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.