Cell-specific models of hiPSC-CMs developed by the gradient-based parameter optimization method fitting two different action potential waveforms

Abstract

Parameter optimization (PO) methods to determine the ionic current composition of experimental cardiac action potential (AP) waveform have been developed using a computer model of cardiac membrane excitation. However, it was suggested that fitting a single AP record in the PO method was not always successful in providing a unique answer because of a shortage of information. We found that the PO method worked perfectly if the PO method was applied to a pair of a control AP and a model output AP in which a single ionic current out of six current species, such as I_Kr, I_CaL, I_Na, I_Ks, I_Kur or I_bNSC was partially blocked in silico. When the target was replaced by a pair of experimental control and I_Kr-blocked records of APs generated spontaneously in human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs), the simultaneous fitting of the two waveforms by the PO method was hampered to some extent by the irregular slow fluctuations in the V_m recording and/or sporadic alteration in AP configurations in the hiPSC-CMs. This technical problem was largely removed by selecting stable segments of the records for the PO method. Moreover, the PO method was made fail-proof by running iteratively in identifying the optimized parameter set to reconstruct both the control and the I_Kr-blocked AP waveforms. In the lead potential analysis, the quantitative ionic mechanisms deduced from the optimized parameter set were totally consistent with the qualitative view of ionic mechanisms of AP so far described in physiological literature.

Figure 1

Convergence of I_xsf (BP) as the MSE magnitude was decreased by the simultaneous two-waveform fitting in the MM mode multi-run test. The BPs were plotted in the coordinate of log(MSE) (ordinate) vs I_xsf (abscissa) during the PO process by the PS method. In each line of graphs, I_Krsf, I_Nasf, I_CaLsf, I_Kssf, and I_bNSCsf log(MSE) were plotted. In the case of the blocked current, the I_xsf was normalized in reference to the blocked level.

Figure 2

The recovery of the AP configuration from the artificial modification of AP by the PO method. The red trace was the target AP, which was generated by the intact baseline model, while the black trace was the model output generated at the end of the PO method as the result. The violet horizontal lines indicate three ranges of AP to weight (6, 1, and 0.3 for each step, independent from the ordinate scale) in calculating the weighted sum of MSE. The fitting to the control trace in (A) was obtained by the simultaneous two-AP-waveform fitting using the 60% I_Kr block. Since the fittings of the control AP in cases of any other I_x block were quite similar to that illustrated in (A), the respective control record for each I_x block was not demonstrated individually. Note that two different percentages of blockage (30% and 60%) were specifically tested for I_Kr.

Figure 3

Continuous recording of the spontaneous AP generation in hiPSC-CM during the I_Kr block by perfusing E-4031. (A–C) Shows three examples of chart recordings of the AP waveform. The red traces indicate the single AP waveforms used for the two-waveform fitting of the PO method, which will be described in the next chapter. (D) Shows time courses of I_xsf of I_Kr (light blue), I_CaL (orange), I_Na (steel blue), I_Kur (yellow) and I_bNSC (gray) obtained by the conventional single waveform fitting of the PS method applied to TC12. See the text for a detailed explanation.

Figure 4

Results of the simultaneous fitting of two AP waveforms in the EM mode of the PO method. The data in three hiPSC-CMs (TC11, TC12, and TC13) were examined for the pair of control and the I_Kr-blocked AP waveforms; the pair of c and b1, and the pair of c and b2 indicated in Fig. 3. In all panels the control APs (red) were superimposed by the model output APs (black). The results of the multi-run test are shown in the right half of figure.

Figure 5

Comparison of the I_xsfs other than I_Krsf examined in the EM test. The results of the two-waveform fitting using the leftmost and middle red traces shown in Fig. 3 are shown in the blue bars, and the results by using the leftmost and rightmost red traces shown in Fig. 3 are shown in the green bars. Note that the blue bars were normalized to 1.0 to compare with the green bars. See the text for the explanation.

Figure 6

The patterns of the correlations between different pairs of I_xsfs were compared among three different POs. The correlation of all 15 pairs of I_xsfs using the top 20 results obtained in the multi-run PO method for TC12 by using the leftmost and middle red traces shown in Fig. 3C (AB), by using the leftmost red trace only (A), and by using the middle red trace only (B) are shown with the lines of different thickness. The thicker lines indicate R² higher than 0.8, 0.6 and 0.4. See text for more details.

Figure 7

The profile of the current flow underlying the AP waveform of the cell-specific model of TC12 optimized by the PS method. The upper row (A) indicates V_m (black) and V_L (red). A1 indicates the control condition (c in Fig. 3C), and A2, A3 indicate the record obtained at two different degrees of the I_Kr block (b1 and b2 in Fig. 3C). The lower rows (B) and (C) indicate outward and inward I_m, respectively. The individual I_m are depicted in different colors. The time scales indicated at the bottom are applied to both V_m and I_m panels. The yellow colors are used to highlight the mechanisms mainly for both the foot and plateau phases of AP. The peak of inward I_CaL is far beyond the graphic display.

Figure 8

The profile of V_L and dV_L/dt elements of the cell-specific model of TC12 revealed by the V_L analysis. The upper row (A) indicates V_L elements. A1 indicates the control condition (c in Fig. 3C), and A2, A3 indicate the record obtained at two different degrees of the I_Kr block. The lower rows (B) and (C) indicate dV_L/dt elements for outward and inward currents, respectively. The individual V_L and dV_L/dt elements are depicted in different colors. The time scales indicated at the bottom are applied to both V_L and dV_L/dt records. The yellow colors are used to highlight the mechanisms underlying both the foot and plateau phases of AP. See the text for more explanation.