Simultaneously calibrating to AP and CaT data improves model predictions

First, we examined whether AP or CaT recordings alone provided sufficient information for conductance parameter calibration and model predictions. We used simulated recordings from baseline physiological conditions without pacing stimuli (spontaneous APs), and supplied 1) only the AP traces, 2) only the CaT traces, or 3) both (Fig 2A) to the genetic algorithm (GA). The GA calibrates parameters by varying them to create a population of Kernik model cells, then iteratively selecting and modifying individual models that generated AP and CaT traces that best matched the supplied data (outlined in Fig 1B) [33]. We ran the genetic algorithm 10 times per input dataset, with each GA run starting on a different initial population of models. This allowed us to assess whether each input dataset provided enough information to consistently estimate parameter values, even when the initial search space varied.

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Fig 2. Calibration error and spread remain similar whether only AP, only CaT, or both are included during calibration.

(A) Schematic of fitted data types. (B) Example of calibrated parameter values from 10 GA runs per data type for one parameter (G_CaL), log-normalized to the ground truth G_CaL value of the fitted model cell. Parameter error and spread calculations are visualized. (C) Parameter errors and spreads calculated by comparing calibrated parameters to the corresponding true parameters of 4 model cells from the in silico dataset. 10 GA calibration runs were performed per model cell. Each point represents the average error or spread over all 16 fitted parameters from a single genetic algorithm run.

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We evaluated each candidate protocol on parameter calibration accuracy (calibration error) and consistency (calibration spread). Calibration error was represented by the absolute values of calibrated parameters, log-normalized to the corresponding ground truth parameter value, and calibration spread was assessed by calculating the standard deviation (spread) in log-normalized calibrated parameter values between the 10 runs (Fig 2B). After averaging over all 16 fitted parameters, we found minimal differences in calibration error (p = 0.11) or spread (p = 0.07) between fitting only voltage, only calcium, or both simultaneously (Fig 2C). From these initial tests, therefore, there appears to be little difference between experimental protocols in how well (or poorly) each can identify model parameters.

We next assessed the calibrated models from each candidate protocol on how well each predicted model cell responses to 30% block of rapid delayed rectifier current I_Kr, as this perturbation is both: 1) independent of the conditions used for model calibration and 2) relevant to cardiac pharmacology [34]. With this evaluation (Fig 3A), we found that models fitted to only AP data or only CaT data differed significantly from the ground truth model (Fig 3B and S1 Fig). When both AP and CaT recordings were used simultaneously during parameter calibration, the resulting calibrated models exhibited substantial improvement in their predictions of 30% I_Kr block. Therefore, fitting parameters to both AP and CaT traces simultaneously is required for accurate prediction of phenotypes that were not used in the fitting process.

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Fig 3. Prediction of iPSC-CM response to an independent perturbation differentiates the models calibrated to AP and CaT simultaneously from those calibrated to single traces.

(A) Schematic illustrating the evaluation of calibrated models on their ability to predict an independent response. (B) AP and/or CaT responses to 30% I_Kr block predicted by 10 calibrated models for one model cell (thinner traces), compared with the true response of the corresponding model cell (thicker red trace).

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Overall parameter error and spread show minimal change with varied protocol conditions

Next, we explored how varying the number and type of simulated conditions in the candidate protocols affected parameter calibration. AP and CaT recordings were simulated under many conditions that could be produced in an electrophysiology laboratory and constructed candidate protocols from various combinations of these conditions, which included: 1) varied buffer calcium, from hypo- to normal to hyper-calcemic conditions, 2) spontaneous beating and varied pacing rates from 1–2 Hz, 3) varied levels of L-type calcium channel (I_CaL) blockade, and 4) a mixture of these conditions (see Methods for details). We also separated these data into shorter protocols, to see if the experimental setup could be further simplified (Fig 4A). Unexpectedly, we found that parameter errors and spread across all 16 maximal conductance parameters did not differ significantly between the protocols with varied cell culture conditions (Fig 4B, p = 0.814 and p = 0.673, respectively). Additionally, we observed no significant differences in average calibration errors (p = 0.088) and spreads (p = 0.137) when varying the number of conditions in the protocol (Fig 4C). Similar findings were observed when evaluating different combinations of these experimental conditions (S2 Fig).

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Fig 4. Varying the types and number of experimental conditions has minimal effect on overall calibration error and spread.

(A) Schematic of candidate protocols to generate data for model calibration: varied buffer calcium concentration, varied pacing rates, varied I_CaL block levels, and a mixture of the 3. (B) Parameter errors and spreads from calibration runs for 4 Kernik model cells (10 GA runs per model cell), using calibration data from each protocol in Fig 4A. Bar plots show the mean calibration errors and spreads over all 16 fitted parameters from all 40 calibration runs. Error bars represent standard deviations over these runs. (C) Schematic of candidate protocols to generate data for model calibration: combinations of 1, 2, or 3 parts of the mixed condition protocol. (D) Parameter errors and spreads from calibration runs for 4 Kernik model cells (10 GA runs per model cell), using calibration data from each protocol in Fig 4B.

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A readily-achievable 3-condition protocol improves predictions of I_Kr block response

As with the results shown in Fig 3, we assessed how well calibrated models predicted the response to I_Kr block, and we found that accuracy depended strongly on the experimental conditions simulated in each candidate protocol (sample AP traces shown in Fig 5A). Out of the protocols using 3 experimental conditions in Fig 4A, the mixed-conditions protocol generated calibrated models with the most accurate predictions of changes in APs with 30% I_Kr block, compared with protocols which varied only the buffer calcium, pacing rates, or I_CaL blockade (Fig 5B–5C). When evaluating whether a shorter version of this protocol could produce equally predictive models, the full protocol with all 3 conditions outperformed protocols with 1 or 2 of the conditions (Fig 5B–5C). These data suggest that an optimal experimental protocol for iPSC-CM model parameter calibration should include voltage and calcium transient fluorescence recordings under at least 3 varieties of cell culture condition changes or perturbations. Of note, this supports our hypothesis that data from iPSC-CMs under a variety of conditions provides sufficient parameter identification to generate predictive models for pharmacological applications.

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Fig 5. Calibrating parameters to data from the mixed condition protocol improves model predictions of IKr block response.

(A) Examples of simulated steady state APs from baseline (black traces) and 30% I_Kr block (red traces) conditions, using the ground truth model cell (solid) and predicted models (dashed). Protocols used for calibration are indicated in the table on the right. (B) Percent error in calibrated model predictions of APD₉₀ values at 30% I_Kr block. Bars represent means over 10 calibration runs, and error bars represent standard deviations from those same calibration runs. APD₉₀ values were normalized to corresponding AP amplitudes before calculating percent error. (C) Percent error in calibrated model predictions of change in APD₉₀ (ΔAPD₉₀) between baseline and 30% I_Kr block. APD₉₀ values were normalized to corresponding AP amplitudes before calculating percent error.

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Normalized fluorescence recordings sufficiently inform parameter calibration

Fluorescence recordings generally detect relative changes and do not provide absolute levels of voltage and calcium. Fluorescent dyes can be calibrated [35,36], and patch clamp can detect true transmembrane potentials, but these are more challenging and lower-throughput techniques compared with straightforward fluorescence recordings. To assess the potential implications for parameter identification, we compared two versions of simulated recordings obtained with our optimized protocol: 1) unscaled (original) in silico data, representing patch clamp and calibrated calcium measurements, and 2) normalized versions of the same waveforms, representing simpler fluorescent recordings (Fig 6A).

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Fig 6. Normalization of calibration data does not significantly affect model calibration results.

(A) Schematic of optimized experimental conditions, normalization of simulated data used to represent fluorescence recordings, and original simulated data used to represent more precise measurement modalities. Photo courtesy of Hamamatsu Photonics K.K. (B) Parameter errors and spreads from calibration runs on data from 4 Kernik model cells (10 GA runs per model cell), using either normalized or original data for calibration. Each point represents the average error or spread over all fitted parameters. (C) For 1 model cell: Predicted AP and CaT responses to 30% I_Kr block (thinner traces) from each set of calibrations, compared to the true response of the model cell (thicker red trace). (D) For the same model cell as in (C): Mean squared errors between data points in the predicted traces (simulated using calibrated models) and the actual model cell’s traces, for simulations under 30% I_Kr block.

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Parameter calibration accuracy and consistency did not differ significantly when comparing calibrated models from the original data with those from the corresponding normalized data (Fig 6B). Notably, calibrated models from these two data types also performed similarly when evaluating predictions of 30% I_Kr block response (Fig 6C). This suggests that fluorescence voltage and calcium recordings from our optimized protocol conditions provide sufficient information to calibrate predictive models. In addition, we ran similar evaluations in which we replaced 30% I_Kr block with 30% block of I_K1, since this inwardly-rectifying current contributed do iPSC-CM diastolic potential. We suspected that, for these predictions, removing the exact membrane potential information would decrease predictive accuracy. In addition, we ran similar evaluations replacing I_Kr block with 30% I_K1 block, since I_K1 contributes to the resting membrane potential in iPSC-CMs. We anticipated that removing exact membrane potential information would decrease prediction accuracy in models calibrated to normalized data, and tried to determine whether recordings from multiple conditions would help to recover prediction accuracy. Surprisingly, the majority of calibrated models from normalized data predicted I_K1 block response with high accuracy, similar to that of the calibrated models from the original data and greatly improved compared with calibrated models from more rudimentary protocols (S3 Fig). This further increased our confidence in using normalized, or optical, AP and CaT recordings for our calibration setup.

Calibrated models predict variability in arrhythmia susceptibility in silico

The primary goal of optimizing a computational pipeline for model calibration is to create cell preparation-specific models that can predict variability in phenotypes, particularly arrhythmia susceptibility, between iPSC-CM lines. To assess the ability of our optimized protocol to predict cell line-specific arrhythmia susceptibility, we calculated the lowest level of I_Kr block (i.e. highest % I_Kr) that induced arrhythmia dynamics (afterdepolarizations, Torsades de Pointes, alternans, beating cessation, or tachycardia) in the same 4 Kernik model cells from our in silico dataset. These calculations defined an “I_Kr block tolerance threshold” for each of the 4 model cells (Fig 7A), ranging from 37% I_Kr block (highest susceptibility) to 62% I_Kr block (highest tolerance) (Fig 7C).

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Fig 7. Models generated by the optimized calibration pipeline predict cell-specific arrhythmia susceptibility.

(A) Schematic of calculation of I_Kr block tolerance threshold. (B) Errors in predictions of I_Kr block tolerance threshold, comparing calibrated models from 3 protocols: 1) normalized AP and CaT recordings from a single physiological condition; 2) normalized AP and CaT recordings from the optimized, 3-condition protocol; and 3) non-normalized AP and CaT recordings from the optimized protocol. Each point represents the I_Kr block threshold error from 1 calibrated model, and data for 40 calibrations are shown (4 model cells x 10 GA runs per model cell). (C) Correlation between true I_Kr block threshold of model cells and their corresponding calibrated models’ predicted I_Kr block thresholds. (D) Correlation between true I_Kr block threshold of model cells and their corresponding calibrated models’ I_Kr block threshold prediction error.

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Predicted I_Kr block tolerance thresholds were also calculated for the calibrated models generated by our computational pipeline. These predicted thresholds were assessed against the ground truth threshold of the model cell. Calibrated models from our computational pipeline predicted I_Kr block thresholds with high accuracy and consistency, with similar error and spread as models calibrated to corresponding non-normalized recordings (Fig 7B). The aggregated calibrated models also predicted relative arrhythmia susceptibility of the 4 model cells, as shown by a significant positive correlation between ground truth and predicted I_Kr block thresholds in Fig 7C. Additionally, there was no correlation between the model cell’s true I_Kr block threshold and its associated calibrated models’ prediction error, suggesting that the accuracy of these predictions would not be affected by variability in arrhythmia susceptibility between iPSC-CM preparations (Fig 7D).

Optimized model calibration process constrains key ionic parameters

Throughout the protocol optimization process, we observed that while calibration error and spread largely remained constant when averaged over all fitted parameters, certain individual parameters consistently showed low calibration spread (e.g. G_Kr, G_NaK) or high calibration spread (e.g. G_rel, G_CaT) (S4 Fig). Thus, we hypothesized that our calibration method only needs to tightly constrain a few key parameters, tolerating inaccuracy or variation in less important parameters while still generating highly predictive calibrated models. To determine whether normalized data from the optimized protocol constrains the parameters that play the largest roles in determining AP and CaT morphology, we analyzed the relationship between parameter calibration accuracy and consistency with the Kernik model’s sensitivity to parameter changes. We used multivariable regression to determine how the 16 calibrated model parameters affect relevant phenotypes such as AP duration, CaT amplitude, and I_Kr block threshold (Fig 8A) [37]. The resulting model coefficients represent the magnitude and direction of the effect of changes in the corresponding parameter on the modeled phenotype (Fig 8A–8C). The most important parameters depended on which model output was considered (Fig 8A–8C), but parameters that appeared frequently included rapid delayed rectifier K⁺ conductance (G_Kr), L-type Ca²⁺ conductance (G_CaL), Na⁺ conductance (G_Na), inward rectifier K⁺ conductance (G_K1), and Na⁺/K⁺ pump conductance (G_NaK).

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Fig 8. Highly sensitive conductance parameters are well-constrained by the optimized calibration pipeline.

(A-C) Regression coefficient magnitudes for each Kernik model maximal conductance parameter’s contribution to (A) APD₉₀, (B) CaT amplitude, and (C) I_Kr block threshold. Blue bars indicate positive coefficients, and red bars indicate negative coefficients. The top 4 and bottom 4 parameters, ranked by regression coefficient magnitude, are bolded and indicated with black dashed lines. (D-F) Distributions of parameter calibration errors (left) and calibration spread (right) from the optimized calibration pipeline, with parameters grouped into the top 4 and bottom 4 regression coefficient magnitudes for (D) APD₉₀, (E) CaT amplitude, and (F) I_Kr block threshold. Each blue dot represents the calibration error or spread value for 1 parameter from calibrations on one model cell (4 parameters per group x 4 model cells = 16 points).

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We then grouped the parameters into the highest and lowest regression coefficient magnitudes for each phenotype, and assessed calibration errors and calibration spreads from the optimized calibration protocol within those groups. The 4 parameters with highest regression coefficient magnitudes for CaT amplitude and I_Kr block threshold showed significantly lower average calibration error and spread compared with the 4 parameters with the lowest regression coefficient magnitudes (Fig 8E–8F). Accordingly, the optimized calibration protocol displayed significant improvement over most other candidate protocols in predictions of CaT amplitude and I_Kr block threshold. We saw similar results when examining calibration errors and spreads in parameters grouped by APD₉₀ sensitivity, though the difference in calibration errors was not statistically significant (Fig 8D). These results suggest that our optimized computational pipeline does constrain the key Kernik model conductance parameters needed to generate predictive models.

Validation of optimized computational pipeline on in vitro iPSC-CM recordings

After optimizing our computational pipeline using in silico data where the ground truth model parameter values were known, we assessed whether our pipeline could still generate predictive models using in vitro data. S5 Fig contains all available in vitro iPSC-CM AP and CaT traces under various experimental conditions. We applied the computational pipeline to normalized fluorescence AP and CaT recordings from one iPSC-CM cell line under combinations of the following conditions: 1) low buffer calcium (1.0 mM) with 1 Hz pacing, 2) physiological buffer calcium (1.8 mM) with 1 Hz pacing, and 3) physiological buffer calcium with 1.25 Hz pacing. Fig 9A outlines the data processing and normalization procedures performed on the fluorescence recordings prior to model calibration. Recordings from a separate condition (1.0 mM buffer calcium with 2 Hz pacing) were left out from model calibration, so they could be used to independently evaluate predictions generated by the calibrated model.

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Fig 9. Preliminary model calibrations to in vitro data support findings from in silico calibrations.

(A) Fluorescence recording processing steps in preparation for model calibration pipeline. (B) Top: Resulting calibrated conductance values (left) normalized to Kernik model baseline values (dashed line at 0) and predicted traces under an independent condition (right) when only data from a single condition (1.8 mM [Ca²⁺]_o, 1.25 Hz pacing) is used to fit parameters. Predicted traces (thinner lines) were simulated from 10 models calibrated to recordings from a single sample (thicker red line). Bottom: Resulting calibrated conductance values (left) normalized to Kernik model baseline values (dashed line at 0) and predicted traces under an independent condition (right) when data from a 3-condition protocol (1.0 mM [Ca²⁺]_o, 1 Hz pacing → 1.8 mM [Ca²⁺]_o, 1 Hz pacing → 1.8 mM [Ca²⁺]_o, 1.25 Hz pacing) are used to fit parameters. Predicted traces (thinner lines) were simulated from 10 models calibrated to recordings from a single sample (thicker red line).

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Calibrating the model conductances using data from only one of these conditions resulted in unconstrained conductance values and highly variable predictions of response to the left-out validation data (Fig 9B). Including data from 2 additional, mixed conditions significantly improved consistency of key conductance parameter calibrations (Fig 9C). When these calibrated parameters were incorporated into the Kernik model and the cell line’s response to a new condition was predicted, we found that models calibrated to recordings from 3 conditions substantially outperformed models calibrated to only 1 condition. These results further supported our findings from in silico protocol optimization, showing that data from fluorescence voltage and calcium transients under 3 varied conditions can constrain key model parameters and generate predictive, cell preparation-specific models.

Calibration of models of cardiac electrophysiology

Parameter values in computational models of cardiac electrophysiology are often determined by manual fits to voltage and current recordings, often collected under one or few experimental conditions. This limits the baseline models’ ability to represent electrophysiological heterogeneity. Additionally, determination of these baseline parameter values may be affected by selection bias for cells with larger currents, inadequate separation of activation and inactivation kinetics, and inter-laboratory differences in current and voltage clamp protocols [38]. These issues have, in many cases, led researchers to recalibrate the model parameters in attempts to better reflect the behaviors of their specific cardiomyocyte preparations. For example, Potse et al. fitted a reaction-diffusion model of ventricular electrical activity to reproduce phenotypes of patients with heart failure or left branch bundle block [39]. Similarly, Lombardo et al. tuned atrial electrophysiology models for patients undergoing ablation therapy [40] whereas Krogh-Madsen et al. used the genetic algorithm to fit a human ventricular cardiac model to clinical QT interval data [41]. In all three cases, these groups found significant discrepancies between the respective initial models and their final, calibrated, fit-for-purpose models. However, to the best of our knowledge, the experimental data used in virtually all previous cardiomyocyte model calibration research come from voltage clamp, patch clamp, or clinical data. Currently, these data are still difficult to obtain from a large group of patients or cell preparations. More recent work has demonstrated the utility of genetic algorithms and the resulting recalibrated models in prediction of arrhythmic behaviors and drug mechanisms, but these also used complex voltage step protocols to calibrate model parameters [42]. These prior results motivated our search for protocols that could calibrate mathematical models using voltage- and calcium-sensitive fluorescent dye measurements, which are considerably easier to acquire than patch-clamp recordings.

Guiding experimental design for optimal parameter calibration

We considered several factors when optimizing the experimental protocol to generate iPSC-CM data for our computational pipeline: 1) the information that the data would provide for parameter calibration, 2) the complexity of the protocol, and 3) the feasibility of the experiment for broad accessibility and high throughput setups. Since the goal of model calibration is usually to improve the accuracy of model parameterizations and predictions, previous work has largely focused on maximizing the information content of experiments used to fit models [43–45]. In particular, research on cardiac electrophysiology models typically usescomplex voltage step protocols that can accurately determine individual ion channel conductances and kinetics [24,46,47]. Here, we emphasize that it is also important to identify adaptable protocols that can be widely adopted. Therefore, we opted to focus on using fluorescence recordings to calibrate model parameters, instead of the usual techniques such as patch clamp. To evaluate different protocols, we created an in silico dataset for testing various data combinations in their ability to inform parameter calibration. This approach provided 2 major advantages. First, guided by experimental feasibility and relevance, we were able to simulate iPSC-CM electrophysiology under many combinations of conditions without the time and financial costs associated with in vitro experiments. Second, because we knew the ground truth ionic parameter values that produced these AP and CaT traces, we could precisely assess which simulated conditions informed which parameters. We also ran multiple rounds of genetic algorithms on each tested in silico protocol, with each round starting from a different initial model population, to assess how consistently each parameter was identified. We used this as a measure of confidence in each parameter estimate.

Just as prior studies have shown that parameter constraint improves when values for more than one output feature are provided [48], we found that calibrating model parameters to fluorescence recordings of AP and CaT traces, as opposed to using only one of the two, resulted in better parameter constraint for some (but not all) parameters. Perhaps more importantly, we found that calibrating to both outputs simultaneously resulted in significant improvement of the calibrated models’ predictions on a new, independent output. This is consistent with prior results which showed that, when translating drug responses across cell types, using multiple electrophysiological features or observations of iPSC-CMs under multiple conditions improved translations [23,49–51]. Similarly, our final optimized protocol included a mixture of 3 experimental conditions. Finally, overall parameter calibration accuracy and consistency, as well as independent predictions of I_Kr block response, were similar between the models fitted to normalized data (representing fluorescence data) and those fitted to corresponding non-normalized data (representing patch clamp and calibrated Ca²⁺ transient data). Collectively, these findings support our hypothesis that data from fluorescence recordings under multiple conditions, which are more practical compared with microelectrode or patch clamp recordings, can be used to calibrate predictive models. Notably, several parameters such as the background Ca²⁺ and Na⁺ conductances, G_Ks, and G_rel were rarely constrained by any of the datasets we tested. Our subsequent parameter sensitivity analysis showed that model conductances that strongly affect relevant model outputs tend to be well-constrained by our optimized protocol.

Prediction of cell-specific arrhythmia susceptibility

After calibrating parameters using fluorescence voltage and calcium recordings under a similar set of experimental conditions, we tested the ability of these models to predict conditions that were not used in during the calibration. In particular, we tested the models’ ability to predict the pro-arrhythmic effects of I_Kr block, given the potential of therapeutics to cause arrhythmias through both on-target and off-target effects [52,53]. This emphasis on prediction rather than parameter identification is consistent with some previous analyses of systems biology models. In an influential paper, Gutenkunst et al. posited that a model that accurately predicts relevant phenotypes even with some parameter value inaccuracies is more useful than a model with high parameter accuracy and consistency, but inaccurate predictions [54]. This suggests that attempting to determine parameter values directly through precise measurements is an inefficient way of optimizing models. Subsequent studies in both cell signaling and cardiac electrophysiology models have demonstrated success in focusing parameter calibrations on optimizing prediction accuracy in place of specific parameter accuracy [25,55,56]. These analyses demonstrate the importance of calibrating models to not only fit available experimental data, but also generate accurate predictions of responses to novel perturbations.

Therefore, while optimizing the computational pipeline, we included a prediction metric in addition to parameter value accuracy and consistency. We created a quantifiable, pharmacologically-relevant measure of cell-specific arrhythmia susceptibility by finding the lowest level of I_Kr block that induced arrhythmic dynamics in each Kernik model (in silico) or iPSC-CM preparation (in vitro), which we termed the “I_Kr block tolerance threshold”. Calibrated models from our optimized computational pipeline were able to predict this threshold consistently and accurately, with similar error as those from calibrating to the original, non-normalized data. The models calibrated to normalized data were also able to correctly rank the I_Kr block arrhythmia susceptibilities of the fitted Kernik model cells, suggesting that the models generated by this pipeline contain enough information to predict cell-specific arrhythmia susceptibilities, despite errors and non-constraint of several smaller conductance parameters.

Limitations and potential directions

The model calibration process developed and optimized in this study can be applied broadly to research that investigates the ionic mechanisms behind iPSC-CM phenotype variability or predicts differential effects of therapeutics on various iPSC-CM cell lines and preparations. However, phenotypic variability also exists within iPSC-CMs from the same preparation. While it is possible to use fluorescent dyes to record electrophysiology of individual cells, we currently focused our efforts on calibrating models to represent multicellular preparations. Future work could include adapting this computational pipeline to calibrate models representing single cardiomyocytes within an iPSC-CM preparation.

Several conductance parameters fitted in our current pipeline did not contribute significantly to electrophysiological phenotype and responses (e.g. G_f, G_SRleak, and G_rel), according to our parameter sensitivity analyses. Many of these same parameters were also less accurately constrained by our computational pipeline. While we showed that the resulting calibrated models could accurately predict several major electrophysiology phenotypes and channel block responses, we do not know whether these models could still predict responses that are strongly affected by one or more of the unconstrained parameters. Additionally, other computational models of iPSC-CMs use ionic current contributions that differ from the Kernik model used in this study [17,32,57]. Future calibrations to APs and CaTs simulated from a variety of computational models could help verify whether our current calibration method can tolerate variation in ion current kinetics or contributions, or if further optimization of the calibration protocol is warranted. If improving parameter calibration accuracy and constraint of particular ionic current(s) is found to be necessary for model predictive power, one option would be to replace the conductances with lowest parameter sensitivity regression coefficient magnitudes with representative kinetic parameters, such as time constants or activation gates. If these kinetic parameters are found to impact electrophysiology in a manner that is detectable by the genetic algorithm, their calibrations will likely be more accurate and constrained, generating more precise cell preparation-specific iPSC-CM models.

Simulations of iPSC-CM electrophysiology

In silico simulations of iPSC-CM electrophysiology (e.g. membrane potential, calcium transients, changes in maximal conductances and ionic currents) were carried out in MATLAB R2020b by solving the ordinary differential equations defined in the Kernik et al. (2019) mathematical model of human iPSC-CMs [20], using the initial conditions listed in S1 Table. In cases where a protocol included cardiomyocyte pacing, electrical stimuli of 60 pA/pF were simulated for a duration of 1 ms at the specified intervals. All simulations were run for 5 minutes, which was sufficient to achieve a steady state using the baseline model and physiological, unperturbed conditions (S3 Table, protocol #19). The voltage and intracellular calcium concentration from the final 5 seconds of each simulation were stored and included in the in silico dataset.

In silico dataset for optimization of iPSC-CM experimental protocol

To simulate a heterogeneous set of iPSC-CM cell lines, a “population” of Kernik model cells was created by drawing multiplier factors for each maximal conductance parameter from a log-normal distribution with mean multiplier = 1, spread = 0.2. This population was then simulated under physiological, unperturbed conditions (S3 Table, protocol 19), and filtered for cells which showed a spontaneous beating frequency between 0.3 Hz and 1.0 Hz, nearly matching the automaticity rate range for human iPSC-CMs reported in [58]. Out of the remaining model cells, 4 were randomly selected for simulation under the 19 different conditions, to generate the final in silico dataset. The Kernik model’s baseline conductance parameter values and the scaled conductances for these 4 model cells are listed in S2 Table. A list of the various conditions these 4 cells were simulated under can be found in S3 Table. All simulations were run for a 5-minute time span (steady state under physiological buffer conditions, without pacing), and membrane potential and intracellular calcium recordings from the final 5 seconds of these simulations were extracted and stored for the in silico dataset. The built-in interp1 function in MATLAB was used to interpolate these data in equal time steps (0.1 ms). To mimic processed data from fluorescence recordings, we also created “normalized” versions of each dataset by scaling the data from a minimum of 0 to a maximum of 1. This dataset allowed for comparison of conductance parameter estimates produced during model calibration against known ground truth conductance values.

Parameter calibration using the genetic algorithm

The data used for calibrating model parameters included the steady state AP and CaT waves from the previously-generated in silico dataset. Individual simulation runs are either included or excluded from the fitting procedure to compare different experimental “candidate protocols”. Rapid delayed rectifier potassium current (I_Kr) block conditions were left out from protocol optimization to use for conductance estimate validation. If the candidate protocol consists of more than 1 condition, the final values of membrane potential, intracellular calcium concentration, and other steady state parameters are used as the starting values for the subsequent protocol condition. To determine the optimal protocol for accurate and consistent parameter identification, Kernik model maximal conductance parameters were fitted to in silico from each candidate protocol simulated for 4 of the dataset’s model cells, using the genetic algorithm (GA) [24,26]. Briefly, the GA creates a new population of Kernik model cells, each randomly assigned a set of conductance parameter scale factors, and simulates the candidate protocol for each of these model cells. Then, the mean squared error between corresponding data points in the GA-generated trace and the trace from the in silico dataset is calculated. The model cells with the lowest errors are retained, while higher-scoring cells have their parameter values altered in the next algorithm iteration. Details about specific GA settings, such as population size and parameter retention/alteration criteria, can be found in S4 Table. This process repeats for 20 iterations, where each new population has a lower average error than the previous. The parameters of the model cell with the lowest error from the final population are selected as the final calibrated parameter values from that run. Parameter calibrations are conducted 10 times per candidate protocol per model cell, with each of the 10 GA runs starting with a different set of initial model populations. The 10 sets of conductance estimates from each GA run are evaluated on 1) accuracy to the ground truth parameter values of the model cells and 2) ability to predict the model cell’s response to a perturbation that was not seen during parameter calibration, such as I_Kr block.

In vitro iPSC-CM tissue culture and optical recordings

Human induced pluripotent stem cells (iPSCs) derived from a single cell line were differentiated into cardiomyocytes (iPSC-CMs) by modulating canonical Wnt signaling [59]. The cardiomyocytes were enriched, then combined with cardiac fibroblasts in a ratio of 90% iPSC-CMs to 10% fibroblasts within a collagen-fibrin hydrogel solution (InvivoSciences, Inc., Madison, WI, USA). The engineered heart tissues (EHTs) thus formed were maintained in a serum-free cardiac maintenance medium, supplemented with penicillin and streptomycin (Thermo Fisher Scientific, Waltham, MA, USA), within 96-well micro culture plates (MC-96, InvivoSciences). EHT maintenance was carried out as previously described in relevant literature [60]. Following a five-day remodeling phase, the EHTs underwent further maturation with biphasic constant current electrical stimulations at a frequency of 1Hz for 8 days.

For optical voltage and calcium transient recordings, the EHTs were loaded with Fluovolt (at a dilution of 1:500, Thermo Fisher Scientific), or Cal-520 AM (also at 1:500, AAT Bioquest), along with PowerLoad (Thermo Fisher Scientific), by incubating them for one hour in Tyrode’s solution. This solution was prepared with either 1.0 mM or 1.8 mM [Ca²⁺]. Following the removal of the dyes, the solution was pH adjusted to 7.4 and warmed, and Tyrode’s solution with the corresponding calcium concentration was reintroduced to aid in recovery from dye loading stress over a 30-minute period. The EHTs were then paced at frequencies of 1.0 Hz, 1.25 Hz, or 2.0 Hz for five minutes. Three replicate samples of each buffer [Ca²⁺] and pacing frequency were prepared in different wells. The steady-state membrane potential and intracellular calcium transients during this period were recorded using a high-throughput fluorescence plate imager, FDSS/μCell (Hamamatsu Photonics K.K., Japan), utilizing 470nm excitation and 540nm emission at a rate of 125 data points per second. The collected data were analyzed with the iVSurfer software (InvivoSciences), specifically designed for high-throughput waveform data analysis, and one recording per experimental condition was taken for further processing in preparation for model calibration.

Processing of in vitro iPSC-CM recordings for the computational pipeline

Fluorescence voltage and calcium recordings were processed in MATLAB with baseline drift subtraction (imerode function), median filtering to remove noise (medfilt1 function), and the same normalization steps as the pseudo-data. Kernik model maximal conductance parameters were fitted to these data using the same workflow as prior fittings to pseudo-data, with the 1.0mM buffer [Ca²⁺], 2.0Hz pacing data left out for validation.