Equivalence between routes of infection in minimal Prion replication models

Prions are proteins encoded within a cellular gene that might be the cause of neurodegenerative diseases such as spongiform encephalopathy in cattle, scrapie n sheep as well as Creutzfeldt-Jacob and Alzheimer n humans. The prion protein has two stable forms: the cellular, PrPC, and the scrapie, PrPSc. The conformation of the latter is rich in β-sheets. PrPSc conformation recruits PrPC to turn them into β-sheets using an autocatalytic mechanism, aggregating them into amyloid fibrils within the brain which provokes rreversible tissue damage and a later fatal outcome. Healthy and pathogenic states are predicted by a minimal phenomenological model that showed good agreement for estimated time incubation periods n prion disease. This manuscript contributes on the prion equivalence routes of infection models. Thus, we show that four minimal models following mass action kinetics addressing the sporadic and exogenous routes of prion infection can support the predicted steady states. Moreover, conditions for periodic behaviour–a dynamical scenario predicted by the phenomenological model–for the minimal models studied are given.