A theoretical model for the prediction of sequence-dependent nucleosome thermodynamic stability

A theoretical model for predicting nucleosome thermodynamic stability in terms of DNA sequence is advanced. The model is based on a statistical mechanical approach, which allows the calculation of the canonical ensemble free energy involved in the competitive nucleosome reconstitution. It is based on the hypothesis that nucleosome stability mainly depends on the bending and twisting elastic energy to transform the DNA intrinsic superstructure into the nucleosomal structure. The ensemble average free energy is calculated starting from the intrinsic curvature, obtained by integrating the dinucleotide step deviations from the canonical B-DNA and expressed in terms of a Fourier series, in the framework of first-order elasticity. The sequence-dependent DNA flexibility is evaluated from the differential double helix thermodynamic stability. A large number of free-energy experimental data, obtained in different laboratories by competitive nucleosome reconstitution assays, are successfully compared to the theoretical results. They support the hypothesis that the stacking energies are the major factor in DNA rigidity and could be a measure of DNA stiffness. A dual role of DNA intrinsic curvature and flexibility emerges in the determination of nucleosome stability. The difference between the experimental and theoretical (elastic) nucleosome-reconstitution free energy for the whole pool of investigated DNAs suggests a significant role for the curvature-dependent DNA hydration and counterion interactions, which appear to destabilize nucleosomes in highly curved DNAs. This model represents an attempt to clarify the main features of the nucleosome thermodynamic stability in terms of physical-chemical parameters and suggests that in molecular systems with a large degree of complexity, the average molecular properties dominate over the local features, as in a statistical ensemble.     

A nonlinear dynamic model of DNA with a sequence-dependent stacking term

No simple model exists that accurately describes the melting behavior and breathing dynamics of double-stranded DNA as a function of nucleotide sequence. This is especially true for homogenous and periodic DNA sequences, which exhibit large deviations in melting temperature from predictions made by additive thermodynamic contributions. Currently, no method exists for analysis of the DNA breathing dynamics of repeats and of highly G/C- or A/T-rich regions, even though such sequences are widespread in vertebrate genomes. Here, we extend the nonlinear Peyrard–Bishop–Dauxois (PBD) model of DNA to include a sequence-dependent stacking term, resulting in a model that can accurately describe the melting behavior of homogenous and periodic sequences. We collect melting data for several DNA oligos, and apply Monte Carlo simulations to establish force constants for the 10 dinucleotide steps (CG, CA, GC, AT, AG, AA, AC, TA, GG, TC). The experiments and numerical simulations confirm that the GG/CC dinucleotide stacking is remarkably unstable, compared with the stacking in GC/CG and CG/GC dinucleotide steps. The extended PBD model will facilitate thermodynamic and dynamic simulations of important genomic regions such as CpG islands and disease-related repeats.     

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.     

Modeling DNA Thermodynamics under Torsional Stress

Negatively twisted DNA is essential to many biological functions. Due to torsional stress, duplex DNA can have local, sequence-dependent structural defects. In this work, a thermodynamic model of DNA was built to qualitatively predict the local sequence-dependent mechanical instabilities under torsional stress. The results were compared to both simulation of a coarse-grained model and experiment results. By using the Kirkwood superposition approximation, we built an analytical model to represent the free energy difference ΔW of a hydrogen-bonded basepair between the B-form helical state and the basepair opened (or locally melted) state, within a given sequence under torsional stress. We showed that ΔW can be well approximated by two-body interactions with its nearest-sequence-neighbor basepairs plus a free energy correction due to long-range correlations. This model is capable of rapidly predicting the position and thermodynamics of local defects in a given sequence. The result qualitatively matches with an in vitro experiment for a long DNA sequence (>4000 basepairs). The 12 parameters used in this model can be further quantitatively refined when more experimental data are available.     

Modeling DNA Thermodynamics under Torsional Stress

Negatively twisted DNA is essential to many biological functions. Due to torsional stress, duplex DNA can have local, sequence-dependent structural defects. In this work, a thermodynamic model of DNA was built to qualitatively predict the local sequence-dependent mechanical instabilities under torsional stress. The results were compared to both simulation of a coarse-grained model and experiment results. By using the Kirkwood superposition approximation, we built an analytical model to represent the free energy difference ΔW of a hydrogen-bonded basepair between the B-form helical state and the basepair opened (or locally melted) state, within a given sequence under torsional stress. We showed that ΔW can be well approximated by two-body interactions with its nearest-sequence-neighbor basepairs plus a free energy correction due to long-range correlations. This model is capable of rapidly predicting the position and thermodynamics of local defects in a given sequence. The result qualitatively matches with an in vitro experiment for a long DNA sequence (>4000 basepairs). The 12 parameters used in this model can be further quantitatively refined when more experimental data are available.     

Structural and Molecular Biology of the eye Lens Membrane

Abstract

The DNA double helix exhibits local sequence-dependent polymorphism at the level of the single base pair and dinucleotide step. Curvature of the DNA molecule occurs in DNA regions with a specific type of nucleotide sequence periodicities. Negative supercoiling induces in vitro local nucleotide sequence-dependent DNA structures such as cruciforms, left-handed DNA, multistranded structures, etc. Techniques based on chemical probes have been proposed that make it possible to study DNA local structures in cells. Recent results suggest that the local DNA structures observed in vitro exist in the cell, but their occurrence and structural details are dependent on the DNA superhelical density in the cell and can be related to some cellular processes.     

Local supercoil-stabilized DNA structures

The DNA double helix exhibits local sequence-dependent polymorphism at the level of the single base pair and dinucleotide step. Curvature of the DNA molecule occurs in DNA regions with a specific type of nucleotide sequence periodicities. Negative supercoiling induces in vitro local nucleotide sequence-dependent DNA structures such as cruciforms, left-handed DNA, multistranded structures, etc. Techniques based on chemical probes have been proposed that make it possible to study DNA local structures in cells. Recent results suggest that the local DNA structures observed in vitro exist in the cell, but their occurrence and structural details are dependent on the DNA superhelical density in the cell and can be related to some cellular processes.     

DNA sequence-dependent deformability--insights from computer simulations

The article reviews some recent developments in studying DNA sequence-dependent deformability, with emphasis on computer modeling. After a brief outline of available experimental techniques, we proceed to computational methods and focus on atomic-resolution molecular dynamics (MD) simulations. A sequence-dependent local (base-pair step) force field inferred from MD is compared with force fields obtained by other techniques. Various methods for establishing global (flexible-rod) DNA elastic constants are reviewed, including an approach based on atomic resolution MD. The problem of defining the global deformation variables, as well as the question of anisotropy and nonlocal effects, are discussed. As an example, both local and global deformability calculations from atomic-resolution MD of EcoRI dodecamer are presented.     

Predicting sequence-dependent melting stability of short duplex DNA oligomers

Many important applications of DNA sequence-dependent hybridization reactions have recently emerged. This has sparked a renewed interest in analytical calculations of sequence-dependent melting stability of duplex DNA. In particular, for many applications it is often desirable to accurately predict the transition temperature, or t_m, of short duplex DNA oligomers (∼ 20 base pairs or less) from their sequence and concentration. The thermodynamic analytical method underlying these predictive calculations is based on the nearest-neighbor model. At least 11 sets of nearest-neighbor sequence-dependent thermodynamic parameters for DNA have been published. These sets are compared. Use of the nearest-neighbor sets in predicting t_m from the DNA sequence is demonstrated, and the ability of the nearest-neighbor parameters to provide accurate predictions of experimental t_m's of short duplex DNA oligomers is assessed. © 1998 John Wiley & Sons, Inc. Biopoly 44: 217–239, 1997     

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.     

Curved DNA

A priori considerations and the concept of the sequence-dependent local curving of the DNA axis. Experimental evidence: electric dichroism (relaxation time measurements); anomalous electrophoretic mobility and gel-filtration of some restriction fragments of DNA; one-sided binding of the nucleosomal DNA to the mica surface. Theoretical predictions concerning the nucleotide sequences of the curved DNA. Discovery of the dinucleotide periodicity in the chromatin DNA. The sequence periodicity as a tool for mapping of the nucleosomes along the sequences. Preferential binding of the histone octamers to the curved pieces of DNA--sequence analysis predictions and comparison with experiments: Theoretical and experimental estimates of the tilt and roll angles for different combinations of the neighboring base-pairs. Inherent sequence-dependent curvature and apparent persistence length of DNA.     

Experimental evaluation of the Liu–Beveridge dinucleotide step model of DNA structure

Methods for predicting DNA curvature have many possible applications. Dinucleotide step models describe DNA shape by characterization of helical twist, deflection angles and the direction of deflection for nearest neighbor base pairs. Liu and Beveridge have extended previous applications of dinucleotide step models with the development and qualitative validation of a predictive method for sequence-dependent DNA curvature (the LB model). We tested whether the LB model accurately predicts experimentally deduced curvature angles and helical repeat parameters for DNA sequences not in its training set, particularly when challenged with quantitative data and subtle sequence phasings. We examined a series of 17 well-characterized DNA sequences to compare electrophoretic and computational results. The LB model is superior to two other models in the prediction of helical repeat parameters. We observed a strong linear correlation between curvature magnitudes predicted using the LB model and those determined by electrophoretic ligation ladder experiments, although the LB model somewhat underestimated apparent curvature. With longer electrophoretic phasing probes the LB model slightly overestimated gel mobility anomalies, with modest deviations in predicted helical repeat parameters. Overall, our analyses suggest that the LB model provides reasonably accurate predictions for the electrophoretic behavior of DNA.     

Theoretical prediction of the gel electrophoretic retardation changes due to point mutations in a tract of SV40 DNA.

The changes of gel electrophoretic retardation due to single base substitutions in a 173 bp fragment of Sv40 DNA were predicted by using a theoretical model based on conformational energy calculations. As described in previous papers, this model allows successful prediction of the gel electrophoretic retardation of synthetic as well as natural DNAs reported in literature. The experimental retardations related to 195 point-mutated DNAs were reproduced with a standard deviation of 0.05 comparable with the experimental one of 0.04. This result, which represents a very critical test for the proposed model, indicates that DNA superstructures can be satisfactorily predicted on the simple physical basis of the integration of the nearest-neighbour perturbations in the dinucleotide steps. Thus, cooperative effects appear, in the majority of cases investigated, to play a second order role.     

Principles of sequence-dependent flexure of DNA

The curvature of a bent rod may be defined in several different, but equivalent ways. The best way of describing the curvature of double-helical DNA is by an angle of turning per base step. Curvature comes mainly from the angle of roll between successive base-pairs, and this is defined as positive when the angle opens up on the minor groove side of the bases. DNA forms a plane curve if the roll angle values along the molecule alternate periodically between positive and negative, with a complete period equal to the helical repeat. It is known from studies of crystallized oligomers that the roll angles for particular dinucleotide steps have preferred values, or lie in preferred ranges of values. Therefore the formation of a plane curve will be easier with some base sequences of DNA than with others. We set up a computer algorithm for determining the ease with which DNA of given sequence will adopt a curved form. The algorithm has two different sets of constants: in model 1 the base step parameters come from an inspection of crystallized oligomers, and in model 2 data from a statistical survey of the incidence of dinucleotide steps in a large number of samples of chicken erythrocyte core DNA is incorporated. Both forms of the algorithm successfully locate the dyad of the nucleosome sequence (modulo 10) in a frog gene, and suggest strongly that sequence-dependent flexural properties of DNA play a part in the recognition of binding sites by nucleosome cores.     

DNA recognition by DNase I

Bovine pancreatic DNase I shows a strong preference for double-stranded substrates and cleaves DNA with strongly varying cutting rates suggesting that the enzyme recognises sequence-dependent structural variations of the DNA double helix. The complicated cleavage pattern indicates that several local as well as global helix parameters influences the cutting frequency of DNase I at a given bond. The high resolution crystal structures of two DNase I-DNA complexes showed that the enzyme binds tightly in the minor groove, and to the sugar-phosphate backbones of both strands, and thereby induces a widening of the minor groove and a bending towards the major grooves. In agreement with biochemical data this suggests that flexibility and minor groove geometry are major parameters determining the cutting rate of DNase I. Experimental observations showing that the sequence environmental of a dinucleotide step strongly affects its cleavage efficiency can be rationalized by that fact that six base pair are in contact with the enzyme. Mutational analysis based on the structural results has identified critical residues for DNA binding and cleavage and has lead to a proposal for the catalytic mechanism.     

Sequence-dependent dynamics of duplex DNA: the applicability of a dinucleotide model

The short-time (submicrosecond) bending dynamics of duplex DNA were measured to determine the effect of sequence on dynamics. All measurements were obtained from a single site on duplex DNA, using a single, site-specific modified base containing a rigidly tethered, electron paramagnetic resonance active spin probe. The observed dynamics are interpreted in terms of single-step sequence-dependent bending force constants, determined from the mean squared amplitude of bending relative to the end-to-end vector using the modified weakly bending rod model. The bending dynamics at a single site are a function of the sequence of the nucleotides constituting the duplex DNA. We developed and examined several dinucleotide-based models for flexibility. The models indicate that the dominant feature of the dynamics is best explained in terms of purine- and pyrimidine-type steps, although distinction is made among all 10 unique steps: It was found that purine-purine steps (which are the same as pyrimidine-pyrimidine steps) were near average in flexibility, but the pyrimidine-purine steps (5' to 3') were nearly twice as flexible, whereas purine-pyrimidine steps were more than half as flexible as average DNA. Therefore, the range of stepwise flexibility is approximately fourfold and is characterized by both the type of base pair step (pyrimidine/purine combination) and the identity of the bases within the pair (G, A, T, or C). All of the four models considered here underscore the complexity of the dependence of dynamics on DNA sequence with certain sequences not satisfactorily explainable in terms of any dinucleotide model. These findings provide a quantitative basis for interpreting the dynamics and kinetics of DNA-sequence-dependent biological processes, including protein recognition and chromatin packaging.     

Nucleosome organization on Kluyveromyces lactis centromeric DNAs

The preferential assembly of specialized nucleosomes on budding yeast centromeres can be due either to the higher stability of specialized centromeric nucleosomes and/or to the lower stability of canonical centromeric nucleosomes with respect to bulk nucleosomes. We have evaluated the thermodynamic stability of canonical nucleosomes, assembled on Kluyveromyces lactis centromeric DNAs, with a competitive reconstitution assay and a theoretical method recently developed by us. The results, obtained by both methods, show that all five known centromeric DNAs from K. lactis are able to organize canonical nucleosomes, characterized by higher stability with respect those of bulk DNA. With 'footprinting' and theoretical prediction, based on sequence-dependent DNA elasticity, we have found that centromeric canonical nucleosomes are characterized by nucleosome dyad axis multiple positioning, rotationally phased. The isoenergetic nucleosome multiple positions are relevant in understanding the transition from canonical to specialized nucleosomes in interacting with centromere protein complexes. The satisfactory agreement between the results obtained from theoretical and experimental methods shows that sequence-dependent centromeric DNA elasticity has a main role in nucleosome thermodynamic stability and positioning.     

DNA basepair step deformability inferred from molecular dynamics simulations

The sequence-dependent DNA deformability at the basepair step level was investigated using large-scale atomic resolution molecular dynamics simulation of two 18-bp DNA oligomers: d(GCCTATAAACGCCTATAA) and d(CTAGGTGGATGACTCATT). From an analysis of the structural fluctuations, the harmonic potential energy functions for all 10 unique steps with respect to the six step parameters have been evaluated. In the case of roll, three distinct groups of steps have been identified: the flexible pyrimidine-purine (YR) steps, intermediate purine-purine (RR), and stiff purine-pyrimidine (RY). The YR steps appear to be the most flexible in tilt and partially in twist. Increasing stiffness from YR through RR to RY was observed for rise, whereas shift and slide lack simple trends. A proposed measure of the relative importance of couplings identifies the slide-rise, twist-roll, and twist-slide couplings to play a major role. The force constants obtained are of similar magnitudes to those based on a crystallographic ensemble. However, the current data have a less complicated and less pronounced sequence dependence. A correlation analysis reveals concerted motions of neighboring steps and thus exposes limitations in the dinucleotide model. The comparison of DNA deformability from this and other studies with recent quantum-chemical stacking energy calculations suggests poor correlation between the stacking and flexibility.     

Studies of DNA dumbbells VII: evaluation of the next-nearest-neighbor sequence-dependent interactions in duplex DNA

Melting experiments were conducted on 22 DNA dumbbells as a function of solvent ionic strength from 25-115 mM Na(+). The dumbbell molecules have short duplex regions comprised of 16-20 base pairs linked on both ends by T(4) single-strand loops. Only the 4-8 central base pairs of the dumbbell stems differ for different molecules, and the six base pairs on both sides of the central sequence and adjoining loops on both ends are the same in every molecule. Results of melting analysis on the 22 new DNA dumbbells are combined with our previous results on 17 other DNA dumbbells, with stem lengths containing from 14-18 base pairs, reported in the first article of this series (Doktycz, Goldstein, Paner, Gallo, and Benight, Biopoly 32, 1992, 849-864). The combination of results comprises a database of optical melting parameters for 39 DNA dumbbells in ionic strengths from 25-115 mM Na(+). This database is employed to evaluate the thermodynamics of singlet, doublet, and triplet sequence-dependent interactions in duplex DNA. Analysis of the 25 mM Na(+) data reveals the existence of significant sequence-dependent triplet or next-nearest-neighbor interactions. The enthalpy of these interactions is evaluated for all possible triplets. Some of the triplet enthalpy values are less than the uncertainty in their evaluation, indicating no measurable interaction for that particular sequence. This finding suggests that the thermodynamic stability of duplex DNA depends on solvent ionic strength in a sequence-dependent manner. As a part of the analysis, the nearest-neighbor (base pair doublet) interactions in 55, 85, and 115 mM Na(+) are also reevaluated from the larger database.