An Analytical Solution to the Kinetics of Breakable Filament Assembly

Dissecting Amyloid Formation Amyloid fibrils are associated with clinical disorders ranging from Alzheimer's disease to type II diabetes. Their self-assembly can be described by a master equation that takes into account nucleation-dependent polymerization and fragmentation. Knowles et al. (p. 1533) now present an analytical solution to the master equation, which shows that amyloid growth kinetics is often limited by the fragmentation rate rather than by the rate of primary nucleation. In addition, the results reveal relationships between system properties (scaling laws) that provide mechanistic insight not only into amyloid growth, but also into related self-assembly processes. The growth kinetics of amyloid fibrils and related self-assembly phenomena are revealed by analytical theory. We present an analytical treatment of a set of coupled kinetic equations that governs the self-assembly of filamentous molecular structures. Application to the case of protein aggregation demonstrates that the kinetics of amyloid growth can often be dominated by secondary rather than by primary nucleation events. Our results further reveal a range of general features of the growth kinetics of fragmenting filamentous structures, including the existence of generic scaling laws that provide mechanistic information in contexts ranging from in vitro amyloid growth to the in vivo development of mammalian prion diseases.

[1]  G. Howlett,et al.  Shear flow induces amyloid fibril formation. , 2006, Biomacromolecules.

[2]  Adam Douglass,et al.  Mechanism of Prion Propagation: Amyloid Growth Occurs by Monomer Addition , 2004, PLoS biology.

[3]  Thorsten Pöschel,et al.  Kinetics of prion growth. , 2003, Biophysical journal.

[4]  C. Dobson,et al.  Protein misfolding, functional amyloid, and human disease. , 2006, Annual review of biochemistry.

[5]  Dalaver H. Anjum,et al.  Polyglutamine disruption of the huntingtin exon1 N-terminus triggers a complex aggregation mechanism , 2009, Nature Structural &Molecular Biology.

[6]  M. Fändrich.  Absolute correlation between lag time and growth rate in the spontaneous formation of several amyloid-like aggregates and fibrils. , 2007, Journal of molecular biology.

[7]  S. Radford,et al.  Systematic analysis of nucleation-dependent polymerization reveals new insights into the mechanism of amyloid self-assembly , 2008, Proceedings of the National Academy of Sciences.

[8]  G. Whitesides,et al.  Molecular self-assembly and nanochemistry: a chemical strategy for the synthesis of nanostructures. , 1991, Science.

[9]  A. Aguzzi,et al.  Prion protein (PrP) with amino‐proximal deletions restoring susceptibility of PrP knockout mice to scrapie. , 1996, The EMBO journal.

[10]  D. Otzen,et al.  Amyloid—a state in many guises: Survival of the fittest fibril fold , 2007, Protein science : a publication of the Protein Society.

[11]  S. Prusiner,et al.  Measurement of the scrapie agent using an incubation time interval assay , 1982, Annals of neurology.

[12]  S. Teichmann,et al.  The importance of sequence diversity in the aggregation and evolution of proteins , 2005, Nature.

[13]  A. Miranker,et al.  Fiber-dependent amyloid formation as catalysis of an existing reaction pathway , 2007, Proceedings of the National Academy of Sciences.

[14]  S. Perrett,et al.  Relationship between stability of folding intermediates and amyloid formation for the yeast prion Ure2p: a quantitative analysis of the effects of pH and buffer system. , 2003, Journal of molecular biology.

[15]  J. Hofrichter,et al.  Kinetics of sickle hemoglobin polymerization. II. A double nucleation mechanism. , 1985, Journal of molecular biology.

[16]  A. Aguzzi,et al.  Prion research: the next frontiers , 1997, Nature.

[17]  D. Cox,et al.  One-dimensional model of yeast prion aggregation. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  M. Bailey,et al.  Apolipoprotein C-II amyloid fibrils assemble via a reversible pathway that includes fibril breaking and rejoining. , 2008, Journal of molecular biology.

[19]  Fumio Oosawa,et al.  Thermodynamics of the polymerization of protein , 1975 .

[20]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[21]  F. Ferrone,et al.  Analysis of protein aggregation kinetics. , 1999, Methods in enzymology.

[22]  A. Fersht,et al.  Rapid amyloid fiber formation from the fast-folding WW domain FBP28 , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[23]  L. Mahadevan,et al.  Physical Limits and Design Principles for Plant and Fungal Movements , 2005, Science.

[24]  P. Lansbury,et al.  Seeding “one-dimensional crystallization” of amyloid: A pathogenic mechanism in Alzheimer's disease and scrapie? , 1993, Cell.

[25]  Jonathan S. Weissman,et al.  The physical basis of how prion conformations determine strain phenotypes , 2006, Nature.

[26]  M. Leone,et al.  Secondary nucleation and accessible surface in insulin amyloid fibril formation. , 2008, The journal of physical chemistry. B.

[27]  Christopher M. Dobson,et al.  Molecular recycling within amyloid fibrils , 2005, Nature.