| Cell divison is one of the most elegant transformations in nature, whereby a mother cell is separated into two identical daughter cells. During mitosis, the genetic material of the cell is separated by an assembled mitotic spindle. This stage is followed by cytokinesis, in which a complex system of forces divides the cell forming two daughter cells. Failure of any of these highly coupled processes can lead to mutant formation that can eventually lead to cancer.;The complexity of processes such as cell division lends itself to the use of mathematical models. High fidelity computational models allow us not only to replicate physiological behavior, but also test system sensitivity and make predictions of new, unobserved behavior. When coupled with high quality biological data, they become a powerful tool for hypothesis testing mitigating the need to perform costly biological experiments.;In this dissertation, we develop computational models and techniques to analyze and quantify the multiple aspects of cell division. Using a multi-agent model, we conduct a systematic study of how an enclosing membrane affects mitotic spindle assembly and suggest a mechanism for how this membrane can help microtubule focusing. Next, we study how coordinated action of multiple biochemical-mediated stresses act on the cell during cytokinesis. A mechanical model of the cell is constructed using the level set method, and relying only on measured biophysical parameters, we simulate cell division under a number of different scenarios. This model identifies individual subsystems within the cell and highlights their relative contributions to cell shape progression during cell division. We develop a series of algorithms for extracting geometrical and dynamical data from biological image data. Finally, we develop a discrete model of contractile structure formation and analyze how biological parameters influence structure topology. This work answers some key questions about the mechanisms involved in cell division, and provides a computational framework on which further experiments and analysis can be conducted. |
