The Structure and Dynamics of Gene Regulation Networks
  The structure and dynamics of a typical biological system are complex due to strong and inhomogeneous interactions between its constituents. The investigation of such systems with classical mathematical tools, such as differential equations for their dynamics, is not always suitable. The graph theoretical models may serve as a rough but powerful tool in such cases. In this thesis, I first consider the network modeling for the representation of the biological systems. Both the topological and dynamical investigation tools are developed and applied to the various model networks. In particular, the attractor features' scaling with system size and distributions are explored for model networks. Moreover, the theoretical robustness expressions are discussed and computational studies are done for confirmation. The main biological research in this thesis is to investigate the transcriptional regulation of gene expression with synchronously and deterministically updated Boolean network models. I explore the attractor structure and the robustness of the known interaction network of the yeast, Saccharomyces Cerevisiae and compare with the model networks. Furthermore, I discuss a recent model claiming a possible root to the topology of the yeast's gene regulation network and investigate this model dynamically. The thesis also included another study which investigates a relation between folding kinetics with a new network representation, namely, the incompatibility network of a protein's native structure. I showed that the conventional topological aspects of these networks are not statistically correlated with the phi-values, for the limited data that is available. 
Murat Tu\u{g}rul