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A discrete mathematical model for the aggregation of β-Amyloid

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Listed:
  • Maher A Dayeh
  • George Livadiotis
  • Saber Elaydi

Abstract

Dementia associated with the Alzheimer's disease is thought to be correlated with the conversion of the β − Amyloid (Aβ) peptides from soluble monomers to aggregated oligomers and insoluble fibrils. We present a discrete-time mathematical model for the aggregation of Aβ monomers into oligomers using concepts from chemical kinetics and population dynamics. Conditions for the stability and instability of the equilibria of the model are established. A formula for the number of monomers that is required for producing oligomers is also given. This may provide compound designers a mechanism to inhibit the Aβ aggregation.

Suggested Citation

  • Maher A Dayeh & George Livadiotis & Saber Elaydi, 2018. "A discrete mathematical model for the aggregation of β-Amyloid," PLOS ONE, Public Library of Science, vol. 13(5), pages 1-13, May.
    • Handle: RePEc:plo:pone00:0196402
    DOI: 10.1371/journal.pone.0196402
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    References listed on IDEAS

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    1. Dominic M. Walsh & Igor Klyubin & Julia V. Fadeeva & William K. Cullen & Roger Anwyl & Michael S. Wolfe & Michael J. Rowan & Dennis J. Selkoe, 2002. "Naturally secreted oligomers of amyloid β protein potently inhibit hippocampal long-term potentiation in vivo," Nature, Nature, vol. 416(6880), pages 535-539, April.
    2. Sylvain Lesné & Ming Teng Koh & Linda Kotilinek & Rakez Kayed & Charles G. Glabe & Austin Yang & Michela Gallagher & Karen H. Ashe, 2006. "RETRACTED ARTICLE: A specific amyloid-β protein assembly in the brain impairs memory," Nature, Nature, vol. 440(7082), pages 352-357, March.
    3. Ishwar K Puri & Liwu Li, 2010. "Mathematical Modeling for the Pathogenesis of Alzheimer's Disease," PLOS ONE, Public Library of Science, vol. 5(12), pages 1-5, December.
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