On bifurcation of Prion disease: A Chemical Reaction Network approach*

Fatal neurodegenerative diseases such as bovine spongiform encephalopathy in cattle, scrapie in sheep, and Creutzfeldt-Jakob disease in humans are caused by prions. A prion is a protein encoded by a normal cellular gene. The cellular form of the prion, namely PrPC, is benign but can be reconfigured into a disease-causing form (named scrapie), PrPSc, by a conformational change from α—helix to β—sheets. Prions replicate by this conformational change; that is, PrPSc interacts with PrPC producing a new molecule of PrPSc. This kind of replication is modeled in this contribution as an autocatalytic Chemical Reaction Network (CRN). The Mass Action Kinetic (MAK) ODEs support three distinct dynamical scenarios: multiple steady states, sustained oscillations and a degenerate steady state. We perform equilibria analysis of each dynamical scenario.