Inversion and computational maturation of drug response using human stem cell derived cardiomyocytes in microphysiological systems

Abstract

While cardiomyocytes differentiated from human induced pluripotent stems cells (hiPSCs) hold great promise for drug screening, the electrophysiological properties of these cells can be variable and immature, producing results that are significantly different from their human adult counterparts. Here, we describe a computational framework to address this limitation, and show how in silico methods, applied to measurements on immature cardiomyocytes, can be used to both identify drug action and to predict its effect in mature cells. Our synthetic and experimental results indicate that optically obtained waveforms of voltage and calcium from microphysiological systems can be inverted into information on drug ion channel blockage, and then, through assuming functional invariance of proteins during maturation, this data can be used to predict drug induced changes in mature ventricular cells. Together, this pipeline of measurements and computational analysis could significantly improve the ability of hiPSC derived cardiomycocytes to predict dangerous drug side effects.

Figure 1

Depiction of in silico modeling and analysis of an MPS system. Optical measurements of calcium and voltage are taken at baseline and in the presence of drug. These waveforms are inverted using a mathematical model of cell dynamics, into a set of parameters that define key ion channel conductances. Changes in this parameter set give information about specific changes in conductances under drug, and this parameter set can then be mapped to a model of mature cell behavior using the assumption of functional invariance of individual channels.

Figure 2

Sensitivity of maximum conductances of the immature base model assessed by the three cost functions defined in (3)–(4) with ε = 0.2. The color intensities correspond to the sum of the cost function upon perturbing the maximum conductance of the given current (or flux) by ±10%.

Figure 3

The cost function (4) with ε = 0.2 for simulated drug data, evaluated with pairwise perturbations of maximum conductances to examine if a unique minimum can be found corresponding to chosen drug effects. Left panels: The effect of Verapamil is simulated by blocking the I_CaL and I_Kr by 50% and 25%, respectively. Right panels: The effect of Cisapride is simulated by blocking the I_Kr by 50%. For both drugs, clear minimums are observed at the specified channel blockages.

Figure 4

Identification of drug effects on M cells based on simulated data of IM cells. Left panel: Results of inversion by minimizing the cost function (4) with ε = 0.2. Middle panel: Action potential (blue) and calcium transient (red) before and after (dotted) the drug is applied. Right panel: Model results after application of the maturation matrix.

Figure 5

The cost function (4) with ε = 0.2 evaluated for pairwise perturbations of the maximum conductances of four major currents for simulated single-channel block of each of the currents. In the upper panel, I_Na is blocked by 50%, and in the next panels, I_CaL, I_Kr and I_K1 are similarly blocked by 50%. Like in Fig. 3, clear minimums are observed at the correct blockages in all four cases.

Figure 6

The cost function (4) with ε = 0.2 evaluated for pairwise perturbations of maximum conductances using measured data from the MPS. Left panels: The effect of a dose of 100 nM of Verapamil is shown; it clearly blocks I_CaL and it also blocks I_Kr. Right panels: The effect of a dose of 10 nM of Cisapride is shown; it clearly blocks I_Kr. The results of the inversion is given in Fig. 7.

Figure 7

Results obtained by applying the inversion procedure to measured MPS data. First column: Results of inversion by minimizing the cost function (4) with ε = 0.2. Second column: Average voltage and calcium traces from MPS measurements. Third column: The AP model of the IM cells. Fourth column: The AP model of the M cells.

Figure 8

Illustration of the assumptions underlying our model of maturation. (A) The immature cell with two types of membrane proteins, with a cytosolic space containing the sarcoplasmic reticulum with associated release and uptake proteins. (B) Maturation is multiplication in the sense that the number of proteins increases at a protein specific rate. (C) A specific protein in the IM cell is the same as in the M cell. (D) A drug affects every single protein in the IM cell in exactly the same manner as for the M cell. (E) Model of the transmembrane potential for IM and M cells, and the relation between these models; and how these models are affected when a drug is applied.

Figure 9

Immature and mature versions of the Paci et al. model and the ten Tusscher et al. (tT) model. The APs of the M cells are shorter and the upstroke velocity of the calcium transient is faster than for the IM case; compare left and right panels.