Populations of seemingly identical cells are often highly variable with respect to phenotype, but the quantitative basis of this variation is rarely understood. The goal of this proposal is to develop and experimentally validate multiscale stochastic and deterministic mathematical models incorporating the sources of this variation: cell division and intracellular constituents. To do so, our studies will exploit and seek to explain metastable prion-based phenotypes in yeast, an experimentally tractable and biologically relevant model. Prions are protein-only genetic elements in which distinct functional states of the same protein are created by self-templating changes in its three-dimensional conformation within the context of an aggregate. Prions in mammals are commonly associated with fatal neurodegenerative disease, but yeast prions appear and disappear through manipulations that exploit biological heterogeneity. In Aim 1 we develop a model of prion appearance with two stages of stochastic regulation: an initial aggregate first must appear and then persist in the population as cells divide. We will analyze our model by directly solving the chemical master equation (CME) over a novel state-space truncation we developed for protein aggregation. We use generating functions to develop a matrix free implementation of the CME enabling us to consider biologically feasible state spaces up to the size of system memory. In Aim 2, we develop a multiscale structured population model (MS-SPM) where aggregates evolve in size and number during a cell's lifetime and are distributed, along with other cellular constituents impacting these dynamics, in accordance with asymmetries in cell division. To solve the MS-SPM - a system of coupled PDEs with non-local boundary conditions - we will generalize numerical methods developed for age-structured population models. We will use our model to study the relationship between cellular age and aggregate composition and to discovery the molecular basis of prion disappearance induced by prion dominant-negative mutants. These models will be used to explain data, estimate parameters and develop hypotheses to guide future experiments.

This proposal seeks to develop novel mathematical strategies to uncover the mechanistic and quantitative basis behind the appearance and disappearance of prion phenotypes. In humans, prions are associated with wide array of diseases including genetic, sporadic and transmissible neurodegenerative disease as well as type II diabetes. Insights from this proposal are relevant to NIH's mission of understanding and treating human disease.