Sequence-dependent conformational energy of DNA derived from molecular dynamics simulations: toward understanding the indirect readout mechanism in protein-DNA recognition

Accurate modeling of DNA conformational flexibility by a multivariate Ising model

The sequence-dependent structure and deformability of DNA play a major role for binding of proteins and regulation of gene expression. So far, most efforts to model DNA flexibility are based on unimodal harmonic stiffness models at base-pair resolution. However, multimodal behavior due to distinct conformational substates also contributes significantly to the conformational flexibility of DNA. Moreover, these local substates are correlated to their nearest-neighbor substates. A description for DNA elasticity which includes both multimodality and nearest-neighbor coupling has remained a challenge, which we solve by combining our multivariate harmonic approximation with an Ising model for the substates. In a series of applications to DNA fluctuations and protein-DNA complexes, we demonstrate substantial improvements over the unimodal stiffness model. Furthermore, our multivariate Ising model reveals a mechanical destabilization for adenine (A)-tracts to undergo nucleosome formation. Our approach offers a wide range of applications to determine sequence-dependent deformation energies of DNA and to investigate indirect readout contributions to protein-DNA recognition.

Energetic funnel facilitates facilitated diffusion

Transcription factors (TFs) are able to associate to their binding sites on DNA faster than the physical limit posed by diffusion. Such high association rates can be achieved by alternating between three-dimensional diffusion and one-dimensional sliding along the DNA chain, a mechanism-dubbed facilitated diffusion. By studying a collection of TF binding sites of Escherichia coli from the RegulonDB database and of Bacillus subtilis from DBTBS, we reveal a funnel in the binding energy landscape around the target sequences. We show that such a funnel is linked to the presence of gradients of AT in the base composition of the DNA region around the binding sites. An extensive computational study of the stochastic sliding process along the energetic landscapes obtained from the database shows that the funnel can significantly enhance the probability of TFs to find their target sequences when sliding in their proximity. We demonstrate that this enhancement leads to a speed-up of the association process.

Predicting conformational ensembles and genome-wide transcription factor binding sites from DNA sequences

DNA shape is emerging as an important determinant of transcription factor binding beyond just the DNA sequence. The only tool for large scale DNA shape estimates, DNAshape was derived from Monte-Carlo simulations and predicts four broad and static DNA shape features, Propeller twist, Helical twist, Minor groove width and Roll. The contributions of other shape features e.g. Shift, Slide and Opening cannot be evaluated using DNAshape. Here, we report a novel method DynaSeq, which predicts molecular dynamics-derived ensembles of a more exhaustive set of DNA shape features. We compared the DNAshape and DynaSeq predictions for the common features and applied both to predict the genome-wide binding sites of 1312 TFs available from protein interaction quantification (PIQ) data. The results indicate a good agreement between the two methods for the common shape features and point to advantages in using DynaSeq. Predictive models employing ensembles from individual conformational parameters revealed that base-pair opening - known to be important in strand separation - was the best predictor of transcription factor-binding sites (TFBS) followed by features employed by DNAshape. Of note, TFBS could be predicted not only from the features at the target motif sites, but also from those as far as 200 nucleotides away from the motif.

Understanding the structural and dynamic consequences of DNA epigenetic modifications: computational insights into cytosine methylation and hydroxymethylation

We report a series of molecular dynamics (MD) simulations of up to a microsecond combined simulation time designed to probe epigenetically modified DNA sequences. More specifically, by monitoring the effects of methylation and hydroxymethylation of cytosine in different DNA sequences, we show, for the first time, that DNA epigenetic modifications change the molecule's dynamical landscape, increasing the propensity of DNA toward different values of twist and/or roll/tilt angles (in relation to the unmodified DNA) at the modification sites. Moreover, both the extent and position of different modifications have significant effects on the amount of structural variation observed. We propose that these conformational differences, which are dependent on the sequence environment, can provide specificity for protein binding.

Truncated variants of the GCN4 transcription activator protein bind DNA with dramatically different dynamical motifs

The yeast protein GCN4 is a transcriptional activator in the basic leucine zipper (bZip) family, whose distinguishing feature is the "chopstick-like" homodimer of alpha helices formed at the DNA-binding interface. While experiments have shown that truncated versions of the protein retain biologically relevant DNA-binding affinity, we present the results of a computational study revealing that these variants show a wide variety of dynamical modes in their interaction with the target DNA sequence. We have performed all-atom molecular dynamics simulations of the full-length GCN4 protein as well as three truncated variants; our data indicate that the truncated mutants show dramatically different correlation patterns. We conclude that although the truncated mutants still retain DNA-binding ability, the bZip interface present in the full-length protein provides important stability for the protein-DNA complex.

Convergence and reproducibility in molecular dynamics simulations of the DNA duplex d(GCACGAACGAACGAACGC)

BACKGROUND

The structure and dynamics of DNA are critically related to its function. Molecular dynamics simulations augment experiment by providing detailed information about the atomic motions. However, to date the simulations have not been long enough for convergence of the dynamics and structural properties of DNA.

METHODS

Molecular dynamics simulations performed with AMBER using the ff99SB force field with the parmbsc0 modifications, including ensembles of independent simulations, were compared to long timescale molecular dynamics performed with the specialized Anton MD engine on the B-DNA structure d(GCACGAACGAACGAACGC). To assess convergence, the decay of the average RMSD values over longer and longer time intervals was evaluated in addition to assessing convergence of the dynamics via the Kullback-Leibler divergence of principal component projection histograms.

RESULTS

These molecular dynamics simulations-including one of the longest simulations of DNA published to date at ~44μs-surprisingly suggest that the structure and dynamics of the DNA helix, neglecting the terminal base pairs, are essentially fully converged on the ~1-5μs timescale.

CONCLUSIONS

We can now reproducibly converge the structure and dynamics of B-DNA helices, omitting the terminal base pairs, on the μs time scale with both the AMBER and CHARMM C36 nucleic acid force fields. Results from independent ensembles of simulations starting from different initial conditions, when aggregated, match the results from long timescale simulations on the specialized Anton MD engine.

GENERAL SIGNIFICANCE

With access to large-scale GPU resources or the specialized MD engine "Anton" it is possible for a variety of molecular systems to reproducibly and reliably converge the conformational ensemble of sampled structures. This article is part of a Special Issue entitled: Recent developments of molecular dynamics.

cgDNA: a software package for the prediction of sequence-dependent coarse-grain free energies of B-form DNA

cgDNA is a package for the prediction of sequence-dependent configuration-space free energies for B-form DNA at the coarse-grain level of rigid bases. For a fragment of any given length and sequence, cgDNA calculates the configuration of the associated free energy minimizer, i.e. the relative positions and orientations of each base, along with a stiffness matrix, which together govern differences in free energies. The model predicts non-local (i.e. beyond base-pair step) sequence dependence of the free energy minimizer. Configurations can be input or output in either the Curves+ definition of the usual helical DNA structural variables, or as a PDB file of coordinates of base atoms. We illustrate the cgDNA package by comparing predictions of free energy minimizers from (a) the cgDNA model, (b) time-averaged atomistic molecular dynamics (or MD) simulations, and (c) NMR or X-ray experimental observation, for (i) the Dickerson–Drew dodecamer and (ii) three oligomers containing A-tracts. The cgDNA predictions are rather close to those of the MD simulations, but many orders of magnitude faster to compute. Both the cgDNA and MD predictions are in reasonable agreement with the available experimental data. Our conclusion is that cgDNA can serve as a highly efficient tool for studying structural variations in B-form DNA over a wide range of sequences.

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.

Mechanical properties of symmetric and asymmetric DNA A-tracts: implications for looping and nucleosome positioning

A-tracts are functionally important DNA sequences which induce helix bending and have peculiar structural properties. While A-tract structure has been qualitatively well characterized, their mechanical properties remain controversial. A-tracts appear structurally rigid and resist nucleosome formation, but seem flexible in DNA looping. In this work, we investigate mechanical properties of symmetric AnTn and asymmetric A2n tracts for n = 3, 4, 5 using two types of coarse-grained models. The first model represents DNA as an ensemble of interacting rigid bases with non-local quadratic deformation energy, the second one treats DNA as an anisotropically bendable and twistable elastic rod. Parameters for both models are inferred from microsecond long, atomic-resolution molecular dynamics simulations. We find that asymmetric A-tracts are more rigid than the control G/C-rich sequence in localized distortions relevant for nucleosome formation, but are more flexible in global bending and twisting relevant for looping. The symmetric tracts, in contrast, are more rigid than asymmetric tracts and the control, both locally and globally. Our results can reconcile the contradictory stiffness data on A-tracts and suggest symmetric A-tracts to be more efficient in nucleosome exclusion than the asymmetric ones. This would open a new possibility of gene expression manipulation using A-tracts.

Temperature effect on poly(dA).poly(dT): molecular dynamics simulation studies of polymeric and oligomeric constructs

Understanding unwinding and melting of double helical DNA is very important to characterize role of DNA in replication, transcription, translation etc. Sequence dependent melting thermodynamics is used extensively for detecting promoter regions but melting studies are generally done for short oligonucleotides. This study reports several molecular dynamics (MD) simulations of homopolymeric poly(dA).poly(dT) as regular oligonucleotide fragments as well as its corresponding polymeric constructs with water and charge-neutralizing counterions at different temperatures ranging from 300 to 400 K. We have eliminated the end-effect or terminal peeling propensity by employing MD simulation of DNA oligonucleotides in such a manner that gives rise to properties of polymeric DNA of infinite length. The dynamic properties such as basepairing and stacking geometry, groove width, backbone conformational parameters, bending, distribution of counter ions and number of hydrogen bonds of oligomeric and polymeric constructs of poly(dA).poly(dT) have been analyzed. The oligomer shows terminal fraying or peeling effect at temperatures above 340 K. The polymer shows partial melting at elevated temperatures although complete denaturations of basepairs do not take place. The analysis of cross strand hydrogen bonds shows that the number of N-H···O hydrogen bonds increases with increase in temperature while C-H···O hydrogen bond frequencies decrease with temperature. Restructuring of counterions in the minor groove with temperature appear as initiation of melting in duplex structures.

Structure, Stiffness and Substates of the Dickerson-Drew Dodecamer

The Dickerson-Drew dodecamer (DD) d-[CGCGAATTCGCG]₂ is a prototypic B-DNA molecule whose sequence-specific structure and dynamics have been investigated by many experimental and computational studies. Here, we present an analysis of DD properties based on extensive atomistic molecular dynamics (MD) simulations using different ionic conditions and water models. The 0.6-2.4-µs-long MD trajectories are compared to modern crystallographic and NMR data. In the simulations, the duplex ends can adopt an alternative base-pairing, which influences the oligomer structure. A clear relationship between the BI/BII backbone substates and the basepair step conformation has been identified, extending previous findings and exposing an interesting structural polymorphism in the helix. For a given end pairing, distributions of the basepair step coordinates can be decomposed into Gaussian-like components associated with the BI/BII backbone states. The nonlocal stiffness matrices for a rigid-base mechanical model of DD are reported for the first time, suggesting salient stiffness features of the central A-tract. The Riemann distance and Kullback-Leibler divergence are used for stiffness matrix comparison. The basic structural parameters converge very well within 300 ns, convergence of the BI/BII populations and stiffness matrices is less sharp. Our work presents new findings about the DD structural dynamics, mechanical properties, and the coupling between basepair and backbone configurations, including their statistical reliability. The results may also be useful for optimizing future force fields for DNA.

A new method for evaluating the specificity of indirect readout in protein-DNA recognition

Proteins recognize a specific DNA sequence not only through direct contact (direct readout) with base pairs but also through sequence-dependent conformation and/or flexibility of DNA (indirect readout). However, it is difficult to assess the contribution of indirect readout to the sequence specificity. What is needed is a straightforward method for quantifying its contributions to specificity. Using Bayesian statistics, we derived the probability of a particular sequence for a given DNA structure from the trajectories of molecular dynamics (MD) simulations of DNAs containing all possible tetramer sequences. Then, we quantified the specificity of indirect readout based on the information entropy associated with the probability. We tested this method with known structures of protein–DNA complexes. This method enabled us to correctly predict those regions where experiments suggested the involvement of indirect readout. The results also indicated new regions where the indirect readout mechanism makes major contributions to the recognition. The present method can be used to estimate the contribution of indirect readout without approximations to the distributions in the conformational ensembles of DNA, and would serve as a powerful tool to study the mechanism of protein–DNA recognition.

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.

Dynamic properties of water around a protein-DNA complex from molecular dynamics simulations

Formation of protein-DNA complex is an important step in regulation of genes in living organisms. One important issue in this problem is the role played by water in mediating the protein-DNA interactions. In this work, we have carried out atomistic molecular dynamics simulations to explore the heterogeneous dynamics of water molecules present in different regions around a complex formed between the DNA binding domain of human TRF1 protein and a telomeric DNA. It is demonstrated that such heterogeneous water motions around the complex are correlated with the relaxation time scales of hydrogen bonds formed by those water molecules with the protein and DNA. The calculations reveal the existence of a fraction of extraordinarily restricted water molecules forming a highly rigid thin layer in between the binding motifs of the protein and DNA. It is further proved that higher rigidity of water layers around the complex originates from more frequent reformations of broken water-water hydrogen bonds. Importantly, it is found that the formation of the complex affects the transverse and longitudinal degrees of freedom of surrounding water molecules in a nonuniform manner.

Physical properties of naked DNA influence nucleosome positioning and correlate with transcription start and termination sites in yeast

Background

In eukaryotic organisms, DNA is packaged into chromatin structure, where most of DNA is wrapped into nucleosomes. DNA compaction and nucleosome positioning have clear functional implications, since they modulate the accessibility of genomic regions to regulatory proteins. Despite the intensive research effort focused in this area, the rules defining nucleosome positioning and the location of DNA regulatory regions still remain elusive.

Results

Naked (histone-free) and nucleosomal DNA from yeast were digested by microccocal nuclease (MNase) and sequenced genome-wide. MNase cutting preferences were determined for both naked and nucleosomal DNAs. Integration of their sequencing profiles with DNA conformational descriptors derived from atomistic molecular dynamic simulations enabled us to extract the physical properties of DNA on a genomic scale and to correlate them with chromatin structure and gene regulation. The local structure of DNA around regulatory regions was found to be unusually flexible and to display a unique pattern of nucleosome positioning. Ab initio physical descriptors derived from molecular dynamics were used to develop a computational method that accurately predicts nucleosome enriched and depleted regions.

Conclusions

Our experimental and computational analyses jointly demonstrate a clear correlation between sequence-dependent physical properties of naked DNA and regulatory signals in the chromatin structure. These results demonstrate that nucleosome positioning around TSS (Transcription Start Site) and TTS (Transcription Termination Site) (at least in yeast) is strongly dependent on DNA physical properties, which can define a basal regulatory mechanism of gene expression.

Evolutionary trends of GC/AT distribution patterns in promoters

Nucleotide distributions in genomes is known not to be random, showing the presence of specific motifs, long and short range correlations, periodicities, etc. Particularly, motifs are critical for the recognition by specific proteins affecting chromosome organization, transcription and DNA replication but little is known about the possible functional effects of nucleotide distributions on the conformational landscape of DNA, putatively leading to differential selective pressures throughout evolution. Promoter sequences have a fundamental role in the regulation of gene activity and a vast literature suggests that their conformational landscapes may be a critical factor in gene expression dynamics. On these grounds, with the aim of investigating the putative existence of phylogenetic patterns of promoter base distributions, we analyzed GC/AT ratios along the 1000 nucleotide sequences upstream of TSS in wide sets of promoters belonging to organisms ranging from bacteria to pluricellular eukaryotes. The data obtained showed very clear phylogenetic trends throughout evolution of promoter sequence base distributions. Particularly, in all cases either GC-rich or AT-rich monotone gradients were observed: the former being present in eukaryotes, the latter in bacteria along with strand biases. Moreover, within eukaryotes, GC-rich gradients increased in length from unicellular organisms to plants, to vertebrates and, within them, from ancestral to more recent species. Finally, results were thoroughly discussed with particular attention to the possible correlation between nucleotide distribution patterns, evolution, and the putative existence of differential selection pressures, deriving from structural and/or functional constraints, between and within prokaryotes and eukaryotes.

Intrinsic flexibility of B-DNA: the experimental TRX scale

B-DNA flexibility, crucial for DNA–protein recognition, is sequence dependent. Free DNA in solution would in principle be the best reference state to uncover the relation between base sequences and their intrinsic flexibility; however, this has long been hampered by a lack of suitable experimental data. We investigated this relationship by compiling and analyzing a large dataset of NMR ³¹P chemical shifts in solution. These measurements reflect the BI ↔ BII equilibrium in DNA, intimately correlated to helicoidal descriptors of the curvature, winding and groove dimensions. Comparing the ten complementary DNA dinucleotide steps indicates that some steps are much more flexible than others. This malleability is primarily controlled at the dinucleotide level, modulated by the tetranucleotide environment. Our analyses provide an experimental scale called TRX that quantifies the intrinsic flexibility of the ten dinucleotide steps in terms of Twist, Roll, and X-disp (base pair displacement). Applying the TRX scale to DNA sequences optimized for nucleosome formation reveals a 10 base-pair periodic alternation of stiff and flexible regions. Thus, DNA flexibility captured by the TRX scale is relevant to nucleosome formation, suggesting that this scale may be of general interest to better understand protein-DNA recognition.

A systematic molecular dynamics study of nearest-neighbor effects on base pair and base pair step conformations and fluctuations in B-DNA

It is well recognized that base sequence exerts a significant influence on the properties of DNA and plays a significant role in protein–DNA interactions vital for cellular processes. Understanding and predicting base sequence effects requires an extensive structural and dynamic dataset which is currently unavailable from experiment. A consortium of laboratories was consequently formed to obtain this information using molecular simulations. This article describes results providing information not only on all 10 unique base pair steps, but also on all possible nearest-neighbor effects on these steps. These results are derived from simulations of 50–100 ns on 39 different DNA oligomers in explicit solvent and using a physiological salt concentration. We demonstrate that the simulations are converged in terms of helical and backbone parameters. The results show that nearest-neighbor effects on base pair steps are very significant, implying that dinucleotide models are insufficient for predicting sequence-dependent behavior. Flanking base sequences can notably lead to base pair step parameters in dynamic equilibrium between two conformational sub-states. Although this study only provides limited data on next-nearest-neighbor effects, we suggest that such effects should be analyzed before attempting to predict the sequence-dependent behavior of DNA.

Protein-DNA binding specificity: a grid-enabled computational approach applied to single and multiple protein assemblies

We use a physics-based approach termed ADAPT to analyse the sequence-specific interactions of three proteins which bind to DNA on the side of the minor groove. The analysis is able to estimate the binding energy for all potential sequences, overcoming the combinatorial problem via a divide-and-conquer approach which breaks the protein-DNA interface down into a series of overlapping oligomeric fragments. All possible base sequences are studied for each fragment. Energy minimisation with an all-atom representation and a conventional force field allows for conformational adaptation of the DNA and of the protein side chains for each new sequence. As a result, the analysis depends linearly on the length of the binding site and complexes as large as the nucleosome can be treated, although this requires access to grid computing facilities. The results on the three complexes studied are in good agreement with experiment. Although they all involve significant DNA deformation, it is found that this does not necessarily imply that the recognition will be dominated by the sequence-dependent mechanical properties of DNA.

An all-atom knowledge-based energy function for protein-DNA threading, docking decoy discrimination, and prediction of transcription-factor binding profiles

How to make an accurate representation of protein-DNA interaction by an energy function is a long-standing unsolved problem in structural biology. Here, we modified a statistical potential based on the distance-scaled, finite ideal-gas reference state so that it is optimized for protein-DNA interactions. The changes include a volume-fraction correction to account for unmixable atom types in proteins and DNA in addition to the usage of a low-count correction, residue/base-specific atom types, and a shorter cutoff distance for protein-DNA interactions. The new statistical energy functions are tested in threading and docking decoy discriminations and prediction of protein-DNA binding affinities and transcription-factor binding profiles. The results indicate that new proposed energy functions are among the best in existing energy functions for protein-DNA interactions. The new energy functions are available as a web-server called DDNA 2.0 at http://sparks.informatics.iupui.edu. The server version was trained by the entire 212 protein-DNA complexes.

A generalized conformational energy function of DNA derived from molecular dynamics simulations

Proteins recognize DNA sequences by two different mechanisms. The first is direct readout, in which recognition is mediated by direct interactions between the protein and the DNA bases. The second is indirect readout, which is caused by the dependence of conformation and the deformability of the DNA structure on the sequence. Various energy functions have been proposed to evaluate the contribution of indirect readout to the free-energy changes in complex formations. We developed a new generalized energy function to estimate the dependence of the deformability of DNA on the sequence. This function was derived from molecular dynamics simulations previously conducted on B-DNA dodecamers, each of which had one possible tetramer sequence embedded at its center. By taking the logarithm of the probability distribution function (PDF) for the base-step parameters of the central base-pair step of the tetramer, its ability to distinguish the native sequence from random ones was superior to that with the previous method that approximated the energy function in harmonic form. From a comparison of the energy profiles calculated with these two methods, we found that the harmonic approximation caused significant errors in the conformational energies of the tetramers that adopted multiple stable conformations.

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.

Energy-based prediction of amino acid-nucleotide base recognition

Despite decades of investigations, it is not yet clear whether there are rules dictating the specificity of the interaction between amino acids and nucleotide bases. This issue was addressed by determining, in a dataset consisting of 100 high-resolution protein-DNA structures, the frequency and energy of interaction between each amino acid and base, and the energetics of water-mediated interactions. The analysis was carried out using HINT, a non-Newtonian force field encoding both enthalpic and entropic contributions, and Rank, a geometry-based tool for evaluating hydrogen bond interactions. A frequency- and energy-based preferential interaction of Arg and Lys with G, Asp and Glu with C, and Asn and Gln with A was found. Not only favorable, but also unfavorable contacts were found to be conserved. Water-mediated interactions strongly increase the probability of Thr-A, Lys-A, and Lys-C contacts. The frequency, interaction energy, and water enhancement factors associated with each amino acid-base pair were used to predict the base triplet recognized by the helix motif in 45 zinc fingers, which represents an ideal case study for the analysis of one-to-one amino acid-base pair contacts. The model correctly predicted 70.4% of 135 amino acid-base pairs, and, by weighting the energetic relevance of each amino acid-base pair to the overall recognition energy, it yielded a prediction rate of 89.7%.

Comparison of DNA hydration patterns obtained using two distinct computational methods, molecular dynamics simulation and three-dimensional reference interaction site model theory

Because proteins and DNA interact with each other and with various small molecules in the presence of water molecules, we cannot ignore their hydration when discussing their structural and energetic properties. Although high-resolution crystal structure analyses have given us a view of tightly bound water molecules on their surface, the structural data are still insufficient to capture the detailed configurations of water molecules around the surface of these biomolecules. Thanks to the invention of various computational algorithms, computer simulations can now provide an atomic view of hydration. Here, we describe the apparent patterns of DNA hydration calculated by using two different computational methods: Molecular dynamics (MD) simulation and three-dimensional reference interaction site model (3D-RISM) theory. Both methods are promising for obtaining hydration properties, but until now there have been no thorough comparisons of the calculated three-dimensional distributions of hydrating water. This rigorous comparison showed that MD and 3D-RISM provide essentially similar hydration patterns when there is sufficient sampling time for MD and a sufficient number of conformations to describe molecular flexibility for 3D-RISM. This suggests that these two computational methods can be used to complement one another when evaluating the reliability of the calculated hydration patterns.

Efficient chain moves for Monte Carlo simulations of a wormlike DNA model: excluded volume, supercoils, site juxtapositions, knots, and comparisons with random-flight and lattice models

We develop two classes of Monte Carlo moves for efficient sampling of wormlike DNA chains that can have significant degrees of supercoiling, a conformational feature that is key to many aspects of biological function including replication, transcription, and recombination. One class of moves entails reversing the coordinates of a segment of the chain along one, two, or three axes of an appropriately chosen local frame of reference. These transformations may be viewed as a generalization, to the continuum, of the Madras-Orlitsky-Shepp algorithm for cubic lattices. Another class of moves, termed T+/-2, allows for interconversions between chains with different lengths by adding or subtracting two beads (monomer units) to or from the chain. Length-changing moves are generally useful for conformational sampling with a given site juxtaposition, as has been shown in previous lattice studies. Here, the continuum T+/-2 moves are designed to enhance their acceptance rate in supercoiled conformations. We apply these moves to a wormlike model in which excluded volume is accounted for by a bond-bond repulsion term. The computed autocorrelation functions for the relaxation of bond length, bond angle, writhe, and branch number indicate that the new moves lead to significantly more efficient sampling than conventional bead displacements and crankshaft rotations. A close correspondence is found in the equilibrium ensemble between the map of writhe computed for pair of chain segments and the map of site juxtapositions or self-contacts. To evaluate the more coarse-grained freely jointed chain (random-flight) and cubic lattice models that are commonly used in DNA investigations, twisting (torsional) potentials are introduced into these models. Conformational properties for a given superhelical density sigma may then be sampled by computing the writhe and using White's formula to relate the degree of twisting to writhe and sigma. Extensive comparisons of contact patterns and knot probabilities of the more coarse-grained models with the wormlike model show that the behaviors of the random-flight model are similar to that of DNA molecules in a solution environment with high ionic strengths, whereas the behaviors of the cubic lattice model with excluded volume are akin to that of DNA molecules under low ionic strengths.

Identification of intrinsic dynamics in a DNA sequence preferentially cleaved by topoisomerase II enzyme

Topoisomerase II enzymes are essential enzymes that modulate DNA topology and play a role in chromatin compaction. While these enzymes appear to recognize and cleave the DNA in a nonrandom fashion, factors that underlie enzyme specificity remain an enigma. To gain new insights on these topics, we undertake, using NMR and molecular dynamics methods, studies of the structural and dynamic features of a 21 bp DNA segment preferentially cleaved by topoisomerases II. The large size of the oligonucleotide did not hamper the determination of structures of sufficient quality, and numerous interesting correlations between helicoidal parameters already depicted in crystals and molecular dynamics simulations are recovered here. The main feature of the sequence is the occurrence of a large opening of the base pairs in a four-residue AT-rich region located immediately at the 5' end of one of the cleaved sites. This opening seems to be largely dependent on sequence context, since a similar opening is not found in the other AT base pairs of the sequence. Furthermore, two adenine nucleotides of the same portion of the oligonucleotide present slow internal motions at the NMR timescale, revealing particular base dynamics. In conclusion, this AT-rich region presents the most salient character in the sequence and could be involved in the preferential cleavage by topoisomerase II. The examination of preferred sites in the literature pointed out the frequent occurrence of AT-rich sequences, namely matrix attachment region and scaffold attachment region sequences, at the sites cleaved by topoisomerase II. We could infer that the particular flexibility of these sequences plays an important role in enabling the formation of a competent cleavage complex. The sequences could then be selected based on their facility to undertake conformational change during the complex formation, rather than purely based on binding affinity.

Recent advances in the study of nucleic acid flexibility by molecular dynamics

The recent use of molecular dynamics (MD) simulations to study flexibility of nucleic acids has been reviewed from an analysis of the publications appearing in the past two years (from 2005 till date). Despite the existence of some unsolved problems in the methodologies, these years have been witness to major advances in the field. Based on a critical review of the most recent contributions, excitement exists on the expected evolution of the field in the next years.

Indirect readout in drug-DNA recognition: role of sequence-dependent DNA conformation

DNA-binding drugs have numerous applications in the engineered gene regulation. However, the drug-DNA recognition mechanism is poorly understood. Drugs can recognize specific DNA sequences not only through direct contacts but also indirectly through sequence-dependent conformation, in a similar manner to the indirect readout mechanism in protein-DNA recognition. We used a knowledge-based technique that takes advantage of known DNA structures to evaluate the conformational energies. We built a dataset of non-redundant free B-DNA crystal structures to calculate the distributions of adjacent base-step and base-pair conformations, and estimated the effective harmonic potentials of mean force (PMF). These PMFs were used to calculate the conformational energy of drug-DNA complexes, and the Z-score as a measure of the binding specificity. Comparing the Z-scores for drug-DNA complexes with those for free DNA structures with the same sequence, we observed that in several cases the Z-scores became more negative upon drug binding. Furthermore, the specificity is position-dependent within the drug-bound region of DNA. These results suggest that DNA conformation plays an important role in the drug-DNA recognition. The presented method provides a tool for the analysis of drug-DNA recognition and can facilitate the development of drugs for targeting a specific DNA sequence.

Thermodynamics of DNA target site recognition by homing endonucleases

The thermodynamic profiles of target site recognition have been surveyed for homing endonucleases from various structural families. Similar to DNA-binding proteins that recognize shorter target sites, homing endonucleases display a narrow range of binding free energies and affinities, mediated by structural interactions that balance the magnitude of enthalpic and entropic forces. While the balance of ΔH and TΔS are not strongly correlated with the overall extent of DNA bending, unfavorable ΔH_binding is associated with unstacking of individual base steps in the target site. The effects of deleterious basepair substitutions in the optimal target sites of two LAGLIDADG homing endonucleases, and the subsequent effect of redesigning one of those endonucleases to accommodate that DNA sequence change, were also measured. The substitution of base-specific hydrogen bonds in a wild-type endonuclease/DNA complex with hydrophobic van der Waals contacts in a redesigned complex reduced the ability to discriminate between sites, due to nonspecific ΔS_binding.

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.

Nucleic acid solvation: from outside to insight

Nucleic acids are polyanionic molecules that were historically considered to be solely surrounded by a shell of water molecules and a neutralizing cloud of monovalent and divalent cations. In this respect, recent experimental and theoretical reports demonstrate that water molecules within complex nucleic acid structures can display very long residency times, and assist drug binding and catalytic reactions. Finally, anions can also bind to these polyanionic systems. Many of these recent insights are provided by state-of-the-art molecular dynamics simulations of nucleic acid systems, which will be described together with relevant methodological issues.

Energetics of protein-DNA interactions

Protein–DNA interactions are vital for many processes in living cells, especially transcriptional regulation and DNA modification. To further our understanding of these important processes on the microscopic level, it is necessary that theoretical models describe the macromolecular interaction energetics accurately. While several methods have been proposed, there has not been a careful comparison of how well the different methods are able to predict biologically important quantities such as the correct DNA binding sequence, total binding free energy and free energy changes caused by DNA mutation. In addition to carrying out the comparison, we present two important theoretical models developed initially in protein folding that have not yet been tried on protein–DNA interactions. In the process, we find that the results of these knowledge-based potentials show a strong dependence on the interaction distance and the derivation method. Finally, we present a knowledge-based potential that gives comparable or superior results to the best of the other methods, including the molecular mechanics force field AMBER99.

Indirect recognition in sequence-specific DNA binding by Escherichia coli integration host factor: the role of DNA deformation energy

Integration host factor (IHF) is a bacterial histone-like protein whose primary biological role is to condense the bacterial nucleoid and to constrain DNA supercoils. It does so by binding in a sequence-independent manner throughout the genome. However, unlike other structurally related bacterial histone-like proteins, IHF has evolved a sequence-dependent, high affinity DNA-binding motif. The high affinity binding sites are important for the regulation of a wide range of cellular processes. A remarkable feature of IHF is that it employs an indirect readout mechanism to bind and wrap DNA at both the nonspecific and high affinity (sequence-dependent) DNA sites. In this study we assessed the contributions of pre-formed and protein-induced DNA conformations to the energetics of IHF binding. Binding energies determined experimentally were compared with energies predicted for the IHF-induced deformation of the DNA helix (DNA deformation energy) in the IHF-DNA complex. Combinatorial sets of de novo DNA sequences were designed to systematically evaluate the influence of sequence-dependent structural characteristics of the conserved IHF recognition elements of the consensus DNA sequence. We show that IHF recognizes pre-formed conformational characteristics of the consensus DNA sequence at high affinity sites, whereas at all other sites relative affinity is determined by the deformational energy required for nearest-neighbor base pairs to adopt the DNA structure of the bound DNA-IHF complex.

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.

ReadOut: structure-based calculation of direct and indirect readout energies and specificities for protein-DNA recognition

Protein-DNA interactions play a central role in regulatory processes at the genetic level. DNA-binding proteins recognize their targets by direct base-amino acid interactions and indirect conformational energy contribution from DNA deformations and elasticity. Knowledge-based approach based on the statistical analysis of protein-DNA complex structures has been successfully used to calculate interaction energies and specificities of direct and indirect readouts in protein-DNA recognition. Here, we have implemented the method as a webserver, which calculates direct and indirect readout energies and Z-scores, as a measure of specificity, using atomic coordinates of protein-DNA complexes. This server is freely available at http://gibk26.bse.kyutech.ac.jp/jouhou/readout/. The only input to this webserver is the Protein Data Bank (PDB) style coordinate data of atoms or the PDB code itself. The server returns total energy Z-scores, which estimate the degree of sequence specificity of the protein-DNA complex. This webserver is expected to be useful for estimating interaction energy and DNA conformation energy, and relative contributions to the specificity from direct and indirect readout. It may also be useful for checking the quality of protein-DNA complex structures, and for engineering proteins and target DNAs.

The stacked-X DNA Holliday junction and protein recognition

The crystal structure of the four-stranded DNA Holliday junction has now been determined in the presence and absence of junction binding proteins, with the extended open-X form of the junction seen in all protein complexes, but the more compact stacked-X structure observed in free DNA. The structures of the stacked-X junction were crystallized because of an unexpected sequence dependence on the stability of this structure. Inverted repeat sequences that contain the general motif NCC or ANC favor formation of stacked-X junctions, with the junction cross-over occurring between the first two positions of the trinucleotides. This review focuses on the sequence dependent structure of the stacked-X junction and how it may play a role in structural recognition by a class of dimeric junction resolving enzymes that themselves show no direct sequence recognition.