualitative patterns of electrical activity of the model cells. As expected, K^＋ channels promote absence of activity, but once a cell is active, they increase the likelihood of having action potential firing. HERG channels were of great importance for determining cell behavior in most of the investigated scenarios. Fast bursting is influenced by the time scales of ion channel activation and, interestingly, by the type of Ca^2＋ channels coupled to BK channels in BK-CaV complexes. Slow, metabolically driven oscillations are promoted mostly by K(ATP) channels. In summary, combining population modeling with machine learning analysis provides insight into the model and generates new hypotheses to be investigated both experimentally, via simulations and through mathematical analysis.

Sensitivity Analysis of Cardiac Alternans and Tachyarrhythmia to Ion Channel Conductance Using Population Modeling

Action potential duration (APD) alternans, an alternating phenomenon between action potentials in cardiomyocytes, causes heart arrhythmia when the heart rate is high. However, some of the APD alternans observed in clinical trials occurs under slow heart rate conditions of 100 to 120 bpm, increasing the likelihood of heart arrhythmias such as atrial fibrillation. Advanced studies have identified the occurrence of this type of APD alternans in terms of electrophysiological ion channel currents in cells. However, they only identified physiological phenomena, such as action potential due to random changes in a particular ion channel’s conductivity through ion models specializing in specific ion channel currents. In this study, we performed parameter sensitivity analysis via population modeling using a validated human ventricular physiology model to check the sensitivity of APD alternans to ion channel conductances. Through population modeling, we expressed the changes in alternans onset cycle length (AOCL) and mean APD in AOCL (AO meanAPD) according to the variations in ion channel conductance. Finally, we identified the ion channel that maximally affected the occurrence of APD alternans. AOCL and AO meanAPD were sensitive to changes in the plateau Ca²⁺ current. Accordingly, it was expected that APD alternans would be vulnerable to changes in intracellular calcium concentration.

Coupling and heterogeneity modulate pacemaking capability in healthy and diseased two-dimensional sinoatrial node tissue models

Both experimental and modeling studies have attempted to determine mechanisms by which a small anatomical region, such as the sinoatrial node (SAN), can robustly drive electrical activity in the human heart. However, despite many advances from prior research, important questions remain unanswered. This study aimed to investigate, through mathematical modeling, the roles of intercellular coupling and cellular heterogeneity in synchronization and pacemaking within the healthy and diseased SAN. In a multicellular computational model of a monolayer of either human or rabbit SAN cells, simulations revealed that heterogenous cells synchronize their discharge frequency into a unique beating rhythm across a wide range of heterogeneity and intercellular coupling values. However, an unanticipated behavior appeared under pathological conditions where perturbation of ionic currents led to reduced excitability. Under these conditions, an intermediate range of intercellular coupling (900-4000 MΩ) was beneficial to SAN automaticity, enabling a very small portion of tissue (3.4%) to drive propagation, with propagation failure occurring at both lower and higher resistances. This protective effect of intercellular coupling and heterogeneity, seen in both human and rabbit tissues, highlights the remarkable resilience of the SAN. Overall, the model presented in this work allowed insight into how spontaneous beating of the SAN tissue may be preserved in the face of perturbations that can cause individual cells to lose automaticity. The simulations suggest that certain degrees of gap junctional coupling protect the SAN from ionic perturbations that can be caused by drugs or mutations.

A phenotype-based forward genetic screen identifies Dnajb6 as a sick sinus syndrome gene

Previously we showed the generation of a protein trap library made with the gene-break transposon (GBT) in zebrafish (Danio rerio) that could be used to facilitate novel functional genome annotation towards understanding molecular underpinnings of human diseases (Ichino et al, 2020). Here, we report a significant application of this library for discovering essential genes for heart rhythm disorders such as sick sinus syndrome (SSS). SSS is a group of heart rhythm disorders caused by malfunction of the sinus node, the heart's primary pacemaker. Partially owing to its aging-associated phenotypic manifestation and low expressivity, molecular mechanisms of SSS remain difficult to decipher. From 609 GBT lines screened, we generated a collection of 35 zebrafish insertional cardiac (ZIC) mutants in which each mutant traps a gene with cardiac expression. We further employed electrocardiographic measurements to screen these 35 ZIC lines and identified three GBT mutants with SSS-like phenotypes. More detailed functional studies on one of the arrhythmogenic mutants, GBT411, in both zebrafish and mouse models unveiled Dnajb6 as a novel SSS causative gene with a unique expression pattern within the subpopulation of sinus node pacemaker cells that partially overlaps with the expression of hyperpolarization activated cyclic nucleotide gated channel 4 (HCN4), supporting heterogeneity of the cardiac pacemaker cells.

Interpretable machine learning of action potential duration restitution kinetics in single-cell models of atrial cardiomyocytes

Action potential duration (APD) restitution curve and its maximal slope (Smax) reflect single cell-level dynamic instability for inducing chaotic heart rhythms. However, conventional parameter sensitivity analysis often fails to describe nonlinear relationships between ion channel parameters and electrophysiological phenotypes, such as Smax. We explored the parameter-phenotype mapping in a population of 5000 single-cell atrial cell models through interpretable machine learning (ML) approaches. Parameter sensitivity analyses could explain the linear relationships between parameters and electrophysiological phenotypes, including APD₉₀, resting membrane potential, Vmax, refractory period, and APD/calcium alternans threshold, but not for Smax. However, neural network models had better prediction performance for Smax. To interpret the ML model, we evaluated the parameter importance at the global and local levels by computing the permutation feature importance and the local interpretable model-agnostic explanations (LIME) values, respectively. Increases in I_CaL, I_NCX, and I_Kr, and decreases in I_K1, I_b,Cl, I_Kur, I_SERCA, and I_to are correlated with higher Smax values. The LIME algorithm determined that I_NaK plays a significant role in determining Smax as well as I_to and I_Kur. The atrial cardiomyocyte population was hierarchically clustered into three distinct groups based on the LIME values and the single-cell simulation confirmed that perturbations in I_NaK resulted in different behaviors of APD restitution curves in three clusters. Our combined top-down interpretable ML and bottom-up mechanistic simulation approaches uncovered the role of I_NaK in heterogeneous behaviors of Smax in the atrial cardiomyocyte population.

A data-assimilation approach to predict population dynamics during epithelial-mesenchymal transition

Epithelial-mesenchymal transition (EMT) is a biological process that plays a central role in embryonic development, tissue regeneration, and cancer metastasis. Transforming growth factor-β (TGFβ) is a potent inducer of this cellular transition, comprising transitions from an epithelial state to partial or hybrid EMT state(s), to a mesenchymal state. Recent experimental studies have shown that, within a population of epithelial cells, heterogeneous phenotypical profiles arise in response to different time- and TGFβ dose-dependent stimuli. This offers a challenge for computational models, as most model parameters are generally obtained to represent typical cell responses, not necessarily specific responses nor to capture population variability. In this study, we applied a data-assimilation approach that combines limited noisy observations with predictions from a computational model, paired with parameter estimation. Synthetic experiments mimic the biological heterogeneity in cell states that is observed in epithelial cell populations by generating a large population of model parameter sets. Analysis of the parameters for virtual epithelial cells with biologically significant characteristics (e.g., EMT prone or resistant) illustrates that these sub-populations have identifiable critical model parameters. We perform a series of in silico experiments in which a forecasting system reconstructs the EMT dynamics of each virtual cell within a heterogeneous population exposed to time-dependent exogenous TGFβ dose and either an EMT-suppressing or EMT-promoting perturbation. We find that estimating population-specific critical parameters significantly improved the prediction accuracy of cell responses. Thus, with appropriate protocol design, we demonstrate that a data-assimilation approach successfully reconstructs and predicts the dynamics of a heterogeneous virtual epithelial cell population in the presence of physiological model error and parameter uncertainty.

Considering population variability of electrophysiological models improves the in silico assessment of drug-induced torsadogenic risk

BACKGROUND AND OBJECTIVE

In silico tools are known to aid in drug cardiotoxicity assessment. However, computational models do not usually consider electrophysiological variability, which may be crucial when predicting rare adverse events such as drug-induced Torsade de Pointes (TdP). In addition, classification tools are usually binary and are not validated using an external data set. Here we analyze the role of incorporating electrophysiological variability in the prediction of drug-induced arrhythmogenic-risk, using a ternary classification and two external validation datasets.

METHODS

The effects of the 12 training CiPA drugs were simulated at three different concentrations using a single baseline model and an electrophysiologically calibrated population of models. 9 biomarkers related with action potential (AP), calcium dynamics and net charge were measured for each simulated concentration. These biomarkers were used to build ternary classifiers based on Support Vector Machines (SVM) methodology. Classifiers were validated using two external drug sets: the 16 validation CiPA drugs and 81 drugs from CredibleMeds database.

RESULTS

Population of models allowed to obtain different AP responses under the same pharmacological intervention and improve the prediction of drug-induced TdP with respect to the baseline model. The classification tools based on population of models achieve an accuracy higher than 0.8 and a mean classification error (MCE) lower than 0.3 for both validation drug sets and for the two electrophysiological action potential models studied (Tomek et al. 2020 and a modified version of O'Hara et al. 2011). In addition, simulations with population of models allowed the identification of individuals with lower conductances of I_Kr, I_Ks, and I_NaK and higher conductances of I_CaL, I_NaL, and I_NCX, which are more prone to develop TdP.

CONCLUSIONS

The methodology presented here provides new opportunities to assess drug-induced TdP-risk, taking into account electrophysiological variability and may be helpful to improve current cardiac safety screening methods.

Advanced Machine Learning Applications to Viscous Oil-Water Multi-Phase Flow

The importance of heavy oil in the world oil market has increased over the past twenty years as light oil reserves have declined steadily. The high viscosity of this kind of unconventional oil results in high energy consumption for its transportation, which significantly increases production costs. A cost-effective solution for the long-distance transport of viscous crudes could be water-lubricated flow technology. A water ring separates the viscous oil-core from the pipe wall in such a pipeline. The main challenge in using this kind of lubricated system is the need for a model that can provide reliable predictions of friction losses. An artificial neural network (ANN) was used in this study to model pressure losses based on 225 data sets from independent sources. The seven input variables used in the current ANN model are pipe diameter, average velocity, oil density, oil viscosity, water density, water viscosity, and water content. The ANN developed using the backpropagation technique with seven processing neurons or nodes in the hidden layer demonstrated to be the optimal architecture. A comparison of ANN with other artificial intelligence and parametric techniques shows the promising precision of the current model. After the model was validated, a sensitivity analysis determined the relative order of significance of the input parameters. Some of the input parameters had linear effects, while other parameters had polynomial effects of varying degrees on the friction losses.

Proarrhythmic risk assessment of drugs by dVm /dt shapes using the convolutional neural network

Comprehensive in vitro Proarrhythmia Assay (CiPA) projects for assessing proarrhythmic drugs suggested a logistic regression model using qNet as the Torsades de Pointes (TdP) risk assessment biomarker, obtained from in silico simulation. However, using a single in silico feature, such as qNet, cannot reflect whole characteristics related to TdP in the entire action potential (AP) shape. Thus, this study proposed a deep convolutional neural network (CNN) model using differential action potential shapes to classify three proarrhythmic risk levels: high, intermediate, and low, considering both characteristics related to TdP not only in the depolarization phase but also the repolarization phase of AP shape. We performed an in silico simulation and got AP shapes with drug effects using half-maximal inhibitory concentration and Hill coefficients of 28 drugs released by CiPA groups. Then, we trained the deep CNN model with the differential AP shapes of 12 drugs and tested it with those of 16 drugs. Our model had a better performance for classifying the proarrhythmic risk of drugs than the traditional logistic regression model using qNet. The classification accuracy was 98% for high-risk level drugs, 94% for intermediate-risk level drugs, and 89% for low-risk level drugs.

A Quantitative Systems Pharmacology Perspective on the Importance of Parameter Identifiability

There is an inherent tension in Quantitative Systems Pharmacology (QSP) between the need to incorporate mathematical descriptions of complex physiology and drug targets with the necessity of developing robust, predictive and well-constrained models. In addition to this, there is no “gold standard” for model development and assessment in QSP. Moreover, there can be confusion over terminology such as model and parameter identifiability; complex and simple models; virtual populations; and other concepts, which leads to potential miscommunication and misapplication of methodologies within modeling communities, both the QSP community and related disciplines. This perspective article highlights the pros and cons of using simple (often identifiable) vs. complex (more physiologically detailed but often non-identifiable) models, as well as aspects of parameter identifiability, sensitivity and inference methodologies for model development and analysis. The paper distills the central themes of the issue of identifiability and optimal model size and discusses open challenges.

Quantitative roles of ion channel dynamics on ventricular action potential

Mathematical models for the action potential (AP) generation of the electrically excitable cells including the heart are involved different mechanisms including the voltage-dependent currents with nonlinear time- and voltage-gating properties. From the shape of the AP waveforms to the duration of the refractory periods or heart rhythms are greatly affected by the functions describing the features or the quantities of these ion channels. In this work, a mathematical measure to analyze the regional contributions of voltage-gated channels is defined by dividing the AP into phases, epochs, and intervals of interest. The contribution of each time-dependent current for the newly defined cardiomyocyte model is successfully calculated and it is found that the contribution of dominant ion channels changes substantially not only for each phase but also for different regions of the cardiac AP. Besides, the defined method can also be applied in all Hodgkin-Huxley types of electrically excitable cell models to be able to understand the underlying dynamics better.

Pathophysiological metabolic changes associated with disease modify the proarrhythmic risk profile of drugs with potential to prolong repolarisation

BACKGROUND AND PURPOSE

Hydroxychloroquine, chloroquine and azithromycin are three drugs that were proposed to treat COVID-19. While concern already existed around their proarrhythmic potential there is little data regarding how altered physiological states encountered in patients such as febrile state, electrolyte imbalances or acidosis might change their risk profiles.

EXPERIMENTAL APPROACH

Potency of hERG block was measured using high-throughput electrophysiology in the presence of variable environmental factors. These potencies informed simulations to predict population risk profiles. Effects on cardiac repolarisation were verified in human induced pluripotent stem cell-derived cardiomyocytes from multiple individuals.

KEY RESULTS

Chloroquine and hydroxychloroquine blocked hERG with IC₅₀ of 1.47±0.07 μM and 3.78±0.17 μM respectively, indicating proarrhythmic risk at concentrations effective against SARS-CoV-2 in vitro. Hypokalaemia and hypermagnesemia increased potency of chloroquine and hydroxychloroquine, indicating increased proarrhythmic risk. Acidosis significantly reduced potency of all drugs, whereas increased temperature decreased potency of chloroquine and hydroxychloroquine against hERG but increased potency for azithromycin. In silico simulations demonstrated that proarrhythmic risk was increased by female sex, hypokalaemia and heart failure, and identified specific genetic backgrounds associated with emergence of arrhythmia.

CONCLUSION AND IMPLICATIONS

Our study demonstrates how proarrhythmic risk can be exacerbated by metabolic changes and pre-existing disease. More broadly, the study acts as a blueprint for how high-throughput in vitro screening, combined with in silico simulations can help guide both preclinical screening and clinical management of patients in relation to drugs with potential to prolong repolarisation.

Quantitative cross-species translators of cardiac myocyte electrophysiology: Model training, experimental validation, and applications

Animal experimentation is key in the evaluation of cardiac efficacy and safety of novel therapeutic compounds. However, interspecies differences in the mechanisms regulating excitation-contraction coupling can limit the translation of experimental findings from animal models to human physiology and undermine the assessment of drugs’ efficacy and safety. Here, we built a suite of translators for quantitatively mapping electrophysiological responses in ventricular myocytes across species. We trained these statistical operators using a broad dataset obtained by simulating populations of our biophysically detailed computational models of action potential and Ca2+ transient in mouse, rabbit, and human. We then tested our translators against experimental data describing the response to stimuli, such as ion channel block, change in beating rate, and β-adrenergic challenge. We demonstrate that this approach is well suited to predicting the effects of perturbations across different species or experimental conditions and suggest its integration into mechanistic studies and drug development pipelines.

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.

Estimating ectopic beat probability with simplified statistical models that account for experimental uncertainty

Ectopic beats (EBs) are cellular arrhythmias that can trigger lethal arrhythmias. Simulations using biophysically-detailed cardiac myocyte models can reveal how model parameters influence the probability of these cellular arrhythmias, however such analyses can pose a huge computational burden. Here, we develop a simplified approach in which logistic regression models (LRMs) are used to define a mapping between the parameters of complex cell models and the probability of EBs (P(EB)). As an example, in this study, we build an LRM for P(EB) as a function of the initial value of diastolic cytosolic Ca²⁺ concentration ([Ca²⁺]_iⁱⁿⁱ), the initial state of sarcoplasmic reticulum (SR) Ca²⁺ load ([Ca²⁺]_SRⁱⁿⁱ), and kinetic parameters of the inward rectifier K⁺ current (I_K1) and ryanodine receptor (RyR). This approach, which we refer to as arrhythmia sensitivity analysis, allows for evaluation of the relationship between these arrhythmic event probabilities and their associated parameters. This LRM is also used to demonstrate how uncertainties in experimentally measured values determine the uncertainty in P(EB). In a study of the role of [Ca²⁺]_SRⁱⁿⁱ uncertainty, we show a special property of the uncertainty in P(EB), where with increasing [Ca²⁺]_SRⁱⁿⁱ uncertainty, P(EB) uncertainty first increases and then decreases. Lastly, we demonstrate that I_K1 suppression, at the level that occurs in heart failure myocytes, increases P(EB).

An ectopic beat is an abnormal cellular electrical event which can trigger dangerous arrhythmias in the heart. Complex biophysical models of the cardiac myocyte can be used to reveal how cell properties affect the probability of ectopic beats. However, such analyses can pose a huge computational burden. We develop a simplified approach that enables a highly complex biophysical model to be reduced to a rather simple statistical model from which the functional relationship between myocyte model parameters and the probability of an ectopic beat is determined. We refer to this approach as arrhythmia sensitivity analysis. Given the efficiency of our approach, we also use it to demonstrate how uncertainties in experimentally measured myocyte model parameters determine the uncertainty in ectopic beat probability. We find that, with increasing model parameter uncertainty, the uncertainty in probability of ectopic beat first increases and then decreases. In general, our approach can efficiently analyze the relationship between cardiac myocyte parameters and the probability of ectopic beats and can be used to study how uncertainty of these cardiac myocyte parameters influences the ectopic beat probability.

Which bidomain conductivity is the most important for modelling heart and torso surface potentials during ischaemia?

Mathematical simulations using the bidomain model, which represents cardiac tissue as consisting of an intracellular and an extracellular space, are a key approach that can be used to improve understanding of heart conditions such as ischaemia. However, key inputs to these models, such as the bidomain conductivity values, are not known with any certainty. Since efforts are underway to measure these values, it would be useful to be able to quantify the effect on model outputs of uncertainty in these inputs, and also to determine, if possible, which are the most important values to focus on in experimental studies. Our previous work has systematically studied the sensitivity of heart surface potentials to the bidomain conductivity values, and this was performed using a half-ellipsoidal model of the left ventricle. This study uses a bi-ventricular heart in a torso model and this time looks at the sensitivity of the torso surface potentials, as well as the heart surface potentials, to various conductivity values (blood, torso and the six bidomain conductivities). We found that both epicardial and torso potentials are the most sensitive to the intracellular longitudinal (along the cardiac fibres) conductivity (g_il) with more minor sensitivity to the torso conductivity, and that changes in g_il have a significant effect on the surface potential distributions on both the torso and the heart.

Prediction of arrhythmia susceptibility through mathematical modeling and machine learning

At present, the QT interval on the electrocardiographic (ECG) waveform is the most common metric for assessing an individual's susceptibility to ventricular arrhythmias, with a long QT, or, at the cellular level, a long action potential duration (APD) considered high risk. However, the limitations of this simple approach have long been recognized. Here, we sought to improve prediction of arrhythmia susceptibility by combining mechanistic mathematical modeling with machine learning (ML). Simulations with a model of the ventricular myocyte were performed to develop a large heterogenous population of cardiomyocytes (n = 10,586), and we tested each variant's ability to withstand three arrhythmogenic triggers: 1) block of the rapid delayed rectifier potassium current (I_Kr Block), 2) augmentation of the L-type calcium current (I_CaL Increase), and 3) injection of inward current (Current Injection). Eight ML algorithms were trained to predict, based on simulated AP features in preperturbed cells, whether each cell would develop arrhythmic dynamics in response to each trigger. We found that APD can accurately predict how cells respond to the simple Current Injection trigger but cannot effectively predict the response to I_Kr Block or I_CaL Increase. ML predictive performance could be improved by incorporating additional AP features and simulations of additional experimental protocols. Importantly, we discovered that the most relevant features and experimental protocols were trigger specific, which shed light on the mechanisms that promoted arrhythmia formation in response to the triggers. Overall, our quantitative approach provides a means to understand and predict differences between individuals in arrhythmia susceptibility.

Sensitivity Analysis of Ion Channel Conductance on Myocardial Electromechanical Delay: Computational Study

It is well known that cardiac electromechanical delay (EMD) can cause dyssynchronous heart failure (DHF), a prominent cardiovascular disease (CVD). This work computationally assesses the conductance variation of every ion channel on the cardiac cell to give rise to EMD prolongation. The electrical and mechanical models of human ventricular tissue were simulated, using a population approach with four conductance reductions for each ion channel. Then, EMD was calculated by determining the difference between the onset of action potential and the start of cell shortening. Finally, EMD data were put into the optimized conductance dimensional stacking to show which ion channel has the most influence in elongating the EMD. We found that major ion channels, such as L-type calcium (CaL), slow-delayed rectifier potassium (Ks), rapid-delayed rectifier potassium (Kr), and inward rectifier potassium (K1), can significantly extend the action potential duration (APD) up to 580 ms. Additionally, the maximum intracellular calcium (Cai) concentration is greatly affected by the reduction in channel CaL, Ks, background calcium, and Kr. However, among the aforementioned major ion channels, only the CaL channel can play a superior role in prolonging the EMD up to 83 ms. Furthermore, ventricular cells with long EMD have been shown to inherit insignificant mechanical response (in terms of how strong the tension can grow and how far length shortening can go) compared with that in normal cells. In conclusion, despite all variations in every ion channel conductance, only the CaL channel can play a significant role in extending EMD. In addition, cardiac cells with long EMD tend to have inferior mechanical responses due to a lack of Cai compared with normal conditions, which are highly likely to result in a compromised pump function of the heart.

Mechanisms of phase-3 early afterdepolarizations and triggered activities in ventricular myocyte models

Early afterdepolarizations (EADs) are abnormal depolarizations during the repolarizing phase of the action potential, which are associated with cardiac arrhythmogenesis. EADs are classified into phase-2 and phase-3 EADs. Phase-2 EADs occur during phase 2 of the action potential, with takeoff potentials typically above -40 mV. Phase-3 EADs occur during phase 3 of the action potential, with takeoff potential between -70 and -50 mV. Since the amplitude of phase-3 EADs can be as large as that of a regular action potential, they are also called triggered activities (TAs). This also makes phase-3 EADs and TAs much more arrhythmogenic than phase-2 EADs since they can propagate easily in tissue. Although phase-2 EADs have been widely observed, phase-3 EADs and TAs have been rarely demonstrated in isolated ventricular myocytes. Here we carry out computer simulations of three widely used ventricular action potential models to investigate the mechanisms of phase-3 EADs and TAs. We show that when the T-type Ca2+ current (ICa,T ) is absent (e.g., in normal ventricular myocytes), besides the requirement of increasing inward currents and reducing outward currents as for phase-2 EADs, the occurrence of phase-3 EADs and TAs requires a substantially large increase of the L-type Ca2+ current and the slow component of the delayed rectifier K+ current. The presence of ICa,T (e.g., in neonatal and failing ventricular myocytes) can greatly reduce the thresholds of these two currents for phase-3 EADs and TAs. This implies that ICa,T may play an important role in arrhythmogenesis in cardiac diseases.

Intracellular Na+ Modulates Pacemaking Activity in Murine Sinoatrial Node Myocytes: An In Silico Analysis

Background: The mechanisms underlying dysfunction in the sinoatrial node (SAN), the heart's primary pacemaker, are incompletely understood. Electrical and Ca2+-handling remodeling have been implicated in SAN dysfunction associated with heart failure, aging, and diabetes. Cardiomyocyte [Na+]i is also elevated in these diseases, where it contributes to arrhythmogenesis. Here, we sought to investigate the largely unexplored role of Na+ homeostasis in SAN pacemaking and test whether [Na+]i dysregulation may contribute to SAN dysfunction. Methods: We developed a dataset-specific computational model of the murine SAN myocyte and simulated alterations in the major processes of Na+ entry (Na+/Ca2+ exchanger, NCX) and removal (Na+/K+ ATPase, NKA). Results: We found that changes in intracellular Na+ homeostatic processes dynamically regulate SAN electrophysiology. Mild reductions in NKA and NCX function increase myocyte firing rate, whereas a stronger reduction causes bursting activity and loss of automaticity. These pathologic phenotypes mimic those observed experimentally in NCX- and ankyrin-B-deficient mice due to altered feedback between the Ca2+ and membrane potential clocks underlying SAN firing. Conclusions: Our study generates new testable predictions and insight linking Na+ homeostasis to Ca2+ handling and membrane potential dynamics in SAN myocytes that may advance our understanding of SAN (dys)function.

Dynamic flux balance analysis of whole-body metabolism for type 1 diabetes

Type 1 diabetes (T1D) mellitus is a systemic disease triggered by a local autoimmune inflammatory reaction in insulin-producing cells that induce organ-wide, long-term metabolic effects. Mathematical modeling of the whole-body regulatory bihormonal system has helped to identify therapeutic interventions but is limited to a coarse-grained representation of metabolism. To extend the depiction of T1D, we developed a whole-body model of organ-specific regulation and metabolism that highlighted chronic inflammation as a hallmark of the disease, identified processes related to neurodegenerative disorders and suggested calcium channel blockers as adjuvants for diabetes control. In addition, whole-body modeling of a patient population allowed for the assessment of between-individual variability to insulin and suggested that peripheral glucose levels are degenerate biomarkers of the internal metabolic state. Taken together, the organ-resolved, dynamic modeling approach enables modeling and simulation of metabolic disease at greater levels of coverage and precision and the generation of hypothesis from a molecular level up to the population level.

Intrinsic plasticity and birdsong learning

Although information processing and storage in the brain is thought to be primarily orchestrated by synaptic plasticity, other neural mechanisms such as intrinsic plasticity are available. While a number of recent studies have described the plasticity of intrinsic excitability in several types of neurons, the significance of non-synaptic mechanisms in memory and learning remains elusive. After reviewing plasticity of intrinsic excitation in relation to learning and homeostatic mechanisms, we focus on the intrinsic properties of a class of basal-ganglia projecting song system neurons in zebra finch, how these related to each bird's unique learned song, how these properties change over development, and how they are maintained dynamically to rapidly change in response to auditory feedback perturbations. We place these results in the broader theme of learning and changes in intrinsic properties, emphasizing the computational implications of this form of plasticity, which are distinct from synaptic plasticity. The results suggest that exploring reciprocal interactions between intrinsic and network properties will be a fruitful avenue for understanding mechanisms of birdsong learning.

Neuronal oscillator robustness to multiple global perturbations

Neuronal activity depends on ion channels and biophysical processes that are strongly and differentially sensitive to physical variables such as temperature and pH. Nonetheless, neuronal oscillators can be surprisingly resilient to perturbations in these variables. We study a three-neuron pacemaker ensemble that drives the pyloric rhythm of the crab, Cancer borealis. These crabs routinely experience a number of global perturbations, including changes in temperature and pH. Although pyloric oscillations are robust to such changes, for sufficiently large deviations the rhythm reversibly breaks down. As temperature increases beyond a tipping point, oscillators transition to silence. Acidic pH deviations also show tipping points, with a reliable transition first to tonic spiking, then to silence. Surprisingly, robustness to perturbations in pH only moderately affects temperature robustness. Consistent with high animal-to-animal variability in biophysical circuit parameters, tipping points in temperature and pH vary across animals. However, the ordering and discrete classes of transitions at critical points are conserved. This implies that qualitative oscillator dynamics are preserved across animals despite high quantitative parameter variability. A universal model of bursting dynamics predicts the existence of these transition types and the order in which they occur.

Identifying Drug Response by Combining Measurements of the Membrane Potential, the Cytosolic Calcium Concentration, and the Extracellular Potential in Microphysiological Systems

Cardiomyocytes derived from human induced pluripotent stem cells (hiPSC-CMs) offer a new means to study and understand the human cardiac action potential, and can give key insight into how compounds may interact with important molecular pathways to destabilize the electrical function of the heart. Important features of the action potential can be readily measured using standard experimental techniques, such as the use of voltage sensitive dyes and fluorescent genetic reporters to estimate transmembrane potentials and cytosolic calcium concentrations. Using previously introduced computational procedures, such measurements can be used to estimate the current density of major ion channels present in hiPSC-CMs, and how compounds may alter their behavior. However, due to the limitations of optical recordings, resolving the sodium current remains difficult from these data. Here we show that if these optical measurements are complemented with observations of the extracellular potential using multi electrode arrays (MEAs), we can accurately estimate the current density of the sodium channels. This inversion of the sodium current relies on observation of the conduction velocity which turns out to be straightforwardly computed using measurements of extracellular waves across the electrodes. The combined data including the membrane potential, the cytosolic calcium concentration and the extracellular potential further opens up for the possibility of accurately estimating the effect of novel drugs applied to hiPSC-CMs.

The transient outward potassium current plays a key role in spiral wave breakup in ventricular tissue

Spiral wave reentry as a mechanism of lethal ventricular arrhythmias has been widely demonstrated in animal experiments and recordings from human hearts. It has been shown that in structurally normal hearts spiral waves are unstable, breaking up into multiple wavelets via dynamical instabilities. However, many of the second-generation action potential models give rise only to stable spiral waves, raising issues regarding the underlying mechanisms of spiral wave breakup. In this study, we carried out computer simulations of two-dimensional homogeneous tissues using five ventricular action potential models. We show that the transient outward potassium current (Ito), although it is not required, plays a key role in promoting spiral wave breakup in all five models. As the maximum conductance of Ito increases, it first promotes spiral wave breakup and then stabilizes the spiral waves. In the absence of Ito, speeding up the L-type calcium kinetics can prevent spiral wave breakup, however, with the same speedup kinetics, spiral wave breakup can be promoted by increasing Ito. Increasing Ito promotes single-cell dynamical instabilities, including action potential duration alternans and chaos, and increasing Ito further suppresses these action potential dynamics. These cellular properties agree with the observation that increasing Ito first promotes spiral wave breakup and then stabilizes spiral waves in tissue. Implications of our observations to spiral wave dynamics in the real hearts and action potential model improvements are discussed.NEW & NOTEWORTHY Spiral wave breakup manifesting as multiple wavelets is a mechanism of ventricular fibrillation. It has been known that spiral wave breakup in cardiac tissue can be caused by a steeply sloped action potential duration restitution curve, a property mainly determined by the recovery of L-type calcium current. Here, we show that the transient outward potassium current (Ito) is another current that plays a key role in spiral wave breakup, that is, spiral waves can be stable for low and high maximum Ito conductance but breakup occurs for intermediate maximum Ito conductance. Since Ito is present in normal hearts of many species and required for Brugada syndrome, it may play an important role in the spiral wave stability and arrhythmogenesis under both normal condition and Brugada syndrome.

In Silico Assessment of Class I Antiarrhythmic Drug Effects on Pitx2-Induced Atrial Fibrillation: Insights from Populations of Electrophysiological Models of Human Atrial Cells and Tissues

Electrical remodelling as a result of homeodomain transcription factor 2 (Pitx2)-dependent gene regulation was linked to atrial fibrillation (AF) and AF patients with single nucleotide polymorphisms at chromosome 4q25 responded favorably to class I antiarrhythmic drugs (AADs). The possible reasons behind this remain elusive. The purpose of this study was to assess the efficacy of the AADs disopyramide, quinidine, and propafenone on human atrial arrhythmias mediated by Pitx2-induced remodelling, from a single cell to the tissue level, using drug binding models with multi-channel pharmacology. Experimentally calibrated populations of human atrial action po-tential (AP) models in both sinus rhythm (SR) and Pitx2-induced AF conditions were constructed by using two distinct models to represent morphological subtypes of AP. Multi-channel pharmaco-logical effects of disopyramide, quinidine, and propafenone on ionic currents were considered. Simulated results showed that Pitx2-induced remodelling increased maximum upstroke velocity (dVdtmax), and decreased AP duration (APD), conduction velocity (CV), and wavelength (WL). At the concentrations tested in this study, these AADs decreased dVdtmax and CV and prolonged APD in the setting of Pitx2-induced AF. Our findings of alterations in WL indicated that disopyramide may be more effective against Pitx2-induced AF than propafenone and quinidine by prolonging WL.

Ranolazine as an Alternative Therapy to Flecainide for SCN5A V411M Long QT Syndrome Type 3 Patients

The prolongation of the QT interval represents the main feature of the long QT syndrome (LQTS), a life-threatening genetic disease. The heterozygous SCN5A V411M mutation of the human sodium channel leads to a LQTS type 3 with severe proarrhythmic effects due to an increase in the late component of the sodium current (INaL). The two sodium blockers flecainide and ranolazine are equally recommended by the current 2015 ESC guidelines to treat patients with LQTS type 3 and persistently prolonged QT intervals. However, awareness of pro-arrhythmic effects of flecainide in LQTS type 3 patients arose upon the study of the SCN5A E1784K mutation. Regarding SCN5A V411M individuals, flecainide showed good results albeit in a reduced number of patients and no evidence supporting the use of ranolazine has ever been released. Therefore, we ought to compare the effect of ranolazine and flecainide in a SCN5A V411M model using an in-silico modeling and simulation approach. We collected clinical data of four patients. Then, we fitted four Markovian models of the human sodium current (INa) to experimental and clinical data. Two of them correspond to the wild type and the heterozygous SCN5A V411M scenarios, and the other two mimic the effects of flecainide and ranolazine on INa. Next, we inserted them into three isolated cell action potential (AP) models for endocardial, midmyocardial and epicardial cells and in a one-dimensional tissue model. The SCN5A V411M mutation produced a 15.9% APD90 prolongation in the isolated endocardial cell model, which corresponded to a 14.3% of the QT interval prolongation in a one-dimensional strand model, in keeping with clinical observations. Although with different underlying mechanisms, flecainide and ranolazine partially countered this prolongation at the isolated endocardial model by reducing the APD90 by 8.7 and 4.3%, and the QT interval by 7.2 and 3.2%, respectively. While flecainide specifically targeted the mutation-induced increase in peak INaL, ranolazine reduced it during the entire AP. Our simulations also suggest that ranolazine could prevent early afterdepolarizations triggered by the SCN5A V411M mutation during bradycardia, as flecainide. We conclude that ranolazine could be used to treat SCN5A V411M patients, specifically when flecainide is contraindicated.

Mechanisms of Premature Ventricular Complexes Caused by QT Prolongation

QT prolongation, due to lengthening of the action potential duration in the ventricles, is a major risk factor of lethal ventricular arrhythmias. A widely known consequence of QT prolongation is the genesis of early afterdepolarizations (EADs), which are associated with arrhythmias through the generation of premature ventricular complexes (PVCs). However, the vast majority of the EADs observed experimentally in isolated ventricular myocytes are phase-2 EADs, and whether phase-2 EADs are mechanistically linked to PVCs in cardiac tissue remains an unanswered question. In this study, we investigate the genesis of PVCs using computer simulations with eight different ventricular action potential models of various species. Based on our results, we classify PVCs as arising from two distinct mechanisms: repolarization gradient (RG)-induced PVCs and phase-2 EAD-induced PVCs. The RG-induced PVCs are promoted by increasing RG and L-type calcium current and are insensitive to gap junction coupling. EADs are not required for this PVC mechanism. In a paced beat, a single or multiple PVCs can occur depending on the properties of the RG. In contrast, phase-2 EAD-induced PVCs occur only when the RG is small and are suppressed by increasing RG and more sensitive to gap junction coupling. Unlike with RG-induced PVCs, in each paced beat, only a single EAD-induced PVC can occur no matter how many EADs in an action potential. In the wide parameter ranges we explore, RG-induced PVCs can be observed in all models, but the EAD-induced PVCs can only be observed in five of the eight models. The links between these two distinct PVC mechanisms and arrhythmogenesis in animal experiments and clinical settings are discussed.

Modeling the Interactions Between Sodium Channels Provides Insight Into the Negative Dominance of Certain Channel Mutations

BACKGROUND

Nav1.5 cardiac Na+ channel mutations can cause arrhythmogenic syndromes. Some of these mutations exert a dominant negative effect on wild-type channels. Recent studies showed that Na+ channels can dimerize, allowing coupled gating. This leads to the hypothesis that allosteric interactions between Na+ channels modulate their function and that these interactions may contribute to the negative dominance of certain mutations.

METHODS

To investigate how allosteric interactions affect microscopic and macroscopic channel function, we developed a modeling paradigm in which Markovian models of two channels are combined. Allosteric interactions are incorporated by modifying the free energies of the composite states and/or barriers between states.

RESULTS

Simulations using two generic 2-state models (C-O, closed-open) revealed that increasing the free energy of the composite states CO/OC leads to coupled gating. Simulations using two 3-state models (closed-open-inactivated) revealed that coupled closings must also involve interactions between further composite states. Using two 6-state cardiac Na+ channel models, we replicated previous experimental results mainly by increasing the energies of the CO/OC states and lowering the energy barriers between the CO/OC and the CO/OO states. The channel model was then modified to simulate a negative dominant mutation (Nav1.5 p.L325R). Simulations of homodimers and heterodimers in the presence and absence of interactions showed that the interactions with the variant channel impair the opening of the wild-type channel and thus contribute to negative dominance.

CONCLUSION

Our new modeling framework recapitulates qualitatively previous experimental observations and helps identifying possible interaction mechanisms between ion channels.