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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. We have developed physiologically relevant models by considering both the prions and their yeast host. In this talk, I will present two models developed by my group to depict distinct phases of the prion pathway within a growing yeast colony. The first considers a stochastic chemical reaction network governing the initial formation of an aggregate and considers cell division as the critical time-scale. In order to simultaneously conform to observations of two distinct prion strains, we uncovered a novel aspect of prion biology. Our second model consists of the stable propagation of aggregates within a growing population of cells. Our goal here is to develop a mathematical framework to estimate the kinetic parameters of prion replication from prion recovery experiments. These experimental results have high variance because the measurements reflect both the dynamics of the aggregates and the yeast population. We develop a structured population model describing the distribution and replication of yeast prions within a growing population of cells. We then employ a likelihood approach for estimating kinetic rates on simulated data and then for six different yeast prion strains. We recover previously observed relationships between strains as well as suggest novel differences between them. 1

Faculty host: Mariel Vazquez Please contact Professor Vazquez if you would like to meet with the speaker or join the dinner after the talk (mariel@math.ucdavis.edu)