Prion proteins are responsible for a variety of neurodegenerative diseases inmammals such as Creutzfeldt-Jakob disease in humans and “mad-cow” disease in cattle. While these diseases are fatal to mammals, a host of harmless phenotypes have been associated with prion proteins in S. cerevisiae, making yeast an ideal model organism for prion diseases. Most mathematical approaches to modeling prion dynamics have focused on either the protein dynamics in isolation, absent from a changing cellular environment,or modeling prion dynamics in a population of cells by considering the “average” behavior. However, such models have been unable to recapitulate in vivo properties of yeast prion strains including experimentally observed rates of prion loss and partial loss/colony sectoring phenotypes.
My group develops physiologically relevant mathematical models by considering both the prion aggregates and their yeast host. We then validate our model and infer parameters through carefully designed in vivo experiments. In this talk, I will present a few recent results. First, we adapt the nucleated polymerization model for aggregate dynamics to a stochastic context to consider a rate limiting event in the establishment of prion disease: the first the successful amplification of an aggregate. We then develop a multi-scale aggregate and generation structured population model to study the amplification of prion aggregates in a growing population of cells. Finally, I will show some results from recent individual based simulations where we study how the organization of a yeast population depends on the division and growth properties of the colonies. In all cases, we gain new insights into prion phenotypes in yeast and quantify how common experimentally observed outcomes depend on population heterogeneity.