Bulletin of Mathematical Biology

, Volume 81, Issue 6, pp 1943–1964 | Cite as

A Mathematical Model for Amyloid-𝜷 Aggregation in the Presence of Metal Ions: A Timescale Analysis for the Progress of Alzheimer Disease

  • Eda Asili
  • Shantia YarahmadianEmail author
  • Hadi Khani
  • Meisam Sharify


The aggregation of amyloid-𝛽 (A𝛽) proteins through their self-assembly into oligomers, fibrils, or senile plaques is advocated as a key process of Alzheimer’s disease. Recent studies have revealed that metal ions play an essential role in modulating the aggregation rate of amyloid-𝛽 (A𝛽) into senile plaques because of high binding affinity between A𝛽 proteins and metal ions. In this paper, we proposed a mathematical model as a set of coupled kinetic equations that models the self-assembly of amyloid-𝛽 (A𝛽) proteins in the presence of metal ions. The numerical simulations capture four timescales in the A𝛽 dynamics associated with three important events which include the formation of the amyloid–metal complex, the homogeneous aggregation of the amyloid–metal complexes, and the non-homogeneous aggregation of the amyloid–metal complexes. The method of singular perturbation is used to identify these timescales in the framework of slow–fast systems.


Alzheimer Metal ions Chemical reactions Timescale analysis 



The authors would like to thank Henry Research Foundation in Mississippi State University for the partial support of this project. The authors would like to thank Dr. Joe Hickey, MD, and Hickey Wellness Center for showing us the importance of this subject and inspiring the second author to start this project.


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Copyright information

© Society for Mathematical Biology 2019

Authors and Affiliations

  • Eda Asili
    • 1
  • Shantia Yarahmadian
    • 1
    Email author
  • Hadi Khani
    • 2
  • Meisam Sharify
    • 3
  1. 1.Department of Mathematics and StatisticsMississippi State UniversityMississippi StateUSA
  2. 2.Department of ChemistryMississippi State UniversityMississippi StateUSA
  3. 3.School of MathematicsInstitute for Research in Fundamental Sciences (IPM)TehranIran

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