Title: Phenomenological Models in Biological Physics
Description: Mathematical modeling has been important in the study of biology. Two main challenges with modeling biological problems are the lack of quantitative data and the complexity of biological problems. With the invention of new techniques, like single molecule transcript counting, very quantitative gene expression measurements at the level of single transcript in individual cells can now be obtained. Biological systems are very complex, involving many reactions and players with unknown reaction rates. To reduce the complexity, scientists have often proposed simplified phenomenological models that are tractable and capture the main essence of the biological systems. These simplified models allow scientists to describe the behavior of biological systems with a few meaningful parameters. In this thesis, by integrating quantitative single-cell measurements with phenomenological modeling, we study the (1) roles of Wnt ligands and receptors in sensing and amplification in Caenorhabditis elegans' P cells and (2) regulation of rDNA transcription in Saccharomyces cerevisiae.