Study of Eukaryotic Cellular Process by Mathematical Modeling: Chemotaxis and Mitosis
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Chemotaxis, the directed cell movement in response to external chemical gradients, is a vital biological process. Single cell organisms, such as bacteria and amoebae, rely on chemotaxis for feeding. In multicellular organisms, it plays an important role during embryogenesis, directing cells of the immune system to sites of infection and disease, wound healing, and in cancer metastasis. In eukaryotic cells, a complex signaling system involving over one hundred biochemical components and numerous redundant pathways mediates chemotaxis. Because of the complexity of this system, it has proved to be advantageous to study chemotaxis by isolating the chemotactic response into a set of simpler processes: motility, gradient sensing, and polarization. Research into chemotaxis has also benefited from numerous theoretical and computational treatments that complement experimental studies. Here, we developed a computational framework using a modular view of the chemotactic behavior in Dictyostelium cells. The starting point is a proposed model that suggests that cells rely on firings of an excitable network to generate pseudopods. In the absence of chemoattractant stimuli, these firings can be triggered by stochastic perturbations in the signaling system. However, chemottractants bias the location of the firings by altering the level of the threshold. Here, we carry out tests of this local-excitation, global-inhibition biased excitable network (LEGI-BEN) hypothesis. In particular, we couple the model to a viscoelastic description of the cell and test through simulation how well the model can recreate observed behaviors of chemotactic cells. Based on these simulations and on new experimental findings, we propose several modifications to the existing models. One additional component incorporates a polarity module that endows cell movement with persistence. A second addition is an oscillatory cytoskeletal network that recreates fast oscillations observed in cells. In addition to the research in chemotaxis, this dissertation also reports on the development of a mathematical model describing mitotic matrix formation after nuclear envelope breakdown. Recent reports show that lamin B, a component of the nuclear lamina in interphase, localizes around the spindle and reassembles to form a mitotic matrix. How this process occurs, however, and what effect it has on the mitotic spindle is unclear. Here, we develop a computational model based on a continuum description to represent the abundance and location of the various molecular species involved during mitosis. We use this model to examine the role for the matrix during spindle formation and to test between several hypotheses regarding the formation of the mitotic matrix.