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

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 s...

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Autores principales:	Magali Tournus, Miguel Escobedo, Wei-Feng Xue, Marie Doumic
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2021
Materias:	Biology (General) QH301-705.5
Acceso en línea:	https://doaj.org/article/9b14117f4cd5478ab1b4b5ddaa9305d9
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spelling	oai:doaj.org-article:9b14117f4cd5478ab1b4b5ddaa9305d92021-12-02T19:57:51ZInsights into the dynamic trajectories of protein filament division revealed by numerical investigation into the mathematical model of pure fragmentation.1553-734X1553-735810.1371/journal.pcbi.1008964https://doaj.org/article/9b14117f4cd5478ab1b4b5ddaa9305d92021-09-01T00:00:00Zhttps://doi.org/10.1371/journal.pcbi.1008964https://doaj.org/toc/1553-734Xhttps://doaj.org/toc/1553-7358The 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.Magali TournusMiguel EscobedoWei-Feng XueMarie DoumicPublic Library of Science (PLoS)articleBiology (General)QH301-705.5ENPLoS Computational Biology, Vol 17, Iss 9, p e1008964 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Biology (General) QH301-705.5
spellingShingle	Biology (General) QH301-705.5 Magali Tournus Miguel Escobedo Wei-Feng Xue Marie Doumic Insights into the dynamic trajectories of protein filament division revealed by numerical investigation into the mathematical model of pure fragmentation.
description	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.
format	article
author	Magali Tournus Miguel Escobedo Wei-Feng Xue Marie Doumic
author_facet	Magali Tournus Miguel Escobedo Wei-Feng Xue Marie Doumic
author_sort	Magali Tournus
title	Insights into the dynamic trajectories of protein filament division revealed by numerical investigation into the mathematical model of pure fragmentation.
title_short	Insights into the dynamic trajectories of protein filament division revealed by numerical investigation into the mathematical model of pure fragmentation.
title_full	Insights into the dynamic trajectories of protein filament division revealed by numerical investigation into the mathematical model of pure fragmentation.
title_fullStr	Insights into the dynamic trajectories of protein filament division revealed by numerical investigation into the mathematical model of pure fragmentation.
title_full_unstemmed	Insights into the dynamic trajectories of protein filament division revealed by numerical investigation into the mathematical model of pure fragmentation.
title_sort	insights into the dynamic trajectories of protein filament division revealed by numerical investigation into the mathematical model of pure fragmentation.
publisher	Public Library of Science (PLoS)
publishDate	2021
url	https://doaj.org/article/9b14117f4cd5478ab1b4b5ddaa9305d9
work_keys_str_mv	AT magalitournus insightsintothedynamictrajectoriesofproteinfilamentdivisionrevealedbynumericalinvestigationintothemathematicalmodelofpurefragmentation AT miguelescobedo insightsintothedynamictrajectoriesofproteinfilamentdivisionrevealedbynumericalinvestigationintothemathematicalmodelofpurefragmentation AT weifengxue insightsintothedynamictrajectoriesofproteinfilamentdivisionrevealedbynumericalinvestigationintothemathematicalmodelofpurefragmentation AT mariedoumic insightsintothedynamictrajectoriesofproteinfilamentdivisionrevealedbynumericalinvestigationintothemathematicalmodelofpurefragmentation
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Insights into the dynamic trajectories of protein filament division revealed by numerical investigation into the mathematical model of pure fragmentation.

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