Alzheimer's disease and prion: analysis of an in vitro mathematical model

Ionel Sorin Ciuperca; Matthieu Dumont; Abdelkader Lakmeche; Pauline Mazzocco; Laurent Pujo-Menjouet; Human Rezaei; Léon M Tine

Alzheimer's disease and prion: analysis of an in vitro mathematical model

Ionel Sorin Ciuperca ¹ Matthieu Dumont ¹ Abdelkader Lakmeche ² Pauline Mazzocco ^{3, 1} Laurent Pujo-Menjouet ^{3, 1} Human Rezaei ⁴ Léon M Tine ^{3, 1}

1 UCBL - Université Claude Bernard Lyon 1

2 Laboratoire de biomathématiques

3 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis

ICJ - Institut Camille Jordan [Villeurbanne], Inria Grenoble - Rhône-Alpes, CGPhiMC - Centre de génétique et de physiologie moléculaire et cellulaire

4 VIM - Unité de recherche Virologie et Immunologie Moléculaires

Abstract : Alzheimer's disease (AD) is a fatal incurable disease leading to progressive neuron destruction. AD is caused in part by the accumulation of Aβ monomers inside the brain, which have the faculty to aggregate into oligomers and fibrils. Oligomers are 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 prions, PrP sc. In this work, we develop a model describing in vitro Aβ polymerization process. We include interactions between oligomers and PrP c , leading to the misconformation of PrP sc. 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.

Type de document :

Article dans une revue

Discrete and Continuous Dynamical Systems - Series B (DCDS-B), American Institute of Mathematical Sciences, In press

Domaine :

Mathématiques [math]

Liste complète des métadonnées

https://hal.inria.fr/hal-01368862
Contributeur : Pauline Mazzocco <>
Soumis le : mardi 20 septembre 2016 - 10:53:23
Dernière modification le : mardi 4 décembre 2018 - 01:22:15

Alzheimer's disease and prion: analysis of an in vitro mathematical model

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