Rapid Characterization of hERG Channel Kinetics II: Temperature Dependence

The impact of uncertainty in hERG binding mechanism on in silico predictions of drug-induced proarrhythmic risk

BACKGROUND AND PURPOSE

Drug-induced reduction of the rapid delayed rectifier potassium current carried by the human Ether-à-go-go-Related Gene (hERG) channel is associated with increased risk of arrhythmias. Recent updates to drug safety regulatory guidelines attempt to capture each drug's hERG binding mechanism by combining in vitro assays with in silico simulations. In this study, we investigate the impact on in silico proarrhythmic risk predictions due to uncertainty in the hERG binding mechanism and physiological hERG current model.

EXPERIMENTAL APPROACH

Possible pharmacological binding models were designed for the hERG channel to account for known and postulated small molecule binding mechanisms. After selecting a subset of plausible binding models for each compound through calibration to available voltage-clamp electrophysiology data, we assessed their effects, and the effects of different physiological models, on proarrhythmic risk predictions.

KEY RESULTS

For some compounds, multiple binding mechanisms can explain the same data produced under the safety testing guidelines, which results in different inferred binding rates. This can result in substantial uncertainty in the predicted torsade risk, which often spans more than one risk category. By comparison, we found that the effect of a different hERG physiological current model on risk classification was subtle.

CONCLUSION AND IMPLICATIONS

The approach developed in this study assesses the impact of uncertainty in hERG binding mechanisms on predictions of drug-induced proarrhythmic risk. For some compounds, these results imply the need for additional binding data to decrease uncertainty in safety-critical applications.

Advances in ion channel high throughput screening: where are we in 2023?

INTRODUCTION

Automated Patch Clamp (APC) technology has become an integral element in ion channel research, drug discovery and development pipelines to overcome the use of the highly time-consuming manual patch clamp (MPC) procedures. This automated technology offers increased throughput and promises a new model in obtaining ion channel recordings, which has significant relevance to the development of novel therapies and safety profiling of candidate therapeutic compounds.

AREAS COVERED

This article reviews the recent innovations in APC technology, including platforms, and highlights how they have facilitated usage in both industry and academia. The review also provides an overview of the ion channel research endeavors and how APC platforms have contributed to the understanding of ion channel research, pharmacological tools and therapeutics. Furthermore, the authors provide their opinion on the challenges and goals for APC technology going forward to accelerate academic research and drug discovery across a host of therapeutic areas.

EXPERT OPINION

It is clear that APC technology has progressed drug discovery programs, specifically in the field of neuroscience and cardiovascular research. The challenge for the future is to keep pace with fundamental research and improve translation of the large datasets obtained.

[Developments of ex vivo cardiac electrical mapping and intelligent labeling of atrial fibrillation substrates]

Cardiac three-dimensional electrophysiological labeling technology is the prerequisite and foundation of atrial fibrillation (AF) ablation surgery, and invasive labeling is the current clinical method, but there are many shortcomings such as large trauma, long procedure duration, and low success rate. In recent years, because of its non-invasive and convenient characteristics, ex vivo labeling has become a new direction for the development of electrophysiological labeling technology. With the rapid development of computer hardware and software as well as the accumulation of clinical database, the application of deep learning technology in electrocardiogram (ECG) data is becoming more extensive and has made great progress, which provides new ideas for the research of ex vivo cardiac mapping and intelligent labeling of AF substrates. This paper reviewed the research progress in the fields of ECG forward problem, ECG inverse problem, and the application of deep learning in AF labeling, discussed the problems of ex vivo intelligent labeling of AF substrates and the possible approaches to solve them, prospected the challenges and future directions for ex vivo cardiac electrophysiology labeling.

Whole-Cell Configuration of the Patch-Clamp Technique in the hERG Channel Assay

In vitro electrophysiological safety studies have become an integral part of the drug development process because, in many instances, compound-induced QT prolongation has been associated with a direct block of human ether-a-go-go-related gene (hERG) potassium channels or their native current, the rapidly activating delayed rectifier potassium current (IKr ). Therefore, according to the ICH S7B guideline, the in vitro hERG channel patch-clamp assay is commonly used as an early screen to predict the ability of a compound to prolong the QT interval prior to first-in-human testing. The protocols described in this article are designed to assess the effects of acute or long-term exposure to new chemical entities on the amplitude of IKr in HEK293 cells stably transfected with the hERG channel (whole-cell configuration of the patch-clamp technique). Examples of results obtained with moxifloxacin, terfenadine, arsenic, pentamidine, erythromycin, and sotalol are provided for illustrative purposes. © 2024 Wiley Periodicals LLC. Basic Protocol: Measurement of the acute effects of test items in the hERG channel test Alternate Protocol: Measurement of the long-term effects of test items in the hERG channel test.

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.

Empirical Quantification of Predictive Uncertainty Due to Model Discrepancy by Training with an Ensemble of Experimental Designs: An Application to Ion Channel Kinetics

When using mathematical models to make quantitative predictions for clinical or industrial use, it is important that predictions come with a reliable estimate of their accuracy (uncertainty quantification). Because models of complex biological systems are always large simplifications, model discrepancy arises-models fail to perfectly recapitulate the true data generating process. This presents a particular challenge for making accurate predictions, and especially for accurately quantifying uncertainty in these predictions. Experimentalists and modellers must choose which experimental procedures (protocols) are used to produce data used to train models. We propose to characterise uncertainty owing to model discrepancy with an ensemble of parameter sets, each of which results from training to data from a different protocol. The variability in predictions from this ensemble provides an empirical estimate of predictive uncertainty owing to model discrepancy, even for unseen protocols. We use the example of electrophysiology experiments that investigate the properties of hERG potassium channels. Here, 'information-rich' protocols allow mathematical models to be trained using numerous short experiments performed on the same cell. In this case, we simulate data with one model and fit it with a different (discrepant) one. For any individual experimental protocol, parameter estimates vary little under repeated samples from the assumed additive independent Gaussian noise model. Yet parameter sets arising from the same model applied to different experiments conflict-highlighting model discrepancy. Our methods will help select more suitable ion channel models for future studies, and will be widely applicable to a range of biological modelling problems.

Model-driven optimal experimental design for calibrating cardiac electrophysiology models

BACKGROUND AND OBJECTIVE

Models of the cardiomyocyte action potential have contributed immensely to the understanding of heart function, pathophysiology, and the origin of heart rhythm disturbances. However, action potential models are highly nonlinear, making them difficult to parameterise and limiting to describing 'average cell' dynamics, when cell-specific models would be ideal to uncover inter-cell variability but are too experimentally challenging to be achieved. Here, we focus on automatically designing experimental protocols that allow us to better identify cell-specific maximum conductance values for each major current type.

METHODS AND RESULTS

We developed an approach that applies optimal experimental designs to patch-clamp experiments, including both voltage-clamp and current-clamp experiments. We assessed the models calibrated to these new optimal designs by comparing them to the models calibrated to some of the commonly used designs in the literature. We showed that optimal designs are not only overall shorter in duration but also able to perform better than many of the existing experiment designs in terms of identifying model parameters and hence model predictive power.

CONCLUSIONS

For cardiac cellular electrophysiology, this approach will allow researchers to define their hypothesis of the dynamics of the system and automatically design experimental protocols that will result in theoretically optimal designs.

The Strength of hERG Inhibition by Erythromycin at Different Temperatures Might Be Due to Its Interacting Features with the Channels

Erythromycin is one of the few compounds that remarkably increase ether-a-go-go-related gene (hERG) inhibition from room temperature (RT) to physiological temperature (PT). Understanding how erythromycin inhibits the hERG could help us to decide which compounds are needed for further studies. The whole-cell patch clamp technique was used to investigate the effects of erythromycin on hERG channels at different temperatures. While erythromycin caused a concentration-dependent inhibition of cardiac hERG channels, it also shifted the steady-state activation and steady-state inactivation of the channel to the left and significantly accelerated the onset of inactivation at both temperatures, although temperature itself caused a profound change in the dynamics of hERG channels. Our data also suggest that the binding pattern to S6 of the channels changes at PT. In contrast, cisapride, a well-known hERG blocker whose inhibition is not affected by temperature, does not change its critical binding sites after the temperature is raised to PT. Our data suggest that erythromycin is unique and that the shift in hERG inhibition may not apply to other compounds.

A need for exhaustive and standardized characterization of ion channels activity. The case of KV11.1

hERG, the pore-forming subunit of the rapid component of the delayed rectifier K⁺ current, plays a key role in ventricular repolarization. Mutations in the KCNH2 gene encoding hERG are associated with several cardiac rhythmic disorders, mainly the Long QT syndrome (LQTS) characterized by prolonged ventricular repolarization, leading to ventricular tachyarrhythmias, sometimes progressing to ventricular fibrillation and sudden death. Over the past few years, the emergence of next-generation sequencing has revealed an increasing number of genetic variants including KCNH2 variants. However, the potential pathogenicity of the majority of the variants remains unknown, thus classifying them as variants of uncertain significance or VUS. With diseases such as LQTS being associated with sudden death, identifying patients at risk by determining the variant pathogenicity, is crucial. The purpose of this review is to describe, on the basis of an exhaustive examination of the 1322 missense variants, the nature of the functional assays undertaken so far and their limitations. A detailed analysis of 38 hERG missense variants identified in Long QT French patients and studied in electrophysiology also underlies the incomplete characterization of the biophysical properties for each variant. These analyses lead to two conclusions: first, the function of many hERG variants has never been looked at and, second, the functional studies done so far are excessively heterogeneous regarding the stimulation protocols, cellular models, experimental temperatures, homozygous and/or the heterozygous condition under study, a context that may lead to conflicting conclusions. The state of the literature emphasizes how necessary and important it is to perform an exhaustive functional characterization of hERG variants and to standardize this effort for meaningful comparison among variants. The review ends with suggestions to create a unique homogeneous protocol that could be shared and adopted among scientists and that would facilitate cardiologists and geneticists in patient counseling and management.

Autocorrelated measurement processes and inference for ordinary differential equation models of biological systems

Ordinary differential equation models are used to describe dynamic processes across biology. To perform likelihood-based parameter inference on these models, it is necessary to specify a statistical process representing the contribution of factors not explicitly included in the mathematical model. For this, independent Gaussian noise is commonly chosen, with its use so widespread that researchers typically provide no explicit justification for this choice. This noise model assumes ‘random’ latent factors affect the system in the ephemeral fashion resulting in unsystematic deviation of observables from their modelled counterparts. However, like the deterministically modelled parts of a system, these latent factors can have persistent effects on observables. Here, we use experimental data from dynamical systems drawn from cardiac physiology and electrochemistry to demonstrate that highly persistent differences between observations and modelled quantities can occur. Considering the case when persistent noise arises owing only to measurement imperfections, we use the Fisher information matrix to quantify how uncertainty in parameter estimates is artificially reduced when erroneously assuming independent noise. We present a workflow to diagnose persistent noise from model fits and describe how to remodel accounting for correlated errors.

Multiple mechanisms underlie reduced potassium conductance in the p.T1019PfsX38 variant of hERG

Long QT syndrome type II (LQT2) is caused by loss‐of‐function mutations in the hERG K⁺ channel, leading to increased incidence of cardiac arrest and sudden death. Many genetic variants have been reported in the hERG gene with various consequences on channel expression, permeation, and gating. Only a small number of LQT2 causing variants has been characterized to define the underlying pathophysiological causes of the disease. We sought to determine the characteristics of the frameshift variant p.Thr1019ProfsX38 (T1019PfsX38) which affects the C‐terminus of the protein. This mutation was identified in an extended Omani family of LQT2. It replaces the last 140 amino acids of hERG with 37 unique amino acids. T1019 is positioned at a distinguished region of the C‐terminal tail of hERG, as predicted from the deep learning system AlphaFold v2.0. We employed the whole‐cell configuration of the patch‐clamp technique to study wild‐type and mutant channels that were transiently expressed in human embryonic kidney 293 (HEK293) cells. Depolarizing voltages elicited slowly deactivating tail currents that appeared upon repolarization of cells that express either wild‐type‐ or T1019PfsX38‐hERG. There were no differences in the voltage and time dependencies of activation between the two variants. However, the rates of hERG channel deactivation at hyperpolarizing potentials were accelerated by T1019PfsX38. In addition, the voltage dependence of inactivation of T1019PfsX38‐hERG was shifted by 20 mV in the negative direction when compared with wild‐type hERG. The rates of channel inactivation were increased in the mutant channel variant. Next, we employed a step‐ramp protocol to mimic membrane repolarization by the cardiac action potential. The amplitudes of outward currents and their integrals were reduced in the mutant variant when compared with the wild‐type variant during repolarization. Thus, changes in the gating dynamics of hERG by the T1019PfsX38 variant contribute to the pathology seen in affected LQT2 patients.

Translating the measurement of hERG kinetics and drug block for CiPA to a high throughput platform

The Comprehensive in vitro Proarrhythmic Assay (CiPA) has promoted use of in silico models of drug effects on cardiac repolarization to improve proarrhythmic risk prediction. These models contain a pharmacodynamic component describing drug binding to hERG channels that required in vitro data for kinetics of block, in addition to potency, to constrain them. To date, development and validation has been undertaken using data from manual patch-clamp. The application of this approach at scale requires the development of a high-throughput, automated patch-clamp (APC) implementation. Here, we present a comprehensive analysis of the implementation of the Milnes, or CiPA dynamic protocol, on an APC platform, including quality control and data analysis. Kinetics and potency of block were assessed for bepridil, cisapride, terfenadine and verapamil with data retention/QC pass rate of 21.8% overall, or as high as 50.4% when only appropriate sweep lengths were considered for drugs with faster kinetics. The variability in IC₅₀ and kinetics between manual and APC was comparable to that seen between sites/platforms in previous APC studies of potency. Whilst the experimental success is less than observed in screens of potency alone, it is still significantly greater than manual patch. With the modifications to protocol design, including sweep length, number of repetitions, and leak correction recommended in this study, this protocol can be applied on APC to acquire data comparable to manual patch clamp.

A nonlinear and time-dependent leak current in the presence of calcium fluoride patch-clamp seal enhancer

Automated patch-clamp platforms are widely used and vital tools in both academia and industry to enable high-throughput studies such as drug screening. A leak current to ground occurs whenever the seal between a pipette and cell (or internal solution and cell in high-throughput machines) is not perfectly insulated from the bath (extracellular) solution. Over 1 GΩ seal resistance between pipette and bath solutions is commonly used as a quality standard for manual patch work. With automated platforms it can be difficult to obtain such a high seal resistance between the intra- and extra-cellular solutions. One suggested method to alleviate this problem is using an F ⁻ containing internal solution together with a Ca ²⁺ containing external solution — so that a CaF ₂ crystal forms when the two solutions meet which ‘plugs the holes’ to enhance the seal resistance. However, we observed an unexpected nonlinear-in-voltage and time-dependent current using these solutions on an automated patch-clamp platform. We performed manual patch-clamp experiments with the automated patch-clamp solutions, but no biological cell, and observed the same nonlinear time-dependent leak current. The current could be completely removed by washing out F ⁻ ions to leave a conventional leak current that was linear and not time-dependent. We therefore conclude fluoride ions interacting with the CaF ₂ crystal are the origin of the nonlinear time-dependent leak current. The consequences of such a nonlinear and time-dependent leak current polluting measurements should be considered carefully if it cannot be isolated and subtracted.

Electrophysiological characterization of the hERG R56Q LQTS variant and targeted rescue by the activator RPR260243

Human Ether-à-go-go (hERG) channels contribute to cardiac repolarization, and inherited variants or drug block are associated with long QT syndrome type 2 (LQTS2) and arrhythmia. Therefore, hERG activator compounds present a therapeutic opportunity for targeted treatment of LQTS. However, a limiting concern is over-activation of hERG resurgent current during the action potential and abbreviated repolarization. Activators that slow deactivation gating (type I), such as RPR260243, may enhance repolarizing hERG current during the refractory period, thus ameliorating arrhythmogenicity with reduced early repolarization risk. Here, we show that, at physiological temperature, RPR260243 enhances hERG channel repolarizing currents conducted in the refractory period in response to premature depolarizations. This occurs with little effect on the resurgent hERG current during the action potential. The effects of RPR260243 were particularly evident in LQTS2-associated R56Q mutant channels, whereby RPR260243 restored WT-like repolarizing drive in the early refractory period and diastolic interval, combating attenuated protective currents. In silico kinetic modeling of channel gating predicted little effect of the R56Q mutation on hERG current conducted during the action potential and a reduced repolarizing protection against afterdepolarizations in the refractory period and diastolic interval, particularly at higher pacing rates. These simulations predicted partial rescue from the arrhythmic effects of R56Q by RPR260243 without risk of early repolarization. Our findings demonstrate that the pathogenicity of some hERG variants may result from reduced repolarizing protection during the refractory period and diastolic interval with limited effect on action potential duration, and that the hERG channel activator RPR260243 may provide targeted antiarrhythmic potential in these cases.

Use of automated patch clamp in cardiac safety assessment: Past, present & future perspectives

There is no doubt that automated patch clamp (APC) technology has revolutionized research in biomedical science. High throughput ion channel screening is now an integral part of the development and safety profiling of the majority of new chemical entities currently developed to address unmet medical needs. The increased throughput it provides has significantly improved the ability to overcome the time-consuming, low throughput bottlenecks resulting from the more conventional manual patch clamp method, considered the 'gold standard', for studying ion channel function and pharmacology. While systems offering the luxury of automation have only been commercially available for two decades, the road leading to this new technology is long and rich in seminal, hands-on, studies dating back as far as the 18th century. So where does this technology currently stand, and what will it look like in the future? In the current article, we review the scientific history leading to the development of APC systems, examine key drivers in the rapid development of this technology (such as failed ion channel programmes and the issue of drug-induced hERG inhibition and QT interval prolongation), highlight key capabilities and finally provide some perspective on the current and future impact of the technology on cardiac safety assessment and biomedical science.

Neural Network Differential Equations For Ion Channel Modelling

Mathematical models of cardiac ion channels have been widely used to study and predict the behaviour of ion currents. Typically models are built using biophysically-based mechanistic principles such as Hodgkin-Huxley or Markov state transitions. These models provide an abstract description of the underlying conformational changes of the ion channels. However, due to the abstracted conformation states and assumptions for the rates of transition between them, there are differences between the models and reality-termed model discrepancy or misspecification. In this paper, we demonstrate the feasibility of using a mechanistically-inspired neural network differential equation model, a hybrid non-parametric model, to model ion channel kinetics. We apply it to the hERG potassium ion channel as an example, with the aim of providing an alternative modelling approach that could alleviate certain limitations of the traditional approach. We compare and discuss multiple ways of using a neural network to approximate extra hidden states or alternative transition rates. In particular we assess their ability to learn the missing dynamics, and ask whether we can use these models to handle model discrepancy. Finally, we discuss the practicality and limitations of using neural networks and their potential applications.

Statistical Approach to Incorporating Experimental Variability into a Mathematical Model of the Voltage-Gated Na+ Channel and Human Atrial Action Potential

The voltage-gated Na⁺ channel Na_v1.5 is critical for normal cardiac myocyte excitability. Mathematical models have been widely used to study Na_v1.5 function and link to a range of cardiac arrhythmias. There is growing appreciation for the importance of incorporating physiological heterogeneity observed even in a healthy population into mathematical models of the cardiac action potential. Here, we apply methods from Bayesian statistics to capture the variability in experimental measurements on human atrial Na_v1.5 across experimental protocols and labs. This variability was used to define a physiological distribution for model parameters in a novel model formulation of Na_v1.5, which was then incorporated into an existing human atrial action potential model. Model validation was performed by comparing the simulated distribution of action potential upstroke velocity measurements to experimental measurements from several different sources. Going forward, we hope to apply this approach to other major atrial ion channels to create a comprehensive model of the human atrial AP. We anticipate that such a model will be useful for understanding excitability at the population level, including variable drug response and penetrance of variants linked to inherited cardiac arrhythmia syndromes.

Use of automated patch clamp in cardiac safety assessment: past, present and future perspectives

There is no doubt that automated patch clamp (APC) technology has revolutionized research in biomedical science. High throughput ion channel screening is now an integral part of the development and safety profiling of the majority of new chemical entities currently developed to address unmet medical needs. The increased throughput it provides has significantly improved the ability to overcome the time-consuming, low throughput bottlenecks resulting from the more conventional manual patch clamp method, considered the 'gold standard', for studying ion channel function and pharmacology. While systems offering the luxury of automation have only been commercially available for two decades, the road leading to this new technology is long and rich in seminal, hands-on, studies dating back as far as the 18th century. So where does this technology currently stand, and what will it look like in the future? In the current article, we review the scientific history leading to the development of APC systems, examine key drivers in the rapid development of this technology (such as failed ion channel programmes and the issue of drug-induced hERG inhibition and QT interval prolongation), highlight key capabilities and finally provide some perspective on the current and future impact of the technology on cardiac safety assessment and biomedical science.

Physiological Roles of the Rapidly Activated Delayed Rectifier K+ Current in Adult Mouse Heart Primary Pacemaker Activity

Robust, spontaneous pacemaker activity originating in the sinoatrial node (SAN) of the heart is essential for cardiovascular function. Anatomical, electrophysiological, and molecular methods as well as mathematical modeling approaches have quite thoroughly characterized the transmembrane fluxes of Na⁺, K⁺ and Ca²⁺ that produce SAN action potentials (AP) and ‘pacemaker depolarizations’ in a number of different in vitro adult mammalian heart preparations. Possible ionic mechanisms that are responsible for SAN primary pacemaker activity are described in terms of: (i) a Ca²⁺-regulated mechanism based on a requirement for phasic release of Ca²⁺ from intracellular stores and activation of an inward current-mediated by Na⁺/Ca²⁺ exchange; (ii) time- and voltage-dependent activation of Na⁺ or Ca²⁺ currents, as well as a cyclic nucleotide-activated current, I_f; and/or (iii) a combination of (i) and (ii). Electrophysiological studies of single spontaneously active SAN myocytes in both adult mouse and rabbit hearts consistently reveal significant expression of a rapidly activating time- and voltage-dependent K⁺ current, often denoted I_Kr, that is selectively expressed in the leading or primary pacemaker region of the adult mouse SAN. The main goal of the present study was to examine by combined experimental and simulation approaches the functional or physiological roles of this K⁺ current in the pacemaker activity. Our patch clamp data of mouse SAN myocytes on the effects of a pharmacological blocker, E4031, revealed that a rapidly activating K⁺ current is essential for action potential (AP) repolarization, and its deactivation during the pacemaker potential contributes a small but significant component to the pacemaker depolarization. Mathematical simulations using a murine SAN AP model confirm that well known biophysical properties of a delayed rectifier K⁺ current can contribute to its role in generating spontaneous myogenic activity.

Calibration of ionic and cellular cardiac electrophysiology models

Cardiac electrophysiology models are among the most mature and well-studied mathematical models of biological systems. This maturity is bringing new challenges as models are being used increasingly to make quantitative rather than qualitative predictions. As such, calibrating the parameters within ion current and action potential (AP) models to experimental data sets is a crucial step in constructing a predictive model. This review highlights some of the fundamental concepts in cardiac model calibration and is intended to be readily understood by computational and mathematical modelers working in other fields of biology. We discuss the classic and latest approaches to calibration in the electrophysiology field, at both the ion channel and cellular AP scales. We end with a discussion of the many challenges that work to date has raised and the need for reproducible descriptions of the calibration process to enable models to be recalibrated to new data sets and built upon for new studies. This article is categorized under: Analytical and Computational Methods > Computational Methods Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Cellular Models.

A nonlinear and time-dependent leak current in the presence of calcium fluoride patch-clamp seal enhancer

Automated patch-clamp platforms are widely used and vital tools in both academia and industry to enable high-throughput studies such as drug screening. A leak current to ground occurs whenever the seal between a pipette and cell (or internal solution and cell in high-throughput machines) is not perfectly insulated from the bath (extracellular) solution. Over 1 GΩ seal resistance between pipette and bath solutions is commonly used as a quality standard for manual patch work. With automated platforms it can be difficult to obtain such a high seal resistance between the intra- and extra-cellular solutions. One suggested method to alleviate this problem is using an F− containing internal solution together with a Ca2+ containing external solution — so that a CaF2 crystal forms when the two solutions meet which ‘plugs the holes’ to enhance the seal resistance. However, we observed an unexpected nonlinear-in-voltage and time-dependent current using these solutions on an automated patch-clamp platform. We performed manual patch-clamp experiments with the automated patch-clamp solutions, but no biological cell, and observed the same nonlinear time-dependent leak current. The current could be completely removed by washing out F− ions to leave a conventional leak current that was linear and not time-dependent. We therefore conclude fluoride ions interacting with the CaF2 crystal are the origin of the nonlinear time-dependent leak current. The consequences of such a nonlinear and time-dependent leak current polluting measurements should be considered carefully if it cannot be isolated and subtracted.

Considering discrepancy when calibrating a mechanistic electrophysiology model

Uncertainty quantification (UQ) is a vital step in using mathematical models and simulations to take decisions. The field of cardiac simulation has begun to explore and adopt UQ methods to characterize uncertainty in model inputs and how that propagates through to outputs or predictions; examples of this can be seen in the papers of this issue. In this review and perspective piece, we draw attention to an important and under-addressed source of uncertainty in our predictions-that of uncertainty in the model structure or the equations themselves. The difference between imperfect models and reality is termed model discrepancy, and we are often uncertain as to the size and consequences of this discrepancy. Here, we provide two examples of the consequences of discrepancy when calibrating models at the ion channel and action potential scales. Furthermore, we attempt to account for this discrepancy when calibrating and validating an ion channel model using different methods, based on modelling the discrepancy using Gaussian processes and autoregressive-moving-average models, then highlight the advantages and shortcomings of each approach. Finally, suggestions and lines of enquiry for future work are provided. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

An audit of uncertainty in multi-scale cardiac electrophysiology models

Models of electrical activation and recovery in cardiac cells and tissue have become valuable research tools, and are beginning to be used in safety-critical applications including guidance for clinical procedures and for drug safety assessment. As a consequence, there is an urgent need for a more detailed and quantitative understanding of the ways that uncertainty and variability influence model predictions. In this paper, we review the sources of uncertainty in these models at different spatial scales, discuss how uncertainties are communicated across scales, and begin to assess their relative importance. We conclude by highlighting important challenges that continue to face the cardiac modelling community, identifying open questions, and making recommendations for future studies. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Accounting for variability in ion current recordings using a mathematical model of artefacts in voltage-clamp experiments

Mathematical models of ion channels, which constitute indispensable components of action potential models, are commonly constructed by fitting to whole-cell patch-clamp data. In a previous study, we fitted cell-specific models to hERG1a (Kv11.1) recordings simultaneously measured using an automated high-throughput system, and studied cell-cell variability by inspecting the resulting model parameters. However, the origin of the observed variability was not identified. Here, we study the source of variability by constructing a model that describes not just ion current dynamics, but the entire voltage-clamp experiment. The experimental artefact components of the model include: series resistance, membrane and pipette capacitance, voltage offsets, imperfect compensations made by the amplifier for these phenomena, and leak current. In this model, variability in the observations can be explained by either cell properties, measurement artefacts, or both. Remarkably, by assuming that variability arises exclusively from measurement artefacts, it is possible to explain a larger amount of the observed variability than when assuming cell-specific ion current kinetics. This assumption also leads to a smaller number of model parameters. This result suggests that most of the observed variability in patch-clamp data measured under the same conditions is caused by experimental artefacts, and hence can be compensated for in post-processing by using our model for the patch-clamp experiment. This study has implications for the question of the extent to which cell-cell variability in ion channel kinetics exists, and opens up routes for better correction of artefacts in patch-clamp data. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.

Cross-site and cross-platform variability of automated patch clamp assessments of drug effects on human cardiac currents in recombinant cells

Automated patch clamp (APC) instruments enable efficient evaluation of electrophysiologic effects of drugs on human cardiac currents in heterologous expression systems. Differences in experimental protocols, instruments, and dissimilar site procedures affect the variability of IC50 values characterizing drug block potency. This impacts the utility of APC platforms for assessing a drug's cardiac safety margin. We determined variability of APC data from multiple sites that measured blocking potency of 12 blinded drugs (with different levels of proarrhythmic risk) against four human cardiac currents (hERG [IKr], hCav1.2 [L-Type ICa], peak hNav1.5, [Peak INa], late hNav1.5 [Late INa]) with recommended protocols (to minimize variance) using five APC platforms across 17 sites. IC50 variability (25/75 percentiles) differed for drugs and currents (e.g., 10.4-fold for dofetilide block of hERG current and 4-fold for mexiletine block of hNav1.5 current). Within-platform variance predominated for 4 of 12 hERG blocking drugs and 4 of 6 hNav1.5 blocking drugs. hERG and hNav1.5 block. Bland-Altman plots depicted varying agreement across APC platforms. A follow-up survey suggested multiple sources of experimental variability that could be further minimized by stricter adherence to standard protocols. Adoption of best practices would ensure less variable APC datasets and improved safety margins and proarrhythmic risk assessments.

Four Ways to Fit an Ion Channel Model

Mathematical models of ionic currents are used to study the electrophysiology of the heart, brain, gut, and several other organs. Increasingly, these models are being used predictively in the clinic, for example, to predict the risks and results of genetic mutations, pharmacological treatments, or surgical procedures. These safety-critical applications depend on accurate characterization of the underlying ionic currents. Four different methods can be found in the literature to fit voltage-sensitive ion channel models to whole-cell current measurements: method 1, fitting model equations directly to time-constant, steady-state, and I-V summary curves; method 2, fitting by comparing simulated versions of these summary curves to their experimental counterparts; method 3, fitting to the current traces themselves from a range of protocols; and method 4, fitting to a single current trace from a short and rapidly fluctuating voltage-clamp protocol. We compare these methods using a set of experiments in which hERG1a current was measured in nine Chinese hamster ovary cells. In each cell, the same sequence of fitting protocols was applied, as well as an independent validation protocol. We show that methods 3 and 4 provide the best predictions on the independent validation set and that short, rapidly fluctuating protocols like that used in method 4 can replace much longer conventional protocols without loss of predictive ability. Although data for method 2 are most readily available from the literature, we find it performs poorly compared to methods 3 and 4 both in accuracy of predictions and computational efficiency. Our results demonstrate how novel experimental and computational approaches can improve the quality of model predictions in safety-critical applications.

Rapid Characterization of hERG Channel Kinetics I: Using an Automated High-Throughput System

Predicting how pharmaceuticals may affect heart rhythm is a crucial step in drug development and requires a deep understanding of a compound’s action on ion channels. In vitro hERG channel current recordings are an important step in evaluating the proarrhythmic potential of small molecules and are now routinely performed using automated high-throughput patch-clamp platforms. These machines can execute traditional voltage-clamp protocols aimed at specific gating processes, but the array of protocols needed to fully characterize a current is typically too long to be applied in a single cell. Shorter high-information protocols have recently been introduced that have this capability, but they are not typically compatible with high-throughput platforms. We present a new 15 second protocol to characterize hERG (Kv11.1) kinetics, suitable for both manual and high-throughput systems. We demonstrate its use on the Nanion SyncroPatch 384PE, a 384-well automated patch-clamp platform, by applying it to Chinese hamster ovary cells stably expressing hERG1a. From these recordings, we construct 124 cell-specific variants/parameterizations of a hERG model at 25°C. A further eight independent protocols are run in each cell and are used to validate the model predictions. We then combine the experimental recordings using a hierarchical Bayesian model, which we use to quantify the uncertainty in the model parameters, and their variability from cell-to-cell; we use this model to suggest reasons for the variability. This study demonstrates a robust method to measure and quantify uncertainty and shows that it is possible and practical to use high-throughput systems to capture full hERG channel kinetics quantitatively and rapidly.