Related Experiment Video
Updated: Feb 10, 2026
13:59
Assaying β-amyloid Toxicity using a Transgenic C. elegans Model
Published on: October 9, 2010
26.7K
A discrete mathematical model for the aggregation of β-Amyloid
Maher A Dayeh1, George Livadiotis1, Saber Elaydi2
1Department of Space Research, Southwest Research Institute, San Antonio, Texas, United States of America.
Plos One
|May 24, 2018
Summary
Alzheimer's disease dementia may stem from beta-amyloid (Aβ) peptide aggregation. This study models Aβ monomer to oligomer conversion, offering insights into inhibiting this process for potential therapeutic development.
Area of Science:
- Biochemistry
- Mathematical Biology
- Neuroscience
Background:
- Alzheimer's disease (AD) dementia is linked to beta-amyloid (Aβ) peptide aggregation.
- Aβ peptides transition from soluble monomers to insoluble fibrils, forming toxic aggregates.
Purpose of the Study:
- To develop a discrete-time mathematical model for Aβ monomer aggregation into oligomers.
- To analyze the stability of the model's equilibria.
- To identify conditions that may inhibit Aβ aggregation.
Main Methods:
- Utilized concepts from chemical kinetics and population dynamics.
- Developed a discrete-time mathematical model.
- Analyzed model equilibria for stability and instability conditions.
Main Results:
- Established conditions for the stability and instability of model equilibria.
- Derived a formula for the number of monomers required for oligomer formation.
- Provided a framework for understanding and potentially inhibiting Aβ aggregation.
Conclusions:
- The mathematical model offers a mechanism to understand Aβ aggregation dynamics.
- Insights gained may guide compound designers in developing inhibitors of Aβ aggregation.
- This research contributes to understanding the molecular basis of Alzheimer's disease.
Related Concept Videos
03:03Amyloid Fibrils
12.0K
Amyloid fibrils are aggregates of misfolded proteins. Under most circumstances, misfolded proteins are either refolded by chaperone proteins or degraded by the proteasome. However, in the case of a mutation or a disease, these proteins can accumulate to form large clusters and often further assemble to form elongated fibers, called fibrils.
Amyloid deposits were observed as early as 1639 in the liver and the spleen. In 1854, Rudolph Virchow performed iodine staining,...
Amyloid deposits were observed as early as 1639 in the liver and the spleen. In 1854, Rudolph Virchow performed iodine staining,...
12.0K
03:03Amyloid Fibrils
6.5K
6.5K
01:29Mathematical Modeling: Problem Solving
386
Mathematical modeling transforms real-world scenarios into mathematical expressions, allowing for structured problem-solving and analysis. This process involves defining the situation, assigning variables to measurable quantities, selecting an appropriate model, and solving the resulting equation. Such models are invaluable in finance, providing precise methods to evaluate investments, loans, and repayment structures.A widely used example is the calculation of fixed monthly payments on a loan,...
386
01:29Mathematical Induction
282
Mathematical induction is a structured method of proof used to confirm the truth of statements involving natural numbers. Consider the sum of the first n natural numbers:This formula describes a pattern that appears to hold true as more terms are added. To verify that it is valid for all natural numbers, mathematical induction proceeds in two essential steps. The first is the base case, where the formula is tested for the initial value, typically n = 1. Substituting into both sides confirms the...
282
01:15Discrete Fourier Transform
921
The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...
921
01:19Fundamental Mathematical Principles in Pharmacokinetics: Mathematical Expressions and Units
1.6K
Mathematical principles play a crucial role in pharmacokinetics, providing a framework for understanding and quantifying drug distribution and elimination dynamics in the body. By utilizing mathematical expressions and units, pharmacologists can accurately characterize the behavior of drugs, optimize dosing regimens, and predict therapeutic outcomes.
One significant application of mathematics in pharmacokinetics is the characterization of drug distribution through the volume of distribution...
One significant application of mathematics in pharmacokinetics is the characterization of drug distribution through the volume of distribution...
1.6K