# Mathematical Modeling of Prion Aggregate Dynamics within a Growing Yeast Population

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Prion proteins are responsible for a variety of neurodegenerative diseases in mammals 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.

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 two 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 rst the successful amplication of an aggregate. We then develop a multi-scale aggregate and generation structured population model to study the amplication of prion aggregates in a growing population of cells. In both cases, we gain new insights into prion phenotypes in yeast and quantify how common experimentally observed outcomes depend on population heterogeneity.