Computational investigations of folded self-avoiding walks related to protein folding

TL;DR

This paper computationally investigates folded and unfoldable self-avoiding walks in relation to protein folding, revealing their equivalence for short walks and differences at typical protein lengths, with detailed methods and a new study tool.

Contribution

It demonstrates the equivalence and divergence of folded and unfoldable self-avoiding walks at various lengths and introduces a computational tool for their analysis.

Findings

Folded and unfoldable self-avoiding walks are equal for walks of length ≤14.

They differ for walks of length ≥108, common in proteins.

A detailed computational method and a new analysis tool are provided.

Abstract

Various subsets of self-avoiding walks naturally appear when investigating existing methods designed to predict the 3D conformation of a protein of interest. Two such subsets, namely the folded and the unfoldable self-avoiding walks, are studied computationally in this article. We show that these two sets are equal and correspond to the whole $n$-step self-avoiding walks for $n\leqslant 14$, but that they are different for numerous $n \geqslant 108$, which are common protein lengths. Concrete counterexamples are provided and the computational methods used to discover them are completely detailed. A tool for studying these subsets of walks related to both pivot moves and proteins conformations is finally presented.