Quantum spin nematics, dimerization, and deconfined criticality in Quasi-1D spin-one magnets

We study theoretically the destruction of spin nematic order due to quantum fluctuations in quasi-one-dimensional spin-1 magnets. If the nematic ordering is disordered by condensing disclinations, then quantum Berry phase effects induce dimerization in the resulting paramagnet. We develop a theory for a Landau-forbidden second order transition between the spin nematic and dimerized states found in recent numerical calculations. Numerical tests of the theory are suggested.

Aggregation studies in crystals of apolar helical peptides: Boc-Aib-Val-Ala-Leu-Aib-Val-Ala-Leu-Aib-OMe

In the crystal, the backbone of Boc-(Aib-Val-Ala-Leu)2-Aib-OMe adopts a helical form with four alpha-type hydrogen bonds in the middle, flanked by 3(10)-type hydrogen bonds at either end. The helical molecules stack in columns with head-to-tail hydrogen bonds, either directly between NH and CO, or bridged by solvent molecules. The packing of the helices is parallel, even in space group P2(1). Cell parameters are a = 9.837(2) A, b = 15.565(3) A, c = 20.087(5) A, beta = 96.42(2) degrees, dcalc = 1.091 g/cm3 for C46H83N9O12.1.5H2O.0.67CH3OH. There appears to be some hydration of the backbone in this apolar helix.

Modular design of synthetic protein mimics. Crystal structures, assembly, and hydration of two 15- and 16-residue apolar, leucyl-rich helical peptides

Two IS- and 16-residue peptides containing a-aminoisobutyric acid (Aib) have been synthesized, as part of a strategy to construct stereochemically rigid peptide helices, in a modular approach to design of protein mimics. The peptides Boc-(Val-Ala-Leu-Aib),-OMe ( I ) and Boc-Val-Ala-Leu-Aib-Val-Ala-Leu-(Val-Ala-Leu-Aib()11z)- OhaMvee been crystallized.Both crystals are stable only in the presence of mother liquor or water. The crystal data are as follows. I: C78H140N16019~2H20,P2,, a = 16.391 (3) A, b = 16.860 (3) A, c = 18.428 (3) A, p = 103.02 (I)O, Z = 2, R = 9.6% for 3445 data with lFol >30(F), resolution 0.93 A. 11: C7,Hl,,N,S018.7.5H,0, C2221, a = 18.348 ( 5 ) A, b = 47.382 (1 1) A, c = 24.157 ( 5 ) A, Z =8, R = l0,6%, for 3147 data with lFol > 3a(F), resolution 1.00 A. The 15-residue peptide (11) is entirely a helical, while the 16-residue peptide ( I ) has a short segment of 310 helix at the N terminus. The packing of the helices in the crystals is rather incfficicnt with no particular attractions between Leu-Leu side chains, or any other pair. Both crystals have fairly large voids, which are filled with water molecules in a disordered fashion. Water molecule sites near the polar head-to-tail regions are well detcrmined, those closer to the hydrophobic side chains less so and a number of possible water sites in the remaining "empty" space are not determined. No interdigitation of Leu side chains is observed in the crystal as is hypothesized in the "leucine zipper" class of DNA binding proteins.

Modular design of synthetic protein mimics. Crystal structure of two seven-residue helical peptide segments linked by .epsilon.-aminocaproic acid

Two seven-residue helical segments, Val-Ala-Leu-Aib-Val-Ala-Leu, were linked synthetically with an epsilon-aminocaproic acid (Acp) linker with the intention of making a stable antiparallel helix-helix motif. The crystal structure of the linked peptide Boc-Val-Ala-Leu-Aib-Val-Ala-Leu-Acp-Val-Ala-Leu-Aib-Val-Ala-Leu-OMe (1) shows the two helices displaced laterally from each other by the linker, but the linker has not folded the molecule into a close-packed antiparallel conformation. Two strong intermolecular NH...O = C hydrogen bonds are formed between the top of the lower helix of one molecule and the bottom of the upper helix in a laterally adjacent molecule to give the appearance of an extended single helix. The composite peptide with Boc and OMe end groups, C76H137N15O18.H2O, crystallize in space group P2(1) with a = 8.802 (1) angstrom, b = 20.409 (4) angstrom, c = 26.315 (3) angstrom, and beta = 90.72 (1)degrees; overall agreement R = 7.86% for 5030 observed reflections (\F(o)\ > 3-sigma(F)); resolution = 0.93 angstrom. Limited evidence for a more compact conformation in solution consistent with an antiparallel helix arrangement is obtained by comparison of the HPLC retention times and CD spectra of peptide 1 with well-characterized continuous helices of similar length and sequence.

Hydration and distortion of peptide helices in crystals. α-Helical structure of a dodecapeptide, Boc-(Ala-Leu-Aib)4-OMe

The dodecapeptide Boc-(Ala-Leu-Aib)(4)-OMe crystallized with two independent helical molecules in a triclinic cell. The two molecules are very similar in conformation, with a 3(10)-helix turn at the N-terminus followed by an alpha-helix, except for an elongated N(7)...O(3) distance in both molecules. All the helices in the crystal pack in a parallel motif. Eleven water sites have been found in the head-to-tail region between the apolar helices that participate in peptide-water hydrogen bonds and a network of water-water hydrogen bonds. The crystal parameters are as follows: 2(C58H104N12O15)+ca. 10H(2)O, space group P1 with a = 12.946(2), b = 17.321(3), c = 20.465(4) Angstrom, alpha = 103.12(2), beta = 105.63(2), gamma = 107.50(2)degrees, Z = 2, R = 10.9% for 5152 data observed > 3 sigma(F), resolution 1.0 Angstrom. In contrast to the shorter sequences [Karle et al. (1988)Proc. Natl. Acad. Sci. USA 85, 299-303] and Boc-(Ala-Leu-Aib)(2)-OMe [Karle et al. (1989) Biopolymers 28, 773-781], no insertion of a water molecule into the helix is observed. However, the elongated N---O distance between Ala(7) NH and Aib(3) CO in both molecules (molecule A, 3.40 Angstrom; molecule B, 3.42 Angstrom) is indicative of an incipient break in the helices. (C) Munksgaard 1994.

Stereochemical Analysis of Higher α,α-Dialkylglycine Containing Peptides. Characterization of Local Helical Conformations at Dipropylglycine Residues and Observation of a Novel Hydrated Multiple β-Turn Structure in Crystals of a Glycine Rich Peptide

The peptide Boc-Gly-Dpg-Gly-Gly-Dpg-Gly-NHMe (1) has been synthesized to examine the conformational preferences of Dpg residues in the context of a poor helix promoting sequence. Single crystals of 1 were obtained in the space group P21/c with a = 13.716(2) Å, b = 12.960(2) Å, c = 22.266(4) Å, and β = 98.05(1)°; R = 6.3% for 3660 data with |Fo| > 4σ. The molecular conformation in crystals revealed that the Gly(1)-Dpg(2) segment adopts φ, ψ values distorted from those expected for an ideal type II‘ β-turn (φGly(1) = +72.0°, ψGly(1) = −166.0°; φDpg(2) = −54.0°, ψDpg(2) = −46.0°) with an inserted water molecule between Boc-CO and Gly(3)NH. The Gly(3)-Gly(4) segment adopts φ, ψ values which lie broadly in the right handed helical region (φGly(3) = −78.0°, ψGly(3) = −9.0°; φGly(4) = −80.0°, ψGly(4) = −18.0°). There is a chiral reversal at Dpg(5) which takes up φ, ψ values in the left handed helical region. The Dpg(5)-Gly(6) segment closely resembles an ideal type I‘ β-turn (φDpg(5) = +56.0°, ψDpg(5) = +32.0°; φGly(6) = +85.0°, ψGly(6) = −3.0°). Molecules of both chiral senses are found in the centrosymmetric crystal. The C-terminus forms a hydrated Schellman motif, with water insertion into the potential 6 → 1 hydrogen bond between Gly(1)CO and Gly(6)NH. NMR studies in CDCl3 suggest substantial retention of the multiple turn conformation observed in crystals. In solution the observed NOEs support local helical conformation at the two Dpg residues.

A combined extended and helical backbone for Boc-(Ala-Leu-Ac(7)c-)(2)-OMe

The structure of the peptide Boc-Ala-Leu-Ac(7)c-Ala-Leu-Ac(7)c-OMe (Ac(7)c,1-aminocycloheptane-1-carboxylic acid) is described in crystals. The presence of two Ac(7)c residues was expected to stabilize a 3(10)-helical fold. Contrary to expectation the structural analysis revealed an unfolded amino terminus, with Ala(1) adopting an extended beta-conformation (phi = -93degrees,psi = 112degrees). Residues 2-5 form a 3(10)-helix, stabilized by three successive intramolecular hydrogen bonds. Notably, two NH groups Ala(1) and Ac(7)c(3) do not form any hydrogen bonds in the crystal. Peptide assembly appears to be dominated by packing of the cycloheptane rings that stack against one another within the molecule and also throughout the crystal in columns.

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.

Potential functions for hydrogen bond interactions - IV. Minimum Energy Conformation of the α-Helical Structure of PoIy-L-Alanine

Making use of the empirical potential functions for peptide NH .. O bonds, developed in this laboratory, the relative stabilities of the rightand left-handed α-helical structures of poly-L-alanine have been investigated, by calculating their conformational energies (V). The value of Vmin of the right-handed helix (αP) is about - 10.4 kcal/mole, and that of the left-handed helix (αM) is about - 9.6 kcal/mole, showing that the former is lower in energy by 0.8 kcal/mole. The helical parameters of the stable conformation of αP are n ∼ 3.6 and h ∼ 1.5 Å. The hydrogen bond of length 2.85 Å and nonlinearity of about 10° adds about 4.0 kcal/ mole to the stabilising energy of the helix in the minimum enregy region. The energy minimum is not sharply defined, but occurs over a long valley, suggesting that a distribution of conformations (φ{symbol}, ψ) of nearly the same energy may occur for the individual residues in a helix. The experimental data of a-helical fibres of poly-L-alanine are in good agreement with the theoretical results for αP. In the case of proteins, the mean values of (φ{symbol}, ψ) for different helices are distributed, but they invariably occur within the contour for V = Vmin + 2 kcal/mole for αP.

Helical Conformations of Hexapeptides Containing N-Terminus Diproline Segments

The role of N-terminus diproline segments in facilitating helical folding in short peptides has been investigated in a set of model hexapeptides of the type Piv-Xxx-Yyy-Aib-Leu-Aib-Phe-OMe (Piv, pivaloyl). Nine sequences have been investigated with the following N-terminus dipeptide segments: (D)Pro-Ala (4) and Pro-Psi Pro (5, Psi, pseudoproline), Ala-Ala (6), Ala-Pro (7), Pro-Ala (8), Aib-Ala (9), Ala-Aib (10). The analog sequences Piv-Pro-Pro-Ala-Leu-Aib-Phe-OMe (2) and Piv-Pro-Pro-Ala-Aib-Ala-Aib-OMe (3) have also been studied. Solid state conformations have been determined by X-ray crystallography for peptides 4, 6, and 8 and compared with the previously determined crystal structure of peptide 1 (Boc-Pro-Pro-Aib-Leu-Aib-Val-OMe); (Rai et al., JACS 2006, 128, 7916-7928). Peptides 1 and 6 adopt almost identical helical conformations with unfolding of the helix at the N-terminus Pro (1) residue. Peptide 4 reveals the anticipated (D)Pro-Ala type II' beta-turn, followed by a stretch of 3(10)-helix. Peptide 8 adopts a folded conformation stabilized by four successive 4 -> 1 intramolecular hydrogen bonds. Ala (2) adopts an alpha(L) conformation, resulting in a type II beta-turn conformation followed by a stretch of 3(10)-helix. Conformational properties in solution were probed using solvent perturbation of NH chemical shifts which permit delineation of hydrogen bonded NH groups and nuclear Overhauser effects (NOEs) between backbone protons, which are diagnostic of local residue conformations. The results suggest that continuous helical conformations are indeed significantly populated for peptides 2 and 3. Comparison of the results for peptides 1 and 2, suggest that there is a significant influence of the residue that follows diproline segments in influencing backbone folding. (C) 2010 Wiley Periodicals, Inc. Biopolymers (Pept Sci) 94: 360-370, 2010.

Helical FDK Algorithms With No Backprojection Weight

In this paper, we present two new filtered backprojection (FBP) type algorithms for cylindrical detector helical cone-beam geometry with no position dependent backprojection weight. The algorithms are extension of the recent exact Hilbert filtering based 2D divergent beam reconstruction with no backprojection weight to the FDK type algorithm for reconstruction in 3D helical trajectory cone-beam tomography. The two algorithms named HFDK-W1 and HFDK-W2 result in better image quality, noise uniformity, lower noise and reduced cone-beam artifacts.

Conformations of synthetic alamethicin fragments. Evidence for 310 helical folding from 270-MHz hydrogen-1 nuclear magnetic resonance and circular dichroism studies

IH NMR studies at 270 MHz on the synthetic alamethicin fragments Z-Aib-Pro-Aib-Ala-Aib-Ala-OMe (1-6), Boc-Gln-Aib-Val-Aib-Gly-Leu-Aib-OMe (7-1 3), Boc-Leu-Aib-Pro-Val-Aib-OMe (1 2-16), and Boc-Gly-Leu- Aib-Pro-Val-Aib-OMe (1 1-16) have been carried out in CDC13 and (CD3)2S0. The intramolecularly hydrogen bonded amide hydrogens in these peptides have been delineated by using solvent titration experiments and temperature coefficientsof NH chemical shifts in (CD3)+30. All the peptides adopt highly folded structures, characterized by intramolecular 4 - 1 hydrogen bonds. The 1-6 fragment adopts a 310 helical conformation with four hydrogen bonds, in agreement with earlier studies (Rao, Ch. P., Nagaraj, R., Rao, C. N. R., & Balaram, P. (1980) Biochemistry 19, 425-4311. The 7-13

A helical peptide containing a majority of valyl residues. The crystal structure of t-butyloxy- carbonyl-(L-valyl-_-aminoisobutyryl)3-L-valyl methyl ester onohydrate

The monohydrate of the heptapeptide t-butyloxycarbonyl-(L-valyl-α-aminoiso-butyryl)3-L-valyl methyl ester crystallizes in the orthorhombic space group P212121 with four molecules in a unit cell with the dimensions α= 9.375, b = 19.413 and c = 25.878 ÅA. The structure has been solved by direct methods and refined to an R value of 0.059 for 3633 observed reflections. The molecule in the structure exists as a slightly distorted 310-helix stabilized by five 4 -> 1 intramolecular hydrogen bonds, indicating the overwhelming influence of α-aminoisobutyryl (Aib) residues in dictating helical fold even when a majority of residues in the peptide have a low intrinsic propensity to be in helices. Contrary to what is expected in helical structures, the valyl side chains, two of which are disordered, exhibit all three possible conformations. The molecules arrange themselves in a head-to-tail fashion along the c-axis. The columns thus generated pack nearly hexagonally in the crystal.