Abstract:The physics of DNA melting has been of interest since 60's. Last decade has seen a renewed interest in the field, due to experimental data supplied by new single-molecule probes and possible use of DNA as a building block for novel nanostructures. After reviewing the basic physics and the existing literature, I will discuss a model we recently developed for DNA rings. The model takes into account the twisting of the two strands around each other. I will show that the conservation of the number of turns ("linking number") imposed by the circular boundary conditions has a dramatic effect on the melting transition. In addition to shifting the somewhat unusual first-order denaturation of the ordinary DNA to a higher-order phase transition, the change in the global topology deforms the system into a Bose-Einstein condensate where a macroscopic denaturation bubble assumes the role of the superfluid.