Watson-Crick pairing, the Heisenberg group and Milnor invariants

We study the secondary structure of RNA determined by Watson-Crick pairing without pseudo-knots using Milnor invariants of links. We focus on the first non-trivial invariant, which we call the Heisenber invariant. The Heisenberg invariant, which is an integer, can be interpreted in terms of the Heisenberg group as well as in terms of lattice paths. We show that the Heisenberg invariant gives a lower bound on the number of unpaired bases in an RNA secondary structure. We also show that the Heisenberg invariant can predict allosteric structures for RNA. Namely, if the Heisenberg invariant is large, then there are widely separated local maxima (i.e., allosteric structures) for the number of Watson-Crick pairs found.

Crystal structure of an intermolecular 2:1 complex between adenine and thymine.Evidence for both Hoogsteen and `quasi-Watson-Crick' interactions

The titled complex, obtained by co-crystallization (EtOH/25 degrees C),is apparently the only known complex of the free bases. Its crystal structure, as determined by X-ray diffraction at both 90 K and 313 K, showed that one A-T pair involves a Hoogsteen interaction, and the other a Watson-Crick interaction but only with respect to the adenine unit. The absence of a clear-cut Watson-Crick base pair raises intriguing questions about the basis of the DNA double helix. (C) 2010 Elsevier Ltd. All rights reserved.

Adenosine-5'-carboxylic Acid

The two molecules in the asymmetric unit of adenosine-5'-carboxylic acid, C10H11N5O5, exist as zwitterions with N1 protonated and the carboxyl groups ionized. Both molecules are in an anti conformation with glycosyl torsion angles of -161.4(3) and -155.5(3)degrees. The ribose moieties adopt a C3-endo-C2-exo twist conformation. The pseudo-rotation parameters are P = 0.01(1) and 6.58(1)degrees, and tau(m) = 36.2(2) and 34.6(2)degrees, for molecules A and B, respectively. The carboxyl groups of A and B are not in the standard g(+), g(-) or t conformations. Both Watson-Crick sites, N1 and N6, of the adenine bases are involved in a pair of hydrogen bonds with the dissociated carboxyl groups, forming a cyclic tetramer. The adenine base of molecule A stacks on the ribose O4' atom of a symmetry-related B molecule at a distance of 2.88 Angstrom; the adenine base of B stacks in an analogous way at a distance of 2.91 Angstrom.

Base-base interactions in nucleic acids containing A-T base pairs: Structure of poly[d(A-T)]

The Watson-Crick type of base pairing is considered to be mandatory for the formation of duplex DNA. However, conformational calculations carried out in our laboratory, have shown that some combinations of backbone torsion angles and sugar pucker lead to duplexes with Hoogsteen type of base pairing also. Here we present the results of energy calculations performed on A-T containing doublet sequences in the D-form with both Hoogsteen and Watson-Crick type of base pairing and the 3 viable models for the A-T containing polynucleotide duplex poly[d(A-T)].

A simplified approach to a three-part Wiener-Hopf problem arising in diffraction theory

A direct and simple approach, utilizing Watson's lemma, is presented for obtaining an approximate solution of a three-part Wiener-Hopf problem associated with the problem of diffraction of a plane wave by a soft strip.

Molecular and crystal structure of deoxyguanosine 5'-phosphate

RECENT crystallographic studies of the dinucleosides ApU (ref. 1) and GpC (ref. 2) have given experimental proof for the base pairing arrangement proposed by Watson and Crick for the DNA double helix3. Another striking feature of this structure relates to the torsional angle about the C5'-C4' bond in the phosphate−sugar backbone chain. In the Crick and Watson model4, this conformation is gauche−trans (GT). Crystal structures of 5'-nucleotides, dinucleosides and dinucleotides so far studied, however, have shown only the gauche−gauche (GG) conformation about this bond. The GG conformer is also the only one found in the refined models of the proposed structure of the double helical nucleic acids and polynucleotides5−7. The only nucleotide with a GT conformation is 6-azauridine-5'-phosphate8 which is not a normal monomer unit of nucleic acids. It is also reported that 5'-dGMP assumes preferentially GT conformation in solution9.

Molecular and crystal structure of deoxyguanosine 5'-phosphate

RECENT crystallographic studies of the dinucleosides ApU (ref. 1) and GpC (ref. 2) have given experimental proof for the base pairing arrangement proposed by Watson and Crick for the DNA double helix3. Another striking feature of this structure relates to the torsional angle about the C5'-C4' bond in the phosphate−sugar backbone chain. In the Crick and Watson model4, this conformation is gauche−trans (GT). Crystal structures of 5'-nucleotides, dinucleosides and dinucleotides so far studied, however, have shown only the gauche−gauche (GG) conformation about this bond. The GG conformer is also the only one found in the refined models of the proposed structure of the double helical nucleic acids and polynucleotides5−7. The only nucleotide with a GT conformation is 6-azauridine-5'-phosphate8 which is not a normal monomer unit of nucleic acids. It is also reported that 5'-dGMP assumes preferentially GT conformation in solution9.

Double standard polynucleotides: two typical alternative conformations for nucleic acids

Two typical alternative conformations for double strandee polynucleotides with Watson-Crick base pairing scheme are presented. these types avoid tangling of the chains. Representative models of these types with two different views, to show the similarity and dissimilarity between these models and the Watson-Crick model, are given.

High-temperature heat capacity and heat content of CaCu3Ti4O12 (CCTO)

The isobaric heat capacity of CaCu3Ti4O12 (CCTO) was measured from 300 to 1100 K using differential scanning calorimetry (DSC). The results were verified using drop calorimetric measurement of enthalpy increment (H-T - H-298.15) at T= 973 and 1073 K. The samples were dropped from room temperature into a calorimeter maintained at high temperature. The results show small negative deviation from Neumann-Kopp rule. The enthalpy and entropy increments are computed as a function of temperature and compared with values available in the literature. The results obtained in this study are consistent with available information on enthalpy and Gibbs energy of formation of CCTO.

On latent heat of vaporization, surface tension, and temperature

A semitheoretical equation for latent heat of vaporization has been derived and tested. The average error in predicting the value at the normal boiling point in the case of about 90 compounds, which includes polar and nonpolar liquids, is about 1.8%. A relation between latent heat of vaporization and surface tension is also derived and is shown to lead to Watson's empirical relation which gives the change of latent heat of vaporization with temperature. This gives a physico-chemical justification for Watson's empirical relation and provides a rapid method of determining latent heats by measuring surface tension.

Interaction between the Z-type DNA duplex and 1,3-propanediamine:crystal structure of d(CACGTG)(2) at 1.2 angstrom resolution

The crystal structure of a hexamer duplex d(CACGTG)(2) has been determined and refined to an R-factor of 18.3% using X-ray data up to 1.2 angstrom resolution. The sequence crystallizes as a left-handed Z-form double helix with Watson-Crick base pairing. There is one hexamer duplex, a spermine molecule, 71 water molecules, and an unexpected diamine (Z-5, 1,3-propanediamine, C3H10N2)) in the asymmetric unit. This is the high-resolution non-disordered structure of a Z-DNA hexamer containing two AT base pairs in the interior of a duplex with no modifications such as bromination or methylation on cytosine bases. This structure does not possess multivalent cations such as cobalt hexaammine that are known to stabilize Z-DNA. The overall duplex structure and its crystal interactions are similar to those of the pure-spermine form of the d(CGCGCG)(2) structure. The spine of hydration in the minor groove is intact except in the vicinity of the T5A8 base pair. The binding of the Z-5 molecule in the minor grove of the d(CACGTG)(2) duplex appears to have a profound effect in conferring stability to a Z-DNA conformation via electrostatic complementarity and hydrogen bonding interactions. The successive base stacking geometry in d(CACGTG)(2) is similar to the corresponding steps in d(CG)(3). These results suggest that specific polyamines such as Z-5 could serve as powerful inducers of Z-type conformation in unmodified DNA sequences with AT base pairs. This structure provides a molecular basis for stabilizing AT base pairs incorporated into an alternating d(CG) sequence.

Capillary-gravity waves against a corrugated vertical cliff

An analysis involving a transformation of the velocity potential and a Fourier Sine Transform technique is described to study the effect of surface tension on incoming surface waves against a vertical cliff with a periodic wall perturbation. Known results are recovered as particular cases of the general problem considered. An analytical expression is derived for the surface elevation, at far distances from the shore-line, by using Watson's lemma and a representative table of numerical values of the coefficients of the resulting asymptotic expansion is also presented.

Some implications of an alternative structure for DNA

We have constructed a space-filling (Corey-Pauling-Koltun) model of an alternative structure for DNA. This structure is not a double helix, but consists of a pair of polynucleotide strands lying side by side and held together by Watson-Crick base pairing. Each of the two strands has alternating right- and left-handed helical segments approximately five base pairs in length. Sugar residues in alternating segments along a strand point in opposite directions. A structure slightly different from the present one proposed earlier by ourselves and another group and in which sugars in a strand all point in the same direction is ruled out. The present structure yields natural solutions to the problems of supercoiling of DNA and of strand separation during DNA replication. This model is energetically more favorable than the double helix.

A glossary of DNA structures from A to Z

The right-handed double-helical Watson-Crick model for B-form DNA is the most commonly known DNA structure. In addition to this classic structure, several other forms of DNA have been observed and it is clear that the DNA molecule can assume different structures depending on the base sequence and environment. The various forms of DNA have been identified as A, B, C etc. In fact, a detailed inspection of the literature reveals that only the letters F, Q, U, V and Y are now available to describe any new DNA structure that may appear in the future. It is also apparent that it may be more relevant to talk about the A, B or C type dinucleotide steps, since several recent structures show mixtures of various different geometries and a careful analysis is essential before identifying it as a 'new structure'. This review provides a glossary of currently identified DNA structures and is quite timely as it outlines the present understanding of DNA structure exactly 50 years after the original discovery of DNA structure by Watson and Crick

Sequence Independent Recombination Triple Helices: A Molecular Dynamics Study

Recent experimental studies have shown that the Rec-A mediated homologous recombination reaction involves a triple helical intermediate, in which the third strand base forms hydrogen bonds with both the bases in the major groove of the Watson-Crick duplex. Such 'mixed' hydrogen bonds allow formation of sequence independent triplexes. DNA triple helices involving 'mixed' hydrogen bonds have been studied, using model building, molecular mechanics (MM) and molecular dynamics (MD). Models were built for a tripler comprising all four possible triplets viz., G.C*C, C.G*G, A.T*T and T.A*A. To check the stability of all the 'mixed' hydrogen bonds in such triplexes and the conformational preferences of such tripler structures, MD studies were carried out starting from two structures with 30 degrees and 36 degrees twist between the basepairs. It was observed that though the two triplexes converged towards a similar structure, the various hydrogen bonds between the WC duplex and the third strand showed differential stabilities. An MD simulation with restrained hydrogen bonds showed that the resulting structure was stable and remained close to the starting structure. These studies help us in defining stable hydrogen bond geometries involving the third strand and the WC duplex. It was observed that in the C.G*G triplets the N7 atom of the second strand is always involved in hydrogen bonding. In the G.C*C triplets, either N3 or O2 in the third strand cytosine can interchangeably act as a hydrogen bond acceptor.