Mathematical Modeling of Multi-Level Behavior of the Embryonic Stem Cell System during Self-Renewal and Differentiation

Embryonic stem cells (ESC) are pluripotent cells derived from the inner cell mass of the blastocyst. These cells have the unique properties of unlimited self-renewal and differentiation capability. ESC therefore hold huge potential for use in therapeutic applications in regenerative medicine. This potential has been demonstrated in vitro by directing differentiation of ESC to various cell types by modulating the soluble and insoluble cues to which the cells are exposed. Despite their great potential, current differentiation methods are still limited in the yield and functionality of the ESC-derived mature phenotype. We hypothesize the lack of mechanistic understanding of the complex differentiation process to be the primary reason behind their restricted success. Mathematical models, coupled to experimental data, can aid in this understanding. While the past several decades have seen advances in the mathematical analysis of biological systems, mathematical approaches to the ESC system have received limited attention. Furthermore, variability of ESC restricts direct application of deterministic approaches towards drawing mechanistic insight.\ud \ud The goal of the current work is to obtain a more thorough mechanistic understanding of the ESC system through mathematical modeling. In ESC, extracellular cues guide single cell behavior in a non-deterministic fashion, giving rise to heterogeneous populations. Therefore, in this work we focus on modeling three levels of the ESC system: intracellular, extracellular, and population. We first developed an optimization framework to identify intracellular gene regulatory interactions from time series data. We show that incorporation of the bootstrapping technique into the formulism allows for accurate prediction of robust interactions from noisy data. A regression approach was then utilized to identify extracellular substrate features influential to cellular behavior. We apply this model to identify fibrin microstructural features which guide differentiation of mESC. Finally, we developed a stochastic model to capture heterogeneous population dynamics of hESC. We demonstrate the usefulness of the model to obtain mechanistic information of cell cycle transition and lineage commitment during differentiation. Through development and utilization of different mathematical approaches to analyze multilevel behavior and variability of ESC self-renewal and differentiation, we demonstrate the applicability of mathematical models in extracting mechanistic information from the ESC system.\u