Denaturation Bubbles in Fluctuating Dna Chains

– A statistical model of DNA, coupling base pair states (unbroken or broken) and thermal chain fluctuations, is formulated and then investigated using an exact solution obtained by transfer kernel techniques. The dependence on temperature and DNA length of the fraction of denaturation bubbles and their correlation length are deduced. Novel results include (i) the melting temperature emerges naturally as a function of double-strand and bubble bending rigidities and (ii) mechanical and statistical properties of DNA, such as persistence length and mean square radius, are explicitly calculated on the same footing as base pair quantities. Introduction. – The stability of double-stranded DNA (dsDNA) at physiological temperature is due to self-assembly: of base pairs within a same strand via base-stacking interactions between neighboring bases and of both strands via hydrogen bonds between pairs of complementary bases. The interaction between each complementary base pair is, however, on the order of k B T [1,2] (thermal energy) and thus thermal fluctuations can lead, even at physiological temperature, to local and transitory unzipping of the double strand [3,4]. The cooperative opening of several consecutive base pairs leads to denaturation bubbles which are likely to play a role from a biological perspective, since they may interfere with mechanisms such as replication, transcription or protein binding. For example, it has been proposed [5] that transcription start sites and regulatory sites could be related to DNA regions which have a higher probability of promoting bubbles. Indeed, the energy needed to break an adenine-thymine (AT) base pair, connected by two hydrogen bonds, is smaller than the energy needed to break a guanine-cytosine (G-C) one (3 hydrogen bonds) [1]. At the same temperature, AT rich sequences present a priori more bubbles than G-C rich ones, even though sequence effects on the occurrence of bubbles are more complex than a simple examination of local AT base abundance [1, 5]. In addition to the sequence, the fraction of denaturation bubbles naturally depends on temperature, as well as on the ionic strength of the solution [3]. In particular, the melting temperature above which DNA is completely denaturated into two single-strand DNA (ssDNA) chains depends on both sequence and ionic strength. More intriguingly, another parameter that affects the melting temperature is the length of the double strand [6]. This is not a purely academic debate because short DNA strands (a few tens of base pairs) are involved in DNA chip experiments where the …