Section: New Results
Alzheimer’s disease and prion: An in vitro mathematical model
Alzheimer's disease () is a fatal incurable disease leading to progressive neuron destruction. is caused in part by the accumulation in the brain of monomers aggregating into oligomers and fibrils. Oligomers are amongst the most toxic structures as they can interact with neurons via membrane receptors, including proteins. This interaction leads to the misconformation of into pathogenic oligomeric prions, . In , we develop a model describing in vitro polymerization process. We include interactions between oligomers and , causing the misconformation of into . The model consists of nine equations, including size structured transport equations, ordinary differential equations and delayed differential equations. We analyse the well-posedness of the model and prove the existence and uniqueness of solutions of our model using Schauder fixed point theorem and Cauchy-Lipschitz theorem. Numerical simulations are also provided to give an illustration of the profiles that can be obtained with this model.