The translation of DNA primary base sequence into three-dimensional structure

A procedure is outlined to obtain a reliable computer-generatedrepresentation of the DNA duplex from its primary sequence ofbase pairs. The calculations are based on the potential energiesof interaction of adjacent side groups. The methods are, however,completely general and can be adapted to any set of base sequencedependent conformational rules. Static representations of theDNA are compared with the distributions of conformations obtainedfrom Monte Carlo simulation studies. Direct matrix generatorcalculations of the average (equilibrium) extension and orientationof various sequences and numerical estimates of the flexibilityof the chains as a whole are also reported. The methods areapplied to three short fragments of kinetoplast DNA from Crithidiafasciculata which exhibit dramatically different behavior onnon-denaturing poly-acrylamide gels. Received on August 17, 1987; accepted on December 19, 1987     

Structure of the hydration envelope of the B-form of polydeoxyribonucleotides poly(dA-dC).poly(dG-dT) and poly(dA-dG).poly(dTs-dT) from the data of Monte-Carlo simulation

The results of a Monte Carlo simulation of the hydration shell of two polynucleotides poly (dA-dC).poly(dG-dT) and poly(dA-dG).poly(dC-dT) are reported. This study is a part of a series of Monte Carlo computations of the hydration of regular polydeoxyribonucleotides with dinucleotide repeat aimed at looking for dependences of hydration shell structure on base sequence. The coordinates of the main local maximal of water density near the polymers and the topology of the most probable one- and two-membered water bridges are published. For most of the sequences a common primary hydration of base edges of successive base pairs is characteristic. The AT-homopolymeric sequence represents an exception with autonomous primary hydration of a base pair in both grooves, which correlates with the sequence-dependent flexibility and the occurrence of bends of DNA.     

Excluded volume of an intermediate-molecular-weight DNA. A Monte Carlo analysis

A Monte Carlo procedure wasused to determine the effect of excluded volume on the dimensions of an intermediate-molecular-weight DNA for different Na⁺ concentrations. The calculation of α, the parameter for the linear expansion due to excluded volume, was accomplished by generating sets of chains and, for each set, comparing the average radius of gyration for the set of chains that do not overlap to that averaged over the entire set of chains. Each chain was defined by cylinders linked with free rotation and with bend angles generated according to a weighted Gaussian distribution. The chain parameters—contour lenght, cylinder lenght and diameter—were fixed in order to resemble published light-scattering experiments on Col E₁ DNA. Values for α were less than 1.08. for Na⁺ concentrations between 0.007 and 1.0M. A previously reported analytical calculation of the excluded-volume correction of intermediate-sized DNA gave results that are closely similar to those from the Monte Carlo analysis.     

Simulations on the Primitive Electrolyte Environment of a High Charge-density Polyelectrolyte. A Sampling Problem and its Solution

Abstract

We show that the classical Metropolis Monte Carlo (MMC) algorithm converges very slowly when applied to the primitive electrolyte environment for a high charge-density polyelectrolyte. This slowness of convergence, which is due to the large density inhomogeneity around the polyelectrolyte, produces noticeable errors in the ion distribution functions for MMC runs of 1.3 × 10⁶ trial steps started from nonequilibrium distributions. We report that an algorithm which we call DSMC (for density-scaled Monte Carlo) overcomes this problem and provides relatively rapid convergence in this application. We suggest that DSMC should be well-suited for other Monte Carlo simulations on physical systems where large density inhomogeneities occur.     

Influences of error distributions of net ecosystem exchange on parameter estimation of a process-based terrestrial model: A case of broad-leaved Korean pine mixed forest in Changbaishan, China

Model predictions can be improved by parameter estimation from measurements. It was assumed that measurement errors of net ecosystem exchange (NEE) of CO₂ follow a normal distribution. However, recent studies have shown that errors in eddy covariance measurements closely follow a double exponential distribution. In this paper, we compared effects of different distributions of measurement errors of NEE data on parameter estimation. NEE measurements in the Changbaishan forest were assimilated into a process-based terrestrial ecosystem model. We used the Markov chain Monte Carlo method to derive probability density functions of estimated parameters. Our results showed that modeled annual total gross primary production (GPP) and ecosystem respiration (Re) using the normal error distribution were higher than those using the double exponential distribution by 61–86 gC m^?2 a^?1 and 107–116 gC m^?2 a^?1, respectively. As a result, modeled annual sum of NEE using the normal error distribution was lower by 29–47 gC m^?2 a^?1 than that using the double exponential error distribution. Especially, modeled daily NEE based on the normal distribution underestimated the strong carbon sink in the Changbaishan forest in the growing season. We concluded that types of measurement error distributions and corresponding cost functions can substantially influence the estimation of parameters and carbon fluxes.     

A Monte Carlo method for generating structures of short single-stranded DNA sequences

A Monte Carlo method has been developed for generating the conformations of short single-stranded DNAs from arbitrary starting states. The chain conformers are constructed from energetically favorable arrangements of the constituent mononucleotides. Minimum energy states of individual dinucleotide monophosphate molecules are identified using a torsion angle minimizer. The glycosyl and acyclic backbone torsions of the dimers are allowed to vary, while the sugar rings are held fixed in one of the two preferred puckered forms. A total of 108 conformationally distinct states per dimer are considered in this first stage of minimization. The torsion angles within 5 kcal/mole of the global minimum in the resulting optimized states are then allowed to vary by ±10° in an effort to estimate the breadth of the different local minima. The energies of a total of 2187 (3⁷) angle combinations are examined per local conformational minimum. Finally, the energies of all dinucleotide conformers are scaled so that the populations of differently puckered sugar rings in the theoretical sample match those found in nmr solution studies. This last step is necessitated by limitations in the theoretical methods to predict DNA sugar puckering accurately. The conformer populations of the individual acyclic torsion angles in the composite dimer ensembles are found to be in good agreement with the distributions of backbone conformations deduced from nmr coupling constants and the frequencies of glycosyl conformations in x-ray crystal structures, suggesting that the low energy states are reasonable. The low energy dimer forms (consisting of 150–325 conformational states per dimer step) are next used as variables in a Monte Carlo algorithm, which generates the conformations of single-stranded d(CX_nG) chains, where X = A, T and n = 3, 4, 5. The oligonucleotides are built sequentially from the 5′ end of the chain using random numbers to select the conformations of overlapping dimer units. The simulations are very fast, involving a total of 10⁶ conformations per chain sequence. The potential errors in the buildup procedure are minimized by taking advantage of known rotational interdependences in the sugar–phosphate backbone. The distributions of oligonucleotide conformations are examined in terms of the magnitudes, positions, and orientations of the end-to-end vectors of the chains. The differences in overall flexibility and extension of the oligomers are discussed in terms of the conformations of the constituent dinucleotide steps, while the general methodology is discussed and compared with other nucleic acid model building techniques. © 1993 John Wiley & Sons, Inc.     

A Refined Prediction Method for Gel Retardation of DNA Oligonucleotides from Dinucleotide Step Parameters: Reconciliation of DNA Bending Models with Crystal Structure Data

Abstract

The development and assessment of a prediction method for gel retardation and sequence dependent curvature of DNA based on dinucleotide 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 structural 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.     

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. © 1994 John Wiley & Sons, Inc.     

Switching effect in prey--predator system

Statistical analysis of DNA base sequences generated from nearest neighbor frequencies by a Monte Carlo technique yields distributions of pyrimidine tracts in good agreement with experimental results. Better agreement with experiment is obtained with nearest-neighbor-frequency based calculations than with calculations based on base composition which assume random base arrangements. The nearest-neighbor-frequency method can also be applied to the analysis of high resolution thermal denaturation profiles, the sequence specific interaction of drugs and proteins, and the distribution of photoproducts produced in DNA by ultraviolet radiation.     

Effect of spontaneous twist on DNA minicircles

Monte Carlo simulations are used to study the effect of spontaneous (intrinsic) twist on the conformation of topologically equilibrated minicircles of dsDNA. The twist, writhe, and radius of gyration distributions and their moments are calculated for different spontaneous twist angles and DNA lengths. The average writhe and twist deviate in an oscillatory fashion (with the period of the double helix) from their spontaneous values, as one spans the range between two neighboring integer values of intrinsic twist. Such deviations vanish in the limit of long DNA plasmids.     

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.     

Understanding apparent DNA flexibility enhancement by HU and HMGB architectural proteins

Understanding and predicting the mechanical properties of protein/DNA complexes are challenging problems in biophysics. Certain architectural proteins bind DNA without sequence specificity and strongly distort the double helix. These proteins rapidly bind and unbind, seemingly enhancing the flexibility of DNA as measured by cyclization kinetics. The ability of architectural proteins to overcome DNA stiffness has important biological consequences, but the detailed mechanism of apparent DNA flexibility enhancement by these proteins has not been clear. Here, we apply a novel Monte Carlo approach that incorporates the precise effects of protein on DNA structure to interpret new experimental data for the bacterial histone-like HU protein and two eukaryotic high-mobility group class B (HMGB) proteins binding to ∼ 200-bp DNA molecules. These data (experimental measurement of protein-induced increase in DNA cyclization) are compared with simulated cyclization propensities to deduce the global structure and binding characteristics of the closed protein/DNA assemblies. The simulations account for all observed (chain length and concentration dependent) effects of protein on DNA behavior, including how the experimental cyclization maxima, observed at DNA lengths that are not an integral helical repeat, reflect the deformation of DNA by the architectural proteins and how random DNA binding by different proteins enhances DNA cyclization to different levels. This combination of experiment and simulation provides a powerful new approach to resolve a long-standing problem in the biophysics of protein/DNA interactions.     

Simulation of DNA fragment distributions after irradiation with photons

The Monte Carlo track structure code PARTRAC has been further improved by implementing electron scattering cross-sections for liquid water and by explicitly modelling the interaction of water radicals with DNA. The model of the genome inside a human cell nucleus in its interphase is based on the atomic coordinates of the DNA double helix with an additional volume for the water shell. The DNA helix is wound around histone complexes, and these nucleosomes are folded into chromatin fibres and further to fibre loops, which are interconnected to build chromosomes with a territorial organisation. Simulations have been performed for the irradiation of human fibroblast cells with carbon K and aluminium K ultrasoft x-rays, 220 kVp x-rays and ⁶⁰Co γ-rays. The ratio single-strand breaks to double-strand breaks (ssb/dsb) for both types of ultrasoft x-rays is lower than for γ-rays by a factor of 2. The contributions of direct and indirect effects to strand break induction are almost independent of photon energy. Strand break patterns from indirect effects reflect differences in the susceptibility of the DNA helix to OH^• attack inside the chromatin fibre. Distributions of small DNA fragments (<3 kbp) are determined by the chromatin fibre structure irrespective of whether direct or indirect effects are causing the breaks. In the calculated fragment size distributions for larger DNA fragments (>30 kbp), a substantial deviation from random breakage is found only for carbon K irradiation, and is attributed to its inhomogeneous dose distribution inside the cell nucleus. For the other radiation qualities, the results for larger fragments can be approximated by random breakage distributions calculated for a yield of dsb which is about 10% lower than the average for the whole genome. The excess of DNA fragments detected experimentally in the 8–300 kbp region after x-ray irradiation is not seen in our simulation results. Received: 19 October 1998 / Accepted in revised form: 14 January 1999     

Extension of torsionally stressed DNA by external force.

Metropolis Monte Carlo simulation was used to study the elasticity of torsionally stressed double-helical DNA. Equilibrium distributions of DNA conformations for different values of linking deficit, external force, and ionic conditions were simulated using the discrete wormlike chain model. Ionic conditions were specified in terms of DNA effective diameter, i.e., hard-core radius of the model chain. The simulations show that entropic elasticity of the double helix depends on how much it is twisted. For low amounts of twisting (less than about one turn per twist persistence length) the force versus extension is nearly the same as in the completely torsionally relaxed case. For more twisting than this, the molecule starts to supercoil, and there is an increase in the force needed to realize a given extension. For sufficiently large amounts of twist, the entire chain is plectonemically supercoiled at low extensions; a finite force must be applied to obtain any extension at all in this regime. The simulation results agree well with the results of recent micromanipulation experiments.     

Prediction of conformation of rat galanin in the presence and absence of water with the use of monte Carlo methods and the ECEPP/3 force field

The conformation of the 29-residue rat galanin neuropeptide was studied using the Monte Carlo with energy minimization (MCM) and electrostatically driven Monte Carlo (EDMC) methods. According to a previously elaborated procedure, the polypeptide chain was first treated in a united-residue approximation, in order to enable extensive exploration of the conformational space to be carried out (with the use of MCM), Then the low-energy united-residue conformations were converted to the all-atom representations, and EDMC simulations were carried out for the all-atom polypeptide chains, using the ECEPP/3 force field with hydration included. In order to estimate the effect of environment on galanin conformation, the low-energy conformations obtained as a result of these simulations were taken as starting structures for further EDMC runs that did not include hydration. The lowest-energy conformation obtained in aqueous solution calculations had a nonhelical N-terminal part packed against the nonpolar face of a residual helix that extended from Pro¹³ toward the C-terminus. One next lowest-energy structure was a nearly-all-helical conformation, but with a markedly higher energy. In contrast, all of the low-energy conformations in the absence of water were all-helical differing only by the extent to which the helix was kinked around Pro¹³. These results are in qualitative agreement with the available NMR and CD data of galanin in aqueous and nonaqueous solvents.     

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.     

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 S ^×2, 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 illustrated in the following paper using conformational energy estimates of the base sequence-dependent flexibility of successive B-DNA base pairs. © 1994 John Wiley & Sons, Inc.     

Nonconjugate Bayesian analysis of variance component models

We consider the usual normal linear mixed model for variance components from a Bayesian viewpoint. With conjugate priors and balanced data, Gibbs sampling is easy to implement; however, simulating from full conditionals can become difficult for the analysis of unbalanced data with possibly nonconjugate priors, thus leading one to consider alternative Markov chain Monte Carlo schemes. We propose and investigate a method for posterior simulation based on an independence chain. The method is customized to exploit the structure of the variance component model, and it works with arbitrary prior distributions. As a default reference prior, we use a version of Jeffreys' prior based on the integrated (restricted) likelihood. We demonstrate the ease of application and flexibility of this approach in familiar settings involving both balanced and unbalanced data.     

Salt contribution to the flexibility of single‐stranded nucleic acid of finite length

Nucleic acids are negatively charged macromolecules and their structure properties are strongly coupled to metal ions in solutions. In this article, the salt effects on the flexibility of single‐stranded (ss) nucleic acid chain ranging from 12 to 120 nucleotides are investigated systematically by the coarse‐grained Monte Carlo simulations where the salt ions are considered explicitly and the ss chain is modeled with the virtual‐bond structural model. Our calculations show that, the increase of ion concentration causes the structural collapse of ss chain and multivalent ions are much more efficient in causing such collapse, and both trivalent/small divalent ions can induce more compact state than a random relaxation state. We found that monovalent, divalent, and trivalent ions can all overcharge ss chain, and the dominating source for such overcharging changes from ion‐exclusion‐volume effect to ion Coulomb correlations. In addition, the predicted Na⁺ and Mg²⁺‐dependent persistence length l_p’s of ss nucleic acid are in accordance with the available experimental data, and through systematic calculations, we obtained the empirical formulas for l_p as a function of [Na⁺], [Mg²⁺] and chain length. © 2012 Wiley Periodicals, Inc. Biopolymers 99: 370–381, 2013.     

Simulations of the solvent structure for macromolecules. I. Solvation of B-DNA double helix at T = 300 K

Monte Carlo simulations are reported for a system of 447 water molecules enclosing a B-DNA double-helix fragment with 12 base pairs and the corresponding sugar and phosphate units. From a detailed analysis on the interaction energies and probability distributions (at a simulated temperature of 300 K), the water molecules can be partitioned into clusters strongly interacting with (1) the phosphates, (2) the sugars, (3) the sugars and the bases, and (4) the base pairs. In addition, transgroove and interphosphate filament of hydrogen-bonded water molecules have been detected. From simulations performed with variable numbers of water molecules, a theoretical isotherm has been obtained, with the characteristic sigmoidal shape, known from absorption–desorption experiments on related systems. The expected main features for the structure of water molecules solvating B-DNA with Na⁺ counterions are briefly discussed at the end of the paper.