Mathematical Models for Understanding Dynamic Cellular Systems

Abstract

Cellular processes, such as fate decisions and mitotic divisions, are dynamic. Complex behaviors emerge from networks of interactions among numerous components: time-varying extracellular signals induce expression of specific genes, and periodic changes in intracellular molecule concentrations coordinate mitotic entry and exit. Quantitative understanding of these processes requires mathematical models. Models can make predictions about system dynamics in conditions that are difficult to probe experimentally, explain how systems-level behaviors emerge from a network of interactions, and convert observed data into constraints on future behaviors. This thesis uses mathematical modeling in each of these ways to learn about various dynamical biological phenomena. In the first chapter, models are used to estimate time-varying signals controlling meiosis that are difficult to measure experimentally. In the second, a simple model of the embryonic cell cycle is used to understand how robust oscillations arise in that system. And in the third and ongoing chapter, a model is used to explore how much we can expect learn about a biochemical mechanism from planned experiments.