# Hamiltonian Dynamics of Saturated Elongation in Amyloid Fiber Formation

Source: [Hamiltonian Dynamics of Saturated Elongation in Amyloid Fiber Formation](<https://www.sota2.com/research/paper/68fa3d311e209131ce8e06ba>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T01:31:01.018Z

Authors: Liu Hong, Xizhou Liu, Thomas C. T. Michaels, Tuomas P. J. Knowles

Published: 2020-11-12T06:21:54.000Z

## Abstract

Elongation is a fundament process in amyloid fiber growth, which is normally characterized by a linear relationship between the fiber elongation rate and the monomer concentration. However, in high concentration regions, a sub-linear dependence was often observed, which could be explained by a universal saturation mechanism. In this paper, we modeled the saturated elongation process through a Michaelis-Menten like mechanism, which is constituted by two sub-steps -- unspecific association and dissociation of a monomer with the fibril end, and subsequent conformational change of the associated monomer to fit itself to the fibrillar structure. Typical saturation concentrations were found to be $7-70\\mu M$ for A$\\beta$40, $\\alpha$-synuclein and etc. Furthermore, by using a novel Hamiltonian formulation, analytical solutions valid for both weak and strong saturated conditions were constructed and applied to the fibrillation kinetics of $\\alpha$-synuclein and silk fibroin.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2011.06222>)

[PDF](<https://arxiv.org/pdf/2011.06222.pdf>)