New Aspects of Analyzing Amyloid Fibrils

TL;DR

This paper introduces new geometric and topological tools for analyzing amyloid fibril structures, providing novel insights and outperforming traditional methods like RMSD in structural comparison.

Contribution

It presents new discrete geometric indicators and topological tools for analyzing amyloid fibril structures, enhancing characterization capabilities.

Findings

Discrete torsion detects hydrogen bonds between fibril layers

Indicators offer novel structural insights

Topological tools outperform RMSD in structural quantification

Abstract

This is a summary of mathematical tools we used in research of analyzing the structure of proteins with amyloid form \cite{xi2024Top}. We defined several geometry indicators on the discrete curve namely the hop distance, the discrete curvature and the discrete torsion. Then, we used these indicators to analyze the structure of amyloid fibrils by regarding its peptide chains as discrete curves in $\Rds^3$. We gave examples to show that these indicators give novel insights in the characterization analysis of the structure of amyloid fibrils, for example the discrete torsion can detect the hydrogen bonds interactions between layers of amyloid fibril. {Moreover,} the topological tool performs better than the root mean square deviation (RMSD) in quantifying the difference of the structure of amyloid fibrils, etc.