The alpha method for solving differential algebraic inequality (DAI) systems

This paper describes an algorithm for ``direct numerical integration'' of the initial value Differential-Algebraic Inequalities (DAI) in a time stepping fashion using a sequential quadratic programming (SQP) method solver for detecting and satisfying active path constraints at each time step. The activation of a path constraint generally increases the condition number of the active discretized differential algebraic equation's (DAE) Jacobian and this difficulty is addressed by a regularization property of the alpha method. The algorithm is locally stable when index 1 and index 2 active path constraints and bounds are active. Subject to available regularization it is seen to be stable for active index 3 active path constraints in the numerical examples. For the high index active path constraints, the algorithm uses a user-selectable parameter to perturb the smaller singular values of the Jacobian with a view to reducing the condition number so that the simulation can proceed. The algorithm can be used as a relatively cheaper estimation tool for trajectory and control planning and in the context of model predictive control solutions. It can also be used to generate initial guess values of optimization variables used as input to inequality path constrained dynamic optimization problems. The method is illustrated with examples from space vehicle trajectory and robot path planning.

Immobilization of Aspergillus oryzae alpha-galactosidase in gelatin and its application in removal of flatulence-inducing sugars in soymilk

Raffinose oligosaccharides (RO) are the major factors responsible for flatulence following ingestion of soybean-derived products. Removal of RO from seeds or soymilk would then have a positive impact on the acceptance of soy-based foods. In this study, alpha-galactosidase from Aspergillus oryzae was entrapped in gelatin using formaldehyde as the hardener. The immobilization yield was 64.3% under the optimum conditions of immobilization. The immobilized alpha-galactosidase showed a shift in optimum pH from 4.8 to 5.4 in acetate buffer. The optimum temperature also shifted from 50 degrees C to 57 degrees C compared with soluble enzyme. Immobilized alpha-galactosidase was used in batch, repeated batch and continuous mode to degrade RO present in soymilk. In the repeated batch, 45% reduction of RO was obtained in the fourth cycle. The performance of immobilized alpha-galactosidase was tested in a fluidized bed reactor at different flow rates and 86% reduction of RO in soymilk was obtained at 25 ml h(-1) flow rate. The study revealed that immobilized alpha-galactosidase in continuous mode is efficient in reduction of RO present in soymilk.

Parallel and antiparallel aggregation of alpha-helices. Crystal structures of two apolar decapeptides X-Trp-Ile-Ala-Aib-Ile-Val-Aib-Leu-Aib-Pro-OMe (X = Boc, Ac)

An apolar helical decapeptide with different end groups, Boc- or Ac-, crystallizes in a completely parallel fashion for the Boc-analog and in an antiparallel fashion for the Ac-analog. In both crystals, the packing motif consists of rows of parallel molecules. In the Boc-crystals, adjacent rows assemble with the helix axes pointed in the same direction. In the Ac-crystals, adjacent rows assemble with the helix axes pointed in opposite directions. The conformations of the molecules in both crystals are quite similar, predominantly alpha-helical, except for the tryptophanyl side chain where chi 1 congruent to 60 degrees in the Boc- analog and congruent to 180 degrees in the Ac-analog. As a result, there is one lateral hydrogen bond between helices, N(1 epsilon)...O(7), in the Ac-analog. The structures do not provide a ready rationalization of packing preference in terms of side-chain interactions and do not support a major role for helix dipole interactions in determining helix orientation in crystals. The crystal parameters are as follow. Boc-analog: C60H97N11O13.C3H7OH, space group Pl with a = 10.250(3) A, b = 12.451(4) A, c = 15.077(6) A, alpha = 96.55(3) degrees, beta = 92.31(3) degrees, gamma = 106.37(3) degrees, Z = 1, R = 5.5% for 5581 data ([F] greater than 3.0 sigma(F)), resolution 0.89 A. Ac-analog: C57H91N11O12, space group P2(1) with a = 9.965(1) A, b = 19.707(3) A, c = 16.648(3) A, beta = 94.08(1), Z = 2, R = 7.2% for 2530 data ([F] greater than 3.0 sigma(F)), resolution 1.00 A.

Conformation of di-n-propylglycine residues (Dpg) in peptides: crystal structures of a type I 'beta-turn forming tetrapeptide and an alpha-helical tetradecapeptide

The crystal structures of two oligopeptides containing di-n-propylglycine (Dpg) residues, Boc-Gly-Dpg-Gly-Leu-OMe (1) and Boc-Val-Ala-Leu-Dpg-Val-Ala-Leu-Val-Ala-Leu-Dpg-Val-Ala-Leu-OMe (2) are presented. Peptide 1 adopts a type I' beta-turn conformation with Dpg(2)-Gly(3) at the corner positions. The 14-residue peptide 2 crystallizes with two molecules in the asymmetric unit, both of which adopt alpha-helical conformations stabilized by 11 successive 5 -> 1 hydrogen bonds. In addition, a single 4 -> 1 hydrogen bond is also observed at the N-terminus. All live Dpg residues adopt backbone torsion angles (phi, psi) in the helical region of conformational space. Evaluation of the available structural data on Dpg peptides confirm the correlation between backbone bond angle N-C-alpha-C' (tau) and the observed backbone phi,psi values. For tau > 106 degrees, helices are observed, while fully extended structures are characterized by tau < 106 degrees. The mean r values for extended and folded conformations for the Dpg residue are 103.6 degrees +/- 1.7 degrees and 109.9 degrees +/- 2.6 degrees, respectively. Copyright (C) 2007 European Peptide Society and John Wiley & Sons, Ltd.

Multiple conformational states in crystals and in solution in alpha gamma hybrid peptides. Fragility of the C-12 helix in short sequences

The conformational properties of foldamers generated from alpha gamma hybrid peptide sequences have been probed in the model sequence Boc-Aib-Gpn-Aib-Gpn-NHMe. The choice of alpha-aminoisobutyryl (Aib) and gabapentin (Gpn) residues greatly restricts sterically accessible coil formational space. This model sequence was anticipated to be a short segment of the alpha gamma C-12 helix, stabilized by three successive 4 -> 1 hydrogen bonds, corresponding to a backbone-expanded analogue of the alpha polypeptide 3(10)-helix. Unexpectedly, three distinct crystalline polymorphs were characterized in the solid state by X-ray diffraction. In one form, two successive C-12 hydrogen bonds were obtained at the N-terminus, while a novel C-17 hydrogen-bonded gamma alpha gamma turn was observed at the C-terminus. In the other two polymorphs, isolated C-9 and C-7 hydrogen-bonded turns were observed at Gpn (2) and Gpn (4). Isolated C-12 and C-9 turns were also crystallographically established in the peptides Boc-Aib-Gpn-Aib-OMe and Boc-Gpn-Aib-NHMe, respectively. Selective line broadening of NH resonances and the observation of medium range NH(i)<-> NH(i+2) NOEs established the presence of conformational heterogeneity for the tetrapeptide in CDCl3 solution. The NMR results are consistent with the limited population of the continuous C-12 helix conformation. Lengthening of the (alpha gamma)(n) sequences in the nonapeptides Boc-Aib-Gpn-Aib-Gpn-Aib-Gpn-Aib-Gpn-Xxx (Xxx = Aib, Leu) resulted in the observation of all of the sequential NOEs characteristic of an alpha gamma C-12 helix. These results establish that conformational fragility is manifested in short hybrid alpha gamma sequences despite the choice of conformationally constrained residues, while stable helices are formed on chain extension.

Dislocation dynamics in alpha titanium Dynamique des dislocations dans le titane alphaVersetzungsdynamik in alpha-Titan

The activation area and activation enthalpy are determined as a function of stress and temperature for alpha titanium. The results indicated that plastic flow below about 700°K occurs by a single thermally activated mechanism. Activation area determined by differential-stress creep tests falls in the range 80−8b2 and does not systematically depend on the impurity content. The total activation enthalpy derived from the temperature and strain-rate dependence of flow stress is 1.15 eV. The experimental data support a lattice hardening mechanism as controlling the low-temperature deformation in alpha titanium.

Conformations of peptides containing Z-alpha,beta-dehydroleucine (delta ZLeu). A comparison of Boc-Pro-delta ZLeu-Gly-NHEt and Boc-Pro-delta ZPhe-Gly-NHEt.

Two tripeptides of the type Boc-Pro-ΔZX-Gly-NHEt (where X = Leu, Phe) have been synthesized and their solution conformations investigated by 270 MHz 1H n.m.r. and i.r. spectroscopy. These conformational studies indicated that ΔZLeu, similar to ΔZPhe, has a strong tendency to stabilize folded Type II β-turn conformations when present at i + 2 position.

Stabilization of unusual structures in peptides using alpha,beta-dehydrophenylalanine: Crystal and solution structures of Boc-Pro-Delta Phe-Val-Delta Phe-Ala-OMe and Boc-Pro-Delta Phe-Gly-Delta Phe-Ala-OMe

The structures of two dehydropentapeptides, Boc-Pro-Delta Phe-Val-Delta Phe-Ala-OMe (I) and Boc-Pro-Delta Phe-Gly-Delta Phe-Ala-OMe (II) (Boc: t-butoxycarbonyl), have been determined by nuclear magnentic resonance (NMR), circular dichroism (CD), and X-ray, crystallographic studies. The peptide I assumes a S-shaped flat beta-bend structure, characterized by two partially overlapping type II beta-bends and absence of a second 1 <- 4 (N4-H center dot center dot center dot O1') intramolecular hydrogen bond. This is in contrast to the generally observed 3(10)-helical conformation in peptides with Delta Phe at alternate positions. This report describes the novel conformation assumed by peptide I and compares it with that of the conserved tip of the V3 loop of the HIV-1 envelope glycoprotein gp120 (sequence, G:P319 to F:P324, PDB code IACY). The tip of the V3 loop also assumes a S-shaped conformation with Arg:P322, making an intramolecular side-chain-backbone interaction with the carbonyl oxygen of Gly:P319. Interestingly, in peptide I, C(gamma)HVal(3) makes a similar side-chain-backbone C-H center dot center dot center dot O hydrogen bond with the carbonyl oxygen of the Boc group. The observed overall similarity indicates the possible use of the peptide as a viral antagonist or synthetic antigen. Peptide 11 adopts a unique turn followed by a 3(10)-helix. Both peptides I and II are classical examples of stabilization of unusual structures in oligopeptides.

Photochemical, photophysical, and theoretical studies on cyclobutanethiones..alpha.-Cleavage reactions

Photophysics and photochemistry of cyclobutanethiones 1-5 have been studied with the view to generalize the a-cleavage reactions of cyclobutanethiones. The above cyclobutanethiones possess a unit intersystem crossing efficiency from S1 to T1, a high self-quenching rate (-4 X lo9 M-' s-'), and a short triplet lifetime (<0.50 ws). Photolysis of 1-5 yields in benzene a product resulting from 1,3-transposition and in methanol two cyclic thioacetals.The origin of these products is traced to the triplet excited state. A mechanistic scheme involving a-cleavage as the primary photoprocess and diradicals and thiacarbenes as intermediates has been formulated to rationalize the formation of thioacetals and rearranged products. The proposed mechanistic scheme is supported by UHF MIND013 calculations performed on four model systems, cyclobutanethiones and 1,3-cyclobutanedithiones 18-21. These calculations indicate that formation of diradical is favored thermodynamically and kinetically for systems analogous to 19 and 21, while rearrangement to thiacarbene is likely only for those similar to 21.

Photochemistry of .alpha.,.beta.-unsaturated thiones: addition to electron-rich olefins from T1

1,1,3-Trimethyl-2-thioxo-1,2-dihydronaphthale(1n)e adds to electron-rich olefins upon excitation to either Sz (PP*) or Sl (ns*) states. Excitation to S2 level resulted in the same mixture of products, namely thietane and 1,4-dithiane, as on excitation to S1 level. Addition occurs to the thiocarbonyl function and not to the carbon-carbon double bond. The addition is site-specific, and the formation of thietane is regiospecific. The ratio of thietane to 1,4-dithiane in the product mixture is dependent on the concentration of the thioenone. The addition is suggested to originate from the lowest triplet state (Tl) and involves diradical intermediates.

Theoretical studies on alpha-helix--DNA interactions

The interaction energies between (Ala)10 and alpha-helix fragment and different nucleotide sequences in right-handed B-form have been optimized using semi-empirical potential energy functions. The energies are calculated for two different orientations of the alpha-helix, viz., when the alpha-helix axis taken in the N----C direction is (i) parallel and (ii) antiparallel to the 5'-3' ascending strand of DNA, proximal to it. When both the DNA molecule as well as the alpha-helix are treated as rigid molecules it is found that a polyalanine alpha-helix has slightly more favourable contacts when it is in the proximity of a four nucleotide sequence of 5'-(N-A-T-N)-3' type, where N is either a purine or a pyrimidine. However, when the two interacting molecules are allowed to undergo local structural variations then the interaction energy appears to be independent of the base sequence confirming the non-specific nature of these interactions.

Conformation of a 16-residue zervamicin IIA analog peptide containing three different structural features: 310-helix, alpha helix and ß-bend ribbon

Boc-Trp-Ile-Ala-Aib-Ile-Val-Aib-Leu-Aib- Pro-Ala-Aib-Pro-Aib-Pro-Phe-OM(we here Boc is t-butoxycarbonyla nd Aib is a-aminoisobutyriac cid), a synthetica polar analog of the membrane-activefu ngal peptide antibioticz ervamtycinII A, crystallizesi n spaceg roupP 1 withZ =1 and cell parameters a = 9.086 ?0.002 A, b = 10.410 ?+ 0.002 A, c = 28.188 ? 0.004 A, a = 86.13 ? 0.01?, 13 = 87.90 ? 0.01?, and y = 89.27 ? 0.01?;o veralla greementf actorR = 7.3% for 7180 data (Fo > 3cr) and 0.91-A resolution. The peptide backbone makes a continuous spiral that begins as a 310-helix at the N-terminus, changes to an a-helix for two turns, and ends in a spiral of three fl-bends in a ribbon. Each of the fl-bends contains a proline residue at one of the corners. The torsion angles 4i range from -51? to -91? (average value -64o), and the torsion angles ai range from -1? to -46? (average value -31?). There are 10 intramolecularN H...OCh ydrogenb onds in the helix and two directh ead-to-taihl ydrogenb ondsb etween successive molecules. Two H20 and two CH30H solvent molecules fill additional space with appropriate hydrogen bonding in the head-to-tail region, and two additional H20 molecules form hydrogen bonds with carbonyl oxygens near the curve in the helix at Pro-10. Since there is only one peptide molecule per cell in space group P1, the molecules repeat only by translation, and consequently the helices pack parallel to each other.

Conformational properties of hybrid peptides containing alpha and omega-amino acids

This review briefly surveys the conformational properties of guest omega-amino acid residues when incorporated into host alpha-peptide sequences. The results presented focus primarily on the use of beta- and gamma-residues in alphaomega sequences. The insertion of additional methylene groups into peptide backbones enhances the range of accessible conformations, introducing additional torsional variables. A nomenclature system, which permits ready comparisons between alpha-peptides and hybrid sequences, is defined. Crystal structure determination of hybrid peptides, which adopt helical and beta-hairpin conformations permits the characterization of backbone conformational parameters for beta- and gamma-residues inserted into regular alpha-polypeptide structures. Substituted beta- and gamma-residues are more limited in the range of accessible conformation than their unsubstituted counterparts. The achiral beta,beta-disubstituted gamma-amino acid, gabapentin, is an example of a stereochemically constrained residue in which the torsion angles about the C-beta-C-gamma (theta(1)) and C-alpha-C-beta (theta(2)) bonds are restricted to the gauche conformation. Hybrid sequences permit the design of novel hydrogen bonded rings in peptide structures.

Processing map for hot working of alpha-zirconium

The hot deformation characteristics of alpha-zirconium in the temperature range of 650 °C to 850 °C and in the strain-rate range of 10-3 to 102 s-1 are studied with the help of a power dissipation map developed on the basis of the Dynamic Materials Model.[7,8,9] The processing map describes the variation of the efficiency of power dissipation (η =2m/m + 1) calculated on the basis of the strain-rate sensitivity parameter (m), which partitions power dissipation between thermal and microstructural means. The processing map reveals a domain of dynamic recrystallization in the range of 730 °C to 850 °C and 10−2 to 1−1 with its peak efficiency of 40 pct at 800 °C and 0.1 s-1 which may be considered as optimum hot-working parameters. The characteristics of dynamic recrystallization are similar to those of static recrystallization regarding the sigmoidal variation of grain size (or hardness) with temperature, although the dynamic recrystallization temperature is much higher. When deformed at 650 °C and 10-3 s-1 texture-induced dynamic recovery occurred, while at strain rates higher than 1 s-1, alpha-zirconium exhibits microstructural instabilities in the form of localized shear bands which are to be avoided in processing.

Stereochemical studies on cyclic peptides. Part XI. Conformation of cyclic pentapeptides having intramolecular 3 leads to 1 hydrogen bonds.

Conformational analysis of cyclic pentapeptides having two intra-ring 3 leads to 1 hydrogen bonds has been carried out. It is found that the structure can easily be formed with trans planar peptide units without causing significant angular strain at the alpha-carbon atoms. Four different types of conformations designated Types I--IV are possible for the backbone structure. Details of these four types of conformations and also the accommodating possibility of these types for allglycyl and all-alanyl residues are presented. Three of the four types have relatively low energies for glycyl residues whereas the other one has a slightly higher energy. When alanyl residues are introduced at the five alpha-carbon atoms, the types that are energetically favourable depend upon the sequence of isomers. Energy calculations have also been carried out for the combinations of glycyl, L- and D-alanyl residues. The theoretical results are compared with available experimental observations both from solution and solid state studies.