Comment on "Why is the DNA denaturation transition first order?".

1 Comment on " Why is the DNA denaturation transition first order? " Recently, Kafri, Mukamel and Peliti (KMP) [1] extended the classical Poland-Scheraga (PS) model for the denaturation transition of DNA [2]. According to PS, the energetic binding of bases in the double helix competes with the entropic contribution of denatured loops, implying that the nature of the transition depends on the exponent c in the statistical weight Ω(2k) ∼ s k k −c for a closed loop of length 2k: for 1 < c ≤ 2 it is of second order, while for c > 2 it is of first order [1, 2]. Fisher, taking the effects of self-avoidance within a denatured loop into account, found c = dν ≈ 1.766 in d = 3, i.e., a second order transition [3]. In Ref. [1] it was obtained that the exponent c is modified if additional effects of self-avoidance between a denatured loop and the vicinal double helices are included. For a single loop within two strands of double helix, it was found that [1] c = dν − 2σ 3 ≈ 2.115 , d = 3 , (1) i.e., a first order transition, where σ 3 is a topological exponent related to a 3-vertex of a polymer network [4]. This conclusion is valid in the asymptotic scaling limit for long flexible, self-avoiding chains, i.e., each of the three segments going out from a vertex must be much longer than the persistence length ℓ p of this segment (even though individual values of the ℓ p may be different). If this condition is fulfilled, the analysis for the PS-inspired model in Ref. [1] is consistent [5, 6]. However , we point out in this Comment that it does not apply to the chains typically used in experiments [7]: the DNA double helix being quite rigid, we expect the transition in such systems to be of second order. The typical length of DNA used in experiments varies from about 100 to 5000 base pairs (bp), the latter corresponding to a whole viral DNA [7]. In such DNA, a chain " monomer " m, which corresponds to a bead in a freely jointed chain, represents one persistence length ℓ p. For the single strand in a denatured loop, typically ℓ p (L) ∼ 40Å (roughly 8 bases), whereas for the double helix ℓ p (H) ∼ 500Å (100 bp) [8]. Even …