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It is now well known that DNA can be regarded as a physical elastic object in a viscous environment. Two strands of double helix are anti-parallel and two polynucleotide chains are coiled about the same axis such that B-DNA (Z-DNA) has right-handed (left-handed) helical sense. In earlier studies it has been shown that elongation verses force characteristics of a DNA molecule1 can be described2 by the worm-like-chain (WLC) which essentially depicts a chain by an elastic continuous curve at thermal equilibrium with a single elastic constant, the persistence length A characterizing the bending energy.3 It has been shown that the analytic solution of WLC can be achieved through the mapping to a quantum mechanical problem. In fact its partition function corresponds to Euclidean path integral for a quantum dumbbell when rotations and vibrations are ignored so that it represents a rigid rotator. The generalization of the WLC with twist rigidity was considered by Bouchiat et al.4 and it was shown that a DNA molecule at small super coiling can be described by a thin elastic rod involving the twist rigidity. It is called the rod –like –chain (RLC) model. The partition function can be mapped onto the path integral representation for a quantum charged particle in the field of a magnetic monopole with nonquantized charge.4 The theory is singular in the continuum limit and needs to be regularized at an intermediate length scale. It is found that the model is in good agreement with the experimental data at small super coiling region.

A simple theoretical analysis of quantum biomathematical model of DNA and heisenberg spin chain model