The homologous recombination system of phage lambda. Pairing activities of beta protein

The red genes of phage lambda specify two proteins, exonuclease and beta protein, which are essential for its general genetic recombination in recA- cells. These proteins seem to occur in vivo as an equimolar complex. In addition, beta protein forms a complex with another polypeptide, probably of phage origin, of Mr 70,000. The 70-kDa protein appears to be neither a precursor nor an aggregated form of either exonuclease or beta protein, since antibodies directed against the latter two proteins failed to react with 70-kDa protein on Ouchterlony double diffusion analysis. beta protein promotes Mg2+-dependent renaturation of complementary strands (Kmiec, E., and Holloman, W. K. (1981) J. Biol. Chem. 256, 12636-12639). To look for other pairing activities of beta protein, we developed methods of purification to free it of associated exonuclease. Exonuclease-free beta protein appeared unable to cause the pairing of a single strand with duplex DNA; however, like Escherichia coli single strand binding protein (SSB), beta protein stimulated formation of joint molecules by recA protein from linear duplex DNA and homologous circular single strands. Like recA protein, but unlike SSB, beta protein promoted the joining of the complementary single-stranded ends of phage lambda DNA. beta protein specifically protected single-stranded DNA from digestion by pancreatic DNase. The half-time for renaturation catalyzed by beta protein was independent of DNA concentration, unlike renaturation promoted by SSB and spontaneous renaturation, which are second order reactions. Thus, beta protein resembles recA protein in its ability to bring single-stranded DNA molecules together and resembles SSB in its ability to reduce secondary structure in single-stranded DNA.

Homologous pairing between nucleosome cores on a linear duplex DNA and nucleoprotein filaments of RecA protein-single stranded DNA

The ability of E coli recA protein to promote homologous pairing with linear duplex DNA bound to HU protein (Nucleosome cores) was found to be differentially affected. The formation of paranemic joint molecules was not affected whereas the formation of plectomic joint molecules was inhibited from the start of the reaction. The formation of paranemic joint molecules between nucleoprotein filaments of recA protein-circular single stranded DNA and closed circular duplex DNA is believed to generate positive supercoiling in the duplex DNA. We found that the positively superhelical duplex DNA was inert in the formation of joint molecules but could be converted into an active substrate, in situ, by the action of wheat germ topoisomerase I. These observations initiate an understanding of the structural features of E coli chromosome such as DNA supercoiling and nucleosome-like structures in homologous recombination.

Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics

In quantum theory, symmetry has to be defined necessarily in terms of the family of unit rays, the state space. The theorem of Wigner asserts that a symmetry so defined at the level of rays can always be lifted into a linear unitary or an antilinear antiunitary operator acting on the underlying Hilbert space. We present two proofs of this theorem which are both elementary and economical. Central to our proofs is the recognition that a given Wigner symmetry can, by post-multiplication by a unitary symmetry, be taken into either the identity or complex conjugation. Our analysis often focuses on the behaviour of certain two-dimensional subspaces of the Hilbert space under the action of a given Wigner symmetry, but the relevance of this behaviour to the larger picture of the whole Hilbert space is made transparent at every stage.

Cubic and ultimate groups of complete symmetry

It is shown that the systems of definite actions described by polar and axial tensors of the second rank and their combinations during the superposition of their elements of complete symmetry with the elements of complete symmetry of the "grey" cube, result in 11 cubic crystallographical groups of complete symmetry. There are 35 ultimate groups (i.e., the groups having the axes of symmetry of infinite order) in complete symmetry of finite figures. 14 out of these groups are ultimate groups of symmetry of polar and axial tensors of the second rank and 24 are new groups. All these 24 ultimate groups are conventional groups since they cannot be presented by certain finite figures possessing the axes of symmetry {Mathematical expression}. Geometrical interpretation for some of the groups of complete symmetry is given. The connection between complete symmetry and physical properties of the crystals (electrical, magnetic and optical) is shown.

The change of complete symmetry of the crystals during the phase transitions in ferroelectrics and ferromagnetics

The extension of the superposition principle of the symmetries (P. Curie principle of symmetry) for the case of complete symmetry is given. The enumeration of all crystallographical groups of complete symmetry is presented, the number of elements having complete symmetry for each class of the crystals being indicated. The change of complete symmetry of the crystals under the phase transitions is obtained by superimposing the elements of complete symmetry of polar or axial vectors on the one hand, and the elements of complete symmetry of the crystals on the other. The tables of complete symmetry changes for the cubic, rhombic, monoclinic and triclinic crystals during the ferroelectric and ferromagnetic phase transitions are given.

Symmetry and shape issues in nanostructure growth

Symmetry plays a key role in dictating the equilibrium morphology of crystals. However, several growth morphologies that deviate from the point group symmetry are routinely observed under several different growth conditions. In this article, we present a summary of symmetry-breaking mechanisms that are operative for crystals grown from the vapour phase as well as those formed as a result of wet chemical synthesis. This understanding is crucial for rationalizing the variety of morphologies observed during nanocrystal synthesis and also providesa rational framework for the synthesis of anisotropic nanostructures.

Hole pairing within an extended Anderson impurity model applicable to the high-Tc cuprates

We calculate the binding energy of a hole pair within the extended Anderson Hamiltonian for the high-Tc cuprates including a Cu impurity and an oxygen-derived band. The results indicate that stable hole pairs can be formed for intra-atomic and interatomic Coulomb repulsion strengths larger than 6 and 3.5 eV, respectively. It is also shown that the total hybridization strength between the Cu 3d and oxygen p band should be less than 2.5 eV. The hole pairing takes place primarily within the oxygen-derived p band. The range of parameter values for which hole pairing occurs is also consistent with the earlier photoemission results from these cuprates.

X-ray diffraction from single Al6CuLi3 grains showing five-fold symmetry

We present here the detailed results of X-ray diffraction from single quasicrystals of Al6CuLi3. X-ray precession photographs taken down the two-, three- and five-fold axes along with rotation and zero-level Weissenberg photographs are shown. Preliminary analysis of the diffraction data rules out the twin hypothesis.

Disulfide Bond Assignments by Mass Spectrometry of Native Natural Peptides: Cysteine Pairing in Disulfide Bonded Conotoxins

The critical, and often most difficult, step in structure elucidation of diverse classes of natural peptides is the determination of correct disulfide pairing between multiple cysteine residues. Here, we present a direct mass spectrometric analytical methodology for the determination of disulfide pairing. Protonated peptides, having multiple disulfide bonds, fragmented under collision induced dissociation (CID) conditions and preferentially cleave along the peptide backbone, with occasional disulfide fragmentation either by C-beta-S bond cleavage through H-alpha abstraction to yield dehydroalanine and cysteinepersulfide, or by S-S bond cleavage through H-beta abstraction to yield the thioaldehyde and cysteine. Further fragmentation of the initial set of product ions (MSn) yields third and fourth generation fragment ions, permitting a distinction between the various possible disulfide bonded structures. This approach is illustrated by establishing cysteine pairing patterns in five conotoxins containing two disulfide bonds. The methodology is extended to the Conus araneosus peptides An 446 and Ar1430, two 14 residue sequences containing 3 disulfide bonds. A distinction between 15 possible disulfide pairing schemes becomes possible using direct mass spectral fragmentation of the native peptides together with fragmentation of enzymatically nicked peptides.

Nucleosomes on linear duplex DNA allow homologous pairing but prevent strand exchange promoted by RecA protein

To understand the molecular basis of gene targeting, we have studied interactions of nucleoprotein filaments comprised of single-stranded DNA and RecA protein with chromatin templates reconstituted from linear duplex DNA and histones. We observed that for the chromatin templates with histone/DNA mass ratios of 0.8 and 1.6, the efficiency of homologous pairing was indistinguishable from that of naked duplex DNA but strand exchange was repressed. In contrast, the chromatin templates with a histone/DNA mass ratio of 9.0 supported neither homologous pairing nor strand exchange. The addition of histone H1, in stoichiometric amounts, to chromatin templates quells homologous pairing. The pairing of chromatin templates with nucleoprotein filaments of RecA protein-single-stranded DNA proceeded without the production of detectable networks of DNA, suggesting that coaggregates are unlikely to be the intermediates in homologous pairing. The application of these observations to strategies for gene targeting and their implications for models of genetic recombination are discussed.

Symmetry preservation during radiation damage

An examination of radiation-damage processes consequent to high-energy irradiation in certain ammonium salts studied using ESR of free radical together with the structural information available from neutron diffraction studies shows that, other factors being equal/nearly equal, symmetry-related bonds are preserved in preference to those unrelated to one another by any symmetry.

Conformational Polymorphism in Telomeric Structures: Loop Orientation and Interloop Pairing in d(G4TnG4),

Sequence repeats constituting the telomeric regions of chromosomes are known to adopt a variety of unusual structures, consisting of a G tetraplex stem and short stretches of thymines or thymines and adenines forming loops over the stem. Detailed model building and molecular mechanics studies have been carried out for these telomeric sequences to elucidate different types of loop orientations and possible conformations of thymines in the loop. The model building studies indicate that a minimum of two thymines have to be interspersed between guanine stretches to form folded-back structures with loops across adjacent strands in a G tetraplex (both over the small as well as large groove), while the minimum number of thymines required to build a loop across the diagonal strands in a G tetraplex is three. For two repeat sequences, these hairpins, resulting from different types of folding, can dimerize in three distinct ways-i.e., with loops across adjacent strands and on same side, with loops across adjacent strands and on opposite sides, and with loops across diagonal strands and on opposite sides-to form hairpin dimer structures. Energy minimization studies indicate that all possible hairpin dimers have very similar total energy values, though different structures are stabilized by different types of interactions. When the two loops are on the same side, in the hairpin dimer structures of d(G(4)T(n)G(4)), the thymines form favorably stacked tetrads in the loop region and there is interloop hydrogen bonding involving two hydrogen bonds for each thymine-thymine pair. Our molecular mechanics calculations on various folded-back as well as parallel tetraplex structures of these telomeric sequences provide a theoretical rationale for the experimentally observed feature that the presence of intervening thymine stretches stabilizes folded-back structures, while isolated stretches of guanines adopt a parallel tetraplex structure

Symmetry adaptation of correlated states in the valence bond basis

Symmetry?adapted linear combinations of valence?bond (VB) diagrams are constructed for arbitrary point groups and total spin S using diagrammatic VB methods. VB diagrams are related uniquely to invariant subspaces whose size reflects the number of group elements; their nonorthogonality leads to sparser matrices and is fully incorporated into a binary integer representation. Symmetry?adapated linear combinations of VB diagrams are constructed for the 1764 singlets of a half?filled cube of eight sites, the 2.8 million ??electron singlets of anthracene, and for illustrative S?0 systems.

E. C. G. Sudarshan and Symmetry in Classical Dynamics, Optics and Quantum Mechanics

We review work initiated and inspired by Sudarshan in relativistic dynamics, beam optics, partial coherence theory, Wigner distribution methods, multimode quantum optical squeezing, and geometric phases. The 1963 No Interaction Theorem using Dirac's instant form and particle World Line Conditions is recalled. Later attempts to overcome this result exploiting constrained Hamiltonian theory, reformulation of the World Line Conditions and extending Dirac's formalism, are reviewed. Dirac's front form leads to a formulation of Fourier Optics for the Maxwell field, determining the actions of First Order Systems (corresponding to matrices of Sp(2,R) and Sp(4,R)) on polarization in a consistent manner. These groups also help characterize properties and propagation of partially coherent Gaussian Schell Model beams, leading to invariant quality parameters and the new Twist phase. The higher dimensional groups Sp(2n,R) appear in the theory of Wigner distributions and in quantum optics. Elegant criteria for a Gaussian phase space function to be a Wigner distribution, expressions for multimode uncertainty principles and squeezing are described. In geometric phase theory we highlight the use of invariance properties that lead to a kinematical formulation and the important role of Bargmann invariants. Special features of these phases arising from unitary Lie group representations, and a new formulation based on the idea of Null Phase Curves, are presented.