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A bi-monomeric, nonlinear Becker-Döring-type system to capture oscillatory aggregation kinetics in prion dynamics.

Marie Doumic1, Klemens Fellner2, Mathieu Mezache3

  • 1Sorbonne Universités, Inria, Université Paris-Diderot, CNRS, Laboratoire Jacques-Louis Lions, Paris F-75005, France; Wolfgang Pauli Institute, C/O University of Vienna, Austria.

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Summary

This study introduces a mathematical model for protein aggregation kinetics, revealing how specific reaction pathways can generate damped oscillations. The findings offer insights into the dynamic behavior of protein aggregation processes.

Keywords:
Asymptotic expansionBecker–Döring systemLotka–Volterra systemLyapunov functionalOscillationsPrion modellingProtein polymerisationStability analysis

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Area of Science:

  • Biophysics
  • Chemical Kinetics
  • Mathematical Biology

Background:

  • Protein aggregation is implicated in various diseases.
  • Understanding the dynamics of protein aggregation is crucial for therapeutic development.
  • Observed oscillations in protein aggregation experiments require mechanistic explanation.

Purpose of the Study:

  • To propose and mathematically analyze a differential system for protein aggregation kinetics.
  • To investigate the origins of oscillations observed in protein aggregation.
  • To model reaction kinetics with finite or infinite n.

Main Methods:

  • Mathematical modeling using differential equations.
  • Analysis of a modified Becker-Döring system.
  • Kinetic analysis of protein aggregation reactions.

Main Results:

  • A novel differential system capable of exhibiting oscillations was developed.
  • The system demonstrates sustained though damped oscillations.
  • The model provides a mathematical framework for observed kinetic behaviors.

Conclusions:

  • The proposed model successfully explains the appearance of oscillations in protein aggregation.
  • This work offers a theoretical basis for understanding dynamic protein aggregation phenomena.
  • The findings contribute to the mechanistic understanding of protein aggregation kinetics.