Journal
PHYSICAL REVIEW LETTERS
Volume 116, Issue 3, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.116.038101
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Funding
- St John's College, Cambridge
- Schiff Foundation
- ERC
- Newman foundation
- BBSRC
- Wellcome Trust
- Leverhulme Trust
- Biotechnology and Biological Sciences Research Council [BB/J002119/1] Funding Source: researchfish
- BBSRC [BB/J002119/1] Funding Source: UKRI
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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.
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