The Landau-Lifshitz equation,elliptic curves and the ward transform

The Landau-Lifshitz (LL) equation is studied from a point of view that is close to that of Segal and Wilson's work on KdV. The LL hierarchy is defined and shown to exist using a dressing transformation that involves parameters ₁, ₂, ₃ that live on an elliptic curve . The crucial role of the groupK ₂ × ₂ of translations by the half-periods of and its non-trivial central extension is brought out and an analogue of Birkhoff factorisation for -equivariant loops in is given. This factorisation theorem is given two treatments, one in terms of the geometry of an infinite-dimensional Grassmannian, and the other in terms of the algebraic geometry of bundles over . Further, a Ward-like transform between a class of holomorphic vector bundles on the total spaceZ of a line-bundle over and solutions of LL is constructed. An appendix is devoted to a careful definition of the Grassmannian of the Frechet spaceC (S ¹).     

Formation of stable Meisenheimer adduct ion pairs in apolar solvents: implications for stereoselective reactions

[reaction: see text] A detailed study concerning the formation of Meisenheimer adducts in biphasic solvent systems is described. The process relies on utilizing a significantly lipophilic quaternary ammonium salt to transfer a nucleophile (e.g., hydroxide ion) between an aqueous and organic layer containing the electron-deficient aromatic substrate. Provided that the organic layer is sufficiently apolar, the resultant Meisenheimer adduct is considerably stable, likely the result of a strong ion-pairing interaction between the large polarizable anionic complex and the diffusively charged tetraalkylammonium cation. Using the diethylamide of 3,5-dinitrobenzoic acid as a model compound, the influence of ion-pairing reagents and solvents on adduct formation was investigated. Dramatically increased equilibrium formation of the Meisenheimer adduct is observed in the biphasic medium (e.g., benzene/2 M NaOH) relative to the same adduct generated in single-phase systems. Spectroscopic studies on this adduct are consistent with those conducted in single-phase polar or dipolar aprotic solvents. The methodology is extended to performing highly enantioselective biphasic kinetic resolutions of several racemic electron-deficient amides.     

Sampling unfolding intermediates in calmodulin by single-molecule spectroscopy

We used single-pair fluorescence resonance energy transfer (spFRET) measurements to characterize denatured and partially denatured states of the multidomain calcium signaling protein calmodulin (CaM) in both its apo and Ca(2+)-bound forms. The results demonstrate the existence of an unfolding intermediate. A CaM mutant (CaM-T34C-T110C) was doubly labeled with fluorescent probes AlexaFlour 488 and Texas Red at opposing globular domains. Single-molecule distributions of the distance between fluorophores were obtained by spFRET at varying levels of the denaturant urea. Multiple conformational states of CaM were observed, and the amplitude of each conformation was dependent on urea concentration, with the amplitude of an extended conformation increasing upon denaturation. The distributions at intermediate urea concentrations could not be adequately described as a combination of native and denatured conformations, showing that CaM does not denature via a two-state process and demonstrating that at least one intermediate is present. The intermediate conformations formed upon addition of urea were different for Ca(2+)-CaM and apoCaM. An increase in the amplitude of a compact conformation in CaM was observed for apoCaM but not for Ca(2+)-CAM upon the addition of urea. The changes in the single-molecule distributions of CaM upon denaturation can be described by either a range of intermediate structures or by the presence of a single unfolding intermediate that grows in amplitude upon denaturation. A model for stepwise unfolding of CaM is suggested in which the domains of CaM unfold sequentially.     

Synthesis and properties of the Co7Se8−xSx and Ni7Se8−xSx solid solutions

We report the synthesis and elementary properties of the Co₇Se_8−xS_x (x=0-8) and Ni₇Se_8−xS_x (x=0-7) solid solutions. Both systems form a NiAs-type structure with metal vacancies. In general, the lattice parameters decrease with increasing x, but in the Ni₇Se_8−xS_x system c increases on going from x=5 to 7. Magnetic susceptibility measurements show that all samples exhibit temperature-independent paramagnetism from 25-250 K. Samples within the Co₇Se_8−xS_x system, as well as Ni₇Se₈ and Ni₇SeS₇, were found to be poor metals with resistivities of ∼0.20 and ∼0.06 mΩ cm at 300 K, respectively. The Sommerfeld constant (γ) was determined from specific heat measurements to be ∼13 mJ/mol_CoK² and ∼7 mJ/mol_NiK² for Co₇Se_8−xS_x and Ni₇Se_8−xS_x, respectively.     

Synthesis and Hydrogen Bonding Capabilities of Biphenyl-Based Amino Acids Designed To Nucleate beta-Sheet Structure

The syntheses of 3'-(aminoethyl)-2-biphenylpropionic acid (1) and 2-amino-3'-biphenylcarboxylic acid (2) are described. These residues were designed to nucleate beta-sheet structure in aqueous solution when incorporated into small, amphiphilic peptides in place of the backbone of the i + 1 and i + 2 residues of the beta-turn. N-Benzyl-3'-(2-(benzylamido)ethyl)-2-biphenylpropamide (3) and N-benzyl-(2-benzylamido)-3'-biphenylamide (4) were synthesized and studied as model compounds to investigate the hydrogen-bonding capabilities of residues 1 and 2, respectively. The X-ray crystal structure of 3 indicates that a 13-membered intramolecular hydrogen-bonded ring is formed, while the remaining amide proton and carbonyl are involved in intermolecular hydrogen bonding. Infrared and variable-temperature NMR experiments indicate that, in solution (CH(2)Cl(2)), 3 exists as an equilibrium mixture of the 13- and the 15-membered intramolecularly hydrogen-bonded conformers with the 15-membered ring conformer being favored. Amide 4 was shown to exist in solution (CH(2)Cl(2)) as an equilibrium mixture of the 11-membered intramolecular hydrogen-bonded ring and a nonbonded conformation. No contribution from the 9-membered hydrogen-bonded ring conformation was observed. The X-ray crystal structure of 4 indicated the absence of intramolecular hydrogen bonding in the solid state.