  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.
