Trigonal Crystals Research Articles

Ligand-field analysis of an Er(III) complex with a heptadentate tripodal N4O3 ligand.

Polarized absorption and emission spectra of trigonal single crystals of an Er(III) complex coordinated to a heptadentate tripodal ligand are reported at temperatures between 8 and 298 K. The assigned energy levels below the onset of ligand absorption (< 25 000 cm(-1)) are fitted to a parametrized electronic Hamiltonian. The C(3) site symmetry of the Er(III) ion requires eight parameters for a full description of the ligand field within a one-electron operator description. This compound shows unusually large splittings of the multiplets, and the fitted parameters imply that this heptadentate ligand imparts the largest ligand field reported for an Er(III) complex. The ligand field was also interpreted within the angular overlap model (AOM). We derive the AOM matrix to include both sigma and anisotropic pi bonding and show that a useful description of the C(3) ligand field can be made using only five parameters. The success of the AOM description is encouraging for applications on isomorphous complexes within the lanthanide series and in describing the ligand field of low-symmetry complexes with less parameters than in the usual spherical harmonic expansion.

OBLIQUE ACOUSTIC AXES IN TRIGONAL CRYSTALS

A general analysis on the subject of acoustic axes for bulk acoustic waves in trigonal crystals is presented. It is shown that the effect of piezoelectricity increases the maximum allowable number of acoustic axes in the plane of elastic symmetry from three to five for trigonal crystals of class 3m, and from 3 to 7 for trigonal crystals of class 32. The theory of acoustic axes of general orientation developed by Khatkevich (1962) is revised. A new, simpler and more general derivation of the conditions for the occurrence of acoustic axes of general orientation in crystals is presented. It is found that the previous analytical results and conclusions stating the absence of such axes in trigonal crystals are incorrect. New correct equations for acoustic axes of general orientation in trigonal nonpiezoelectric crystals are derived and confirmed by independent numerical calculations. Acoustic axes of general orientation oblique to the elastic symmetry planes are found to exist in berlinite (class 32) and in nonpiezoelectric lithium niobate (class 3m), however piezoelectricity eliminates these axes in the latter crystal. Some illustrative examples of the relationship between leaky surface acoustic wave branches and acoustic axes in trigonal crystals are given.

Topological Analysis of Defects in Epitaxial Nitride Films and Interfaces

The present work is a review of the topological theory of defects and interfaces in crystalline materials, aimed at illustrating cases that have been studied under this framework in nitride films and interfaces. The review adresses crystallographic calculations in hexagonal and trigonal crystals using the Frank system. It also presents the principal methods of a priori and a posteriori defect characterization in a unified manner, showing their equivalence, the circumstances under which they are applicable, and practical aspects of their deployment. A number of experimental observations are analysed, and useful conclusions are extracted, for example, concerning admissible defects, structure–mechanism relations, and the influence of defects on properties. These include (i) threading, stacking-fault and interfacial dislocations in GaN epilayers, (ii) the influence of the epitaxial interface on the systematic appearance of inversion and stacking disorder, (iii) structural transformations of inversion domain boundaries due to their intersections with stacking faults, and (iv) double-positioning twinning in TiN contact layers deposited on GaN.

Individual interactions influence the crystalline order for membrane proteins

The role of contact interactions in the crystallization of membrane proteins was assessed by mutation of amino-acid residues on the surface of the reaction center from Rhodobacter sphaeroides. Five single-site mutants were constructed, with changes in contact regions found in the trigonal and tetragonal forms but not the orthorhombic form. Crystallization trials for the tetragonal form yielded either no crystals or crystals with an altered morphology, whereas crystals grew in the other two forms, indicating that these interactions are essential for the stability of the tetragonal crystals. Changes in the structures determined by X-ray diffraction of trigonal crystals for each mutant were related to the quality of the diffraction. Significant differences in the resolution limit of the crystals were associated with the loss of specific interactions between neighboring proteins. The results suggest that the contact regions are crucial for obtaining highly ordered crystals of membrane proteins.

Microscopic instabilities related to H 3O + dynamics in monoguanidinium dioxonium trinitrate

Trigonal crystals of monoguanidinium dioxonium trinitrate have been synthesized and investigated as a function of temperature by X-ray diffraction and by DTA. The strongly anisotropic crystals, built of hydrogen-bonded corrugated sheets with clearly pyramidal H 3O + cations, are stable below 280 K, and show an onset of negative thermal expansion along the hydrogen-bonded sheets at 140 K, analogous to that in H 2O ice Ih below 80 K. We have also detected a similar negative expansion region about 80 K in guanidinium nitrate, [C(NH 2) 3] +·NO 3 −, measured by neutron powder diffraction between 4 and 160 K. Factors destabilizing the [C(NH 2) 3] +·2H 3O +·3NO 3 − structure above 280 K have been discussed, and the role of the dynamics of the H 3O + cations postulated.

Solving a 300 kDa multimeric protein by low-resolution MAD phasing and averaging/phase extension.

The structure of the conjugative coupling protein TrwBDeltaN70 from Escherichia coli plasmid R388 was solved using two crystal forms. This large multimeric membrane protein of 437 residues per monomer is involved in cell-to-cell single-strand DNA transfer. Diffraction data to 2.4 A were available from trigonal crystals obtained from ammonium sulfate and to 2.5 A from monoclinic crystals grown from tartrate. A single tantalum bromide (Ta(6)Br(12)(2+)) derivative of the trigonal form, which presented a protein hexamer with C6 local symmetry in the asymmetric unit, was used in a three-wavelength MAD experiment to achieve 4.5 A resolution for initial phases. Sixfold averaging and phase extension increased the effective phasing resolution and eventually produced a straightforwardly traceable electron-density map. The monoclinic structure was solved by molecular replacement, i.e. a hexamer of the trigonal form was used as a search model. Two such hexamers are present in the asymmetric unit.

Absolute sense of twist of the benzil molecule in its enantiomorphous crystals and inclusion complexes with optically active hosts

The solid-state CD spectra were measured for optically active trigonal crystals of benzil (dibenzoyl) and its crystalline inclusion complexes with cholic and deoxycholic acids. The observed negative Cotton effect corresponding to the lowest energy n–π* transition was correlated with the P helicity of the strongly twisted α-diketone moiety. The absolute configuration of the enclathrated guest molecule in the 1:2 inclusion complex between benzil and cholic acid was also determined by X-ray crystal analysis.

Crystal Structure of the C-type Lectin-like Domain from the Human Hematopoietic Cell Receptor CD69

CD69, one of the earliest specific antigens acquired during lymphoid activation, acts as a signal-transducing receptor involved in cellular activation events, including proliferation and induction of specific genes. CD69 belongs to a family of receptors that modulate the immune response and whose genes are clustered in the natural killer (NK) gene complex. The extracellular portion of these receptors represent a subfamily of C-type lectin-like domains (CTLDs), which are divergent from true C-type lectins and are referred to as NK-cell domains (NKDs). We have determined the three-dimensional structure of human CD69 NKD in two different crystal forms. CD69 NKD adopts the canonical CTLD fold but lacks the features involved in Ca(2+) and carbohydrate binding by C-type lectins. CD69 NKD dimerizes noncovalently, both in solution and in crystalline state. The dimer interface consists of a hydrophobic, loosely packed core, surrounded by polar interactions, including an interdomain beta sheet. The intersubunit core shows certain structural plasticity that may facilitate conformational rearrangements for binding to ligands. The surface equivalent to the binding site of other members of the CTLD superfamily reveals a hydrophobic patch surrounded by conserved charged residues that probably constitutes the CD69 ligand-binding site.

Growth Mechanisms and Kinetics of Trypsin Crystallization

The surface morphologies of orthorhombic and trigonal trypsin crystals grown from solution were investigated by in situ atomic force microscopy. {001} and {100} faces of trigonal and {110} faces of orthorhombic crystals grew strictly by two-dimensional (2D) nucleation. For {101} faces, no 2D nucleation was observed even at relatively high supersaturations. For the {101} face, from the supersaturation dependency of the slope of dislocation hillocks and tangential step rates the surface free energy of step edges α and the tangential kinetic coefficient β were calculated to be 5 ± 1 erg/cm2 and (1.1 ± 0.2) 10-4 cm/s, respectively. The high value of α is thought to be the cause for the absence of 2D nucleation on this face. It was also found that growth of the trigonal {001} face proceeds by alternating deposition of three symmetry-related growth layers with a height equal to one-third of the unit cell parameter c. Using periodic bond chain (PBC) analysis it was demonstrated that the observed morphology as well as the anisotropic growth of the 2D nuclei are controlled by the underlying structure. We believe that this is the first report of growth by symmetry-related layers for a system with a 3-fold screw axis.

Defect Structure of Co2+ Center in α-LiIO3 Crystal

Abstract In this paper we establish the formulas of EPR g||, g⟂, for 3d7 ions in trigonal octahedral crystals from a cluster approach. In these formulas, the contributions from configuration interaction-and covalency-effects are considered. The parameters related to both effects can be determined from the optical spectra and the structural parameters of the studied crystal. With these formulas, the defect structure of a Co2+ center in α-LiIO3 crystal is studied. It is found that, to reach good fits between the calculated and observed g||, g⟂ , the O2_ ions between Co2+ and Li+ vacancy (VLi) should shift away from the VLi by about 0.49 Å. The displacement direction is consistent with those obtained for Cr3+ , Fe3+ , and Mn2+ centers in α-LiIO3 crystals as well as with the expectation based on the electrostatic interaction model.

Trigonal Dendritic Calcite Crystals Forming from Hot Spring Waters at Waikite, North Island, New Zealand

Amorphous silica and calcite form the deposits in the vent and on the discharge apron of Waikite Spring 100 (WS-100), which is located in the Waikite Geothermal area on North Island, New Zealand. These precipitates formed from spring water that has a temperature of >90°C and a pH of 8.1-8.8. The opaline silica is restricted to areas around the vent where cooling and evaporation of the spring water triggered precipitation. The calcite deposits in the spring vent and on the discharge apron are formed of large (up to 15 cm long) asymmetrical dendrite crystals that are characterized by multiple levels of branching. Branches grew preferentially from the downflow side of their parent branch. All branches have a trigonal transverse cross section except in areas where competition for growth space induced merger of neighboring crystals. The primary branches of the dendrite crystals are (sub)perpendicular to the substrate even in areas where the discharge apron slopes at a high angle (up to 80°). On the steeper parts of the discharge apron, the plate-like primary branches form the floors of the small terrace pools whereas their distal edges form the rims of the pools. Growth of these dendrite crystals is attributed to abiotic processes. High levels of saturation with respect to calcite were caused by rapid CO2 degassing of the sheets of spring water that flowed down the steep discharge apron. Calcite crystals with different crystal morphologies characterize other springs near this spring. The variation in crystal morphologies from spring to spring is attributed to different levels of saturation that are related to the initial PCO2 of the spring water upon discharge and the rate of CO2 degassing at each spring.

Crystallization and preliminary X-ray analysis of native and recombinant human bile-salt dependent lipase: strategies for improvement of diffraction quality.

Human bile-salt dependent lipase (BSDL), secreted into both the digestive tract and human milk, is integral to the effective absorption of dietary lipids. In attempts to obtain crystals suitable for high-resolution X-ray crystallographic studies, various forms of the enzyme have been crystallized, including native and desialidated human milk BSDL and both intact recombinant BSDL and a truncated form lacking the heavily glycosylated C-terminal repeat region. Trigonal crystals of native BSDL, with unit-cell parameters a = b = 90.0, c = 156.1 A, were obtained using 15-20%(w/v) PEG 8000 as precipitant. These crystals diffract to 3.5 A along the unique axis, but to only 5-7 A in orthogonal directions. Crystals of recombinant truncated BSDL grown from 15-20%(w/v) PEG 6000 are orthorhombic, space group P2(1)2(1)2(1), with unit-cell parameters a = 59.2, b = 90.0, c = 107.7 A, and diffract to 2.6 A resolution. These are suitable for structural analysis by X-ray crystallography.

Crystallization and preliminary X-ray diffraction studies of human epidermal growth factor.

Human epidermal growth factor (hEGF), a 6.2 kDa protein of 53 amino acids with three internal disulfide bridges, has been crystallized by the hanging-drop method. hEGF crystallizes in space group P3(1)21 (or P3(2)21) using MgCl(2) as precipitant, with unit-cell parameters a = b = 61.4, c = 87.0 A. Another type of crystal, obtained using NaCl as precipitant, belongs to a tetragonal point group and has unit-cell dimensions a = b = 102.5, c = 166.6 A. The trigonal crystals with the smaller unit cell diffract X-rays better and a native data set from a single crystal has been collected to 3.0 A resolution.

Static light scattering studies of OmpF porin: implications for integral membrane protein crystallization.

Integral membrane proteins carry out some of the most important functions of living cells, yet relatively few details are known about their structures. This is due, in large part, to the difficulties associated with preparing membrane protein crystals suitable for X-ray diffraction analysis. Mechanistic studies of membrane protein crystallization may provide insights that will aid in determining future membrane protein structures. Accordingly, the solution behavior of the bacterial outer membrane protein OmpF porin was studied by static light scattering under conditions favorable for crystal growth. The second osmotic virial coefficient (B22) was found to be a predictor of the crystallization behavior of porin, as has previously been found for soluble proteins. Both tetragonal and trigonal porin crystals were found to form only within a narrow window of B22 values located at approximately -0.5 to -2 X 10(-4) mol mL g(-2), which is similar to the "crystallization slot" observed for soluble proteins. The B22 behavior of protein-free detergent micelles proved very similar to that of porin-detergent complexes, suggesting that the detergent's contribution dominates the behavior of protein-detergent complexes under crystallizing conditions. This observation implies that, for any given detergent, it may be possible to construct membrane protein crystallization screens of general utility by manipulating the solution properties so as to drive detergent B22 values into the crystallization slot. Such screens would limit the screening effort to the detergent systems most likely to yield crystals, thereby minimizing protein requirements and improving productivity.

Trigonal Dendritic Calcite Crystals Forming from Hot Spring Waters at Waikite, North Island, New Zealand

Trigonal Dendritic Calcite Crystals Forming from Hot Spring Waters at Waikite, North Island, New Zealand

Linear elastic eigenstates of the compliance tensor for trigonal crystals

The spectral decomposition of the compliance fourth-rank tensor, representative of a trigonal crystalline or other anisotropic medium, is offered in this paper, and its characteristic values and idempotent fourth-rank tensors are established, with respect to the Cartesian tensor components. Consequently, it is proven that the idempotent tensors serve to analyse the second-rank symmetric tensor space into orthogonal subspaces, resolving the stress and strain tensors for the trigonal medium into their eigentensors, and, finally, decomposing the total elastic strain energy density into distinct, autonomous components. Finally, bounds on the values of the compliance tensor components for the trigonal system, dictated by the classical thermodynamical argument for the elastic potential to be positive definite, are estimated by imposing the characteristic values of the compliance tensor to be strictly positive.

Crystallization of the N-terminal domain of human sex hormone-binding globulin, the major sex steroid carrier in blood.

The amino-teminal laminin G-like domain of human sex hormone-binding globulin (SHBG), which contains the steroid-binding site and the dimerization domain, has been produced in Escherichia coli, purified to homogeneity and crystallized in complex with 5alpha--dihydrotestosterone (DHT) in two different crystal forms. Native data sets have been collected for tetragonal crystals (space group P4(1)22 or P4(3)22; unit-cell parameters a = 52.2, c = 148.4 A) diffracting to 3.3 A and trigonal crystals (R32; a = 104.0, c = 84.4 A) diffracting to better than 1.6 A. Since both crystal forms can only accommodate a single monomer in the asymmetric unit and share twofold rotational symmetry, it is proposed that the homodimer of this truncated form of SHBG, as observed in ultracentrifugation experiments, displays C(2) point-group symmetry.

Refined X-ray Structures of the Oxidized, at 1.3 Å, and Reduced, at 1.17 Å, [2Fe−2S] Ferredoxin from the Cyanobacterium Anabaena PCC7119 Show Redox-Linked Conformational Changes

The chemical sequence of the [2Fe-2S] ferredoxin from the cyanobacterium AnabaenaPCC7119 (Fd7119) and its high-resolution X-ray structures in the oxidized and reduced states have been determined. The Fd7119 sequence is identical to that of the ferredoxin from the PCC7120 strain (Fd7120). X-ray diffraction data were collected at 100 K with an oxidized trigonal Fd7119 crystal, at 1.3 A resolution, and with an orthorhombic crystal, previously reduced with dithionite and flash frozen under anaerobic conditions, at 1.17 A resolution. The two molecular models were determined by molecular replacement with the [2Fe-2S] ferredoxin from the strain PCC7120 (Rypniewski, W. R., Breiter, D. R., Benning, M. M., Wesenberg, G., Oh, B.-H., Markley, J. L., Rayment, I., and Holden, H. M. (1991) Biochemistry 30, 4126-4131.) The final R-factors are 0. 140 (for the reduced crystal) and 0.138 (for the oxidized crystal). The [2Fe-2S] cluster appears as a significantly distorted lozenge in the reduced and oxidized redox states. The major conformational difference between the two redox forms concerns the peptide bond linking Cys46 and Ser47 which points its carbonyl oxygen away from the [2Fe-2S] cluster ("CO out") in the reduced molecule and toward it ("CO in") in the oxidized one. The "CO out" conformation could be the signature of the reduction of the iron atom Fe1, which is close to the molecular surface. Superposition of the three crystallographically independent molecules shows that the putative recognition site with the physiological partner (FNR) involves charged, hydrophobic residues and invariant water molecules.

Characterization and crystallization of soluble human Fc gamma receptor II (CD32) isoforms produced in insect cells.

Fc gamma RII (CD32), the receptor for the Fc part of IgG, is responsible for the clearance of immunocomplexes by macrophages and plays a role in the regulation of antibody production by B cells. To investigate the process of immunocomplex binding in terms of stoichiometry and stability of the Fc gamma RII:IgG complex, we produced both Fc gamma RII isoforms (Fc gamma RIIa and Fc gamma RIIb) as soluble proteins in insect cells. The expressed proteins could be purified in high yields and were biologically active as judged by their ability to bind IgG. Thus, the minor glycosylation performed by the insect cells is not crucial for the binding of the usually highly glycosylated Fc gamma RII to IgG. The dissociation constant of the sFc gamma RIIa:IgG-hFc complex was determined by fluorescence titration (KD = 2.5 x 10(-)7 M). Complementary sFc gamma RIIa antagonizes immunocomplex binding to B cells. Here sFc gamma RIIa showed a comparable dissociation constant (KD = 1.7 x 10(-)7 M) which was almost 10-fold lower than the constant for Fc gamma RIIb. The stoichiometry of the FcRIIa:IgG-hFc complex was determined by equilibrium gel filtration and shows that IgG is able to bind alternatively one or two Fc gamma RII molecules in a noncooperative manner. Furthermore, in an ELISA-based assay the isotype specificity of various anti-Fc gamma RII monoclonal antibodies was measured as well as their ability to interfere with the IgG recognition through its receptors. To further investigate the molecular basis of the Fc gamma RII-ligand interaction, we crystallized Fc gamma RIIb. Trigonal crystals diffracted to 3 A and the structure solution is in progress.

Recombinant human thyroid peroxidase expressed in insect cells is soluble at high concentrations and forms diffracting crystals.

Human thyroid peroxidase (TPO), the key enzyme in thyroid hormone synthesis, can be produced in active form in the High Five insect cell line and when purified from the cell culture medium is soluble at concentrations of up to 18 mg/ml. This contrasts to a recent report in which human TPO produced in insect cells was found to be insoluble at high concentrations. Our concentrated TPO grows trigonal trapezohedral crystals of up to 0.5 mm in length in a vapour diffusion apparatus using polyethelene glycol as a precipitant. The crystals diffract X-rays to a 6 A resolution and the diffraction data from the crystals have been analysed giving unit cell dimensions. A potential molecular replacement solution has been identified using myeloperoxidase (MPO) as a phasing model.