During the recent years, there has been an increasing interest among both biologists and mathematicians to model and understand gene regulatory mechanisms that drive cell differentiation processes. Mathematical modeling of these processes is often based on the assumption of homogeneous cell population. However, in many applications the cell populations of interest can be heterogeneous. For example, CD4+ T cell populations that are studied in this thesis may consist of many distinct T helper (Th) cell subtypes. Consequently, cell populations in cell differentiation studies are inevitably heterogeneous.
In this thesis, we develop a new modeling approach that takes the possibility of a heterogeneous population into account and apply this approach to study the Th17 cell differentiation. More specifically, we design ordinary differential equation (ODE) models that take the heterogeneity into account by describing approximative subpopulations that evolve in parallel within a population and have cell type specific regulatory mechanisms and dynamics. In our application, we allow the cell population to be split into two subpopulations, an activated T helper (Th0) cell subpopulation and an actively differentiating Th17 cell subpopulation. Both Th0 and Th17 cell dynamics share the same rate parameters to describe the common reaction mechanisms within the subtypes. Three models, homogeneous population (M1), replicate-independent heterogeneous population (M2) and replicate-dependent heterogeneous population (M3), are constructed.
In order to infer Th17 cell differentiation dynamics and to detect possible heterogeneity during differentiation in a data-driven manner, we combine mathematical modeling with RNA sequencing (RNA-Seq) data using statistical modeling. To carry out posterior analysis, we use Bayesian inference with population-based Markov chain Monte Carlo (popMCMC) sampling method. Our results show strong evidence for the replicate-dependent heterogeneous population model (M3) evolving in Th17 lineage polarizing condition. In addition, the model makes it possible to predict the resulting molecular dynamics.
