Large-scale synthetic data enable digital twins of human excitable cells
- Center for Precision Medicine and Data Science, University of California, Davis, United States
- Department of Physiology and Membrane Biology, University of California, Davis, United States
- Department of Internal Medicine, Division of Cardiovascular Medicine, University of California, Davis, United States
- Institute for Regenerative Cures, University of California, Davis, United States
- Department of Pharmacology, University of California, Davis, United States
Figures
Figure 1
Huge variability captured in simulated induced pluripotent stem cell (iPSC)-derived cardiomyocyte populations.
(A) To illustrate population variability, 20 action potentials (APs) were shown, each resulting from ±40% random variation applied to 52 parameters governing six key ionic currents (IKr, ICaL, INa, IKs, IK1, and If) in the baseline Kernik induced pluripotent stem cell-derived cardiomyocyte (iPSC-CM) model Kernik et al., 2019, within a simulated population of 200,000 spontaneously beating cells. (B) These perturbations yielded a wide spectrum of APs, with substantial variation in both waveform and frequency. The corresponding total ionic current (C) and its decomposition into individual current components (D–I) are shown.
Figure 2
Digital twins of human induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs) from one simple voltage-clamp recording.
A large population of synthetic iPSC-CMs (left) is generated by introducing variation to 52 biophysical parameters governing key ionic currents in the baseline model: IKr, ICaL, INa, IKs, IK1, and If (highlighted with red asterisks in the schematic on the right). A computationally optimized voltage-clamp protocol (black trace, left middle) is applied to generate a distinct whole-cell current (ITotal, red trace), enabling cell-wide excitation of key ion channels. The simulated whole-cell currents ITotal from large synthetic datasets serve as inputs to a fully connected neural network trained to map raw current responses to the 52 underlying model parameters. The deep learning model is trained to predict optimized parameter values by inferring gating kinetics and maximal conductance for each ionic species. An example formulation for the fast sodium current (INa) is shown, with inferred parameters (x₁–x₅) contributing to gating and conductance (right).
Figure 3
Deep learning guided optimization of a voltage clamp protocol.
Each iteration began with a −100 mV holding potential for 250 ms, followed by sequential testing potentials from −120 to +50 mV in 10 mV increments. A total of 200,000 synthetic samples were generated per training cycle. The optimal testing potential, identified by the lowest mean squared error (MSE) from the deep learning model, was then applied for 250 ms. This optimization cycle repeated every 7000 ms. At 6000 ms, the potential was transiently stepped to −120 mV for 250 ms before resuming the next testing potential sequence. The schematic illustrates the iterative loop of model evaluation, MSE-based selection, and protocol updating, leading to the optimized composite voltage.
Figure 4
Massive synthetic data to train and test a deep learning algorithm for ion channel parameter estimation.
(A) A deep learning-derived optimized voltage-clamp protocol (left) was designed to activate a broad set of ionic currents in induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs) by applying dynamic membrane potential steps (black trace), producing distinctive whole-cell current responses (ITotal, red trace). The inset highlights fine-scale current kinetics captured during the protocol. These ITotal serve as network inputs for parameter inference. (B) Prediction accuracy for individual model parameters was evaluated using training datasets of 1000, 10,000, and 200,000 synthetic cells (left to right), generated with a ±20% parameter perturbation range. For the smallest dataset, the test error exhibited an asymmetric U-shaped curve across training epochs, indicating limited generalizability. As the dataset size increased, training and test errors converged, with median mean absolute errors (MAE) of 0.041, 0.038, and 0.020 for the three dataset sizes, respectively. Bottom panels show MAE distributions across parameters, demonstrating progressively narrower error ranges as training datasets grow. (C) Action potentials (APs) (Vm), intracellular calcium transients (Cai), total ionic current (ITotal), and six major individual ionic currents (IKr, ICaL, IKs, IK1, INa, If) were simulated from the predicted parameters of a single test cell using the deep learning network trained on 200,000 samples. Blue traces represent the original simulated data (input), and red traces show the model outputs. The close overlap confirms faithful reproduction of cell-specific electrophysiological behavior. See Appendix 1—figure 1 for a detailed comparison of the corresponding parameter values.
Figure 5
Digital twin generation and predictive modeling from real cells in induced pluripotent stem cell-derived cardiomyocyte (iPSC-CM) experimental recordings.
(A, B, top) Whole-cell currents from two live iPSC-CMs in response to the optimized voltage-clamp protocol (Figure 3) were used as input to the trained deep learning network. Insets show expanded views of the responses. (A, B, bottom) Ten simulated action potentials (APs) from a synthetic population of 1,100,000 iPSC-CMs at room temperature were generated by introducing ±40% random variation to 52 biophysical model parameters from baseline, governing six major ionic currents: (IKr, ICaL, IKs, IK1, INa, If). Colored traces represent exemplar simulated cells from training data; overlaid black traces are experimentally recorded APs from two representative iPSC-CMs of the human iPSC cell line iPS-6-9-9T.B. (C, D) Digital twin models of the same experimental iPSC-CMs shown in panels A and B. Digital twins were created by extracting all 52 model parameters from the experimental whole-cell current using the deep learning inference pipeline. These parameters were used to instantiate cell-specific computational models, and AP simulations (red traces) were generated. The close overlay between the experimental traces (black) and digital twin predictions (red) demonstrates the success of the framework to accurately derive cell-specific digital twins from real cells.
Figure 6
Cell-to-cell variability drives population-level responses to drug application in large synthetic induced pluripotent stem cell-derived cardiomyocyte (iPSC-CM) digital twins.
(A) iPSC-CM model Cell 1 (corresponding to Figure 5A). (B) iPSC-CM model Cell 2 (corresponding to Figure 5B). In both panels, the top traces show control simulations at physiological temperature (37 °C). The middle row shows responses in the presence of E-4031 (50 nM). EADs occurred in Cell 1 (red) at 50 nM, but not in Cell 2 (blue). (C) We applied ±20% perturbations to all parameters governing six key ionic currents (IK1, IKr, IKs, ICaL, INa, If) in Cell 1 (orange) and Cell 2 (cyan) to generate a population of virtual cells (n=4000), capturing the full spectrum of cell variability within a cell line. Overlaid membrane potential traces (black) show APs from Cell 1 and Cell 2. The population average action potential duration at 90% repolarization (APD90) was 403±47 ms. (D) Incidence of EADs (%) in the virtual population as a function of E-4031 concentration.
Appendix 1—figure 1
Comparison of model parameter values before and after perturbation.
Each parameter (see Appendix 1—table 1) is represented by two markers: open circles denote baseline values and filled circles denote updated values. Parameters are grouped by ionic current (IK1, IKr, IKs, ICaL, INa, If), with colors indicating group membership. Within each group, parameters are ordered by the transformed value of the updated condition. Values are displayed on a signed logarithmic scale (sign(x)·log₁₀(1+|x|)) to accommodate both positive and negative values across a wide dynamic range. The vertical dashed line indicates zero. Horizontal dotted lines separate parameter groups.
Tables
Appendix 1—table 1
Definitions and correspondence of model parameters (P1–P52) with the variables used in the mathematical equations below.
| IK1 | IKr | IKs | ICaL | INa | If | ||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| P1 | GK1 | P7 | GKr | P16 | GKs | P22 | pCaL | P33 | GNa | P47 | Gf |
| P2 | xK11 | P8 | Xr1_1 | P17 | ks1 | P23 | d1 | P34 | m1 | P48 | xF1 |
| P3 | XK12 | P9 | Xr1_2 | P18 | ks2 | P24 | d2 | P35 | m2 | P49 | xF2 |
| P4 | XK13 | P10 | Xr1_5 | P19 | ks5 | P25 | d5 | P36 | m5 | P50 | xF5 |
| P5 | XK14 | P11 | Xr1_6 | P20 | ks6 | P26 | d6 | P37 | m6 | P51 | xF6 |
| P6 | XK15 | P12 | Xr2_1 | P21 | ks_const | P27 | f1 | P38 | h1 | P52 | xFconst |
| P13 | Xr2_2 | P28 | f2 | P39 | h2 | ||||||
| P14 | Xr2_5 | P29 | f5 | P40 | h5 | ||||||
| P15 | Xr2_6 | P30 | f6 | P41 | h6 | ||||||
| P31 | d_const | P42 | j1 | ||||||||
| P32 | f_const | P43 | j2 | ||||||||
| P44 | m_const | ||||||||||
| P45 | h_const | ||||||||||
| P46 | j_const | ||||||||||
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Large-scale synthetic data enable digital twins of human excitable cells
eLife 15:RP110013.
https://doi.org/10.7554/eLife.110013.3
