Dynamic and equilibrium modeling of metabolic network, protein-DNA and protein-peptide interactions

This thesis explores various aspects of protein interactions in the cell using several theoretical techniques. Three broad topics are covered: steady-state models of metabolic networks, kinetic models of transcription factor-DNA interactions, and equilibrium models of protein-peptide interactions. In the first section of the thesis, we seek to find a topology-based method to characterize the functioning of metabolic networks. We develop a metric, synthetic accessibility, to describe the connectivity of the metabolic network from its inputs to its outputs. We compare this metric to other methods, which depend on both the metabolic network topology and biochemical parameters, and show that synthetic accessibility can predict the viability of metabolic gene knockouts in E. coli and S. cerevisiae as well as the parameter-dependent methods. In the second section, we study the mechanism by which transcription factors search for their binding sites. This process is known to involve a combination of three-dimensional (3D) diffusion through the volume of the DNA and one-dimensional (1D) diffusion along the DNA. The 1D component of the process causes transcription factors that start near their binding sites to find them more quickly. We present simulations and analytical results that describe the distance dependence of the search process. We use this framework to interpret seemingly conflicting experimental results and suggest a kinetic explanation for the observed co-localization of transcription factor genes and their binding sites in prokaryotic genomes. This kinetic explanation is possible because transcription and translation are coupled in bacteria; therefore, proteins are synthesized in the vicinity of their genes. Using bioinformatics, we find evidence for this hypothesis in the organization of prokaryotic genomes. In the final section of the thesis, we study the interactions between a family of peptide recognition modules, the SH2 protein domain family, and their peptides they recognize, which all contain a phosphorylated tyrosine residue. We develop a method for identifying amino acid positions in the domains and peptides that are important for recognition and for constructing an energy potential that describe amino-acid interactions. We use these positions and the energy potential to predict which pairs of SH2 domains and peptides will interact.