Analysis of sequences of twist angles in DNA double helix

By assuming that the realistic DNA chains are random sequence of bases and using the Tung-Harvey formula for the prediction of twist angles, it is shown that the mean value of the sequence of twist angles is almost sequence-independent. In general the variance for the A, T-rich sequence is larger than that of G, C-rich sequence. There exists an upper bound for the variance of all possible sequences, i.e., the variance is not greater than 27 deg2. It is pointed out that the large conformational deviation from ideal DNA is an important factor for the recognition of DNA with protein/enzyme.     

The ten helical twist angles of B-DNA.

On the assumption that the twist angles between adjacent base-pairs in the DNA molecule are additive a linear system of 40 equations was derived from experimental measurements of the total twist angles for different pieces of DNA of known sequences. This system of equations is found to be statistically consistent providing a solution for all ten possible twist angles of B-DNA by a least squares fitting procedure. Four of the calculated twist angles were not known before (tau AC, tau AG, tau CA, tau TA). The other six twist angles calculated are very close to the experimentally measured ones (tau AA, tau AT, tau CC, tau OG, tau GA, tau GC). The data used were obtained by the electrophoretic band-shift method (1-3), crystallography (4) and nuclease digestion of DNA adsorbed to mica or Ca-phosphate surface (5,6). The validity of the principle of additivity of the twist angles implies that the angle between any particular two base-pairs is a function of only these base-pairs, independent of nearest neighbours.     

Writhe of DNA induced by a terminal twist

This paper considers the three-dimensional structure of B-form DNA. The molecule may be open or covalently closed. For the former, its two ends are not allowed to move or rotate freely in space unless the molecule is under the influence of rigid body motions of the ambient space. Implied by the elastic rod model for DNA, the molecule writhes immediately when subject to a terminal twist as long as its axis is none of the following curves: lines, circular arcs, circular helices. This result is remarkably different from well-known results about DNA of other conformations. For example, if a DNA is regarded as an elastic rod whose axis is a circle, then it has no induced writhe when subject to a terminal twist until the latter meets a critical extent. To my mother for her 70th birthday An erratum to this article is available at .     

Directed graphs of DNA sequences and their numerical characterization

In this paper we (1) introduce a directed graphical representation of DNA primary sequences; (2) describe a scheme that transforms the directed graph of a DNA sequence into an upper triangular matrix; (3) investigate whether or not the existing matrix-based invariants of DNA sequences are compatible for the upper triangular matrix representation. The utility of our method is illustrated by an examination of the similarity between human and other seven species.     

Probing Rad51-DNA interactions by changing DNA twist

In eukaryotes, Rad51 protein is responsible for the recombinational repair of double-strand DNA breaks. Rad51 monomers cooperatively assemble on exonuclease-processed broken ends forming helical nucleo-protein filaments that can pair with homologous regions of sister chromatids. Homologous pairing allows the broken ends to be reunited in a complex but error-free repair process. Rad51 protein has ATPase activity but its role is poorly understood, as homologous pairing is independent of adenosine triphosphate (ATP) hydrolysis. Here we use magnetic tweezers and electron microscopy to investigate how changes of DNA twist affect the structure of Rad51-DNA complexes and how ATP hydrolysis participates in this process. We show that Rad51 protein can bind to double-stranded DNA in two different modes depending on the enforced DNA twist. The stretching mode is observed when DNA is unwound towards a helical repeat of 18.6 bp/turn, whereas a non-stretching mode is observed when DNA molecules are not permitted to change their native helical repeat. We also show that the two forms of complexes are interconvertible and that by enforcing changes of DNA twist one can induce transitions between the two forms. Our observations permit a better understanding of the role of ATP hydrolysis in Rad51-mediated homologous pairing and strand exchange.     

The infectivity of adenovirus genomes lacking DNA sequences from their left-hand termini.

Deletions extending various distances into the left-hand terminal DNA sequences of the adenovirus type 2 (Ad2) genome were generated in a plasmid containing a cloned fragment spanning from 0 to 4.9 map units. The altered Ad2 DNA sequences were introduced into viral genomes by ligating a plasmid-derived fragment, which included the sequences extending to 3.8 map units, to the 3.8-100 map unit fragment generated by XbaI cleavage of the DNA of the Ad5 variant, d1309 (N.Jones and T.Shenk, Cell 17 683-689, 1979). The infectivity of the ligation products was studied by transfection of line 293 cells. Genomes lacking 11, 40, or 51 nucleotides from their left-hand termini, or containing an additional 18dG residues linked to this position were infectious, and analysis of the progeny virus genomes demonstrated that the structure of these modified termini had been restored to normal. In contrast, genomes from which the first 160 base pairs (bp), including the entire 102 bp left hand inverted terminal repeat (ITR), had been removed were non-infectious. The results indicate that the ITRs present at the opposite ends of transfecting DNA molecules are able to interact in vivo, and enable the production of viable viruses containing corrected left-hand terminal sequences. Possible mechanisms for this interaction are discussed.     

A new twist for DNA

A computer-aided design strategy allows scientists to 'staple' DNA molecules into a wide variety of two-dimensional shapes, generating precisely arranged scaffolds that could serve as promising platforms for nanoscale research applications.     

A molecular mechanical model to predict the helix twist angles of B-DNA

We present here a model for the prediction of helix twist angles in B-DNA, a model composed of a collection of torsional springs. Statistically averaged conformational energy calculations show that, for a specified basepair step, the basepair-basepair conformational energy is quadratically dependent on the helix twist angle, so the calculations provide the spring parameters for the basepair-basepair interactions. Torsional springs can also be used to model the effects of the backbone on the helix twist, and the parameters for those springs are derived by fitting the model to experimental data. The model predicts a macroscopic torsional stiffness and a longitudinal compressibility (Young's modulus) which are both in good agreement with experiment. One biological consequence of the model is examined, the sequence specificity of the Eco RI restriction endonuclease, and it is shown that the discriminatory power of the enzyme receives a substantial contribution from the energetic cost of torsional deformations of the DNA when wrong sequences are forced into the enzyme binding site.     

Steiner minimal trees, twist angles, and the protein folding problem

The Steiner Minimal Tree (SMT) problem determines the minimal length network for connecting a given set of vertices in three-dimensional space. SMTs have been shown to be useful in the geometric modeling and characterization of proteins. Even though the SMT problem is an NP-Hard Optimization problem, one can define planes within the amino acids that have a surprising regularity property for the twist angles of the planes. This angular property is quantified for all amino acids through the Steiner tree topology structure. The twist angle properties and other associated geometric properties unique for the remaining amino acids are documented in this paper. We also examine the relationship between the Steiner ratio rho and the torsion energy in amino acids with respect to the side chain torsion angle chi(1). The rho value is shown to be inversely proportional to the torsion energy. Hence, it should be a useful approximation to the potential energy function. Finally, the Steiner ratio is used to evaluate folded and misfolded protein structures. We examine all the native proteins and their decoys at http://dd.stanford.edu. and compare their Steiner ratio values. Because these decoy structures have been delicately misfolded, they look even more favorable than the native proteins from the potential energy viewpoint. However, the rho value of a decoy folded protein is shown to be much closer to the average value of an empirical Steiner ratio for each residue involved than that of the corresponding native one, so that we recognize the native folded structure more easily. The inverse relationship between the Steiner ratio and the energy level in the protein is shown to be a significant measure to distinguish native and decoy structures. These properties should be ultimately useful in the ab initio protein folding prediction.     

The early days of DNA sequences

Fred Sanger was awarded the rare distinction of two Nobel Prizes for Chemistry, in 1958 and 1980. The first was for his work on the structure of proteins, particularly that of insulin, the latter for his contribution concerning the determination of nucleic acid sequences, the foundation work that ultimately led to The Human Genome Project.     

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.     

Clustering DNA sequences by feature vectors

We represent all DNA sequences as points in twelve-dimensional space in such a way that homologous DNA sequences are clustered together, from which a new genomic space is created for global DNA sequences comparison of millions of genes simultaneously. More specifically, basing on the contents of four nucleotides, their distances from the origin and their distribution along the sequences, a twelve-dimensional vector is given to any DNA sequence. The applicability of this analysis on global comparison of gene structures was tested on myoglobin, beta-globin, histone-4, lysozyme, and rhodopsin families. Members from each family exhibit smaller vector distances relative to the distances of members from different families. The vector distance also distinguishes random sequences generated based on same bases composition. Sequence comparisons showed consistency with the BLAST method. Once the new gene is discovered, we can compute the location of this new gene in our genomic space. It is natural to predict that the properties of this new gene are similar to the properties of known genes that are locating near by. Biologists can do various experiments to test these properties.     

Molecular cloning of human satellite DNA sequences and their use in detecting DNA polymorphism

A approximately 400 bp HaeIII human genomic satellite DNA band was cloned into pUC18 to construct a partial library. A fragment of bacteriophage M13 containing a sequence homologous to the human minisatellite core was cloned in pUC18 and was used as a probe to isolate a approximately 350 bp human satellite clone (pTRF5.6) from the partial library. Other clones from this library showed a wide variation in terms of size and hybridization to the pTRF5.6 clone. Human DNA from different individuals was digested with restriction enzymes, Southern transferred and probed with TRF5.6. Individual-specific complex pattern of DNA bands was produced. TRF5.6, therefore, could be useful as a probe for detecting genetic polymorphism.     

The role of DNA twist in the packaging of viral genomes

We performed molecular dynamics simulations of the genome packaging of bacteriophage P4 using two coarse-grained models of DNA. The first model, 1DNA6 (one pseudo-atom per six DNA basepairs), represents DNA as a string of beads, for which DNA torsions are undefined. The second model, 3DNA6 (three pseudo-atoms per six DNA basepairs), represents DNA as a series of base planes with torsions defined by the angles between successive planes. Bacteriophage P4 was packaged with 1DNA6, 3DNA6 in a torsionally relaxed state, and 3DNA6 in a torsionally strained state. We observed good agreement between the packed conformation of 1DNA6 and the packed conformations of 3DNA6. The free energies of packaging were in agreement, as well. Our results suggest that DNA torsions can be omitted from coarse-grained bacteriophage packaging simulations without significantly altering the DNA conformations or free energies of packaging that the simulations predict.     

New measurements of DNA twist elasticity.

The symmetries of the DNA double helix require a new term in its linear response to stress: the coupling between twist and stretch. Recent experiments with torsionally constrained single molecules give the first direct measurement of this new material parameter. We extract its value from a recent experiment. Finally, we sketch the effect of constrained twist on entropic elasticity of DNA arising from the connection between Link, Twist, and Writhe.     

Molecular dynamics simulation study of DNA triplex formed by mixed sequences in solution

The unrestrained molecular dynamics simulation of the triple helical DNA with mix sequences d(GACTGGTGAC).d(CTGACCACTG)*d (GACTGGTGAC), using the particle mesh Ewald sum, is presented here. The Ewald summation method effectively eliminates the usualcut-of of the long range interactions and allowed us to evaluate the full effect of the electrostatic forces. The AMBER5.0 force field has been used during the simulation in solvent. The MD results support a dynamically stable model of DNA triplex over the entire length of the trajectory. The duplex structure assumes the conformation, which is very close to B-DNA. In mixed sequences the purine bases occurs in both strand of DNA duplex. The bases of third strand do not favor the Hoogsteen or/and reverse Hoogsteen type of Hydrogen bonding but they form hydrogen bonds with the bases of both the strand of DNA duplex. The orientation of the third strand is parallel to one of the strand of duplex and all nucleotides (C, A, G & T) show isomorphic behavior with respect to the DNA duplex. The conformation of all the three strands is almost same except few exceptions. Due to interaction of third strand the conformational change in the duplex structure and a finite amount of displacement in the W-C base pairs have been observed. The conformational variation of the back bone torsion angles and helicoidal parameters, groove widths have been discussed. The sequence dependent effects on local conformation, helicoidal and morphological structure, width of the grooves of DNA helix may have important implication for understanding the functional energetics and specificity of interactions of DNA and its triplexes with proteins, pharmaceutical agents and other ligands.