Kinematic geometry of mass-triangles and reduction of Schrödinger’s equation of three-body systems to partial differential equations solely defined on triangular parameters

Schrödinger’s equation of a three-body system is a linear partial differential equation (PDE) defined on the 9-dimensional configuration space, ℝ9, naturally equipped with Jacobi’s kinematic metric and with translational and rotational symmetries. The natural invariance of Schrödinger’s equation with respect to the translational symmetry enables us to reduce the configuration space to that of a 6-dimensional one, while that of the rotational symmetry provides the quantum mechanical version of angular momentum conservation. However, the problem of maximizing the use of rotational invariance so as to enable us to reduce Schrödinger’s equation to corresponding PDEs solely defined on triangular parameters—i.e., at the level of ℝ6/SO(3)—has never been adequately treated. This article describes the results on the orbital geometry and the harmonic analysis of (SO(3),ℝ6) which enable us to obtain such a reduction of Schrödinger’s equation of three-body systems to PDEs solely defined on triangular parameters.

A molecular level picture of the stabilization of A-DNA in mixed ethanol–water solutions

Advances in computer power, methodology, and empirical force fields now allow routine “stable” nanosecond-length molecular dynamics simulations of DNA in water. The accurate representation of environmental influences on structure remains a major, unresolved issue. In contrast to simulations of A-DNA in water (where an A-DNA to B-DNA transition is observed) and in pure ethanol (where disruption of the structure is observed), A-DNA in ≈85% ethanol solution remains in a canonical A-DNA geometry as expected. The stabilization of A-DNA by ethanol is likely due to disruption of the spine of hydration in the minor groove and the presence of ion-mediated interhelical bonds and extensive hydration across the major groove.

Subtle atomic group discrimination in the RNA minor groove

As a problem in molecular recognition and for drug discovery, great interest has developed around the possibility that RNA structures could be discriminated by peptides and other small molecules. Although small peptides have been shown to have the capacity to discriminate specific bulges and loops in RNA molecules, discrimination of double helical regions by a peptide binder has not been reported. Indeed, the most accessible part of an RNA helix is the minor groove, and fundamental stereochemical considerations have suggested that discrimination of at least some base pairs would be difficult in the minor groove. Here we report the design and isolation of a peptide binder that manifests the most subtle kind of discrimination of base pair differences in the RNA minor groove. Functional discrimination of a single atomic group is demonstrated as well as the difference between two different angular orientations of the same group. This report of RNA helix discrimination by a peptide binder suggests a richer potential for RNA minor groove recognition than previously thought.

Geometry of circular vectors and pattern recognition of shape of a boundary

This paper deals with pattern recognition of the shape of the boundary of closed figures on the basis of a circular sequence of measurements taken on the boundary at equal intervals of a suitably chosen argument with an arbitrary starting point. A distance measure between two boundaries is defined in such a way that it has zero value when the associated sequences of measurements coincide by shifting the starting point of one of the sequences. Such a distance measure, which is invariant to the starting point of the sequence of measurements, is used in identification or discrimination by the shape of the boundary of a closed figure. The mean shape of a given set of closed figures is defined, and tests of significance of differences in mean shape between populations are proposed.

On the geometry of solutions of the quasi-geostrophic and Euler equations

We study solutions of the two-dimensional quasi-geostrophic thermal active scalar equation involving simple hyperbolic saddles. There is a naturally associated notion of simple hyperbolic saddle breakdown. It is proved that such breakdown cannot occur in finite time. At large time, these solutions may grow at most at a quadruple-exponential rate. Analogous results hold for the incompressible three-dimensional Euler equation.

Specific molecular recognition of mixed nucleic acid sequences: An aromatic dication that binds in the DNA minor groove as a dimer

Phenylamidine cationic groups linked by a furan ring (furamidine) and related compounds bind as monomers to AT sequences of DNA. An unsymmetric derivative (DB293) with one of the phenyl rings of furamidine replaced with a benzimidazole has been found by quantitative footprinting analyses to bind to GC-containing sites on DNA more strongly than to pure AT sequences. NMR structural analysis and surface plasmon resonance binding results clearly demonstrate that DB293 binds in the minor groove at specific GC-containing sequences of DNA in a highly cooperative manner as a stacked dimer. Neither the symmetric bisphenyl nor bisbenzimidazole analogs of DB293 bind significantly to the GC containing sequences. DB293 provides a paradigm for design of compounds for specific recognition of mixed DNA sequences and extends the boundaries for small molecule-DNA recognition.

Structural analysis of the binding modes of minor groove ligands comprised of disubstituted benzenes

Two-dimensional homonuclear NMR was used to characterize synthetic DNA minor groove-binding ligands in complexes with oligonucleotides containing three different A-T binding sites. The three ligands studied have a C2 axis of symmetry and have the same general structural motif of a central para-substituted benzene ring flanked by two meta-substituted rings, giving the molecules a crescent shape. As with other ligands of this shape, specificity seems to arise from a tight fit in the narrow minor groove of the preferred A-T-rich sequences. We found that these ligands slide between binding subsites, behavior attributed to the fact that all of the amide protons in the ligand backbone cannot hydrogen bond to the minor groove simultaneously.

RegA proteins from phage T4 and RB69 have conserved helix–loop groove RNA binding motifs but different RNA binding specificities

The RegA proteins from the bacteriophage T4 and RB69 are translational repressors that control the expression of multiple phage mRNAs. RegA proteins from the two phages share 78% sequence identity; however, in vivo expression studies have suggested that the RB69 RegA protein binds target RNAs with a higher affinity than T4 RegA protein. To study the RNA binding properties of T4 and RB69 RegA proteins more directly, the binding sites of RB69 RegA protein on synthetic RNAs corresponding to the translation initiation region of two RB69 target genes were mapped by RNase protection assays. These assays revealed that RB69 RegA protein protects nucleotides –9 to –3 (relative to the start codon) on RB69 gene 44, which contains the sequence GAAAAUU. On RB69 gene 45, the protected site (nucleotides –8 to –3) contains a similar purine-rich sequence: GAAAUA. Interestingly, T4 RegA protein protected the same nucleotides on these RNAs. To examine the specificity of RNA binding, quantitative RNA gel shift assays were performed with synthetic RNAs corresponding to recognition elements (REs) in three T4 and three RB69 mRNAs. Comparative gel shift assays demonstrated that RB69 RegA protein has an ∼7-fold higher affinity for T4 gene 44 RE RNA than T4 RegA protein. RB69 RegA protein also binds RB69 gene 44 RE RNA with a 4-fold higher affinity than T4 RegA protein. On the other hand, T4 RegA exhibited a higher affinity than RB69 RegA protein for RB69 gene 45 RE RNA. With respect to their affinities for cognate RNAs, both RegA proteins exhibited the following hierarchy of affinities: gene 44 > gene 45 > regA. Interestingly, T4 RegA exhibited the highest affinity towards RB69 gene 45 RE RNA, whereas RB69 RegA protein had the highest affinity for T4 gene 44 RE RNA. The helix–loop groove RNA binding motif of T4 RegA protein is fully conserved in RB69 RegA protein. However, homology modeling of the structure of RB69 RegA protein reveals that the divergent residues are clustered in two areas of the surface, and that there are two large areas of high conservation near the helix–loop groove, which may also play a role in RNA binding.

Induced fit DNA recognition by a minor groove binding analogue of Hoechst 33258: fluctuations in DNA A tract structure investigated by NMR and molecular dynamics simulations

NMR analysis and molecular dynamics simulations of d(GGTAATTACC)2 and its complex with a tetrahydropyrimidinium analogue of Hoechst 33258 suggest that DNA minor groove recognition in solution involves a combination of conformational selection and induced fit, rather than binding to a preorganised site. Analysis of structural fluctuations in the bound and unbound states suggests that the degree of induced fit observed is primarily a consequence of optimising van der Waals contacts with the walls of the minor groove resulting in groove narrowing through: (i) changes in base step parameters, including increased helical twist and propeller twist; (ii) changes to the sugar–phosphate backbone conformation to engulf the bound ligand; (iii) suppression of bending modes at the TpA steps. In contrast, the geometrical arrangement of hydrogen bond acceptors on the groove floor appears to be relatively insensitive to DNA conformation (helical twist and propeller twist). We suggest that effective recognition of DNA sequences (in this case an A tract structure) appears to depend to a significant extent on the sequence being flexible enough to be able to adopt the geometrically optimal conformation compatible with the various binding interactions, rather than involving ‘lock and key’ recognition.

Fos and Jun bend the AP-1 site: effects of probe geometry on the detection of protein-induced DNA bending.

The effect of Fos and Jun binding on the structure of the AP-1 recognition site is controversial. Results from phasing analysis and phase-sensitive detection studies of DNA bending by Fos and Jun have led to opposite conclusions. The differences between these assays, the length of the spacer between two bends and the length of the sequences flanking the bends, are investigated here using intrinsic DNA bend standards. Both an increase in the spacer length as well as a decrease in the length of flanking sequences resulted in a reduction in the phase-dependent variation in electrophoretic mobilities. Probes with a wide separation between the bends and short flanking sequences, such as those used in the phase-sensitive detection studies, displayed no phase-dependent mobility variation. This shape-dependent variation in electrophoretic mobilities was reproduced by complexes formed by truncated Fos and Jun. Results from ligase-catalyzed cyclization experiments have been interpreted to indicate the absence of DNA bending in the Fos-Jun-AP-1 complex. However, truncated Fos and Jun can alter the relative rates of inter- and intramolecular ligation through mechanisms unrelated to DNA bending, confounding the interpretation of cyclization data. The analogous phase- and shape-dependence of the electrophoretic mobilities of the Fos-Jun-AP-1 complex and an intrinsic DNA bend confirm that Fos and Jun bend DNA, which may contribute to their functions in transcription regulation.

Binding of a hairpin polyamide in the minor groove of DNA: sequence-specific enthalpic discrimination.

Hairpin polyamides are synthetic ligands for sequence-specific recognition in the minor groove of double-helical DNA. A thermodynamic characterization of the DNA-binding properties exhibited by a six-ring hairpin polyamide, ImPyPy-gamma-PyPyPy-beta-Dp (where Im = imidazole, Py = pyrrole, gamma = gamma-aminobutyric acid, beta = beta-alanine, and Dp = dimethylaminopropylamide), reveals an approximately 1-2 kcal/mol greater affinity for the designated match site, 5'-TGTTA-3', relative to the single base pair mismatch sites, 5'-TGGTA-3' and 5'-TATTA-3'. The enthalpy and entropy data at 20 degrees C reveal this sequence specificity to be entirely enthalpic in origin. Correlations between the thermodynamic driving forces underlying the sequence specificity exhibited by ImPyPy-gamma-PyPyPy-beta-Dp and the structural properties of the heterodimeric complex of PyPyPy and ImPyPy bound to the minor groove of DNA provide insight into the molecular forces that govern the affinity and specificity of pyrrole-imidazole polyamides.

Sequence-specific arrest of primer extension on single-stranded DNA by an oligonucleotide-minor groove binder conjugate.

A minor groove binder (MGB) derivative (N-3-carbamoyl-1,2-dihydro-3H-pyrrolo[3,2-e]indole-7-carboxylate tripeptide; CDPI3) was covalently linked to the 5' or 3' end of several oligodeoxyribonucleotides (ODNs) totally complementary or possessing a single mismatch to M13mp19 single-stranded DNA. Absorption thermal denaturation and slot-blot hybridization studies showed that conjugation of CDPI3 to these ODNs increased both the specificity and the strength with which they hybridized. Primer extension of the same phage DNA by a modified form of phage T7 DNA polymerase (Sequenase) was physically blocked when a complementary 16-mer with a conjugated 5'-CDPI3 moiety was hybridized to a downstream site. Approximately 50% of the replicating complexes were arrested when the blocking ODN was equimolar to the phage DNA. Inhibition was unaffected by 3'-capping of the ODN with a hexanol group or by elimination of a preannealing step. Blockage was abolished when a single mismatch was introduced into the ODN or when the MGB was either removed or replaced by a 5'-acridine group. A 16-mer with a 3'-CDPI3 moiety failed to arrest primer extension, as did an unmodified 32-mer. We attribute the exceptional stability of hybrids formed by ODNs conjugated to a CDPI3 to the tethered tripeptide binding in the minor groove of the hybrid. When that group is linked to the 5' end of a hybridized ODN, it probably blocks DNA synthesis by inhibiting strand displacement. These ODNs conjugated to CDPI3 offer attractive features as diagnostic probes and antigene agents.