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Alzheimer's disease and prion: An in vitro mathematical model

Abstract : Alzheimer's disease (AD) is a fatal incurable disease leading to progressive neuron destruction. AD is caused in part by the accumulation in the brain of Aβ monomers aggre-gating into oligomers and fibrils. Oligomers are amongst the most toxic structures as they can interact with neurons via membrane receptors, including PrP c proteins. This interaction leads to the misconformation of PrP c into pathogenic oligomeric prions, PrP ol. In this work, we develop a model describing in vitro Aβ polymerization process. We include interactions between oligomers and PrP c , causing the misconformation of PrP c into PrP ol. 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.
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https://hal.archives-ouvertes.fr/hal-02414635
Contributor : Laurent Pujo-Menjouet <>
Submitted on : Monday, December 16, 2019 - 4:54:22 PM
Last modification on : Tuesday, March 2, 2021 - 3:56:02 PM
Long-term archiving on: : Tuesday, March 17, 2020 - 10:07:02 PM

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Ionel Ciuperca, Matthieu Dumont, Abdelkader Lakmeche, Pauline Mazzocco, Laurent Pujo-Menjouet, et al.. Alzheimer's disease and prion: An in vitro mathematical model. Discrete and Continuous Dynamical Systems - Series B, American Institute of Mathematical Sciences, 2019, 24 (10), pp.5225-5260. ⟨10.3934/dcdsb.2019057⟩. ⟨hal-02414635⟩

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