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Updated: Aug 8, 2026

Investigating the Spreading and Toxicity of Prion-like Proteins Using the Metazoan Model Organism C. elegans
Published on: January 8, 2015
A mathematical analysis of the dynamics of prion proliferation
Meredith L Greer1, Laurent Pujo-Menjouet, Glenn F Webb
1Department of Mathematics, Bates College, 213 Hathorn Hall Bates College, Lewiston, Maine 04240, USA. mgreer@bates.edu
Abstract:
How do the normal prion protein (PrP(C)) and infectious prion protein (PrP(Sc)) populations interact in an infected host? To answer this question, we analyse the behavior of the two populations by studying a system of differential equations. The system is constructed under the assumption that PrP(Sc) proliferates using the mechanism of nucleated polymerization. We prove that with parameter input consistent with experimentally determined values, we obtain the persistence of PrP(Sc). We also prove local stability results for the disease steady state, and a global stability result for the disease free steady state. Finally, we give numerical simulations, which are confirmed by experimental data.
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