Caulobacter crescentus goes through a classic dimorphic cell division cycle to adapt to the stringent environment and reduce intraspecific competition. Caulobacter mother cell gives rise to two progenies with distinct morphology - a motile swarmer cell equipped with a flagellum and a sessile stalked cell equipped with a stalk. Because of the nature of dimorphic lifestyle, Caulobacter becomes a model bacterium to study the cell differentiation, signalling transduction, stress response, and asymmetry development of prokaryotes. The dimorphic cell cycle of Caulobacter is driven by the elaborate spatiotemporal organization of regulatory molecules through regulations of synthesis, degradation, phosphorelay, and localization. There is a wealth of experimental observations about gene/protein interactions and localizations accumulated in recent decades, while several mathematical models have been proposed to study the cell cycle progression in Caulobacter. However, the specific control mechanisms of stress response and spatial asymmetry establishment are yet clearly elucidated, while these mechanisms are of fundamental importance to understanding the bacterial survival strategy and developing the microbial industry. Here we utilize mathematical modeling to study the regulatory network of cell cycle control in C. crescentus, focusing on the stress response and asymmetry development. First, we investigate the starvation response of Caulobacter through the connection of phosphotransferase systems (PTS) and guanine nucleotide-based second messenger system. We have developed a mathematical model to capture the temporal dynamics of vital regulatory second messengers, c-di-GMP (cdG) and guanosine pentaphosphate or tetraphosphate (pppGpp or ppGpp), under normal and stressful conditions. This research suggests that the RelA-SpoT homolog enzymes have the potential to effectively influence the cell cycle in response to nutrition changes by regulating cdG and (p)ppGpp levels. We further integrate the second messenger network into a temporal cell cycle model to investigate molecular mechanisms underlying responses of Caulobacter to nutrition starvation. Our model suggests that the cdG-relevant starvation signal is essential but not sufficient to robustly arrest the cell cycle of Caulobacter. We also demonstrate that there may be unknown pathway(s) reducing CtrA under starvation conditions, which results in delayed cytokinesis in starved stalked cells. The cell cycle development of Caulobacter is determined by the periodical activation and deactivation of the master regulator CtrA. cdG is an essential component of the ClpXP pro- tease complex, which is specifically responsible for the degradation of CtrA. We propose a mathematical model for the hierarchical assembly of ClpXP complexes, together with modeling DNA replication, transcription, and protein interactions, to characterize the Caulobacter cell cycle. Our model suggests that the ClpXP-based proteolysis system contributes to the timing and robustness of the cell cycle progression. Furthermore, we construct a spatiotemporal model with Turing-pattern mechanism to study the morphogenesis and asymmetry establishment during the cell cycle of Caulobacter. We apply reaction-diffusion equations to capture the spatial dynamics of scaffolding proteins PodJ, PopZ, and SpmX, which organize two distinct poles of Caulobacter. The spatial regulations influence the activity and distribution of key cell cycle regulators, governing the dimorphic lifestyle of Caulobacter. Our model captures major spatiotemporal experimental observations of wild-type and mutant cells. It provides predictions of novel mutant strains and explains the spatial regulatory mechanisms of bacterial cell cycle progression. / Doctor of Philosophy / Cell is the basic unit of life that undergoes a process called 'cell cycle' consisting of DNA replication and cell division to exhibit various functions, abilities, and behaviors. The cell cycle is well organized by complex regulations in time and space that determine when and where changes take place. The regulations behind cell cycle development play important roles for living organisms but are not fully understood. In this dissertation, we utilize mathematical models and focus on a model bacterium, Caulobacter crescentus, to capture characteristics of cell cycle and study the underlying regulations. Caulobacter is widely distributed in freshwater, including environments with poor nutrients. It divides asymmetrically, generating a pair of daughter cells with different appearances and replicative potentials. Therefore, Caulobacter population has the flexibility to save energy by halting DNA replication and to reduce the competition with siblings by settling into different places. We utilize the nature of the asymmetrical division of Caulobacter to quantitatively investigate the control mechanisms of cell cycle development, including how cells detect and respond to external cues and develop different organelles at specific times and locations.

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.

Mathematical modeling has become increasingly popular as a tool to study regulatory interactions within gene-protein networks. From the modeler's perspective, two challenges arise in the process of building a mathematical model. First, the same regulatory network can be translated into different types of models at different levels of detail, and the modeler must choose an appropriate level to describe the network. Second, realistic regulatory networks are complicated due to the large number of biochemical species and interactions that govern any physiological process. Constructing and validating a realistic mathematical model of such a network can be a difficult and lengthy task. To confront the first challenge, we develop a new modeling approach that classifies components in the networks into three classes of variables, which are described by different rate laws. These three classes serve as "building blocks" that can be connected to build a complex regulatory network. We show that our approach combines the best features of different types of models, and we demonstrate its utility by applying it to the budding yeast cell cycle. To confront the second challenge, modelers have developed rule-based modeling as a framework to build complex mathematical models. In this approach, the modeler describes a set of rules that instructs the computer to automatically generate all possible chemical reactions in the network. Building a mathematical model using rule-based modeling is not only less time-consuming and error-prone, but also allows modelers to account comprehensively for many different mechanistic details of a molecular regulatory system. We demonstrate the potential of rule-based modeling by applying it to the generation of circadian rhythms in cyanobacteria. / Ph. D.

The life cycle of Caulobacter crescentus is of interest because of the asymmetric nature of cell division that gives rise to progeny that have distinct morphology and function. One daughter called the stalked cell is sessile and capable of DNA replication, while the second daughter called the swarmer cell is motile but quiescent. Advances in microscopy combined with molecular biology techniques have revealed that macromolecules are localized in a non-homogeneous fashion in the cell cytoplasm, and that dynamic localization of proteins is critical for cell cycle progression and asymmetry. However, the molecular-level mechanisms that govern protein localization, and enable the cell to exploit subcellular localization towards orchestrating an asymmetric life cycle remain obscure. There are also instances of researchers using intuitive reasoning to develop very different verbal explanations of the same biological process. To provide a complementary view of the molecular mechanism controlling the asymmetric division cycle of Caulobacter, we have developed a mathematical model of the cell cycle regulatory network. Our reaction-diffusion models provide additional insight into specific mechanism regulating different aspects of the cell cycle. We describe a molecular mechanism by which the bifunctional histidine kinase PleC exhibits bistable transitions between phosphatase and kinase forms. We demonstrate that the kinase form of PleC is crucial for both swarmer-to-stalked cell morphogenesis, and for replicative asymmetry in the predivisional cell. We propose that localization of the scaffolding protein PopZ can be explained by a Turing-type mechanism. Finally, we discuss a preliminary model of ParA- dependent chromosome segregation. Our model simulations are in agreement with experimentally observed protein distributions in wild-type and mutant cells. In addition to predicting novel mutants that can be tested in the laboratory, we use our models to reconcile competing hypotheses and provide a unified view of the regulatory mechanisms that direct the Caulobacter cell cycle. / Ph. D.