All high-level living organisms are made of small cell units, containing DNA, RNA, genes, proteins etc. Genes are important components of the cells and it is necessary to understand the inter-gene relations, in order to comprehend, predict and ultimately intervene in the cells’ dynamics. Genetic regulatory networks (GRN) represent the gene interactions that dictate the cell behavior. Translational genomics aims to mathematically model GRNs and one of the main goals is to alter the networks’ behavior away from undesirable phenotypes such as cancer. The mathematical framework that has been often used for modeling GRNs is the probabilistic Boolean network (PBN), which is a collection of constituent Boolean networks with perturbation, BNp. This dissertation uses BNps, to model gene regulatory networks with an intent of designing stationary control policies (CP) for the networks to shift their dynamics toward more desirable states. Markov Chains (MC) are used to represent the PBNs and stochastic control has been employed to find stationary control policies to affect steady-state distribution of the MC. However, as the number of genes increases, it becomes computationally burdensome, or even infeasible, to derive optimal or greedy intervention policies. This dissertation considers the problem of modeling and intervening in large GRNs. To overcome the computational challenges associated with large networks, two approaches are proposed: first, a reduction mapping that deletes genes from the network; and second, a greedy control policy that can be directly designed on large networks. Simulation results show that these methods achieve the goal of controlling large networks by shifting the steady-state distribution of the networks toward more desirable states. Furthermore, a new inference method is used to derive a large 17-gene Boolean network from microarray experiments on gastrointestinal cancer samples. The new algorithm has similarities to a previously developed well-known inference method, which uses seed genes to grow subnetworks, out of a large network; however, it has major differences with that algorithm. Most importantly, the objective of the new algorithm is to infer a network from a seed gene with an intention to derive the Gene Activity Profile toward more desirable phenotypes. The newly introduced reduction mappings approach is used to delete genes from the 17-gene GRN and when the network is small enough, an intervention policy is designed for the reduced network and induced back to the original network. In another experiment, the greedy control policy approach is used to directly design an intervention policy on the large 17-gene network to beneficially change the long-run behavior of the network. Finally, a novel algorithm is developed for selecting only non-isomorphic BNs, while generating synthetic networks, using a method that generates synthetic BNs, with a prescribed set of attractors. The goal of the new method described in this dissertation is to discard isomorphic networks.

The area of systems biology evolved in an attempt to introduce mathematical systems theory principles in biology. Although we believe that all biological processes are essentially chemical reactions, describing those using precise mathematical rules is not easy, primarily due to the complexity and enormity of biological systems. Here we introduce a formal approach for modeling biological dynamical relationships and diseases such as cancer. The immediate motivation behind this research is the urgency to find a practicable cure of cancer, the emperor of all maladies. Unlike other deadly endemic diseases such as plague, dengue and AIDS, cancer is characteristically heterogenic and hence requires a closer look into the genesis of the disease. The actual cause of cancer lies within our physiology. The process of cell division holds the clue to unravel the mysteries surrounding this disease. In normal scenario, all control mechanisms work in tandem and cell divides only when the division is required, for instance, to heal a wound platelet derived growth factor triggers cell division. The control mechanism is tightly regulated by several biochemical interactions commonly known as signal transduction pathways. However, from mathematical point of view, these pathways are marginal in nature and unable to cope with the multi-variability of a heterogenic disease like cancer. The present research is possibly one first attempt towards unraveling the mysteries surrounding the dynamics of a proliferating cell. A novel yet simple methodology is developed to bring all the marginal knowledge of the signaling pathways together to form the simplest mathematical abstract known as the Boolean Network. The malfunctioning in the cell by genetic mutations is formally modeled as stuck-at faults in the underlying Network. Finally a mathematical methodology is discovered to optimally find out the possible best combination drug therapy which can drive the cell from an undesirable condition of proliferation to a desirable condition of quiescence or apoptosis. Although, the complete biological validation was beyond the scope of the current research, the process of in-vitro validation has been already initiated by our collaborators. Once validated, this research will lead to a bright future in the field on personalized cancer therapy.