Denaturation and unzipping of DNA: statistical mechanics of interacting loops

When DNA molecules are heated they undergo a denaturation transition by which the two strands of the molecule are separated and become unbound. Experimental studies strongly indicate that the denaturation transition is first order. The main theoretical approach to study this transition, introduced in the early 1960s, considers microscopic configurations of a DNA molecule as given by an alternating sequence of non-interacting bound segments and denaturated loops. Studies of this model usually neglect the repulsive, self-avoiding, interaction between different loops and segments and have invariably yielded continuous denaturation transitions. It is shown that the excluded volume interaction between denaturated loops and bound segments may be taken into account using recent results on the scaling properties of polymer networks of arbitrary topology. These interactions are found to drive the transition first order, compatible with experimental observations. The unzipping transition of DNA which takes place when the two strands are pulled apart by an external force acting on one end may also be considered within this approach, again yielding a first-order transition. Although the denaturation and unzipping transitions are thermodynamically first order, they do exhibit critical fluctuations in some of their properties. This appears, for example, in the algebraic decay of the loop size distribution at the thermal denaturation and in the divergence of the length of the end segment as the transition is approached in both thermal- and force-induced transitions.