Implicit methods for modeling gene regulatory networks

Advancements in high-throughput technologies to measure increasingly complex biological phenomena at the genomic level are rapidly changing the face of biological research from single-gene single-protein experimental approach to studying the behaviour of a gene in the context of the entire genome (and proteome). This shift in research methodologies has resulted in a new field of network biology that deals with modeling cellular behaviour in terms of network structures that represent the influence of different biological entities such as genes, proteins and metabolites on each other. These different biological entities interact with each other giving rise to a dynamical system. Even though there exists a mature field of dynamical systems theory to model such network structures, some technical challenges that are unique to biology such as the inability to measure precise kinetic information on gene-gene or gene-protein interactions and the need to model large networks comprising of thousands of nodes have renewed interest in developing new computational techniques for modeling these complex biological systems. In this thesis, I introduce a framework for modeling such regulatory networks in biology based on Boolean algebra and finite-state machines that are reminiscent of the approach used for digital circuit synthesis and simulations in the field of very-large-scale integration (VLSI). The proposed formalism enables a common mathematical framework to develop computational techniques for modeling different aspects of the regulatory networks such as steady state behaviour, stochasticity and gene perturbation experiments. Further, the proposed algorithms have been implemented under the modeling toolbox "genYsis" using implicit representation techniques based on reduced ordered binary decision diagrams (ROBDDs) and algebraic decision diagrams (ADDs) enabling the modeling of large regulatory networks.