Quantum perspective on the localized strand separation and cyclization of DNA double helix

We apply Heisenberg model to study local strand separation and cyclization of double-stranded DNA molecule. By mapping the conformational properties of DNA onto the Heisenberg spin system, we show that denaturation can be viewed as a quench-induced quantum phase transition (QPT) at a finite non-zero temperature. These phase transitions lead to the formation of kinks in Heisenberg model that, in turn, correspond to sharp bends in helical axes of double-stranded DNA molecule. In this scenario we study the cyclization of DNA fragments of short length. Our results are in agreement with the reported observation that there is 1 open bp per circle of about 70 bp. Also we have computed the probability of the formation of kinks in circles of various sizes and have observed that beyond 100 bp it decreases sharply which is in agreement with experimental result.