On bifurcation of Prion disease: A Chemical Reaction Network approach

Abstract 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 P r P C , is benign but can be reconfigured into a disease-causing form (named scrapie), P r P Sc , by a conformational change from α—helix to β—sheets. Prions replicate by this conformational change; that is, P r P Sc interacts with P r P C producing a new molecule of P r P Sc . 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.