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Background and PurposeDrug-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 combiningin vitroassays within silicosimulations. In this study, we investigate the impact onin silicoproarrhythmic risk predictions due to uncertainty in the hERG binding mechanism and physiological hERG current model.Experimental ApproachPossible 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 ResultsFor 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 ImplicationsThe 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.

Nicotinamide, the amide form of Vitamin B3, is a common nutrient supplement that plays important role in human fetal development. Nicotinamide has been widely used in clinical treatments, including the treatment of diseases during pregnancy. However, its impacts during embryogenesis have not been fully understood. In this study, we show that nicotinamide plays multiplex roles in mesoderm differentiation of human embryonic stem cells (hESCs). Nicotinamide promotes cardiomyocyte fate from mesoderm progenitor cells, and suppresses the emergence of other cell types. Independent of its functions in PARP and Sirtuin pathways, nicotinamide modulates differentiation through kinase inhibition. A KINOMEscan assay identifies 14 novel nicotinamide targets among 468 kinase candidates. We demonstrate that nicotinamide promotes cardiomyocyte differentiation through p38 MAP kinase inhibition. Furthermore, we show that nicotinamide enhances cardiomyocyte survival as a Rho-associated protein kinase (ROCK) inhibitor. This study reveals nicotinamide as a pleiotropic molecule that promotes the derivation and survival of cardiomyocytes, and it could become a useful tool for cardiomyocyte production for regenerative medicine. It also provides a theoretical foundation for physicians when nicotinamide is considered for treatments for pregnant women.

Models of the cardiomyocyte action potential (AP) have contributed immensely to the understanding of heart function, pathophysiology, and the origin of heart rhythm disturbances. However, AP models are nonlinear, complex, and can contain more than a hundred differential equations, making them difficult to parameterise. Therefore, cellular cardiac models have been limited 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—optimal experimental designs—for both voltage-clamp and current-clamp experiments. We show that optimal designs are able to perform better than many of the existing experiment designs in the literature in terms of identifying model parameters and hence model predictive power. 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.

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, and 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. Here, we usein silicoandin vitrostudies to demonstrate how seal-leak current depolarises action potentials (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 recording accurate measures of Rsealduring an experiment. Using simulation, we show that Rsealmeasures: 1) change during an experiment, invalidating the use of pre-rupture values, and 2) are polluted by the presence of transmembrane currents at every voltage. Finally, we posit 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. Based on these findings, we make three 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.Key pointsHuman induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs) are an essential tool in the study of cardiac arrhythmia mechanisms.Their immature and heterogeneous action potential phenotype complicates the interpretation of experimental data, and has slowed their acceptance in industry and academia.We suggest that a leak current caused by an imperfect pipette-membrane seal during single-cell patch-clamp experiments is partly responsible for inducing this phenotype.Usingin vitroexperiments and computational modelling, we show that this seal-leak current affects iPSC-CM AP morphology, even under ‘ideal’ experimental conditions.Based on these findings, we make recommendations that should be considered when interpreting, analysing and fitting iPSC-CM data.

Peer reviewed: True, 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.

Whether an outbreak of infectious disease is likely to grow or dissipate is determined through the time-varying reproduction number,Rt. Real-time or retrospective identification of changes inRtfollowing the imposition or relaxation of interventions can thus contribute important evidence about disease transmission dynamics which can inform policymaking. Here, we present a method for estimating shifts inRtwithin a renewal model framework. Our method, which we call EpiCluster, is a Bayesian nonparametric model based on the Pitman-Yor process. We assume thatRtis piecewise-constant, and the incidence data and priors determine when or whetherRtshould change and how many times it should do so throughout the series. We also introduce a prior which induces sparsity over the number of changepoints. Being Bayesian, our approach yields a measure of uncertainty inRtand its changepoints. EpiCluster is fast, straightforward to use, and we demonstrate that it provides automated detection of rapid changes in transmission, either in real-time or retrospectively, for synthetic data series where theRtprofile is known. We illustrate the practical utility of our method by fitting it to case data of outbreaks of COVID-19 in Australia and Hong Kong, where it finds changepoints coinciding with the imposition of non-pharmaceutical interventions. Bayesian nonparametric methods, such as ours, allow the volume and complexity of the data to dictate the number of parameters required to approximate the process and should find wide application in epidemiology.HighlightsIdentifying periods of rapid change in transmission is important for devising strategies to control epidemics.We assume that the time-varying reproduction number,Rt, is piecewise-constant and transmission is determined by a Poisson renewal model.We develop a Bayesian nonparametric method, called EpiCluster, which uses a Pitman Yor process to infer changepoints inRt.Using simulated incidence series, we demonstrate that our method is adept at inferring changepoints.Using real COVID-19 incidence series, we infer abrupt changes in transmission at times coinciding with the imposition of non-pharmaceutical interventions.

Funder: W D Armstrong Trust; the Macao Postgraduate Scholarship Fund, Funder: UM Macao Fellowship; the Clarendon Scholarship Fund, Funder: Baroness de Turckheim Fund, Trinity College Cambridge, Funder: the Cambridge Hearing Trust; the Evelyn Trust, Cochlear implants restore hearing in patients with severe to profound deafness by delivering electrical stimuli inside the cochlea. Understanding stimulus current spread, and how it correlates to patient-dependent factors, is hampered by the poor accessibility of the inner ear and by the lack of clinically-relevant in vitro, in vivo or in silico models. Here, we present 3D printing-neural network co-modelling for interpreting electric field imaging profiles of cochlear implant patients. With tuneable electro-anatomy, the 3D printed cochleae can replicate clinical scenarios of electric field imaging profiles at the off-stimuli positions. The co-modelling framework demonstrated autonomous and robust predictions of patient profiles or cochlear geometry, unfolded the electro-anatomical factors causing current spread, assisted on-demand printing for implant testing, and inferred patients' in vivo cochlear tissue resistivity (estimated mean = 6.6 k��cm). We anticipate our framework will facilitate physical modelling and digital twin innovations for neuromodulation implants.

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 MethodsPhysiology > Mammalian Physiology in Health and DiseaseModels of Systems Properties and Processes > Cellular Models, A schematic of a cardiac electrophysiology model, highlighting the components described by equations that need to be calibrated using experimental data.

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 characterise uncertainty in model inputs and how that propagates through to outputs or predictions. In this 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 (GPs) and autoregressive-moving-average (ARMA) models, then highlight the advantages and shortcomings of each approach. Finally, suggestions and lines of enquiry for future work are provided., Comment: This version is published in Philosophical Transactions of the Royal Society A; Updated in response to reviewer comments, including: added details to the introduction, fixed mathematical notations for clarity, and moved the original Table 3 to the supplement to avoid confusion

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’.

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 vitrohERG-channel current recordings are an important step in evaluating the pro-arrhythmic 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 characterise a current is typically too long to be applied in a single cell. Shorter high-information protocols have recently been introduced which have this capability, but they are not typically compatible with high-throughput platforms. We present a new high-information 15 s protocol to characterise 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 CHO cells stably expressing hERG1a. From these recordings we construct 124 cell-specific variants/parameterisations of a hERG model at 25 °C. A further 8 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, which we use 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.Statement of SignificanceWe present a method for high-throughput characterisation of hERG potassium channel kinetics, via fitting a mathematical model to results of over one hundred single cell patch clamp measurements collected simultaneously on an automated voltage clamp platform. The automated patch clamp data are used to parameterise a mathematical ion channel model fully, opening a new era of automated and rapid development of mathematical models from quick and cheap experiments. The method also allows ample data for independent validation of the models and enables us to study experimental variability and propose its origins. In future the method can be applied to characterise changes to hERG currents in different conditions, for instance at different temperatures (see Part II of the study) or under mutations or the action of pharmaceuticals; and should be easily adapted to study many other currents.

Islet β-cells are responsible for secreting all circulating insulin in response to rising plasma glucose concentrations. These cells are a phenotypically diverse population that express great functional heterogeneity. In mice, certain β-cells (termed ‘hubs’) have been shown to be crucial for dictating the islet response to high glucose, with inhibition of these hub cells abolishing the coordinated Ca2+ oscillations necessary for driving insulin secretion. These β-cell hubs were found to be highly metabolic and susceptible to pro-inflammatory and glucolipotoxic insults. In this study, we explored the importance of hub cells in human by constructing mathematical models of Ca2+ activity in human islets. Our simulations revealed that hubs dictate the coordinated Ca2+ response in both mouse and human islets; silencing a small proportion of hubs abolished whole-islet Ca2+ activity. We also observed that if hubs are assumed to be preferentially gap junction coupled, then the simulations better adhere to the available experimental data. Our simulations of 16 size-matched mouse and human islet architectures revealed that there are species differences in the role of hubs; Ca2+ activity in human islets was more vulnerable to hub inhibition than mouse islets. These simulation results not only substantiate the existence of β-cell hubs, but also suggest that hubs may be favorably coupled in the electrical and metabolic network of the islet, and that targeted destruction of these cells would greatly impair human islet function.

Islet β-cells are responsible for secreting all circulating insulin in response to rising plasma glucose concentrations. These cells are a phenotypically diverse population that express great functional heterogeneity. In mice, certain β-cells (termed ‘hubs’) have been shown to be crucial for dictating the islet response to high glucose, with inhibition of these hub cells abolishing the coordinated Ca2+ oscillations necessary for driving insulin secretion. These β-cell hubs were found to be highly metabolic and susceptible to pro-inflammatory and glucolipotoxic insults. In this study, we explored the importance of hub cells in human by constructing mathematical models of Ca2+ activity in human islets. Our simulations revealed that hubs dictate the coordinated Ca2+ response in both mouse and human islets; silencing a small proportion of hubs abolished whole-islet Ca2+ activity. We also observed that if hubs are assumed to be preferentially gap junction coupled, then the simulations better adhere to the available experimental data. Our simulations of 16 size-matched mouse and human islet architectures revealed that there are species differences in the role of hubs; Ca2+ activity in human islets was more vulnerable to hub inhibition than mouse islets. These simulation results not only substantiate the existence of β-cell hubs, but also suggest that hubs may be favorably coupled in the electrical and metabolic network of the islet, and that targeted destruction of these cells would greatly impair human islet function.

Time series models are ubiquitous in science, arising in any situation where researchers seek to understand how a system’s behaviour changes over time. A key problem in time series modelling is inference; determining properties of the underlying system based on observed time series. For both statistical and mechanistic models, inference involves finding parameter values, or distributions of parameters values, which produce outputs consistent with observations. A wide variety of inference techniques are available and different approaches are suitable for different classes of problems. This variety presents a challenge for researchers, who may not have the resources or expertise to implement and experiment with these methods. PINTS (Probabilistic Inference on Noisy Time Series — https://github.com/pints-team/pints ) is an open-source (BSD 3-clause license) Python library that provides researchers with a broad suite of non-linear optimisation and sampling methods. It allows users to wrap a model and data in a transparent and straightforward interface, which can then be used with custom or pre-defined error measures for optimisation, or with likelihood functions for Bayesian inference or maximum-likelihood estimation. Derivative-free optimisation algorithms — which work without harder-to-obtain gradient information — are included, as well as inference algorithms such as adaptive Markov chain Monte Carlo and nested sampling, which estimate distributions over parameter values. By making these statistical techniques available in an open and easy-to-use framework, PINTS brings the power of these modern methods to a wider scientific audience. Funding statement: M.C., G.R.M. and D.J.G. acknowledge support from the UK Biotechnology and Biological Sciences Research Council [BBSRC grant number BB/P010008/1]; M.R., S.G. and D.J.G. gratefully acknowledge research support from the UK Engineering and Physical Sciences Research Council Cross-Disciplinary Interface Programme [EPSRC grant number EP/I017909/1]; C.L.L. acknowledges support from the Clarendon Scholarship Fund, the EPSRC and the UK Medical Research Council (MRC) [EPSRC grant number EP/L016044/1]; B.L. acknowledges support from the UK Engineering and Physical Sciences Research Council [EPSRC grant number EP/F500394/1]; and S.G. and G.R.M. acknowledge support from the Wellcome Trust & Royal Society [Wellcome Trust grant numbers 101222/Z/13/Z and 212203/Z/18/Z].

Human induced pluripotent stem cell derived cardiomyocytes (iPSC-CMs) have applications in disease modeling, cell therapy, drug screening and personalized medicine. Computational models can be used to interpret experimental findings in iPSC-CMs, provide mechanistic insights, and translate these findings to adult cardiomyocyte (CM) electrophysiology. However, different cell lines display different expression of ion channels, pumps and receptors, and show differences in electrophysiology. In this exploratory study, we use a mathematical model based on iPSC-CMs from Cellular Dynamic International (CDI, iCell), and compare its predictions to novel experimental recordings made with the Axiogenesis Cor.4U line. We show that tailoring this model to the specific cell line, even using limited data and a relatively simple approach, leads to improved predictions of baseline behavior and response to drugs. This demonstrates the need and the feasibility to tailor models to individual cell lines, although a more refined approach will be needed to characterize individual currents, address differences in ion current kinetics, and further improve these results.