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A reaction–diffusion model of spatial propagation of A\(\beta \) oligomers in early stage Alzheimer’s disease

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Abstract

The misconformation and aggregation of the protein Amyloid-Beta (A\(\beta \)) is a key event in the propagation of Alzheimer’s Disease (AD). Different types of assemblies are identified, with long fibrils and plaques deposing during the late stages of AD. In the earlier stages, the disease spread is driven by the formation and the spatial propagation of small amorphous assemblies called oligomers. We propose a model dedicated to studying those early stages, in the vicinity of a few neurons and after a polymer seed has been formed. We build a reaction–diffusion model, with a Becker–Döring-like system that includes fragmentation and size-dependent diffusion. We hereby establish the theoretical framework necessary for the proper use of this model, by proving the existence of solutions using a fixed point method.

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Authors and Affiliations

  1. Department of Applied Mathematics and Computer Science, Universidad del Rosario, Bogotá, 111711, Colombia

    Martin Andrade-Restrepo

  2. Institut Jacques Monod, CNRS UMR 7592, Université Paris Diderot, Université de Paris, 750205, Paris, France

    Martin Andrade-Restrepo

  3. Institut Camille Jordan, CNRS UMR 5208, Université Claude Bernard Lyon 1, Univ Lyon, 69622, Villeurbanne, France

    Ionel Sorin Ciuperca, Paul Lemarre, Laurent Pujo-Menjouet & Léon Matar Tine

Authors
  1. Martin Andrade-Restrepo
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  2. Ionel Sorin Ciuperca
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  3. Paul Lemarre
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  4. Laurent Pujo-Menjouet
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  5. Léon Matar Tine
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Correspondence to Léon Matar Tine.

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Andrade-Restrepo, M., Ciuperca, I.S., Lemarre, P. et al. A reaction–diffusion model of spatial propagation of A\(\beta \) oligomers in early stage Alzheimer’s disease. J. Math. Biol. 82, 39 (2021). https://doi.org/10.1007/s00285-021-01593-3

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  • DOI: https://doi.org/10.1007/s00285-021-01593-3

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