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.