Twist neutrality, a zero sum rule for oriented closed space curves with applications to circular DNA

TL;DR

This paper introduces the twist neutrality rule for closed space curves, revealing how it constrains the geometry of circular DNA, predicts minimum length and concavity, and explains observed DNA shapes.

Contribution

It formulates a zero sum twist neutrality rule for closed curves, linking topology and local geometry, with specific implications for circular DNA structure.

Findings

Minimum length for double-stranded microDNA derived

All microDNAs longer than minimum are concave

Predicted total negative curvature as a function of length

Abstract

The interplay between global constraints and local material properties of chain molecules is a subject of emerging interest. Studies of molecules that are intrinsically chiral, such as double-stranded DNA, is one example. Their properties generally depend on the local geometry, i.e. on curvature and torsion, yet the paths of closed molecules are globally restricted by topology. Molecules that fulfill a twist neutrality condition, a zero sum rule for the incremental change in the rate of winding along the curve, will behave neutrally to strain. This has implications for plasmids. For small circular microDNAs it follows that there must exist a minimum length for these to be double-stranded. It also follows that all microDNAs longer than the minimum length must be concave. This counterintuitive result is consistent with the kink-like appearance which has been observed for circular DNA. A prediction for the total negative curvature of a circular microDNA is given as a function of its length.