Topological chirality and achirality of DNA knots

Abstract

In this paper, the novel topology of DNA knots is discussed on the basis of the Seifert construction in knot theory. Our result shows that T 4 k -DNA knots possess the point symmetry group S 1 and T 2 k + 1 -DNA knots possess the point symmetry group C 1. Hence, C 1 represents the most chiral and S 1the least achiral. We say that a structure with C 1 symmetry is topologically chiral, while a structure with S 1 symmetry is shown to have the properties of a topological rubber glove, and that the orientability of the Seifert construction is a primary tool for the left-right classification of molecular knots.