Markov chains, R-trivial monoids and representation theory

We develop a general theory of Markov chains realizable as random walks on R-trivial monoids. It provides explicit and simple formulas for the eigenvalues of the transition matrix, for multiplicities of the eigenvalues via Mobius inversion along a lattice, a condition for diagonalizability of the transition matrix and some techniques for bounding the mixing time. In addition, we discuss several examples, such as Toom-Tsetlin models, an exchange walk for finite Coxeter groups, as well as examples previously studied by the authors, such as nonabelian sandpile models and the promotion Markov chain on posets. Many of these examples can be viewed as random walks on quotients of free tree monoids, a new class of monoids whose combinatorics we develop.

Structural characterization of folded and extended conformations in peptides containing gamma amino acids with proteinogenic side chains: crystal structures of gamma(n), (alpha gamma)(n) and gamma gamma delta gamma sequences

The crystal structures of nine peptides containing gamma(4)Val and gamma(4)Leu are described. The short sequences Boc-gamma(4)(R)Val](2)-OMe 1, Boc-gamma(4)(R)Val](3)-NHMe 2 and Boc-gamma(4)(S)Val-gamma(4)(R)Val-OMe 3 adopt extended apolar, sheet like structures. The tetrapeptide Boc-gamma(4)(R)Val](4)-OMe 4 adopts an extended conformation, in contrast to the folded C-14 helical structure determined previously for Boc-gamma(4)(R)Leu](4)-OMe. The hybrid alpha gamma sequence Boc-Ala-gamma(4)(R)Leu](2)-OMe 5 adopts an S-shaped structure devoid of intramolecular hydrogen bonds, with both alpha residues adopting local helical conformations. In sharp contrast, the tetrapeptides Boc-Aib-gamma(4)(S)Leu](2)-OMe 6 and Boc-Leu-gamma(4)(R)Leu](2)-OMe 7 adopt folded structures stabilized by two successive C-12 hydrogen bonds. gamma(4)Val residues have also been incorporated into the strand segments of a crystalline octapeptide, Boc-Leu-gamma(4)(R)Val-Val-(D)Pro-Gly-Leu-gamma(4)(R)Val-Val-OMe 8. The gamma gamma delta gamma tetrapeptide containing gamma(4)Val and delta(5)Leu residues adopts an extended sheet like structure. The hydrogen bonding pattern at gamma residues corresponds to an apolar sheet, while a polar sheet is observed at the lone delta residue. The transition between folded and extended structures at gamma residues involves a change of the torsion angle from the gauche to the trans conformation about the C-beta-C-alpha bond.

Chiral molecular self-assembly of phospholipid tubules: A circular dichroism study

We report on spectroscopic studies of the chiral structure in phospholipid tubules formed in mixtures of alcohol and water. Synthetic phospholipids containing diacetylenic moieties in the acyl chains self-assemble into hollow, cylindrical tubules in appropriate conditions. Circular dichroism provides a direct measure of chirality of the molecular structure. We find that the CD spectra of tubules formed in mixtures of alcohol and water depends strongly on the alcohol used and the lipid concentration. The relative spectral intensity of different circular dichroism bands correlates with the number of bilayers observed using microscopy. The results provide experimental evidence that tubule formation is based on chiral packing of the lipid molecules and that interbilayer interactions are important to the tubule structure

Small-angle neutron scattering study of micellar structures of dimeric surfactants

Dimeric or gemini surfactants consist of two hydrophobic chains and two hydrophilic head groups co; valently connected by a hydrocarbon spacer. Small-angle neutron scattering measurements from bis-cationic C16H33N+(CH3)(2)-(CH2)(m)-N+(CH3)(2)C(16)H(33)2Br(-) dimeric surfactants, referred to-as 16-m-16, for different length of hydrocarbon spacers m-3-6, 8, 10, and 12, are reported. The measurements have been carried out at various concentrations: C=2.5 and 10 mM for all m and C=30 and 50 mM for m greater than or equal to 5. It is found that micellar structure depends on the length of the spacer. Micelles are disks for m=3, cylindrical for m=4, and prolate ellipsoidals for other values of m. These structural results are in agreement with the theoretical predictions based on the packing parameter. It has also been observed that conformation of the spacer and the hydrophobic chains in the interior of the micelle change as the length of the spacer is increased. The concentration dependence for m greater than or equal to 5 shows that the effect of surfactant concentration on the size of the micelle is more pronounced for m=5 and 12 than for the intermediate spacers. The fractional charge on the micelle increases with the increase in spacer length and decreases when the concentration is increased.

A New Class Of Photo-Cross-Linkable Side-Chain Liquid Crystalline Polymers Containing Bis(Benzylidene)Cyclohexanone Units

This paper reports a new class of photo-cross-linkable side chain liquid crystalline polymers (PSCLCPs) based on the bis(benzylidene)cyclohexanone unit, which functions as both a mesogen and a photoactive center. Polymers with the bis(benzylidene)cyclohexanone unit and varying spacer length have been synthesized. Copolymers of bis(benzylidene)cyclohexanone containing monomer and cholesterol benzoate containing monomer with different compositions have also been prepared. All these polymers have been structurally characterized by spectroscopic techniques. Thermal transitions were studied by DSC, and mesophases were identified by polarized light optical microscopy (POM). The intermediate compounds OH-x, the monomers SCLCM-x, and the corresponding polymers PSCLCP-x, which are essentially based on bis(benzylidene)cyclohexanone, all show a nematic mesophase. Transition temperatures were observed to decrease with increasing spacer length. The copolymers with varying compositions exhibit a cholesteric mesophase, and the transition temperatures increase with the cholesteric benzoate units in the copolymer. Photolysis of the low molecular weight liquid crystalline bis(benzylidene)-cyclohexanone compound reveals that there are two kinds of photoreactions in these systems: the EZ photoisomerization and 2 pi + 2 pi addition. The EZ photoisomerization in the LC phase disrupts the parallel stacking of the mesogens, resulting in the transition from the LC phase to the isotropic phase. The photoreaction involving the 2 pi + 2 pi addition of the bis(benzylidene)cyclohexanone units in the polymer results in the cross-linking of the chains. The liquid crystalline induced circular dichroism (LCICD) studies of the cholesterol benzoate copolymers revealed that the cholesteric supramolecular order remains even after the photo-cross-linking.

Structural and lithium ion transport studies in sol-gel-prepared lithium silicophosphate glasses

Lithium silicophosphate glasses have been prepared by a sol-gel route over a wide range of compositions. Their structural and electrical properties have been investigated. Infrared spectroscopic studies show the presence of hydroxyl groups attached to Si and P. MAS NMR investigations provide evidence for the presence of different phosphatic units in the structure. The variations of de conductivities at 423 K and activation energies have been studied as a function of composition, and both exhibit an increasing trend with the ratio of nonbridging oxygen to bridging oxygen in the structure. Ac conductivity behavior shows that the power law exponent, s, is temperature dependent and exhibits a minimum. Relaxation behavior has been examined in detail using an electrical modulus formalism, and modulus data were fitted to Kohlraush-William-Watts stretched exponential function. A structural model has been proposed and the unusual properties exhibited by this unique system of glasses have been rationalized using this model. Ion transport in these glasses appears to be confined to unidimensional conduits defined by modified phosphate chains and interspersed with unmodified silica units.

Structural correlations in GexSe1-x glasses - a neutron diffraction study

Neutron diffraction measurement is carried out on GexSe1-x glasses, where 0.1 less than or equal to x less than or equal to 0.4, in a Q interval of 0.55-13.8 Angstrom(-1). The first sharp diffraction peak (FSDP) in the structure factor, S(Q), shows a systematic increase in the intensity and shifts to a lower Q with increasing Ge concentration. The coherence length of FSDP increases with x and becomes maximum for 0.33 less than or equal to x less than or equal to 0.4. The Monte-Carlo method, due to Soper, is used to generate S(Q) and also the pair correlation function, g(r). The generated S(Q) is in agreement with the experimental data for all x. Analysis of the first four peaks in the total correlation function, T(r), shows that the short range order in GeSe2 glass is due to Ge(Se-1/2)(4) tetrahedra, in agreement with earlier reports. Se-rich glasses contain Se-chains which are cross-linked with Ge(Se-1/2)(4) tetrahedra. Ge-2(Se-1/2)(6) molecular units are the basic structural units in Ge-rich, x = 0.4, glass. For x = 0.2, 0.33 and 0.4 there is evidence for some of the tetrahedra being in an edge-shared configuration. The number of edge-shared tetrahedra in these glasses increase with increasing Ge content.

Exact ground state and kink-like excitations of a two-dimensional Heisenberg antiferromagnet

A rare example of a two-dimensional Heisenberg model with an exact dimerized ground state is presented. This model, which can be regarded as a variation on the kagome' lattice, has several features of interest: it has a highly (but not macroscopically) degenerate ground state; it is closely related to spin chains studied by earlier authors; in particular, it exhibits domain-wall-like "kink" excitations normally associated only with one-dimensional systems. In some limits it decouples into noninteracting chains; unusually, this happens in the limit of strong, rather than weak, interchain coupling. [S0163-1829(99)50338-X].

2-[2-(Hydroxymethyl)phenyl]-1-phenylethanol

The title compound, C15H16O2, has a dihedral angle of 19.10 (5)degrees between the mean planes of the two benzene rings. There is an intramolecular O-H center dot center dot center dot O hydrogen bond and the C-C-C-C torsion angle across the bridge between the two rings is 173.13 (14)degrees. The molecules form intermolecular O-H center dot center dot center dot O hydrogen-bonded chains extending along the a axis. C-H center dot center dot center dot pi contacts are also observed between molecules within the chains.

3-(1,3-Dioxolan-2-yl)-2-hydrazino-7-methylquinoline

In the title molecule, C13H15N3O2, the dihedral angle between the mean plane of the 1,3-dioxolane group and the 2-hydrazino-7-methylisoquinoline unit is 85.21 (5)degrees. The conformation of the molecule is influenced by bifurcated N-H center dot center dot center dot(O, O) and N-H center dot center dot center dot N intramolecular hydrogen bonds. In the crystal structure, molecules are linked via intermolecular N-H center dot center dot center dot O hydrogen bonds, forming extended chains along [001].

Synthesis of macrocyclic diacyl/dialkyl glycerols containing disulfide tether and studies of their effects upon incorporation in DPPC membranes. Implications in the design of phospholipase A(2) modulators

A general method for the preparation of novel disulfide-tethered macrocyclic diacylglycerols (DAGs) has been described. Overall synthesis involved stepwise protection, acylation, and deprotection to yield the bis(omega-bromoacyl) glycerols. In the crucial macrocyclization step, a unique reagent, benzyltriethylammonium tetrathiomolybdate (BTAT), has been used to convert individual bis(omega-bromoacyl) glycerols to their respective macrocyclic disulfides. DAG 6, which had ether linkages between hydrocarbon chains and the glycerol backbone, was also synthesized from an appropriate precursor using a similar protocol. One of the DAGs (DAG 5) had a carbon-carbon tether instead of a disulfide one and was synthesized using modified Glaser coupling. Preparation of alpha-disulfide-tethered DAG (DAG 4) required an alternative method, as treatment of the bisbromo precursor with BTAT gave a mixture of several compounds from which separation of the target molecule was cumbersome. To avoid this problem, the bisbromide was converted to its corresponding dithiocyanate, which on further treatment with BTAT yielded the desired DAG (DAG 4) in good yield. Upon treatment with the reducing agent dithiothreitol (DTT), the DAGs that contain a disulfide tether could be quantitatively converted to their "open-chain" thiol analogues. These macrocyclic DAGs and their reduced "open-chain" analogues have been incorporated in DPPC vesicles to study their effect on model membranes. Upon incorporation of DAG 1 in DPPC vesicles, formation of new isotropic phases was observed by P-31 NMR, These isotropic phases disappeared completely on opening the macrocyclic ring by a reducing agent. The thermotropic properties of DPPC bilayers having DAGs (1-6) incorporated at various concentrations were studied by differential scanning calorimetry. Incorporation of DAGs in general reduced the cooperativity unit (CU) of the vesicles. Similar experiments with reduced "open-chain" DAGs incorporated in a DPPC bilayer indicated a recovery of CU with respect to their macrocyclic "disulfide" counterparts. The effect of inclusion of these DAGs on the activity of phospholipase A(2) (PLA(2)) was studied in vitro. Incorporation of DAC 1 in DPPC membranes potentiated both bee venom and cobra venom PLA(2) activities.

Thermal Degradation Processes in Poly(xylylene sulfides) Investigated by Comparative Direct Pyrolysis MS and Flash Pyrolysis GC/MS Experiments

The thermal degradation processes of two sulfur polymers, poly(xylylene sulfide) (PXM) and poly(xylylene disulfide) (PXD), were investigated in parallel by direct pyrolysis mass spectrometry (DPMS) and flash pyrolysis GC/MS (Py-GC/MS). Thermogravimetric data showed that these polymers decompose with two separate steps in the temperature ranges of 250-280 and 600-650 degrees C, leaving a high amount of residue (about 50% at 800 degrees C). The pyrolysis products detected by DPMS in the first degradation step of PXM and PXD were terminated by three types of end groups, -CH3, -CH2SH, and -CH=S, originating from thermal cleavage reactions involving a series of homolytic chain scissions followed by hydrogen transfer reactions, generating several oligomers containing some intact xylylene sulfide repeating units. The presence of pyrolysis compounds containing some stilbene-like units in the first degradation step has also been observed. Their formation has been accounted for with a parallel cleavage involving the elimination of H2S from the PXM main chains. These unsaturated units can undergo cross-linking at higher temperatures, producing the high amount of char residue observed. The thermal degradation compounds detected by DPMS in the second decomposition step at about 600-650 degrees C were constituted of condensed aromatic molecules containing dihydrofenanthrene and fenanthrene units. These compounds might be generated from the polymer chains containing stilbene units, by isomerization and dehydrogenation reactions. The pyrolysis products obtained in the Py-GC/MS of PXM and PXD at 610 degrees C are almost identical. The relative abundance in the pyrolysate and the spectral properties of the main pyrolysis products were found to be in generally good agreement with those obtained by DPMS. Polycyclic aromatic hydrocarbons (PAHs) were also detected by Py-GC/MS but in minor amounts with respect to DPMS. This apparent discrepancy was due to the simultaneous detection of PAHs together with all pyrolysis products in the Py-GC/MS, whereas in DPMS they were detected in the second thermal degradation step without the greatest part of pyrolysis compounds generated in the first degradation step. The results obtained by DPMS and PSI-GC/MS experiments showed complementary data for the degradation of PXM and PXD and, therefore, allowed the unequivocal formulation of the thermal degradation mechanism for these sulfur-containing polymers.

Structural and Sequence Characteristics of Long alpha Helices in Globular Proteins

Elucidation of the detailed structural features and sequence requirements for iv helices of various lengths could be very important in understanding secondary structure formation in proteins and, hence. in the protein folding mechanism. An algorithm to characterize the geometry of an alpha helix from its C-alpha coordinates has been developed and used to analyze the structures of long cu helices (number of residues greater than or equal to 25) found in globular proteins, the crystal structure coordinates of which are available from the Brookhaven Protein Data Bank, Ail long a helices can be unambiguously characterized as belonging to one of three classes: linear, curved, or kinked, with a majority being curved. Analysis of the sequences of these helices reveals that the long alpha helices have unique sequence characteristics that distinguish them from the short alpha helices in globular proteins, The distribution and statistical propensities of individual amino acids to occur in long alpha heices are different from those found in short alpha helices, with amino acids having longer side chains and/or having a greater number of functional groups occurring more frequently in these helices, The sequences of the long alpha helices can be correlated with their gross structural features, i.e., whether they are curved, linear, or kinked, and in case of the curved helices, with their curvature.

In search of inorganic nonlinear optical materials for second harmonic generation

In a search for inorganic oxide materials showing second-order nonlinear optical (NLO) susceptibility, we investigated several berates, silicates, and a phosphate containing trans-connected MO6, octahedral chains or MO5 square pyramids, where, M = d(0): Ti(IV), Nb(V), or Ta(V), Our investigations identified two new NLO structures: batisite, Na2Ba(TiO)(2)Si4O12, containing trans-connected TiO5 octahedral chains, and fresnoite, Ba2TiOSi2O7, containing square-pyramidal TiO5. Investigation of two other materials containing square-pyramidal TiO5 viz,, Cs2TiOP2O7 and Na4Ti2Si8O22. 4H(2)O, revealed that isolated TiO5, square pyramids alone do not cause a second harmonic generation (SHG) response; rather, the orientation of TiO5 units to produce -Ti-O-Ti-O- chains with alternating long and short Ti-O distances in the fresnoite structure is most likely the origin of a strong SHG response in fresnoite,

Synthesis of novel disulfide containing macrocyclic diacylglycerols

New diacylglycerols (2-4) containing intramolecular disulfide linkages between pendant acyl chains were synthesized. Due to the differences in the location of disulfide units, the present method allows synthesis of macrocycles that vary in sizes. Copyright.