| Cell division is a complex process that involves carefully orchestrated chemical and mechanical events. Tight regulation is vital during division, since a breakdown in control mechanisms can lead to serious disorders such as cancer. A key step in division is the movement of chromosomes to specific locations in the cell with remarkable precision. In higher eukaryotes, the movement of chromosomes has been well observed over the course of hundreds of years. Yet, the mechanisms underlying chromosome motility and the control of precise chromosome localizations in the cell are poorly understood. More recently, a wealth of experimental data has become available for bacterial division. Despite the long supported theory that bacteria and eukaryotes differ widely when undergoing division, it is emerging that similar mechanisms for motility and cell cycle control might be at play in both cell types. Mathematical modeling is useful in the study of these dynamic cellular environments, where it is difficult to experimentally uncover the mechanisms that drive a multitude of mechanical and chemical events. In this dissertation, we develop various mathematical models that address the question of how dynamic polymers can move large objects such as chromosomes in higher eukaryotes and in bacteria. Then, we develop models that address how chemical and mechanical signals can be coordinated to control the precise localization of a chromosome. The mathematical models proposed here employ stochastic differential equations, ordinary differential equations and partial differential equations. The models are numerically simulated to obtain solutions for various parameter values, but we also use tools from bifurcation theory, asymptotic and perturbation methods for our model analysis. Our mathematical models can not only reproduce the experimental data at hand, but also make predictions about the mechanisms underlying chromosome motility in dividing cells. |
