Computer simulation of packing of particles with size distributions produced by fragmentation processes

Fragmentation schemes inspired by theoretical results and conjectures of Kolmogorov are applied to produce particle size distributions of different natures, depending on fragmentation parameters. A two-dimensional computer simulation method of packing is applied to the resulting distributions and the void fraction is evaluated. The relationship between the void fraction and characteristic parameters of the fragmentation process is studied.

Analysis, reliability and optimization of reinforced concrete 2-D structures

In this paper a consistent analysis of reinforced concrete (RC) two-dimensional (2-D) structures,namely slab structures subjected to in-plane and out-plane forces, is presented. By using this method of analysis the well established methodology for dimensioning and verifying RC sections of beam structures is extended to 2-D structures. The validity of the proposed analysis results is checked by comparing them with some published experimental test results. Several examples show some of these proposed analysis features, such as the influence of the reinforcement layout on the service and ultimate behavior of a slab structure and the non straightforward problem of the optimal dimension at a slab point subjected to several loading cases. Also, in these examples, the method applications to design situations as multiple steel families and non orthogonal reinforcement layout are commented.

Two-dimensional isostatic meshes in the finite element method

In a Finite Element (FE) analysis of elastic solids several items are usually considered, namely, type and shape of the elements, number of nodes per element, node positions, FE mesh, total number of degrees of freedom (dot) among others. In this paper a method to improve a given FE mesh used for a particular analysis is described. For the improvement criterion different objective functions have been chosen (Total potential energy and Average quadratic error) and the number of nodes and dof's of the new mesh remain constant and equal to the initial FE mesh. In order to find the mesh producing the minimum of the selected objective function the steepest descent gradient technique has been applied as optimization algorithm. However this efficient technique has the drawback that demands a large computation power. Extensive application of this methodology to different 2-D elasticity problems leads to the conclusion that isometric isostatic meshes (ii-meshes) produce better results than the standard reasonably initial regular meshes used in practice. This conclusion seems to be independent on the objective function used for comparison. These ii-meshes are obtained by placing FE nodes along the isostatic lines, i.e. curves tangent at each point to the principal direction lines of the elastic problem to be solved and they should be regularly spaced in order to build regular elements. That means ii-meshes are usually obtained by iteration, i.e. with the initial FE mesh the elastic analysis is carried out. By using the obtained results of this analysis the net of isostatic lines can be drawn and in a first trial an ii-mesh can be built. This first ii-mesh can be improved, if it necessary, by analyzing again the problem and generate after the FE analysis the new and improved ii-mesh. Typically, after two first tentative ii-meshes it is sufficient to produce good FE results from the elastic analysis. Several example of this procedure are presented.

Membrane-bound state of the colicin E1 channel domain as an extended two-dimensional helical array

Atomic level structures have been determined for the soluble forms of several colicins and toxins, but the structural changes that occur after membrane binding have not been well characterized. Changes occurring in the transition from the soluble to membrane-bound state of the C-terminal 190-residue channel polypeptide of colicin E1 (P190) bound to anionic membranes are described. In the membrane-bound state, the α-helical content increases from 60–64% to 80–90%, with a concomitant increase in the average length of the helical segments from 12 to 16 or 17 residues, close to the length required to span the membrane bilayer in the open channel state. The average distance between helical segments is increased and interhelix interactions are weakened, as shown by a major loss of tertiary structure interactions, decreased efficiency of fluorescence resonance energy transfer from an energy donor on helix V of P190 to an acceptor on helix IX, and decreased resonance energy transfer at higher temperatures, not observed in soluble P190, implying freedom of motion of helical segments. Weaker interactions are also shown by a calorimetric thermal transition of low cooperativity, and the extended nature of the helical array is shown by a 3- to 4-fold increase in the average area subtended per molecule to 4,200 Å2 on the membrane surface. The latter, with analysis of the heat capacity changes, implies the absence of a developed hydrophobic core in the membrane-bound P190. The membrane interfacial layer thus serves to promote formation of a highly helical extended two-dimensional flexible net. The properties of the membrane-bound state of the colicin channel domain (i.e., hydrophobic anchor, lengthened and loosely coupled α-helices, and close association with the membrane interfacial layer) are plausible structural features for the state that is a prerequisite for voltage gating, formation of transmembrane helices, and channel opening.

Crystal structure of 2,5-diketo-d-gluconic acid reductase A complexed with NADPH at 2.1-Å resolution

The three-dimensional structure of Corynebacterium 2,5-diketo-d-gluconic acid reductase A (2,5-DKGR A; EC 1.1.1.-), in complex with cofactor NADPH, has been solved by using x-ray crystallographic data to 2.1-Å resolution. This enzyme catalyzes stereospecific reduction of 2,5-diketo-d-gluconate (2,5-DKG) to 2-keto-l-gulonate. Thus the three-dimensional structure has now been solved for a prokaryotic example of the aldo–keto reductase superfamily. The details of the binding of the NADPH cofactor help to explain why 2,5-DKGR exhibits lower binding affinity for cofactor than the related human aldose reductase does. Furthermore, changes in the local loop structure near the cofactor suggest that 2,5-DKGR will not exhibit the biphasic cofactor binding characteristics observed in aldose reductase. Although the crystal structure does not include substrate, the two ordered water molecules present within the substrate-binding pocket are postulated to provide positional landmarks for the substrate 5-keto and 4-hydroxyl groups. The structural basis for several previously described active-site mutants of 2,5-DKGR A is also proposed. Recent research efforts have described a novel approach to the synthesis of l-ascorbate (vitamin C) by using a genetically engineered microorganism that is capable of synthesizing 2,5-DKG from glucose and subsequently is transformed with the gene for 2,5-DKGR. These modifications create a microorganism capable of direct production of 2-keto-l-gulonate from d-glucose, and the gulonate can subsequently be converted into vitamin C. In economic terms, vitamin C is the single most important specialty chemical manufactured in the world. Understanding the structural determinants of specificity, catalysis, and stability for 2,5-DKGR A is of substantial commercial interest.

Structural basis of an embryonically lethal single Ala → Thr mutation in the vnd/NK-2 homeodomain

The structural and DNA binding behavior is described for an analog of the vnd/NK-2 homeodomain, which contains a single amino acid residue alanine to threonine replacement in position 35 of the homeodomain. Multidimensional nuclear magnetic resonance, circular dichroism, and electrophoretic gel retardation assays were carried out on recombinant 80-aa residue proteins that encompass the wild-type and mutant homeodomains. The mutant A35T vnd/NK-2 homeodomain is unable to adopt a folded conformation free in solution at temperatures down to −5°C in contrast to the behavior of the corresponding wild-type vnd/NK-2 homeodomain, which is folded into a functional three-dimensional structure below 25°C. The A35T vnd/NK-2 binds specifically to the vnd/NK-2 target DNA sequence, but with an affinity that is 50-fold lower than that of the wild-type homeodomain. Although the three-dimensional structure of the mutant A35T vnd/NK-2 in the DNA bound state shows characteristic helix–turn–helix behavior similar to that of the wild-type homeodomain, a notable structural deviation in the mutant A35T analog is observed for the amide proton of leucine-40. The wild-type homeodomain forms an unusual i,i-5 hydrogen bond with the backbone amide oxygen of residue 35. In the A35T mutant this amide proton resonance is shifted upfield by 1.27 ppm relative to the resonance frequency for the wild-type analog, thereby indicating a significant alteration of this i,i-5 hydrogen bond.

Three-dimensional structure of NADPH–cytochrome P450 reductase: Prototype for FMN- and FAD-containing enzymes

Microsomal NADPH–cytochrome P450 reductase (CPR) is one of only two mammalian enzymes known to contain both FAD and FMN, the other being nitric-oxide synthase. CPR is a membrane-bound protein and catalyzes electron transfer from NADPH to all known microsomal cytochromes P450. The structure of rat liver CPR, expressed in Escherichia coli and solubilized by limited trypsinolysis, has been determined by x-ray crystallography at 2.6 Å resolution. The molecule is composed of four structural domains: (from the N- to C- termini) the FMN-binding domain, the connecting domain, and the FAD- and NADPH-binding domains. The FMN-binding domain is similar to the structure of flavodoxin, whereas the two C-terminal dinucleotide-binding domains are similar to those of ferredoxin–NADP+ reductase (FNR). The connecting domain, situated between the FMN-binding and FNR-like domains, is responsible for the relative orientation of the other domains, ensuring the proper alignment of the two flavins necessary for efficient electron transfer. The two flavin isoalloxazine rings are juxtaposed, with the closest distance between them being about 4 Å. The bowl-shaped surface near the FMN-binding site is likely the docking site of cytochrome c and the physiological redox partners, including cytochromes P450 and b5 and heme oxygenase.

The solution structure of the N-terminal domain of α2-macroglobulin receptor-associated protein

The three-dimensional structure of the N-terminal domain (residues 18–112) of α2-macroglobulin receptor-associated protein (RAP) has been determined by NMR spectroscopy. The structure consists of three helices composed of residues 23–34, 39–65, and 73–88. The three helices are arranged in an up-down-up antiparallel topology. The C-terminal 20 residues were shown not to be in a well defined conformation. A structural model for the binding of RAP to the family of low-density lipoprotein receptors is proposed. It defines a role in binding for both the unordered C terminus and the structural scaffold of the core structure. Pathogenic epitopes for the rat disease Heymann nephritis, an experimental model of human membranous glomerulonephritis, have been identified in RAP and in the large endocytic receptor gp330/megalin. Here we provide the three-dimensional structure of the pathogenic epitope in RAP. The amino acid residues known to form the epitope are in a helix–loop–helix conformation, and from the structure it is possible to rationalize the published results obtained from studies of fragments of the N-terminal domain.

Crystal structure of glutamate-1-semialdehyde aminomutase: An α2-dimeric vitamin B6-dependent enzyme with asymmetry in structure and active site reactivity

The three-dimensional structure of glutamate-1-semialdehyde aminomutase (EC 5.4.3.8), an α2-dimeric enzyme from Synechococcus, has been determined by x-ray crystallography using heavy atom derivative phasing. The structure, refined at 2.4-Å resolution to an R-factor of 18.7% and good stereochemistry, explains many of the enzyme’s unusual specificity and functional properties. The overall fold is that of aspartate aminotransferase and related B6 enzymes, but it also has specific features. The structure of the complex with gabaculine, a substrate analogue, shows unexpectedly that the substrate binding site involves residues from the N-terminal domain of the molecule, notably Arg-32. Glu-406 is suitably positioned to repel α-carboxylic acids, thereby suggesting a basis for the enzyme’s reaction specificity. The subunits show asymmetry in cofactor binding and in the mobilities of the residues 153–181. In the unliganded enzyme, one subunit has the cofactor bound as an aldimine of pyridoxal phosphate with Lys-273 and, in this subunit, residues 153–181 are disordered. In the other subunit in which the cofactor is not covalently bound, residues 153–181 are well defined. Consistent with the crystallographically demonstrated asymmetry, a form of the enzyme in which both subunits have pyridoxal phosphate bound to Lys-273 through a Schiff base showed biphasic reduction by borohydride in solution. Analysis of absorption spectra during reduction provided evidence of communication between the subunits. The crystal structure of the reduced form of the enzyme shows that, despite identical cofactor binding in each monomer, the structural asymmetry at residues 153–181 remains.

Channel formation by antiapoptotic protein Bcl-2

Bcl-2 is the prototypical member of a large family of apoptosis-regulating proteins, consisting of blockers and promoters of cell death. The three-dimensional structure of a Bcl-2 homologue, Bcl-XL, suggests striking similarity to the pore-forming domains of diphtheria toxin and the bacterial colicins, prompting exploration of whether Bcl-2 is capable of forming pores in lipid membranes. Using chloride efflux from KCl-loaded unilamellar lipid vesicles as an assay, purified recombinant Bcl-2 protein exhibited pore-forming activity with properties similar to those of the bacterial toxins, diphtheria toxin, and colicins, i.e., dependence on low pH and acidic lipid membranes. In contrast, a mutant of Bcl-2 lacking the two core hydrophobic α-helices (helices 5 and 6), predicted to be required for membrane insertion and channel formation, produced only nonspecific effects. In planar lipid bilayers, where detection of single channels is possible, Bcl-2 formed discrete ion-conducting, cation-selective channels, whereas the Bcl-2 (Δh5, 6) mutant did not. The most frequent conductance observed (18 ± 2 pS in 0.5 M KCl at pH 7.4) is consistent with a four-helix bundle structure arising from Bcl-2 dimers. However, larger channel conductances (41 ± 2 pS and 90 ± 10 pS) also were detected with progressively lower occurrence, implying the step-wise formation of larger oligomers of Bcl-2 in membranes. These findings thus provide biophysical evidence that Bcl-2 forms channels in lipid membranes, suggesting a novel function for this antiapoptotic protein.

Third-generation synchrotron x-ray diffraction of 6-μm crystal of raite, ≈Na3Mn3Ti0.25Si8O20(OH)2⋅10H2O, opens up new chemistry and physics of low-temperature minerals

The crystal structure of raite was solved and refined from data collected at Beamline Insertion Device 13 at the European Synchrotron Radiation Facility, using a 3 × 3 × 65 μm single crystal. The refined lattice constants of the monoclinic unit cell are a = 15.1(1) Å; b = 17.6(1) Å; c = 5.290(4) Å; β = 100.5(2)°; space group C2/m. The structure, including all reflections, refined to a final R = 0.07. Raite occurs in hyperalkaline rocks from the Kola peninsula, Russia. The structure consists of alternating layers of a hexagonal chicken-wire pattern of 6-membered SiO4 rings. Tetrahedral apices of a chain of Si six-rings, parallel to the c-axis, alternate in pointing up and down. Two six-ring Si layers are connected by edge-sharing octahedral bands of Na+ and Mn3+ also parallel to c. The band consists of the alternation of finite Mn–Mn and Na–Mn–Na chains. As a consequence of the misfit between octahedral and tetrahedral elements, regions of the Si–O layers are arched and form one-dimensional channels bounded by 12 Si tetrahedra and 2 Na octahedra. The channels along the short c-axis in raite are filled by isolated Na(OH,H2O)6 octahedra. The distorted octahedrally coordinated Ti4+ also resides in the channel and provides the weak linkage of these isolated Na octahedra and the mixed octahedral tetrahedral framework. Raite is structurally related to intersilite, palygorskite, sepiolite, and amphibole.

α1 and α2 Integrins Mediate Invasive Activity of Mouse Mammary Carcinoma Cells through Regulation of Stromelysin-1 Expression

Tumor cell invasion relies on cell migration and extracellular matrix proteolysis. We investigated the contribution of different integrins to the invasive activity of mouse mammary carcinoma cells. Antibodies against integrin subunits α6 and β1, but not against α1 and α2, inhibited cell locomotion on a reconstituted basement membrane in two-dimensional cell migration assays, whereas antibodies against β1, but not against α6 or α2, interfered with cell adhesion to basement membrane constituents. Blocking antibodies against α1 integrins impaired only cell adhesion to type IV collagen. Antibodies against α1, α2, α6, and β1, but not α5, integrin subunits reduced invasion of a reconstituted basement membrane. Integrins α1 and α2, which contributed only marginally to motility and adhesion, regulated proteinase production. Antibodies against α1 and α2, but not α6 and β1, integrin subunits inhibited both transcription and protein expression of the matrix metalloproteinase stromelysin-1. Inhibition of tumor cell invasion by antibodies against α1 and α2 was reversed by addition of recombinant stromelysin-1. In contrast, stromelysin-1 could not rescue invasion inhibited by anti-α6 antibodies. Our data indicate that α1 and α2 integrins confer invasive behavior by regulating stromelysin-1 expression, whereas α6 integrins regulate cell motility. These results provide new insights into the specific functions of integrins during tumor cell invasion.

Recognition Signal for C-Mannosylation of Trp-7 in RNase 2 Consists of Sequence Trp-x-x-Trp

C2-α-Mannosyltryptophan was discovered in human RNase 2, an enzyme that occurs in eosinophils and is involved in host defense. It represents a novel way of attaching carbohydrate to a protein in addition to the well-known N- and O-glycosylations. The reaction is specific, as in RNase 2 Trp-7, but never Trp-10, which is modified. In this article, we address which structural features provide the specificity of the reaction. Expression of chimeras of RNase 2 and nonglycosylated RNase 4 and deletion mutants in HEK293 cells identified residues 1–13 to be sufficient for C-mannosylation. Site-directed mutagenesis revealed the sequence Trp-x-x-Trp, in which the first Trp becomes mannosylated, as the specificity determinant. The Trp residue at position +3 can be replaced by Phe, which reduces the efficiency of the reaction threefold. Interpretation of the data in the context of the three-dimensional structure of RNase 2 strongly suggests that the primary, rather than the tertiary, structure forms the determinant. The sequence motif occurs in 336 mammalian proteins currently present in protein databases. Two of these proteins were analyzed protein chemically, which showed partial C-glycosylation of recombinant human interleukin 12. The frequent occurrence of the protein recognition motif suggests that C-glycosides could be part of the structure of more proteins than assumed so far.

Three-dimensional modeling of and ligand docking to vitamin D receptor ligand binding domain

The ligand binding domain of the human vitamin D receptor (VDR) was modeled based on the crystal structure of the retinoic acid receptor. The ligand binding pocket of our VDR model is spacious at the helix 11 site and confined at the β-turn site. The ligand 1α,25-dihydroxyvitamin D3 was assumed to be anchored in the ligand binding pocket with its side chain heading to helix 11 (site 2) and the A-ring toward the β-turn (site 1). Three residues forming hydrogen bonds with the functionally important 1α- and 25-hydroxyl groups of 1α,25-dihydroxyvitamin D3 were identified and confirmed by mutational analysis: the 1α-hydroxyl group is forming pincer-type hydrogen bonds with S237 and R274 and the 25-hydroxyl group is interacting with H397. Docking potential for various ligands to the VDR model was examined, and the results are in good agreement with our previous three-dimensional structure-function theory.

Three-dimensional structure of poliovirus receptor bound to poliovirus

Poliovirus initiates infection by binding to its cellular receptor (Pvr). We have studied this interaction by using cryoelectron microscopy to determine the structure, at 21-Å resolution, of poliovirus complexed with a soluble form of its receptor (sPvr). This density map aided construction of a homology-based model of sPvr and, in conjunction with the known crystal structure of the virus, allowed delineation of the binding site. The virion does not change significantly in structure on binding sPvr in short incubations at 4°C. We infer that the binding configuration visualized represents the initial interaction that is followed by structural changes in the virion as infection proceeds. sPvr is segmented into three well-defined Ig-like domains. The two domains closest to the virion (domains 1 and 2) are aligned and rigidly connected, whereas domain 3 diverges at an angle of ≈60°. Two nodules of density on domain 2 are identified as glycosylation sites. Domain 1 penetrates the “canyon” that surrounds the 5-fold protrusion on the capsid surface, and its binding site involves all three major capsid proteins. The inferred pattern of virus–sPvr interactions accounts for most mutations that affect the binding of Pvr to poliovirus.