Expanding the Peptide beta-Turn in alpha gamma Hybrid Sequences: 12 Atom Hydrogen Bonded Helical and Hairpin Turns

Hybrid peptide segments containing contiguous alpha and gamma amino acid residues can form C-12 hydrogen bonded turns which may be considered as backbone expanded analogues of C-10 beta-turns) found in alpha alpha segments. Exploration of the regular hydrogen bonded conformations accessible for hybrid alpha gamma sequences is facilitated by the use of a stereochemically constrained gamma amino acid residue gabapentin (1-aminomethylcyclohexaneacetic acid, Gpn), in which the two torsion angles about C-gamma-C-beta (theta(1)) and C-beta-C-alpha (theta(2)) are predominantly restricted to gauche conformations. The crystal structures of the octapeptides Boc-Gpn-Aib-Gpn-Aib-Gpn-Aib-Gpn-Aib-OMe (1) and Boc-Leu-Phe-Val-Aib-Gpn-Leu-Phe-Val-OMe (2) reveal two distinct conformations for the Aib-Gpn segment. Peptide 1 forms a continuous helix over the Aib(2)-Aib(6) segment, while the peptide 2 forms beta-hairpin structure stabilized by four cross-strand hydrogen bonds with the Aib-Gpn segment forming a nonhelical C-12 turn. The robustness of the helix in peptide 1 in solution is demonstrated by NMR methods. Peptide 2 is conformationally fragile in solution with evidence of beta-hairpin conformations being obtained in methanol. Theoretical calculations permit delineation of the various C-12 hydrogen bonded structures which are energetically feasible in alpha gamma and gamma alpha sequences.

Conformation of di-n-propylglycine residues (Dpg) in peptides: crystal structures of a type I-turn forming tetrapeptide and an -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-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 -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 five Dpg residues adopt backbone torsion angles (, ) in the helical region of conformational space. Evaluation of the available structural data on Dpg peptides confirm the correlation between backbone bond angle NCC() and the observed backbone , values. For > 106° , helices are observed, while fully extended structures are characterized by < 106° . The mean values for extended and folded conformations for the Dpg residue are 103.6° ± 1.7° and 109.9° ± 2.6° , respectively.

Hybrid peptide design. Hydrogen bonded conformations in peptides containing the stereochemically constrained gamma-amino acid residue, gabapentin

he crystal structure of 12 peptides containing the conformationally constrained 1-(aminomethyl)cyclohexaneacetic acid, gabapentin (Gpn), are reported. In all the 39 Gpn residues conformationally characterized so far, the torsion angles about the C-alpha-C-beta and C-beta-C-gamma bonds are restricted to the gauche conformation (+/- 60 degrees). The Gpn residue is constrained to adopt folded conformations resulting in the formation of intramolecularly hydrogen-bonded structures even in short peptides. The peptides Boc-Ac(6)c-Gpn-OMe 1 and Boc-Gpn-Aib-Gpn-Aib-OMe 2 provide examples of C-7 conformation; peptides Boc-Gpn-Aib-OH 3, Boc-Ac(6)c-Gpn-OH 4, Boc-Val-Pro-Gpn-OH 5, Piv-Pro-Gpn-Val-OMe 6, and Boc-Gpn-Gpn-Leu-OMe 7 provide examples of C-9 conformation; peptide Boc-Ala-Aib-Gpn-Aib-Ala-OMe 8 provides an example of C-12 conformation and peptides Boc-beta Leu-Gpn-Val-OMe 9 and Boc-beta Phe-Gpn-Phe-OMe 10 provide examples of C-13 conformation. Gpn peptides provide examples of backbone expanded mimetics for canonical alpha-peptide turns like the gamma (C-7) and the beta (C-10) turns. The hybrid beta gamma sequences provide an example of a mimetic of the C-13 alpha-turn formed by three contiguous alpha-amino acid residues. Two examples of folded tripeptide structures, Boc-Gpn-beta Phe-Leu-OMe 11 and Boc-Aib-Gpn-beta Phg-NHMe 12, lacking internal hydrogen bonds are also presented. An analysis of available Gpn residue conformations provides the basis for future design of folded hybrid peptides.

Optimal configurations of active fiber composites based on asymptotic torsional analysis - art. no. 641413

Active Fiber Composites (AFC) possess desirable characteristics over a wide range of smart structure applications, such as vibration, shape and flow control as well as structural health monitoring. This type of material, capable of collocated actuation and sensing, call be used in smart structures with self-sensing circuits. This paper proposes four novel applications of AFC structures undergoing torsion: sensors and actuators shaped as strips and tubes; and concludes with a preliminary failure analysis. To enable this, a powerful mathematical technique, the Variational Asymptotic Method (VAM) was used to perform cross-sectional analyses of thin generally anisotropic AFC beams. The resulting closed form expressions have been utilized in the applications presented herein.

Boundary value problems for third-order nonlinear ordinary differential equations

In this paper, we describe how to analyze boundary value problems for third-order nonlinear ordinary differential equations over an infinite interval. Several physical problems of interest are governed by such systems. The seminumerical schemes described here offer some advantages over solutions obtained by using traditional methods such as finite differences, shooting method, etc. These techniques also reveal the analytic structure of the solution function. For illustrative purposes, several physical problems, mainly drawn from fluid mechanics, are considered; they clearly demonstrate the efficiency of the techniques presented here.

Existence and approximations of solutions to some fractional order functional integral equations

In this paper we shall study a fractional order functional integral equation. In the first part of the paper, we proved the existence and uniqueness of mile and global solutions in a Banach space. In the second part of the paper, we used the analytic semigroups theory oflinear operators and the fixed point method to establish the existence, uniqueness and convergence of approximate solutions of the given problem in a separable Hilbert space. We also proved the existence and convergence of Faedo-Galerkin approximate solution to the given problem. Finally, we give an example.

Stereochemical analysis of the antigenic tip of the V3 loop peptide of HIV-1 gp120

A novel multiple turn conformation has been observed for a segment GPGRAFY in the crystal structure of a complex of HIV-1 gp120 V3 loop peptide with the Fab fragment of a neutralizing antibody [Ghiara ct al. (1994) Science 264, 82-85]. A structural motif has been defined for the peptide segment, employing idealized backbone conformations characterized by ranges of virtual C-alpha torsion angles and bond angles. A search of 122 high-resolution protein crystal structures has permitted identification of 24 examples of similar structural motifs. Two major conformational families have been identified, which differ primarily in the conformation at residue 3. The observed conformation at residue 3 in family 1 is left-handed helical (alpha(L)) and that in family 2 is right-handed helical (alpha(R)). Of the 10 examples in family 1, 9 examples have Gly residues at position 3. Of the 12 examples in family 2, 7 examples have Asn/Asp at position 3. Computer modeling of the V3 loop tip sequence using the two backbone conformational families as starting points leads to minimum-energy conformations in which antigenically important side-chains occupy similar spatial arrangements. This stereochemical analysis of the V3 loop tip sequence suggests a rational basis for the design of synthetic analog peptides for use as viral antagonists or synthetic antigens. (C) Munksgaard 1995.

Polypeptide Helices in Hybrid Peptide Sequences

A new class of polypeptide helices in hybrid sequences containing alpha-, beta-, and gamma-residues is described. The molecular conformations in crystals determined for the synthetic peptides Boc-Leu-Phe-Val-Aib-beta Phe-Leu-Phe-Val-OMe 1 (beta Phe: (S)-beta(3)-homophenylalanine) and Boc-Aib-Gpn-AibGpn-OM2(Gpn:1-(aminomethyl)cycl hexaneacetic acid) reveal expanded helical turns in the hybrid sequences (alpha alpha beta)(n) and (ay), In 1, a repetitive helical structure composed Of C-14 hydrogen-bonded units is observed, whereas 2 provides an example of a repetitive C-12 hydrogen-bonded structure. Using experimentally determined backbone torsion angles for the hydrogen-bonded units formed by hybrid sequences, we have generated energetically favorable hybrid helices. Conformational parameters are provided for C-11, C-12, C-13, C-14, and C-15 helices in hybrid sequences.

Non-Protein Amino Acids in the Design of Secondary Structure Scaffolds

The use of stereochemically constrained amino acids permits the design of short peptides as models for protein secondary structures. Amino acid residues that are restrained to a limited range of backbone torsion angles (ϕ-ψ) may be used as folding nuclei in the design of helices and β-hairpins. α-Amino-isobutyric acid (Aib) and related Cαα dialkylated residues are strong promoters of helix formation, as exemplified by a large body of experimentally determined structures of helical peptides. DPro-Xxx sequences strongly favor type II’ turn conformations, which serve to nucleate registered β-hairpin formation. Appropriately positioned DPro-Xxx segments may be used to nucleate the formation of multistranded antiparallel β-sheet structures. Mixed (α/β) secondary structures can be generated by linking rigid modules of helices and β-hairpins. The approach of using stereochemically constrained residues promotes folding by limiting the local structural space at specific residues. Several aspects of secondary structure design are outlined in this chapter, along with commonly used methods of spectroscopic characterization.

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.

On the effect of matrix cracks in composite helicopter rotor blade

This paper investigates the feasibility of an on-line damage detection capability for helicopter main rotor blades made of composite material. Damage modeled in the composite is matrix cracking. A box-beam with stiffness properties similar to a hingeless rotor blade is designed using genetic algorithm for the typical [+/-theta(m)/90(n)](s) family of composites. The effect of matrix cracks is included in an analytical model of composite box-beam. An aeroelastic analysis of the helicopter rotor based on finite elements in space and time is used to study the effects of matrix cracking in the rotor blade in forward flight. For global fault detection, rotating frequencies, tip bending and torsion response, and blade root loads are studied. It is observed that the effect of matrix cracking on lag bending and elastic twist deflection at the blade tip and blade root yawing moment is significant and these parameters can be monitored for online health monitoring. For implementation of local fault detection technique, the effect on axial and shear strain, for matrix cracks in the whole blade as well as matrix cracks occurring locally is studied. It is observed that using strain measurement along the blade it is possible to locate the matrix cracks as well as to predict density of matrix cracks. (C) 2004 Elsevier Ltd. All rights reserved.

Family of Mixed-Valence Oxovanadium(IV/V) Dinuclear Entities Incorporating N4O3-Coordinating Heptadentate Ligands: Synthesis, Structure, and EPR Spectra

Dinuclear ((VVV)-V-IV) oxophenoxovanadates of general formula [V2O3L] have been synthesized in excellent yields by reacting bis(acetylacetonato)oxovanadium(IV) with H3L in a 2:1 ratio in acetone under an N-2 atmosphere. Here L3- is the deprotonated form of 2,6-bis[{{(2-hydroxybenzyl)(N',N'-(dimethylamino)ethyl)}amino}methyl]-4-methylphenol (H3L1), 2,6-bis[{{(5-methyl-2-hydroxybenzyl)(N',N'-(dimethylamino)ethyl)}amino}methyl]-4-methylphenol (H3L2) 2,6-bis[ {{(5-tert-butyl-2-hydroxybenzyl)(N',N'-(dimethylamino)ethyl)}amino}methyl]-4-methylphenoI (H3L3), 2,6-bis[{{(5-chloro-2-hydroxybenzyl)(N',N'-(dimethylamino)ethyl)}amino}methyl]-4-methylphenol (H3L4) , 2,6-bis[{{(5-bromo-2-hydroxybenzyl)(N',N'-(dimethylamino)ethyl)}amino}methyl]-4-methylphenol (H3L5), or 2,6-bis[{{(5-methoxy-2-hydroxybenzyl)(N',N'-(dimethylamino)ethyl)}amino}methyl]-4-methylphenol (H3L6). In [V2O3L1], both the metal atoms have distorted octahedral geometry. The relative disposition of two terminal V=O groups in the complex is essentially cis. The O=V...V=O torsion angle is 24.6(2)degrees. The V-O-oxo-V and V-O-phenoxo-V angles are 117.5(4) and 93.4(3)degrees, respectively. The V...V bond distance is 3.173(5) Angstrom. X-ray crystallography, IR, UV-vis, and H-1 and V-51 NMR measurements show that the mixed-valence complexes contain two indistinguishable vanadium atoms (type 111). The thermal ellipsoids of O2, O4, C10, C14, and C15 also suggests a type III complex in the solid state. EPR spectra of solid complexes at 77 K display a single line indicating the localization of the odd electron (3d(xy)(1)). Valence localization at 77 K is also consistent with the V-51 hyperfine structure of the axial EPR spectra (3d(xy)(1) ground state) of the complexes in frozen (77 K) dichloromethane solution: S = 1/2, g(parallel to) similar to 1.94, g(perpendicular to) similar to 1.98, A(parallel to) similar to 166 x 10(-4) cm(-1), and A(perpendicular to) similar to 68 x 10(-4) cm(-1). In contrast isotropic room-temperature solution spectra of the family have 15 hyperfine lines (g(iso) similar to 1.974 and A(iso) similar to 50 x 10(-4) cm(-1)) revealing that the unpaired electron is delocalized between the metal centers. Crystal data for the [V2O3L1].CH2Cl2 complex are as follows: chemical formula, C32H43O6N4C12V2; crystal system, monoclinic; space group, C2/c; a = 18.461(4), b = 17.230(3), c = 13.700(3) Angstrom; beta = 117.88(3)degrees; Z = 8.

Boundary value problems for third-order nonlinear ordinary differential equations

In this paper, we describe how to analyze boundary value problems for third-order nonlinear ordinary differential equations over an infinite interval. Several physical problems of interest are governed by such systems. The seminumerical schemes described here offer some advantages over solutions obtained by using traditional methods such as finite differences, shooting method, etc. These techniques also reveal the analytic structure of the solution function. For illustrative purposes, several physical problems, mainly drawn from fluid mechanics, are considered; they clearly demonstrate the efficiency of the techniques presented here.

Studies on the conformation of amino acids XII. Energy calculations on prolyl residue

The favoured conformations of the prolyl residue have been obtained by calculating their potential energies arising from bond-angle strain, torsion-angle strain, non-bonded and electrostatic interatomic energies. In addition to the five membered ring, the peptide unit at the amino end (with ω = 180°) and the C′ atom at the carboxyl end have been taken into account. It is found that there are two local minima in the configurational space of the parameters defining the conformation, as is actually observed-one (denoted by B) with Cγ displaced on the same side as C′, which is lower in energy than the other (denoted by A) with Cγ displaced on the opposite side of C′. The other four atoms Cδ, N, Cα, Cβ are nearly in a plane. The conformations of minimum energy (for both A and B) have bond angles very close to the mean observed values while the torsion angles are well within the range observed in various structures for each type. Taking into account the fact that the influence of neighbouring molecules in a crystal structure may make the conformation of a molecule different from the minimal one, the ranges of the conformational parameters for which the energy is within 0.6 kcal/mole above the minimum value (called the "most probable range") and within 1.2 kcal/mole (called the "probable range") have been determined. The ranges thus obtained, agree well with observation, and most of the observed data lie within the most probable ranges, although differing appreciably from the conformation of minimum energy. The study has been extended, in a limited way, to the conformation of the ring in the amino acid proline. Since the nitrogen is tetrahedral in this (as contrasted with being planar in the prolyl residue), it is found that any one of the five atoms can be out of plane (either way), with the other four lying nearly in a plane. These correspond to low energy conformations (up to 1.2 kcal/mole above the minimum). One such example, in which the Cα atom is out of plane is known for dl-proline · HCl. It is also shown that in these calculations energies due to bond length distortions can be neglected to a good degree of approximation, provided the 'best' values of the bond lengths for the particular compound are used in the theoretical calculations.

Heat transfer in rarefied couette flow on the basis of discrete ordinate method

The method of discrete ordinates, in conjunction with the modified "half-range" quadrature, is applied to the study of heat transfer in rarefied gas flows. Analytic expressions for the reduced distribution function, the macroscopic temperature profile and the heat flux are obtained in the general n-th approximation. The results for temperature profile and heat flux are in sufficiently good accord both with the results of the previous investigators and with the experimental data.