Topology and Elastic Theory of DNA Molecule

Abstract

We have determined at this point that the DNA molecule may be considered as a long chain of an antiferromagnetic spin adjustment when the spin is accurate to be situated on the axis of the supercoil. Furthermore, we examine that as two polynucleotide chains are coiled regarding the same axis with an exact helical sense in a DNA molecule, this can be considered as if a spin with a specific point of reference is confined on the axis of the coil such that two contiguous coils have reverse direction of the spin. Actually, with each turn two strands move in the opposite side of the axis and so the spin direction accredited for the two adjacent coils should be opposite to each other. As soon as spins are defined in the Lie algebra of SU (2) the linking number can be established from the Chern-Simon’s topology linked with the spin system. We shall study the topological property of a DNA supercoil from the angle of such a spin chain. Also, we shall put together the elastic properties of a DNA molecule from on analysis of the spin degrees of freedom. As spins are considered at this time as gauge currents formulated from SU (2) gauge fields we map the elastic properties onto the space of gauge potentials. In quantum field theory the divergence of this current is non-zero which gives increase to chiral anomaly caused by chiral balance contravention.