Mathematical modeling of the eukaryotic heat shock response and associated ultrasensitive signaling cascades

All cells, tissues, and organisms experience many stresses over their lifetime. The primary effect of these various stresses is damage to the most basic intracellular machinery, the folded protein. This protein damage drives protein-protein self association into protein aggregates. These protein aggregates are implicated in the onset of a number of neurodegenerative diseases including Alzheimer's, Huntington's, and others. The heat shock response is an evolutionarily conserved pathway for maintaining protein homeostasis under stress. The primary components of the heat shock response are the heat shock proteins (HSPs), which the cell expresses transiently to very high concentrations under stress. The HSPs function by interacting with unfolded or aggregated proteins, sequestering them from causing further damage and helping them back to their native structure.; In this thesis, I present our work on developing mathematical models to analyze the process of protein quality control under stress. Using a mathematical model for the association of HSP70 with unfolded or aggregated substrates, we offer an interpretation for experimental findings of a threshold onset for protein aggregation. Our models propose the hypothesis that the origin of the threshold in protein aggregation is due to the presence of bistability in the system. Our analysis of the model demonstrates several consequences for bistability in protein aggregation, including the potential for irreversible aggregation in neurons with an impaired heat shock mechanism.; Because of the essential role of HSP70 for preventing the formation of protein aggregates, we also developed a mathematical model for the expression and regulation of HSP70 under heat stress. Using sensitivity analysis, we identified key kinetic and thermodynamic parameters for altering the expression of HSP70.; Finally, we developed a model of a prototypical signaling pathway to understand the properties of the types of protein kinases that likely activate HSF1. Specifically, we examined how the dimensionless parameters of signaling cascades interplay to produce cooperative or ultrasensitive responses. Our analysis identified an optimal set of kinase affinities and kinase concentrations for generating a nearly on/off response from a three-cascade signaling pathway. These studies will guide future investigation into the design of signaling cascades in different contexts, including synthetic biochemical switches.