title: The length distribution of frangible biofilaments.
abstract: A number of different proteins possess the ability to polymerize into filamentous structures. Certain classes of such assemblies can have key functional roles in the cell, such as providing the structural basis for the cytoskeleton in the case of actin and tubulin, while others are implicated in the development of many pathological conditions, including Alzheimer's and Parkinson's diseases. In general, the fragmentation of such structures changes the total number of filament ends, which act as growth sites, and hence is a key feature of the dynamics of filamentous growth phenomena. In this paper, we present an analytical study of the master equation of breakable filament assembly and derive closed-form expressions for the time evolution of the filament length distribution for both open and closed systems with infinite and finite monomer supply, respectively. We use this theoretical framework to analyse experimental data for length distributions of insulin amyloid fibrils and show that our theory allows insights into the microscopic mechanisms of biofilament assembly to be obtained beyond those available from the conventional analysis of filament mass only.
authors.affiliation: Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.
authors.forename: Thomas C T
authors.initials: TC
authors.lastname: Michaels
authors.affiliation: Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen, Denmark.
authors.forename: Pernille
authors.initials: P
authors.lastname: Yde
authors.affiliation: Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.
authors.forename: Julian C W
authors.initials: JC
authors.lastname: Willis
authors.affiliation: Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen, Denmark.
authors.forename: Mogens H
authors.initials: MH
authors.lastname: Jensen
authors.affiliation: Interdisciplinary Nanoscience Center, Department of Molecular Biology and Genetics, Center for Insoluble Protein Structures, Aarhus University, Gustav Wieds Vej 14, 8000 Aarhus C, Denmark.
authors.forename: Daniel
authors.initials: D
authors.lastname: Otzen
authors.affiliation: Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.
authors.forename: Christopher M
authors.initials: CM
authors.lastname: Dobson
authors.affiliation: Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.
authors.forename: Alexander K
authors.initials: AK
authors.lastname: Buell
authors.affiliation: Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.
authors.forename: Tuomas P J
authors.initials: TP
authors.lastname: Knowles
mesh_terms: D000682:Amyloid / Q000737:chemistry* / Q000648:ultrastructure; D000818:Animals; D002417:Cattle; D006801:Humans; D007328:Insulin / Q000737:chemistry*; D007700:Kinetics; D008954:Models, Biological; D058105:Polymerization; D066329:Protein Aggregates
chemical_list: D000682:Amyloid; D007328:Insulin; D066329:Protein Aggregates