Denaturation of Heterogeneous DNA

The effect of heterogeneous sequence composition on the denaturation of double stranded DNA is investigated. The resulting pair-binding energy variation is found to have a negligible effect on the critical properties of the smooth second order melting transition in the simplest (Peyrard-Bishop) model. However, sequence heterogeneity is dramatically amplified upon adopting a more realistic treatment of the backbone stiffness. The model yields features of " multi-step melting " similar to those observed in experiments. The denaturation or melting of double-stranded DNA molecules upon changes in ambient temperatures or solvent conditions is a subject which has had a long history [1,2]. In early theoretical studies [1,3], DNA melting was described by the nearest-neighbor 1d Ising model which yielded only a sharp crossover but not a thermo-dynamic phase transition [4]. A smooth second order transition was later demonstrated in a modified version of the 1d Ising model [5], after including an effective long-range interaction arising from the configurational entropy gain of the denatured segments. Experimentally, a purified DNA sample containing an unique sequence and length is found to exhibit distinct multi-step melting, where the " melting curves " (to be specified below) exhibit sharp features consisted of plateaus of variable sizes separated by steps [2,6]. These fine features have been attributed to the melting of individual " domains " associated with variations in the composition of the nucleotide sequences, since the binding energies of the two kinds of base pairs, adenine-thymine (AT) and guanine-cytosine (GC), are significantly different [7]. The effect of binding energy variation has been studied previously using the nearest-neighbor 1d Ising model [1,8]. In this paper, we investigate this effect in detail by incorporating the important configurational entropy of the denatured strands in a systematic way. We find that sequence heterogene-ity itself is not sufficient to produce multi-step melting, with the phase transition remaining to be of the second-order. Nevertheless, heterogeneity can be dramatically amplified by small changes in the detailed form of the configurational entropy, leading to the apparent multi-step melting behavior for finite length sequences. A simple way of incorporating the entropy of the single-stranded segments is to model the two single strands r