Global Analysis of the Flows of Fluids with Pressure-Dependent Viscosities

 To describe the flows of fluids over a wide range of pressures, it is necessary to take into account the fact that the viscosity of the fluid depends on the pressure. That the viscosity depends on the pressure has been verified by numerous careful experiments. While the existence of solutions local-in-time to the equations governing the flows of such fluids are available for small, special data and rather unrealistic dependence of the viscosity on the pressure, no global existence results are in place. Our interest here is to establish the existence of weak solutions for spatially periodic three-dimensional flows that are global in time, for a large class of physically meaningful viscosity-pressure relationships. (Accepted May 1, 2002) Published online November 15, 2002 Communicated by S. S. ANTMAN     

3‐Deoxy‐β‐d‐ribo‐hexopyranose (3‐deoxy‐β‐d‐glucopyranose)

The β‐pyranose form, (III), of 3‐deoxy‐d ‐ribo‐hexose (3‐deoxy‐d ‐glucose), C₆H₁₂O₅, crystallizes from water at 298 K in a slightly distorted ⁴C₁ chair conformation. Structural analyses of (III), β‐d ‐glucopyranose, (IV), and 2‐deoxy‐β‐d ‐arabino‐hexopyranose (2‐deoxy‐β‐d ‐glucopyranose), (V), show significantly different C—O bond torsions involving the anomeric carbon, with the H—C—O—H torsion angle approaching an eclipsed conformation in (III) (−10.9°) compared with 32.8 and 32.5° in (IV) and (V), respectively. Ring carbon deoxygenation significantly affects the endo‐ and exocyclic C—C and C—O bond lengths throughout the pyranose ring, with longer bonds generally observed in the monodeoxygenated species (III) and (V) compared with (IV). These structural changes are attributed to differences in exocyclic C—O bond conformations and/or hydrogen‐bonding patterns superimposed on the direct (intrinsic) effect of monodeoxygenation. The exocyclic hydroxymethyl conformation in (III) (gt) differs from that observed in (IV) and (V) (gg).     

1‐(β‐d‐Erythrofuranos­yl)cytidine (β‐erythrocytidine)

1‐(β‐d ‐Erythrofuranosyl)cytidine, C₈H₁₁N₃O₄, (I), a derivative of β‐cytidine, (II), lacks an exocyclic hydroxy­methyl (–CH₂OH) substituent at C4′ and crystallizes in a global conformation different from that observed for (II). In (I), the β‐d ‐erythrofuranosyl ring assumes an E₃ conformation (C3′‐exo; S, i.e. south), and the N‐glycoside bond conformation is syn. In contrast, (II) contains a β‐d ‐ribofuranosyl ring in a ³T₂ conformation (N, i.e. north) and an anti‐N‐glycoside linkage. These crystallographic properties mimic those found in aqueous solution by NMR with respect to furan­ose conformation. Removal of the –CH₂OH group thus affects the global conformation of the aldofuranosyl ring. These results provide further support for S/syn–anti and N/anti correlations in pyrimidine nucleosides. The crystal structure of (I) was determined at 200 K.     

13C-labeled platinum(IV)-carbohydrate complexes: structure determination based on (1)H-(1)H, (13)C-(1)H, and (13)C-(13)C spin-spin coupling constants

The reaction of D-mannose and D-allose with [PtMe(3)(Me(2)CO)(3)]BF(4) 1 in acetone affords complexes [PtMe(3)L]BF(4) 5 and 6 (5, L = alpha-D-mannofuranose; 6, L = beta-D-allofuranose). The coordination mode and conformation of the carbohydrate ligands in 5 and 6 in acetone-d(6) have been determined from an analysis of J(HH), J(CH), and J(CC) in complexes formed using site-specific (13)C-labeled D-mannose and D-allose. These coupling data are compared to those measured in (13)C-labeled complex [PtMe(3)L]BF(4) 2 (L = 1, 2-O-isopropylidene-alpha-D-glucofuranose) and 1, 2-O-isopropylidene-alpha-D-glucofuranose 3, whose solid-state structures are known, and in (13)C-labeled 1,2;5, 6-di-O-isopropylidene-alpha-D-glucofuranose 4. The preferred furanose ring conformations in 2 and 5 are very similar ((3)E/E(4) and E(4)/(o)E/E(1), respectively; eastern hemisphere of the pseudorotational itinerary), with platinum coordination involving O3, O5, and O6 of the saccharide. In contrast, the furanose ring of 6 prefers an (4)E/E(o)/(1)E geometry (western hemisphere of the pseudorotational itinerary) resulting from altered complexation involving O1, O5, and O6. Couplings within the exocyclic fragments of 2, 5, and 6 also support the existence of two different platinum coordination modes. In addition to establishing the structures and conformations of 2, 5, and 6 in solution, one-, two-, and three-bond J(CH) and J(CC) observed in these complexes provide new insights into the effect of structure and conformation on the magnitudes of these couplings in saccharides. Weak platinum(IV) complexation with the carbohydrate conformationally restricts the furanose and exocyclic fragment without introducing undesirable structural strain, thereby allowing more reliable correlations between structure and coupling magnitude.     

Kink instability in applied-field magneto-plasma-dynamic thrusters

Measurements of magnetic and electrostatic fluctuations in an applied field magneto-plasma-dynamic thruster have shown that a m/n=1/1 kink mode becomes unstable whenever the Kruskal-Shafranov limit is violated. A positive correlation is established between the kink and performance degradation at high current, which has until now prevented the use of this kind of thruster in space missions.     

Deuterium nuclear spin-lattice relaxation times and quadrupolar coupling constants in isotopically labeled saccharides

(13)C and (2)H spin-lattice relaxation times have been determined by inversion recovery in a range of site-specific (13)C- and (2)H-labeled saccharides under identical solution conditions, and the data were used to calculate deuterium nuclear quadrupolar coupling constants ((2)H NQCC) at specific sites within cyclic and acyclic forms in solution. (13)C T(1) values ranged from approximately 0.6 to 8.2 s, and (2)H T(1) values ranged from approximately 79 to 450 ms, depending on molecular structure (0.4 M sugar in 5 mM EDTA (disodium salt) in (2)H(2)O-depleted H(2)O, pH 4. 8, 30 degrees C). In addition to providing new information on (13)C and (2)H relaxation behavior of saccharides in solution, the resulting (2)H1 NQCC values reveal a dependency on anomeric configuration within aldopyranose rings, whereas (2)H NQCC values at other ring sites appear less sensitive to configuration at C1. In contrast, (2)H NQCC values at both anomeric and nonanomeric sites within aldofuranose rings appear to be influenced by anomeric configuration. These experimental observations were confirmed by density functional theory (DFT) calculations of (2)H NQCC values in model aldopyranosyl and aldofuranosyl rings.     

Co‐crystals of 3‐deoxy‐3‐fluoro‐α‐d‐glucopyranose and 3‐deoxy‐3‐fluoro‐β‐d‐glucopyranose

3‐Deoxy‐3‐fluoro‐d ‐glucopyranose crystallizes from acetone to give a unit cell containing two crystallographically independent molecules. One of these molecules (at site A) is structurally homogeneous and corresponds to 3‐deoxy‐3‐fluoro‐β‐d ‐glucopyranose, C₆H₁₁FO₅, (I). The second molecule (at site B) is structurally heterogeneous and corresponds to a mixture of (I) and 3‐deoxy‐3‐fluoro‐α‐d ‐glucopyranose, (II); treatment of the diffraction data using partial‐occupancy oxygen at the anomeric center gave a high‐quality packing model with an occupancy ratio of 0.84:0.16 for (II):(I) at site B. The mixture of α‐ and β‐anomers at site B appears to be accommodated in the lattice because hydrogen‐bonding partners are present to hydrogen bond to the anomeric OH group in either an axial or equatorial orientation. Cremer–Pople analysis of (I) and (II) shows the pyranosyl ring of (II) to be slightly more distorted than that of (I) [θ_(I) = 3.85 (15)° and θ_(II) = 6.35 (16)°], but the general direction of distortion is similar in both structures [ϕ_(I) = 67 (2)° (B_C1,C4) and ϕ_(II) = 26.0 (15)° (^C3TB_C1); B = boat conformation and TB = twist‐boat conformation]. The exocyclic hydroxymethyl (–CH₂OH) conformation is gg (gauche–gauche) (H5 anti to O6) in both (I) and (II). Structural comparisons of (I) and (II) to related unsubstituted, deoxy and fluorine‐substituted monosaccharides show that the gluco ring can assume a wide range of distorted chair structures in the crystalline state depending on ring substitution patterns.     

Rearrangement of 3-deoxy-D-erythro-hexos-2-ulose in aqueous solution: NMR evidence of intramolecular 1,2-hydrogen transfer

Selective (13)C- and (2)H-labeling, and (13)C NMR spectroscopy, have been used to show that the 1,2-dicarbonyl compound (osone), 3-deoxy-D-erythro-hexos-2-ulose (3-deoxy-D-glucosone) (1; 3DG), degrades to 3-deoxy-D-ribo-hexonic acid 2 and 3-deoxy-D-arabino-hexonic acid 3 exclusively via an intramolecular 1,2-hydrogen transfer mechanism in aqueous phosphate buffer at pH 7.5 at 37 °C. Acids 2 and 3 are produced in significantly different amounts (1:6 ratio) despite the prochiral C3 in 1, and two potential reaction mechanisms are considered to explain the observed stereoselectivity. One mechanism involves acyclic forms of 1 as reactants, whereas the other assumes cyclic pyranose reactants. In the former (2-keto-hydrate or 2KH mechanism), putative transition state structures based on density functional theory (DFT) calculations arise from the C1 hydrate form of acyclic 1 having the C1-H1 bond roughly orthogonal to the C2 carbonyl plane. The relative orientation of the alkoxide oxygen atom at C1 and the C2 carbonyl oxygen, and H-bonding between C(1)OH and the C2 carbonyl oxygen, contribute to the stability of the transition state. DFT calculations of the natural charges on individual atoms in the transition state show the migrating hydrogen to have an almost neutral charge, implying that it may more closely resemble a hydrogen atom than a hydride anion during transfer from C1 to C2. A second mechanism (2-keto-pyranose or 2KP mechanism) involving the cyclic 2-keto-pyranoses of 1 as reactants aligns the C1-H1 bond orthogonal to the C2 carbonyl plane in different ring conformations of both anomers, with the β-pyranose giving 3 and the α-pyranose giving 2. While both the 2KH and 2KP mechanisms are possible, the latter readily leads to a prediction of the reaction stereospecificity that is consistent with the experimental data.     

Guided modes of integrated optical guides. A mathematical study

A waveguide in integrated optics is defined by its refractiveindex. The guide is assumed to be invariant in the propagationdirection while in the transverse direction it is supposed tobe a compact perturbation of an unbounded stratified medium.We are interested in the modes guided by this device, whichare waves with a transverse energy confined in a neighbourhoodof the perturbation. Our goal is to analyse the existence of such guided modes. Underthe assumptions of weak guidance the problem reduces to a two-dimensionaleigenvalue problem for a scalar field. The associated operatoris unbounded, selfadjoint, and bounded from below. Its spectrumconsists of the discrete spectrum corresponding to the guidedmodes and of the essential spectrum corresponding to the radiationmodes. We present existence results of guided modes and an asymptoticstudy at high frequencies, which shows that contrarily to thecase of optical fibers, the number of guided modes can remainbounded. The major tools are the min-max principle and comparisonof results between different eigenvalue problems. The originalityof the present study lies in the stratified character of theunbounded reference medium.     

Interaction of the mu-opioid receptor with GPR177 (Wntless) inhibits Wnt secretion: potential implications for opioid dependence

Background  

Opioid agonist drugs produce analgesia. However, long-term exposure to opioid agonists may lead to opioid dependence. The analgesic and addictive properties of opioid agonist drugs are mediated primarily via the mu-opioid receptor (MOR). Opioid agonists appear to alter neuronal morphology in key brain regions implicated in the development of opioid dependence. However, the precise role of the MOR in the development of these neuronal alterations remains elusive. We hypothesize that identifying and characterizing novel MOR interacting proteins (MORIPs) may help to elucidate the underlying mechanisms involved in the development of opioid dependence.