The Equilibrium Flux Method for the calculation of flows with non-equilbrium chemical reactions

The Equilibrium Flux Method [1] is a kinetic theory based finite volume method for calculating the flow of a compressible ideal gas. It is shown here that, in effect, the method solves the Euler equations with added pseudo-dissipative terms and that it is a natural upwinding scheme. The method can be easily modified so that the flow of a chemically reacting gas mixture can be calculated. Results from the method for a one-dimensional non-equilibrium reacting flow are shown to agree well with a conventional continuum solution. Results are also presented for the calculation of a plane two-dimensional flow, at hypersonic speed, of a dissociating gas around a blunt-nosed body.

Non-Equilibrium Reaction Rates in the Macroscopic Chemistry Method for DSMC Calculations

The Direct Simulation Monte Carlo (DSMC) method is used to simulate the flow of rarefied gases. In the Macroscopic Chemistry Method (MCM) for DSMC, chemical reaction rates calculated from local macroscopic flow properties are enforced in each cell. Unlike the standard total collision energy (TCE) chemistry model for DSMC, the new method is not restricted to an Arrhenius form of the reaction rate coefficient, nor is it restricted to a collision cross-section which yields a simple power-law viscosity. For reaction rates of interest in aerospace applications, chemically reacting collisions are generally infrequent events and, as such, local equilibrium conditions are established before a significant number of chemical reactions occur. Hence, the reaction rates which have been used in MCM have been calculated from the reaction rate data which are expected to be correct only for conditions of thermal equilibrium. Here we consider artificially high reaction rates so that the fraction of reacting collisions is not small and propose a simple method of estimating the rates of chemical reactions which can be used in the Macroscopic Chemistry Method in both equilibrium and non-equilibrium conditions. Two tests are presented: (1) The dissociation rates under conditions of thermal non-equilibrium are determined from a zero-dimensional Monte-Carlo sampling procedure which simulates ‘intra-modal’ non-equilibrium; that is, equilibrium distributions in each of the translational, rotational and vibrational modes but with different temperatures for each mode; (2) The 2-D hypersonic flow of molecular oxygen over a vertical plate at Mach 30 is calculated. In both cases the new method produces results in close agreement with those given by the standard TCE model in the same highly nonequilibrium conditions. We conclude that the general method of estimating the non-equilibrium reaction rate is a simple means by which information contained within non-equilibrium distribution functions predicted by the DSMC method can be included in the Macroscopic Chemistry Method.

Volatile products and new polymer structures formed on Co-60 gamma-radiolysis of poly(lactic acid) and poly(glycolic acid)

A gas product analysis has been conducted on gamma-irradiated samples of poly(lactic acid) (PLA) and poly(glycolic acid) (PGA) by means of gas chromatography. The major volatile products have been identified to be CO, CO2, CH4 and C2H6 for PLA, and CO and CO2 for PGA. In addition, the yield of evolved gases for PLA has been found to be 1.81 for CO2, 0.98 for CO, 0.026 for CH4 and 0.012 for C2H6; and that for PGA to be 1.70 for CO2 and 0.42 for CO. The new chain ends formed due to gamma-induced bond cleavage in PLA have been assigned to CH3-CH2-CO-O- and CH3-CH2-O-CO-, and the G values for formation of these chain ends were found to be 1.9 and 0.6, respectively. The G value for chain scission reported previously of 2.3 is comparable with that for the formation of the propanoic acid end group. (C) 1997 Elsevier Science Limited.

Calcium is essential for the structural integrity of the cysteine-rich, ligand-binding repeat of the low-density lipoprotein receptor

Seven cysteine-rich repeats form the ligand-binding region of the low-density lipoprotein (LDL) receptor. Each of these repeats is assumed to bind a calcium ion, which is needed for association of the receptor with its ligands, LDL and beta-VLDL. The effects of metal ions on the folding of the reduced N-terminal cysteine-rich repeat have been examined by using reverse-phase high-performance liquid chromatography to follow the formation of fully oxidized isomers with different disulfide connectivities. in the absence of calcium many of the 15 possible isomers formed on oxidation, whereas in its presence the predominant product at equilibrium had the native disulfide bond connectivities. Other metals were far less effective at directing disulfide bond formation: Mn2+ partly mimicked the action of Ca2+, but Ba2+, Sr2+, and Mg2+ had little effect. This metal-ion specificity was also observed in two-dimensional H-1 NMR spectral studies: only Ca2+ induced the native three-dimensional fold. The two paramagnetic ions, Gd3+ and Mn2+, and Cd2+ did not promote adoption of a well-defined structure, and the two paramagnetic ions did not displace calcium ions. The location of calcium ion binding sites in the repeat was also explored by NMR spectroscopy. The absence of chemical shift changes for the side chain proton resonances of Asp26, Asp36, and Glu37 from pH 3.9 to 6.8 in the presence of calcium ions and their proximal location in the NMR structures implicated these side chains as calcium ligands. Deuterium exchange NMR experiments also revealed a network of hydrogen bonds that stabilizes the putative calcium-binding loop.

Analysis and application of an equilibrium model for in vitro bioassay systems with three components: Receptor, hormone and hormone-binding-protein

A simple theoretical framework is presented for bioassay studies using three component in vitro systems. An equilibrium model is used to derive equations useful for predicting changes in biological response after addition of hormone-binding-protein or as a consequence of increased hormone affinity. Sets of possible solutions for receptor occupancy and binding protein occupancy are found for typical values of receptor and binding protein affinity constants. Unique equilibrium solutions are dictated by the initial condition of total hormone concentration. According to the occupancy theory of drug action, increasing the affinity of a hormone for its receptor will result in a proportional increase in biological potency. However, the three component model predicts that the magnitude of increase in biological potency will be a small fraction of the proportional increase in affinity. With typical initial conditions a two-fold increase in hormone affinity for its receptor is predicted to result in only a 33% increase in biological response. Under the same conditions an Ii-fold increase in hormone affinity for receptor would be needed to produce a two-fold increase in biological potency. Some currently used bioassay systems may be unrecognized three component systems and gross errors in biopotency estimates will result if the effect of binding protein is not calculated. An algorithm derived from the three component model is used to predict changes in biological response after addition of binding protein to in vitro systems. The algorithm is tested by application to a published data set from an experimental study in an in vitro system (Lim et al., 1990, Endocrinology 127, 1287-1291). Predicted changes show good agreement (within 8%) with experimental observations. (C) 1998 Academic Press Limited.

Crystal structures of reduced and oxidized DsbA: investigation of domain motion and thiolate stabilization

Background: The redox proteins that incorporate a thioredoxin fold have diverse properties and functions. The bacterial protein-folding factor DsbA is the most oxidizing of the thioredoxin family. DsbA catalyzes disulfide-bond formation during the folding of secreted proteins, The extremely oxidizing nature of DsbA has been proposed to result from either domain motion or stabilizing active-site interactions in the reduced form. In the domain motion model, hinge bending between the two domains of DsbA occurs as a result of redox-related conformational changes. Results: We have determined the crystal structures of reduced and oxidized DsbA in the same crystal form and at the same pH (5.6). The crystal structure of a lower pH form of oxidized DsbA has also been determined (pH 5.0). These new crystal structures of DsbA, and the previously determined structure of oxidized DsbA at pH 6.5, provide the foundation for analysis of structural changes that occur upon reduction of the active-site disulfide bond. Conclusions: The structures of reduced and oxidized DsbA reveal that hinge bending motions do occur between the two domains. These motions are independent of redox state, however, and therefore do not contribute to the energetic differences between the two redox states, instead, the observed domain motion is proposed to be a consequence of substrate binding. Furthermore, DsbA's highly oxidizing nature is a result of hydrogen bond, electrostatic and helix-dipole interactions that favour the thiolate over the disulfide at the active site.

Crystallization of a trimeric human T cell leukemia virus type 1 gp21 ectodomain fragment as a chimera with maltose-binding protein

We present a novel protein crystallization strategy, applied to the crystallization of human T cell leukemia virus type 1 (HTLV-1) transmembrane protein gp21 lacking the fusion peptide and the transmembrane domain, as a chimera with the Escherichia coli maltose binding protein (MBP). Crystals could not be obtained with a MBP/gp21 fusion protein in which fusion partners were separated by a flexible linker, but were obtained after connecting the MBP C-terminal alpha-helix to the predicted N-terminal alpha-helical sequence of gp21 via three alanine residues. The gp21 sequences conferred a trimeric structure to the soluble fusion proteins as assessed by sedimentation equilibrium and X-ray diffraction, consistent with the trimeric structures of other retroviral transmembrane proteins. The envelope protein precursor, gp62, is likewise trimeric when expressed in mammalian cells. Our results suggest that MBP may have a general application for the crystallization of proteins containing N-terminal alpha-helical sequences.

Structures of free and complexed forms of Escherichia coli xanthine-guanine phosphoribosyltransferase

Structures of free, substrate-bound and product-bound forms of Escherichia coli xanthine-guanine phosphoribosyltransferase (XGPRT) have been determined by X-ray crystallography. These are compared with the previously determined structure of magnesium and sulphate-bound XPRT. The structure of free XGPRT at 2.25 Angstrom resolution confirms the flexibility of residues in and around a mobile loop identified in other PRTases and shows that the cis-peptide conformation of Arg37 at the active site is maintained in the absence of bound ligands. The structures of XGPRT complexed with the purine base substrates guanine or xanthine in combination with cPRib-PP, an analog of the second substrate PRib-PP, have been solved to 2.0 Angstrom resolution. In these two structures the disordered phosphate-binding loop of uncomplexed XGPRT becomes ordered through interactions with the 5'-phosphate group of cPRib-PP. The cyclopentane ring of cPRib-PP has the C3 exo pucker conformation, stabilised by the cPRib-PP-bound Mg2+. The purine base specificity of XGPRT appears to be due to water-mediated interactions between the 2-exocyclic groups of guanine or xanthine and side-chains of Glu136 and Asp140, as well as the main-chain oxygen atom of Ile135. Asp92, together with Lys115, could help stabilise the N7-protonated tautomer of the incoming base and could act as a general base to remove the proton from N7 .when the nucleotide product is formed. The 2.6 Angstrom resolution structure of XGPRT complexed with product GMP is similar to the substrate-bound complexes. However, the ribose ring of GMP is rotated by similar to 24 degrees compared with the equivalent ring in cPRib-PP. This rotation results in the loss of all interactions between the ribosyl group and the enzyme in the product complex. (C) 1998 Academic Press.

Finite element modelling of dissipative structures for nonequilibrium chemical reactions in fluid-saturated porous media

We use the finite element method to model and predict the dissipative structures of chemical species for a nonequilibrium chemical reaction system in a fluid-saturated porous medium. In particular, we explore the conditions under which dissipative structures of the species may exist in the Brusselator type of nonequilibrium chemical reaction. Since this is the first time the finite element method and related strategies have been used to study the chemical instability problems in a fluid-saturated porous medium, it is essential to validate the method and strategies before they are put into application. For this purpose, we have rigorously derived the analytical solutions for dissipative structures of chemical species in a benchmark problem, which geometrically is a square. Comparison of the numerical solutions with the analytical ones demonstrates that the proposed numerical method and strategy are robust enough to solve chemical instability problems in a fluid-saturated porous medium. Finally, the related numerical results from two application examples indicate that both the regime and the magnitude of pore-fluid flow have significant effects on the nature of the dissipative structures that developed for a nonequilibrium chemical reaction system in a fluid-saturated porous medium. The motivation for this study is that self-organization under conditions of pore-fluid flow in a porous medium is a potential mechanism of the orebody formation and mineralization in the upper crust of the Earth. (C) 2000 Elsevier Science S.A. All rights reserved.

Bonding effects and the crystal structures of (NH4)(2)[Cu(H2O)(6)](SO4)(2) and its (H2O)-O-18 substituted form at 9.5 K

The crystal structures of the Tutton salts (NH4)(2)[Cu(H2O)(6)](SO4)(2), diammonium hexaaquacopper disulfate, formed with normal water and isotopically substituted (H2O)-O-18, have been determined by X-ray diffraction at 9.5 K and are very similar, with Cu-O(7) the longest of the Cu-O bonds of the Jahn-Teller distorted octahedral [Cu(H2O)(6)](2+) complex. It is known that structural differences accompany deuteration of (NH4)(2)[Cu(H2O)(6)](SO4)(2), the most dramatic of which is a switch to Cu-O(8) as the longest such bond. The present result suggests that the structural differences are associated with hydrogen-bonding effects rather than with increased mass of the water ligands affecting the Jahn-Teller coupling. The Jahn-Teller distortions and hydrogen-bonding contacts in the compounds are compared with those reported for other Tutton salts at ambient and high pressure.

Solution structures in aqueous SDS micelles of two amyloid beta peptides of A beta(1-28) mutated at the alpha-secretase cleavage site (K16E, K16F)

NMR solution structures are reported for two mutants (K16E, K16F) of the soluble amyloid beta peptide A beta(1-28). The structural effects of these mutations of a positively charged residue to anionic and hydrophobic residues at the alpha-secretase cleavage site (Lys16-Leu17) were examined in the membrane-simulating solvent aqueous SDS micelles. Overall the three-dimensional structures were similar to that for the native A beta(1-28) sequence in that they contained an unstructured N-terminus and a helical C-terminus. These structural elements are similar to those seen in the corresponding regions of full-length A beta peptides A beta(1-40) and A beta(1-42), showing that the shorter peptides are valid model systems. The K16E mutation, which might be expected to stabilize the macrodipole of the helix, slightly increased the helix length (residues 13-24) relative to the K16F mutation, which shortened the helix to between residues 16 and 24. The observed sequence-dependent control over conformation in this region provides an insight into possible conformational switching roles of mutations in the amyloid precursor protein from which A beta peptides are derived. In addition, if conformational transitions from helix to random coil to sheet precede aggregation of A beta peptides in vivo, as they do in vitro, the conformation-inducing effects of mutations at Lys16 may also influence aggregation and fibril formation. (C) 2000 Academic Press.

Mesoionic pyridopyrimidinylium and pyridooxazinylium olates and non-mesoionic pyridopyrimidinones. Structures in the solid state, solution, and matrices

X-Ray crystal structures, C-13 NMR spectra and theoretical calculations (B3LYP/6-31G*) are reported for the mesoionic (zwitterionic) pyridopyrimidinylium- and pyridooxazinyliumolates 2a, 3a and 5a,b as well as the enol ether 11b and the enamine 11c. The 1-NH compounds like 1a, 2a and 3a exist in the mesoionic form in the crystal and in solution, but the OH tautomers such as 1b and 2b dominate in the gas phase as revealed by the Ar matrix IR spectra in conjunction with DFT calculations. All data indicate that the mesoionic compounds can be regarded as intramolecular pyridine-ketene zwitterions (cf. 16 --> 17) with a high degree of positive charge on the pyridinium nitrogen, a long pyridinium N-CO bond (ca. 1.44-1.49 Angstrom), and normal C=O double bonds (ca. 1.22 Angstrom). All mesoionic compounds exhibit a pronounced tilting of the olate C=O groups (the C=O groups formally derived from a ketene) towards the pyridinium nitrogen, giving NCO angles of 110-118 degrees. Calculations reveal a hydrogen bond with 6-CH, analogous to what is found in ketene-pyridine zwitterions and the C3O2-pyridine complex. The 2-OH tautomers of type 1b, 2b, and 11 also show a high degree of zwitterionic character as indicated by the canonical structures 11 12.