Distance measures and evolution of polymer chains in their topological space

TL;DR

This paper introduces a theoretical framework for topological transitions in biomolecular systems, focusing on conformational changes linked to molecular topology, and proposes distance measures as reaction coordinates to study these transitions.

Contribution

It presents a novel theoretical approach to topological transitions in biomolecules, including new distance measures and an algorithm for estimating intermediate topologies.

Findings

Certain topological classes are more accessible from random topologies.

Off-pathways can hinder evolution to desired topologies.

An algorithm for counting intermediate topologies is introduced.

Abstract

Conformational transitions are ubiquitous in biomolecular systems, have significant functional roles and are subject to evolutionary pressures. Here we provide a first theoretical framework for topological transition, i.e. conformational transitions that are associated with changes in molecular topology. For folded linear biomolecules, arrangement of intramolecular contacts is identified as a key topological property, termed as circuit topology. Distance measures are proposed as reaction coordinates to represent progress along a pathway from initial topology to final topology. Certain topological classes are shown to be more accessible from a random topology. We study dynamic stability and pathway degeneracy associated with a topological reaction and found that off-pathways might seriously hamper evolution to desired topologies. Finally we present an algorithm for estimating the number of intermediate topologies visited during a topological reaction. The results of this study are relevant to, among others, structural studies of RNA and proteins, analysis of topologically associated domains in chromosomes, and molecular evolution.