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Computational models of the electrical potential across a cell membrane are longstanding and vital tools in electrophysiology research and applications. These models describe how ionic currents, internal fluxes, and buffering interact to determine membrane voltage and form action potentials (APs). Although this relationship is usually expressed as a differential equation, previous studies have shown it can be rewritten in an algebraic form, allowing direct calculation of membrane voltage. Rewriting in this form requires the introduction of a new parameter, called Γ 0 in this manuscript, which represents the net concentration of all charges that influence membrane voltage but are not considered in the model. Although several studies have examined the impact of Γ 0 on long-term stability and drift in model predictions, there has been little examination of its effects on model predictions, particularly when a model is refit to new data. In this study, we illustrate how Γ 0 affects important physiological properties such as action potential duration restitution, and examine the effects of (in)correctly specifying Γ 0 during model calibration. We show that, although physiologically plausible, the range of concentrations used in popular models leads to orders of magnitude differences in Γ 0 , which can lead to very different model predictions. In model calibration, we find that using an incorrect value of Γ 0 can lead to biased estimates of the inferred parameters, but that the predictive power of these models can be restored by fitting Γ 0 as a separate parameter. These results show the value of making Γ 0 explicit in model formulations, as it forces modellers and experimenters to consider the effects of uncertainty and potential discrepancy in initial concentrations upon model predictions., Competing Interests: Authors KW and LP were employees of F. Hoffmann-La Roche Ltd. and KW is a shareholder. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2022 Barral, Shuttleworth, Clerx, Whittaker, Wang, Polonchuk, Gavaghan and Mirams.)

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., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2021 Lei and Mirams.)

Although plasma electrolyte levels are quickly and precisely regulated in the mammalian cardiovascular system, even small transient changes in K + , Na + , Ca 2+ , and/or Mg 2+ can significantly alter physiological responses in the heart, blood vessels, and intrinsic (intracardiac) autonomic nervous system. We have used mathematical models of the human atrial action potential (AP) to explore the electrophysiological mechanisms that underlie changes in resting potential (V r ) and the AP following decreases in plasma K + , [K + ] o , that were selected to mimic clinical hypokalemia. Such changes may be associated with arrhythmias and are commonly encountered in patients (i) in therapy for hypertension and heart failure; (ii) undergoing renal dialysis; (iii) with any disease with acid-base imbalance; or (iv) post-operatively. Our study emphasizes clinically-relevant hypokalemic conditions, corresponding to [K + ] o reductions of approximately 1.5 mM from the normal value of 4 to 4.5 mM. We show how the resulting electrophysiological responses in human atrial myocytes progress within two distinct time frames: (i) Immediately after [K + ] o is reduced, the K + -sensing mechanism of the background inward rectifier current (I K1 ) responds. Specifically, its highly non-linear current-voltage relationship changes significantly as judged by the voltage dependence of its region of outward current. This rapidly alters, and sometimes even depolarizes, V r and can also markedly prolong the final repolarization phase of the AP, thus modulating excitability and refractoriness. (ii) A second much slower electrophysiological response (developing 5-10 minutes after [K + ] o is reduced) results from alterations in the intracellular electrolyte balance. A progressive shift in intracellular [Na + ] i causes a change in the outward electrogenic current generated by the Na + /K + pump, thereby modifying V r and AP repolarization and changing the human atrial electrophysiological substrate. In this study, these two effects were investigated quantitatively, using seven published models of the human atrial AP. This highlighted the important role of I K1 rectification when analyzing both the mechanisms by which [K + ] o regulates V r and how the AP waveform may contribute to "trigger" mechanisms within the proarrhythmic substrate. Our simulations complement and extend previous studies aimed at understanding key factors by which decreases in [K + ] o can produce effects that are known to promote atrial arrhythmias in human hearts., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2021 Clerx, Mirams, Rogers, Narayan and Giles.)

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.

The Comprehensive in vitro Proarrhythmia Assay (CiPA) is a global initiative intended to improve drug proarrhythmia risk assessment using a new paradigm of mechanistic assays. Under the CiPA paradigm, the relative risk of drug-induced Torsade de Pointes (TdP) is assessed using an in silico model of the human ventricular action potential (AP) that integrates in vitro pharmacology data from multiple ion channels. Thus, modeling predictions of cardiac risk liability will depend critically on the variability in pharmacology data, and uncertainty quantification (UQ) must comprise an essential component of the in silico assay. This study explores UQ methods that may be incorporated into the CiPA framework. Recently, we proposed a promising in silico TdP risk metric (qNet), which is derived from AP simulations and allows separation of a set of CiPA training compounds into Low, Intermediate, and High TdP risk categories. The purpose of this study was to use UQ to evaluate the robustness of TdP risk separation by qNet. Uncertainty in the model parameters used to describe drug binding and ionic current block was estimated using the non-parametric bootstrap method and a Bayesian inference approach. Uncertainty was then propagated through AP simulations to quantify uncertainty in qNet for each drug. UQ revealed lower uncertainty and more accurate TdP risk stratification by qNet when simulations were run at concentrations below 5× the maximum therapeutic exposure (C max ). However, when drug effects were extrapolated above 10× C max , UQ showed that qNet could no longer clearly separate drugs by TdP risk. This was because for most of the pharmacology data, the amount of current block measured was <60%, preventing reliable estimation of IC 50 -values. The results of this study demonstrate that the accuracy of TdP risk prediction depends both on the intrinsic variability in ion channel pharmacology data as well as on experimental design considerations that preclude an accurate determination of drug IC 50 -values in vitro . Thus, we demonstrate that UQ provides valuable information about in silico modeling predictions that can inform future proarrhythmic risk evaluation of drugs under the CiPA paradigm.

Chaste is an open-source C++ library for computational biology that has well-developed cardiac electrophysiology tissue simulation support. In this paper, we introduce the features available for performing cardiac electrophysiology action potential simulations using a wide range of models from the Physiome repository. The mathematics of the models are described in CellML, with units for all quantities. The primary idea is that the model is defined in one place (the CellML file), and all model code is auto-generated at compile or run time; it never has to be manually edited. We use ontological annotation to identify model variables describing certain biological quantities (membrane voltage, capacitance, etc.) to allow us to import any relevant CellML models into the Chaste framework in consistent units and to interact with them via consistent interfaces. This approach provides a great deal of flexibility for analysing different models of the same system. Chaste provides a wide choice of numerical methods for solving the ordinary differential equations that describe the models. Fixed-timestep explicit and implicit solvers are provided, as discussed in previous work. Here we introduce the Rush-Larsen and Generalized Rush-Larsen integration techniques, made available via symbolic manipulation of the model equations, which are automatically rearranged into the forms required by these approaches. We have also integrated the CVODE solvers, a 'gold standard' for stiff systems, and we have developed support for symbolic computation of the Jacobian matrix, yielding further increases in the performance and accuracy of CVODE. We discuss some of the technical details of this work and compare the performance of the available numerical methods. Finally, we discuss how this is generalized in our functional curation framework, which uses a domain-specific language for defining complex experiments as a basis for comparison of model behavior.