Bounds for the generalized Marcum function of the second kind

The Ramanujan Journal - This paper provides elementary proofs for several types of congruences involving multipartitions and self-convolutions of the divisor function. Our computations use...     

Effects of thioamide substitutions on the conformation and stability of alpha- and 3(10)-helices

Thiopeptides, formed by replacing the amide oxygen atom with a sp(2) sulfur atom, are useful in protein engineering and drug design because they confer resistance to enzymatic degradation and are predicted to be more rigid. This report describes our free molecular dynamics simulations with explicit water and free energy calculations on the effects of thio substitutions on the conformation of alpha-helices, 3(10)-helices, and their relative stability. The most prominent structural effect of thio substitution is the increase in the hydrogen bond distance from 2.1 A for normal peptides to 2.7 A for thiopeptides. To accommodate for the longer C[double bond]S...H-N hydrogen bond, the (phi, psi) dihedral angles of the alpha-helix changed from (-66 degrees, -42 degrees) to (-68 degrees, -38 degrees), and the rise per turn increased from 5.5 to 6.3 A. For 3(10)-helices, the (phi, psi) dihedral angles (-60 degrees, -20 degrees) and rise per turn (6.0 A) changed to (-66 degrees, -12 degrees) and 6.8 A, respectively. In terms of relative stability, the most prominent change upon thio substitution is the decrease in the free energy difference, Delta A(alpha --> 3(10)), from 14 to 3.5 kcal/mol. Therefore, normal peptides are less likely to form 3(10)-helix than are thiopeptides. Component analysis of the Delta A(alpha --> 3(10)) reviews that the entropy advantage of the 3(10)-helix for both Ac-Ala(10)-NHMe and Act-Alat(10)-NHMe is attributed to the 3(10)-helix being more flexible than the alpha-helix. Interestingly, upon thio substitution, this differential flexibility is even more apparent because the alpha-helix conformation of Act-Alat(10)-NHMe becomes more rigid due to the bulkier sulfur atom.     

Synthesis,Conformation, and Metabolism of a Selenium Bilirubin

Summary. A symmetrical C(10)-selena-bilirubin analog, 8,12-bis(2-carboxyethyl)-7,13-dimethyl-2,3,17,18-tetraethyl-10-selenabiladiene-ac-1,19(21H,24H)-dione was synthesized from 8-(2-carboxyethyl)-2,3-diethyl-7-methyl-(10H)-dipyrrin-1-one in one step by reaction with diselenyl dichloride. The selena-rubin exhibited UV-vis and NMR spectroscopic properties similar to those of the parent mesobilirubin, and like bilirubin and mesobilirubin, it adopts an intramolecularly hydrogen-bonded conformation, shaped like a ridge-tile but with a steeper pitch. The longer C–Se bond lengths (2.2Å) and smaller bond angles at C–Se–C (88°), as compared to C–CH₂–C (1.5Å, 106°), lead to an interplanar angle between the two dipyrrinones of only 72°, which is considerably less than that of bilirubin (100°) and close to that (74°) of its 10-thia-rubin analog. Despite the conformational distortion, the sensitivity of Se toward oxidation and the typically weak C–Se bond, the selena-rubin is metabolized in normal rats, like bilirubin, to acyl glucuronides, which are secreted into bile. In mutant (Gunn) rats lacking bilirubin glucuronosyl transferase (UGT1A1), glucuronide or other metabolites of the selena-rubin were not detected in bile, demonstrating the importance of hepatic glucuronidation for its biliary excretion.     

Stereospecific synthesis of 1,2-cis glycosides by vinyl-mediated IAD

[reaction: see text] Stereospecific 1,2-cis glycosylation of 2-O-vinyl thioglycosides, synthesized from the corresponding alcohols by Ir-catalyzed transvinylation with vinyl acetate, is achieved by iodine-mediated tethering of a range of primary and secondary carbohydrate acceptors, followed by intramolecular aglycon delivery (IAD). The use of such an intramolecular glycosylation strategy furnishes the desired alpha-gluco and beta-manno disaccharides in an entirely stereoselective manner.     

A Bloembergen–Purcell–Pound <Superscript>13</Superscript>C NMR relaxation study of the ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate

The molecular structure and rotational motion of the ionic liquid 1-butyl-3-methylimidazolium hexafluorophosphate ([BMIM][PF6]) were studied over a wide temperature range using the Bloembergen–Purcell–Pound ¹³C NMR spin–lattice relaxation method and NOE factors. Examination of the spin–lattice relaxation times (T ₁) and the rates (R ₁=1/T ₁) of the 1-butyl-3-methylimidazolium cation reveals the relative motions of each carbon in the imidazolium cation. The rotational characteristics of the [BMIM] cation are supported by ab-initio molecular structures of [BMIM][PF6] using density functional theory (DFT) and Hartree–Fock (HF) methods. The ab-initio gas phase structures of [BMIM][PF6] indicate that the 1-butyl-3-methylimidazolium C2 hydrogen, the ring methyl group, and the butyl side-chain hydrogen atoms form hydrogen bonds with the hexafluorophosphate anion.     

Does alpha-fluorination affect the structural trans-influence and kinetic trans-effect of an alkyl ligand? Molecular structures of Pd(TMEDA)(CH(3))(R(F)) and a kinetic study of the trans to cis isomerization of Pt(TMEDA)(CH(3))(2)I(R(F)) [R(F) = CF(2)CF(3), CFHCF(3), CH(2)CF(3)

Reaction of Pd(TMEDA)(CH(3))(2) [TMEDA = tetramethylethylenediamine] with fluoroalkyl iodides R(F)I affords a series of square planar Pd(II) complexes Pd(TMEDA)(CH(3))(R(F)) [R(F) = CF(2)CF(3) (9), CFHCF(3) (10), CH(2)CF(3) (11)], presumably by oxidative addition followed by reductive elimination of CH(3)I. The solid-state structures of each compound have been determined by single crystal X-ray diffraction studies, allowing the effect of increasing alpha-fluorination on the structural trans-influence of alkyl ligands to be examined. In these compounds there is no significant difference observed in the trans-influence of the three fluorinated alkyl ligands toward the trans-N atom, although a significant cis-influence on the neighboring methyl ligand is apparent. Oxidative addition of the same series of fluoroalkyl ligands to the corresponding Pt(TMEDA)(CH(3))(2) affords octahedral Pt(IV) complexes trans-Pt(TMEDA)(CH(3))(2)(R(F))I [R(F) = CF(2)CF(3) (12), CFHCF(3) (13), CH(2)CF(3) (14)] as the kinetic products. In each case, subsequent isomerization to the corresponding all cis-isomers is observed; in the case of 13, the stereocenter at the alpha-carbon results in two diastereomeric cis-isomers, which are formed at different rates. The molecular structures of 13 and its more stable all cis-isomer 16b have been crystallographically determined. Kinetic studies of the trans-cis isomerization reactions show the mechanism to involve a polar transition state, presumably involving iodide dissociation, followed by rearrangement of the cation, and iodide recombination. High dielectric solvents increase the rate, but solvent coordinating ability has no effect. Dissolved salts (LiI, LiOTf) show normal accelerative salt effects, with no inhibition in the case of added iodide, consistent with the formation of an intimate ion pair intermediate. The kinetic parameters show that the trans-effects of fluoroalkyl ligands in these compounds follow the order expected from the relative sigma-donor properties of the ligands, with CF(2)CF(3) < CFHCF(3) < CH(2)CF(3).     

Tuning the reactivity and chemoselectivity of electron-poor pyrroles as dienophiles in cycloadditions with electron-rich dienes

Activation by Lewis acid catalysis and high pressure allows pyrrole derivatives to react with electron-rich dienes in normal electron demand [4+2] cycloadditions, provided that the aromatic ring is substituted by at least two electron-withdrawing groups. The dienophilic behavior of the heterocycle is expressed through the involvement of either the aromatic carbon-carbon double bond in an all-carbon process or the carbonyl moiety of the substituent in a heterocycloaddition reaction. In this regard, the nature of the heterocyclic substituents is shown to have a dramatic influence and to direct both the reactivity and the chemoselectivity of the cycloaddition.     

Stereoselective 1,2-cis glycosylation of 2-O-allyl protected thioglycosides

The technique of intramolecular aglycon delivery (IAD), whereby a glycosyl acceptor is temporarily appended to a hydroxyl group of a glycosyl donor is an attractive method that can allow the synthesis of 1,2-cis glycosides in an entirely stereoselective fashion. 2-O-Allyl protected thioglycoside donors are excellent substrates for IAD, and may be glycosylated stereoselectively through a three-step reaction sequence. This sequence consists of quantitative yielding allyl bond isomerisation, to produce vinyl ethers that can then undergo N-iodosuccinimide mediated tethering of the desired glycosyl acceptor, and subsequent intramolecular glycosylation, to yield either alpha-glucosides or beta-mannosides accordingly. Although attempted one-pot tethering and glycosylation is hampered by competitive intermolecular reaction with excess glycosyl acceptor, this problem can be simply overcome by the use of excess glycosyl donor. Allyl mediated IAD is a widely applicable practical alternative to other IAD approaches for the synthesis of beta-mannosides, that is equally applicable for alpha-gluco linkages. It is advantageous in terms of both simplicity of application and yield, and in addition has no requirement for cyclic 4,6-protection of the glycosyl donor.