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.
|Journal||Preprint on arXiv|
|Publication status||Published - 12 Sep 2019|
Barbensi, A., Celoria, D., Harrington, H. A., Stasiak, A., & Buck, D. (2019). Grid diagrams as tools to investigate knot spaces and topoisomerase-mediated simplification of DNA topology. Preprint on arXiv.