Stochastic Modeling and Analysis of Pathway Regulation and Dynamics

To effectively understand and treat complex diseases such as cancer, mathematical and statistical modeling is essential if one wants to represent and characterize the interactions among the different regulatory components that govern the underlying decision making process. Like in any other complex decision making networks, the regulatory power is not evenly distributed among its individual members, but rather concentrated in a few high power "commanders". In biology, such commanders are usually called masters or canalizing genes. Characterizing and detecting such genes are thus highly valuable for the treatment of cancer. Chapter II is devoted to this task, where we present a Bayesian framework to model pathway interactions and then study the behavior of master genes and canalizing genes. We also propose a hypothesis testing procedure to detect a "cut" in pathways, which is useful for discerning drugs' therapeutic effect.

In Chapter III, we shift our focus to the understanding of the mechanisms of action (MOA) of cancer drugs. For a new drug, the correct understanding of its MOA is a key step for its application to cancer treatments. Using the Green Fluorescent Protein technology, researchers have been able to track various reporter genes from the same cell population for an extended period of time. Such dynamic gene expression data forms the basis for drug similarity comparisons. In Chapter III, we design an algorithm that can identify mechanistic similarities in drug responses, which leads to the characterization of their respective MOAs.

Finally, in the course of drug MOA study, we observe that cells in a hypothetical homogeneous population do not respond to drug treatments in a uniform and synchronous way. Instead, each cell makes a large shift in its gene expression level independently and asynchronously from the others. Hence, to systematically study such behavior, we propose a mathematical model that describes the gene expression dynamics for a population of cells after drug treatments. The application of this model to dose response data proviodes us new insights of the dosing effects. Furthermore, the model is capable of generating useful hypotheses for future experimental design.