A discrete mathematical model for the aggregation of β-Amyloid

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...

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Bibliographic Details
Published in:PloS one 2018-05, Vol.13 (5), p.e0196402-e0196402
Main Authors: Dayeh, Maher A, Livadiotis, George, Elaydi, Saber
Format: Article
Language:English
Subjects:
Agglomeration
Alzheimer's disease
Biology and Life Sciences
Brain research
Chemical kinetics
Dementia disorders
Dynamic stability
Experiments
Fibrils
Hypotheses
Kinetics
Mathematical analysis
Mathematical models
Medicine and Health Sciences
Microscopy
Monomers
Neurodegenerative diseases
Oligomers
Peptides
Physical Sciences
Proteins
Reaction kinetics
Research and Analysis Methods
β-Amyloid
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Summary: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.
ISSN:1932-6203
1932-6203
DOI:10.1371/journal.pone.0196402