Cells generally manage to maintain stable phenotypes in the face of widely varying environmental conditions. This fact is particularly surprising since the key step of gene expression is fundamentally a stochastic process. Many hypotheses have been suggested to explain this robustness. First, the special topology of gene regulatory networks (GRNs) seems to be an important factor as they possess feedforward loops and certain other topological features much more frequently than expected. Second, genes often regulate each other in a canalizing fashion: there exists a dominance order amidst the regulators of a gene, which in silico leads to very robust phenotypes. Lastly, an entirely novel gene regulatory mechanism, discovered and studied during the last two decades, which is believed to play an important role in cancer, is shedding some light on how canalization may in fact take place as part of a cell’s gene regulatory program. Short segments of single-stranded RNA, so-called microRNAs, which are embedded in several different types of feedforward loops, help smooth out noise and generate canalizing effects in gene regulation by overriding the effect of certain genes on others.

Boolean networks and their multi-state extensions have been successfully used to model GRNs for many years. In this dissertation, GRNs are represented in the time- and statediscrete framework of Stochastic Discrete Dynamical Systems (SDDS), which captures the cell-inherent stochasticity. Each gene has finitely many different concentration levels and its concentration at the next time step is determined by a gene-specific update rule that depends on the current concentration of the gene’s regulators. The update rules in published gene regulatory networks are often nested canalizing functions. In Chapter 2, this class of functions is introduced, generalized and analyzed with respect to its potential to confer robustness. Chapter 3 describes a simulation study, which supports the hypothesis that microRNA-mediated feedforward loops have a stabilizing effect on GRNs. Chapter 4 focuses on the cellular DNA mismatch repair machinery. A first regulatory network for this machinery is introduced, partly validated and analyzed with regard to the role of microRNAs and certain genes in conferring robustness to this particular network. Due to steady exposure to mutations, GRNs have evolved over time into their current form. In Chapter 5, a new framework for modeling the evolution of GRNs is developed and then used to identify topological features that seem to stabilize GRNs on an evolutionary time-scale. Chapter 6 addresses a completely separate project in Bioinformatics. A novel functional enrichment method is developed and compared to various popular methods.

Funding for this work was provided by NSF grant CMMI-0908201 and NSF grant 1062878.