Mathematical modeling of biological dynamics

This dissertation unravels intricate biological dynamics in three distinct biological systems as the following. These studies combine mathematical models with experimental data to enhance our understanding of these complex processes.

1. Bipolar Spindle Assembly: Mitosis relies on the formation of a bipolar mitotic spindle, which ensures an even distribution of duplicated chromosomes to daughter cells. We address the issue of how the spindle can robustly recover bipolarity from the irregular forms caused by centrosome defects/perturbations. By developing a biophysical model based on experimental data, we uncover the mechanisms that guide the separation and/or clustering of centrosomes. Our model identifies key biophysical factors that play a critical role in achieving robust spindle bipolarization, when centrosomes initially organize a monopolar or multipolar spindle. These factors encompass force fluctuations between centrosomes, balance between repulsive and attractive inter-centrosomal forces, centrosome exclusion from the cell center, proper cell size and geometry, and limitation of the centrosome number.
2. Chromosome Oscillation: During mitotic metaphase, chromosomes align at the spindle equator in preparation for segregation, and form the metaphase plate. However, these chromosomes are not static; they exhibit continuous oscillations around the spindle equator. Notably, either increasing or decreasing centromeric stiffness in PtK1 cells can lead to prolonged metaphase chromosome oscillations. To understand this biphasic relationship, we employ a force-balance model to reveal how oscillation arises in the spindle, and how the amplitude and period of chromosome oscillations depend on the biological properties of spindle components, including centromeric stiffness.
3. Pattern Formation in Bacterial-Phage Systems: The coexistence of bacteriophages (phages) and their host bacteria is essential for maintaining microbial communities. In resource-limited environments, mobile bacteria actively move toward nutrient-rich areas, while phages, lacking mobility, infect these motile bacterial hosts and disperse spatially through them. We utilize a combination of experimental methods and mathematical modeling to explore the coexistence and co-propagation of lytic phages and their mobile host bacteria. Our mathematical model highlights the role of local nutrient depletion in shaping a sector-shaped lysis pattern in the 2D phage-bacteria system. Our model further shows that this pattern, characterized by straight radial boundaries, is a distinctive indicator of extended coexistence and co-propagation of bacteria and phages. Such patterns rely on a delicate balance among the intrinsic biological characteristics of phages and bacteria, which have likely arisen from the coevolution of cognate pairs of phages and bacteria.