  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.
