Sequence-dependent motions of DNA: a normal mode analysis at the base-pair level

Temperature-dependent elasticity of DNA, RNA, and hybrid double helices

Nucleic acid double helices in their DNA, RNA, and DNA-RNA hybrid form play a fundamental role in biology and are main building blocks of artificial nanostructures, but how their properties depend on temperature remains poorly understood. Here, we report thermal dependence of dynamic bending persistence length, twist rigidity, stretch modulus, and twist-stretch coupling for DNA, RNA, and hybrid duplexes between 7°C and 47°C. The results are based on all-atom molecular dynamics simulations using different force field parameterizations. We first demonstrate that unrestrained molecular dynamics can reproduce experimentally known mechanical properties of the duplexes at room temperature. Beyond experimentally known features, we also infer the twist rigidity and twist-stretch coupling of the hybrid duplex. As for the temperature dependence, we found that increasing temperature softens all the duplexes with respect to bending, twisting, and stretching. The relative decrease of the stretch moduli is 0.003-0.004/°C, similar for all the duplex variants despite their very different stretching stiffness, whereas RNA twist stiffness decreases by 0.003/°C, and smaller values are found for the other elastic moduli. The twist-stretch couplings are nearly unaffected by temperature. The stretching, bending, and twisting stiffness all include an important entropic component. Relation of our results to the two-state model of DNA flexibility is discussed. Our work provides temperature-dependent elasticity of nucleic acid duplexes at the microsecond scale relevant for initial stages of protein binding.

A perspective on the molecular simulation of DNA from structural and functional aspects

As genetic material, DNA not only carries genetic information by sequence, but also affects biological functions ranging from base modification to replication, transcription and gene regulation through its structural and dynamic properties and variations. The motion and structural properties of DNA involved in related biological processes are also multi-scale, ranging from single base flipping to local DNA deformation, TF binding, G-quadruplex and i-motif formation, TAD establishment, compartmentalization and even chromosome territory formation, just to name a few. The sequence-dependent physical properties of DNA play vital role in all these events, and thus it is interesting to examine how simple sequence information affects DNA and the formation of the chromatin structure in these different hierarchical orders. Accordingly, molecular simulations can provide atomistic details of interactions and conformational dynamics involved in different biological processes of DNA, including those inaccessible by current experimental methods. In this perspective, which is mainly based on our recent studies, we provide a brief overview of the atomistic simulations on how the hierarchical structure and dynamics of DNA can be influenced by its sequences, base modifications, environmental factors and protein binding in the context of the protein-DNA interactions, gene regulation and structural organization of chromatin. We try to connect the DNA sequence, the hierarchical structures of DNA and gene regulation.

On the length scale dependence of DNA conformational change under local perturbation

Conformational change of a DNA molecule is frequently observed in multiple biological processes and has been modeled using a chain of strongly coupled oscillators with a nonlinear bistable potential. While the mechanism and properties of conformational change in the model have been investigated and several reduced order models developed, the conformational dynamics as a function of the length of the oscillator chain is relatively less clear. To address this, we use a modified Lindstedt-Poincare method and numerical computations. We calculate a perturbation expansion of the frequency of the model's nonzero modes, finding that approximating these modes with their unperturbed dynamics, as in a previous reduced order model, may not hold when the length of the DNA model increases. We investigate the conformational change to the local perturbation in models of varying lengths, finding that for the chosen input and parameters, there are two regions of DNA length in the model - first, where the minimum energy required to undergo the conformational change increases with the DNA length; and second, where it is almost independent of the length of the DNA model. We analyze the conformational change in these models by adding randomness to the local perturbation, finding that the tendency of the system to remain in a stable conformation against random perturbation decreases with increase in DNA length. These results should help to understand the role of the length of a DNA molecule in influencing its conformational dynamics.

Heterochromatin protein 1 (HP1): interactions with itself and chromatin components

Isoforms of heterochromatin protein 1 (HP1) have been known to perform a multitude of functions ranging from gene silencing, gene activation to cell cycle regulation, and cell differentiation. This functional diversity arises from the dissimilarities coded in protein sequence which confers different biophysical and biochemical properties to individual structural elements of HP1 and thereby different behavior and interaction patterns. Hence, an understanding of various interactions of the structural elements of HP1 will be of utmost importance to better elucidate chromatin dynamics in its presence. In this review, we have gathered available information about interactions of HP1 both within and with itself as well as with chromatin elements. Also, the possible implications of these interactions are discussed.

Structural Studies of Overlapping Dinucleosomes in Solution

An overlapping dinucleosome (OLDN) is a structure composed of one hexasome and one octasome and appears to be formed through nucleosome collision promoted by nucleosome remodeling factor(s). In this study, the solution structure of the OLDN was investigated through the integration of small-angle x-ray and neutron scattering (SAXS and SANS, respectively), computer modeling, and molecular dynamics simulations. Starting from the crystal structure, we generated a conformational ensemble based on normal mode analysis and searched for the conformations that reproduced the SAXS and SANS scattering curves well. We found that inclusion of histone tails, which are not observed in the crystal structure, greatly improved model quality. The obtained structural models suggest that OLDNs adopt a variety of conformations stabilized by histone tails situated at the interface between the hexasome and octasome, simultaneously binding to both the hexasomal and octasomal DNA. In addition, our models define a possible direction for the conformational changes or dynamics, which may provide important information that furthers our understanding of the role of chromatin dynamics in gene regulation.

Molecular Modeling Applied to Nucleic Acid-Based Molecule Development

Molecular modeling by means of docking and molecular dynamics (MD) has become an integral part of early drug discovery projects, enabling the screening and enrichment of large libraries of small molecules. In the past decades, special emphasis was drawn to nucleic acid (NA)-based molecules in the fields of therapy, diagnosis, and drug delivery. Research has increased dramatically with the advent of the SELEX (systematic evolution of ligands by exponential enrichment) technique, which results in single-stranded DNA or RNA sequences that bind with high affinity and specificity to their targets. Herein, we discuss the role and contribution of docking and MD to the development and optimization of new nucleic acid-based molecules. This review focuses on the different approaches currently available for molecular modeling applied to NA interaction with proteins. We discuss topics ranging from structure prediction to docking and MD, highlighting their main advantages and limitations and the influence of flexibility on their calculations.

The Duplexing of the Genetic Code and Sequence-Dependent DNA Geometry

It is well known that sequences of bases in DNA are translated into sequences of amino acids in cells via the genetic code. More recently, it has been discovered that the sequence of DNA bases also influences the geometry and deformability of the DNA. These two correspondences represent a naturally arising example of duplexed codes, providing two different ways of interpreting the same DNA sequence. This paper will set up the notation and basic results necessary to mathematically investigate the relationship between these two natural DNA codes. It then undertakes two very different such investigations: one graphical approach based only on expected values and another analytic approach incorporating the deformability of the DNA molecule and approximating the mutual information of the two codes. Special emphasis is paid to whether there is evidence that pressure to maximize the duplexing efficiency influenced the evolution of the genetic code. Disappointingly, the results fail to support the hypothesis that the genetic code was influenced in this way. In fact, applying both methods to samples of realistic alternative genetic codes shows that the duplexing of the genetic code found in nature is just slightly less efficient than average. The implications of this negative result are considered in the final section of the paper.

Dynamics of physiologically relevant noncanonical DNA structures: an overview from experimental and theoretical studies

DNA is a complex molecule with phenomenal inherent plasticity and the ability to form different hydrogen bonding patterns of varying stabilities. These properties enable DNA to attain a variety of structural and conformational polymorphic forms. Structurally, DNA can exist in single-stranded form or as higher-order structures, which include the canonical double helix as well as the noncanonical duplex, triplex and quadruplex species. Each of these structural forms in turn encompasses an ensemble of dynamically heterogeneous conformers depending on the sequence composition and environmental context. In vivo, the widely populated canonical B-DNA attains these noncanonical polymorphs during important cellular processes. While several investigations have focused on the structure of these noncanonical DNA, studying their dynamics has remained nontrivial. Here, we outline findings from some recent advanced experimental and molecular simulation techniques that have significantly contributed toward understanding the complex dynamics of physiologically relevant noncanonical forms of DNA.

Kinetic theory for DNA melting with vibrational entropy

By treating DNA as a vibrating nonlinear lattice, an activated kinetic theory for DNA melting is developed to capture the breakage of the hydrogen bonds and subsequent softening of torsional and bending vibration modes. With a coarse-grained lattice model, we identify a key bending mode with GHz frequency that replaces the hydrogen vibration modes as the dominant out-of-phase phonon vibration at the transition state. By associating its bending modulus to a universal in-phase bending vibration modulus at equilibrium, we can hence estimate the entropic change in the out-of-phase vibration from near-equilibrium all-atom simulations. This and estimates of torsional and bending entropy changes lead to the first predictive and sequence-dependent theory with good quantitative agreement with experimental data for the activation energy of melting of short DNA molecules without intermediate hairpin structures.

Evidence of protein-free homology recognition in magnetic bead force-extension experiments

Earlier theoretical studies have proposed that the homology-dependent pairing of large tracts of dsDNA may be due to physical interactions between homologous regions. Such interactions could contribute to the sequence-dependent pairing of chromosome regions that may occur in the presence or the absence of double-strand breaks. Several experiments have indicated the recognition of homologous sequences in pure electrolytic solutions without proteins. Here, we report single-molecule force experiments with a designed 60 kb long dsDNA construct; one end attached to a solid surface and the other end to a magnetic bead. The 60 kb constructs contain two 10 kb long homologous tracts oriented head to head, so that their sequences match if the two tracts fold on each other. The distance between the bead and the surface is measured as a function of the force applied to the bead. At low forces, the construct molecules extend substantially less than normal, control dsDNA, indicating the existence of preferential interaction between the homologous regions. The force increase causes no abrupt but continuous unfolding of the paired homologous regions. Simple semi-phenomenological models of the unfolding mechanics are proposed, and their predictions are compared with the data.

Normal-Mode Analysis of Circular DNA at the Base-Pair Level. 1. Comparison of Computed Motions with the Predicted Behavior of an Ideal Elastic Rod

We have extended a newly developed approach to study the low-frequency normal modes of mesoscopic fragments of linear DNA in order to investigate the dynamics of closed circular molecules of comparable size, i.e., a few hundred base pairs. We have added restraint energy terms and a global minimization step to treat the more complicated, spatially constrained duplex in terms of the intrinsic conformation and flexibility of the constituent base-pair "step" parameters. Initial application of the methodology to the normal modes of an ideal closed circular DNA molecule [Formula: see text] which is naturally straight in its relaxed open linear state, inextensible, and capable of isotropic bending and independent twisting at the base-pair level [Formula: see text] matches theoretical predictions of elastic rod dynamics. The energy-optimized closed circular states and the types of low frequency motions follow expected behavior, with (1) uniform twist density and uniform energy density in the minimum energy state; (2) a near-zero frequency torsional mode with "free" rotation about the global helical axis; (3) higher-order torsional modes accompanied by global rocking motions and pure in-plane and out-of-plane bending motions in the torsionally relaxed circle; and (4) mixed modes of bending when the chain is supercoiled (over- or undertwisted). Furthermore, the computed changes in normal-mode frequencies with imposed supercoiling or with variation of chain length are virtually identical to theoretically predicted values.

Simple Elastic Network Models for Exhaustive Analysis of Long Double-Stranded DNA Dynamics with Sequence Geometry Dependence

Simple elastic network models of DNA were developed to reveal the structure-dynamics relationships for several nucleotide sequences. First, we propose a simple all-atom elastic network model of DNA that can explain the profiles of temperature factors for several crystal structures of DNA. Second, we propose a coarse-grained elastic network model of DNA, where each nucleotide is described only by one node. This model could effectively reproduce the detailed dynamics obtained with the all-atom elastic network model according to the sequence-dependent geometry. Through normal-mode analysis for the coarse-grained elastic network model, we exhaustively analyzed the dynamic features of a large number of long DNA sequences, approximately ∼150 bp in length. These analyses revealed positive correlations between the nucleosome-forming abilities and the inter-strand fluctuation strength of double-stranded DNA for several DNA sequences.

DNA, flexibly flexible

Investigators have constructed dsDNA molecules with several different base modifications and have characterized their bending and twisting flexibilities using atomic force microscopy, DNA ring closure, and single-molecule force spectroscopy with optical tweezers. The three methods provide persistence length measurements that agree semiquantitatively, and they show that the persistence length is surprisingly similar for all of the modified DNAs. The circular dichroism spectra of modified DNAs differ substantially. Simple explanations based on base stacking strength, polymer charge, or groove occupancy by functional groups cannot explain the results, which will guide further high-resolution theory and experiments.

Playing the notes of DNA with light: extremely high frequency nanomechanical oscillations

We use a double nanohole (DNH) optical tweezer with two trapping lasers beating to excite the vibrational modes of single-stranded DNA (ssDNA) fragments in the extremely high frequency range. We find the resonant vibration frequency of a 20 base ssDNA to be 40 GHz. We show that the change in the resonant frequency for different lengths of the DNA strand is in good agreement with one dimensional lattice vibration theory. Thus the DNH tweezer system could distinguish between different lengths of DNA strands with resolution down to a few bases. By varying the base sequence and length, it is possible to adjust the resonance frequency vibration spectrum. The technique shows the potential for use in sequencing applications if we can improve the resolution of the present system to detect changes in resonant frequency for a single base change in a given sequence. The technique is single-molecule and label-free as compared to the existing methods used for DNA characterization like gel electrophoresis.

Blind predictions of DNA and RNA tweezers experiments with force and torque

Single-molecule tweezers measurements of double-stranded nucleic acids (dsDNA and dsRNA) provide unprecedented opportunities to dissect how these fundamental molecules respond to forces and torques analogous to those applied by topoisomerases, viral capsids, and other biological partners. However, tweezers data are still most commonly interpreted post facto in the framework of simple analytical models. Testing falsifiable predictions of state-of-the-art nucleic acid models would be more illuminating but has not been performed. Here we describe a blind challenge in which numerical predictions of nucleic acid mechanical properties were compared to experimental data obtained recently for dsRNA under applied force and torque. The predictions were enabled by the HelixMC package, first presented in this paper. HelixMC advances crystallography-derived base-pair level models (BPLMs) to simulate kilobase-length dsDNAs and dsRNAs under external forces and torques, including their global linking numbers. These calculations recovered the experimental bending persistence length of dsRNA within the error of the simulations and accurately predicted that dsRNA's “spring-like” conformation would give a two-fold decrease of stretch modulus relative to dsDNA. Further blind predictions of helix torsional properties, however, exposed inaccuracies in current BPLM theory, including three-fold discrepancies in torsional persistence length at the high force limit and the incorrect sign of dsRNA link-extension (twist-stretch) coupling. Beyond these experiments, HelixMC predicted that ‘nucleosome-excluding’ poly(A)/poly(T) is at least two-fold stiffer than random-sequence dsDNA in bending, stretching, and torsional behaviors; Z-DNA to be at least three-fold stiffer than random-sequence dsDNA, with a near-zero link-extension coupling; and non-negligible effects from base pair step correlations. We propose that experimentally testing these predictions should be powerful next steps for understanding the flexibility of dsDNA and dsRNA in sequence contexts and under mechanical stresses relevant to their biology.

DNA and RNA are fundamental molecules in the central dogma of molecular biology. Many biological behaviors of double-stranded DNA and RNA – including transcription/translation by proteins and packaging into compact structures – depend on their ability to flex and twist. Single-molecule tweezers now provide accurate mechanical measurements of DNA and RNA helices under force and torque but have not been used to rigorously falsify and thereby advance computational models. Here we present the first such blind challenge, involving recent dsRNA tweezers data that were kept hidden from modelers and a new HelixMC toolkit that resolves challenges in simulating long double helices from base-pair level models. The predictions gave excellent agreement with bending and stretching measurements of dsRNA but failed to recover twisting properties, pinpointing a critical area of future investigation. HelixMC also predicted that poly(A)/poly(T) and Z-DNA–biologically important variants whose elastic responses have not been studied with tweezers–will have distinct mechanical properties. These results open a route to iteratively falsifying and refining computational models of long nucleic acid helices, as is necessary for attaining a predictive understanding of their biological behaviors.

Atomistic account of structural and dynamical changes induced by small binders in the double helix of a short DNA

Nucleic acids are flexible molecules and their dynamical properties play a key role in molecular recognition events. Small binders interacting with DNA fragments induce both structural and dynamical changes in the double helix. We study the dynamics of a DNA dodecamer and of its complexes with Hoechst 33258, which is a minor groove binder, and with the ethidium cation, which is an intercalator, by molecular dynamics simulation. The thermodynamics of DNA-drug interaction is evaluated in connection with the structure and the dynamics of the resulting complexes. We identify and characterize the relevant changes in the configurational distribution of the DNA helix and relate them to the corresponding entropic contributions to the binding free energy. The binder Hoechst locks the breathing motion of the minor groove inducing a reduction of the configurational entropy of the helix, which amounts to 20 kcal mol(-1). In contrast, intercalations with the ethidium cation enhance the flexibility of the double helix. We show that the balance between the energy required to deform the helix for the intercalation and the gain in configurational entropy is the origin of cooperativity in the binding of a second ethidium and of anti-cooperativity in the binding of a third one. The results of our study provide an understanding of the relation between structure, dynamics and energetics in the interaction between DNA fragments and small binders, highlighting the role of dynamical changes and consequent variation of the configurational entropy of the DNA double helix for both types of binders.

Twenty-five years of nucleic acid simulations

We present a brief, and largely personal, history of computer simulations of DNA and RNA oligonucleotides, with an emphasis on duplex structures and the Amber force fields. Both explicit and implicit solvent models are described, and methods for estimating structures, thermodynamics and mechanical properties of duplexes are illustrated. This overview, covering about two decades of work, provides a perspective for a discussion of prospects and obstacles for future simulations of RNA and DNA.

Conformational changes in DNA-binding proteins: relationships with precomplex features and contributions to specificity and stability

Both Proteins and DNA undergo conformational changes in order to form functional complexes and also to facilitate interactions with other molecules. These changes have direct implications for the stability and specificity of the complex, as well as the cooperativity of interactions between multiple entities. In this work, we have extensively analyzed conformational changes in DNA-binding proteins by superimposing DNA-bound and unbound pairs of protein structures in a curated database of 90 proteins. We manually examined each of these pairs, unified the authors' annotations, and summarized our observations by classifying conformational changes into six structural categories. We explored a relationship between conformational changes and functional classes, binding motifs, target specificity, biophysical features of unbound proteins, and stability of the complex. In addition, we have also investigated the degree to which the intrinsic flexibility can explain conformational changes in a subset of 52 proteins with high quality coordinate data. Our results indicate that conformational changes in DNA-binding proteins contribute significantly to both the stability of the complex and the specificity of targets recognized by them. We also conclude that most conformational changes occur in proteins interacting with specific DNA targets, even though unbound protein structures may have sufficient information to interact with DNA in a nonspecific manner.

Twenty-five years of nucleic acid simulations

We present a brief, and largely personal, history of computer simulations of DNA and RNA oligonucleotides, with an emphasis on duplex structures and the Amber force fields. Both explicit and implicit solvent models are described, and methods for estimating structures, thermodynamics and mechanical properties of duplexes are illustrated. This overview, covering about two decades of work, provides a perspective for a discussion of prospects and obstacles for future simulations of RNA and DNA.

Structural ensemble and microscopic elasticity of freely diffusing DNA by direct measurement of fluctuations

Precisely measuring the ensemble of conformers that a macromolecule populates in solution is highly challenging. Thus, it has been difficult to confirm or falsify the predictions of nanometer-scale dynamical modeling. Here, we apply an X-ray interferometry technique to probe the solution structure and fluctuations of B-form DNA on a length scale comparable to a protein-binding site. We determine an extensive set of intrahelix distance distributions between pairs of probes placed at distinct points on the surface of the DNA duplex. The distributions of measured distances reveal the nature and extent of the thermally driven mechanical deformations of the helix. We describe these deformations in terms of elastic constants, as is common for DNA and other polymers. The average solution structure and microscopic elasticity measured by X-ray interferometry are in striking agreement with values derived from DNA-protein crystal structures and measured by force spectroscopy, with one exception. The observed microscopic torsional rigidity of DNA is much lower than is measured by single-molecule twisting experiments, suggesting that torsional rigidity increases when DNA is stretched. Looking forward, molecular-level interferometry can provide a general tool for characterizing solution-phase structural ensembles.

RNA 3D structure prediction by using a coarse-grained model and experimental data

RNAs form complex secondary and three-dimensional structures, and their biological functions highly rely on their structures and dynamics. Here we developed a general coarse-grained framework for RNA 3D structure prediction. A new, hybrid coarse-grained model that explicitly describes the electrostatics and hydrogen-bond interactions has been constructed based on experimental structural statistics. With the simulated annealing simulation protocol, several RNAs of less than 30-nt were folded to within 4.0 Å of the native structures. In addition, with limited restraints on Watson-Crick basepairing based on the data from NMR spectroscopy and small-angle X-ray scattering (SAXS) information, the current model was able to characterize the complex tertiary structures of large size RNAs, such as 5S ribosome and U2/U6 snRNA. We also demonstrated that the pseudoknot structure was better captured when the coordinating Mg(2+) cations and limited basepairing restraints were included. The accuracy of our model has been compared favorably with other RNA structure prediction methods presented in the previous study of RNA-Puzzles. Therefore the coarse-grained model presented here offers a unique approach for accurate prediction and modeling of RNA structures.

The ABCs of molecular dynamics simulations on B-DNA, circa 2012

This article provides a retrospective on the ABC initiative in the area of all-atom molecular dynamics (MD) simulations including explicit solvent on all tetranucleotide steps of duplex B-form DNA duplex, ca. 2012. The ABC consortium has completed two phases of simulations, the most current being a set of 50-100 trajectories based on the AMBER ff99 force field together with the parmbsc0 modification. Some general perspectives on the field of MD on DNA and sequence effects on DNA structure are provided, followed by an overview our MD results, including a detailed comparison of the ff99/parmbsc0 results with crystal and NMR structures available for d(CGCGAATTCGCG). Some projects inspired by or related to the ABC initiative and database are also reviewed, including methods for the trajectory analyses, informatics of dealing with the large database of results, compressions of trajectories for efficacy of distribution, DNA solvation by water and ions, parameterization of coarse-grained models with applications and gene finding and genome annotation.

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.

The harmonic analysis of cylindrically symmetric proteins: a comparison of Dronpa and a DNA sliding clamp

The harmonic analysis of two types of proteins with cylindrical symmetry is performed by the Standard Force Field Normal Mode Analysis and by the elastic network model. For both proteins the global elastic modes are assigned to their characteristic topologies. Dronpa is a rigid β-barrel structure, presenting the twisting, bending and breathing motion of a cylindrical rod. The β sliding clamp of Escherichia coli is a hexagonal β-wheel, consisting of rigid segments. In its spectrum four classes of vibrations are identified which are characteristic of an elastic torus. Correlation diagrams and RMSF analysis are compared. The results provide not only a comprehensive validation of the use of both methods to describe the elastic behavior according to the low-frequency normal modes, but also depict the correlated motions of β-barrel and β-wheel proteins. The harmonic flexibility of the Dronpa protein is compared to the principal components of molecular dynamics (MD) simulation. A functionally important localized cleft opening mode is found, which is not detected by harmonic analysis.

Toward a consensus view of duplex RNA flexibility

The structure and flexibility of the RNA duplex has been studied using extended molecular dynamics simulations on four diverse 18-mer oligonucleotides designed to contain many copies of the 10 unique dinucleotide steps in different sequence environments. Simulations were performed using the two most popular force fields for nucleic acids simulations (AMBER and CHARMM) in their latest versions, trying to arrive to a consensus picture of the RNA flexibility. Contrary to what was found for DNA duplex (DNA(2)), no clear convergence is found for the RNA duplex (RNA(2)), but one of the force field seems to agree better with experimental data. MD simulations performed with this force field were used to fully characterize, for the first time to our knowledge, the sequence-dependent elastic properties of RNA duplexes at different levels of resolutions. The flexibility pattern of RNA(2) shows similarities with DNA(2), but also surprising differences, which help us to understand the different biological functions of both molecules. A full mesoscopic model of RNA duplex at different resolution levels is derived to be used for genome-wide description of the flexibility of double-helical fragments of RNA.

Nucleic-acid structural deformability deduced from anisotropic displacement parameters

The growing numbers of very well resolved nucleic-acid crystal structures with anisotropic displacement parameters provide an unprecedented opportunity to learn about the natural motions of DNA and RNA. Here we report a new Monte-Carlo approach that takes direct account of this information to extract the distortions of covalent structure, base pairing, and dinucleotide geometry intrinsic to regularly organized double-helical molecules. We present new methods to test the validity of the anisotropic parameters and examine the apparent deformability of a variety of structures, including several A, B, and Z DNA duplexes, an AB helical intermediate, an RNA, a ligand-DNA complex, and an enzyme-bound DNA. The rigid-body parameters characterizing the positions of the bases in the structures mirror the mean parameters found when atomic motion is taken into account. The base-pair fluctuations intrinsic to a single structure, however, differ from those extracted from collections of nucleic-acid structures, although selected base-pair steps undergo conformational excursions along routes suggested by the ensembles. The computations reveal surprising new molecular insights, such as the stiffening of DNA and concomitant separation of motions of contacted nucleotides on opposite strands by the binding of Escherichia coli endonuclease VIII, which suggest how the protein may direct enzymatic action.

Coarse-grained model for simulation of RNA three-dimensional structures

The accurate prediction of an RNA's three-dimensional structure from its "primary structure" will have a tremendous influence on the experimental design and its interpretation and ultimately our understanding of the many functions of RNA. This paper presents a general coarse-grained (CG) potential for modeling RNA 3-D structures. Each nucleotide is represented by five pseudo atoms, two for the backbone (one for the phosphate and another for the sugar) and three for the base to represent base-stacking interactions. The CG potential has been parametrized from statistical analysis of 688 RNA experimental structures. Molecular dynamic simulations of 15 RNA molecules with the length of 12-27 nucleotides have been performed using the CG potential, with performance comparable to that from all-atom simulations. For ~75% of systems tested, simulated annealing led to native-like structures at least once out of multiple repeated runs. Furthermore, with weak distance restraints based on the knowledge of three to five canonical Watson-Crick pairs, all 15 RNAs tested are successfully folded to within 6.5 Å of native structures using the CG potential and simulated annealing. The results reveal that with a limited secondary structure model the current CG potential can reliably predict the 3-D structures for small RNA molecules. We also explored an all-atom force field to construct atomic structures from the CG simulations.

DNA curvature and flexibility in vitro and in vivo

It has been more than 50 years since the elucidation of the structure of double-helical DNA. Despite active research and progress in DNA biology and biochemistry, much remains to be learned in the field of DNA biophysics. Predicting the sequence-dependent curvature and flexibility of DNA is difficult. Applicability of the conventional worm-like chain polymer model of DNA has been challenged. The fundamental forces responsible for the remarkable resistance of DNA to bending and twisting remain controversial. The apparent 'softening' of DNA measured in vivo in the presence of kinking proteins and superhelical strain is incompletely understood. New methods and insights are being applied to these problems. This review places current work on DNA biophysics in historical context and illustrates the ongoing interplay between theory and experiment in this exciting field.

Effect of probe characteristics on the subtractive hybridization efficiency of human genomic DNA

Background

The detection sensitivity of low abundance pathogenic species by polymerase chain reaction (PCR) can be significantly enhanced by removing host nucleic acids. This selective removal can be performed using a magnetic bead-based solid phase with covalently immobilized capture probes. One of the requirements to attain efficient host background nucleic acids subtraction is the capture probe characteristics.

Findings

In this study we investigate how various capture probe characteristics influence the subtraction efficiency. While the primary focus of this report is the impact of probe length, we also studied the impact of probe conformation as well as the amount of capture probe attached to the solid phase. The probes were immobilized on magnetic microbeads functionalized with a phosphorous dendrimer. The subtraction efficiency was assessed by quantitative real time PCR using a single-step capture protocol and genomic DNA as target. Our results indicate that short probes (100 to 200 bp) exhibit the best subtraction efficiency. Additionally, higher subtraction efficiencies with these probes were obtained as the amount of probe immobilized on the solid phase decreased. Under optimal probes condition, our protocol showed a 90 - 95% subtraction efficiency of human genomic DNA.

Conclusions

The characteristics of the capture probe are important for the design of efficient solid phases. The length, conformation and abundance of the probes determine the capture efficiency of the solid phase.

Global conformational changes of ribosome observed by normal mode fitting for 3D Cryo-EM structures

Many three-dimensional density maps of 70S ribosome at various functional states are available now in the Electron Microscopy DataBank at EBI. We used our new flexible-fitting approach to systematically analyze these maps to reveal the global conformational differences between the EM structures. Large-scale ratchet-like deformations were observed in an EM structure of the initiation complex and in some EM structures bound with EFG, RF3, and RRF. In most of them, the L1 stalk, which interacts with the tRNA molecule at the E site of ribosome and is considered to be involved in the release of the tRNA, was in "the blocking state" for the E-tRNA. Furthermore, we found that the EM structures bound with EFG or RRF were aligned in the conformational space, suggesting that the large-scale conformational changes of the 70S ribosome bound with these factors occur along a specific pathway in a concerted manner.

How stiff is DNA?

The natural stiffness of DNA, which contributes to the interactions of the many proteins involved in its biological processing and packaging, also plays an important role in modern nanotechnology. Here we report new Monte-Carlo simulations of deformable DNA molecules of potential utility in understanding the behavior of the long, double-helical polymer in the tight confines of a cell and in the design of novel nanomaterials and molecular devices. We directly determine the fluctuations in end-to-end extension associated with the conventional elastic-rod representation of DNA and with more realistic models that take account of the precise deformability of the constituent base-pair steps. Notably, the variance of end-to-end distance shows a quadratic increase with chain length in short chains of both types. We also consider the contributions to chain extension from the chemical linkages used to attach small molecular probes to DNA. The distribution of computed distances is sensitive to the intrinsic structure and allowed deformations of the tether. Surprisingly, the enhancement in end-to-end variance associated with the presence of the probe depends upon chain length, even when the probe is rigidly connected to DNA. We find that the elastic rod model of DNA in combination with a slightly fluctuating tether accounts satisfactorily for the distributions of end-to-end distances extracted from the small-angle X-ray scattering of gold nanocrystals covalently linked to the ends of short DNAs. There is no need to introduce additional structural fluctuations to reproduce the measured uptake in end-to-end fluctuations with chain length.

Sequence dependencies of DNA deformability and hydration in the minor groove

DNA deformability and hydration are both sequence-dependent and are essential in specific DNA sequence recognition by proteins. However, the relationship between the two is not well understood. Here, systematic molecular dynamics simulations of 136 DNA sequences that differ from each other in their central tetramer revealed that sequence dependence of hydration is clearly correlated with that of deformability. We show that this correlation can be illustrated by four typical cases. Most rigid basepair steps are highly likely to form an ordered hydration pattern composed of one water molecule forming a bridge between the bases of distinct strands, but a few exceptions favor another ordered hydration composed of two water molecules forming such a bridge. Steps with medium deformability can display both of these hydration patterns with frequent transition. Highly flexible steps do not have any stable hydration pattern. A detailed picture of this correlation demonstrates that motions of hydration water molecules and DNA bases are tightly coupled with each other at the atomic level. These results contribute to our understanding of the entropic contribution from water molecules in protein or drug binding and could be applied for the purpose of predicting binding sites.

DNA sequence-directed organization of chromatin: structure-based computational analysis of nucleosome-binding sequences

The folding of DNA on the nucleosome core particle governs many fundamental issues in eukaryotic molecular biology. In this study, an updated set of sequence-dependent empirical "energy" functions, derived from the structures of other protein-bound DNA molecules, is used to investigate the extent to which the architecture of nucleosomal DNA is dictated by its underlying sequence. The potentials are used to estimate the cost of deforming a collection of sequences known to bind or resist uptake in nucleosomes along various left-handed superhelical pathways and to deduce the features of sequence contributing to a particular structural form. The deformation scores reflect the choice of template, the deviations of structural parameters at each step of the nucleosome-bound DNA from their intrinsic values, and the sequence-dependent "deformability" of a given dimer. The correspondence between the computed scores and binding propensities points to a subtle interplay between DNA sequence and nucleosomal folding, e.g., sequences with periodically spaced pyrimidine-purine steps deform at low cost along a kinked template whereas sequences that resist deformation prefer a smoother spatial pathway. Successful prediction of the known settings of some of the best-resolved nucleosome-positioning sequences, however, requires a template with "kink-and-slide" steps like those found in high-resolution nucleosome structures.

Mesoscale modeling of multi-protein-DNA assemblies: the role of the catabolic activator protein in Lac-repressor-mediated looping

DNA looping plays a key role in the regulation of the lac operon in Escherichia coli. The presence of a tightly bent loop (between sequentially distant sites of Lac repressor protein binding) purportedly hinders the binding of RNA polymerase and subsequent transcription of the genetic message. The unexpectedly favorable binding interaction of this protein-DNA assembly with the catabolic activator protein (CAP), a protein that also bends DNA and paradoxically facilitates the binding of RNA polymerase, stimulated extension of our base-pair level theory of DNA elasticity to the treatment of DNA loops formed in the presence of several proteins. Here we describe in detail a procedure to determine the structures and free energies of multi-protein-DNA assemblies and illustrate the predicted effects of CAP binding on the configurations of the wild-type 92-bp Lac repressor-mediated O3-O1 DNA loop. We show that the DNA loop adopts an antiparallel orientation in the most likely structure and that this loop accounts for the published experimental observation that, when CAP is bound to the loop, one of the arms of LacR binds to an alternative site that is displaced from the original site by 5 bp.

Key interactions in integrin ectodomain responsible for global conformational change detected by elastic network normal-mode analysis

Integrin, a membrane protein with a huge extracellular domain, participates in cell-cell and cell-extracellular-matrix interactions for metazoan. A group of integrins is known to perform a large-scale structural change when the protein is activated, but the activation mechanism and generality of the conformational change remain to be elucidated. We performed normal-mode analysis of the elastic network model on integrin alpha(V)beta(3) ectodomain in the bent form and identified key residues that influenced molecular motions. Iterative normal-mode calculations demonstrated that the specific nonbonded interactions involving the key residues work as a snap to keep integrin in the bent form. The importance of the key residues for the conformational change was further verified by mutation experiments, in which integrin alpha(IIb)beta(3) was used. The conservation pattern of amino acid residues among the integrin family showed that the characteristic pattern of residues seen around these key residues is found in the limited groups of integrin beta-chains. This conservation pattern suggests that the molecular mechanism of the conformational change relying on the interactions found in integrin alpha(V)beta(3) is unique to the limited types of integrins.

Multiscale modeling of nucleic acids: insights into DNA flexibility

The elastic rod theory is used together with all-atom normal mode analysis in implicit solvent to characterize the mechanical flexibility of duplex DNA. The bending, twisting, stretching rigidities extracted from all-atom simulations (on linear duplexes from 60 to 150 base pairs in length and from 94-bp minicircles) are in reasonable agreement with experimental results. We focus on salt concentration and sequence effects on the overall flexibility. Bending persistence lengths are about 20% higher than most experimental estimates, but the transition from low-salt to high-salt behavior is reproduced well, as is the dependence of the stretching modulus on salt (which is opposite to that of bending). CTG and CGG trinucleotide repeats, responsible for several degenerative disorders, are found to be more flexible than random DNA, in agreement with several recent studies, whereas poly(dA).poly(dT) is the stiffest sequence we have encountered. The results suggest that current all-atom potentials, which were parameterized on small molecules and short oligonucleotides, also provide a useful description of duplex DNA at much longer length scales.

3DNA: a versatile, integrated software system for the analysis, rebuilding and visualization of three-dimensional nucleic-acid structures

We present a set of protocols showing how to use the 3DNA suite of programs to analyze, rebuild and visualize three-dimensional nucleic-acid structures. The software determines a wide range of conformational parameters, including the identities and rigid-body parameters of interacting bases and base-pair steps, the nucleotides comprising helical fragments, the area of overlap of stacked bases and so on. The reconstruction of three-dimensional structure takes advantage of rigorously defined rigid-body parameters, producing rectangular block representations of the nucleic-acid bases and base pairs and all-atom models with approximate sugar-phosphate backbones. The visualization components create vector-based drawings and scenes that can be rendered as raster-graphics images, allowing for easy generation of publication-quality figures. The utility programs use geometric variables to control the view and scale of an object, for comparison of related structures. The commands run in seconds even for large structures. The software and related information are available at http://3dna.rutgers.edu/.

Sequence-dependent DNA deformability studied using molecular dynamics simulations

Proteins recognize specific DNA sequences not only through direct contact between amino acids and bases, but also indirectly based on the sequence-dependent conformation and deformability of the DNA (indirect readout). We used molecular dynamics simulations to analyze the sequence-dependent DNA conformations of all 136 possible tetrameric sequences sandwiched between CGCG sequences. The deformability of dimeric steps obtained by the simulations is consistent with that by the crystal structures. The simulation results further showed that the conformation and deformability of the tetramers can highly depend on the flanking base pairs. The conformations of xATx tetramers show the most rigidity and are not affected by the flanking base pairs and the xYRx show by contrast the greatest flexibility and change their conformations depending on the base pairs at both ends, suggesting tetramers with the same central dimer can show different deformabilities. These results suggest that analysis of dimeric steps alone may overlook some conformational features of DNA and provide insight into the mechanism of indirect readout during protein-DNA recognition. Moreover, the sequence dependence of DNA conformation and deformability may be used to estimate the contribution of indirect readout to the specificity of protein-DNA recognition as well as nucleosome positioning and large-scale behavior of nucleic acids.

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

The elasticity of double-helical DNA on a nm length scale is captured in detail by the rigid base-pair model, whose conformation variables are the relative positions and orientations of adjacent base pairs. Corresponding sequence-dependent elastic potentials have been obtained from all-atom MD simulation and from high-resolution structural data. On the scale of 100 nm, DNA is successfully described by a continuous wormlike chain model with homogeneous elastic properties, characterized by a set of four elastic constants which have been 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 to an effective wormlike chain description. The average helical geometry of the molecule is accounted for exactly, and repetitive as well as random sequences are considered. Structural disorder is shown to produce a small, additive and short-range correction to thermal conformation fluctuations as well as to entropic elasticity. We also discuss the limits of applicability of the homogeneous wormlike chain on short scales, quantifying the anisotropy of bending stiffness, the non-Gaussian bend angle distribution and the variability of stiffness, all of which are noticeable below a helical turn. The coarse-grained elastic parameters show remarkable overall agreement with experimental wormlike chain stiffness. For the best-matching potential, bending persistence lengths of dinucleotide repeats span a range of 37-53 nm, with a random DNA value of 43 nm. While twist stiffness is somewhat underestimated and stretch stiffness is overestimated, the counterintuitive negative sign and the magnitude of the twist-stretch coupling agree with recent experimental findings.

Molecular seismology: An inverse problem in nanobiology

The density profile of an elastic fiber like DNA will change in space and time as ligands associate with it. This observation affords a new direction in single molecule studies provided that density profiles can be measured in space and time. In fact, this is precisely the objective of seismology, where the mathematics of inverse problems have been employed with success. We argue that inverse problems in elastic media can be directly applied to biophysical problems of fiber-ligand association, and demonstrate that robust algorithms exist to perform density reconstruction in the condensed phase.

A coarse grain model for DNA

Understanding the behavior of DNA at the molecular level is of considerable fundamental and engineering importance. While adequate representations of DNA exist at the atomic and continuum level, there is a relative lack of models capable of describing the behavior of DNA at mesoscopic length scales. We present a mesoscale model of DNA that reduces the complexity of a nucleotide to three interactions sites, one each for the phosphate, sugar, and base, thereby rendering the investigation of DNA up to a few microns in length computationally tractable. The charges on these sites are considered explicitly. The model is parametrized using thermal denaturation experimental data at a fixed salt concentration. The validity of the model is established by its ability to predict several aspects of DNA behavior, including salt-dependent melting, bubble formation and rehybridization, and the mechanical properties of the molecule as a function of salt concentration.

A simple physical description of DNA dynamics: quasi-harmonic analysis as a route to the configurational entropy

It has become increasingly apparent that the dynamic as well as the structural properties of biological macromolecules are important to their function. However, information concerning molecular flexibility can be difficult to obtain experimentally at the atomic level. Computer modelling techniques such as molecular dynamics (MD) have therefore proved invaluable in advancing our understanding of biomolecular flexibility. This paper describes how a combination of atomistic MD simulations and quasi-harmonic analysis can be used to describe the dynamics of duplex DNA, with a particular emphasis on methods for calculating differences in configurational entropies. We demonstrate that DNA possesses remarkably simple mechanical properties relative to globular proteins, making it an ideal system for exploring biomolecular flexibility in general. Our results also highlight the importance of solvent viscosity in determining the dynamic behaviour of DNA in aqueous solution.

Indirect readout: detection of optimized subsequences and calculation of relative binding affinities using different DNA elastic potentials

Essential biological processes require that proteins bind to a set of specific DNA sites with tuned relative affinities. We focus on the indirect readout mechanism and discuss its theoretical description in relation to the present understanding of DNA elasticity on the rigid base pair level. Combining existing parametrizations of elastic potentials for DNA, we derive elastic free energies directly related to competitive binding experiments, and propose a computationally inexpensive local marker for elastically optimized subsequences in protein-DNA co-crystals. We test our approach in an application to the bacteriophage 434 repressor. In agreement with known results we find that indirect readout dominates at the central, non-contacted bases of the binding site. Elastic optimization involves all deformation modes and is mainly due to the adapted equilibrium structure of the operator, while sequence-dependent elasticity plays a minor role. These qualitative observations are robust with respect to current parametrization uncertainties. Predictions for relative affinities mediated by indirect readout depend sensitively on the chosen parametrization. Their quantitative comparison with experimental data allows for a critical evaluation of DNA elastic potentials and of the correspondence between crystal and solution structures. The software written for the presented analysis is included as Supplementary Data.

Modeling DNA loops using the theory of elasticity

An elastic rod model of a protein-bound DNA loop is adapted for application in multi-scale simulations of protein-DNA complexes. The classical Kirchhoff system of equations which describes the equilibrium structure of the elastic loop is modified to account for the intrinsic twist and curvature, anisotropic bending properties, and electrostatic charge of DNA. The effects of bending anisotropy and electrostatics are studied for the DNA loop clamped by the lac repressor protein. For two possible lengths of the loop, several topologically different conformations are predicted and extensively analyzed over the broad range of model parameters describing DNA bending and electrostatic properties. The scope and applications of the model in already accomplished and in future multi-scale studies of protein-DNA complexes are discussed.

PREDICTED EFFECTS OF LOCAL CONFORMATIONAL COUPLING AND EXTERNAL RESTRAINTS ON THE TORSIONAL PROPERTIES OF SINGLE DNA MOLECULES

A newly developed, coarse-grained treatment of the low-frequency normal modes of DNA has been adapted to study the torsional properties of fully extended, double-helical molecules. Each base pair is approximated in this scheme as a rigid body, and molecular structure is described in terms of the relative position and orientation of successive base pairs. The torsional modulus C is computed from the lowest-frequency normal twisting mode using expressions valid for a homogeneous, naturally straight elastic rod. Fluctuations of local dimeric structure, including the coupled variation of conformational parameters, are based on the observed arrangements of neighboring base pairs in high-resolution structures. Chain ends are restrained by an elastic energy term. The calculations show how the end-to-end constraints placed on a naturally straight DNA molecule, in combination with the natural conformational features of the double helix, can account for the substantially larger torsional moduli determined with state-of-the-art, single-molecule experiments compared to values extracted from solution measurements and/or incorporated into theories to account for the force-extension properties of single molecules. The computed normal-mode frequencies and torsional moduli increase substantially if base pairs are inclined with respect to the double-helical axis and the deformations of selected conformational variables follow known interdependent patterns. The changes are greatest if the fluctuations in dimeric twisting are coupled with parameters that directly alter the end-to-end displacement. Imposed restraints that mimic the end-to-end conditions of single-molecule experiments then impede the twisting of base pairs and increase the torsional modulus. The natural inclination of base pairs concomitantly softens the Young's modulus, i.e., ease of duplex stretching. The analysis of naturally curved DNA points to a drop in the torsional modulus upon imposed extension of the double-helical molecule.

Conformational Analysis of Stiff Chiral Polymers with End-Constraints

We present a Lie-group-theoretic method for the kinematic and dynamic analysis of chiral semi-flexible polymers with end constraints. The first is to determine the minimum energy conformations of semi-flexible polymers with end constraints, and the second is to perform normal mode analysis based on the determined minimum energy conformations. In this paper, we use concepts from the theory of Lie groups and principles of variational calculus to model such polymers as inextensible or extensible chiral elastic rods with coupling between twisting and bending stiffnesses, and/or between twisting and extension stiffnesses. This method is general enough to include any stiffness and chirality parameters in the context of elastic filament models with the quadratic elastic potential energy function. As an application of this formulation, the analysis of DNA conformations is discussed. We demonstrate our method with examples of DNA conformations in which topological properties such as writhe, twist, and linking number are calculated from the results of the proposed method. Given these minimum energy conformations, we describe how to perform the normal mode analysis. The results presented here build both on recent experimental work in which DNA mechanical properties have been measured, and theoretical work in which the mechanics of non-chiral elastic rods has been studied.

Molecular dynamics simulations of the 136 unique tetranucleotide sequences of DNA oligonucleotides. II: sequence context effects on the dynamical structures of the 10 unique dinucleotide steps

Molecular dynamics (MD) simulations including water and counterions on B-DNA oligomers containing all 136 unique tetranucleotide basepair steps are reported. The objective is to obtain the calculated dynamical structure for at least two copies of each case, use the results to examine issues with regard to convergence and dynamical stability of MD on DNA, and determine the significance of sequence context effects on all unique dinucleotide steps. This information is essential to understand sequence effects on DNA structure and has implications on diverse problems in the structural biology of DNA. Calculations were carried out on the 136 cases embedded in 39 DNA oligomers with repeating tetranucleotide sequences, capped on both ends by GC pairs and each having a total length of 15 nucleotide pairs. All simulations were carried out using a well-defined state-of-the-art MD protocol, the AMBER suite of programs, and the parm94 force field. In a previous article (Beveridge et al. 2004. Biophysical Journal. 87:3799-3813), the research design, details of the simulation protocol, and informatics issues were described. Preliminary results from 15 ns MD trajectories were presented for the d(CpG) step in all 10 unique sequence contexts. The results indicated the sequence context effects to be small for this step, but revealed that MD on DNA at this length of trajectory is subject to surprisingly persistent cooperative transitions of the sugar-phosphate backbone torsion angles alpha and gamma. In this article, we report detailed analysis of the entire trajectory database and occurrence of various conformational substates and its impact on studies of context effects. The analysis reveals a possible direct correspondence between the sequence-dependent dynamical tendencies of DNA structure and the tendency to undergo transitions that "trap" them in nonstandard conformational substates. The difference in mean of the observed basepair step helicoidal parameter distribution with different flanking sequence sometimes differs by as much as one standard deviation, indicating that the extent of sequence effects could be significant. The observations reveal that the impact of a flexible dinucleotide such as CpG could extend beyond the immediate basepair neighbors. The results in general provide new insight into MD on DNA and the sequence-dependent dynamical structural characteristics of DNA.