The local polynomial hull near a degenerate CR singularity: Bishop discs revisited

Let be a smooth real surface in and let be a point at which the tangent plane is a complex line. How does one determine whether or not is locally polynomially convex at such a p-i.e. at a CR singularity? Even when the order of contact of with at p equals 2, no clean characterisation exists; difficulties are posed by parabolic points. Hence, we study non-parabolic CR singularities. We show that the presence or absence of Bishop discs around certain non-parabolic CR singularities is completely determined by a Maslov-type index. This result subsumes all known facts about Bishop discs around order-two, non-parabolic CR singularities. Sufficient conditions for Bishop discs have earlier been investigated at CR singularities having high order of contact with . These results relied upon a subharmonicity condition, which fails in many simple cases. Hence, we look beyond potential theory and refine certain ideas going back to Bishop.

Understanding the Magnetization Reversal in Six-Fold Anisotropic Hexagonal Networks

Isolated magnetic nanowires have been studied extensively and the magnetization reversal mechanism is well understood in these systems. But when these nanowires are joined together in different architectures, they behave differently and can give novel properties. Using this approach, one can engineer the network architectures to get artificial anisotropy. Here, we report six-fold anisotropy by joining the magnetic nanowires into hexagonal network. For this study, we also benchmark the widely used micromagnetic packages: OOMMF, Nmag, and LLG-simulator. Further, we propose a local hysteresis method by post processing the spatial magnetization information. With this approach we obtained the hysteresis of nanowires to understand the six-fold anisotropy and the reversal mechanism within the hexagonal networks.

Interaction Signatures Stabilizing the NAD(P)-Binding Rossmann Fold: A Structure Network Approach

The fidelity of the folding pathways being encoded in the amino acid sequence is met with challenge in instances where proteins with no sequence homology, performing different functions and no apparent evolutionary linkage, adopt a similar fold. The problem stated otherwise is that a limited fold space is available to a repertoire of diverse sequences. The key question is what factors lead to the formation of a fold from diverse sequences. Here, with the NAD(P)-binding Rossmann fold domains as a case study and using the concepts of network theory, we have unveiled the consensus structural features that drive the formation of this fold. We have proposed a graph theoretic formalism to capture the structural details in terms of the conserved atomic interactions in global milieu, and hence extract the essential topological features from diverse sequences. A unified mathematical representation of the different structures together with a judicious concoction of several network parameters enabled us to probe into the structural features driving the adoption of the NAD(P)-binding Rossmann fold. The atomic interactions at key positions seem to be better conserved in proteins, as compared to the residues participating in these interactions. We propose a ``spatial motif'' and several ``fold specific hot spots'' that form the signature structural blueprints of the NAD(P)-binding Rossmann fold domain. Excellent agreement of our data with previous experimental and theoretical studies validates the robustness and validity of the approach. Additionally, comparison of our results with statistical coupling analysis (SCA) provides further support. The methodology proposed here is general and can be applied to similar problems of interest.

Generation of Ligand Specificity and Modes of Oligomerization in beta-Prism I Fold Lectins

beta-Prism I fold lectins constitute one of the five widely occurring structural classes of plant lectins. Each single domain subunit is made up of three Greek key motifs arranged in a threefold symmetric fashion. The threefold symmetry is not reflected in the sequence except in the case of the lectin from banana, a monocot, which carries two sugar-binding sites instead of the one in other lectins of known three-dimensional structure, all from dicots. This is believed to be a consequence of the different evolutionary paths followed by the lectin in monocots and dicots. The galactose-specific lectins among them have two chains produced by posttranslational proteolysis and contain three aromatic residues at the binding site. The extended binding sites of galactose- and mannose-specific lectins have been thoroughly characterized. Ligand binding at the sites involves both conformational selection and induced fit. Molecular plasticity of some of the lectins in the family has been characterized. The plasticity appears to be such as to promote variability in quaternary association which could be dimeric, tetrameric, or octameric. Structural and evolutionary reasons for the variability have been explored, and the relation of oligomerization to ligand binding and conformational selection investigated.

The exploration of Kemp's triacid (KTA) as the core for the synthesis of 3-fold symmetric 2(3)-cyclophane, 2(2)-cyclophane and novel linker directed designs

For the first time, two units of KTA have been linked to three units of cyst-di-OMe. The reaction is noteworthy since it involves the formation of six amide bonds leading to a three-fold symmetric 23-cyclophane (3) harboring a cluster of three S-S bridges. The major product is a di-imide (4), arising from the interaction of a cystine NH with a neighbouring activated ester. A third reaction of tethering KTA with a single cyst-di-OMe unit afforded the flexible compound 6 and, with benzidine, the novel linker directed 7 with orthogonally disposed anchor modules.

FOLD TYPE II PYRIDOXAL 5 `-PHOSPHATE DEPENDENT ENZYMES: STRUCTURE, SUBSTRATE RECOGNITION AND CATALYSIS

Enzymes utilizing pyridoxal 5'-phosphate dependent mechanism for catalysis are observed in all cellular forms of living organisms. PLP-dependent enzymes catalyze a wide variety of reactions involving amino acid substrates and their analogs. Structurally, these ubiquitous enzymes have been classified into four major fold types. We have carried out investigations on the structure and function of fold type I enzymes serine hydroxymethyl transferase and acetylornithine amino transferase, fold type n enzymes catabolic threonine deaminase, D-serine deaminase, D-cysteine desulfhydrase and diaminopropionate ammonia lyase. This review summarizes the major findings of investigations on fold type II enzymes in the context of similar studies on other PLP-dependent enzymes. Fold type II enzymes participate in pathways of both degradation and synthesis of amino acids. Polypeptide folds of these enzymes, features of their active sites, nature of interactions between the cofactor and the polypeptide, oligomeric structure, catalytic activities with various ligands, origin of specificity and plausible regulation of activity are briefly described. Analysis of the available crystal structures of fold type II enzymes revealed five different classes. The dimeric interfaces found in these enzymes vary across the classes and probably have functional significance.

Low tension strings on a cosmological singularity

It has recently been argued that the singularity of the Milne orbifold can be resolved in higher spin theories. In string theory scattering amplitudes, however, the Milne singularity gives rise to ultraviolet divergences that signal uncontrolled backreaction. Since string theory in the low tension limit is expected to be a higher spin theory (although precise proposals only exist in special cases), we investigate what happens to these scattering amplitudes in the low tension limit. We point out that the known problematic ultraviolet divergences disappear in this limit. In addition we systematically identify all divergences of the simplest 2-to-2 tree-level string scattering amplitude on the Milne orbifold, and argue that the divergences that survive in the low tension limit have sensible infrared interpretations.

Exploring the Consequences of a Representative ``Disallowed'' Conformation of Aib on a 3(10)-Helical Fold

The structural effects of a representative disallowed conformation of Aib on the 3(10)-helical fold of an octapeptidomimetic are explored. The 1D (H-1, C-13) & 2D NMR, FT-IR and CD data reveal that the octapeptide 1, adopts a 3(10)-helical conformation in solution, as it does in its crystal structure. The C-terminal methyl carboxylate (CO2Me) of 1 was modified into an 1,3-oxazine (Oxa) functional group in the peptidomimetic 2. This modification results in the stabilization of the backbone of the C-terminal Aib (Aib*-Oxa) of 2, in a conformation (phi, =180, 0) that is natively disallowed to Aib. Consequent to the presence of this natively disallowed conformation, the 3(10)-helical fold is not disrupted in the body of the peptidomimetic 2. But the structural distortions that do occur in 2 are primarily in residues in the immediate vicinity of the natively disallowed conformation, rather than in the whole peptide body. Non-native electronic effects resulting from modifications in backbone functional groups can be at the origin of stabilizing residues in natively disallowed conformations. (c) 2014 Wiley Periodicals, Inc. Biopolymers (Pept Sci) 104: 21-36, 2015.

Nonvanishing of Koecher-Maass series attached to Siegel cusp forms

We prove a nonvanishing result for Koecher-Maass series attached to Siegel cusp forms of weight k and degree n in certain strips on the complex plane. When n = 2, we prove such a result for forms orthogonal to the space of the Saito-Kurokawa lifts `up to finitely many exceptions', in bounded regions. (C) 2015 Elsevier Inc. All rights reserved.

Exploring the Consequences of a Representative ``Disallowed'' Conformation of Aib on a 3(10)-Helical Fold

The structural effects of a representative ``disallowed'' conformation of Aib on the 3(10)-helical fold of an octapeptidomimetic are explored. The 1D (H-1, C-13) & 2D NMR, FT-IR and CD data reveal that the octapeptide 1, adopts a 3(10)- helical conformation in solution, as it does in its crystal structure. The C-terminal methyl carboxylate (CO2Me) of 1 was modified into an 1,3-oxazine (Oxa) functional group in the peptidomimetic 2. This modification results in the stabilization of the backbone of the C-terminal Aib (Aib(star)-Oxa) of 2, in a conformation (phi, psi = 180, 0) that is natively disallowed to Aib. Consequent to the presence of this natively disallowed conformation, the 3(10)- helical fold is not disrupted in the body of the peptidomimetic 2. But the structural distortions that do occur in 2 are primarily in residues in the immediate vicinity of the natively disallowed conformation, rather than in the whole peptide body. Non-native electronic effects resulting from modifications in backbone functional groups can be at the origin of stabilizing residues in natively disallowed conformations. (C) 2014 Wiley Periodicals, Inc. Biopolymers

Exploring the Consequences of a Representative ``Disallowed'' Conformation of Aib on a 3(10)-Helical Fold

The structural effects of a representative ``disallowed'' conformation of Aib on the 3(10)-helical fold of an octapeptidomimetic are explored. The 1D (H-1, C-13) & 2D NMR, FT-IR and CD data reveal that the octapeptide 1, adopts a 3(10)- helical conformation in solution, as it does in its crystal structure. The C-terminal methyl carboxylate (CO2Me) of 1 was modified into an 1,3-oxazine (Oxa) functional group in the peptidomimetic 2. This modification results in the stabilization of the backbone of the C-terminal Aib (Aib(star)-Oxa) of 2, in a conformation (phi, psi = 180, 0) that is natively disallowed to Aib. Consequent to the presence of this natively disallowed conformation, the 3(10)- helical fold is not disrupted in the body of the peptidomimetic 2. But the structural distortions that do occur in 2 are primarily in residues in the immediate vicinity of the natively disallowed conformation, rather than in the whole peptide body. Non-native electronic effects resulting from modifications in backbone functional groups can be at the origin of stabilizing residues in natively disallowed conformations. (C) 2014 Wiley Periodicals, Inc. Biopolymers

Evolutionary and structural analyses of heterodimeric proteins composed of subunits with same fold

Heterodimeric proteins with homologous subunits of same fold are involved in various biological processes. The objective of this study is to understand the evolution of structural and functional features of such heterodimers. Using a non-redundant dataset of 70 such heterodimers of known 3D structure and an independent dataset of 173 heterodimers from yeast, we note that the mean sequence identity between interacting homologous subunits is only 23-24% suggesting that, generally, highly diverged paralogues assemble to form such a heterodimer. We also note that the functional roles of interacting subunits/domains are generally quite different. This suggests that, though the interacting subunits/domains are homologous, the high evolutionary divergence characterize their high functional divergence which contributes to a gross function for the heterodimer considered as a whole. The inverse relationship between sequence identity and RMSD of interacting homologues in heterodimers is not followed. We also addressed the question of formation of homodimers of the subunits of heterodimers by generating models of fictitious homodimers on the basis of the 3D structures of the heterodimers. Interaction energies associated with these homodimers suggests that, in overwhelming majority of the cases, such homodimers are unlikely to be stable. Majority of the homologues of heterodimers of known structures form heterodimers (51.8%) and a small proportion (14.6%) form homodimers. Comparison of 3D structures of heterodimers with homologous homodimers suggests that interfacial nature of residues is not well conserved. In over 90% of the cases we note that the interacting subunits of heterodimers are co-localized in the cell. Proteins 2015; 83:1766-1786. (c) 2015 Wiley Periodicals, Inc.

Physiological role of FolD (methylenetetrahydrofolate dehydrogenase), FchA (methenyltetrahydrofolate cyclohydrolase) and Fhs (formyltetrahydrofolate synthetase) from Clostridium perfringens in a heterologous model of Escherichia coli

Most organisms possess bifunctional FolD 5,10-methylenetetrahydrofolate (5,10-CH2-THF) dehydrogenase-cyclohydrolase] to generate NADPH and 10-formyltetrandrofolate (10-CHO-THF) required in various metabolic steps. In addition, some organisms including Clostridium perfringens possess another protein, Fhs (formyltetrahydrofolate synthetase), to synthesize 10-CHO-THF. Here, we show that unlike the bifunctional FolD of Escherichia coli (Eco FolD), and contrary to its annotated bifunctional nature, C. perfringens FolD (Cpe FoID) is a monofunctional 5,10-CH2-THF dehydrogenase. The dehydrogenase activity of Cpe FoID is about five times more efficient than that of Eco FolD. The 5,10-methenyltetrahydrofolate (5,10-CH+-THF) cyclohydrolase activity in C. perfringens is provided by another protein, FchA (5,10-CH+-THF cyclohydrolase), whose cyclohydrolase activity is similar to 10 times more efficient than that of Eco FolD. Kinetic parameters for Cpe Fhs were also determined for utilization of all of its substrates. Both Cpe FoID and Cpe FchA are required to substitute for the single bifunctional FolD in E. coli. The simultaneous presence of Cpe FoID and Cpe FchA is also necessary to rescue an E coli folD deletion strain (harbouring Cpe Fhs support) for its formate and glycine auxotrophies, and to alleviate its susceptibility to trimethoprim (an antifolate drug) or UV light. The presence of the three clostridial proteins (FolD, FchA and Fhs) is required to maintain folate homeostasis in the cell.

A NOTE ON SMALL GAPS BETWEEN NONZERO FOURIER COEFFICIENTS OF CUSP FORMS

It is shown that there are infinitely many primitive cusp forms f of weight 2 with the property that for all X large enough, every interval (X, X + cX(1/4)), where c > 0 depends only on the form, contains an integer n such that the n-th Fourier coefficient of f is nonzero.

Singularity characteristics for a lip-shaped crack subjected to remote biaxial loading

In this paper, the conformal mapping method was adopted to solve the problem of an infinite plate containing a central lip-shaped crack subjected to remote biaxial loading. A kind of leaf-shaped configuration was also constructed in order to solve the problem. The analytical result showed that the singularity order of the stress field at the tip of a lip-shaped crack remains -1/2, despite the difference in notch-crack width.