Taxonomy of DNA conformations within complex nucleoprotein assemblies

Here we discuss the paradigms both for modelling complex nucleoprotein assemblies as rational tangles, and the associated enzymatic action as rational subtangle replacement. We harness the correspondence between specific curves on the boundary of a rational tangle and on the boundary of its branched double cover to classify rational tangles of distance d = 2 from a given rational tangle, in turn limiting the underlying DNA geometry.