From ionic to cellular variability in human atrial myocytes: an integrative computational and experimental study

Figures

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  Fig. 1.. Experimental variability in action potential (AP) and current densities cannot be captured with a single in silico model of human atrial electrophysiology, motivating the use of a population-of-models approach. A: AP biomarkers used in this study. APD20, APD50, and APD90, AP duration at 20%, 50%, and 90% repolarization, respectively (in ms); RMP, resting membrane potential (in mV); APA, action potential amplitude (in mV); V, voltage. B–E: outputs of generic Courtemanche, Maleckar, and Grandi models compared with experimental AP traces (B), AP biomarkers (C), and ionic current densities (D and E). In C, outputs of Courtemanche, Maleckar, and Grandi models are represented with a diamond, square, and circle, with ex vivo data plotted as crosses. E: two peaks in L-type Ca2+ current (ICaL) density were observed ex vivo. To capture these, modifications to half-potential of activation (Vact) of the ICaL d-gate were introduced to generic models (see Modifications to the generic models to capture two peaks in ICaL density in the appendix).

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  Fig. 2.. Linear relationship between action potential (AP) duration (APD) at 20% and 50% repolarization (APD20 and APD50) properties at five pacing frequencies ex vivo. Experimental data are shown as crosses, dashed-dotted lines are the least-squares fits to the data (corresponding R2 value given at the top of each plot), and solid black lines represent constraints corresponding to aAPD20 + bupper ≥ APD50 ≥ aAPD20 + blower imposed on APD20 and APD50 properties generated by in silico models. The constant a was obtained from the least-squares fit, whereas blower and bupper were determined from the values of the outermost experimental data points.

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  Fig. 3.. Populations of models with a substantial variability in maximal conductances can yield action potential (AP) and ionic current characteristics overlapping with ex vivo data set even if generic model outputs are far away from experiment. A–C: in silico AP biomarkers at 0.25, 1, and 3 Hz (A), full AP traces (B), and ionic current densities of transient outward K+ current (Ito), ultrarapid K+ current (IKur), inward rectifier (IK1), and L-type Ca2+ current (ICaL) (with peaks at 10 and 20 mV (C) in the Maleckar-based population of n = 1,493 models following calibration with AP biomarker data compared with ex vivo measurements. D–F: analogous plots for the Grandi-based in silico population of n = 554 models. Both in silico populations were generated with Latin hypercube sampling. Throughout, in silico “accepted” models, meaning those models that fulfill experimental AP calibration constraints, are plotted in dark gray; A and D additionally show AP biomarkers of in silico “rejected” models in light gray. Ex vivo data are shown as crosses. RMP, resting membrane potential; APA, AP amplitude; APD20, APD50, and APD90, AP duration at 20%, 50%, and 90% repolarization.

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  Fig. 4.. In silico action potential (AP) biomarkers at 0.25, 1, and 3 Hz (A) and full AP traces in the Courtemanche-based population of n = 1,553 models (B) following calibration with AP biomarker data compared with ex vivo measurements. In silico population was generated with Latin hypercube sampling. In silico accepted models, i.e., those models that fulfill experimental AP calibration constraints, are plotted in dark gray; A additionally shows AP biomarkers of in silico rejected models in light gray. Ex vivo data are shown as crosses.

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  Fig. 5.. In silico action potential (AP) biomarkers at 0.25, 1, and 3 Hz (A), full AP traces (B), and ionic current densities (C) of transient outward K+ current (Ito), atrial-specific ultrarapid K+ current (IKur), inward rectifier K+ current (IK1), and L-type Ca2+ current (ICaL) (with peaks at 10 and 20 mV) in the Maleckar-based population of n = 754 models following calibration with AP biomarker data compared with ex vivo measurements. The in silico population was generated with sequential Monte Carlo. In silico accepted models, i.e., those models that fulfill experimental AP calibration constraints, are plotted in gray dots, whereas ex vivo data are shown as crosses.

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  Fig. 6.. In silico action potential (AP) biomarkers at 0.25, 1, and 3 Hz (A), full AP traces (B), and ionic current densities (C) of transient outward K+ current (Ito), atrial-specific ultrarapid K+ current (IKur), inward rectifier K+ current (IK1), and L-type Ca2+ current (ICaL) (with peaks at 10 and 20 mV) in the Grandi-based population of n = 479 models following calibration with AP biomarker data compared with ex vivo measurements. In silico population was generated with sequential Monte Carlo. In silico accepted models, i.e., those models that fulfill experimental AP calibration constraints, are plotted in light gray, whereas ex vivo data are shown as crosses.

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  Fig. 7.. In silico action potential (AP) biomarkers at 0.25, 1, and 3 Hz (A) and full AP traces (B) in the Courtemanche-based population of n = 819 models following calibration with AP biomarker data compared with ex vivo measurements. In silico population was generated with sequential Monte Carlo. In silico accepted models, i.e., those models that fulfill experimental AP calibration constraints, are plotted as light gray, whereas ex vivo data are shown as crosses.

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  Fig. 8.. Calibration with action potential (AP) data constrains currents affecting upstroke and resting potential, but current redundancy during repolarization allows wide ranges of variability in currents impacting AP duration (APD). A and B: selected pairwise plots of maximal conductances (A) and partial correlation coefficients (PCCs) between AP biomarkers and maximal conductances (B), computed at 0.25, 1, and 3 Hz, for the Maleckar-based population. C and D: analogous results for the Grandi-based population. In B and D, positive (+) and negative (−) correlations are highlighted.

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  Fig. 9.. Further calibration with ionic currents active during repolarization constrains current density but not cellular phenotypic variability in action potential (AP). A and B: pairwise scatter plots of maximal conductances (A) and AP biomarkers (B) in the populations calibrated with AP, AP + L-type Ca2+ current (ICaL), and AP + ICaL + inward rectifier K+ current (IK1) ex vivo data in the Maleckar-based in silico population, plotted in light gray, dark gray, and black, respectively. C and D: AP traces (C) and ionic current densities (D) in the Maleckar-based population of n = 102 models calibrated with AP and voltage-clamp recordings, shown in dark gray, compared with ex vivo data in light gray.

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  Fig. 10.. Further calibration with ionic currents active during repolarization constrains current density but not cellular phenotypic variability in action potential (AP). A and B: pairwise scatterplots of maximal conductances (A) and AP biomarkers (B) in the populations calibrated with AP, AP + L-type Ca2+ current (ICaL), and AP + ICaL + inward rectifier K+ current (IK1) ex vivo data in the Grandi-based in silico population, plotted in light gray, dark gray, and black, respectively. C and D: AP traces (C) and ionic current densities (D) in the Maleckar-based population of n = 228 models calibrated with AP and voltage-clamp recordings, shown in dark gray, compared with ex vivo data in light gray.

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  Fig. 11.. Box plots of maximal current conductances in the Maleckar-based in silico population of models following calibration with AP, AP + ICaL, and AP + ICaL + IK1 data, shown in light gray, dark gray, and black, respectively. Black dots indicate outliers.

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  Fig. 12.. Box plots of maximal current conductances in the Grandi-based in silico population of models following calibration with action potential (AP), AP + L-type Ca2+ current (ICaL), and AP + ICaL + inward rectifier K+ current (IK1) data, shown in light gray, dark gray, and black, respectively. Black dots indicate outliers.