The mechanisms by which human embryonic stem cells (hESC) differentiate to endodermal lineage have not been extensively studied. Mathematical models can aid in the identification of mechanistic information. In this work we use a population-based modeling approach to understand the mechanism of endoderm induction in hESC, performed experimentally with exposure to Activin A and Activin A supplemented with growth factors (basic fibroblast growth factor (FGF2) and bone morphogenetic protein 4 (BMP4)). The differentiating cell population is analyzed daily for cellular growth, cell death, and expression of the endoderm proteins Sox17 and CXCR4. The stochastic model starts with a population of undifferentiated cells, wherefrom it evolves in time by assigning each cell a propensity to proliferate, die and differentiate using certain user defined rules. Twelve alternate mechanisms which might describe the observed dynamics were simulated, and an ensemble parameter estimation was performed on each mechanism. A comparison of the quality of agreement of experimental data with simulations for several competing mechanisms led to the identification of one which adequately describes the observed dynamics under both induction conditions. The results indicate that hESC commitment to endoderm occurs through an intermediate mesendoderm germ layer which further differentiates into mesoderm and endoderm, and that during induction proliferation of the endoderm germ layer is promoted. Furthermore, our model suggests that CXCR4 is expressed in mesendoderm and endoderm, but is not expressed in mesoderm. Comparison between the two induction conditions indicates that supplementing FGF2 and BMP4 to Activin A enhances the kinetics of differentiation than Activin A alone. This mechanistic information can aid in the derivation of functional, mature cells from their progenitors. While applied to initial endoderm commitment of hESC, the model is general enough to be applicable either to a system of adult stem cells or later stages of ESC differentiation.
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