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

Shedding Light on Cardiac Excitation: In Vitro and In Silico Analysis of Native Ca2+ Channel Activation in Guinea Pig Cardiomyocytes Using Organic Photovoltaic Devices

OBJECTIVE

This study aims to explore the potential of organic electrolytic photocapacitors (OEPCs), an innovative photovoltaic device, in mediating the activation of native voltage-gated Cav1.2 channels (ICa,L) in Guinea pig ventricular cardiomyocytes.

METHODS

Whole-cell patch-clamp recordings were employed to examine light-triggered OEPC mediated ICa,L activation, integrating the channel's kinetic properties into a multicompartment cell model to take intracellular ion concentrations into account. A multidomain model was additionally incorporated to evaluate effects of OEPC-mediated stimulation. The final model combines external stimulation, multicompartmental cell simulation, and a patch-clamp amplifier equivalent circuit to assess the impact on achievable intracellular voltage changes.

RESULTS

Light pulses activated ICa,L, with amplitudes similar to voltage-clamp activation and high sensitivity to the L-type Ca2+ channel blocker, nifedipine. Light-triggered ICa,L inactivation exhibited kinetic parameters comparable to voltage-induced inactivation.

CONCLUSION

OEPC-mediated activation of ICa,L demonstrates their potential for nongenetic optical modulation of cellular physiology potentially paving the way for the development of innovative therapies in cardiovascular health. The integrated model proves the light-mediated activation of ICa,L and advances the understanding of the interplay between the patch-clamp amplifier and external stimulation devices.

SIGNIFICANCE

Treating cardiac conduction disorders by minimal-invasive means without genetic modifications could advance therapeutic approaches increasing patients' quality of life compared with conventional methods employing electronic devices.

Single-cell ionic current phenotyping elucidates non-canonical features and predictive potential of cardiomyocytes during automated drug experiments

All new drugs must go through preclinical screening tests to determine their proarrhythmic potential. While these assays effectively filter out dangerous drugs, they are too conservative, often misclassifying safe compounds as proarrhythmic. In this study, we attempt to address this shortcoming with a novel, medium-throughput drug-screening approach: we use an automated patch-clamp system to acquire optimized voltage clamp (VC) and action potential (AP) data from human induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs) at several drug concentrations (baseline, 3×, 10× and 20× the effective free plasma concentrations). With our novel method, we show correlations between INa block and upstroke slowing after treatment with flecainide or quinine. Additionally, after quinine treatment, we identify significant reductions in current during voltage steps designed to isolate If and IKs. However, we do not detect any IKr block by either drug, and upon further investigation, do not see any IKr present in the iPSC-CMs when prepared for automated patch experiments (i.e. in suspension) - this is in contrast to similar experiments we have conducted with these cells using the manual patch setup. In this study, we: (1) present a proof-of-concept demonstration of a single-cell medium-throughput drug study, and (2) characterize the non-canonical electrophysiology of iPSC-CMs when prepared for experiments in a medium-throughput setting. KEY POINTS: Human induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs) offer potential as an in vitro model to study the proarrhythmic potential of drugs, but insights from these cells are often limited by the low throughput of manual patch-clamp. In this study, we use a medium-throughput automated patch-clamp system to acquire action potential (AP) and complex voltage clamp (VC) data from single iPSC-CMs at multiple drug concentrations. A correlation between AP upstroke and INa transients was identified and drug-induced changes in ionic currents found. We also characterize the substantially altered physiology of iPSC-CMs when patched in an automated system, suggesting the need to investigate differences between manual and automated patch experiments.

Single-cell ionic current phenotyping explains stem cell-derived cardiomyocyte action potential morphology

Human induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs) are a promising tool to study arrhythmia-related factors, but the variability of action potential (AP) recordings from these cells limits their use as an in vitro model. In this study, we use recently published brief (10 s), dynamic voltage-clamp (VC) data to provide mechanistic insights into the ionic currents contributing to AP heterogeneity; we call this approach rapid ionic current phenotyping (RICP). Features of this VC data were correlated to AP recordings from the same cells, and we used computational models to generate mechanistic insights into cellular heterogeneity. This analysis uncovered several interesting links between AP morphology and ionic current density: both L-type calcium and sodium currents contribute to upstroke velocity, rapid delayed rectifier K+ current is the main determinant of the maximal diastolic potential, and an outward current in the activation range of slow delayed rectifier K+ is the main determinant of AP duration. Our analysis also identified an outward current in several cells at 6 mV that is not reproduced by iPSC-CM mathematical models but contributes to determining AP duration. RICP can be used to explain how cell-to-cell variability in ionic currents gives rise to AP heterogeneity. Because of its brief duration (10 s) and ease of data interpretation, we recommend the use of RICP for single-cell patch-clamp experiments that include the acquisition of APs.NEW & NOTEWORTHY We present rapid ionic current phenotyping (RICP), a current quantification approach based on an optimized voltage-clamp protocol. The method captures a rich snapshot of the ionic current dynamics, providing quantitative information about multiple currents (e.g., ICa,L, IKr) in the same cell. The protocol helped to identify key ionic determinants of cellular action potential heterogeneity in iPSC-CMs. This included unexpected results, such as the critical role of IKr in establishing the maximum diastolic potential.

Estimation of persistent sodium-current density in rat hippocampal mossy fibre boutons: Correction of space-clamp errors

We used whole-cell patch clamp to estimate the stationary voltage dependence of persistent sodium-current density (iNaP) in rat hippocampal mossy fibre boutons. Cox's method for correcting space-clamp errors was extended to the case of an isopotential compartment with attached neurites. The method was applied to voltage-ramp experiments, in which iNaP is assumed to gate instantaneously. The raw estimates of iNaP led to predicted clamp currents that were at variance with observation, hence an algorithm was devised to improve these estimates. Optionally, the method also allows an estimate of the membrane specific capacitance, although values of the axial resistivity and seal resistance must be provided. Assuming that membrane specific capacitance and axial resistivity were constant, we conclude that seal resistance continued to fall after adding TTX to the bath. This might have been attributable to a further deterioration of the seal after baseline rather than an unlikely effect of TTX. There was an increase in the membrane specific resistance in TTX. The reason for this is unknown, but it meant that iNaP could not be determined by simple subtraction. Attempts to account for iNaP with a Hodgkin-Huxley model of the transient sodium conductance met with mixed results. One thing to emerge was the importance of voltage shifts. Also, a large variability in previously reported values of transient sodium conductance in mossy fibre boutons made comparisons with our results difficult. Various other possible sources of error are discussed. Simulations suggest a role for iNaP in modulating the axonal attenuation of EPSPs. KEY POINTS: We used whole-cell patch clamp to estimate the stationary voltage dependence of persistent sodium-current density (iNaP) in rat hippocampal mossy fibre boutons, using a KCl-based internal (pipette) solution and correcting for the liquid junction potential (2 mV). Space-clamp errors and deterioration of the patch-clamp seal during the experiment were corrected for by compartmental modelling. Attempts to account for iNaP in terms of the transient sodium conductance met with mixed results. One possibility is that the transient sodium conductance is higher in mossy fibre boutons than in the axon shaft. The analysis illustrates the need to account for various voltage shifts (Donnan potentials, liquid junction potentials and, possibly, other voltage shifts). Simulations suggest a role for iNaP in modulating the axonal attenuation of excitatory postsynaptic potentials, hence analog signalling by dentate granule cells.

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.

Human sodium current voltage-dependence at physiological temperature measured by coupling a patch-clamp experiment to a mathematical model

Voltage-gated Na+ channels are crucial to action potential propagation in excitable tissues. Because of the high amplitude and rapid activation of the Na+ current, voltage-clamp measurements are very challenging and are usually performed at room temperature. In this study, we measured Na+ current voltage-dependence in stem cell-derived cardiomyocytes at physiological temperature. While the apparent activation and inactivation curves, measured as the dependence of current amplitude on voltage, fall within the range reported in previous studies, we identified a systematic error in our measurements. This error is caused by the deviation of the membrane potential from the command potential of the amplifier. We demonstrate that it is possible to account for this artifact using computer simulation of the patch-clamp experiment. We obtained surprising results through patch-clamp model optimization: a half-activation of -11.5 mV and a half-inactivation of -87 mV. Although the half-activation deviates from previous research, we demonstrate that this estimate reproduces the conduction velocity dependence on extracellular potassium concentration. KEY POINTS: Voltage-gated Na+ currents play a crucial role in excitable tissues including neurons, cardiac and skeletal muscle. Measurement of Na+ current is challenging because of its high amplitude and rapid kinetics, especially at physiological temperature. We have used the patch-clamp technique to measure human Na+ current voltage-dependence in human induced pluripotent stem cell-derived cardiomyocytes. The patch-clamp data were processed by optimization of the model accounting for voltage-clamp experiment artifacts, revealing a large difference between apparent parameters of Na+ current and the results of the optimization. We conclude that actual Na+ current activation is extremely depolarized in comparison to previous studies. The new Na+ current model provides a better understanding of action potential propagation; we demonstrate that it explains propagation in hyperkalaemic conditions.

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.

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.

Rapid ionic current phenotyping (RICP) identifies mechanistic underpinnings of iPSC-CM AP heterogeneity

As a renewable, easily accessible, human-derived in vitro model, human induced pluripotent stem cell derived cardiomyocytes (iPSC-CMs) are a promising tool for studying arrhythmia-related factors, including cardiotoxicity and congenital proarrhythmia risks. An oft-mentioned limitation of iPSC-CMs is the abundant cell-to-cell variability in recordings of their electrical activity. Here, we develop a new method, rapid ionic current phenotyping (RICP), that utilizes a short (10 s) voltage clamp protocol to quantify cell-to-cell heterogeneity in key ionic currents. We correlate these ionic current dynamics to action potential recordings from the same cells and produce mechanistic insights into cellular heterogeneity. We present evidence that the L-type calcium current is the main determinant of upstroke velocity, rapid delayed rectifier K+ current is the main determinant of the maximal diastolic potential, and an outward current in the excitable range of slow delayed rectifier K+ is the main determinant of action potential duration. We measure an unidentified outward current in several cells at 6 mV that is not recapitulated by iPSC-CM mathematical models but contributes to determining action potential duration. In this way, our study both quantifies cell-to-cell variability in membrane potential and ionic currents, and demonstrates how the ionic current variability gives rise to action potential heterogeneity. Based on these results, we argue that iPSC-CM heterogeneity should not be viewed simply as a problem to be solved but as a model system to understand the mechanistic underpinnings of cellular variability.

Leak current, even with gigaohm seals, can cause misinterpretation of stem cell-derived cardiomyocyte action potential recordings

AIMS

Human-induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs) have become an essential tool to study arrhythmia mechanisms. Much of the foundational work on these cells, as well as the computational models built from the resultant data, has overlooked the contribution of seal-leak current on the immature and heterogeneous phenotype that has come to define these cells. The aim of this study is to understand the effect of seal-leak current on recordings of action potential (AP) morphology.

METHODS AND RESULTS

Action potentials were recorded in human iPSC-CMs using patch clamp and simulated using previously published mathematical models. Our in silico and in vitro studies demonstrate how seal-leak current depolarizes APs, substantially affecting their morphology, even with seal resistances (Rseal) above 1 GΩ. We show that compensation of this leak current is difficult due to challenges with obtaining accurate measures of Rseal during an experiment. Using simulation, we show that Rseal measures (i) change during an experiment, invalidating the use of pre-rupture values, and (ii) are polluted by the presence of transmembrane currents at every voltage. Finally, we posit that the background sodium current in baseline iPSC-CM models imitates the effects of seal-leak current and is increased to a level that masks the effects of seal-leak current on iPSC-CMs.

CONCLUSION

Based on these findings, we make recommendations to improve iPSC-CM AP data acquisition, interpretation, and model-building. Taking these recommendations into account will improve our understanding of iPSC-CM physiology and the descriptive ability of models built from such data.

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.

Models of the cardiac L-type calcium current: A quantitative review

The L-type calcium current (I CaL ) plays a critical role in cardiac electrophysiology, and models ofI CaL are vital tools to predict arrhythmogenicity of drugs and mutations. Five decades of measuring and modelingI CaL have resulted in several competing theories (encoded in mathematical equations). However, the introduction of new models has not typically been accompanied by a data-driven critical comparison with previous work, so that it is unclear which model is best suited for any particular application. In this review, we describe and compare 73 published mammalianI CaL models and use simulated experiments to show that there is a large variability in their predictions, which is not substantially diminished when grouping by species or other categories. We provide model code for 60 models, list major data sources, and discuss experimental and modeling work that will be required to reduce this huge list of competing theories and ultimately develop a community consensus model ofI CaL . This article is categorized under: Cardiovascular Diseases > Computational Models Cardiovascular Diseases > Molecular and Cellular Physiology.

An in silico-in vitro pipeline for drug cardiotoxicity screening identifies ionic pro-arrhythmia mechanisms

BACKGROUND AND PURPOSE

Before advancing to clinical trials, new drugs are screened for their pro-arrhythmic potential using a method that is overly conservative and provides limited mechanistic insight. The shortcomings of this approach can lead to the mis-classification of beneficial drugs as pro-arrhythmic.

EXPERIMENTAL APPROACH

An in silico-in vitro pipeline was developed to circumvent these shortcomings. A computational human induced pluripotent stem cell-derived cardiomyocyte (iPSC-CM) model was used as part of a genetic algorithm to design experiments, specifically electrophysiological voltage clamp (VC) protocols, to identify which of several cardiac ion channels were blocked during in vitro drug studies. Such VC data, along with dynamically clamped action potentials (AP), were acquired from iPSC-CMs before and after treatment with a control solution or a low- (verapamil), intermediate- (cisapride or quinine) or high-risk (quinidine) drug.

KEY RESULTS

Significant AP prolongation (a pro-arrhythmia marker) was seen in response to quinidine and quinine. The VC protocol identified block of IKr (a source of arrhythmias) by all strong IKr blockers, including cisapride, quinidine and quinine. The protocol also detected block of ICaL by verapamil and Ito by quinidine. Further demonstrating the power of the approach, the VC data uncovered a previously unidentified If block by quinine, which was confirmed with experiments using a HEK-293 expression system and automated patch-clamp.

CONCLUSION AND IMPLICATIONS

We developed an in silico-in vitro pipeline that simultaneously identifies pro-arrhythmia risk and mechanism of ion channel-blocking drugs. The approach offers a new tool for evaluating cardiotoxicity during preclinical drug screening.

Computational cardiac physiology for new modelers: Origins, foundations, and future

Mathematical models of the cardiovascular system have come a long way since they were first introduced in the early 19th century. Driven by a rapid development of experimental techniques, numerical methods, and computer hardware, detailed models that describe physical scales from the molecular level up to organs and organ systems have been derived and used for physiological research. Mathematical and computational models can be seen as condensed and quantitative formulations of extensive physiological knowledge and are used for formulating and testing hypotheses, interpreting and directing experimental research, and have contributed substantially to our understanding of cardiovascular physiology. However, in spite of the strengths of mathematics to precisely describe complex relationships and the obvious need for the mathematical and computational models to be informed by experimental data, there still exist considerable barriers between experimental and computational physiological research. In this review, we present a historical overview of the development of mathematical and computational models in cardiovascular physiology, including the current state of the art. We further argue why a tighter integration is needed between experimental and computational scientists in physiology, and point out important obstacles and challenges that must be overcome in order to fully realize the synergy of experimental and computational physiological research.

Bayesian inference of kinetic schemes for ion channels by Kalman filtering

Inferring adequate kinetic schemes for ion channel gating from ensemble currents is a daunting task due to limited information in the data. We address this problem by using a parallelized Bayesian filter to specify hidden Markov models for current and fluorescence data. We demonstrate the flexibility of this algorithm by including different noise distributions. Our generalized Kalman filter outperforms both a classical Kalman filter and a rate equation approach when applied to patch-clamp data exhibiting realistic open-channel noise. The derived generalization also enables inclusion of orthogonal fluorescence data, making unidentifiable parameters identifiable and increasing the accuracy of the parameter estimates by an order of magnitude. By using Bayesian highest credibility volumes, we found that our approach, in contrast to the rate equation approach, yields a realistic uncertainty quantification. Furthermore, the Bayesian filter delivers negligibly biased estimates for a wider range of data quality. For some data sets, it identifies more parameters than the rate equation approach. These results also demonstrate the power of assessing the validity of algorithms by Bayesian credibility volumes in general. Finally, we show that our Bayesian filter is more robust against errors induced by either analog filtering before analog-to-digital conversion or by limited time resolution of fluorescence data than a rate equation approach.

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.

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.

A549 in-silico 1.0: A first computational model to simulate cell cycle dependent ion current modulation in the human lung adenocarcinoma

Lung cancer is still a leading cause of death worldwide. In recent years, knowledge has been obtained of the mechanisms modulating ion channel kinetics and thus of cell bioelectric properties, which is promising for oncological biomarkers and targets. The complex interplay of channel expression and its consequences on malignant processes, however, is still insufficiently understood. We here introduce the first approach of an in-silico whole-cell ion current model of a cancer cell, in particular of the A549 human lung adenocarcinoma, including the main functionally expressed ion channels in the plasma membrane as so far known. This hidden Markov-based model represents the electrophysiology behind proliferation of the A549 cell, describing its rhythmic oscillation of the membrane potential able to trigger the transition between cell cycle phases, and it predicts membrane potential changes over the cell cycle provoked by targeted ion channel modulation. This first A549 in-silico cell model opens up a deeper insight and understanding of possible ion channel interactions in tumor development and progression, and is a valuable tool for simulating altered ion channel function in lung cancer electrophysiology.

Advances in the understanding of functional alterations at genetic, epigenetic or protein expression and the expanding knowledge in mechanisms modulating ion channel kinetics and thus the cells’ bioelectric properties have arisen as promising cancer biomarkers and oncological targets. Our hidden Markov-based in-silico cell model represents the electrophysiology behind proliferation of the A549 cell line, explaining the cell’s rhythmic oscillation from hyperpolarized to depolarized states of the membrane potential, able to trigger the transition between cell cycle phases. The model enables the prediction of membrane potential changes over the cell cycle provoked by targeted modulation of specific ion channels, leading to cell cycle promotion or interruption. We are encouraged that the availability of this first cancer cell model will provide profound insight into possible roles and interactions of ion channels in tumor development and progression, and may aid in the testing of research hypotheses in lung cancer electrophysiology.

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.

Computer modeling of whole-cell voltage-clamp analyses to delineate guidelines for good practice of manual and automated patch-clamp

The patch-clamp technique and more recently the high throughput patch-clamp technique have contributed to major advances in the characterization of ion channels. However, the whole-cell voltage-clamp technique presents certain limits that need to be considered for robust data generation. One major caveat is that increasing current amplitude profoundly impacts the accuracy of the biophysical analyses of macroscopic ion currents under study. Using mathematical kinetic models of a cardiac voltage-gated sodium channel and a cardiac voltage-gated potassium channel, we demonstrated how large current amplitude and series resistance artefacts induce an undetected alteration in the actual membrane potential and affect the characterization of voltage-dependent activation and inactivation processes. We also computed how dose-response curves are hindered by high current amplitudes. This is of high interest since stable cell lines frequently demonstrating high current amplitudes are used for safety pharmacology using the high throughput patch-clamp technique. It is therefore critical to set experimental limits for current amplitude recordings to prevent inaccuracy in the characterization of channel properties or drug activity, such limits being different from one channel type to another. Based on the predictions generated by the kinetic models, we draw simple guidelines for good practice of whole-cell voltage-clamp recordings.

Data-Driven Uncertainty Quantification for Cardiac Electrophysiological Models: Impact of Physiological Variability on Action Potential and Spiral Wave Dynamics

Computational modeling of cardiac electrophysiology (EP) has recently transitioned from a scientific research tool to clinical applications. To ensure reliability of clinical or regulatory decisions made using cardiac EP models, it is vital to evaluate the uncertainty in model predictions. Model predictions are uncertain because there is typically substantial uncertainty in model input parameters, due to measurement error or natural variability. While there has been much recent uncertainty quantification (UQ) research for cardiac EP models, all previous work has been limited by either: (i) considering uncertainty in only a subset of the full set of parameters; and/or (ii) assigning arbitrary variation to parameters (e.g., ±10 or 50% around mean value) rather than basing the parameter uncertainty on experimental data. In our recent work we overcame the first limitation by performing UQ and sensitivity analysis using a novel canine action potential model, allowing all parameters to be uncertain, but with arbitrary variation. Here, we address the second limitation by extending our previous work to use data-driven estimates of parameter uncertainty. Overall, we estimated uncertainty due to population variability in all parameters in five currents active during repolarization: inward potassium rectifier, transient outward potassium, L-type calcium, rapidly and slowly activating delayed potassium rectifier; 25 parameters in total (all model parameters except fast sodium current parameters). A variety of methods was used to estimate the variability in these parameters. We then propagated the uncertainties through the model to determine their impact on predictions of action potential shape, action potential duration (APD) prolongation due to drug block, and spiral wave dynamics. Parameter uncertainty had a significant effect on model predictions, especially L-type calcium current parameters. Correlation between physiological parameters was determined to play a role in physiological realism of action potentials. Surprisingly, even model outputs that were relative differences, specifically drug-induced APD prolongation, were heavily impacted by the underlying uncertainty. This is the first data-driven end-to-end UQ analysis in cardiac EP accounting for uncertainty in the vast majority of parameters, including first in tissue, and demonstrates how future UQ could be used to ensure model-based decisions are robust to all underlying parameter uncertainties.

Development, Implementation and Testing of a Multicellular Dynamic Action Potential Clamp Simulator for Drug Cardiac Safety Assessment

As drugs can be multichannel blockers it is important to assess their cardiac safety taking into account multiple currents. In silico action potential (AP) models have been proposed for being able to integrate drugs effect on ionic currents and generate the resulting AP. However, a mathematical description of drug effects is required, which could be inaccurate. Dynamic Clamp has been proposed for drug cardiac safety assessment. In the dynamic action potential clamp (dAPC) configuration it creates an hybrid model connecting a real cell with a computer simulation. This way, drugs could be administrated directly to real cells, and effects on currents can be taken into account when generating the AP. Here we design and simulate a parallel multichannel dAPC system. The system includes the real cells overexpressing the currents of interest, the voltage clamp acquisition system, and the AP in silico model.

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'.