An Accurate Numerical Solution to the Kinetics of Breakable Filament Assembly

Details An Accurate Numerical Solution to the Kinetics of Breakable Filament Assembly An Accurate Numerical Solution to the Kinetics of Breakable Filament Assembly

2010-06-15

arxiv.org/abs/1006.3022v1

Physics

Biological Physics

28 pages,8 figures

Scientific paper

Proteinaceous aggregation occurs through self-assembly-- a process not entirely understood. In a recent article [1], an analytical theory for amyloid fibril growth via secondary rather than primary nucleation was presented. Remarkably, with only a single kinetic parameter, the authors were able to unify growth characteristics for a variety of experimental data. In essence, they seem to have uncovered the underlying allometric laws governing the evolution of filament elongation simply from two coupled non-linear ordinary differential equations (ODEs) stemming from a master equation. While this work adds significantly to our understanding of filament self-assembly, it required an approximate analytical solution representation. Here, we show that the same results are found by purely numerical means once a straightforward and reliable numerical solution to the set of ODEs has been established.

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