DNA: From rigid base-pairs to semiflexible polymers

The sequence-dependent elasticity of double-helical DNA on a nm length scale can be captured by the rigid base-pair model, whose strains are the relative position and orientation of adjacent base-pairs. Corresponding elastic potentials have been obtained from all-atom MD simulation and from high-resolution structural data. On the scale of a hundred nm, DNA is successfully described by a continuous worm-like chain model with homogeneous elastic properties characterized by a set of four elastic constants, which have been directly measured in single-molecule experiments. We present here a theory that links these experiments on different scales, by systematically coarse-graining the rigid base-pair model for random sequence DNA to an effective worm-like chain description. The average helical geometry of the molecule is exactly taken into account in our approach. We find that the available microscopic parameters sets predict qualitatively similar mesoscopic parameters. The thermal bending and twisting persistence lengths computed from MD data are 42 and 48 nm, respectively. The static persistence lengths are generally much higher, in agreement with cyclization experiments. All microscopic parameter sets predict negative twist-stretch coupling. The variability and anisotropy of bending stiffness in short random chains lead to non-Gaussian bend angle distributions, but become unimportant after two helical turns.Comment: 13 pages, 6 figures, 6 table

Towards a molecular dynamics consensus view of B-DNA flexibility

We present a systematic study of B-DNA flexibility in aqueous solution using long-scale molecular dynamics simulations with the two more recent versions of nucleic acids force fields (CHARMM27 and parmbsc0) using four long duplexes designed to contain several copies of each individual base pair step. Our study highlights some differences between pambsc0 and CHARMM27 families of simulations, but also extensive agreement in the representation of DNA flexibility. We also performed additional simulations with the older AMBER force fields parm94 and parm99, corrected for non-canonical backbone flips. Taken together, the results allow us to draw for the first time a consensus molecular dynamics picture of B-DNA flexibilit

The relative flexibility of B-DNA and A-RNA duplexes: database analysis

An extensive analysis of structural databases is carried out to investigate the relative flexibility of B-DNA and A-RNA duplexes in crystal form. Our results show that the general anisotropic concept of flexibility is not very useful to compare the deformability of B-DNA and A-RNA duplexes, since the flexibility patterns of B-DNA and A-RNA are quite different. In other words, ‘flexibility' is a dangerous word for describing macromolecules, unless it is clearly defined. A few soft essential movements explain most of the natural flexibility of A-RNA, whereas many are necessary for B-DNA. Essential movements occurring in naked B-DNAs are identical to those necessary to deform DNA in DNA-protein complexes, which suggest that evolution has designed DNA-protein complexes so that B-DNA is deformed according to its natural tendency. DNA is generally more flexible, but for some distortions A-RNA is easier to deform. Local stiffness constants obtained for naked B-DNAs and DNA complexes are very close, demonstrating that global distortions in DNA necessary for binding to proteins are the result of the addition of small concerted deformations at the base-pair level. Finally, it is worth noting that in general the picture of the relative deformability of A-RNA and DNA derived from database analysis agrees very well with that derived from state of the art molecular dynamics (MD) simulation

Effect of Bending Anisotropy on the 3D Conformation of Short DNA Loops

The equilibrium three dimensional shape of relatively short loops of DNA is studied using an elastic model that takes into account anisotropy in bending rigidities. Using a reasonable estimate for the anisotropy, it is found that cyclized DNA with lengths that are not integer multiples of the pitch take on nontrivial shapes that involve bending out of planes and formation of kinks. The effect of sequence inhomogeneity on the shape of DNA is addressed, and shown to enhance the geometrical features. These findings could shed some light on the role of DNA conformation in protein--DNA interactions

Macroscopic Dynamics of Complex Metastable Systems: Theory, Algorithms, and Application to B-DNA

This article is a survey of the present state of the transfer operator approach to the effective dynamics of metastable complex systems, and the variety of algorithms associated with it. We introduce new methods, and we emphasize both the conceptional foundations and the concrete application to the conformation dynamics of a biomolecular system. The algorithmic aspects are illustrated by means of several examples of various degrees of complexity, culminating in their application to a full-scale molecular dynamics simulation of a B-DNA oligomer

Geometrical correlations in the nucleosomal DNA conformation and the role of the covalent bonds rigidity

We develop a simple elastic model to study the conformation of DNA in the nucleosome core particle. In this model, the changes in the energy of the covalent bonds that connect the base pairs of each strand of the DNA double helix, as well as the lateral displacements and the rotation of adjacent base pairs are considered. We show that because of the rigidity of the covalent bonds in the sugar-phosphate backbones, the base pair parameters are highly correlated, especially, strong twist-roll-slide correlation in the conformation of the nucleosomal DNA is vividly observed in the calculated results. This simple model succeeds to account for the detailed features of the structure of the nucleosomal DNA, particularly, its more important base pair parameters, roll and slide, in good agreement with the experimental results

Towards a molecular dynamics consensus view of B-DNA flexibility

We present a systematic study of B-DNA flexibility in aqueous solution using long-scale molecular dynamics simulations with the two more recent versions of nucleic acids force fields (CHARMM27 and parmbsc0) using four long duplexes designed to contain several copies of each individual base pair step. Our study highlights some differences between pambsc0 and CHARMM27 families of simulations, but also extensive agreement in the representation of DNA flexibility. We also performed additional simulations with the older AMBER force fields parm94 and parm99, corrected for non-canonical backbone flips. Taken together, the results allow us to draw for the first time a consensus molecular dynamics picture of B-DNA flexibility

A measure of bending in nucleic acids structures applied to A-tract DNA

A method is proposed to measure global bending in DNA and RNA structures. It relies on a properly defined averaging of base-fixed coordinate frames, computes mean frames of suitably chosen groups of bases and uses these mean frames to evaluate bending. The method is applied to DNA A-tracts, known to induce considerable bend to the double helix. We performed atomistic molecular dynamics simulations of sequences containing the A4T4 and T4A4 tracts, in a single copy and in two copies phased with the helical repeat. Various temperature and salt conditions were investigated. Our simulations indicate bending by roughly 10° per A4T4 tract into the minor groove, and an essentially straight structure containing T4A4, in agreement with electrophoretic mobility data. In contrast, we show that the published NMR structures of analogous sequences containing A4T4 and T4A4 tracts are significantly bent into the minor groove for both sequences, although bending is less pronounced for the T4A4 containing sequence. The bending magnitudes obtained by frame averaging are confirmed by the analysis of superhelices composed of repeated tract monomers

Salerno's model of DNA reanalysed: could solitons have biological significance?

We investigate the sequence-dependent behaviour of localised excitations in a toy, nonlinear model of DNA base-pair opening originally proposed by Salerno. Specifically we ask whether ``breather'' solitons could play a role in the facilitated location of promoters by RNA polymerase. In an effective potential formalism, we find excellent correlation between potential minima and {\em Escherichia coli} promoter recognition sites in the T7 bacteriophage genome. Evidence for a similar relationship between phage promoters and downstream coding regions is found and alternative reasons for links between AT richness and transcriptionally-significant sites are discussed. Consideration of the soliton energy of translocation provides a novel dynamical picture of sliding: steep potential gradients correspond to deterministic motion, while ``flat'' regions, corresponding to homogeneous AT or GC content, are governed by random, thermal motion. Finally we demonstrate an interesting equivalence between planar, breather solitons and the helical motion of a sliding protein ``particle'' about a bent DNA axis.Comment: Latex file 20 pages, 5 figures. Manuscript of paper to appear in J. Biol. Phys., accepted 02/09/0

Wringing out DNA

The chiral nature of DNA plays a crucial role in cellular processes. Here we use magnetic tweezers to explore one of the signatures of this chirality, the coupling between stretch and twist deformations. We show that the extension of a stretched DNA molecule increases linearly by 0.42 nm per excess turn applied to the double helix. This result contradicts the intuition that DNA should lengthen as it is unwound and get shorter with overwinding. We then present numerical results of energy minimizations of torsionally restrained DNA that display a behaviour similar to the experimental data and shed light on the molecular details of this surprising effect.Comment: 4 pages revtex4, 4 figure