Four Ways to Fit an Ion Channel Model

© 2019 Biophysical Society 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

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’

A multiple timescale analysis of a mathematical model of the Wnt/β−catenin signalling pathway

The Wnt signalling pathway is involved in stem cell maintenance, differentiation and tissue development. Its disregulation has also been implicated in many cancers. β-catenin is a protein that regulates both transcription of many genes and cell-cell adhesion; in response to an external Wnt stimulus the intracellular levels of β-catenin are controlled by the proteins which make up the Wnt/β-catenin signalling pathway. In this paper we present a systematic asymptotic analysis of an existing model of the Wnt signalling pathway due to Lee et al. (PLoS Biol 1:116-132, 2003), highlighting the operation of different pathway components over different timescales. Guided by t

Messenger RNA expression levels predict cellular electrophysiologic remodeling in failing human hearts using a population−based simulation study

Differences in mRNA expression levels have been observed in failing versus non-failing human hearts for several membrane channel proteins and accessory subunits. These differences may play a causal role in electrophysiological changes observed in human heart failure and atrial fibrillation, such as action potential (AP) prolongation, increased AP triangulation, decreased intracellular calcium transient (CaT) magnitude and decreased CaT triangulation. Our goal is to investigate whether the information contained in mRNA measurements can be used to predict cardiac electrophysiological remodeling in heart failure using computational modeling. Using mRNA data recently obtained from failing and non-failing human hearts, we construct failing and non-failing cell populations incorporating natural variability and up/down regulation of channel conductivities. Six biomarkers are calculated for each cell in each population, at cycle lengths between 1500 ms and 300 ms. Regression analysis is performed to determine which ion channels drive biomarker variability in failing versus non-failing cardiomyocytes. Our models suggest that reported mRNA expression changes are consistent with AP prolongation, increased AP triangulation, increased CaT duration, decreased CaT triangulation and amplitude, and increased delay between AP and CaT upstrokes in the failing population. Regression analysis reveals that changes in AP biomarkers are driven primarily by reduction in I[Image: see text], and changes in CaT biomarkers are driven predominantly by reduction in I[Image: see text] and SERCA. In particular, the role of I[Image: see text] is pacing rate dependent. Additionally, alternans developed at fast pacing rates for both failing and non-failing cardiomyocytes, but the underlying mechanisms are different in control and heart failure

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

Novel approaches to assessing cardiac safety-proceedings of a workshop : Regulators, Industry and Academia Discuss the Future of In Silico Cardiac Modelling to Predict the Proarrhythmic Safety of Drugs

This work was supported in part by the European Union (EU)-funded FP6-project ePIXnet, and in part by the FP7-project BOOM.Fletcher, K.; Shah, RR.; Thomas, A.; Tobin, F.; Rodríguez, B.; Mirams, GR.; Saiz Rodríguez, FJ.... (2011). Novel approaches to assessing cardiac safety-proceedings of a workshop : Regulators, Industry and Academia Discuss the Future of In Silico Cardiac Modelling to Predict the Proarrhythmic Safety of Drugs. Drug Safety. 34(5):439-443. https://doi.org/10.2165/11591950-000000000-00000S439443345Rodriguez, B., Burrage, K., Gavaghan, D., Grau, V., Kohl, P., & Noble, D. (2010). The Systems Biology Approach to Drug Development: Application to Toxicity Assessment of Cardiac Drugs. Clinical Pharmacology & Therapeutics, 88(1), 130-134. doi:10.1038/clpt.2010.9

Simulation of multiple ion channel block provides improved early prediction of compounds' clinical torsadogenic risk

Aims: The level of inhibition of the human Ether-à-go-go-related gene (hERG) channel is one of the earliest preclinical markers used to predict the risk of a compound causing Torsade-de-Pointes (TdP) arrhythmias. While avoiding the use of drugs with maximum therapeutic concentrations within 30-fold of their hERG inhibitory concentration 50% (IC50) values has been suggested, there are drugs that are exceptions to this rule: hERG inhibitors that do not cause TdP, and drugs that can cause TdP but are not strong hERG inhibitors. In this study, we investigate whether a simulated evaluation of multi-channel effects could be used to improve this early prediction of TdP risk. Methods and results: We collected multiple ion channel data (hERG, Na, l-type Ca) on 31 drugs associated with varied risks of TdP. To integrate the information on multi-channel block, we have performed simulations with a variety of mathematical models of cardiac cells (for rabbit, dog, and human ventricular myocyte models). Drug action is modelled using IC50 values, and therapeutic drug concentrations to calculate the proportion of blocked channels and the channel conductances are modified accordingly. Various pacing protocols are simulated, and classification analysis is performed to evaluate the predictive power of the models for TdP risk. We find that simulation of action potential duration prolongation, at therapeutic concentrations, provides improved prediction of the TdP risk associated with a compound, above that provided by existing markers. Conclusion: The suggested calculations improve the reliability of early cardiac safety assessments, beyond those based solely on a hERG block effect