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.

A consistent method of analysis of RC shell structures

In this paper some topics related to the design of reinforced concrete (RC) shells are addressed. The influence of the reinforcement layout on the service and ultimate behavior of the shell structure is commented. The well established methodology for dimensioning and verifying RC sections of beam structures is extended. In this way it is possible to treat within a unified procedure the design and verification of RC two dimensional structures, in particular membrane and shell structures. Realistic design situations as multiple steel farnilies and non orthogonal reinforcement layout can be handled. Finally, some examples and applications of the proposed methodology are presented.

A non-linear analysis of lying a floating pipeline on the seabed

In this article, a model for the determination of displacements, deformations and tensions of a submarine pipeline during the construction is presented. The process is carried out from an initial floating situation to the final laying position on the seabed. The existence of currents and small waves are also considered. Firstly, this technique, usually applied to polyethylene pipelines, is described in this paper as well as some real world examples, as well as the variables that can be modified to control the behavior of the structure. A detailed description of the actions in this process is considered, specially the ones related to marine environment, as Archimedes force, current and sea waves. The behavior of the pipeline is modeled with a non linear elasto dynamic model where geometric non linearities are taken into account. A 3-D beam model, without cross section deformation effects, is developed. Special care is taken in the numerical analysis, developed within an updated lagrangian formulation framework, with the sea bed contact, the follower forces due to the external water pressures and the dynamic actions. Finally, some subroutines are implemented into ANSYS to simulate the two dimensional case, where the whole construction process is achieved. With this software, a sensibility analysis of the bending moments, axial forces and stresses obtained with different values of the control variables in order to optimize the construction steps. These control variables are, the axial load in the pipe, the inundated inner length and the distance of the control barge from the coast.

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.

Two-dimensional IR correlation spectroscopy: Sequential events in the unfolding process of the λ Cro-V55C repressor protein

A question often posed in protein folding/unfolding studies is whether the process is fully cooperative or whether it contains sequential elements. To address this question, one needs tools capable of resolving different events. It seems that, at least in certain cases, two-dimensional (2D) IR correlation spectroscopy can provide answers to this question. To illustrate this point, we have turned to the Cro-V55C dimer of the λ Cro repressor, a protein known to undergo thermal unfolding in two discrete steps through a stable equilibrium intermediate. The secondary structure of this intermediate is compatible with that of a partially unfolded protein and involves a reorganization of the N terminus, whereas the antiparallel β-ribbon formed by the C-terminal part of each subunit remains largely intact. To establish whether the unfolding process involves sequential events, we have performed a 2D correlation analysis of IR spectra recorded over the temperature range of 20–95°C. The 2D IR correlation analysis indeed provides evidence for a sequential formation of the stable intermediate, which is created in three (closely related) steps. A first step entails the unfolding of the short N-terminal β-strand, followed by the unfolding of the α-helices in a second step, and the third step comprises the reorganization of the remaining β-sheet and of some unordered segments in the protein. The complete unfolding of the stable intermediate at higher temperatures also undergoes sequential events that ultimately end with the breaking of the H bonds between the two β-strands at the dimer interface.

Systematic derivation of partition functions for ligand binding to two-dimensional lattices

The Ising problem consists in finding the analytical solution of the partition function of a lattice once the interaction geometry among its elements is specified. No general analytical solution is available for this problem, except for the one-dimensional case. Using site-specific thermodynamics, it is shown that the partition function for ligand binding to a two-dimensional lattice can be obtained from those of one-dimensional lattices with known solution. The complexity of the lattice is reduced recursively by application of a contact transformation that involves a relatively small number of steps. The transformation implemented in a computer code solves the partition function of the lattice by operating on the connectivity matrix of the graph associated with it. This provides a powerful new approach to the Ising problem, and enables a systematic analysis of two-dimensional lattices that model many biologically relevant phenomena. Application of this approach to finite two-dimensional lattices with positive cooperativity indicates that the binding capacity per site diverges as Na (N = number of sites in the lattice) and experiences a phase-transition-like discontinuity in the thermodynamic limit N → ∞. The zeroes of the partition function tend to distribute on a slightly distorted unit circle in complex plane and approach the positive real axis already for a 5×5 square lattice. When the lattice has negative cooperativity, its properties mimic those of a system composed of two classes of independent sites with the apparent population of low-affinity binding sites increasing with the size of the lattice, thereby accounting for a phenomenon encountered in many ligand-receptor interactions.

Nuclear Pore Complex Number and Distribution throughout the Saccharomyces cerevisiae Cell Cycle by Three-Dimensional Reconstruction from Electron Micrographs of Nuclear Envelopes

The number of nuclear pore complexes (NPCs) in individual nuclei of the yeast Saccharomyces cerevisiae was determined by computer-aided reconstruction of entire nuclei from electron micrographs of serially sectioned cells. Nuclei of 32 haploid cells at various points in the cell cycle were modeled and found to contain between 65 and 182 NPCs. Morphological markers, such as cell shape and nuclear shape, were used to determine the cell cycle stage of the cell being examined. NPC number was correlated with cell cycle stage to reveal that the number of NPCs increases steadily, beginning in G1-phase, suggesting that NPC assembly occurs continuously throughout the cell cycle. However, the accumulation of nuclear envelope observed during the cell cycle, indicated by nuclear surface area, is not continuous at the same rate, such that the density of NPCs per unit area of nuclear envelope peaks in apparent S-phase cells. Analysis of the nuclear envelope reconstructions also revealed no preferred NPC-to-NPC distance. However, NPCs were found in large clusters over regions of the nuclear envelope. Interestingly, clusters of NPCs were most pronounced in early mitotic nuclei and were found to be associated with the spindle pole bodies, but the functional significance of this association is unknown.

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.

Analysis of receptor signaling pathways by mass spectrometry: Identification of Vav-2 as a substrate of the epidermal and platelet-derived growth factor receptors

Oligomerization of receptor protein tyrosine kinases such as the epidermal growth factor receptor (EGFR) by their cognate ligands leads to activation of the receptor. Transphosphorylation of the receptor subunits is followed by the recruitment of signaling molecules containing src homology 2 (SH2) or phosphotyrosine interaction domains (PID). Additionally, several cytoplasmic proteins that may or may not associate with the receptor undergo tyrosine phosphorylation. To identify several components of the EGFR signaling pathway in a single step, we have immunoprecipitated molecules that are tyrosine phosphorylated in response to EGF and analyzed them by one-dimensional gel electrophoresis followed by mass spectrometry. Combining matrix-assisted laser desorption/ionization (MALDI) and nanoelectrospray tandem mass spectrometry (MS/MS) led to the identification of nine signaling molecules, seven of which had previously been implicated in EGFR signaling. Several of these molecules were identified from low femtomole levels of protein loaded onto the gel. We identified Vav-2, a recently discovered guanosine nucleotide exchange factor that is expressed ubiquitously, as a substrate of the EGFR. We demonstrate that Vav-2 is phosphorylated on tyrosine residues in response to EGF and associates with the EGFR in vivo. Binding of Vav-2 to the EGFR is mediated by the SH2 domain of Vav-2. In keeping with its ubiquitous expression, Vav-2 seems to be a general signaling molecule, since it also associates with the platelet-derived growth factor (PDGF) receptor and undergoes tyrosine phosphorylation in fibroblasts upon PDGF stimulation. The strategy suggested here can be used for routine identification of downstream components of cell surface receptors in mammalian cells.

Tight frames of k-plane ridgelets and the problem of representing objects that are smooth away from d-dimensional singularities in Rn

For each pair (n, k) with 1 ≤ k < n, we construct a tight frame (ρλ : λ ∈ Λ) for L2 (Rn), which we call a frame of k-plane ridgelets. The intent is to efficiently represent functions that are smooth away from singularities along k-planes in Rn. We also develop tools to help decide whether k-plane ridgelets provide the desired efficient representation. We first construct a wavelet-like tight frame on the X-ray bundle χn,k—the fiber bundle having the Grassman manifold Gn,k of k-planes in Rn for base space, and for fibers the orthocomplements of those planes. This wavelet-like tight frame is the pushout to χn,k, via the smooth local coordinates of Gn,k, of an orthonormal basis of tensor Meyer wavelets on Euclidean space Rk(n−k) × Rn−k. We then use the X-ray isometry [Solmon, D. C. (1976) J. Math. Anal. Appl. 56, 61–83] to map this tight frame isometrically to a tight frame for L2(Rn)—the k-plane ridgelets. This construction makes analysis of a function f ∈ L2(Rn) by k-plane ridgelets identical to the analysis of the k-plane X-ray transform of f by an appropriate wavelet-like system for χn,k. As wavelets are typically effective at representing point singularities, it may be expected that these new systems will be effective at representing objects whose k-plane X-ray transform has a point singularity. Objects with discontinuities across hyperplanes are of this form, for k = n − 1.

Molecular phylogenetic analysis of evolutionary trends in stonefly wing structure and locomotor behavior

Insects in the order Plecoptera (stoneflies) use a form of two-dimensional aerodynamic locomotion called surface skimming to move across water surfaces. Because their weight is supported by water, skimmers can achieve effective aerodynamic locomotion even with small wings and weak flight muscles. These mechanical features stimulated the hypothesis that surface skimming may have been an intermediate stage in the evolution of insect flight, which has perhaps been retained in certain modern stoneflies. Here we present a phylogeny of Plecoptera based on nucleotide sequence data from the small subunit rRNA (18S) gene. By mapping locomotor behavior and wing structural data onto the phylogeny, we distinguish between the competing hypotheses that skimming is a retained ancestral trait or, alternatively, a relatively recent loss of flight. Our results show that basal stoneflies are surface skimmers, and that various forms of surface skimming are distributed widely across the plecopteran phylogeny. Stonefly wings show evolutionary trends in the number of cross veins and the thickness of the cuticle of the longitudinal veins that are consistent with elaboration and diversification of flight-related traits. These data support the hypothesis that the first stoneflies were surface skimmers, and that wing structures important for aerial flight have become elaborated and more diverse during the radiation of modern stoneflies.

Structural analysis of the binding modes of minor groove ligands comprised of disubstituted benzenes

Two-dimensional homonuclear NMR was used to characterize synthetic DNA minor groove-binding ligands in complexes with oligonucleotides containing three different A-T binding sites. The three ligands studied have a C2 axis of symmetry and have the same general structural motif of a central para-substituted benzene ring flanked by two meta-substituted rings, giving the molecules a crescent shape. As with other ligands of this shape, specificity seems to arise from a tight fit in the narrow minor groove of the preferred A-T-rich sequences. We found that these ligands slide between binding subsites, behavior attributed to the fact that all of the amide protons in the ligand backbone cannot hydrogen bond to the minor groove simultaneously.

Pseudoknots in prion protein mRNAs confirmed by comparative sequence analysis and pattern searching

The human prion gene contains five copies of a 24 nt repeat that is highly conserved among species. An analysis of folding free energies of the human prion mRNA, in particular in the repeat region, suggested biased codon selection and the presence of RNA patterns. In particular, pseudoknots, similar to the one predicted by Wills in the human prion mRNA, were identified in the repeat region of all available prion mRNAs available in GenBank, but not those of birds and the red slider turtle. An alignment of these mRNAs, which share low sequence homology, shows several co-variations that maintain the pseudoknot pattern. The presence of pseudoknots in yeast Sup35p and Rnq1 suggests acquisition in the prokaryotic era. Computer generated three-dimensional structures of the human prion pseudoknot highlight protein and RNA interaction domains, which suggest a possible effect in prion protein translation. The role of pseudoknots in prion diseases is discussed as individuals with extra copies of the 24 nt repeat develop the familial form of Creutzfeldt–Jakob disease.

Phylogenetic analysis of tmRNA genes within a bacterial subgroup reveals a specific structural signature

Bacterial tmRNA mediates a trans-translation reaction, which permits the recycling of stalled ribosomes and probably also contributes to the regulated expression of a subset of genes. Its action results in the addition of a small number of C-terminal amino acids to protein whose synthesis had stalled and these constitute a proteolytic recognition tag for the degradation of these incompletely synthesized proteins. Previous work has identified pseudoknots and stem–loops that are widely conserved in divergent bacteria. In the present work an alignment of tmRNA gene sequences within 13 β-proteobacteria reveals an additional sub-structure specific for this bacterial group. This sub-structure is in pseudoknot Pk2, and consists of one to two additional stem–loop(s) capped by stable GNRA tetraloop(s). Three-dimensional models of tmRNA pseudoknot 2 (Pk2) containing various topological versions of the additional sub-structure suggest that the sub-structures likely point away from the core of the RNA, containing both the tRNA and the mRNA domains. A putative tertiary interaction has also been identified.