Modeling Prion Replication within a Growing Yeast Population
Tuesday, May 29, 2018 - 2:00pm - 2:50pm
Prion proteins cause a variety of fatal neurodegenerative diseases in mammals but are harmless to yeast, making it an ideal model organism for these diseases. My research focuses on stochastic and deterministic models of both prion protein dynamics within individual yeast cells as well as how those yeast cells grow and divide to create a heterogeneous colony of cells. Determining kinetic parameters of prion replication in yeast are complicated because experiments reflect both the disease and yeast population dynamics. I present two mathematical formulations targeted at estimating kinetic rates of protein dynamics, assuming we know what is happening with the cellular dynamics. The first is a stochastic formulation where we study the probability the introduction of infectious prion protein leads to a stable infection at the population level. In this case we observe that in particular parameter regimes different kinetic processes may lead to loss of prions. My second model is deterministic and consists of a structured population model describing the growth of yeast cells and logistic growth reaction governing the intracellular prion replication. In this second model, I employ the Porohov metric to estimate kinetic parameters from experiments and find a bi-modal distribution of prion replication rates.