A discrete mathematical model for the aggregation of β-Amyloid

Maher A Dayeh; George Livadiotis; Saber Elaydi

doi:10.1371/journal.pone.0196402

A discrete mathematical model for the aggregation of β-Amyloid

PLoS One. 2018 May 23;13(5):e0196402. doi: 10.1371/journal.pone.0196402. eCollection 2018.

Authors

Maher A Dayeh¹, George Livadiotis¹, Saber Elaydi²

Affiliations

¹ Department of Space Research, Southwest Research Institute, San Antonio, Texas, United States of America.
² Department of Mathematics, Trinity University, San Antonio, Texas, United States of America.

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.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Alzheimer Disease / etiology
Alzheimer Disease / metabolism
Amyloid beta-Peptides / chemistry*
Amyloid beta-Peptides / metabolism*
Humans
Kinetics
Mathematical Concepts
Models, Chemical
Models, Molecular
Protein Aggregates*
Protein Aggregation, Pathological / metabolism*
Protein Multimerization
Protein Stability

Substances

Amyloid beta-Peptides
Protein Aggregates

Grants and funding

This work was supported by a grant from King Abdul Aziz University, SAU. The funder had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.