title: Hamiltonian Dynamics of Protein Filament Formation.
abstract: We establish the Hamiltonian structure of the rate equations describing the formation of protein filaments. We then show that this formalism provides a unified view of the behavior of a range of biological self-assembling systems as diverse as actin, prions, and amyloidogenic polypeptides. We further demonstrate that the time-translation symmetry of the resulting Hamiltonian leads to previously unsuggested conservation laws that connect the number and mass concentrations of fibrils and allow linear growth phenomena to be equated with autocatalytic growth processes. We finally show how these results reveal simple rate laws that provide the basis for interpreting experimental data in terms of specific mechanisms controlling the proliferation of fibrils.
authors: Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.
authors: Thomas C T
authors: TC
authors: Michaels
authors: Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.
authors: Samuel I A
authors: SI
authors: Cohen
authors: Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.
authors: Michele
authors: M
authors: Vendruscolo
authors: Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.
authors: Christopher M
authors: CM
authors: Dobson
authors: Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.
authors: Tuomas P J
authors: TP
authors: Knowles
mesh_terms: D000682:Amyloid / Q000737:chemistry / Q000378:metabolism; D008954:Models, Biological; D008956:Models, Chemical; D017711:Nonlinear Dynamics; D011506:Proteins / Q000737:chemistry* / Q000378:metabolism; D013816:Thermodynamics
chemical_list: D000682:Amyloid; D011506:Proteins