A mathematical analysis of the dynamics of prion proliferation.
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.
Greer
Meredith L
ML
Department of Mathematics, Bates College, 213 Hathorn Hall Bates College, Lewiston, Maine 04240, USA. mgreer@bates.edu
Pujo-Menjouet
Laurent
L
Webb
Glenn F
GF
D019943:Amino Acid Substitution; D000818:Animals; D001921:Brain / Q000378:metabolism*; D003198:Computer Simulation; D018450:Disease Progression; D006801:Humans; D008954:Models, Biological; D008956:Models, Chemical; D011108:Polymers; D018621:PrPC Proteins / Q000737:chemistry; D018620:PrPSc Proteins / Q000737:chemistry; D017096:Prion Diseases / Q000378:metabolism* / Q000635:transmission; D011328:Prions / Q000737:chemistry*; D011487:Protein Conformation
D011108:Polymers; D018621:PrPC Proteins; D018620:PrPSc Proteins; D011328:Prions