WASP: A software package for correctly characterizing the topological development of ribbon structures

Abstract

We introduce the Writhe Application Software Package (WASP) which can be used to characterise the topology of ribbon structures, the underlying mathematical model of DNA, Biopolymers, superfluid vorticies, elastic ropes and magnetic flux ropes. This characterisation is achieved by the general twist-writhe decomposition of both open and closed ribbons, in particular through a quantity termed the polar writhe. We demonstrate how this decomposition is far more natural and straightforward than artificial closure methods commonly utilized in DNA modelling. In particular, we demonstrate how the decomposition of the polar writhe in local and non-local components distinctly characterizes local helical structure and knotting/linking of the ribbon. This decomposition provides additional information not given by alternative approaches. As an example application, the WASP routines are used to characterise the evolving topology (writhe) of DNA minicircle and open ended plectoneme formation magnetic/optical tweezer simulations. Finally it is demonstrated that a number of well known alternative writhe expressions are actually simplifications of the polar writhe measure.