Abstract
We introduce the Writhe Application Software Package (WASP) which can be used to characterisze the topology of ribbon structures, the underlying mathematical model of DNA, Biopolymers, superfluid vorticies, elastic ropes and magnetic flux ropes. This characterization 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 into local and non-local components distinctly characterizes the local helical structure and knotting/linking of the ribbon. This decomposition provides additional information not given by alternative approaches. As example applications, the WASP routines are used to characterise the evolving topology (writhe) of DNA minicircle and open ended plectoneme formation magnetic/optical tweezer simulations, and it is shown that the decomponsition into local and non-local components is particularly important for the detection of plectonemes. Finally it is demonstrated that a number of well known alternative writhe expressions are actually simplifications of the polar writhe measure.
Highlights
Introduction to the polar writheIn typical applications, Lk is a prescribed quantity, and the twist Tw can be calculated as Lk-Wr
Writhe is a fundamental measurement for characterizing the topology of ribbon structures and is extensively utilized in multiple fields ranging from biophysics to solar physics to aneurysm detection[30,31,32,52,53]
The most commonly utilized formalism for writhe is only applicable to the subset of problems in which the system under study is a closed loop. This limitation has been overcome through the development of polar writhe, it is largely underutilized in the biophysical community
Summary
Lk is a prescribed quantity (i.e. a fixed applied number of rotations of the structure in plectoneme experiments), and the twist Tw can be calculated as Lk-Wr. we focus on the definition of the writhing as the key quantity to be calculated. In16,26 the definition of writhing was given the name the polar writhe which we label Wp to distinguish from the pre-existing closed ribbon definition (the reason for this name will be clarified shortly). We introduce the quantity Wp through a series of instructive examples. The polar writhe[16] is the sum of a local component (W pl ) and a non-local component (W pnl): Wp = Wpl + Wpnl
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