Skip to main content
Kent Academic Repository

Insights into the dynamic trajectories of protein filament division revealed by numerical investigation into the mathematical model of pure fragmentation

Tournus, Magali, Escobedo, Miguel, Xue, Wei-Feng, Doumic, Marie (2021) Insights into the dynamic trajectories of protein filament division revealed by numerical investigation into the mathematical model of pure fragmentation. PLoS Computational Biology, 17 (9). e1008964. ISSN 1553-734X. (doi:10.1371/journal.pcbi.1008964) (KAR id:93217)

Abstract

The dynamics by which polymeric protein filaments divide in the presence of negligible growth, for example due to the depletion of free monomeric precursors, can be described by the universal mathematical equations of ‘pure fragmentation’. The rates of fragmentation reactions reflect the stability of the protein filaments towards breakage, which is of importance in biology and biomedicine for instance in governing the creation of amyloid seeds and the propagation of prions. Here, we devised from mathematical theory inversion formulae to recover the division rates and division kernel information from time-dependent experimental measurements of filament size distribution. The numerical approach to systematically analyze the behaviour of pure fragmentation trajectories was also developed. We illustrate how these formulae can be used, provide some insights on their robustness, and show how they inform the design of experiments to measure fibril fragmentation dynamics. These advances are made possible by our central theoretical result on how the length distribution profile of the solution to the pure fragmentation equation aligns with a steady distribution profile for large times.

Item Type: Article
DOI/Identification number: 10.1371/journal.pcbi.1008964
Subjects: Q Science
Q Science > QA Mathematics (inc Computing science)
Q Science > QA Mathematics (inc Computing science) > QA297 Numerical analysis
Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations
Divisions: Divisions > Division of Natural Sciences > Biosciences
Depositing User: Wei-Feng Xue
Date Deposited: 16 Feb 2022 14:56 UTC
Last Modified: 18 Feb 2022 17:45 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/93217 (The current URI for this page, for reference purposes)

University of Kent Author Information

  • Depositors only (login required):

Total unique views for this document in KAR since July 2020. For more details click on the image.