Simplified Langevin approach to the Peyrard-Bishop-Dauxois model of DNA

Abstract

A simple Langevin approach is used to study stationary properties of the Peyrard-Bishop-Dauxois model for DNA, allowing known properties to be recovered in an easy way. Results are shown for the denaturation transition in homogeneous samples, for which some implications, so far overlooked, of an analogy with equilibrium wetting transitions are highlighted. This analogy implies that the order-parameter, asymptotically, exhibits a second order transition even if it may be very abrupt for non-zero values of the stiffness parameter. Not surprisingly, we also find that for heterogeneous DNA, within this model the largest bubbles in the pre-melting stage appear in adenine-thymine rich regions, while we suggest the possibility of some sort of not strictly local effects owing to the merging of bubbles.PACS numbers: 02.50.-r,64.60.Ht 87.14.GgThe DNA thermal melting transition (also called denaturation, coiling, or un-zipping) occurs when, above a certain critical temperature, the double-stranded DNA molecule unravels into two separate coils, while for smaller temperatures (pre-melting stage) only localized openings or bubbles exist [1]. This phase transition is of importance for DNA duplication and transcription, and many studies have scrutinized its nature (whether first or second order), trying to pin down the relevant traits of the rich phenomenology experimentally observed (a nonexhaustive list of references is [2,3,4,5,6,7]). Moreover, it has been suggested that the dynamics of a DNA molecule in its pre-melting stage may play a role in its own transcription initiation. Indeed, bubbles are determined by sequence specificity and they have been reported to occur with high probability in the neighborhood of the, functionally relevant, transcription start site (TSS) and near other regulatory sites, facilitating further microbiological activity [7,8,9].This relation between thermal dynamics and biological functionality has been claimed to be borne out by experimental data from real promoter DNA sequences and is supported by results from a theoretical model (see below) [8,9]. Even if this might differ from biological, protein mediated processes, studies of thermal properties of the DNA by itself are a first step forward in understanding more complex situations [1] (see [10] for a different view).Let us mention some observations in this context, which have been the object of recent analyses. Even though one would expect that adenine-thymine (AT-)rich regions should be more prone to sustain bubbles than guanine-cytosine-(GC-)rich ones (as AT pairs bind the two strands more weakly than GC ones [1]), counterintuitive situations in which this is not the case have been reported [7,11]. In the same vein, the dependence of bubble formation on the specific base-pair sequence was reported to be highly nonlocal: Upon mutation of two AT base-pairs into two (stronger) GC base-pairs near the TSS, rendering a specific promoter sequence completely inactive for transcription, the opening profiles of the original sequence and its mutant var...

A new approach to microscopic modeling of a hole transfer in heteropolymer DNA

“…The problem of how the transfer of a cation-radical relates to fluctuations of base overlap integrals is to be studied in the future. Further development of our approach implies the direct coupling of matrix elements' fluctuations with thermal dynamics of DNA in PBH model (Langevin approach, see, e. g., [36]). An alternative way is the design of a more quick semistochastic algorithm of charge transport simulation in a long heterogeneous DNA.…”

Denaturation patterns in heterogeneous DNA

“…The latter has been found responsible for a denaturation with an entropy jump corresponding to an effective latent heat reminiscent of a first order phase transition in homogeneous DNA [21]. However, no consensus has been reached so far regarding the nature of the transition, whether first or second order [22][23][24][25][26][27][28][29][30].…”

Path integral method for DNA denaturation

“…In this regard, the Poland-Scheraga model [4] has been path-breaking and still makes the base of several investigations [5,6,7,8,9,10]. Despite extensive analytical and numerical work [11,12,13,14,15,16], establishing character and nature of the melting phase transition, whether first or second order, remains a challenging task [17]. A significant advance towards a comprehension of the DNA dynamics was made after Peyrard and Bishop (PB) introduced a 1D Hamiltonian model [18] which recognized the role of nonlinearities in the molecule [19] and reduced its great complexity to two essential interactions: i) a nonlinear coupling between the two bases in a pair connected by hydrogen bonds, ii) a harmonic stacking potential between adjacent bases along the strand.…”