https://orcid.org/0009-0004-2268-5669
Figures
Abstract
During drug development, candidate compounds are extensively tested for proarrhythmic risk and in particular risk of Torsade de Pointes (TdP), as indicated by prolongation of the QT interval. Drugs that inhibit the rapid delayed rectifier current (
) can prolong the action potential duration (APD) and thereby the QT interval, and so are routinely rejected. However, simultaneous inhibition of the L-type
current (
) can mitigate the effect of
inhibition, so that including both effects can improve test specificity. Mathematical models of the action potential (AP) can be used to predict the APD prolongation resulting from a given level of
and
inhibition, but for use in safety-testing their predictive capabilities should first be carefully verified. We present the first systematic comparison between experimental drug-induced APD and predictions by AP models. New experimental data were obtained ex vivo for APD response to
and/or
inhibition by applying 9 compounds at different concentrations to adult human ventricular trabeculae at physiological temperature. Compounds with similar effects on
and
exhibited less APD prolongation compared to selective
inhibitors. We then integrated in vitro
patch-clamp data for
and
inhibition by the tested compounds into simulations with AP models. Models were assessed against the ex vivo data on their ability to recapitulate drug-induced APD changes observed experimentally. None of the tested AP models reproduced the APD changes observed experimentally across all combinations and degrees of
and/or
inhibition: they matched the data either for selective
inhibitors or for compounds with comparable effects on
and
. This work introduces a new benchmarking framework to assess the predictivity of current and future AP models for APD response to
and/or
inhibition. This is an essential primary step towards an in silico framework that integrates in vitro data for translational clinical cardiac safety.
Author summary
Before an investigational drug reaches patients, it is tested in vitro to ensure it does not disrupt the heart’s electric activity. This testing often focuses on the drug’s ability to block a specific current called , which, if inhibited, can prolong the heart cells’ action potential duration (APD), which is associated with an increased risk of irregular heartbeats (proarrhythmia). Our study examines how blocking another current,
, along with
, affects APD. We found that adding
inhibition may mitigate the proarrhythmic effects caused by
inhibition alone. Understanding this balance can improve how we assess the cardiac safety of new drugs, potentially saving promising compounds from being incorrectly discarded. Currently, mathematical models help predict such cardiac responses, but no existing model accurately predicted our findings. Our new data could aid in developing more predictive models in the future. This will contribute to safer drug development and more effective treatments.
Citation: Barral Y-SHM, Polonchuk L, Clerx M, Gavaghan DJ, Mirams GR, Wang K (2025) Comparison of in silico predictions of action potential duration in response to inhibition of IKr and ICaL with new human ex vivo recordings. PLoS Comput Biol 21(7): e1012913. https://doi.org/10.1371/journal.pcbi.1012913
Editor: Alain Nogaret, University of Bath, UNITED KINGDOM OF GREAT BRITAIN AND NORTHERN IRELAND
Received: February 24, 2025; Accepted: June 12, 2025; Published: July 7, 2025
Copyright: © 2025 Barral et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: The data, models, and scripts used to generate the results in this paper are available at the GitHub repository at the address: https://github.com/CardiacModelling/APD90_ex_vivo_vs_in_silico. Zenodo (permanent archive of Github): https://doi.org/10.5281/zenodo.14791284.
Funding: This research was funded in part by the Wellcome Trust [212203/Z/18/Z]. GRM and MC acknowledge support from the Wellcome Trust via a Wellcome Trust Senior Research Fellowship to GRM. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: I have read the journal’s policy and the authors of this manuscript have the following competing interests: Authors YSHMB, KW, and LP were employees of F. Hoffmann-La Roche Ltd. at the time of the study 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.
1. Introduction
The rapid delayed rectifier current (
) is a major ionic current responsible for the repolarisation of ventricular cardiomyocytes [1]. Inhibition of
prolongs the action potential (AP) duration (APD) and the QT interval [2]. Many drugs inhibiting
have been shown to increase the risk of Torsade de Pointes (TdP), a potentially deadly arrhythmia [2,3]. Regulatory bodies established guidelines ICH S7B and ICH E14 to prevent the development of new compounds with unacceptable pro-arrhythmic risk [4,5]. According to ICH S7B, the ability of compounds to inhibit
should be tested in vitro. Redfern et al. suggested a “safety margin” such that drugs should have a half-maximal inhibitory concentration (
) of over 30 times their maximal free therapeutic plasma concentration [2].
Multiple ion channels affect the TdP risk, notably the inhibition of the L-type current (
) mitigates the arrhythmogenicity of
inhibitors [6]. AP models can improve the limited specificity of
–centric TdP risk assessment by accounting for simultaneous inhibition of multiple ionic currents [7]. The Comprehensive in Vitro Proarrhythmia Assay (CiPA) initiative has encouraged the adoption of biophysically-detailed mathematical AP models as a framework to integrate in vitro ion channel data and assess drug-induced TdP risk [8]. Yet, AP model predictions of APD changes induced by simultaneous inhibition of
and
have not been validated against human data.
In this study, we measure ex vivo the APD at 90% repolarisation () in human adult ventricular trabeculae, with inhibition of
and/or
by 9 compounds (Chlorpromazine, Clozapine, Dofetilide, Fluoxetine, Mesoridazine, Nifedipine, Quinidine, Thioridazine, Verapamil). For each compound, we subsequently use patch clamp data to calculate the percentage of block of
and/or
at the compound concentrations in trabeculae experiments. These numbers are then used as inputs into AP simulations to compare the predictions of 11 in silico AP models with the ex vivo data.
changes from baseline (
) induced by
and
inhibition are linked to QT changes [9]. By comparing predictions by existing AP models with the ex vivo data, we assess their predictivity in a context relevant to drug development. We thus introduce a benchmarking framework to validate current and future AP models. Therefore, this work can be re-used to help develop predictive models for QT change induced by
and/or
inhibition.
2. Results
2.1. Experimental change in 
from baseline with drug exposure
Experimental measured after 25 min of steady 1 Hz pacing are summarised in Table 1 for the 9 tested compounds. The standard error of the mean (SEM) is also reported in the Table 1.
Chlorpromazine, Clozapine, Fluoxetine, and Mesoridazine induced little or no change in as the effects of
and
inhibition on
compensated each other. Verapamil, whilst exhibiting similar effects on
and
, substantially shortened
(–15 ms to –20 ms on average) with high variability in
(SEM up to 35 ms).
Substantial variability of baseline was observed in trabeculae tested with Mesoridazine, Clozapine, and Nifedipine (SD of 60 ms, 51 ms, and 55 ms respectively), but this did not lead to particularly high variability in drug induced
. The SEM of
was below 7 ms, 9 ms, and 6 ms for Mesoridazine, Clozapine, and Nifedipine, respectively. Fluoxetine-induced
also exhibited low SEM (
ms). In contrast, Dofetilide induced the most variable
with up to 33 ms SEM for 200 nM Dofetilide.
The 2-D maps of experimental are plotted in Fig 1, with
and
inhibition computed with both the CiPA and Pharm datasets.
and
inhibition were computed using the Hill equation (Eq 1), with the CiPA (left) and Pharm (right) datasets. The bottom panels report the inter-trabeculae variability observed experimentally. The marker type indicates the drug used to apply the
and
inhibition.
With increasing inhibition,
was shortened (shown as darker blue colors). On the other hand, the more
was inhibited, the more
was prolonged.
and
inhibition differed from one dataset to another, with the CiPA dataset exhibiting more sensitivity to inhibition of
than the Pharm dataset.
Note the biggest outlier from the surface, where 1 M Verapamil induced
ms at 1
M, with
and
inhibition. For comparison, 3
M Clozapine induced
ms with
and
inhibition.
2.2. 2-D maps of 
predicted by literature AP models
The 2-D maps of prediction for all 11 models and variants are shown in Fig 2 with cubic surfaces fitted through experimental data points.
Right: 2-D maps of predicted change from baseline after
and
inhibition. The colour scale indicates shortening of
(i.e.,
< 0 ms) for colours towards dark blue, and
prolongation (i.e.,
> 0 ms) for colours towards red.
values below –50 ms and above + 320 ms were set to dark blue and red, respectively, for better visualisation. For
and
inhibition leading to
ms, the pixel is coloured in white.
A clear distinction was observed between models similar to the ORd model, which were most sensitive to inhibition, and TP-like models, which were more sensitive to
inhibition. On 2-D maps for the BPS, ORd, ORd-CiPA, ORd-KM, ORd-M, and ToR-ORd models, the 0 ms line was mostly vertical, indicating little mitigation of
inhibition-induced
by
inhibition. These results align with previous observations [10].
In the BPS model, nearly no mitigation of inhibition by
inhibition was observed, and the 0 ms line was vertical.
inhibition even prolonged
:
and
inhibition yielded
ms, whilst
and
inhibition yielded
ms.
predicted by the BPS model was not monotonic. Initially,
inhibition prolonged
, but with more than
inhibition,
decreased drastically.
The ToR-ORd model also exhibited a non-monotonic 2-D map: for
and
inhibition, no change in APD90 was predicted; further
inhibition increased
. In simulations, the strongly reduced
shrinks the
concentration in the subspace compartment, reducing the repolarising calcium-activated
- current (
), and therefore prolonging
.
The TP-like models (TP, TP-M, GPB, and GPB-M) predicted similar 0 ms lines, almost linear with slopes between 0.5 and 1.3. The original TP and GPB models exhibited much lower sensitivities of to selective
inhibition (
ms and + 51 ms respectively), than observed experimentally with 200 nM Dofetilide (
ms). Adjustments by Mann et al. increased their sensitivity to
inhibition [11] : the TP-M and GPB-M models predicted
ms and + 144 ms with
inhibition, respectively.
The TNNP model behaved differently, with its 0 ms line in an “S” shape, and nearly no prolongation of , even with
inhibition (
ms).
Visually comparing model predictions with ex vivo data, the TP-M and GPB-M models appear closest to the truth. This is quantitatively investigated in the next section.
2.3. Comparison of in-silico prediction of 
with ex vivo data
Fig 3 presents the quantitative comparison of the ex vivo data with predictions, using external ionic concentrations in simulations that matched the experimental settings. The error in
is shown as a multiple of the experimental SEM in
(
), directly visualising each condition’s contribution to the error measure, E (Eq 2).
CiPA (triangle) and Pharm (circle) datasets for values were used to compute drug perturbation.
denotes here the experimental standard error of the mean
response to each drug perturbation.
The ORd-like models performed similarly in predicting experimental consistently with their 2-D maps (Fig 2). Predictions for selective
and
inhibitors by the ORd-CiPA and ToR-ORd models were largely correct (light colors). However, ORd-like models overpredicted
prolongation induced by simultaneous
and
inhibition (dark red).
The TP-like models underpredicted the response to selective
inhibition (blue) but provided good predictions for mitigation by
inhibition. The GPB model predicted excessive
shortening after more than
inhibition, but its predictions for simultaneous inhibition of
and
were within
. The GPB-M and TP-M models overpredicted
prolongation induced by simultaneous
and
inhibition, depending on the
dataset. An alternative visualisation of performances of the various models is provided in S1 Appendix.
Fig 4A compares E (Eq 2) for all 10 models using the CiPA and Pharm datasets. Fig 4B and 4C detail E for each drug.
The lower the error measure (Eq 2), the more accurate the model predictions. A: The error measure was summed over all the drugs used in this study, when using the CiPA and Pharm protocols to compute the reduction of ionic currents by drugs. For each model, two bar plots were plotted, to compare the predictive power of models with the Pharm (left bar) and the CiPA (right bar) datasets. B and C: Detail of the error measures associated with each of the drugs using the CiPA and Pharm datasets, respectively, for each model. The log10 of the error measure is plotted along the radial-axis.
The TP model yielded the lowest errors E = 76.6 and 83.8 using the CiPA and Pharm datasets, respectively. Low errors were found for all drugs with similar effects on and
. The largest E for the TP model were for Dofetilide (24.2–31.2) and Nifedipine (8.3–9.8). All TP-like models showed high E for Dofetilide and Nifedipine, consistent with Fig 3, where the largest E was for selective
or
inhibition.
For the TP and GPB models, E computed using the two datasets did not differ significantly. In contrast, models reformulated by Mann et al. [11] and ORd-like models showed stronger dependency on the dataset. A difference of 51.2 was obtained between the CiPA and Pharm datasets with the ORd model: E = 486.6 versus E = 537.8, respectively.
ORd-like models performed similarly, with low errors for Dofetilide and Nifedipine but high errors for other drugs (up to 193.1 for Mesoridazine with the Pharm dataset for the ORd model). These models reproduced the response to selective
or
inhibition well but did not capture the mitigation of
inhibition by
inhibition.
3. Discussion
3.1. Main findings
The performance of 11 literature AP models was evaluated against new ex vivo data from adult human ventricular trabeculae, which measured response to inhibition of
and/or
by 9 different drugs.
The TP-like models exhibited less sensitivity to inhibition compared to the ORd-like models. The error measure for
prediction, E (Eq 2), was lower with the TP-like models, with the lowest error obtained for the TP model using the Pharm dataset. Their predictions are closer to experimental values for the mitigation of
response to
inhibition by
inhibition, but are less accurate for selective
and
inhibitors.
The opposite was observed with ORd-like models. They make accurate predictions of response to selective
inhibition, but do not capture the mitigating effect of
inhibition on
inhibition-induced
prolongation.
Mann et al. demonstrated that rescaling maximal conductance parameters of the TP and GPB models and adding a component for can increase their sensitivity to
inhibition whilst preserving the compensating effects of
and
inhibition on
[11].
In summary, our novel data can be used as a benchmark to assess the predictivity of any future AP model for response to
and/or
inhibition. Of the currently available models we selected, the TP and GPB-M models showed better overall performance. They therefore appear as promising base models for predicting
response to multi-ion channel inhibitors and subsequent QT changes, upon further development.
3.2. Model differences
Several models in this study were validated against previous experimental data for prolongation following
inhibition [11–16].
shortening with selective
inhibition was also included in the development of the BPS, ORd, and ToR-ORd models. For instance, the ORd model’s
predictions were validated for
response to
inhibition in guinea pig cardiomyocytes [17] and to
inhibition in rat cardiomyocytes [18]. whilst the model qualitatively agrees with experimental
responses to selective
and
inhibitors, ORd-like models fail to predict
for simultaneous
and
inhibition. Predictions show an
-dominated prolongation where ex vivo data show mitigation by
inhibition.
This emphasises the need for context-specific model validation [19]. For example, the ORd-CiPA model, validated for TdP risk classification [20], tends to overestimate APD response to simultaneous and
inhibition. Similarly, the BPS model, validated for 100%
inhibition [16], struggles to predict responses to milder
inhibition.
The TP model, though not validated against current reduction data, showed a low error measure (E = 76.6–83.8) but completely failed to reproduce the increase induced by 100 nM Dofetilide ( + 26 ms predicted vs
ms experimentally). This is partially due to its significantly higher
maximal conductance (0.392 mS
F) compared to ORd-like models (from 0.0011 mS/
F in the ToR-ORd model to 0.0196 mS
F in the ORd-M model), providing greater repolarisation reserve [21].
These findings highlight the importance of thoroughly examining model capabilities. This will help identifying in which context which AP model should (and should not) be used. The Cardiac Electrophysiology Web Lab facilitates this by testing models under various experimental protocols [22].
3.3. 
in the context of proarrhythmic risk assessment
The TdP risk of 28 reference compounds was categorised under the CiPA initiative [7]. The metric, simulated with the ORd-CiPA model, predicts TdP risk based on inhibition of major ionic currents [20]. The 2-D map for
(S1 Appendix), computed with similar methods to those for
, shows that low TdP risk combinations of
and/or
inhibition qualitatively match the combinations leading to
ms. This suggests a qualitative agreement between drug-induced
and TdP risk for drugs inhibiting
and
.
Quinidine and Verapamil, which both inhibit similarly and
, exerted a mitigated effect on
. Their
effects align with their effects on the
and
interval of the ECG [9]. Our new ex vivo data suggest that sufficient
inhibition can prevent changes in
,
, and
intervals, even at concentrations higher than
— assuming the compound affects cardiomyocytes only through
and
inhibition. This may explain discrepancies between ICH S7B (high risk with
blockade) and ICH E14 (low risk with no
change) guidelines, potentially leading to false positives in pre-clinical risk assessments [23].
De Ponti estimated that 60% of new chemical entities inhibit , possibly including useful compounds with
inhibition mitigating the TdP risk [24]. But due to the prevalence of the
–centric risk assessment, these compounds are rarely developed. Identifying combinations of
and
inhibition that do not prolong
could help develop compounds incorrectly deemed proarrhythmic. However, effects on blood pressure and myocardial contractility due to
inhibition still require attention.
3.4. Study limitations
The tested compounds were assumed to primarily affect and
, though literature suggests they may influence other ionic currents [20,25–29]. Moreover, the drug-binding kinetics may require more complex models than the simple Hill equation used here [30,31]. Ionic current response in adult cardiomyocytes may also differ from the response of hERG1a and
expression systems such as those used in the present work, for instance due to different native ion channels isoform and subunit composition or regulatory processes [32]. Our patch-clamp methods comply with the ICH S7B guideline [4] and best practices for in vitro assays, but refining these modelling assumptions with additional data would improve in silico predictions of drug responses.
The inhibitory potency of drugs on IKr and ICaL differed between the CiPA and Pharm datasets, yet with a substantial correlation in across datasets (r2 = 0.84). No correlation was observed for h (r2 = 0.03). Incorporating this
variability when benchmarking models against ex vivo data enables a qualitative assessment of the models’ sensitivity to their in vitro inputs. In this study,
variability introduced substantial differences in
and
inhibition across datasets for some drug conditions (Fig 1). Yet, observations were overall consistent and the tested models showed consistent performance across both datasets (Fig 4). Individual variability was not addressed, but future work could incorporate a population of models approach [33] to account for it.
Most ex vivo data were generated from drugs with similar inhibitory effects on and
(Chlorpromazine, Clozapine, Mesoridazine, Quinidine). These drugs mainly yielded small
responses, highlighting the importance of more detailed risk assessment for multi-channel ‘balanced’ inhibitors. Furthermore, our error measure, E, tends to favour models that accurately reproduce minimal
prolongation from mixed inhibition. An AP model predicting
ms for all combinations would score E = 59.0, outperforming all models studied here, indicating that E alone offers limited model comparison. Combining E with 2-D maps of
prediction (Fig 2) and error maps (Fig 3) helps identifying promising models for further refinement.
Concentration measurements were only available for half of the trabeculae, and drug concentrations were generally lower than nominal values, altering the positions of ex vivo data points on our maps. Yet, the fitted cubic surface and model comparisons were not significantly impacted by the use of only nominal concentrations (S1 Appendix).
4. Methods
4.1. Ex vivo action potential acquisition
4.1.1. Sharp electrode recording protocol for data acquisition.
Experimental AP data were produced by the AnaBios Corporation, following the methods previously described by Page et al. [34]. In brief, trabeculae were extracted from adult human hearts that were not suitable for transplantation, sharp electrodes were impaled in isolated cardiac muscle fibers, their electrophysiological activity was recorded at physiological temperature with vehicle or drugs added. Up to three trabeculae per heart were obtained from the inner endocardial wall of the left (78 trabeculae) and right (4 trabeculae) ventricles. 4 to 15 trabeculae were exposed to the same drug.
In each trabecula, the electrophysiological activity was recorded under baseline conditions, then with three increasing drug concentrations. After the last drug condition, a positive control for prolongation with
inhibition was finally performed with 100 nM Dofetilide addition.
At each drug concentration, each trabecula was paced at 1 Hz for a minimum of 25 min, until voltage recordings were stabilised for at least 2 mins. The stability of APs was assessed qualitatively by the experimenter, based on approximate measurements of the resting membrane potential (RMP), AP amplitude (APA) and . After reaching stable recordings, each trabecula was paced at 2 Hz for 3 min then paced again at 1 Hz for 3 min. The experimental protocol for drug administration is shown in Fig 5.
After baseline conditions, the response to three conditions with drug was recorded. At the end of the experiments, 100 nM Dofetilide was added as a positive control for prolongation with
block.
For more information on the experimental protocol, see [34].
4.1.2. Selected drugs and tested drug concentrations.
The tested drugs inhibit and
with various potencies, so that
changes induced by 29 different drug perturbations of
and
could be explored experimentally. The drugs used for this study and their concentrations are reported in Table 2. We call the intended drug concentration (targetted when making up solutions) the nominal concentration.
Experiments were undertaken in two distinct phases (2014–2016 and 2020–2022). In the second phase (2020–2022), a bioanalysis of the bath solution was performed to measure the drug concentration more precisely at the end of each 25 min period of steady 1 Hz pacing, in case the compound concentration was lowered by absorption by (e.g.) pipettes, tubing or the tissue itself. The sample analysis was performed according to the operating procedure for sample preparation for liquid chromatography–mass spectrometry or mass spectrometry analysis in a bioanalytical laboratory. For data gathered in the first phase (2014–2016), measured concentrations were not available, therefore drug concentrations were assumed to correspond to the nominal concentrations (Table 2).
4.1.3. Ex vivo data post-processing.
Voltage was recorded with a time resolution of 0.05 ms and filtered to remove 60 Hz harmonics. The “peak voltage” for calculating percent repolarisation was measured as the upper 95th percentile of voltage [35]. The resting membrane potential (RMP) was the average voltage over the last 150 ms of the AP. was computed from these reference points and averaged over 30 consecutive APs at the end of steady 1 Hz stimulation.
was defined as the difference from baseline
. Recordings with 2 Hz pacing were not stabilised after 3 min, so
at 2 Hz was not analysed further.
Sudden changes in resting and peak voltages sometimes occurred, which were attributed to electrode movements: normalized APs showed these did not impact , so
was due to drug effects [36]. Data following voltage discontinuities were discarded if
was also suddenly altered. Conditions where early after-depolarisations (EADs) were observed (one trabecula with 100 nM Dofetilide) were not analyzed.
was finally averaged over trabeculae exposed to the same drug conditions.
Drug-induced showed little correlation with baseline
(S1 Appendix). To align with clinical safety guidelines [5],
was not normalised to baseline and it therefore represents the absolute change from baseline.
4.2. Patch clamp measurements of 
and 
inhibition
Drug effects were modelled as simple pore block, using the Hill equation [37] to characterise it with a half-inhibitory concentration () and a Hill coefficient (h). Different voltage-clamp protocols were applied to CHO cells expressing hERG and
channels, and exposed to increasing drug concentrations to measure the drug-induced inhibition of ionic currents.
For inhibition, two voltage-clamp protocols, denoted “
CiPA” [38] and “
Pharm”, were used. Similarly, two voltage-clamp protocols were used to measure the drug-induced
inhibition (“
CiPA” [20] and “
Pharm”). Thereby, two datasets for
and h for
and
were obtained, denoted the CiPA and Pharm datasets. With these two datasets, the impact of the variability of patch-clamp data [38] and of kinetics of drug binding to ion channels [39] can be qualitatively observed. For more details on the generation of the CiPA and Pharm datasets, please refer to S1 Appendix.
The retrieved and h values are reported in Table 3. Dofetilide’s
and Nifedipine’s
were above the highest tested concentration. Therefore, Dofetilide was modelled as a selective
inhibitor and Nifedipine effect as a selective
inhibitor.
4.3. Simulation of 
with in silico action potential models
4.3.1. Selected models.
We selected six main models representative of recent efforts to model the human ventricular AP: Ten Tusscher et al. (TNNP) [40], Ten Tusscher & Panfilov (TP) [41], Grandi et al. (GPB) [13], O’Hara et al. (ORd) [12], Tomek et al. (ToR-ORd) [14], and Bartolucci et al. (BPS) [16]. Since their release, five new parameterisations and variants of these models have been published. Dutta et al. replaced the component of the ORd model with a 6-state Markov model [7] and rescaled the maximal conductances of five ionic currents (
,
,
,
,
) [42]. The GPB, TP, and ORd models were rescaled by Mann et al. to capture the effects of
and
inhibition and to reproduce
features observed in long QT Syndrome (LQTS) populations [11]. Mann et al. added a late sodium component to their versions of the GPB and TP models, based on the ORd model. Krogh-Madsen et al. proposed a version of the ORd model with rescaled maximal conductance parameters for six ionic currents (
,
,
,
,
,
) to capture populations with long QT syndrome, which was also included in the present study [15]. All these variant models were included in the present study and are summarised in Table 4.
To maximise consistency with the trabeculae measurements, the endocardial variant of the AP models was used when available.
4.3.2. Action potential simulations.
Published CellML models were obtained from the Physiome Repository [43]. Stimulus current width, amplitude, and responsible ions (for instance [44]) were not changed. 1 Hz steady pacing was applied in line with the ex vivo experiments. We simulated 1500 s to reach a steady-state response to 1 Hz pacing. In all models, the convergence to steady-state was achieved with 1500 pre-paces. The
AP was then recorded with time resolution of 0.05 ms, matching the resolution of the ex vivo data, and allowing for precise estimation of
.
When computing 2-D maps of as a function of
and
inhibition (Sect 2.2), default initial internal and external concentrations from the CellML files were used. When comparing quantitative model predictions with trabeculae recordings (Sect 2.3), external concentrations of
,
, and
were set to 4 mM, 148.35 mM, and 1.8 mM respectively, matching concentrations used experimentally [34].
The steady-state APs simulated with the included models are shown in Fig 6 for visual comparison. Note that the TNNP model does not predict a physiological AP when external ionic concentrations match experimental values. Therefore, predictions with the TNNP model were not quantitatively compared with the ex vivo data in Sect 2.3.
External concentrations were set to experimental values (dashed line) or left at the values in the original CellML model (solid line).
In vitro data for inhibition of and
were integrated into model predictions by applying a rescaling factor, computed with the Hill equation [37,45], to each affected ionic current:
with I(D) the simulated ionic current, D the drug concentration, and I0 = I(0) the ionic current without drug. and h were taken from Table 3.
4.4. Comparison of model predictive power with experimental action potential data
4.4.1. Qualitative comparison with 2-D maps of 
versus current inhibition.
With each model, we simulated APs under combinations of
and
inhibition conditions, ranging from 0% to 100% inhibition.
was computed for each
/
inhibition combination.
was shown using a colour-map that was kept consistent across all the models and which covered the experimental range of drug-induced
. Combinations of
and/or
inhibition for which no change in
were observed or predicted (
ms) were plotted as white pixels, thus highlighting a “0 ms line”.
The experimental drug-induced data was reported with similar methods. Additionally, a cubic surface of
as a function of
and
inhibition was fitted through the ex vivo data points (details in S1 Appendix) to facilitate visual comparison of ex vivo data with simulations.
Fig 7 shows a schematic visualisation of the methods for 2-D map simulations.
Simulated was computed from the in silico AP model run for 1500 paces, using
and/or
inhibition as input for the model. The corresponding point was then added to the 2-D map, with
reported with the colour-map.
4.4.2. Metric for the quantification of model predictivity.
To quantitatively compare measurements and predictions, APs were simulated at all nominal drug concentrations, or at actual drug concentrations where available. An error measure, E, was then designed to quantify the error in predicted
whilst accounting for experimental variability. E was defined as:
with and
the experimental and simulated
for the drug perturbation k, and
the SEM of experimental
across the trabeculae tested with k. Indices k span all concentrations of the nine drugs (Table 2).
5. Conclusion
Our new experimental data provide quantitative understanding of the relationship between and acute
and/or
inhibition in adult human ventricular cardiac muscle. Combined with in vitro data, they make a valuable benchmark for assessing the performance of in silico AP models. Although certain models accurately predict
prolongation for selective
inhibitors, they struggle to replicate the mitigating effects of simultaneous
inhibition observed experimentally. The TP and GPB-M models appear to be the most promising starting points for developing more advanced AP models that can account for multi-ion channel inhibition in cardiac safety risk predictions. Of the ORd-like models, the ToR-ORd model exhibits the most promising balance between
and
and its predictivity may be improved upon reparameterisation. Our study emphasises the importance of context-specific validation of AP models: rigorous testing across various ion channel inhibitions and drug concentrations is essential to ensure models can reliably predict cardiac responses. Extended model validation, alongside high-quality experimental data, will ultimately lead to more accurate and reliable in silico frameworks for predicting proarrhythmic risk from in vitro data. Such frameworks can be vital in improving the specificity of early identification of potential cardiac safety issues in drug development.
Declaration of generative AI and AI-assisted technologies in the writing process
During the preparation of this work the authors used ChatGPT (public v3 and internal Roche v4O) in order to enhance general text readability and conciseness, and to debug code. After using this tool, the authors reviewed and edited the content as needed and take full accountability for the content of the publication.
Supporting information
S1 Appendix. All supplementary materials, including Supplementary Figs A–K and Tables A–E.
The appendix includes details on patch-clamp experimental protocols, additional figures supporting the main text, and a 2-D map of .
https://doi.org/10.1371/journal.pcbi.1012913.s001
(PDF)
Acknowledgments
The authors thank Dr. Abi-Gerges (AnaBios Corporation) for his support with experimental oversight for ex vivo data analysis. The authors thank Dr. Bartolucci and Dr. Severi for their help in implementing the BPS model [16]. The authors thank Evgenia Gissinger and Fabian Häusermann (Dr. Polonchuk’s lab) for performing the patch-clamp experiments.
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