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A mathematical model of the dynamics of prion aggregates with chaperone-mediated fragmentation

Jason K Davis1, Suzanne S Sindi2

  • 1University of California, 5200 N Lake Rd, Merced, 95343, USA.

Journal of Mathematical Biology
|August 23, 2015
PubMed

Insights

This study introduces the enzyme-limited nucleated polymerization model (ELNPM) to explain prion dynamics, including the role of molecular chaperones like Hsp104. The ELNPM accurately models yeast prion behavior and allows for multiple prion strains, unlike previous models.

Area of Science:

  • Biophysics
  • Molecular Biology
  • Mathematical Modeling

Background:

  • Prions are misfolded proteins causing neurodegenerative diseases in mammals and heritable traits in yeast.
  • The nucleated polymerization model (NPM) is the dominant mathematical framework for prion aggregate dynamics.
  • Molecular chaperones, like Hsp104, are crucial for yeast prion propagation and interact with mammalian prions.

Purpose of the Study:

  • To generalize the NPM by incorporating molecular chaperones.
  • To develop and analyze the enzyme-limited nucleated polymerization model (ELNPM).
  • To demonstrate the ELNPM's ability to explain phenomena not captured by the NPM, such as multiple prion strains.

Main Methods:

  • Development of the enzyme-limited nucleated polymerization model (ELNPM).
  • Mathematical analysis of the model's solutions for existence, uniqueness, and stability.
  • Validation of the ELNPM using experimental data for the yeast prion PSI(+).

Main Results:

  • The ELNPM generalizes the NPM, with the NPM being a quasi-steady-state reduction of the ELNPM.
  • The ELNPM accurately explains experimental results for the yeast prion PSI(+) that the NPM could not.
  • The ELNPM demonstrates the coexistence of multiple prion strains, a capability lacking in the NPM.

Conclusions:

  • The ELNPM provides a more comprehensive framework for understanding prion dynamics, especially in the presence of molecular chaperones.
  • The model's ability to account for chaperone activity and multiple prion strains offers new insights into prion biology.
  • This generalized model has implications for both yeast and mammalian prion research.
Keywords:
Nucleated polymerizationPrionsProtein aggregationProtein misfoldingYeast

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