Modelling the rabbit cardiac action potential – Can simulations replace the experiment in pharmaceutical cardiosafety assessment?

Model of the Month created by Marcel Mohr, Sanofi, Frankfurt/Germany (Preclinical Safety, Digital Toxicology)

Original model – MODEL2204250001

Introduction

Drug-induced cardiac arrhythmia is a severe but common off-target effect of a drug and a leading cause of preclinical failure. The mechanism of action is mostly related to interactions of the drug with multiple cardiac ion channels. If at least one of these channels is blocked by a drug, the fine balance of multiple time- and voltage-dependent ionic currents may be disturbed, potentially leading to a change in cardiac action potential (AP) and eventually to cardiac arrhythmia. The complex interplay of multiple ion channel interactions is difficult to interpret solely at the level of in vitro assays, but it can be managed by multiscale cardiac AP models dedicated to preclinical endpoints.

As a branch of quantitative systems toxicology, simulations based on mathematical models are of growing attractiveness to guide preclinical cardiosafety risk assessments, progressively substituting in vitro/in vivo assays. The field of mathematical modeling of cardiac electrophysiology has grown considerably within the last decades, creating a plethora of models covering different cardiac cell types and diverse species. Validation of these models is a prerequisite for acceptance and credibility showing that they provide the same outcome as traditional experimental methods for a defined endpoint. The rabbit Purkinje fiber assay is a well-established and translatable ex vivo tissue model, which includes the major mechanisms contributing to AP genesis [Roche et al. (2010)]. This assay allows testing a drug’s integrated influence on changes in the AP and was used as a benchmark for a retrospective evaluation of AP models.

We performed a comparative benchmark study and investigated a set of 16 mathematical cardiac AP models, including a newly developed minimalistic model specifically tailored to the AP of rabbit Purkinje cells, for their ability to replace the rabbit Purkinje fiber assay. We quantified each model’s ability to reproduce experimental findings by their percentage of generating simulations which match experimental data best. The simulated changes in AP duration (dAPD90) at increasing drug concentrations were matched to experimental results from about 600 Sanofi-internal Purkinje fiber studies covering about 560 different drugs with diverse modes of action.

Model

Despite differences in complexity, most AP models share a common mathematical basis. Ion currents are generally represented either as a set of Markov transitions between discrete states or as a Hodgkin-Huxley formulation describing a series of independent two-state reactions known as ‘gates’. Parameters may either be directly stated as numbers or formulated as solutions of ordinary differential equations (ODEs). The cell membrane is modeled as a capacitor connected in parallel with variable resistances and batteries representing the different ionic currents and pumps. The electrical properties of a single cardiac cell expressed as voltage change per unit of time are then mathematically formulated using the following ODE

$\frac{dV}{dt} = \frac{1}{C_{m}} (\sum I_{j} + I_{stim})$

where I_stim is the externally applied stimulus current, and represents the cell capacitance.

To reduce model complexity and the potential risk of overfitting, we built a new model tailored to the cardiac AP of a rabbit Purkinje cell. The model structure is composed of the most important ionic currents responsible for AP genesis where the dynamics of ionic concentrations or any intracellular processes are neglected. Each variable and parameter can be related to electrophysiological quantities.

In all cardiac electrophysiology models, drug-induced ion channel inhibition for the four most prominent and influential ionic currents hERG, hCav1.2, hNav1.5 and hKv4.3 is introduced by ‘conductance block’ [Mirams et al. (2011)], where the maximal conductance of an ion channel is reduced by a factor which is a function of the inhibitory potential (IC50) of the tested drug for the respective channel, and the concentration of that drug. Experimental testing of ion channel inhibitions for a compound was internally performed on engineered immortalized cell lines. Many, yet not all the compounds assessed in the rabbit Purkinje fiber assay have been annotated with experimental IC50 data. Consequently, in silico models based on QSAR (Quantitative-Structure-Activity-Relationship) machine learning algorithms were used to predict missing IC50 values and to fill gaps in the ion channel profiles to support simulation of drug influence on cardiac electrophysiology [Mohr et al. (2022)].

Results

The newly developed rabbit Purkinje cardiac AP model could reproduce the AP morphology under drug-induced blockage of the main ion channels at decreased computational cost and simulation time as compared to more complex models (Figure 1). Using the novel model, 80% of the Purkinje experiments could be quantitatively reproduced. This retrospective and comparative evaluation prompts to broaden the usage of the model in a prospective manner, for the early risk identification of drug-induced arrhythmia, allowing for significant saving of experimental effort in early pharmaceutical research setting and for reduction of animal experiments.

To deploy the model in an industrial setting, we created a computational framework CAPSim for predicting AP biomarkers (Figure 2). It is based on open-source software Chaste and ApPredict [Williams et al. (2015)] and allows integrating experimental and predicted ion channel inhibition data with AP models, adapting model parameters and visualizing AP curves and biomarker responses. This way, a smooth adaptation of public models and tailored model developments can be deployed in standardized CellML format. Resulting AP curves are visualized, while simultaneous assessment of 100s and 1000s of simulations can be performed in a batch mode. This way, the simulation framework has made cardiac AP simulations a convenient effort which is regularly applied in drug discovery programs.

Discussion

Mathematical cardiac AP models bear the promise to support safety pharmacology sciences with early cardiac hazard and risk assessment and ultimately target to substitute animal testing. As of today, a remarkable heritage tree of computational models indicates that the diversity of biology in different species and tissue types enforces tailored modeling solutions to specific assays. Our tailored rabbit Purkinje electrophysiology model with minimalized complexity outperformed most other benchmarked models in the endpoint dAPD90, allowing for high reliability and robustness at comparably low simulation times. This way, the model qualifies for broad application in lead identification and lead optimization programs, e.g., for model-driven selection of the most promising testing candidates to reduce the need for experimental studies. This way, in silico simulation is embedded in pharmaceutical research programs at an appropriate scale, seeking to optimize novel drug candidates.

References

Mirams et al. (2011). Simulation of multiple ion channel block provides improved early prediction of compounds’ clinical torsadogenic risk. Cardiovascular Research, 91(1), 53–61. https://doi.org/10.1093/cvr/cvr044

Mohr et al. (2022). Accurate in silico simulation of the rabbit Purkinje fiber electrophysiological assay to facilitate early pharmaceutical cardiosafety assessment: Dream or reality? Journal of Pharmacological and Toxicological Methods, 115, 107172. https://doi.org/10.1016/j.vascn.2022.107172

Roche et al. (2010). The isolated rabbit heart and Purkinje fibers as models for identifying proarrhythmic liability. Journal of Pharmacological and Toxicological Methods, 61(3), 238–250. https://doi.org/10.1016/j.vascn.2010.01.011

Williams et al. (2015). A web portal for in-silico action potential predictions. Journal of Pharmacological and Toxicological Methods, 75, 10–16. https://doi.org/10.1016/j.vascn.2015.05.002