A continuous-time mathematical model and discrete approximations for the aggregation of β-Amyloid

Azmy S. Ackleh, Saber Elaydi, George Livadiotis, Amy Veprauskas

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Alzheimer's disease is a degenerative disorder characterized by the loss of synapses and neurons from the brain, as well as the accumulation of amyloid-based neuritic plaques. While it remains a matter of contention whether β-amyloid causes the neurodegeneration, β-amyloid aggregation is associated with the disease progression. Therefore, gaining a clearer understanding of this aggregation may help to better understand the disease. We develop a continuous-time model for β-amyloid aggregation using concepts from chemical kinetics and population dynamics. We show the model conserves mass and establish conditions for the existence and stability of equilibria. We also develop two discrete-time approximations to the model that are dynamically consistent. We show numerically that the continuous-time model produces sigmoidal growth, while the discrete-time approximations may exhibit oscillatory dynamics. Finally, sensitivity analysis reveals that aggregate concentration is most sensitive to parameters involved in monomer production and nucleation, suggesting the need for good estimates of such parameters.

Original languageEnglish (US)
Pages (from-to)109-136
Number of pages28
JournalJournal of Biological Dynamics
Issue number1
StatePublished - 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Ecology, Evolution, Behavior and Systematics
  • Ecology


  • aggregation
  • Alzheimer's disease
  • neurodegenerative diseases
  • nonstandard discretization schemes
  • β-Amyloid


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