Amyloid-β42 is a protein polymer that catalyzes the formation of pathogenic amyloid plaques that are a prominent feature in the brain tissue of patients who suffer from Alzheimer’s disease. Aβ42 polymerizes via a nucleation-elongation mechanism; several monomers must first congregate into a nucleus before it can elongate into a polymer. The nucleation step is energetically unfavorable since a nucleus smaller than 7 to 8 monomeric units is unstable, therefore the pieces tend to dissociate faster than they can bond together. A solution of Aβ42 will consist of 100% monomers and oligomers smaller than the nucleus when the total concentration is below the critical level. However, once the concentration of free monomers meets the critical level, polymerization can happen spontaneously and there is a sharp increase in the percentage of polymers at equilibrium. This mechanism, also known as cooperative polymerization, can be understood by simplifying the polymer concentrations as terms of a geometric series. Having a better understanding of the thermodynamic and kinetic properties of Aβ42 polymerization can be very useful in finding a way to control the accumulation of amyloid fibrils in Alzheimer’s patients.
"Equilibrium Ratio of Polymers to Monomers in Cooperative Polymerization of Amyloid-β Protein,"
Undergraduate Journal of Mathematical Modeling: One + Two:
2, Article 2.
DOI: https://doi.org/10.5038/2326-3622.214.171.12401 Available at: https://digitalcommons.usf.edu/ujmm/vol9/iss2/2
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Arcadii Grinshpan, Mathematics and Statistics
Martin Muschol, Physics
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