3DNA: a versatile, integrated software system for the analysis, rebuilding and visualization of three-dimensional nucleic-acid structures

We present a set of protocols showing how to use the 3DNA suite of programs to analyze, rebuild and visualize three-dimensional nucleic-acid structures. The software determines a wide range of conformational parameters, including the identities and rigid-body parameters of interacting bases and base-pair steps, the nucleotides comprising helical fragments, the area of overlap of stacked bases and so on. The reconstruction of three-dimensional structure takes advantage of rigorously defined rigid-body parameters, producing rectangular block representations of the nucleic-acid bases and base pairs and all-atom models with approximate sugar-phosphate backbones. The visualization components create vector-based drawings and scenes that can be rendered as raster-graphics images, allowing for easy generation of publication-quality figures. The utility programs use geometric variables to control the view and scale of an object, for comparison of related structures. The commands run in seconds even for large structures. The software and related information are available at http://3dna.rutgers.edu/.     

Nucleic Acid Structure Analysis: A Users Guide to a Collection of New Analysis Programs

Abstract

Common nomenclature describing the geometry of nucleic acid structures was established at a 1988 EMBO Workshop on DNA Curvature and Bending (Diekmann, S. (1988) J. Mol. Biol. 208, 787–791; Diekmann, S. (1989) The EMBO Journal 8, 1–4; Sarma, RH. (1988) J. Biomol. Structure & Dynamics 6, 391–395; Dickerson, R.E. (1989) J. Biomol. Structured Dynamics 6, 627–634; Dickerson, RE. et al. (1989)Nuc. Acids Res. 17, 1979–1803). We have subsequently developed and incorporated sophisticated mathematics in a computer program to calculate the parameters described by the guidelines. The program calculates all the local parameters relating complementary bases and neighboring base and base pairs in both Cartesian and helical coordinate frames. In addition, the main mathematical property requested by the EMBO guidelines—that the magnitude of the parameters be independent of strand or direction of measurement—is accomplished without the use of a midway coordinate frame for the rotational parameters. The mathematics preserve the physical intuition used in defining the parameters; in particular, the rotational parameters are true rotations based on a simple physical model (rotation at constant angular velocity for a unit amount of time), not Euler angles or angles between vectors and planes as is the case with other approaches. As a result, the mathematical equations are symmetric with the property that a 5° tilt is the same as a 5° roll or a 5° twist, except that the rotations take place about different axes. In other approaches, a 5° tilt can mean a different amount of net rotation from a 5° roll or a 5° twist. In addition, a great deal of flexibility is built into the program so that the user has control over the analysis, including the input format, the coordinate frame used for the base pairing relationship, the point about which the rotations are performed, and which geometric relationships are analyzed. While there is a great deal of flexibility, the program is easy to use. Interactive queries and user accessible files make the options in the program very convenient to tailor to individual needs. In addition, there is also a program that calculates bond lengths, valence angles, and torsion angles along the nucleic acid backbone, and within the sugar and base rings. Another program ‘learns’ the identities of the bond lengths, valence angles, and torsion angles that the user would like to determine. This last program is especially useful for calculating the hydrogen bonds between atoms in complementary strands as well as the unusual hydrogen bonds found in recently determined nucleic acid NMR structures or within protein/nucleic acid complexes.     

Mlab--a mathematical modeling tool

An interactive interpreter called Mlab is described. One uses Mlab by typing commands. In this sense, Mlab is a programming language. It has various mathematical and graphical facilities which make it a useful tool for mathematical modeling. The curve fitting capabilities of Mlab are augmented with differential-equation-handling and matrix-manipulation capabilities which provide a powerful and civilized facility for curve fitting. Many people are engaged in this activity, and, in general, they use programs which are neither sufficiently general nor easy to use. (Some conventional programming is usually required, for example.) Mlab purports to be easier than alternate approaches. The nature of Mlab is discussed with accompanying examples. The main example is the use of curve fitting to determine molecular weight from ultracentrifuge data. This example was chosen because it exhibits a special feature of Mlab, namely the root operator, which appears in the definition of the model function.     

A user's experience with a standard non-linear regression program (BMDP3R).

A study was made to test and compare the behavior of a standard non-linear regression program (BMDP3R) in fitting data from six classical least-squares problems. The use of three program control parameters is discussed and four measures of regression failure are utilized to give a quantitative reference of success. Recommendations are given to aid the user of packaged programs in the parameter estimation of non-linear regression models.     

ANALYSIS OF RELATIVE POSITIONS OF RIBONUCLEOTIDE BASES IN A CRYSTAL STRUCTURE OF RIBOSOME

ABSTRACT

Relative positions of bases to bases in a crystal structure of ribosome were analyzed extensively. It was found that there is no clear relation between bases apart more than 15 Å and, thus, the relative location of bases can be analyzed within 15 Å of the reference bases. As for base pairing, major positioning was found to be due to the Watson-Crick type base pairs. Some other positions corresponding to non-Watson-Crick type base pairs were also found in some extents. As for base–base stacking, it was observed that the bases stacked to adenine base are dispersive. It was found that less non-Watson-Crick base pairs was found close to the protein binding site, suggesting that the protein components have a tendency to bind to the regular stem structures. The database of relative location of bases must be useful for improvement of structural determination and structural modeling systems.     

Analysis of relative positions of ribonucleotide bases in a crystal structure of ribosome

Relative positions of bases to bases in a crystal structure of ribosome were analyzed extensively. It was found that there is no clear relation between bases apart more than 15 A and, thus, the relative location of bases can be analyzed within 15 A of the reference bases. As for base pairing, major positioning was found to be due to the Watson-Crick type base pairs. Some other positions corresponding to non-Watson-Crick type base pairs were also found in some extents. As for base-base stacking, it was observed that the bases stacked to adenine base are dispersive. It was found that less non-Watson-Crick base pairs was found close to the protein binding site, suggesting that the protein components have a tendency to bind to the regular stem structures. The database of relative location of bases must be useful for improvement of structural determination and structural modeling systems.     

A stochastic analysis of three viral sequences.

This paper analyzes the nucleotide sequences of three viruses: Kunjin, west Nile, and yellow fever. Each virus has one long open reading frame of greater than 10,200 nucleotides that codes for four structural and seven nonstructural genes. The Kunjin and west Nile viruses are the most closely related pair, when assessed on the basis of matches between their nucleotide sequences. As would be expected, the matching is least for bases at third-position codon sites and is greatest for second-position sites. Statistics are presented for the numbers of mismatches that are transitions or transversions. Nucleotide base usage is also reported. To each of the 33 virus-gene segments, nonhomogeneous Markov chain models have been fitted to describe the sequences of nucleotide bases. The models allow for different transition probabilities ("transition" is used in the mathematical sense here) and for different degrees of dependency, at the three sites in the codons. Reasonably satisfactory fits can be obtained for many of the genes by using models that are first order for both first- and second-position sites in the codon but that are second order for third-position sites. One consequence of such a model is that the correlation between one amino acid and the next is limited to the correlation of the last base of the former with the first base of the latter. Other consequences are that the model can (and does) prohibit the occurrence of stop codons within a gene and that subsequences of only first-position bases, or only third-position bases, are also first-order Markov chains. In theory, second-position subsequences may not be Markov chains at all. In practice, the data suggest that each of these subsequences is effectively a zero-order Markov chain, i.e., bases spaced three apart are statistically independent. Stationarity of nucleotide base distributions can be interpreted in either of two ways: (1) spatially along the sites or (2) temporally at each site. These interpretations must often be inconsistent, when the former allows for Markov dependence between adjacent sites whereas the latter assumes independence between sites. The inconsistency can be overcome, for these viruses, if subsequences at different codon positions are analyzed separately.     

An approach for searching insertions in bacterial genes leading to the phase shift of triplet periodicity

The concept of the phase shift of triplet periodicity (TP) was used for searching potential DNA insertions in genes from 17 bacterial genomes. A mathematical algorithm for detection of these insertions has been developed. This approach can detect potential insertions and deletions with lengths that are not multiples of three bases, especially insertions of relatively large DNA fragments (>100 bases). New similarity measure between triplet matrixes was employed to improve the sensitivity for detecting the TP phase shift. Sequences of 17,220 bacterial genes with each consisting of more than 1,200 bases were analyzed, and the presence of a TP phase shift has been shown in ～16% of analysed genes (2,809 genes), which is about 4 times more than that detected in our previous work. We propose that shifts of the TP phase may indicate the shifts of reading frame in genes after insertions of the DNA fragments with lengths that are not multiples of three bases. A relationship between the phase shifts of TP and the frame shifts in genes is discussed.     

血栓弹力图的新数学模型及其应用

血栓弹力是动态凝血过程中切应力大小随时间变化的,也是复旨性模量在小的直接反映。提出了一个新的三参数的数学模型表达血栓弹力图,研究了模型参数变化对模型曲线的影响及模型参数与血栓弹力图章是的对应关系,给出了模型参数确切的生理、病理意义。对西苑区院大量血栓弹力图的拟合表明,该模型能比较精确地表达正常及各种病理条件下不正常血栓弹力图的完整变化曲线,而且参数少,拟合出的参数值相当确定,提供了明确直观的凝血机     

On computational approaches for size-and-shape distributions from sedimentation velocity analytical ultracentrifugation

Sedimentation velocity analytical ultracentrifugation has become a very popular technique to study size distributions and interactions of macromolecules. Recently, a method termed two-dimensional spectrum analysis (2DSA) for the determination of size-and-shape distributions was described by Demeler and colleagues (Eur Biophys J 2009). It is based on novel ideas conceived for fitting the integral equations of the size-and-shape distribution to experimental data, illustrated with an example but provided without proof of the principle of the algorithm. In the present work, we examine the 2DSA algorithm by comparison with the mathematical reference frame and simple well-known numerical concepts for solving Fredholm integral equations, and test the key assumptions underlying the 2DSA method in an example application. While the 2DSA appears computationally excessively wasteful, key elements also appear to be in conflict with mathematical results. This raises doubts about the correctness of the results from 2DSA analysis.     

Sequence search on a supercomputer.

A set of programs was developed for searching nucleic acid and protein sequence data bases for sequences similar to a given sequence. The programs, written in FORTRAN 77, were optimized for vector processing on a Hitachi S810-20 supercomputer. A search of a 500-residue protein sequence against the entire PIR data base Ver. 1.0 (1) (0.5 M residues) is carried out in a CPU time of 45 sec. About 4 min is required for an exhaustive search of a 1500-base nucleotide sequence against all mammalian sequences (1.2M bases) in Genbank Ver. 29.0. The CPU time is reduced to about a quarter with a faster version.     

Polynucleotide models. II. Prediction of the radial position and tilt of the bases from the helical parameters

A simple geometrical analysis is applied to base-stacking interactions in helical polynucleotides. A base-pair or other H-bonded arrangement of bases is represented by a corresponding plane. In a helical structure, these planes will intersect each other if the bases are not perpendicular to the helix axis. The tilt of the bases and the position of intersection of these planes are geometrically related, and demonstrate the interrelation of the tilt of the bases with their radial position. This approach may be coupled with a constraint which predicts the radial position of the bases based solely upon the helical parameters. These two constraints taken together allow a simple means to predict the approximate position and tilt of a given H-bonded arrangement of bases placed according to specified helical parameters. For a number of polydeoxyribonucleotides, there is more than one base position and tilt consistent with these constraints, while there is only one base position and tilt indicated for each of the polyribonucleotides examined.     

A computational study of expanded heterocyclic nucleosides in DNA

The first molecular dynamics study of a series of heterospacer-expanded tricyclic bases in DNA using modified force field parameters in AMBER is detailed. The expanded purine nucleoside monomers have been designed to probe the effects of a heteroaromatic spacer ring on the structure, function, and dynamics of the DNA helix. The heterobase scaffold has been expanded with a furan, pyrrole, or thiophene spacer ring. This structural modification increases the polarizability of the bases and provides an additional hydrogen bond donor with the amine hydrogen of the pyrrole ring or hydrogen bond acceptor with the furan or thiophene ring free electron pairs. The polarizability of the expanded bases were determined by AM1 calculations and the results of the MD simulations of 20-mers predict that the modified curvature of the expanded base leads to a much larger major groove, while the effect on the minor groove is negligible. Overall, the structure resembles A-DNA. MD simulations of 10-mers suggest that the balance between base pairing vs. base stacking and intercalation can be shifted towards the latter due to the increased surface area and polarizability of the expanded bases.     

Use of Approximate Bayesian Computation to Assess and Fit Models of Mycobacterium leprae to Predict Outcomes of the Brazilian Control Program

Hansen’s disease (leprosy) elimination has proven difficult in several countries, including Brazil, and there is a need for a mathematical model that can predict control program efficacy. This study applied the Approximate Bayesian Computation algorithm to fit 6 different proposed models to each of the 5 regions of Brazil, then fitted hierarchical models based on the best-fit regional models to the entire country. The best model proposed for most regions was a simple model. Posterior checks found that the model results were more similar to the observed incidence after fitting than before, and that parameters varied slightly by region. Current control programs were predicted to require additional measures to eliminate Hansen’s Disease as a public health problem in Brazil.     

A New Approach to Determine the Effect of Mismatches on Kinetic Parameters in DNA Hybridization Using an Optical Biosensor

We have demonstrated a simple yet direct method for determiningthe kinetic parameters in DNA-DNA interactions using biosensortechnology based on the surface plasmon resonance phenomenon;a technique that does not require complex DNA labeling. To determinethe effect of mismatches on the kinetics involved in DNA-DNAinteractions, DNA hybridization kinetics were monitored in realtime using synthetic oligonucleotides less than 20 bases inlength which contained either a complementary sequence or mismatchedbases. Upon analysis of the kinetic parameters obtained in oligonucleotidehybridization, we found that they were significantly affectedby the presence of mismatches as well as by their number andlocation in a DNA duplex. In addition, the presented biosensormethod is sensitive enough to detect kinetic effects causedby the presence of a single-mismatched base pair. Our findingsstrongly suggest that analysis of kinetic parameters involvedin DNA-DNA interactions is advantageous for detecting the presenceof mismatch base pairs in a DNA duplex.     

Parallel multiplex thermodynamic analysis of coaxial base stacking in DNA duplexes by oligodeoxyribonucleotide microchips

Parallel thermodynamic analysis of the coaxial stacking effect of two bases localized in one strand of DNA duplexes has been performed. Oligonucleotides were immobilized in an array of three-dimensional polyacrylamide gel pads of microchips (MAGIChips‘). The stacking effect was studied for all combinations of two bases and assessed by measuring the increase in melting temperature and in the free energy of duplexes formed by 5mers stacked to microchip-immobilized 10mers. For any given interface, the effect was studied for perfectly paired bases, as well as terminal mismatches, single base overlaps, single and double gaps, and modified terminal bases. Thermodynamic parameters of contiguous stacking determined by using microchips closely correlated with data obtained in solution. The extension of immobilized oligonucleotides with 5,6-dihydroxyuridine, a urea derivative of deoxyribose, or by phosphate, decreased the stacking effect moderately, while extension with FITC or Texas Red virtually eliminated stacking. The extension of the immobilized oligonucleotides with either acridine or 5-nitroindole increased stacking to mispaired bases and in some GC-rich interfaces. The measurements of stacking parameters were performed in different melting buffers. Although melting temperatures of AT- and GC-rich oligonucleotides in 5 M tetramethylammonium chloride were equalized, the energy of stacking interaction was significantly diminished.     

Conformational features of benzo‐homologated yDNA duplexes by molecular dynamics simulation

yDNA is a base‐modified nucleic acid duplex containing size‐expanded nucleobases. Base‐modified nucleic acids could expand the genetic alphabet and thereby enhance the functional potential of DNA. Unrestrained 100 ns MD simulations were performed in explicit solvent on the yDNA NMR sequence [5′(yA T yA yA T yA T T yA T)₂] and two modeled yDNA duplexes, [5′(yC yC G yC yC G G yC G G)₂] and [(yT5′ G yT A yC yG C yA yG T3′)?(yA5′ C T C yG C G yT A yC A3′)]. The force field parameters for the yDNA bases were derived in consistent with the well‐established AMBER force field. Our results show that DNA backbone can withstand the stretched size of the bases retaining the Watson‐Crick base pairing in the duplexes. The duplexes retained their double helical structure throughout the simulations accommodating the strain due to expanded bases in the backbone torsion angles, sugar pucker and helical parameters. The effect of the benzo‐expansion is clearly reflected in the extended C1′‐C1′ distances and enlarged groove widths. The size expanded base modification leads to reduction in base pair twist resulting in larger overlapping area between the stacked bases, enhancing inter and intra strand stacking interactions in yDNA in comparison with BDNA. This geometry could favour enhanced interactions with the groove binders and DNA binding proteins., 2016. © 2015 Wiley Periodicals, Inc. Biopolymers 105: 55–64, 2016