Writhe formulas and antipodal points in plectonemic DNA configurations

TL;DR

This paper investigates the limitations of a simplified formula for calculating linking and writhing numbers in supercoiled DNA, revealing its inapplicability to plectonemic configurations due to overlooked assumptions.

Contribution

It clarifies the conditions under which the simplified formula is valid and highlights the importance of Fuller theorem's hypotheses in DNA topology calculations.

Findings

The simplified formula cannot be used for plectonemic DNA.

Fuller theorem's hypotheses are crucial for the formula's applicability.

Many previous works overlooked these assumptions.

Abstract

The linking and writhing numbers are key quantities when characterizing the structure of a piece of supercoiled DNA. Defined as double integrals over the shape of the double-helix, these numbers are not always straightforward to compute, though a simplified formula exists. We examine the range of applicability of this widely-used simplified formula, and show that it cannot be employed for plectonemic DNA. We show that inapplicability is due to a hypothesis of Fuller theorem that is not met. The hypothesis seems to have been overlooked in many works.