Mechanisms of prion disease progression: 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. Prion is a protein encoded by a normal cellular gene. The cellular form of the prion, namely PrP^C, is benign but can be converted into a disease-causing form (named scrapie), PrPS^C, by a conformational change from α-helix to β-sheets. Prions replicate by this conformational change; that is, PrPS^C interacts with PrPc producing a new molecule of PrP^SC. 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 PrP^SC 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.