Grid diagrams as tools to investigate knot spaces and topoisomerase-mediated simplification of DNA topology

TL;DR

This paper demonstrates that grid diagrams, a simple mathematical tool, can effectively model complex 3D DNA topoisomerase processes like preferential unknotting, offering a new computational framework for studying biopolymer entanglement.

Contribution

It introduces a novel application of grid diagrams to model topoisomerase-mediated DNA unknotting, bridging 2D mathematical formalism with 3D biological processes.

Findings

Grid diagrams can model DNA topoisomerase activity.

The approach captures the selectivity of topoisomerase in unknotting.

Provides a new computational framework for biopolymer entanglement.

Abstract

Grid diagrams with their relatively simple mathematical formalism provide a convenient way to generate and model projections of various knots. It has been an open question whether these 2D diagrams can be used to model a complex 3D process such as the topoisomerase-mediated preferential unknotting of DNA molecules. We model here topoisomerase-mediated passages of double-stranded DNA segments through each other using the formalism of grid diagrams. We show that this grid diagram-based modelling approach captures the essence of the preferential unknotting mechanism, based on topoisomerase selectivity of hooked DNA juxtapositions as the sites of intersegmental passages. We show that grid diagram-based approach provide an important, new and computationally convenient framework for investigating entanglement in biopolymers.