Thomas Michaels — University of Cambridge #
Hamiltonian Dynamics of Protein Filament Formation#
The formation of protein filaments is associated with a wide 
range of cellular functions, including transport and scaffolding, as 
well as a variety of disorders, such as Alzheimer's, Parkinson's and 
prion diseases. The complexity and diversity of these phenomena have 
made it challenging to establish whether a general predictive 
description can be formulated to account quantitatively for the kinetics 
of the formation of filaments in the different cases using a unified 
theoretical framework. We show here that it is possible to achieve this 
goal by establishing 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.