Mathematical modeling of biological systems can be useful to reveal new insights into biological observations. Here we apply mathematical modeling to study the underlying molecular networks driving observed behaviors of two systems. First, we apply systems biology and dynamic systems theory techniques to reveal new insights into the process of hematopoiesis. More specifically, we search the literature to deduce the underlying molecular mechanism that drives cell fate determination in granulocyte-monocyte progenitor (GMP) cells that are exposed to various cytokines. By converting this molecular mechanism into a set of ordinary differential equations (ODEs), we acquired new insights into the behavior of differentiating GMP cells. Next, we explore the cell cycle of the model prokaryotic organism, Caulobacter crescentus. Caulobacter is a uniquely successful oligotrophic bacterium, found abundantly in freshwater systems. While it is not a pathogenic species, Caulobacter is extremely well studied due to its distinguishable asymmetrical morphology and the ability to synchronize populations by cell cycle stage. We built a detailed mathematical model of the molecular mechanism driving the cell cycle. This research suggests a previously unknown role for the unknown form of the master regulator, CtrA, in regulating the G1-S transition. Furthermore, we incorporate a nutrient signaling model into the cell cycle model to investigate how Caulobacter responds to nutrient deprivation. We find that regulation of DivK phosphorylation is an essential component of the nutrient signaling pathway and demonstrate how starvation signals work together in synergy to manifest in observed cell cycle response. / Doctor of Philosophy / Every cell in the human body has the same DNA, yet there are cells of all kinds with different jobs, appearances and behaviors. This simple concept is a consequence of complex regulatory systems within cells that dictate what genes are expressed and when. This dissertation breaks down the molecular mechanisms that regulate gene expression in cells and how these mechanisms result in the interesting behaviors and morphologies that have been observed experimentally. By deriving mathematical equations to describe the molecular mechanisms, we simulate how cell behavior might change under different conditions to make novel discoveries. More specifically, we utilize these techniques to study the freshwater bacterium, Caulobacter crescentus, and human cells of the white blood cell lineage. We utilize our models to identify previously unknown aspects of the molecular mechanisms, develop explanations for mysterious cell behaviors and provide interesting predictions that have not been explored experimentally.