Eisenstein series and Ramanujan-type series for 1/π

Using certain representations for Eisenstein series, we uniformly derive several Ramanujan-type series for 1/π.     

Capturing a Pentacyclic Fragment-Based Library Derived from Perophoramidine: Their Design,Synthesis and Evaluation as Anticancer Compounds by DNA Double-Strand Breaks (DSB) and PARP-1 Inhibition

Herein we have reported the discovery of a pentacyclic building block comprised of fused indole-quinoline and piperidinone from the natural product perophoramidine as a formidable anticancer agent. The compounds were synthesized in six steps where the key steps involved a blue LED mediated intramolecular cyclopropanation of the indole intermediates and concomitant reduction of the associated aryl nitro moiety to nitroso in the molecule. Cytotoxicity screening of the compounds against an array of cancer cells that is, MCF7, HCT116 and A549 demonstrated 0.6 to 9 μM IC₅₀s by few of the compounds. γH2AX immunofluorescence assay of the two most potent molecules from the phenotypic screening with anti-γ-H2AX Alexa Fluor 488 antibody revealed extensive DNA damage of the A549 cells which indicated probable PARP inhibition (similar to Perophoramidine). Through molecular docking and molecular dynamic (MD) simulation studies the binding efficiency of our compounds with poly(ADP-ribose)polymerase 1 (PARP 1) enzyme was determined. Chemiluminescent PARP Assay with Histone-coated strips indicated that the most active compounds from the phenotypic screening induced PARP-1 inhibition with IC₅₀s of 1.3→1.5 μM.     

Longitudinal Structure Function F L of Proton from Regge Like Behaviour of Structure Function at Small-x

The evolutions of longitudinal structure function F _L from quantum chromodynamics (QCD) evolution equation in next-to-leading order at small-x is presented using the Regge like behaviour of the structure function. The proposed simple analytical expression for F _L structure function provides the t- and x-evolution equations to study the behaviour of F _L structure function at small-x. The calculated results are compared with the data of H1, ZEUS collaborations and results of Block model, Donnachie–Landshoff model. Our calculated results can be described within the framework of perturbative QCD.     

Density-functional study of two Fe4-based single-molecule magnets

We present the results of our all-electron density-functional calculations on the electronic structure and magnetic anisotropy energy of the [Fe4(OMe)6(dpm)6] and [Fe4(thme)2(dpm)6] molecular clusters, which are experimentally found to behave as single-molecule magnets. The calculated magnetic anisotropy energy barriers are 2.65 and 15.8 K, respectively, which agree with the experimental data. We also present a density-functional study on the effect of the structure distortions on the magnetic anisotropy of the [Fe(H2O)6]3+ complex. This study, together with an analysis of the projected anisotropies of each iron ion in both molecular clusters, allows us to qualitatively understand why the magnetic anisotropy energy (MAE) barrier of the second single-molecule magnet (SMM) is larger than the MAE of the first SMM.     

BODIPY-based hydroxyaryl derivatives as fluorescent pH probes

[structures: see text] Seven new 4,4-difluoro-4-bora-3a,4a-diaza-s-indacene (BODIPY) dyes with phenolic or naphtholic subunits on position 8 and with substituents having different electron driving forces on positions 3 and 5 were synthesized. Their absorption and steady-state fluorescence properties were investigated as a function of solvent. The novel compounds, with the exception of 4,4-difluoro-8-(4-hydroxyphenyl)-3,5-bis-(4-methoxyphenyl)-4-bora-3a,4a-diaza-s-indacene, are characterized by absorption maxima in the range 493-515 nm and small (400-600 cm(-1)) Stokes shifts. The exceptional dye has absorption maxima in the 570-580 nm region and fluorescence emission maxima around 610-620 nm, depending on the solvent. In aqueous solution, the dyes show a large fluorescent enhancement upon increasing the acidity of the solution. They can be used in aqueous solution as fluorescent pH probes excitable with visible light, with pKa values ranging from 7.5 to 9.3, depending on the substitution pattern on positions 3, 5, and 8.     

Structural variations in self-assembled cadmium benzoate complexes

A series of mixed ligand cadmium(II) complexes having 3,5-dimethylpyrazole and aromatic carboxylate are structurally characterized. The effect of substituent on aromatic ring and also the effect of composition on co-ordination behavior of these complexes are ascertained. Hydrogen bonded self-assembled mononuclear complexes are obtained from composition [Cd(L)₂(L_a)₂] where L_a = 3,5-dimethylpyrazole L = R–C₆H₄COO– [R = H (1), 2-Cl (2), 4-OH (3), 2-OH (4)]. The cadmium complex (5) having composition [Cd(L)₂(L_a)(H₂O)] (L = 2-NO₂–C₆H₄COO–) is tetra-nuclear. The complex has eight and six co-ordination around cadmium and self-assembles through hydrogen bonding leading to form extended chain structure. The four complexes (1–4) have six co-ordinated trigonal prismatic geometry around cadmium ions. Cadmium complexes having composition [Cd(L)₂(L_a)] such as R = 4-NO₂ (6), 4-Cl (7), and 1-naphthoate complex (8) are co-ordination polymers with seven co-ordination geometry around cadmium. In these co-ordination polymers different Cd–Cd distances are observed for alternate pair of cadmium ions. For example in the case of the co-ordination polymer of 4-nitro-benzoate complex the Cd–Cd distance between alternate pairs are 4.138 Å, and 3.748 Å. The 1-naphthoate complex having pyridine has composition [Cd(L)₂(L_b)₂](H₂O)] (9) where L_b = pyridine and L = 1-naphthoate has seven co-ordination with a distorted pentagonal bipyramid geometry.     

Ring opening reactions of pyromellitic dianhydride for the synthesis of first row transition metal dicarboxylate complexes

The ring opening reaction of pyromellitic dianhydride by methanol is an effective method to prepare first row transition metal dicarboxylate complexes. The reactions of different first row transition metal salts with pyromellitic dianhydride in the presence of nitrogen donating bidentate ligands such as 1,10-phenanthroline and 2,2′-bipyridine gives different compositions depending on the ligand and the metal salts used. For example, the reaction of nickel(II) acetate with pyromellitic dianhydride in the presence of 1,10-phenanthroline results in the formation of a carboxylato bridged nickel(II) metallacycle through the ring opening reaction of pyromellitic dianhydride (PAH) at the 1 and 3-positions, whereas a mononuclear tetra-aqua 2,2′-bipyridine nickel(II) complex is formed in a similar reaction of nickel(II) acetate through ring opening at the 1,4-position of PAH. Mononuclear cobalt(II) dicarboxylate complexes are formed from the ring opening reaction of pyromellitic dianhydride in methanol in the presence of the nitrogen donor ligands 1,10-phenanthroline or 2,2′-bipyridine. Copper(II) chloride on reaction with PAH and 2,2′-bipyridine gives a mononuclear complex via ring opening at the 1 and 4-positions; having chlorides inside and outside the coordination sphere. Whereas, the reaction of copper(II)acetate gives dinuclear copper complexes having a monodentate carboxylato bridge arising from the carboxylato groups at the 1 and 4-positions on the aromatic ring. The crystal structures of all the complexes have been determined.     

Enforcing periodic secondary structures in hybrid peptides: a novel hybrid foldamer containing periodic gamma-turn motifs

This note describes the design, synthesis, and conformational studies of a novel hybrid foldamer that adopts a definite compact, three-dimensional structure determined by a combined effect of the special conformational properties of the foldamer constituents. The striking feature of this de novo designed foldamer is its ability to display periodic gamma-turn conformations stabilized by intramolecular hydrogen bonds. Conformational investigations by single-crystal X-ray studies, solution-state NMR, and ab initio MO theory at the HF/6-31G* level strongly support the prevalence of gamma-turn motifs in both the di- and tetrapeptide foldamers, which are presumably stabilized by bifurcated hydrogen bonds in the solid and solution states. The strategy disclosed herein for the construction of hybrid foldamers with periodic gamma-turn motifs has the potential to significantly augment the conformational space available for foldamer design with diverse backbone structures and conformations.     

Ligational behaviour of two biologically active N−S donors towards cobalt(III), iron(III), iron(II) and rhodium(III)

Summary The chelating behaviour of two biologically active ligands, pyridine-2-carboxaldehyde(4-phenyl) thiosemicarbazone(L₁H) and pyridine-2-carboxaldehyde thiosemicarbazone(LH), towards Fe^III, Co^III, Fe^II and Rh^III has been investigated. The ligands act as tridentate N–N–S donors, resulting in the formation of bis-chelate complexes of the type M^III(A)₂X·nH₂O (A=L₁ or L; X=Cl, ClO₄; M=Co^III, Rh^III, Fe^III), Fe^II(L₁H)₂SO₄·2H₂O and Fe^II(L₁)₂·H₂O. Biological activity of the ligands and the metal complexes in the form ofin vitro antibacterial activities towardsE. coli has been evaluated and the possible reasons for enhancement of the activity of ligands on coordination to metal ion is discussed.     

Reaction of 2-phenyl-4-methyl-Δ2-oxazolin-5-one with imines. A convenient synthesis of 3-amido-β-lactams

Azlactone 3a reacted with furan-2-aldehyde and thiophene-2-aldehyde imines to give corresponding 3-amido-β-lactams in good yields.