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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. 
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A Study in Nucleated Polymerization Models of Protein Aggregation.

Jason K Davis1, Suzanne S Sindi1

  • 1University of California, Merced, School of Natural Sciences, 5200 N Lake Rd, Merced, CA 95343.

Applied Mathematics Letters
|November 7, 2019
PubMed
Summary

We solved the discrete nucleated polymerization model for protein aggregate size distributions. This provides a new method for analyzing diseases like Alzheimer's and Parkinson's, improving accuracy over continuous models.

Keywords:
difference equationgenerating functionnucleated polymerizationprionsprotein aggregates

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Area of Science:

  • Biophysics
  • Mathematical Biology
  • Neurodegenerative Diseases

Background:

  • The nucleated polymerization model analyzes protein aggregation dynamics.
  • This model is crucial for understanding prion and amyloid diseases (e.g., Alzheimer's, Parkinson's).
  • Previous solutions assumed continuous aggregate sizes.

Purpose of the Study:

  • To present an explicit steady-state solution for the discrete nucleated polymerization model.
  • To enable direct computation and parameter inference for aggregate size distributions.
  • To facilitate accuracy estimates of the continuous approximation.

Main Methods:

  • Developed a mathematical framework for discrete nucleated polymerization.
  • Derived an explicit steady-state solution for aggregate size distribution.
  • Analyzed the discrete model in comparison to continuous approximations.

Main Results:

  • An explicit steady-state solution for the discrete nucleated polymerization equations was obtained.
  • The discrete solution allows for direct computation and parameter inference.
  • This discrete solution aids in estimating the accuracy of continuous approximations.

Conclusions:

  • The discrete steady-state solution offers a more accurate method for analyzing protein aggregate dynamics.
  • This framework enhances the study of neurodegenerative diseases driven by protein aggregation.
  • The findings facilitate improved computational analysis and parameter estimation in disease modeling.