A mathematical model of the dynamics of prion aggregates with chaperone-mediated fragmentation.

Prions are proteins most commonly associated with fatal neurodegenerative diseases in mammals but are also responsible for a number of harmless heritable phenotypes in yeast. These states arise when a misfolded form of a protein appears and, rather than be removed by cellular quality control mechanisms, persists. The misfolded prion protein forms aggregates and is capable of converting normally folded protein to the misfolded state through direct interaction between the two forms. The dominant mathematical model for prion aggregate dynamics has been the nucleated polymerization model (NPM) which considers the dynamics of only the normal protein and the aggregates. However, for yeast prions the molecular chaperone Hsp104 is essential for prion propagation. Further, although mammals do not express Hsp104, experimental assays have shown Hsp104 also interacts with mammalian prion aggregates. In this study, we generalize the NPM to account for molecular chaperones and develop what we call the enzyme-limited nucleated polymerization model (ELNPM). We discuss existence, uniqueness and stability of solutions to our model and demonstrate that the NPM represents a quasi-steady-state reduction of our model. We validate the ELNPM by demonstrating agreement with experimental results on the yeast prion PSI(+) that could not be supported by the NPM. Finally, we demonstrate that, in contrast to the NPM, the ELNPM permits the coexistence of multiple prion strains.