title: Distance measures and evolution of polymer chains in their topological space.
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.
authors.affiliation: Harvard Medical School, Harvard University, Boston, Massachusetts, USA. Alireza_Mashaghi-Tabari@meei.harvard.edu.
authors.forename: Alireza
authors.initials: A
authors.lastname: Mashaghi
authors.forename: Abolfazl
authors.initials: A
authors.lastname: Ramezanpour
mesh_terms: D000465:Algorithms; D019143:Evolution, Molecular; D008962:Models, Theoretical; D008968:Molecular Conformation; D011108:Polymers / Q000737:chemistry*; D011336:Probability
chemical_list: D011108:Polymers