Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

Mathematical Modeling of Prion Aggregate Dynamics and Transmission in Yeast
Suzanne S. Sindi

Last modified: 2014-06-09


Prion proteins are responsible for a variety of neurodegenerative diseases in mammals such as Creutzfeldt-Jakob disease in humans and “mad-cow diease” (Bovine Spongiform Encephalopathy or BSE) in cattle. While these diseases are fatal to mammals, a host of harmless phenotypes have been associated with prion proteins in the yeast S. cerevisiae, making yeast an ideal model organism for prion diseases.

According to the prion hypothesis, new phenotypes arise when misfolded versions of a protein appears and are joined together in aggregates. The misfolded (prion) state is infectious and can spread to normal proteins within the cell by converting their conformation to the misfolded state.

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. We first generalize a previously developed nucleated polymerization model for aggregate dynamics. We next discuss a stochastic model of prion protein dynamics in the context of a growing yeast culture. Our model is based on a stochastic chemical reaction network within a cell and a Crump–Mode–Jagers branching process model of population growth. In order to simultaneously conform to observations of two distinct prion strains we uncovered several novel aspects of prion biology that had not been previously reported in either the mathematical or biological communities. Most importantly, in conjunction with yeast prion biologists, we demonstrated that prion aggregate transmission depends strongly on aggregate size.