IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0196402.html
   My bibliography  Save this article

A discrete mathematical model for the aggregation of β-Amyloid

Author

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
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0196402
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0196402&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0196402?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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. "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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Begoña López-Arias & Enrique Turiégano & Ignacio Monedero & Inmaculada Canal & Laura Torroja, 2017. "Presynaptic Aβ40 prevents synapse addition in the adult Drosophila neuromuscular junction," PLOS ONE, Public Library of Science, vol. 12(5), pages 1-22, May.
    2. Xiaohang Li & Jin Cui & Yang Yu & Wei Li & Yujun Hou & Xin Wang & Dapeng Qin & Cun Zhao & Xinsheng Yao & Jian Zhao & Gang Pei, 2016. "Traditional Chinese Nootropic Medicine Radix Polygalae and Its Active Constituent Onjisaponin B Reduce β-Amyloid Production and Improve Cognitive Impairments," PLOS ONE, Public Library of Science, vol. 11(3), pages 1-19, March.
    3. Ya Zhu & Xiaowen Lin & Xin Zong & Shuo Han & Mu Wang & Yuxuan Su & Limin Ma & Xiaojing Chu & Cuiying Yi & Qiang Zhao & Beili Wu, 2022. "Structural basis of FPR2 in recognition of Aβ42 and neuroprotection by humanin," Nature Communications, Nature, vol. 13(1), pages 1-10, December.
    4. Massih Khorvash & Nick Blinov & Carol Ladner-Keay & Jie Lu & Judith M Silverman & Ebrima Gibbs & Yu Tian Wang & Andriy Kovalenko & David Wishart & Neil R Cashman, 2020. "Molecular interactions between monoclonal oligomer-specific antibody 5E3 and its amyloid beta cognates," PLOS ONE, Public Library of Science, vol. 15(5), pages 1-35, May.
    5. Xiuhua Yin & Hong Zhou & Mengling Zhang & Juan Su & Xiao Wang & Sijie Li & Zaixing Yang & Zhenhui Kang & Ruhong Zhou, 2023. "C3N nanodots inhibits Aβ peptides aggregation pathogenic path in Alzheimer’s disease," Nature Communications, Nature, vol. 14(1), pages 1-15, December.
    6. Jain, Ani & Roy, Parimita, 2023. "Obesity and Alzheimer’s: An attempt to decipher the role of obesity in blood–brain barrier degradation," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    7. Mookyung Cheon & Iksoo Chang & Sandipan Mohanty & Leila M Luheshi & Christopher M Dobson & Michele Vendruscolo & Giorgio Favrin, 2007. "Structural Reorganisation and Potential Toxicity of Oligomeric Species Formed during the Assembly of Amyloid Fibrils," PLOS Computational Biology, Public Library of Science, vol. 3(9), pages 1-12, September.
    8. Andrew C Gill, 2014. "β-Hairpin-Mediated Formation of Structurally Distinct Multimers of Neurotoxic Prion Peptides," PLOS ONE, Public Library of Science, vol. 9(1), pages 1-17, January.
    9. Noah S Bieler & Tuomas P J Knowles & Daan Frenkel & Robert Vácha, 2012. "Connecting Macroscopic Observables and Microscopic Assembly Events in Amyloid Formation Using Coarse Grained Simulations," PLOS Computational Biology, Public Library of Science, vol. 8(10), pages 1-10, October.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:plo:pone00:0196402. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.