Extended Topological Persistence and Contact Arrangements in Folded Linear Molecules

Abstract

Structure plays a pivotal role in determining the functional properties of self-interacting linear biomolecular chains, for example proteins and nucleic acids. In this paper, we propose a method for representing each such molecule combinatorially—as a one-dimensional simplicial complex—in a novel way that takes into account intra-chain contacts. The representation allows for efficient quantification of structural similarities and differences between molecules, and for studying molecular topology using extended persistence. This method performs a multi-scale analysis on a filtered simplicial complex as it tracks clusters, holes, and higher dimensional voids in the filtration. From extended persistence we extract information about the arrangement of intra-chain interactions, a topological property which demonstrably affects folding and unfolding dynamics of the linear chains.