An Accurate Numerical Solution to the Kinetics of Breakable Filament Assembly

TL;DR

This paper presents a reliable numerical method to solve the ODEs describing filament assembly kinetics, confirming previous analytical results and enhancing understanding of protein aggregation processes.

Contribution

It introduces a straightforward numerical approach to solve the ODEs for filament growth, validating and extending prior analytical theories.

Findings

Numerical solutions match analytical results.

The method provides a reliable way to analyze filament assembly.

Enhanced understanding of amyloid fibril growth mechanisms.

Abstract

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.