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arXiv · 1909.05937

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

Agnese Barbensi·Daniele Celoria·Heather A. Harrington·Andrzej Stasiak·Dorothy Buck
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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.

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Agnese Barbensi, Daniele Celoria, Heather A. Harrington, Andrzej Stasiak, Dorothy Buck. 2019-09-12. Grid diagrams as tools to investigate knot spaces and topoisomerase-mediated simplification of DNA topology. https://arxiv.org/abs/1909.05937

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