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Mathematical model of Alzheimer’s disease with prion proteins interactions and treatment

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  • Li, Huixia
  • Zhao, Hongyong

Abstract

The accumulation of β-amyloid (Aβ) is one of the most important pathogenic factors in the occurrence of Alzheimer’s disease (AD). Studies have shown that oligomers are more toxic in the process of Aβ aggregation because oligomers can interact with receptors such as prion proteins (Prpc) and the interaction causes Prpc to be misfolded into pathogenic oligomeric prion proteins (Prpol). In this paper, we propose an AD model including two types of Aβ, the interaction of oligomers with Prpc and anti-Aβ drugs treatment. The existence, uniqueness, and non-negativity of the solutions are analyzed. Furthermore, we prove that the model admits a unique globally asymptotically stable equilibrium, which means the drug cannot cure AD completely. Finally, we present some numerical simulations and investigate the relative contributions to AD with two types of Aβ, Aβ40 and Aβ42. In addition, elastic analysis description Aβ42 paranuclei can be used as a therapeutic target.

Suggested Citation

  • Li, Huixia & Zhao, Hongyong, 2022. "Mathematical model of Alzheimer’s disease with prion proteins interactions and treatment," Applied Mathematics and Computation, Elsevier, vol. 433(C).
    • Handle: RePEc:eee:apmaco:v:433:y:2022:i:c:s0096300322004519
    DOI: 10.1016/j.amc.2022.127377
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    References listed on IDEAS

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    1. Rebecca G. Canter & Jay Penney & Li-Huei Tsai, 2016. "The road to restoring neural circuits for the treatment of Alzheimer's disease," Nature, Nature, vol. 539(7628), pages 187-196, November.
    2. Ghosh, P. & Pateras, J. & Rangachari, V. & Vaidya, A., 2021. "A network thermodynamic analysis of amyloid aggregation along competing pathways," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    3. Peter T. Lansbury & Hilal A. Lashuel, 2006. "A century-old debate on protein aggregation and neurodegeneration enters the clinic," Nature, Nature, vol. 443(7113), pages 774-779, October.
    4. Jeff Sevigny & Ping Chiao & Thierry Bussière & Paul H. Weinreb & Leslie Williams & Marcel Maier & Robert Dunstan & Stephen Salloway & Tianle Chen & Yan Ling & John O’Gorman & Fang Qian & Mahin Arastu , 2016. "The antibody aducanumab reduces Aβ plaques in Alzheimer’s disease," Nature, Nature, vol. 537(7618), pages 50-56, September.
    5. Moustapha Cisse & Lennart Mucke, 2009. "A prion protein connection," Nature, Nature, vol. 457(7233), pages 1090-1091, February.
    6. Juha Laurén & David A. Gimbel & Haakon B. Nygaard & John W. Gilbert & Stephen M. Strittmatter, 2009. "Cellular prion protein mediates impairment of synaptic plasticity by amyloid-β oligomers," Nature, Nature, vol. 457(7233), pages 1128-1132, February.
    7. Wang, Weiping & He, Chang & Wang, Zhen & Hramov, Alexander & Fan, Denggui & Yuan, Manman & Luo, Xiong & Kurths, Jürgen, 2021. "Dynamic analysis of synaptic loss and synaptic compensation in the process of associative memory ability decline in Alzheimer’s disease," Applied Mathematics and Computation, Elsevier, vol. 408(C).
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