An Accurate Numerical Solution to the Kinetics of Breakable Filament Assembly

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Proteinaceous aggregation occurs through self-assembly-a process not entirely understood. In a recent article, Knowles and colleagues (2009) presented an analytical theory for amyloid fibril growth via secondary rather than primary nucleation. 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 law governing the evolution of filament elongation simply from two coupled nonlinear ordinary differential equations originally obtained from a master equation. While this work adds significantly to our understanding of filament self-assembly, it required an "approximate" analytical solution representation for the moments of the chain length distribution. If this were always true, the discovery of such scaling laws would be infrequent. Here, we show that the same results are found by purely numerical means. In addition, the numerical method used features a highly accurate solution strategy for the coupled Ordinary Differential Equations (ODEs) based only on a fundamental finite difference scheme and convergence acceleration. Once a reliable numerical solution has been established, a dimensional analysis then provides the scaling laws.

Original languageEnglish (US)
Pages (from-to)153-174
Number of pages22
JournalTransport Theory and Statistical Physics
Volume41
Issue number1-2
DOIs
StatePublished - Jan 2012

Fingerprint

Scaling laws
Self-assembly
Scaling Laws
Filament
Ordinary differential equations
scaling laws
Self assembly
self assembly
filaments
differential equations
assembly
Kinetics
Numerical Solution
Convergence Acceleration
scaling
Law
Dimensional Analysis
dimensional analysis
kinetics
Nonlinear Ordinary Differential Equations

Keywords

  • convergence acceleration
  • finite difference
  • ordinary differential equations
  • proteiniaceous aggregation
  • Richardsons extrapolation
  • Wynn-epsilon acceleration

ASJC Scopus subject areas

  • Applied Mathematics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Transportation

Cite this

An Accurate Numerical Solution to the Kinetics of Breakable Filament Assembly. / Ganapol, Barry D.

In: Transport Theory and Statistical Physics, Vol. 41, No. 1-2, 01.2012, p. 153-174.

Research output: Contribution to journalArticle

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