In silico modeling of directed differentiation of induced pluripotent stem cells to definitive endoderm

Differentiation of embryonic stem cells and induced pluripotent stem cells (iPSCs) into endoderm derivatives, including thyroid, thymus, lungs, liver, and pancreas, has broad implications for disease modeling and therapy. We utilize and expand a model development approach previously outlined by the authors to construct a model for the directed differentiation of iPSCs into definitive endoderm (DE). Assuming discrete intermediate stages in the differentiation process with a homogeneous population in each stage, three lineage models with two, three, and four populations and three growth models are constructed. Additionally, three models for error distribution are defined, resulting in a total of 27 models. Experimental data obtained in vitro are used for model calibration, model selection, and final validation. Model selection suggests that no transitory state during differentiation expresses the DE biomarkers CD117 and CD184, a finding corroborated by existing literature. Additionally, space-limited growth models, such as logistic and Gompertz growth, outperform exponential growth. Validation of the inferred model with leave-out data results in prediction errors of 26.4%. Using the inferred model, it is predicted that the optimal differentiation period is between 1.9 and 2.4 days, plating populations closer to 300 000 cells per well result in the highest yield efficiency, and that iPSC differentiation outpaces the DE proliferation as the main driver of the population dynamics. We also demonstrate that the model can predict the effect of growth modulators on cell population dynamics. Our model serves as a valuable tool for optimizing differentiation protocols, providing insights into developmental biology.Author summary: The directed differentiation of induced pluripotent stem cells (iPSCs) into definitive endoderm (DE) represents the first step in deriving many endoderm-derived tissues, such as lung, liver, and pancreas cells. Here, we report a mathematical model of iPSC differentiation into DE, thus providing a tool for optimizing directed differentiation protocols. Biologically informed models are developed using experimental data to capture population dynamics, including proliferation, differentiation, and death. The optimal lineage model and growth model are identified for the differentiation process by performing model selection and validation. Model validation is performed by calculating the normalized root-mean-square error on leave-out data to be 26.4%, which is below the threshold of 30%. Using the validated model, we examined questions related to the optimization of DE induction. Model predictions suggest that the optimal differentiation period is approximately 2 days and that the optimal plating population is 300,000 cells per well. We also conducted an in silico investigation into the effect of supplementation of culture medium with growth modulators on the yield of DEs. We found that this may lead to an increase in DE yield of up to 39% at lower plating populations. These studies showcase the value of mathematical modeling in optimizing cell culture protocols by reducing the need for extensive experimentation in the laboratory. The model also provides insight into the differentiation process, aiding developmental biology and regenerative medicine research.