Base sequence effects in double helical DNA. I. Potential energy estimates of local base morphology

Evaluation of DNA bending models in their capacity to predict electrophoretic migration anomalies of satellite DNA sequences

DNA containing a sequence that generates a local curvature exhibits a pronounced retardation in electrophoretic mobility. Various theoretical models have been proposed to explain relationship between DNA structural features and migration anomaly. Here, we studied the capacity of 15 static wedge-bending models to predict electrophoretic behavior of 69 satellite monomers derived from four divergent families. All monomers exhibited retarded mobility in PAGE corresponding to retardation factors ranging 1.02-1.54. The curvature varied both within and across the groups and correlated with the number, position, and lengths of A-tracts. Two dinucleotide models provided strong correlation between gel mobility and curvature prediction; two trinucleotide models were satisfactory while remaining dinucleotide models provided intermediate results with reliable prediction for subsets of sequences only. In some cases, similarly shaped molecules exhibited relatively large differences in mobility and vice versa. Generally less accurate predictions were obtained in groups containing less homogeneous sequences possessing distinct structural features. In conclusion, relatively universal theoretical models were identified suitable for the analysis of natural sequences known to harbor relatively moderate curvature. These models could be potentially applied to genome wide studies. However, in silico predictions should be viewed in context of experimental measurement of intrinsic DNA curvature.

Can We Accurately Describe the Structure of Adenine Tracts in B-DNA? Reference Quantum-Chemical Computations Reveal Overstabilization of Stacking by Molecular Mechanics

Sequence-dependent local variations of helical parameters, structure, and flexibility are crucial for molecular recognition processes involving B-DNA. A-tracts, i.e., stretches of several consecutive adenines in one strand that are in phase with the DNA helical repeat, mediate significant DNA bending. During the past few decades, there have been intense efforts to understand the sequence dependence of helical parameters in DNA. Molecular dynamics (MD) simulations can provide valuable insights into the molecular mechanism behind the relationship between sequence and structure. However, although recent improvements in empirical force fields have helped to capture many sequence-dependent B-DNA properties, several problems remain, such as underestimation of the helical twist and suspected underestimation of the propeller twist in A-tracts. Here, we employ reference quantum mechanical (QM) calculations, explicit solvent MD, and bioinformatics to analyze the underestimation of propeller twisting of A-tracts in simulations. Although we did not identify a straightforward explanation, we discovered two imbalances in the empirical force fields. The first was overestimation of stacking interactions accompanied by underestimation of base-pairing energy, which we attribute to anisotropic polarizabilities that are not reflected by the isotropic force fields. This may lead to overstacking with potentially important consequences for MD simulations of nucleic acids. The second observed imbalance was steric clash between A(N1) and T(N3) nitrogens of AT base pairs in force-field descriptions, resulting in overestimation of the AT pair stretch in MD simulations. We also substantially extend the available set of benchmark estimated CCSD(T)/CBS data for B-DNA base stacking and provide a code that allows the generation of diverse base-stacking geometries suitable for QM computations with predefined intra- and interbase pair parameters.

Small local variations in B-form DNA lead to a large variety of global geometries which can accommodate most DNA-binding protein motifs

BACKGROUND

An important question of biological relevance is the polymorphism of the double-helical DNA structure in its free form, and the changes that it undergoes upon protein-binding. We have analysed a database of free DNA crystal structures to assess the inherent variability of the free DNA structure and have compared it with a database of protein-bound DNA crystal structures to ascertain the protein-induced variations.

RESULTS

Most of the dinucleotide steps in free DNA display high flexibility, assuming different conformations in a sequence-dependent fashion. With the exception of the AA/TT and GA/TC steps, which are 'A-phobic', and the GG/CC step, which is 'A-philic', the dinucleotide steps show no preference for A or B forms of DNA. Protein-bound DNA adopts the B-conformation most often. However, in certain cases, protein-binding causes the DNA backbone to take up energetically unfavourable conformations. At the gross structural level, several protein-bound DNA duplexes are observed to assume a curved conformation in the absence of any large distortions, indicating that a series of normal structural parameters at the dinucleotide and trinucleotide level, similar to the ones in free B-DNA, can give rise to curvature at the overall level.

CONCLUSION

The results illustrate that the free DNA molecule, even in the crystalline state, samples a large amount of conformational space, encompassing both the A and the B-forms, in the absence of any large ligands. A-form as well as some non-A, non-B, distorted geometries are observed for a small number of dinucleotide steps in DNA structures bound to the proteins belonging to a few specific families. However, for most of the bound DNA structures, across a wide variety of protein families, the average step parameters for various dinucleotide sequences as well as backbone torsion angles are observed to be quite close to the free 'B-like' DNA oligomer values, highlighting the flexibility and biological significance of this structural form.

Nature of base stacking: reference quantum-chemical stacking energies in ten unique B-DNA base-pair steps

Base-stacking energies in ten unique B-DNA base-pair steps and some other arrangements were evaluated by the second-order Møller-Plesset (MP2) method, complete basis set (CBS) extrapolation, and correction for triple (T) electron-correlation contributions. The CBS(T) calculations were compared with decade-old MP2/6-31G*(0.25) reference data and AMBER force field. The new calculations show modest increases in stacking stabilization compared to the MP2/6-31G*(0.25) data and surprisingly large sequence-dependent variation of stacking energies. The absolute force-field values are in better agreement with the new reference data, while relative discrepancies between quantum-chemical (QM) and force-field values increase modestly. Nevertheless, the force field provides good qualitative description of stacking, and there is no need to introduce additional pair-additive electrostatic terms, such as distributed multipoles or out-of-plane charges. There is a rather surprising difference of about 0.1 A between the vertical separation of base pairs predicted by quantum chemistry and derived from crystal structures. Evaluations of different local arrangements of the 5'-CG-3' step indicate a sensitivity of the relative stacking energies to the level of calculation. Thus, describing quantitative relations between local DNA geometrical variations and stacking may be more complicated than usually assumed. The reference calculations are complemented by continuum-solvent assessment of solvent-screening effects.

SRY and human sex determination: the basic tail of the HMG box functions as a kinetic clamp to augment DNA bending

Human testis-determining factor SRY contains a high-mobility-group (HMG) box, an alpha-helical DNA-binding domain that binds within an expanded minor groove to induce DNA bending. This motif is flanked on the C-terminal end by a basic tail, which functions both as a nuclear localization signal and accessory DNA-binding element. Whereas the HMG box is broadly conserved among otherwise unrelated transcription factors, tails differ in sequence and mode of DNA binding. Contrasting examples are provided by SRY and lymphoid enhancer factor 1 (LEF-1): whereas the SRY tail remains in the minor groove distal to the HMG box, the LEF-1 tail binds back across the center of the bent DNA site. The LEF-1 tail relieves electrostatic repulsion that would otherwise be incurred within the compressed major groove to enable sharp DNA bending with high affinity. Here, we demonstrate that the analogous SRY tail functions as a "kinetic clamp" to regulate the lifetime of the bent DNA complex. As in LEF-1, partial truncation of the distal SRY tail reduces specific DNA affinity and DNA bending, but these perturbations are modest: binding is reduced by only 1.8-fold, and bending by only 7-10 degrees . "Tailed" and truncated SRY complexes exhibit similar structures (as probed by NMR) and distributions of long-range conformational substates (as probed by time-resolved fluorescence resonance energy transfer). Surprisingly, however, the SRY tail retards dissociation of the protein-DNA complex by 20-fold. The marked and compensating changes in rates of association and dissociation observed on tail truncation, disproportionate to perturbations in affinity or structure, suggest that this accessory element functions as a kinetic clamp to regulate the lifetime of the SRY-DNA complex. We speculate that the kinetic stability of a bent DNA complex is critical to the assembly and maintenance of a sex-specific transcriptional pre-initiation complex.

Origin of the intrinsic rigidity of DNA

The intrinsic rigidities of DNA and RNA helices are generally thought to arise from some combination of vertical base-stacking interactions and intra-helix phosphate-phosphate charge repulsion; however, the relative contributions of these two types of interaction to helix rigidity have not been quantified. To address this issue, we have measured the rotational decay times of a 'gapped-duplex' DNA molecule possessing a central, single-stranded region, dT24, before and after addition of the free purine base, N6-methyladenine ((me)A). Upon addition of (me)A, the bases pair with the T residues, forming a continuous stack within the gap region. Formation of the gapped duplex is accompanied by a nearly 2-fold increase in decay time, to values that are indistinguishable from the full duplex control for monovalent salt concentrations up to 90 mM. These results indicate that at least 90% of the rigidity of the dT(n)-dA(n) homopolymer derives from base pair stacking effects, with phosphate-phosphate interactions contributing relatively little to net helix rigidity at moderate salt concentrations.

An assessment of three dinucleotide parameters to predict DNA curvature by quantitative comparison with experimental data

Curved DNA fragments are often found near functionally important sites such as promoters and origins of replication, and hence sequence-dependent DNA curvature prediction is of great utility in genomics and bioinformatics. In light of this, an assessment of three different dinucleotide step parameters (based on gel retardation as well as crystal structure data) is carried out. These parameters (BMHT, LB and CS) are evaluated quantitatively for their ability to predict correctly the experimental results of a large set of nucleic acid sequences containing A-tracts as well as GC-rich motifs. This set contained around 40 synthetic as well as natural sequences whose solution properties have been well characterized experimentally. All three models could account reasonably well for curvature in the various DNA sequences. The CS model, where dinucleotide parameters are calculated from crystal structure data, consistently shows slightly better correlation with experimental data. Our simple analysis also indicates that presently available trinucleotide parameters fail to predict curvature in some of the well-characterized sequences. The study shows that the dinucleotide parameters with some further refinement can be used to predict sequence-dependent curvature correctly in genomic sequences.

A refined prediction method for gel retardation of DNA oligonucleotides from dinucleotide step parameters: reconciliation of DNA bending models with crystal structure data

The development and assessment of a prediction method for gel retardation and sequence dependent curvature of DNA based on dinulcleotide step parameters are described. The method is formulated using the Babcock-Olson equations for base pair step geometry (1) and employs Monte Carlo simulated annealing for parameter optimization against experimental data. The refined base pair step parameters define a stuctural construct which, when the width of observed parameter distributions is taken into account, is consistent with the results of DNA oligonucleotide crystal structures. The predictive power of the method is demonstrated and tested via comparisons with DNA bending data on sets of sequences not included in the training set, including A-tracts with and without periodic helix phasing, phased A4T4 and T4A4 motifs, a sequence with a phased GGGCCC motif, some "unconventional" helix phasing sequences, and three short fragments of kinetoplast DNA from Crithidia fasiculata that exhibit significantly different behavior on non-denaturing polyacrylamide gels. The nature of the structural construct produced by the methodology is discussed with respect to static and dynamic models of structure and representations of bending and bendability. An independent theoretical account of sequence dependent chemical footprinting results is provided. Detailed analysis of sequences with A-tract induced axis bending forms the basis for a critical discussion of the applicability of wedge models,junction models and non A-tract, general sequence models for understanding the origin of DNA curvature at the molecular level.

A statistical mechanical model for predicting B-DNA curvature and flexibility

A statistical mechanical model taking into account the symmetric twisting, tilting, sliding fluctuations and asymmetric rolling fluctuations has been proposed to predict the macroscopic curvature and flexibility of B-DNA. Based on the statistical data of structural parameters of double helix in nucleic acid database and the related theoretical analysis, the equilibrium angular parameters (Omega, rho and tau) describing the orientation of successive base-pair planes, the translation parameters (D(y)) along the long axis of neighboring base-pair step and the corresponding force constants are arranged for ten dimers appropriately. Under the assumption of independent angular parameters, independent base-pair steps and a simple energy function, we can calculate the macroscopic curvature and the flexibility of DNA sequences through the transformation matrix <R> and the Boltzmann ensemble average. The predictions on curvature and flexibility of DNA have been compared with the corresponding experimental data. The agreement is remarkably good. It is demonstrated that the lowering of the temperature does increase the DNA curvature.

TIT for TAT: the properties of inosine and adenosine in TATA box DNA

The sequence dependent conformation, flexibility and hydration properties of DNA molecules constitute selectivity determinants in the formation of protein-DNA complexes. TATA boxes in which AT basepairs (bp) have been substituted by IC bp (TITI box) allow for probing these selectivity determinants for the complexation with the TATA box-binding protein (TBP) with different sequences but identical chemical surfaces. The reference promoter Adenovirus 2 Major Late Promoter (mlp) is formed by the apposition of two sequences with very different dynamic properties: an alternating TATA sequence and an A-tract. For a comparative study, we carried out molecular dynamics simulations of two DNA oligomers, one containing the mlp sequence (2 ns), and the other an analog where AT basepairs were substituted by IC basepairs (1 ns). The simulations, carried out with explicit solvent and counterinons, yield straight purine tracts, the A-tract being stiffer than the I-tract, an alternating structure for the YRYR tracts, and hydration patterns that differ between the purine tracts and the alternating sequence tracts. A detailed analysis of the proposed interactions responsible for the stiffness of the purine tracts indicates that the stacking between the bases bears the strongest correlation to stiffness. The hydration properties of the minor groove in the two oligomers are distinctly different. Such differences are likely to be responsible for the stronger binding of TBP to mlp over the inosine-substituted variant. The calculations were made possible by the development, described here, of a new set of forcefield parameters for inosine that complement the published CHARMM all-hydrogen nucleic acid parametrization.

Small structural ensembles for a 17-nucleotide mimic of the tRNA T psi C-loop via fitting dipolar relaxation rates with the quadratic programming algorithm

Solution structures are typically average structures determined with the help of nmr-derived distance and torsion angle information. However, when a biomolecule populates significantly different conformations, the average structure might be prone to artifacts, and other refinement strategies are necessary. For example, when experimental restraints are used in molecular dynamics simulations in a time-averaged fashion (MDtar), the experimental structural information does no longer need to be satisfied at each step of the simulation; instead, the whole trajectory must agree with the restraints. However, the resulting structural ensembles are large and not unique and it is not trivial to extract the essential dynamic features for a system. Here we demonstrate that large MDtar ensembles can be simplified substantially by reducing the number of members to just a few on the basis of adjusting the individual probabilities of the members with the PDQPRO program [N. B. Ulyanov et al. Biophysical Journal (1995), Vol. 68, p. 13]. This algorithm finds the global minimum for a search function that represents the best match of a given ensemble with the experimental dipolar interproton relaxation rates. We have applied this strategy to a 17-residue RNA hairpin, whose loop exhibited considerable flexibility evident from nmr data. This 17mer is a mimic of the T psi C-loop of tRNA, where nucleotide 54 is usually a ribosylthymidine. The methylation of U54, which is completely buried in transfer ribonucleic acid, is administered by tRNA (m5 U54)-methyltransferase (RUMT). Since the 17mer is a good substrate for RUMT, we previously concluded that the flexibility of the 17mer's loop is a key to how RUMT gains access to the methylation site [L. J. Yao et al. Journal of Biomolecular NMR (1996) Vol. 9. p. 229]. Application of the PDQPRO algorithm to the previously acquired MDtar trajectories allowed us to reduce the number of conformations from several hundred to one major and five or six minor conformations with individual populations from approximately 5% to approximately 50% without any deterioration in the match with the experimental data. The major conformation exhibits a continuation of A-form helicity through part of the loop, involving C60 and U59. In this and most other conformations the methylation site in U54 is no longer buried.

Does TATA matter? A structural exploration of the selectivity determinants in its complexes with TATA box-binding protein

The binding of the TATA box-binding protein (TBP) to a TATA sequence in DNA is essential for eukaryotic basal transcription. TBP binds in the minor groove of DNA, causing a large distortion of the DNA helix. Given the apparent stereochemical equivalence of AT and TA basepairs in the minor groove, DNA deformability must play a significant role in binding site selection, because not all AT-rich sequences are bound effectively by TBP. To gain insight into the precise role that the properties of the TATA sequence have in determining the specificity of the DNA substrates of TBP, the solution structure and dynamics of seven DNA dodecamers have been studied by using molecular dynamics simulations. The analysis of the structural properties of basepair steps in these TATA sequences suggests a reason for the preference for alternating pyrimidine-purine (YR) sequences, but indicates that these properties cannot be the sole determinant of the sequence specificity of TBP. Rather, recognition depends on the interplay between the inherent deformability of the DNA and steric complementarity at the molecular interface.

Molecular dynamics simulations of small DNA plasmids: effects of sequence and supercoiling on intramolecular motions

Small (600 base pair) DNA plasmids were modeled with a simplified representation (3DNA) and the intramolecular motions were studied using molecular mechanics and molecular dynamics techniques. The model is detailed enough to incorporate sequence effects. At the same time, it is simple enough to allow long molecular dynamics simulations. The simulations revealed that large-scale slithering occurs in a homogeneous sequence. In a heterogeneous sequence, containing numerous small intrinsic curves, the centers of the curves are preferentially positioned at the tips of loops. With more curves than loop tips (two in unbranched supercoiled DNA), the heterogeneous sequence plasmid slithers short distances to reposition other curves into the loop tips. However, the DNA is immobilized most of the time, with the loop tips positioned over a few favored curve centers. Branching or looping also appears in the heterogeneous sequence as a new method of repositioning the loop tips. Instead of a smooth progression of increasing writhing with increasing linking difference, theoretical studies have predicted that there is a threshold between unwrithed and writhed DNA at a linking difference between one and two. This has previously been observed in simulations of static structures and is demonstrated here for dynamic homogeneous closed DNA. Such an abrupt transition is not found in the heterogeneous sequence in both the static and dynamic cases.

Action at a distance in supercoiled DNA: effects of sequence on slither, branching, and intramolecular concentration

We report a computer modeling study of DNA supercoiling in model plasmids over the size range of 140-1260 bp. We used a computer model with basepair resolution. Molecular dynamics was used to produce ensembles at 300 K and to investigate intramolecular motions. The plasmid models varied by their sequence. The sequence types employed for comparison included a curve-bearing plasmid, a heterogenous sequence plasmid, and a homogenous sequence. Within the three sequence types tested at the 1260-bp plasmid size, we observed several sequence-dependent phenomena. Writhe, radius of gyration, slither motion, and branching probability were seen to be sequence dependent. Branching probability was the least in the homogenous plasmid and the greatest in the curve-bearing plasmid. The curve imposed a symmetry on the plasmid that was absent in the heterogenous sequence. Significant localizations and enhancements of intramolecular concentration were seen to a persistence length. Molecular dynamics allowed us to observe the mechanism of branch formation and reabsorption. We observed a size-dependent change in the types of motion observed in plasmids. Slither motion predominated in plasmids up to 600 bp in size, whereas global rearrangements were more important in the 1260 mer.

Structural prediction of A- and B-DNA duplexes based on coordinates of the phosphorus atoms

The sequence-dependent structure of DNA double helices was studied extensively during the past 10 years. How the backbone structure correlates with the base structure in a duplex conformation is still an important yet open question. Using a set of reduced coordinates and a least-squares fitting procedure, we have developed a method to predict structures for B-DNA duplexes based on coordinates of the phosphorus atoms. This method can be used to predict all-atom structures for both bent and straight molecules. We estimated the accuracies of the predictions by studying a set of 10 oligonucleotides with their structures available from the Protein Data Bank. We used this method to construct a modeled structure for the bacteriophage lambda cro operator for which the phosphorus coordinates were known from 3.5-angstrum resolution crystal data (4CRO).

What is the basis of sequence-directed curvature in DNAs containing A tracts?

A variety of solution and gel experiments show that DNAs containing tracts of 4-8 A's repeated in phase with the helix repeat are curved. Several independent analyses of these experiments argue that curvature resides in the A tracts themselves. In x-ray crystallographic studies of several DNAs containing A tracts, however, the A tracts are uncurved, leading to models in which curvature resides in the non-A tracts. This "curved general sequence model" has several problems, in our view. We review those, and we describe recent experiments that show that the dehydrating agents commonly used in x-ray crystallography markedly reduce curvature in gels and in solution, calling into question the ability of crystallography to determine the structural basis of DNA curvature. Finally, we discuss the critical role of hydration in curved DNAs and suggest new experiments that we hope could finally determine exactly which sequences are responsible for curvature.

Flexing and folding double helical DNA

DNA base sequence, once thought to be interesting only as a carrier of the genetic blueprint, is now recognized as playing a structural role in modulating the biological activity of genes. Primary sequences of nucleic acid bases describe real three-dimensional structures with properties reflecting those structures. Moreover, the structures are base sequence dependent with individual residues adopting characteristic spatial forms. As a consequence, the double helix can fold into tertiary arrangements, although the deformation is much more gradual and spread over a larger molecular scale than in proteins. As part of an effort to understand how local structural irregularities are translated at the macromolecular level in DNA and recognized by proteins, a series of calculations probing the structure and properties of the double helix have been performed. By combining several computational techniques, complementary information as well as a series of built-in checks and balances for assessing the significance of the findings are obtained. The known sequence dependent bending, twisting, and translation of simple dimeric fragments have been incorporated into computer models of long open DNAs of varying length and chemical composition as well as in closed double helical circles and loops. The extent to which the double helix can be forced to bend and twist is monitored with newly parameterized base sequence dependent elastic energy potentials based on the observed configurations of adjacent base pairs in the B-DNA crystallographic literature.

Static contributions to the persistence length of DNA and dynamic contributions to DNA curvature

Long molecules of DNA have the statistical properties of a worm-like coil. Deviations from linearity occur both because of small dynamic bends induced by thermal motion and from a random distribution of static bends. The latter originate in the different conformations of each of the possible base pair sequences. In this paper a statistical theory of the persistence length of DNA is developed which includes both static and dynamic effects for each base pair sequence, as well as the sequence-dependent correlations of bending angles. The result applies to a generic DNA, i.e., the average over an ensemble of all possible sequences. The theory is also applied to the generation of the average properties of curved DNAs by an analytic method that includes dynamic averaging as well as correlated bends. These results provide information which supplements that obtained by others using Monte Carlo methods. The additivity relation 1/P = 1/P(S) + 1/P(d) proposed by Trifonov et al., where P is the persistence length and P(S) and P(d) are the persistence lengths arising from purely static and dynamic effects, respectively, has been verified to be accurate to better than 0.5%. This is true for both a simplified model and one that includes a complete set of static bends at all base pair sequences.

Dehydrating agents sharply reduce curvature in DNAs containing A tracts

The structural basis of DNA curvature remains elusive, because models for curvature based on crystallographic structures of molecules containing A tracts do not agree with any of the models for sequence-directed curvature based on solution studies. Here we demonstrate that the difference is probably due to MPD (2-methyl-2,4-pentanediol), the dehydrating agent commonly used in crystallography. One characteristic signature of curved DNA molecules is that they run anomalously slowly on polyacrylamide gels, appearing to be larger than they actually are. The gel anomalies of three curved DNAs from trypanosome kinetoplast minicircles drop monotonically with increasing MPD concentration, indicating that MPD straightens molecules that are curved in aqueous solution. This is not due to some non-specific effect of MPD on poly(dA) or polypurine tracts, because control molecules containing dA70 and dG43 run normally over the full range of MPD concentrations. Circular dichroism spectra are not affected by MPD, ruling out a conformational change to a structure outside the B-DNA family. The effect is not due to MPD-induced changes in phasing of the curved sequences, because MPD has virtually no effect on the linking numbers of relaxed plasmids containing either curved sequences or dA70. At the concentrations of MPD used in X-ray crystallography, the curvature of DNAs containing A tracts is substantially lower than in solution, which probably explains the ongoing discrepancies between the crystallographic results and models based on solution studies.

Bending and curvature calculations in B-DNA

A simple program, BEND, has been written to calculate the magnitude of local bending and macroscopic curvature at each point along an arbitrary B-DNA sequence, using any desired bending model that specifies values of twist, roll and tilt as a function of sequence. The program has been used to evaluate six different DNA bending models in three categories. Two are bent non-A-tract models: (a) A new model based on the nucleosome positioning data of Satchwell et al 1986 (J. Mol. Biol. 191, 659-675), (b) The model of Calladine et al 1988 (J. Mol. Biol. 201, 127-137). Three are bent A-tract models: (c) The wedge model of Bolshoy et al 1991 (Proc. Natl. Acad. Sci. USA 88, 2312-2316), (d) The model of Cacchione et al 1989 (Biochem. 28, 8706-8713), (e) A reversed version of model (b). The last is a junction model: (f) The model of Koo & Crothers 1988 (Proc. Natl. Acad. Sci. USA 85, 1763-1767). Although they have widely different assumptions and values for twist, roll and tilt, all six models correctly predict experimental A-tract curvature as measured by gel retardation and cyclization kinetics, but only the new nucleosome positioning model is successful in predicting curvature in regions containing phased GGGCCC sequences. This model--showing local bending at mixed sequence DNA, strong bends at the sequence GGC, and straight, rigid A-tracts--is the only model consistent with both solution data from gel retardation and cyclization kinetics and structural data from x-ray crystallography.

DNA structural patterns and nucleosome positioning

There is no clear picture to date of the mechanisms determining nucleosome positioning. Generally, local DNA sequence signals (sequence-dependent positioning) or non-local signals (e.g. boundary effects) are possible. We have analyzed the DNA sequences of a series of positioned and mapped nucleosome cores in a systematic search for local sequence signals. The data set consists of 113 mapped nucleosome cores, mapped in vivo, in situ, or in reconstituted chromatin. The analysis focuses on the periodic distribution of sequence elements implied by each of six different published DNA structural models. We have also investigated the periodic distribution of all mono-, di-, and trinucleotides. An identical analysis was performed on a set of isolated chicken nucleosome cores (nucleosome data from the literature) that are presumably positioned due to local sequence signals. The results show that the sequences of the isolated nucleosome cores have a number of characteristic features that distinguish them clearly from randomly chosen reference DNA. This confirms that the positioning of these nucleosomes is mainly sequence-dependent (i.e., dependent on local octamer-DNA interactions) and that our algorithms are able to detect these patterns. Using the same algorithms, the sequences of the mapped nucleosome cores, however, are on average very similar to randomly chosen reference DNA. This suggests that the position of the majority of these nucleosomes can not be attributed to the sequence patterns implemented in our algorithms. The arrangement of positioned nucleosomes seems to be the result of a dynamic interplay of octamer-DNA interactions, nucleosome-nucleosome interactions and other positioning signals with varying relative contributions along the DNA.

Configurational statistics of the DNA duplex: extended generator matrices to treat the rotations and translations of adjacent residues

The base-to-base virtual bond treatment of nucleic acids used in statistical mechanical calculations of polynucleotide chain properties has been refined by incorporating the six parameters that relate the positions and orientations of sequential rigid bodies. The scheme allows for the sequence-dependent bending, twisting, and displacement of base pairs as well as for asymmetry in the angular and translational fluctuations of individual residues. Expressions are developed for the generator matrices required for the computation, as a function of chain length, of various parameters measuring the overall mean extension and shape of the DNA. Quantities of interest include the end-to-end vector r, the square of the end-to-end distance r2, the square radius of gyration s2, the center-of-gravity vector g, the second moments of inertia Sx2, and the higher moments of r and g. The matrix expressions introduced in the 1960s by Flory and co-workers for the determination of configuration-dependent polymer chain averages are decomposed into their translational and orientational contributions so that the methods can be extended to the rigid body analysis of chemical moieties. The new expressions permit, for the first time, examination of the effects of sequence-dependent translations, such as the lateral sliding of residues in A- and B-helices and the vertical opening of base pairs in drug-DNA complexes, on the average extension and shape of the long flexible double helix. The approach is in the following paper using conformational energy estimates of the base sequence-dependent flexibility of successive B-DNA base pairs.

Spatial translational motions of base pairs in DNA molecules: application of the extended matrix generator method

We have used the elementary generator matrices outlined in the preceding paper to examine the conformational plasticity of the nucleic acid double helix. Here we investigate kinked DNA structures made up of alternating B- and A-type helices and intrinsically curved duplexes perturbed by the intercalation of ligands. We model the B-to-A transition by the lateral translation of adjacent base pairs, and the intercalation of ligands by the vertical displacement of neighboring residues. We report a complete set of average configuration-dependent parameters, ranging from scalars (i.e., persistence lengths) to first- and second-order tensor parameters (i.e., average second moments of inertia), as well as approximations of the associated spatial distributions of the DNA and their angular correlations. The average structures of short chains (of lengths less than 100 base pairs) with local kinks or intrinsically curved sequences are essentially rigid rods. At the smallest chain lengths (10 base pairs), the kinked and curved chains exhibit similar average properties, although they are structurally perturbed compared to the standard B-DNA duplex. In contrast, at lengths of 200 base pairs, the curved and kinked chains are more compact on average and are located in a different space from the standard B- or A-DNA helix. While A-DNA is shorter and thicker than B-DNA in x-ray models, the long flexible A-DNA helix is thinner and more extended on average than its B-DNA counterpart because of more limited fluctuations in local structure. Curved polymers of 50 base pairs or longer also show significantly greater asymmetry than other DNAs (in terms of the distribution of base pairs with respect to the center of gravity of the chain). The intercalation of drugs in the curved DNA straightens and extends the smoothly deformed template. The dimensions of the average ellipsoidal boundaries defining the configurations of the intercalated polymers are roughly double those of the intrinsically curved chain. The altered proportions and orientations of these density functions reflect the changing shape and flexibility of the double helix. The calculations shed new light on the possible structural role of short A-DNA fragments in long B-type duplexes and also offer a model for understanding how GC-specific intercalative ligands can straighten naturally curved DNA. The mechanism is not immediately obvious from current models of DNA curvature, which attribute the bending of the chain to a perturbed structure in repeating tracts of A.T base pairs.

Theoretical analysis of the base stacking in DNA: choice of the force field and a comparison with the oligonucleotide crystal structures

It follows from previous studies that changes in the base pair vertical separation (BPVS) influence the architecture of DNA much more than any other conformational parameter. This inspired us to compare BPVS in the available oligonucleotide crystal structures with the optimum values provided by nine different empirical potentials employed in the theoretical studies of DNA conformation. This comparison shows that BPVS is reproduced by three fields in all steps of the highly resolved oligonucleotide crystal structures while the remaining six empirical potentials, including AMBER, GROMOS and CHARMM, provide systematic deviations. We further find that the base pairs are poorly stacked (mostly compressed) in some other refined DNA crystal structures. Our analysis indicates that this poor stacking originates from improperly determined positions of the bases. The approach described in the present communication can be used to identify DNA structures which are not accurate enough for studies of the relationships between the base sequence and DNA conformation.

The effect of intrinsic curvature on supercoiling: predictions of elasticity theory

Elasticity theory of naturally curved rods is employed to study the effects of intrinsic curvature on the properties of the equilibrium conformations of supercoiled DNA. The results stand in sharp contrast to those obtained when the molecule is viewed as being straight in its relaxed form. Starting from very fundamental principles of the theory, we show that the torsion of an open segment with a curved duplex axis can vary when the temperature, and along with it, the intrinsic twist is changed. Conversely, an imposed helicity, such as might be associated with binding to a histone, can change the intrinsic twist. It is also shown that another consequence of the presence of naturally curved sequences is that the twist density will, in general, vary with position along the chain in all equilibrium states. Then portions of the molecule will be more or less susceptible to interaction with other agents sensitive to such a variation. Finally, some closed equilibrium global structures uniquely associated with intrinsic curvature are discussed.

Persistence analysis of the static and dynamical helix deformations of DNA oligonucleotides: application to the crystal structure and molecular dynamics simulation of d(CGCGAATTCGCG)2

A theory and graphical presentation for the analysis of helix structure and deformations in oligonucleotides is presented. The parameters "persistence" and "flexibility" as defined in the configurational statistics of polymers of infinite length are reformulated at the oligonucleotide level in an extension of J. A. Schellman's method [(1974) Biopolymers, Vol. 17, pp. 217-226], and used as a basis for a systematic "Persistence Analysis" of the helix deformation properties for all possible subsequences in the structure. The basis for the analysis is a set of link vectors referenced to individual base pairs, and is limited to sequences exhibiting only perturbed rod-like behavior, i.e., below the threshold for supercoiling. The present application of the method is concerned with a physical model for the angular component of bending, so the link vectors are defined as the unit components of a global helix axis obtained by the procedure "Curves" of R. Lavery and H. Sklenar [(1988) J. Biomol. Struct. Dynam., Vol. 6, pp. 63-91; (1989) ibid., Vol. 6, pp. 655-667]. A discussion of the relationship between global bending and relative orientation of base pairs is provided. Our approach is illustrated by analysis of some model oligonucleotide structures with intrinsic kinks, the crystal structure of the dodecamer d(CGCGAATTCGCG)2, and the results of two molecular dynamics simulations on this dodecamer using two variations of the GROMOS force field. The results indicate that essentially all aspects of curvature in short oligonucleotides can be determined, such as the position and orientation of each bend, the sharpness or smoothness, and the location and linearity of subsequences. In the case of molecular dynamics simulations, where a Boltzmann ensemble of structures is analyzed, the spatial extent of the deformations (flexibility) is also considered.

Cytosine methylation can induce local distortions in the structure of duplex DNA

Methyl groups at the C5 position of pyrimidines located within oligopurine-oligopyrimidine tracts in DNA have been shown previously to modulate curvature generated by those tracts. However, it was not known whether the influence of such methyl groups is consequent to the altered helical structure within the tracts themselves. In the current study, it is demonstrated that methylation of cytosines up to three base pairs away from a (dA)5.(dT)5 tract (A-tract) can still result in alterations of the net curvature of the A-tract-containing DNA, as measured by alterations in electrophoretic mobility. This latter effect depends strongly on both the sequence of the non-A-tract DNA and the positions of the methylated C residues. The current results lend further support to the notion that the biological consequences of cytosine methylation may be effected through local alterations in DNA structure as well as through direct protein-DNA interactions.

DNA associations: packing calculations in A-, B-, and Z-DNA structures

A detailed theoretical study has been carried out to examine the modes of DNA-DNA interactions on the basis of hard-sphere contact criteria. Two helices of identical structure and length are oriented side-by-side and their relative positions are controlled by translations along and rotations about specific axes. Short atomic contacts between pairs of atoms in the structures are assessed and contact-free configurations are compiled. The computed contact-free arrangements of A, B, and Z double helices are found to be remarkably similar to the packing motifs observed in DNA crystals and stretched fibers. Equally interesting in the study are the broad ranges of sterically acceptable arrangements that preserve the overall packing morphology of neighboring duplexes: Among the most notable morphological features in the helical complexes are extended "super" major and minor grooves which might facilitate the wrapping and packaging of DNA chains in supramolecular assemblies. The hard-sphere computations, however, are insufficient for quantitative interpretation of the packing of DNA helices in the solid state. The results are, nevertheless, a useful starting point for energy based studies as well as relevant to the analysis of long-range interactions in DNA supercoils and cruciforms.

Sequence effects on the propeller twist of base pairs in DNA helices

Molecular mechanics calculations are performed on all the ten base pair steps (duplex dimers) and also a number of trimer and tetramer duplexes comprising them, in an attempt to systematically examine the possible base sequence effects on the magnitudes of propeller twists of base pairs at a given step. The analysis reveals that though propeller twist is a base pair property, it behaves very much like other base step parameters such as slide, roll, twist etc., Hence, it may be necessary to monitor the nature and variation of magnitudes of pt at a step. Calculations performed on 45 out of the 136 unique tetramer combinations involving all the ten unique base steps show that the difference in magnitudes of propeller twists of the base pairs of a given step has been found to be either steep or moderate depending on base pairs that flank the base step. These observations compare very well with the available experimental data. Tetramer sequences, wherein a base pair of a base step repeats in the same direction, exhibit a relatively steep difference in propeller twist at the step. Tetramers other than these exhibit moderate difference in propeller twist. Such sequences are broadly classified as type-I and type-II respectively. Practically all the tetrads considered in the study, excepting those with GT step and a few involving CG and GC steps, conform to the above classification.

Systematic study of nuclear Overhauser effects vis-à-vis local helical parameters, sugar puckers, and glycosidic torsions in B DNA: insensitivity of NOE to local transitions in B DNA oligonucleotides due to internal structural compensations

A method has been developed to solve structures of DNA oligomers in solution from the experimental NOE data. The method is a combination of two approaches: (1) full matrix NOESY simulations and (2) conformational calculations of DNA double helix based on generalized helical parameters. The process of the refinement of a solution structure does not involve NMR-derived interproton distance constraints; rather it consists of a direct fitting of a structure to the experimental NOE data, a weighted sum of energy, and R factor being under minimization. A helical parameters-based generation of DNA forms makes it possible to organize the search for the optimal structure more effectively, systematically varying starting conformations. The method has been used to calculate a structure for the self-complementary DNA hexamer GGATCC, which is consistent with the available experimental data. The structure belongs to the B family of forms, although the local structural heterogeneity is very strong. Sugar puckers vary from O4'-exo to C3'-exo; helical steps are open with different magnitudes toward the minor groove. Next, we have addressed the question of how uniquely the structure is defined by the existing NMR data. Different structural parameters have been systematically varied, and their effect on individual NOE's and the R factor has been studied. Two energetically conjugated parameters, sugar puckers and glycosidic angles, can be determined very reliably, because of the strong dependences of the intraresidue H6/H8 to H2'/H2''/H3' NOE's. In contrast, the local helical conformation of DNA and the geometry of base pairs proved to be underdetermined by the existing NOE information, because the effect of any helical parameter on interproton distances can be compensated by the concerted changes in other parameters.

Flexibility of DNA in 2:1 drug-DNA complexes--simultaneous binding of two DAPI molecules to DNA

Simultaneous binding of two DAPI molecules in the minor groove of (dA)15.(dT)15 B-DNA helix has been simulated by molecular mechanics calculations. The energy minimised structure shows some novel features in relation to binding of DAPI molecules as well as the flexibility of the grooves of DNA helices. The minor groove of the helix expands locally considerably (to 15 angstroms) to accommodate the two DAPI molecules and is achieved by positive propeller twisting of base pairs at the binding site concomitant with small variations in the local nucleotide stereochemistry. The expansion also brings forth simultaneously a contraction in the width of the major groove spread over to a few phosphates. These findings demonstrate another facet of the flexible stereochemistry of DNA helices in which the local features are significantly altered without being propagated beyond a few base pairs, and with the rest of the regions retaining the normal structure. Both the DAPI molecules are engaged in specific hydrogen bonds with the bases and non specific interactions with phosphates. Stacking interactions of DAPI molecules between themselves as well as with sugar-phosphate backbone contribute to the stability of the complex. The studies provide a stereochemical support to the experimental findings that under high drug-DNA ratio DAPI could bind in the 2:1 ratio.

The electrostatic contribution to DNA base-stacking interactions

Base-stacking and phosphate-phosphate interactions in B-DNA are studied using the finite difference Poisson-Boltzmann equation. Interaction energies and dielectric constants are calculated and compared to the predictions of simple dielectric models. No extant simple dielectric model adequately describes phosphate-phosphate interactions. Electrostatic effects contribute negligibly to the sequence and conformational dependence of base-stacking interactions. Electrostatic base-stacking interactions can be adequately modeled using the Hingerty screening function. The repulsive and dispersive Lennard-Jones interactions dominate the dependence of the stacking interactions on roll, tilt, twist, and propellor. The Lennard-Jones stacking energy in ideal B-DNA is found to be essentially independent of sequence.

Static and dynamic conformational properties of AT sequences in B-DNA

A theoretical study of the optimal conformations of nucleic acid oligomers containing tracts of AT base pairs is presented. The oligomers are studied in isolation and complexed with netropsin, a minor groove binding ligand. The flexibility of the oligomers and of their complexes is calculated by adiabatic mapping with respect to the total winding angle. The results of this study show that in uncomplexed oligomers the dinucleotide junctions AA, AT and TA have very different structural parameters and different responses to winding stress. The TA junction is clearly the most flexible and is the principal site for accommodating the imposed overwinding. Complexation by netropsin leads to two important effects: firstly, the three junctions adopt more uniform structures, the largest changes again being observed for TA, secondly, the differences in flexibility as a function of sequence are strongly attenuated.

Efficient detection of three-dimensional structural motifs in biological macromolecules by computer vision techniques

Macromolecules carrying biological information often consist of independent modules containing recurring structural motifs. Detection of a specific structural motif within a protein (or DNA) aids in elucidating the role played by the protein (DNA element) and the mechanism of its operation. The number of crystallographically known structures at high resolution is increasing very rapidly. Yet, comparison of three-dimensional structures is a laborious time-consuming procedure that typically requires a manual phase. To date, there is no fast automated procedure for structural comparisons. We present an efficient O(n3) worst case time complexity algorithm for achieving such a goal (where n is the number of atoms in the examined structure). The method is truly three-dimensional, sequence-order-independent, and thus insensitive to gaps, insertions, or deletions. This algorithm is based on the geometric hashing paradigm, which was originally developed for object recognition problems in computer vision. It introduces an indexing approach based on transformation invariant representations and is especially geared toward efficient recognition of partial structures in rigid objects belonging to large data bases. This algorithm is suitable for quick scanning of structural data bases and will detect a recurring structural motif that is a priori unknown. The algorithm uses protein (or DNA) structures, atomic labels, and their three-dimensional coordinates. Additional information pertaining to the structure speeds the comparisons. The algorithm is straightforwardly parallelizable, and several versions of it for computer vision applications have been implemented on the massively parallel connection machine. A prototype version of the algorithm has been implemented and applied to the detection of substructures in proteins.

End-to-End Diffusion and Distance Distributions of Flexible Donor-Acceptor Systems Observed by Intramolecular Energy Transfer and Frequency-Domain Fluorometry; Enhanced Resolution by Global Analysis of Externally Quenched and Nonquenched Samples

We used time-dependent fluorescence energy transfer of externally quenched and nonquenched samples, and global analysis of the data, to recover the end-to-end distance distributions and diffusion coefficients of flexible fluorescent molecules in low-viscosity solution. The fluorescence decays of tryptamine covalently linked to a dansyl acceptor by a polyethylene chain of 22 methylene groups were measured by the frequency-domain method. The data were fitted using numerical solutions of the diffusion equation which predicts the time- and distance-dependent population of the excited-state donors in the presence of energy transfer, followed by transformation to the frequency domain for nonlinear least-squares fitting to the experimental data. From the simulation study we found that the time- and distance-dependent population of the excited-state donors are significantly different for nonquenched and quenched samples and that the effects of end-to-end diffusion on the donor decay is decreased by collisional quenching. Importantly, the resolution is dramatically improved by the use of simultaneous analysis of quenched and nonquenched samples. This method was applied to the tryptamine-dansyl system using acrylamide as an external quencher. The recovered initial (t = 0) distance distribution, R av = 18.9 Å, hw = 17.1 Å, is very similar to that obtained for diffusion-free conditions. The end-to-end diffusion coefficient of D = 1.26 × 10-5 cm2/s is comparable to that expected for molecules the size of indole and dansyl. This value is about twice smaller than that obtained from diffusion-dependent intermolecular energy transfer using unlinked indole and dansylamide as the donor and acceptor, respectively, which may reflect the effects of the linker on diffusion of the chromophores.

Resolution of end-to-end diffusion coefficients and distance distributions of flexible molecules using fluorescent donor-acceptor and donor-quencher pairs

We used time-dependent fluorescence energy transfer, time-dependent collisional quenching, and global analysis of the data resulting from these through-space and contact interactions to recover the end-to-end distance distributions and diffusion coefficients of flexible fluorescent molecules. The fluorescence decays of covalently linked tryptamine-acceptor and tryptamine-quencher pairs were measured by the frequency-domain method. These data were fit using numerical solutions of the differential equation, which predicts the time- and distance-dependent population of the excited state donors in the presence of energy transfer or collisional quenching, followed by transformation to the frequency domain for nonlinear least-squares comparison with the experimental data. We found that the energy transfer data for the donor-acceptor pair alone were adequate to recover the starting distribution and the end-to-end diffusion coefficient; however, the resolution is dramatically improved by the use of both the through-space and contact interactions.

Static and statistical bending of DNA evaluated by Monte Carlo simulations

To investigate the influence of thermal fluctuations on DNA curvature the Metropolis procedure at 300 K was applied to B-DNA decamers containing A5.T5 and A4.T4 blocks. Monte Carlo simulations have confirmed the DNA bending anisotropy: B-DNA bends most easily in a groove direction (roll). The A5.T5 block is more rigid than the other sequences; the pyrimidine-purine dimers are found to be the most flexible. For A5TCTCT, A5CTCTC, and A5GAGAG, the average bend angle per decamer is 20-25 degrees in a direction toward the minor groove in the center of the A5.T5 tract, which is consistent with both the "junction" and "wedge AA" models. However, in A5T5, A4T4CG, and T4A4GC, bending is directed into the grooves at the 5' and 3' ends of purine tracts. Thus, directionality of bending caused by An.Tn blocks strongly depends on their neighboring sequences. These calculations demonstrate that the sequence-dependent variation of the minor-groove width mimics the observed hydroxyl radical cleavage pattern. To estimate the effect of fluctuations on the overall shape of curved DNA fragments, longer pieces of DNA (up to 200 base pairs) were generated. For sequences with strong curvature (A5X5 and A4T4CG), the static model and Monte Carlo ensemble give similar results but, for moderately and slightly curved sequences (A5T5 or T4A4GC), the static model predicts a much smaller degree of bending than does the statistical representation. Considering fluctuations is important for quantitative interpretation of the gel electrophoresis measurements of DNA curvature, where both the static and statistical bends are operative.