A mathematical analysis of the dynamics of prion proliferation. (English) Zbl 1447.92089
Summary: How do the normal prion protein \(( \operatorname{PrP}^{\operatorname{C}})\) and infectious prion protein \(( \operatorname{PrP}^{\operatorname{Sc}})\) 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 \(\operatorname{PrP}^{\operatorname{Sc}}\) proliferates using the mechanism of nucleated polymerization. We prove that with parameter input consistent with experimentally determined values, we obtain the persistence of \(\operatorname{PrP}^{\operatorname{Sc}}\). 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.
MSC:
| 92C32 | Pathology, pathophysiology |
| 92C40 | Biochemistry, molecular biology |
| 34D20 | Stability of solutions to ordinary differential equations |
| 34D23 | Global stability of solutions to ordinary differential equations |
Keywords:
prion diseases; prion proliferation; solution persistence; nucleated polymerization mechanismReferences:
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