The progression towards Alzheimer's disease described as a bistable switch arising from the positive loop between amyloids and Ca2+

Alzheimer's disease is a progressive neurodegenerative disorder affecting millions of people. It is characterized by the slow deposition of cerebral amyloid-β peptides in the brain and by dysregulations in neuronal Ca2+ homeostasis. Numerous experimental studies have revealed the existence of a feed-forward loop wherein amyloids-β disturb neuronal Ca2+ levels, which in turn affect the production of amyloids. Here, we formalize this positive loop in a minimal, qualitative model and show that it exhibits bistability. Thus, a stable steady state characterized by low levels of Ca2+ and amyloids, corresponding to a healthy situation, coexists with another 'pathological state' where the levels of both compounds are high. The onset of the disease corresponds to the switch from the lower steady state to the higher one induced by a large-enough perturbation in either the metabolism of amyloids or the homeostasis of intracellular Ca2+. Numerical simulations of the model reproduce a variety of experimental observations about the disease, as its irreversible character, the threshold-like transition to a severe pathology after the slow accumulation of symptoms, the effect of presenilins, the so-called 'prion-like' autocatalytic behaviour of amyloids and the inherent random character of the apparition of the disease that is well known for the sporadic form. The model thus provides a conceptual framework that could be useful when developing therapeutic protocols to slow down the progression of Alzheimer's disease.