Bubble statistics and positioning in superhelically stressed DNA

Abstract

We present a general framework to study the thermodynamic denaturation of double-stranded DNA under superhelical stress. We report calculations of position-and size-dependent opening probabilities for bubbles along the sequence. Our results are obtained from transfer-matrix solutions of the Zimm-Bragg model for unconstrained DNA and of a self-consistent linearization of the Benham model for superhelical DNA. The numerical efficiency of our method allows for the analysis of entire genomes and of random sequences of corresponding length (10 6 10 9 base pairs). We show that, at physiological conditions, opening in superhelical DNA is strongly cooperative with average bubble sizes of 10 2 10 3 base pairs (bp), and orders of magnitude higher than in unconstrained DNA. In heterogeneous sequences, the average degree of base-pair opening is self-averaging, while bubble localization and statistics are dominated by sequence disorder. Compared to random sequences with identical GC-content, genomic DNA has a significantly increased probability to open large bubbles under superhelical stress. These bubbles are frequently located directly upstream of transcription start sites.

Physics of base-pairing dynamics in DNA

“…In this model, each nucleotide is mapped onto three interaction sites, so that 9 coordinates are necessary to describe its position. This is about one order of magnitude larger than for most mechanical models aimed at investigating DNA denaturation, [16][17][18][19][20][21][22][23][24] and about two orders of magnitude larger than for "beads and springs" models of DNA and the model we have developed to study DNA-protein interactions, [39][40][41][42][43][44][45][59][60][61] but calculations involving a few thousands of base pairs are still affordable with nowadays computers.…”

“…It has been known for a while that a torsionally constrained DNA, either by applying an external torque on it or by closure of the molecule into a superhelical ring (such as in plasmids) or by the formation of loops through regular attachments to a network of proteins in the nucleosome, can be locally denaturated through the nucleation of one or several denaturation bubbles under certain conditions [10,22,245,62,246,247]. Still with the goal of deciphering basic biological mechanisms on physical grounds, the statistical physics of this phenomenon in equilibrium has been extensively studied by Benham and others [23,57,58,59,248], including sequence effects and their connection with biologically relevant sites [24].…”

A polymer model of bacterial supercoiled DNA including structural transitions of the double helix

“…Solving the thermodynamics of the 2sRLC model is challenging because of the self-avoidance constraints. Yet, following upon previous studies on single DNA forms [70] and on the statistics of DNA denaturation [59,60], it is possible to integrate out the torsional degrees of freedom (the φ i 's) under the constraint of a fixed Lk. This leads to an equivalent effective model that has the benefit to offer much better simulation performances [39,42] and further analytic treatment (see below).…”

Dynamical control of denaturation bubble nucleation in supercoiled DNA minicircles

“…However, these approaches did not consider explicitly the twist dynamics, and/or were not able to reach the 100 μs experimental timescale, as measured in in vitro experiments [10], of long-lived thermally-assisted denaturation bubbles extending over more than 4 bps. Furthermore, other approaches studied the interplay between denaturation and writhe, but they were limited to non-equilibrium conditions imposed by the dynamic introduction of bending-or torque-driven stress [16][17][18][19][20], which did not give information about equilibrium nucleation and closure rates potentially relevant for fundamental biological processes.…”