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 \emph{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 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. In both cases, we gain new insights into prion phenotypes in yeast and quantify how common experimentally observed outcomes depend on population heterogeneity.