ABSTRACT:

Fatal neurodegenerative diseases such as bovine spongiform encephalopathy in cattle, scrapie in sheep and Creutzfeldt-Jakob disease in humans are caused by prions. Prion is a protein encoded by a normal cellular gene. The cellular form of the prion, namely PrPC, is benign but can be converted 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 modelled in this contribution as an autocatalytic process. The kinetic model accounts for two of the three epidemiological manifestations: sporadic and infectious. By assuming irreversibility of the PrPSC replication and describing a first-order reaction for the degradation of cellular tissue, the authors explore dynamical scenarios for prion progression, such as oscillations and conditions for multiplicity of equilibria. Feinberg's chemical reaction network theory is exploited to identify multiple steady states and their associate kinetic constants.