From rigid base pairs to semiflexible polymers: coarse-graining DNA

DNA supercoiling in bacteria: state of play and challenges from a viewpoint of physics based modeling

DNA supercoiling is central to many fundamental processes of living organisms. Its average level along the chromosome and over time reflects the dynamic equilibrium of opposite activities of topoisomerases, which are required to relax mechanical stresses that are inevitably produced during DNA replication and gene transcription. Supercoiling affects all scales of the spatio-temporal organization of bacterial DNA, from the base pair to the large scale chromosome conformation. Highlighted in vitro and in vivo in the 1960s and 1970s, respectively, the first physical models were proposed concomitantly in order to predict the deformation properties of the double helix. About fifteen years later, polymer physics models demonstrated on larger scales the plectonemic nature and the tree-like organization of supercoiled DNA. Since then, many works have tried to establish a better understanding of the multiple structuring and physiological properties of bacterial DNA in thermodynamic equilibrium and far from equilibrium. The purpose of this essay is to address upcoming challenges by thoroughly exploring the relevance, predictive capacity, and limitations of current physical models, with a specific focus on structural properties beyond the scale of the double helix. We discuss more particularly the problem of DNA conformations, the interplay between DNA supercoiling with gene transcription and DNA replication, its role on nucleoid formation and, finally, the problem of scaling up models. Our primary objective is to foster increased collaboration between physicists and biologists. To achieve this, we have reduced the respective jargon to a minimum and we provide some explanatory background material for the two communities.

Coarse Graining DNA: Symmetry, Nonlocal Elasticity, and Persistence Length

While the behavior of double-stranded DNA at mesoscopic scales is fairly well understood, less is known about its relation to the rich mechanical properties in the base-pair scale, which is crucial, for instance, to understand DNA-protein interactions and the nucleosome diffusion mechanism. Here, by employing the rigid base-pair model, we connect its microscopic parameters to the persistence length. Combined with all-atom molecular dynamic simulations, our scheme identifies relevant couplings between different degrees of freedom at each coarse-graining step. This allows us to clarify how the scale dependence of the elastic moduli is determined in a systematic way encompassing the role of previously unnoticed off-site couplings between deformations with different parity.

Genome Dashboards: Framework and Examples

Genomics is a sequence-based informatics science and a three-dimensional-structure-based material science. However, in practice, most genomics researchers utilize sequence-based informatics approaches or three-dimensional-structure-based material science techniques, not both. This division is, at least in part, the result of historical developments rather than a fundamental necessity. The underlying computational tools, experimental techniques, and theoretical models were developed independently. The primary result presented here is a framework for the unification of informatics- and physics-based data associated with DNA, nucleosomes, and chromatin. The framework is based on the mathematical representation of geometrically exact rods and the generalization of DNA basepair step parameters. Data unification enables researchers to integrate computational, experimental, and theoretical approaches for the study of chromatin biology. The framework can be implemented using model-view-controller design principles, existing genome browsers, and existing molecular visualization tools. We developed a minimal, web-based genome dashboard, G-Dash-min, and applied it to two simple examples to demonstrate the usefulness of data unification and proof of concept. Genome dashboards developed using the framework and design principles presented here are extensible and customizable and are therefore more broadly applicable than the examples presented. We expect a number of purpose-specific genome dashboards to emerge as a novel means of investigating structure-function relationships for genomes that range from basepairs to entire chromosomes and for generating, validating, and testing mechanistic hypotheses.

Encoding and selecting coarse-grain mapping operators with hierarchical graphs

Coarse-grained (CG) molecular dynamics (MD) can simulate systems inaccessible to fine-grained (FG) MD simulations. A CG simulation decreases the degrees of freedom by mapping atoms from an FG representation into agglomerate CG particles. The FG to CG mapping is not unique. Research into systematic selection of these mappings is challenging due to their combinatorial growth with respect to the number of atoms in a molecule. Here we present a method of reducing the total count of mappings by imposing molecular topology and symmetry constraints. The count reduction is illustrated by considering all mappings for nearly 50 000 molecules. The resulting number of mapping operators is still large, so we introduce a novel hierarchical graphical approach which encodes multiple CG mapping operators. The encoding method is demonstrated for methanol and a 14-mer peptide. With the test cases, we show how the encoding can be used for automated selection of reasonable CG mapping operators.

Representation of DNA environment: Spiral staircase distribution function

In the present study, we investigated the local structure of DNA and its environment using a new visualization technique. The spiral staircase distribution function (SSDF) is determined as two-dimensional density distribution of atoms of water and ligands in local reference frames linked with each base pair of poly-DNA molecule, either GC or AT. This property of SSDF provides opportunity to study sequence-specific binding of ions, peptides, and other agents derived from a molecular dynamics computer simulation. The spatial structure of double-stranded DNA environment in water solution containing either Mg²⁺ or Na⁺ ions was investigated using of SSDF. The distributions of ions around GC and AT base pairs are shown separately. It is observed that Mg²⁺ ions interact with DNA atoms by means of the layer of water molecules and penetrate into the major groove only. Na⁺ ions have a direct contact with DNA atoms and penetrate both into the major and minor grooves of DNA. © 2018 Wiley Periodicals, Inc.

The temperature dependence of the helical twist of DNA

DNA is the carrier of all cellular genetic information and increasingly used in nanotechnology. Quantitative understanding and optimization of its functions requires precise experimental characterization and accurate modeling of DNA properties. A defining feature of DNA is its helicity. DNA unwinds with increasing temperature, even for temperatures well below the melting temperature. However, accurate quantitation of DNA unwinding under external forces and a microscopic understanding of the corresponding structural changes are currently lacking. Here we combine single-molecule magnetic tweezers measurements with atomistic molecular dynamics and coarse-grained simulations to obtain a comprehensive view of the temperature dependence of DNA twist. Experimentally, we find that DNA twist changes by ΔTw(T) = (-11.0 ± 1.2)°/(°C·kbp), independent of applied force, in the range of forces where torque-induced melting is negligible. Our atomistic simulations predict ΔTw(T) = (-11.1 ± 0.3)°/(°C·kbp), in quantitative agreement with experiments, and suggest that the untwisting of DNA with temperature is predominantly due to changes in DNA structure for defined backbone substates, while the effects of changes in substate populations are minor. Coarse-grained simulations using the oxDNA framework yield a value of ΔTw(T) = (-6.4 ± 0.2)°/(°C·kbp) in semi-quantitative agreement with experiments.

Structure and conformational dynamics of scaffolded DNA origami nanoparticles

Synthetic DNA is a highly programmable nanoscale material that can be designed to self-assemble into 3D structures that are fully determined by underlying Watson–Crick base pairing. The double crossover (DX) design motif has demonstrated versatility in synthesizing arbitrary DNA nanoparticles on the 5–100 nm scale for diverse applications in biotechnology. Prior computational investigations of these assemblies include all-atom and coarse-grained modeling, but modeling their conformational dynamics remains challenging due to their long relaxation times and associated computational cost. We apply all-atom molecular dynamics and coarse-grained finite element modeling to DX-based nanoparticles to elucidate their fine-scale and global conformational structure and dynamics. We use our coarse-grained model with a set of secondary structural motifs to predict the equilibrium solution structures of 45 DX-based DNA origami nanoparticles including a tetrahedron, octahedron, icosahedron, cuboctahedron and reinforced cube. Coarse-grained models are compared with 3D cryo-electron microscopy density maps for these five DNA nanoparticles and with all-atom molecular dynamics simulations for the tetrahedron and octahedron. Our results elucidate non-intuitive atomic-level structural details of DX-based DNA nanoparticles, and offer a general framework for efficient computational prediction of global and local structural and mechanical properties of DX-based assemblies that are inaccessible to all-atom based models alone.

The "sugar" coarse-grained DNA model

More than 20 coarse-grained (CG) DNA models have been developed for simulating the behavior of this molecule under various conditions, including those required for nanotechnology. However, none of these models reproduces the DNA polymorphism associated with conformational changes in the ribose rings of the DNA backbone. These changes make an essential contribution to the DNA local deformability and provide the possibility of the transition of the DNA double helix from the B-form to the A-form during interactions with biological molecules. We propose a CG representation of the ribose conformational flexibility. We substantiate the choice of the CG sites (six per nucleotide) needed for the "sugar" GC DNA model, and obtain the potentials of the CG interactions between the sites by the "bottom-up" approach using the all-atom AMBER force field. We show that the representation of the ribose flexibility requires one non-harmonic and one three-particle potential, the forms of both the potentials being different from the ones generally used. The model also includes (i) explicit representation of ions (in an implicit solvent) and (ii) sequence dependence. With these features, the sugar CG DNA model reproduces (with the same parameters) both the B- and A- stable forms under corresponding conditions and demonstrates both the A to B and the B to A phase transitions. Graphical Abstract The proposed coarse-grained DNA model allows to reproduce both the B- and A- DNA forms and the transitions between them under corresponding conditions.

Stiffer double-stranded DNA in two-dimensional confinement due to bending anisotropy

Using analytical approach and Monte Carlo (MC) simulations, we study the elastic behavior of the intrinsically twisted elastic ribbons with bending anisotropy, such as double-stranded DNA (dsDNA), in two-dimensional (2D) confinement. We show that, due to the bending anisotropy, the persistence length of dsDNA in 2D conformations is always greater than three-dimensional (3D) conformations. This result is in consistence with the measured values for DNA persistence length in 2D and 3D in equal biological conditions. We also show that in two dimensions, an anisotropic, intrinsically twisted polymer exhibits an implicit twist-bend coupling, which leads to the transient curvature increasing with a half helical turn periodicity along the bent polymer.

Hybrid simulation approach incorporating microscopic interaction along with rigid body degrees of freedom for stacking between base pairs

Stacking interaction between the aromatic heterocyclic bases plays an important role in the double helical structures of nucleic acids. Considering the base as rigid body, there are total of 18 degrees of freedom of a dinucleotide step. Some of these parameters show sequence preferences, indicating that the detailed atomic interactions are important in the stacking. Large variants of non-canonical base pairs have been seen in the crystallographic structures of RNA. However, their stacking preferences are not thoroughly deciphered yet from experimental results. The current theoretical approaches use either the rigid body degrees of freedom where the atomic information are lost or computationally expensive all atom simulations. We have used a hybrid simulation approach incorporating Monte-Carlo Metropolis sampling in the hyperspace of 18 stacking parameters where the interaction energies using AMBER-parm99bsc0 and CHARMM-36 force-fields were calculated from atomic positions. We have also performed stacking energy calculations for structures from Monte-Carlo ensemble by Dispersion corrected density functional theory. The available experimental data with Watson-Crick base pairs are compared to establish the validity of the method. Stacking interaction involving A:U and G:C base pairs with non-canonical G:U base pairs also were calculated and showed that these structures were also sequence dependent. This approach could be useful to generate multiscale modeling of nucleic acids in terms of coarse-grained parameters where the atomic interactions are preserved. This method would also be useful to predict structure and dynamics of different base pair steps containing non Watson-Crick base pairs, as found often in the non-coding RNA structures. © 2015 Wiley Periodicals, Inc. Biopolymers 105: 212-226, 2016.

Explaining the striking difference in twist-stretch coupling between DNA and RNA: A comparative molecular dynamics analysis

Double stranded helical DNA and RNA are flexible molecules that can undergo global conformational fluctuations. Their bending, twisting and stretching deformabilities are of similar magnitude. However, recent single-molecule experiments revealed a striking qualitative difference indicating an opposite sign for the twist-stretch couplings of dsDNA and dsRNA [Lipfert et al. 2014. Proc. Natl. Acad. Sci. U.S.A. 111, 15408] that is not explained by existing models. Employing unconstrained Molecular Dynamics (MD) simulations we are able to reproduce the qualitatively different twist-stretch coupling for dsDNA and dsRNA in semi-quantitative agreement with experiment. Similar results are also found in simulations that include an external torque to induce over- or unwinding of DNA and RNA. Detailed analysis of the helical deformations coupled to twist indicate that the interplay of helical rise, base pair inclination and displacement from the helix axis upon twist changes are responsible for the different twist-stretch correlations. Overwinding of RNA results in more compact conformations with a narrower major groove and consequently reduced helical extension. Overwinding of DNA decreases the size of the minor groove and the resulting positive base pair inclination leads to a slender and more extended helical structure.

Advanced EPR Methods for Studying Conformational Dynamics of Nucleic Acids

Pulsed electron paramagnetic resonance (EPR) spectroscopy has become an important tool for structural characterization of biomolecules allowing measurement of the distances between two paramagnetic spin labels attached to a biomolecule in the 2-8 nm range. In this chapter, we will focus on applications of this approach to investigate tertiary structure elements as well as conformational dynamics of nucleic acid molecules. Both aspects take advantage of using specific spin labels that are rigidly attached to the nucleobases, as they allow obtaining not only the distance but also the relative orientation between both nitroxide moieties with high accuracy. Thus, not only the distance but additionally the three Euler angles between both the nitroxide axis systems and the two polar angles of the interconnecting vector with respect to the nitroxide axis systems can be extracted from a single pair of spin labels. To extract all these parameters independently and unambiguously, a set of multifrequency/multifield pulsed EPR experiments have to be performed. We will describe the experimental procedure as well as newly developed spin labels, which are helpful to disentangle all these parameters, and tools which we have developed to analyze such data sets. The procedures and analyses will be illustrated by examples from our laboratory.

Temperature dependence of the DNA double helix at the nanoscale: structure, elasticity, and fluctuations

Biological organisms exist over a broad temperature range of -15°C to +120°C, where many molecular processes involving DNA depend on the nanoscale properties of the double helix. Here, we present results of extensive molecular dynamics simulations of DNA oligomers at different temperatures. We show that internal basepair conformations are strongly temperature-dependent, particularly in the stretch and opening degrees of freedom whose harmonic fluctuations can be considered the initial steps of the DNA melting pathway. The basepair step elasticity contains a weaker, but detectable, entropic contribution in the roll, tilt, and rise degrees of freedom. To extend the validity of our results to the temperature interval beyond the standard melting transition relevant to extremophiles, we estimate the effects of superhelical stress on the stability of the basepair steps, as computed from the Benham model. We predict that although the average twist decreases with temperature in vitro, the stabilizing external torque in vivo results in an increase of ∼1°/bp (or a superhelical density of Δσ ≃ +0.03) in the interval 0-100°C. In the final step, we show that the experimentally observed apparent bending persistence length of torsionally unconstrained DNA can be calculated from a hybrid model that accounts for the softening of the double helix and the presence of transient denaturation bubbles. Although the latter dominate the behavior close to the melting transition, the inclusion of helix softening is important around standard physiological temperatures.

Coarse-graining DNA for simulations of DNA nanotechnology

To simulate long time and length scale processes involving DNA it is necessary to use a coarse-grained description. Here we provide an overview of different approaches to such coarse-graining, focussing on those at the nucleotide level that allow the self-assembly processes associated with DNA nanotechnology to be studied. OxDNA, our recently-developed coarse-grained DNA model, is particularly suited to this task, and has opened up this field to systematic study by simulations. We illustrate some of the range of DNA nanotechnology systems to which the model is being applied, as well as the insights it can provide into fundamental biophysical properties of DNA.

Effect of 8-oxoguanine on DNA structure and deformability

8-Oxoguanine (oxoG) is an abundant product of oxidative DNA damage. It is removed by repair glycosylases, but exactly how the enzymes recognize oxoG in the large surplus of undamaged bases is not fully understood. The lesion may induce changes in the properties of naked DNA that facilitate the recognition. In this work, we assess the effect of oxoG on DNA structure and mechanical deformability. We performed extensive unrestrained, atomic resolution molecular dynamics simulations to parametrize a nonlocal, rigid base mechanical model of DNA. Our data indicate that oxoG induces unwinding of the base pair step at the 5'-side of the lesion. This brings the damaged DNA closer to its conformation in the initial complex with bacterial glycosylase MutM. The untwisting is partially caused by different BII substate populations and is further enhanced by the base-sugar repulsion within oxoG. On the other hand, our analysis shows that damaged and undamaged DNA have very similar harmonic stiffness. These results suggest an indirect readout component of the MutM-DNA initial complex formation. They also help one to understand the effect of oxoG on the formation of nucleosomes and looped gene regulatory complexes.

Confinement dynamics of a semiflexible chain inside nano-spheres

We study the conformations of a semiflexible chain, confined in nano-scaled spherical cavities, under two distinct processes of confinement. Radial contraction and packaging are employed as two confining procedures. The former method is performed by gradually decreasing the diameter of a spherical shell which envelopes a confined chain. The latter procedure is carried out by injecting the chain inside a spherical shell through a hole on the shell surface. The chain is modeled with a rigid body molecular dynamics simulation and its parameters are adjusted to DNA base-pair elasticity. Directional order parameter is employed to analyze and compare the confined chain and the conformations of the chain for two different sizes of the spheres are studied in both procedures. It is shown that for the confined chains in the sphere sizes of our study, they appear in spiral or tennis-ball structures, and the tennis-ball structure is more likely to be observed in more compact confinements. Our results also show that the dynamical procedure of confinement and the rate of the confinement are influential parameters of the structure of the chain inside spherical cavities.

Ab initio determination of coarse-grained interactions in double-stranded DNA

We derive the coarse-grained interactions between DNA nucleotides from ab initio total-energy calculations based on density functional theory (DFT). The interactions take into account base and sequence specificity, and are decomposed into physically distinct contributions that include hydrogen bonding, stacking interactions, backbone, and backbone-base interactions. The interaction energies of each contribution are calculated from DFT for a wide range of configurations and are fitted by simple analytical expressions for use in the coarse-grained model, which reduces each nucleotide into two sites. This model is not derived from experimental data, yet it successfully reproduces the stable B-DNA structure and gives good predictions for the persistence length. It may be used to realistically probe dynamics of DNA strands in various environments at the μs time scale and the μm length scale.

Formation and analysis of topographical domains between lipid membranes tethered by DNA hybrids of different lengths

We recently described a strategy to prepare DNA-tethered lipid membranes either to fixed DNA on a surface or to DNA displayed on a supported bilayer [Boxer et al., J. Struct. Biol., 2009, 168, 190; Boxer et al., Langmuir, 2011, 27, 5492]. With the latter system, the DNA hybrids are laterally mobile; when orthogonal sense-antisense pairs of different lengths are used, the DNA hybrids segregate by height and the tethered membrane deforms to accommodate the height difference. This architecture is particularly useful for modelling interactions between membranes mediated by molecular recognition and resembles cell-to-cell junctions. The length, affinity and population of the DNA hybrids between the membranes are completely controllable. Interesting patterns of height segregation are observed by fluorescence interference contrast microscopy. Diverse behavior is observed in the segregation and pattern forming process and possible mechanisms are discussed. This model system captures some of the essential physics of synapse formation and is a step towards understanding lipid membrane behaviour in cell-to-cell junctions.

Exploring polymorphisms in B-DNA helical conformations

The traditional mesoscopic paradigm represents DNA as a series of base-pair steps whose energy response to equilibrium perturbations is elastic, with harmonic oscillations (defining local stiffness) around a single equilibrium conformation. In addition, base sequence effects are often analysed as a succession of independent XpY base-pair steps (i.e. a nearest-neighbour (NN) model with only 10 unique cases). Unfortunately, recent massive simulations carried out by the ABC consortium suggest that the real picture of DNA flexibility may be much more complex. The paradigm of DNA flexibility therefore needs to be revisited. In this article, we explore in detail one of the most obvious violations of the elastic NN model of flexibility: the bimodal distributions of some helical parameters. We perform here an in-depth statistical analysis of a very large set of MD trajectories and also of experimental structures, which lead to very solid evidence of bimodality. We then suggest ways to improve mesoscopic models to account for this deviation from the elastic regime.

Multiscale modeling of double-helical DNA and RNA: a unification through Lie groups

Several different mechanical models of double-helical nucleic-acid structures that have been presented in the literature are reviewed here together with a new analysis method that provides a reconciliation between these disparate models. In all cases, terminology and basic results from the theory of Lie groups are used to describe rigid-body motions in a coordinate-free way, and when necessary, coordinates are introduced in a way in which simple equations result. We consider double-helical DNAs and RNAs which, in their unstressed referential state, have backbones that are either straight, slightly precurved, or bent by the action of a protein or other bound molecule. At the coarsest level, we consider worm-like chains with anisotropic bending stiffness. Then, we show how bi-rod models converge to this for sufficiently long filament lengths. At a finer level, we examine elastic networks of rigid bases and show how these relate to the coarser models. Finally, we show how results from molecular dynamics simulation at full atomic resolution (which is the finest scale considered here) and AFM experimental measurements (which is at the coarsest scale) relate to these models.

Structure and mechanical properties of the ribosomal L1 stalk three-way junction

The L1 stalk is a key mobile element of the large ribosomal subunit which interacts with tRNA during translocation. Here, we investigate the structure and mechanical properties of the rRNA H76/H75/H79 three-way junction at the base of the L1 stalk from four different prokaryotic organisms. We propose a coarse-grained elastic model and parameterize it using large-scale atomistic molecular dynamics simulations. Global properties of the junction are well described by a model in which the H76 helix is represented by a straight, isotropically flexible elastic rod, while the junction core is represented by an isotropically flexible spherical hinge. Both the core and the helix contribute substantially to the overall H76 bending fluctuations. The presence of wobble pairs in H76 does not induce any increased flexibility or anisotropy to the helix. The half-closed conformation of the L1 stalk seems to be accessible by thermal fluctuations of the junction itself, without any long-range allosteric effects. Bending fluctuations of H76 with a bulge introduced in it suggest a rationale for the precise position of the bulge in eukaryotes. Our elastic model can be generalized to other RNA junctions found in biological systems or in nanotechnology.

Modelling Nucleic Acid Structure and Flexibility: From Atomic to Mesoscopic Scale

This chapter surveys some of the recent developments in coarse-grained modelling of nucleic acids. We first discuss models based on pseudoatoms, effective spherical particles representing groups of atoms. A major part of the chapter is devoted to models in which bases or base pairs are represented as independent, interacting rigid bodies. Two popular definitions of internal coordinates, as implemented in the programs 3DNA and Curves+, are outlined from a common perspective. Recently developed rigid base and basepair models with nonlocal quadratic interactions are presented. A statistical mechanical description of the models on their full phase space yields exact relations between model parameters and expected values of some state functions. We estimated shape and stiffness parameters for nonlocal rigid base and basepair models of a DNA oligomer containing A-tract. The parameterization is based on atomic-resolution molecular dynamics simulation data. We found that the rigid base model is consistent with a local interaction pattern, while interactions in the rigid basepair model are visibly non-local, in agreement with earlier findings. Differences in shape and stiffness parameters obtained using Curves+ and 3DNA coordinates are found to be small for structures within the B-DNA family. Anharmonic effects, coarser models, and other approaches to describe nucleic acid structure and flexibility are discussed.

From crystal and NMR structures, footprints and cryo-electron-micrographs to large and soft structures: nanoscale modeling of the nucleosomal stem

The interaction of histone H1 with linker DNA results in the formation of the nucleosomal stem structure, with considerable influence on chromatin organization. In a recent paper [Syed,S.H., Goutte-Gattat,D., Becker,N., Meyer,S., Shukla,M.S., Hayes,J.J., Everaers,R., Angelov,D., Bednar,J. and Dimitrov,S. (2010) Single-base resolution mapping of H1-nucleosome interactions and 3D organization of the nucleosome. Proc. Natl Acad. Sci. USA, 107, 9620-9625], we published results of biochemical footprinting and cryo-electron-micrographs of reconstituted mono-, di- and tri-nucleosomes, for H1 variants with different lengths of the cationic C-terminus. Here, we present a detailed account of the analysis of the experimental data and we include thermal fluctuations into our nano-scale model of the stem structure. By combining (i) crystal and NMR structures of the nucleosome core particle and H1, (ii) the known nano-scale structure and elasticity of DNA, (iii) footprinting information on the location of protected sites on the DNA backbone and (iv) cryo-electron micrographs of reconstituted tri-nucleosomes, we arrive at a description of a polymorphic, hierarchically organized stem with a typical length of 20 ± 2 base pairs. A comparison to linker conformations inferred for poly-601 fibers with different linker lengths suggests, that intra-stem interactions stabilize and facilitate the formation of dense chromatin fibers.

Heat conductivity of DNA double helix

Thermal conductivity of isolated single molecule DNA fragments is of importance for nanotechnology, but has not yet been measured experimentally. Theoretical estimates based on simplified (1D) models predict anomalously high thermal conductivity. To investigate thermal properties of single molecule DNA we have developed a 3D coarse-grained (CG) model that retains the realism of the full all-atom description, but is significantly more efficient. Within the proposed model each nucleotide is represented by 6 particles or grains; the grains interact via effective potentials inferred from classical molecular dynamics (MD) trajectories based on a well-established all-atom potential function. Comparisons of 10 ns long MD trajectories between the CG and the corresponding all-atom model show similar root-mean-square deviations from the canonical B-form DNA, and similar structural fluctuations. At the same time, the CG model is 10 to 100 times faster depending on the length of the DNA fragment in the simulation. Analysis of dispersion curves derived from the CG model yields longitudinal sound velocity and torsional stiffness in close agreement with existing experiments. The computational efficiency of the CG model makes it possible to calculate thermal conductivity of a single DNA molecule not yet available experimentally. For a uniform (polyG-polyC) DNA, the estimated conductivity coefficient is 0.3 W/mK which is half the value of thermal conductivity for water. This result is in stark contrast with estimates of thermal conductivity for simplified, effectively 1D chains ("beads on a spring") that predict anomalous (infinite) thermal conductivity. Thus, full 3D character of DNA double-helix retained in the proposed model appears to be essential for describing its thermal properties at a single molecule level.

A Coarse Grained Model for Atomic-Detailed DNA Simulations with Explicit Electrostatics

Coarse-grain (CG) techniques allow considerable extension of the accessible size and time scales in simulations of biological systems. Although many CG representations are available for the most common biomacromolecules, very few have been reported for nucleic acids. Here, we present a CG model for molecular dynamics simulations of DNA on the multi-microsecond time scale. Our model maps the complexity of each nucleotide onto six effective superatoms keeping the "chemical sense" of specific Watson-Crick recognition. Molecular interactions are evaluated using a classical Hamiltonian with explicit electrostatics calculated under the framework of the generalized Born approach. This CG representation is able to accurately reproduce experimental structures, breathing dynamics, and conformational transitions from the A to the B form in double helical fragments. The model achieves a good qualitative reproduction of temperature-driven melting and its dependence on size, ionic strength, and sequence specificity. Reconstruction of atomistic models from CG trajectories give remarkable agreement with structural, dynamic, and energetic features obtained from fully atomistic simulation, opening the possibility to acquire nearly atomic detail data from CG trajectories.

Comment on "Remeasuring the double helix"

Mathew-Fenn et al. (Reports, 17 October 2008, p. 446) reported unexpected distance fluctuations in short end-labeled DNA constructs and interpreted them as evidence for cooperative DNA stretching modes. We show that when accounting for a subtle linker leverage effect, their data can be understood within standard noncooperative DNA elasticity.

Steering chiral swimmers along noisy helical paths

Chemotaxis along helical paths towards a target releasing a chemoattractant is found in sperm cells and many microorganisms. We discuss the stochastic differential geometry of the noisy helical swimming path of a chiral swimmer. A chiral swimmer equipped with a simple feedback system can navigate in a concentration gradient of chemoattractant. We derive an effective equation for the alignment of helical paths with a concentration gradient which is related to the alignment of a dipole in an external field and discuss the chemotaxis index.

Asymmetric elastic rod model for DNA

In this paper we consider the anharmonic corrections to the anisotropic elastic rod model for DNA. Our model accounts for the difference between the bending energies of positive and negative rolls, which comes from the asymmetric structure of the DNA molecule. We will show that the model can explain the high flexibility of DNA at small length scales, as well as kink formation at high deformation limit.

DNA nanomechanics in the nucleosome

The sequence-dependent mechanics of DNA-histone binding are essential for nucleosome positioning and mobility. Here we reanalyze nucleosome crystal structures in terms of the well-characterized base-pair scale DNA elasticity, extracting the forces and torques acting on all bound DNA base pairs. We find that the strongest forces follow a characteristic repeating pattern that recovers the 12 known DNA backbone-histone contact sites. DNA twist defects and histone point mutations modify this pattern in interpretable ways. Additional, irregular forces between contact sites reveal histone tail-DNA interactions, whereas requiring the absence of external forces leads to a structural refinement of linker DNA. Based on these observations, we propose a simple, structure-based mechanical model of the nucleosome that is able to explain the placement of DNA twist defects in 146 base-pair nucleosomes and allows an estimate of the elastic energy spectrum of nucleosome twist defect states.

Search along persistent random walks

Optimal search strategies and their implementations in biological systems are a subject of active research. Here we study a search problem which is motivated by the hunt of sperm cells for the egg. We ask for the probability for an active swimmer to find a target under the condition that the swimmer starts at a certain distance from the target. We find that success probability is maximal for a certain level of fluctuations characterized by the persistence length of the swimming path of the swimmer. We derive a scaling law for the optimal persistence length as a function of the initial target distance and search time by mapping the search on a polymer physics problem.

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.