Two-dimensional direct rainfall hydraulic models applied to direct calculation of hydrologic events in dams to prevent overtopping

One of the main concerns when conducting a dam test is the acute determination of the hydrograph for a specific flood event. The use of 2D direct rainfall hydraulic mathematical models on a finite elements mesh, combined with the efficiency of vector calculus that provides CUDA (Compute Unified Device Architecture) technology, enables nowadays the simulation of complex hydrological models without the need for terrain subbasin and transit splitting (as in HEC-HMS). Both the Spanish PNOA (National Plan of Aereal Orthophotography) Digital Terrain Model GRID with a 5 x 5 m accuracy and the CORINE GIS Land Cover (Coordination of INformation of the Environment) that allows assessment of the ground roughness, provide enough data to easily build these kind of models

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 freezing in the liquid–vapor interface of a dilute Pb:Ga alloy

We report the results of x-ray reflectivity and grazing incidence x-ray diffraction studies of the liquid–vapor interface of a dilute alloy of Pb in Ga over the temperature range of 23–76°C. Our data show that the liquid–vapor interface of this alloy is stratified for several atomic diameters into the bulk liquid and that a monolayer of Pb forms the outermost stratum of the interface. Over the temperature range of 23–56°C, the monolayer of Pb is in an ordered hexagonal phase. At about 58°C, this monolayer undergoes a first-order transition to a hexatic phase, which remains stable to 76°C. An analogy between the observed transition and the first-order melting transition in a one-component classical plasma is suggested.

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.

Linking genome and proteome by mass spectrometry: Large-scale identification of yeast proteins from two dimensional gels

The function of many of the uncharacterized open reading frames discovered by genomic sequencing can be determined at the level of expressed gene products, the proteome. However, identifying the cognate gene from minute amounts of protein has been one of the major problems in molecular biology. Using yeast as an example, we demonstrate here that mass spectrometric protein identification is a general solution to this problem given a completely sequenced genome. As a first screen, our strategy uses automated laser desorption ionization mass spectrometry of the peptide mixtures produced by in-gel tryptic digestion of a protein. Up to 90% of proteins are identified by searching sequence data bases by lists of peptide masses obtained with high accuracy. The remaining proteins are identified by partially sequencing several peptides of the unseparated mixture by nanoelectrospray tandem mass spectrometry followed by data base searching with multiple peptide sequence tags. In blind trials, the method led to unambiguous identification in all cases. In the largest individual protein identification project to date, a total of 150 gel spots—many of them at subpicomole amounts—were successfully analyzed, greatly enlarging a yeast two-dimensional gel data base. More than 32 proteins were novel and matched to previously uncharacterized open reading frames in the yeast genome. This study establishes that mass spectrometry provides the required throughput, the certainty of identification, and the general applicability to serve as the method of choice to connect genome and proteome.

The two-dimensional IR nonlinear spectroscopy of a cyclic penta-peptide in relation to its three-dimensional structure

A form of two-dimensional (2D) vibrational spectroscopy, which uses two ultrafast IR laser pulses, is used to examine the structure of a cyclic penta-peptide in solution. Spectrally resolved cross peaks occur in the off-diagonal region of the 2D IR spectrum of the amide I region, analogous to those in 2D NMR spectroscopy. These cross peaks measure the coupling between the different amide groups in the structure. Their intensities and polarizations relate directly to the three-dimensional structure of the peptide. With the help of a model coupling Hamiltonian, supplemented by density functional calculations, the spectra of this penta-peptide can be regenerated from the known solution phase structure. This 2D-IR measurement, with an intrinsic time resolution of less than 1 ps, could be used in all time regimes of interest in biology.

Field theory in superfluid 3He: What are the lessons for particle physics, gravity, and high-temperature superconductivity?

There are several classes of homogeneous Fermi systems that are characterized by the topology of the energy spectrum of fermionic quasiparticles: (i) gapless systems with a Fermi surface, (ii) systems with a gap in their spectrum, (iii) gapless systems with topologically stable point nodes (Fermi points), and (iv) gapless systems with topologically unstable lines of nodes (Fermi lines). Superfluid 3He-A and electroweak vacuum belong to the universality class 3. The fermionic quasiparticles (particles) in this class are chiral: they are left-handed or right-handed. The collective bosonic modes of systems of class 3 are the effective gauge and gravitational fields. The great advantage of superfluid 3He-A is that we can perform experiments by using this condensed matter and thereby simulate many phenomena in high energy physics, including axial anomaly, baryoproduction, and magnetogenesis. 3He-A textures induce a nontrivial effective metrics of the space, where the free quasiparticles move along geodesics. With 3He-A one can simulate event horizons, Hawking radiation, rotating vacuum, etc. High-temperature superconductors are believed to belong to class 4. They have gapless fermionic quasiparticles with a “relativistic” spectrum close to gap nodes, which allows application of ideas developed for superfluid 3He-A.

Two-dimensional infrared spectroscopy of peptides by phase-controlled femtosecond vibrational photon echoes

Two-dimensional infrared spectra of peptides are introduced that are the direct analogues of two- and three-pulse multiple quantum NMR. Phase matching and heterodyning are used to isolate the phase and amplitudes of the electric fields of vibrational photon echoes as a function of multiple pulse delays. Structural information is made available on the time scale of a few picoseconds. Line narrowed spectra of acyl-proline-NH2 and cross peaks implying the coupling between its amide-I modes are obtained, as are the phases of the various contributions to the signals. Solvent-sensitive structural differences are seen for the dipeptide. The methods show great promise to measure structure changes in biology on a wide range of time scales.

Two-dimensional confocal images of organization, density, and gating of focal Ca2+ release sites in rat cardiac myocytes

In cardiac myocytes Ca2+ cross-signaling between Ca2+ channels and ryanodine receptors takes place by exchange of Ca2+ signals in microdomains surrounding dyadic junctions, allowing first the activation and then the inactivation of the two Ca2+-transporting proteins. To explore the details of Ca2+ signaling between the two sets of receptors we measured the two-dimensional cellular distribution of Ca2+ at 240 Hz by using a novel confocal imaging technique. Ca2+ channel-triggered Ca2+ transients could be resolved into dynamic “Ca2+ stripes” composed of hundreds of discrete focal Ca2+ releases, appearing as bright fluorescence spots (radius ≅ 0.5 μm) at reproducible sites, which often coincided with t-tubules as visualized with fluorescent staining of the cell membrane. Focal Ca2+ releases triggered stochastically by Ca2+ current (ICa) changed little in duration (≅7 ms) and size (≅100,000 Ca ions) between −40 and +60 mV, but their frequency of activation and first latency mirrored the kinetics and voltage dependence of ICa. The resolution of 0.95 ± 0.13 reproducible focal Ca2+ release sites per μm3 in highly Ca2+-buffered cells, where diffusion of Ca2+ is limited to 50 nm, suggests the presence of about one independent, functional Ca2+ release site per half sarcomere. The density and distribution of Ca2+ release sites suggest they correspond to dyadic junctions. The abrupt onset and termination of focal Ca2+ releases indicate that the cluster of ryanodine receptors in individual dyadic junctions may operate in a coordinated fashion.

Behavior of several two-dimensional fluid equations in singular scenarios

We give conditions that rule out formation of sharp fronts for certain two-dimensional incompressible flows. We show that a necessary condition of having a sharp front is that the flow has to have uncontrolled velocity growth. In the case of the quasi-geostrophic equation and two-dimensional Euler equation, we obtain estimates on the formation of semi-uniform fronts.

Two-dimensional protein crystallization via metal-ion coordination by naturally occurring surface histidines.

A powerful and potentially general approach to the targeting and crystallization of proteins on lipid interfaces through coordination of surface histidine residues to lipid-chelated divalent metal ions is presented. This approach, which should be applicable to the crystallization of a wide range of naturally occurring or engineered proteins, is illustrated here by the crystallization of streptavidin on a monolayer of an iminodiacetate-Cu(II) lipid spread at the air-water interface. This method allows control of the protein orientation at interfaces, which is significant for the facile production of highly ordered protein arrays and for electron density mapping in structural analysis of two-dimensional crystals. Binding of native streptavidin to the iminodiacetate-Cu lipids occurs via His-87, located on the protein surface near the biotin binding pocket. The two-dimensional streptavidin crystals show a previously undescribed microscopic shape that differs from that of crystals formed beneath biotinylated lipids.

Rapid mass spectrometric peptide sequencing and mass matching for characterization of human melanoma proteins isolated by two-dimensional PAGE.

We report a general mass spectrometric approach for the rapid identification and characterization of proteins isolated by preparative two-dimensional polyacrylamide gel electrophoresis. This method possesses the inherent power to detect and structurally characterize covalent modifications. Absolute sensitivities of matrix-assisted laser desorption ionization and high-energy collision-induced dissociation tandem mass spectrometry are exploited to determine the mass and sequence of subpicomole sample quantities of tryptic peptides. These data permit mass matching and sequence homology searching of computerized peptide mass and protein sequence data bases for known proteins and design of oligonucleotide probes for cloning unknown proteins. We have identified 11 proteins in lysates of human A375 melanoma cells, including: alpha-enolase, cytokeratin, stathmin, protein disulfide isomerase, tropomyosin, Cu/Zn superoxide dismutase, nucleoside diphosphate kinase A, galaptin, and triosephosphate isomerase. We have characterized several posttranslational modifications and chemical modifications that may result from electrophoresis or subsequent sample processing steps. Detection of comigrating and covalently modified proteins illustrates the necessity of peptide sequencing and the advantages of tandem mass spectrometry to reliably and unambiguously establish the identity of each protein. This technology paves the way for studies of cell-type dependent gene expression and studies of large suites of cellular proteins with unprecedented speed and rigor to provide information complementary to the ongoing Human Genome Project.