Phenomenological Models in Biological Physics: Cell Polarity and rDNA Transcription

Abstract

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. The initiation of cell polarity consists of two sequential processes: an external gradient is first sensed and then the resulting signal is amplified by intracellular signaling. It is challenging to determine the role of proteins towards sensing and amplification as these two processes are intertwined. We integrated quantitative single-cell measurements with phenomenological modeling to determine the roles of Wnt ligands and receptors in sensing and amplification in the P cells of Caenorhabditis elegans. By systematically exploring how P cell polarity is altered in Wnt ligand and receptor mutants, we inferred that ligands predominantly affect sensing, whereas receptors are needed for both sensing and amplification. Most eukaryotes contain many tandem repeats of ribosomal RNA genes of which only a subset is transcribed at any given time. Current biochemical methods allow for the determination of the fraction of transcribing repeats (ON) versus nontranscribing repeats (OFF) but do not provide any dynamical information. By using the single molecule transcript counting technique complemented with theoretical modeling, we determine the rate of switching from OFF to ON (activation rate) and the average number of RNA molecules produced during each transcriptional burst (burst size). We explore how these two variables change in mutants and different growth conditions.