A new method for understanding the relations between the molecular design and topological chirality has been developed on the basis of the Seifert construction of knot theory. Tis interesting problem of topological chirality has been solved by applying the topological symmetry concept to the molecular mobius ladders with citber 2n+1 or 2n half-twists (n≥1). Our results show that the T2n+1-Mobius ladders possess the point symmetry group C2n+1 when Lγ=(2n+1)m. and that the Tπ-Mobius ladders possess the point symmetry group Cπ when Lγ=2nm or Lγ=2nm+n(m=1,2,…). Hence both sets are topological chiral.

In this paper we set up a topological model which can be used to describe closed circular (cc) DNAs on the basis of Seifert construction in knot theory. We visually prove that the backbones of T2n-ccDNAs (n=1,2,…) in the crystal which are topological chiral possess the point symmetry group C and that the backbones of T2n-ccDNAs in solution which are topological achiral possess the point symmetry groups Sn2, Sn and S2n. Topological achirality leads us to believe that right handed DNA can be flipped over into a left handed hcilx. Further it also proveides a sound basis for the investigation of this surprising manifestation of DNA supereoiling. Replication. transcription and recombination.

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 T4k-DNA knots possess the point symmetry group S1 and T2k+1-DNA knots possess the point symmetry group C1-Hence, C, represents the most chiral and S1 the least achiral We say that a structure with C1 symmetry is topologically chiral, wile a structure with S1 Symmetry is shown to have the properties of a topological rubber glove, and that the orientability of the Seifert construction is primary tool for the left-right classification of molecular knots.