Validity of the nearest-neighbor approximation in the evaluation of the electrophoretic manifestations of DNA curvature

The validity of a theoretical nearest-neighbor model based on conformational energy calculations, for translating the deterministic fluctuations of DNA base sequences in superstructural elements, is tested on the electrophoretic data of 450 multimeric, duplex oligonucleotides with different sequence, periodicity, and complexity, corresponding to all the experimental data so far published. An accurate semiempirical linear relation between the gel electrophoretic retardation and the dispersion of the theoretical curvature was found which allows a prediction of electrophoretic anomalies of DNA tracts, e.g., the cyclic permutation gel assays, with great confidence. Such a pattern of agreement allows the interpretation of the gel electrophoresis retardation as due to an increase of activation energy required in straightening the DNA axis.     

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 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.     

Periodical polydeoxynucleotides and DNA curvature

A theoretical method to predict DNA curvature was developed, and a strikingly good correlation between the experimental retardations and theoretical curvature of all the periodical biosynthetic DNAs so far reported in the literature was found. The analysis has been extended to G- and C-rich synthetic polynucleotides, which show a behavior in agreement with the theoretical prediction. A possible application of the method to biologically significant DNA tracts is shown in the case of the regulative region of one of the genes which code for the small subunit of ribulose-1,5-bisphosphate carboxylase in Pisum sativum. While curvature measurements have not so far been reported for this system, biochemical analysis has indicated short nucleotide sequences (boxes I-III) as recognition sites for regulative proteins. On the basis of the theoretical curvature profile of the region and of the electrophoretic retardation measurements of synthetic polynucleotides, obtained by ligating monomers mimicking the boxes, we suggest that the proteins could use DNA local curvature as structural motif in the recognition process.     

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 theoretical method to predict DNA permutation gel electrophoresis from the sequence.

The gel electrophoretic permutation assays of DNA fragments experimentally investigated by different authors were theoretically reproduced using our theoretical model of sequence-dependent curvature. The general pattern of agreement obtained suggests that our method can be usefully adopted as an alternative to the experimental assay, in particular where the lack of a sufficient number of unique restriction sites in the fragment prevents the correct localization of the main bend site.     

Dual role of sequence-dependent DNA curvature in nucleosome stability: the critical test of highly bent Crithidia fasciculata DNA tract

In spite of the knowledge of the nucleosome molecular structure, the role of DNA intrinsic curvature in determining nucleosome stabilization is still an open question. In this paper, we describe a general model that allows the prediction of the nucleosome stability, tested on 83 different DNA sequences, in surprising good agreement with the experimental data, carried out in ours as well as in many other laboratories. The model is based on the dual role of DNA curvature in nucleosome thermodynamic stabilization. A critical test is the evaluation of the nucleosome free energy relative to a Crithidia fasciculata kinetoplast DNA fragment, which represents the most curved DNA found so far in biological systems and, therefore, is generally believed to form a highly stable nucleosome.     

New coarse-grained DNA model

A new coarse-grained model of the DNA molecule has been proposed, which was elaborated on the basis of its all-atomic model analysis. The model has been shown to rather well reproduce the DNA structure under low and room temperatures. The Young's and torsion moduli calculated using the coarse-grained model are in close agreement with experimental data and the theoretical results of other authors. The model can be used for DNA fragments of several hundreds base pairs for rather long time scales (of the order of micros) and for simulating their interactions with other structures.     

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.     

New coarse-grained DNA model

A new coarse-grained model of the DNA molecule has been proposed, which was elaborated on the basis of its all-atomic model analysis. The model has been shown to rather well reproduce the DNA structure under low and room temperatures. The Young’s and torsion moduli calculated using the coarse-grained model are in close agreement with experimental data and the theoretical results of other authors. The model can be used for DNA fragments of several hundreds base pairs for rather long time scales (of the order of μs) and for simulating their interactions with other structures.     

A quantitative measure of DNA curvature enabling the comparison of predicted structures

A growing body of data indicates that the equilibrium structures of some DNA fragments are curved and that curvature is sequence-directed. We describe a quantitative measure of DNA curvature that can be used for evaluating and comparing current proposed models for the molecular basis of DNA curvature. We demonstrate that this measure, in conjunction with any given prediction model, enables both the comparison of experimental data to predictions and the scanning of nucleotide sequence databases for potential curved regions.     

Electron microscopy mapping of pBR322 DNA curvature. Comparison with theoretical models.

A map of local curvature of the pBR322 DNA has been established by electron microscopy analysis of linearized plasmid molecules. To determine their polarity these molecules are one end labelled with an avidin-ferritin-biotin complex and the images are digitized. Local curvature is calculated from two mathematical treatments of the DNA trajectory and expressed in term of a mean dinucleotide wedge angle. Eight regions of curvature are distinguished. The four main regions of curvature have a high content of phased AA runs. The experimental curvature map is compared to theoretical maps of curvature obtained from four available models for DNA curvature.     

Precipitation of DNA by polyamines: a polyelectrolyte behavior.

Conditions of double-stranded DNA precipitation by the polyamines spermidine and spermine have been determined experimentally and compared to theoretical predictions. The influence of the concentrations of DNA and added monovalent salt, and of the DNA length has been investigated in a systematic manner. Three regimes of DNA concentrations are observed. We clarify the dependence of these regimes on the monovalent salt concentration and on the DNA length. Our observations make possible a rationalization of the experimental results reported in the literature. A comparison of the precipitation conditions of different kinds of polyelectrolytes suggests a general process. Our experimental data are compared to the "ion-bridging" model based on short-range electrostatic attractions. By starting from the spinodal equation, predicted by this model, and using the limiting form of Manning's fractions of condensed counterions, analytical expressions of the precipitation conditions have been found in the three regimes. Experimental and theoretical results are in good agreement.     

A Quantitative Measure of DNA Curvature Enabling the Comparison of Predicted Structures

Abstract

A growing body of data indicates that the equilibrium structures of some DNA fragments are curved and that curvature is sequence-directed. We describe a quantitative measure of DNA curvature that can be used for evaluating and comparing current proposed models for the molecular basis of DNA curvature. We demonstrate that this measure, in conjunction with any given prediction model, enables both the comparison of experimental data to predictions and the scanning of nucleotide sequence databases for potential curved regions.     

Thermodynamics and equilibrium sedimentation analysis of the close approach of DNA molecules and a molecular ordering transition

Measurement of the equilibrium distribution of persistence length fragments of DNA in high concentration in the ultracentrifuge shows that the reduced osmotic pressure rises much faster than linearly. From analysis of the data in terms of the Zimm cluster integral we infer that the net interactions between helices are purely repulsive at all distances. A theoretical equation of state derived from scaled particle theory with one adjustable parameter is in excellent agreement with the experimental data so long as the salt concentration is not excessively low. The parameter represents the hard-core radius in a simplified approximation to the potential function for the electrostatic repulsion between helices. Its value depends on the salt concentration, and it shrinks at high salt to a radius in close agreement with direct structural estimates. At a particular value of the osmotic pressure that is only slightly salt dependent, the solution undergoes a reversible transition to a denser, turbid, optically anisotropic phase. The relation between DNA volume fraction, including the electrostatic radius, at the transition point and the effective asymmetry of the molecules as a function of salt is in approximate correspondence with various theoretical treatments. However, the experimental function extrapolates to the correct limit for spherical particles. The work needed to bring DNA to a high concentration is estimated. The results suggest that the phase transition is first order.     

Application of the Poisson Boltzmann polyelectrolyte model for analysis of thermal denaturation of DNA in the presence of Na+ and polyamine cations

The Poisson Boltzmann (PB) cell model of polyelectrolyte solution has been used for calculation of the electrostatic free energy difference, Delta G(el), between double- and single-stranded DNA. The calculations have been performed for conditions relevant to describe the DNA helix-coil transition in NaCl solution in the presence of the natural polyamines putrescine(2+), spermidine(3+), spermine(4+) and their synthetic homologs with different spacing between the charged amino groups, for which experimental values of the DNA 'melting' transition temperature (T(m)) are available. Using the PB theory and the polyamine ion radius as an adjusting parameter provides quantitative agreement between experimental and theoretical T(m)--salt concentration dependencies only by using physically unreasonable radii for the polyamine. Thus, modeling the linear and flexible polyamines as charged spheres within the PB cell model is an implausible oversimplification. We propose another explanation for the experimental observations, still within the frame of the 'primitive' PB polyelectrolyte theory. This explanation is based on an analysis of the Delta G(el) dependence on the stoichiometry of polyamine-polyanion binding to double- and single-stranded DNA.     

The effect of intrinsic curvature on conformational properties of circular DNA.

Both thermal fluctuations and the intrinsic curvature of DNA contribute to conformations of the DNA axis. We looked for a way to estimate the relative contributions of these two components of the double-helix curvature for DNA with a typical sequence. We developed a model and Monte Carlo procedure to simulate the Boltzmann distribution of DNA conformations with a specific intrinsic curvature. Two steps were used to construct the equilibrium conformation of the model chain. We first specified the equilibrium DNA conformation at the base pair level of resolution, using a set of the equilibrium dinucleotide angles and DNA sequence. This conformation was then approximated by the conformation of the model chain consisting of a reduced number of longer, straight cylindrical segments. Each segment of the chain corresponded to a certain number of DNA base pairs. We simulated conformational properties of nicked circular DNA for different sets of equilibrium dinucleotide angles, different random DNA sequences, and lengths. Only random sequences of DNA generated with equal probability of appearance for all types of bases at any site of the sequence were used. The results showed that for a broad range of intrinsic curvature parameters, the radius of gyration of DNA circles should be nearly independent of DNA sequence for all DNA lengths studied. We found, however, a DNA properly that should strongly depend on DNA sequence if the double helix has essential intrinsic curvature. This property is the equilibrium distribution of the linking number for DNA circles that are 300-1000 bp in length. We found that a large fraction of the distributions corresponding to random DNA sequences should have two separate maxima. The physical nature of this unexpected effect is discussed. This finding opens new opportunities for joined experimental and theoretical studies of DNA intrinsic curvature.     

A model for the dynamics of mammalian family X DNA polymerases

Based on available structural studies, a model is presented for polymerization dynamics of mammalian family X DNA polymerases, including polymerases β, λ, μ, and terminal deoxynucleotidyl transferase (TdT). Using the model, distinct polymerization activities and processivities of the four polymerases acting on different forms of DNA substrate are analyzed and studied theoretically. A “gradient” of template dependence of polymerases β, λ, μ, and TdT is well explained. The much higher occurrence frequencies of the −1 frameshift DNA synthesis by pols λ and μ than that by pol β are well explained. The theoretical results on the polymerization processivities are also in agreement with the available experimental data.     

Abasic sites in duplex DNA: molecular modeling of sequence-dependent effects on conformation

Molecular modeling calculations using JUnction Minimization of Nucleic Acids (JUMNA) have been used to study sequence effects on the conformation of abasic sites within duplex DNA. We have considered lesions leading to all possible unpaired bases (X), adenine, guanine, cytosine, or thymine contained within two distinct sequence contexts, CXC and GXG. Calculations were carried out on DNA 11-mers using extensive conformational search techniques to locate the most stable abasic conformations and using Poisson-Boltzmann corrected electrostatics to account for solvation effects. The results, which are in very good agreement with available experimental data, point to strong sequence effects on both the position of the unpaired base (intra or extrahelical) and on the overall curvature induced by the abasic lesion. For CXC, unpaired purines are found to lie within the helix, while unpaired pyrimidines are either extrahelical or in equilibrium between the intra and extrahelical forms. For GXG, all unpaired bases lead to intrahelical forms, but with marked, sequence-dependent differences in induced curvature.     

Theories for analyzing polymorphism data in duplicated genes

A simple model for the evolutionary process of a pair of duplicated genes under concerted evolution is developed. The model considers mutation, recombination and gene conversion between two genes in a finite population. Based on diffusion theory, the expected amount of DNA variation within and between two genes are obtained. To investigate the pattern of DNA polymorphism, a coalescent tool to simulate patterns of polymorphism is developed. The theoretical results are well in agreement with polymorphism data in duplicated genes. The effect of selection on the pattern of polymorphism is also considered.