On geodetic distance computations in spatial modeling

Statisticians analyzing spatial data often need to detect and model associations based upon distances on the Earth's surface. Accurate computation of distances are sought for exploratory and interpretation purposes, as well as for developing numerically stable estimation algorithms. When the data come from locations on the spherical Earth, application of Euclidean or planar metrics for computing distances is not straightforward. Yet, planar metrics are desirable because of their easier interpretability, easy availability in software packages, and well-established theoretical properties. While distance computations are indispensable in spatial modeling, their importance and impact upon statistical estimation and prediction have gone largely unaddressed. This article explores the different options in using planar metrics and investigates their impact upon spatial modeling.     

Supramolecular recognition: association of palladium molecular clefts with planar platinum complexes

The crystal structures of two new molecular recognition adducts formed between a dicationic, di-terpyridyl-Pd-Cl molecular cleft and two square planar platinum complexes are reported. In both structures, the planar platinum-containing guests are located within the molecular cleft formed by the two parallel disposed terpyridyl-Pd-Cl⁺ units of the receptor. The crystal structure of the adduct formed between the molecular cleft and a neutral platinum complex has interplanar distances between the host and guest of 3.24 Å, a distance shorter than that usually ascribed to π-stacking interaction (∼3.45 Å). The short distance is likely the result of metal-metal interaction between the host and guest. The second adduct, that between the dicationic molecular receptor and an anionic platinum complex, also bears the guest within the molecular cleft. The interplanar distances between the cationic terpyridyl-Pd-Cl units of the host and the anionic guest (3.21 and 3.29 Å) are also shorter than typical π-stacking distances but no metal-metal interaction is present. Coulombic attraction between the host and guest is believed to be responsible for the short interplanar separation. These data are discussed in relation to analogous systems that associate through π-π and metal-metal interaction.     

Channel-forming properties and structural homology of major outer membrane proteins from Pseudomonas fluorescens MFO and OE 28.3

Abstract The major outer membrane proteins (OprF) from Pseudomonas fluorescens MFO and OE 28.3 were purified by a new method involving native electrophoresis in octyl-polyoxyethylene media. Both proteins, characterized by the same size, heat-modifiability and N-terminal sequence were re-incorporated in virtually solvent-free planar lipid bilayers. They displayed very similar channel-forming properties: the major conductance level was between 250 pS and 270 pS in l M NaCl. From experiments of zero-current potential, both porins were determined weakly cation selective. Amplification by PCR and sequencing of the oprF gene of strain MFO allowed to point out 94% identity between the amino acid sequences of these two OprFs isolated from ecological niches as different as milk (strain MFO) and soil (strain OE 28.3).     

Resonance energy transfer imaging of phospholipid vesicle interaction with a planar phospholipid membrane: undulations and attachment sites in the region of calcium-mediated membrane--membrane adhesion

Membrane fusion of a phospholipid vesicle with a planar lipid bilayer is preceded by an initial prefusion stage in which a region of the vesicle membrane adheres to the planar membrane. A resonance energy transfer (RET) imaging microscope, with measured spectral transfer functions and a pair of radiometrically calibrated video cameras, was used to determine both the area of the contact region and the distances between the membranes within this zone. Large vesicles (5-20 microns diam) were labeled with the donor fluorophore coumarin- phosphatidylethanolamine (PE), while the planar membrane was labeled with the acceptor rhodamine-PE. The donor was excited with 390 nm light, and separate images of donor and acceptor emission were formed by the microscope. Distances between the membranes at each location in the image were determined from the RET rate constant (kt) computed from the acceptor:donor emission intensity ratio. In the absence of an osmotic gradient, the vesicles stably adhered to the planar membrane, and the dyes did not migrate between membranes. The region of contact was detected as an area of planar membrane, coincident with the vesicle image, over which rhodamine fluorescence was sensitized by RET. The total area of the contact region depended biphasically on the Ca2+ concentration, but the distance between the bilayers in this zone decreased with increasing [Ca2+]. The changes in area and separation were probably related to divalent cation effects on electrostatic screening and binding to charged membranes. At each [Ca2+], the intermembrane separation varied between 1 and 6 nm within each contact region, indicating membrane undulation prior to adhesion. Intermembrane separation distances < or = 2 nm were localized to discrete sites that formed in an ordered arrangement throughout the contact region. The area of the contact region occupied by these punctate attachment sites was increased at high [Ca2+]. Membrane fusion may be initiated at these sites of closest membrane apposition.     

Vectorial information for Arabidopsis planar polarity is mediated by combined AUX1, EIN2, and GNOM activity

Cell polarity is commonly coordinated within the plane of a single tissue layer (planar polarity), and hair positioning has been exploited as a simple marker for planar polarization of animal epithelia . The root epidermis of the plant Arabidopsis similarly reveals planar polarity of hair localization close to root tip-oriented (basal) ends of hair-forming cells . Hair position is directed toward a concentration maximum of the hormone auxin in the root tip , but mechanisms driving this plant-specific planar polarity remain elusive. Here, we report that combinatorial action of the auxin influx carrier AUX1, ETHYLENE-INSENSITIVE2 (EIN2) , and GNOM genes mediates the vector for coordinate hair positioning. In aux1;ein2;gnom eb triple mutant roots, hairs display axial (apical or basal) instead of coordinate polar (basal) position, and recruitment of Rho-of-Plant (ROP) GTPases to the hair initiation site reveals the same polar-to-axial switch. The auxin concentration gradient is virtually abolished in aux1;ein2;gnom eb roots, where locally applied auxin can coordinate hair positioning. Moreover, auxin overproduction in sectors of wild-type roots enhances planar ROP and hair polarity over long and short distances. Hence, auxin may provide vectorial information for planar polarity that requires combinatorial AUX1, EIN2, and GNOM activity upstream of ROP positioning.     

Culture of Azolla filiculoides in artificial conditions

Abstract

Azolla filiculoides showed a planar development in four culture media, but with overlapping of sporophytes after 28 days, and curled roots in all cases except for IRRI2. The difference in biomass between the media IRRI2 and IRRI1‐Fe10x was statistically significant at Days 14, 21 and 28 by ANOVA. Medium IRRI2 gave the highest duplication time.     

CH...Metal(II) axial interaction in planar complexes (metal=Cu, Pd) and implications for possible environmental effects of alkyl groups at biological copper sites

Intramolecular M(II)...H-C interactions (M(II)=Cu(II), Pd(II)) involving a side chain alkyl group of planar d8 and d9 metal complexes of the N-alkyl (R) derivatives of N,N-bis(2-pyridylmethyl)amine with an N3Cl donor set were established by structural and spectroscopic methods. The methyl group from the branched alkyl group (R=2,2-dimethylpropyl and 2-methylbutyl) axially interacts with the metal ion with the M...C and M...H distances of 3.056(3)-3.352(9) and 2.317(1)-2.606(1) A, respectively, and the M-H-C angles of 122.4-162.3 degrees . The Cu(II) complexes showing the interaction have a higher redox potential as compared with those without it, and the (1)H NMR signals of the interacting methyl group in Pd(II) complexes shifted downfield relative to the ligand signals. Dependence of the downshift values on the dielectric constants of the solvents used indicated that the M(II)...H-C interaction is mainly electrostatic in nature and may be regarded as a weak hydrogen bond. Implications for possible environmental effects of the leucine alkyl group at the type 1 Cu site of fungal laccase are also discussed.     

Spatial arrangement of rhodopsin in retinal rod outer segment membranes studied by spin-labeling and pulsed electron double resonance

We have determined the spatial arrangement of rhodopsin in the retinal rod outer segment (ROS) membrane by measuring the distances between rhodopsin molecules in which native cysteines were spin-labeled at ～1.0mol/mol rhodopsin. The echo modulation decay of pulsed electron double resonance (PELDOR) from spin-labeled ROS curved slightly with strong background decay. This indicated that the rhodopsin was densely packed in the retina and that the rhodopsin molecules were not aligned well. The curve was simulated by a model in which rhodopsin is distributed randomly as monomers in a planar membrane.     

Miniaturized Supercapacitors: Focused Ion Beam Reduced Graphene Oxide Supercapacitors with Enhanced Performance Metrics

Miniaturization of energy storage devices with enhanced performance metrics can reduce the footprint of microdevices being used in our daily life. Micro‐­supercapacitor architectures with planar geometry provides several advantages, such as, the ability to control and reduce the distances ions travel between two electrodes, easy integration to microdevices, and offer the potential of being extended into 3D without compromising the interelectrode distances. Here, focused ion beam (FIB) technology is used to directly write miniaturized planar electrode systems of reduced graphene oxide (FIB‐rGO) on films of graphene oxide. Using optimized ion beam irradiation, interdigitated FIB‐rGO electrode designs with 40 μm long and 3.5 μm wide fingers with ultrasmall interelectrode spacing of 1 μm demonstrate a large capacitance (102 mF cm^?2), ultrasmall time response (0.03 ms), low equivalent series resistance (0.35 mΩ cm²), and retain 95% of the capacitance after 1000 cycles at an ultrahigh current density of 45 mA cm^?2. These performance metrics show remarkable improvements on several counts of supercapacitor performance over existing reports due to the miniaturized electrode dimensions and minimal damage to the graphene sheets. It is believed that these results can provide avenues for large‐scale fabrication of arrayed, planar, high‐performance micro‐supercapacitors with a small environmental footprint.     

The vacuole system is a significant intracellular pathway for longitudinal solute transport in basidiomycete fungi

Mycelial fungi have a growth form which is unique among multicellular organisms. The data presented here suggest that they have developed a unique solution to internal solute translocation involving a complex, extended vacuole. In all filamentous fungi examined, this extended vacuole forms an interconnected network, dynamically linked by tubules, which has been hypothesized to act as an internal distribution system. We have tested this hypothesis directly by quantifying solute movement within the organelle by photobleaching a fluorescent vacuolar marker. Predictive simulation models were then used to determine the transport characteristics over extended length scales. This modeling showed that the vacuolar organelle forms a functionally important, bidirectional diffusive transport pathway over distances of millimeters to centimeters. Flux through the pathway is regulated by the dynamic tubular connections involving homotypic fusion and fission. There is also a strongly predicted interaction among vacuolar organization, predicted diffusion transport distances, and the architecture of the branching colony margin.     

The nature and extent of histopathologic injury in human avulsed arteries and veins and in experimentally avulsed monkey arteries

To determine the end point of histopathologic damage in avulsed arteries, the forearm arteries of five monkeys being sacrificed were avulsed longitudinally and samples of proximal and distal arteries prepared for light microscopy and transmission and scanning electron microscopy. A severe and consistent circumferential skip lesion was found on the luminal surface involving the intima and media. In 30 percent of vessels, histopathologic damage extended more than 3.0 cm from the rupture point. Similar circumferential tears occurred on the luminal surface of resected human avulsed arteries collected at the time of replantation surgery. No consistent lesions were noted in resected veins from human avulsed amputations. It is possible that in the human artery (as in the monkey) circumferential lesions frequently extend many centimeters from the rupture point and therefore beyond resection distances. Lesions present in the vessel after resection and microsurgical repair might be the site of thrombosis and subsequent occlusion.     

TRANSLATIONAL MOBILITY OF THE MEMBRANE INTERCALATED PARTICLES OF HUMAN ERYTHROCYTE GHOSTS : pH-Dependent, Reversible Aggregation

This paper demonstrates the translational movement along the plane of the human erythrocyte ghost of the membrane particles exposed by freeze-fracture. The membrane particles can be aggregated by incubation of the ghosts in media with a pH in the vicinity of 5 5 or 3 5. The particles are disaggregated in neutral and alkaline media (pH 9 5) and also at pH 4.5 Aggregation of the particles at pH 5.5 is reversible, prevented by prefixation in glutaraldehyde and by media of high ionic strength. Particle aggregation occurs within 2–4 min. These results are consistent with the concept that the erythrocyte ghost membrane is a planar fluid domain formed by a bilayer membrane continuum which is interrupted by localized, yet mobile, proteic intercalations.     

Synthesis and structure of μ-3,3′-[ 1,2-ethanediyl-bis(nitrilomethylidyne)-bis(2-hydroxybenzoato)] aquadicopper(II) hydrate

The complex μ-3,3′-[1,2-ethanediyl-bis(nitrilome- thylidyne)-bis(2-hydroxybenzoato)] aquadicopper(II) hydrate, C₁₈H₁₆N₂O₈Cu₂, was isolated from an attempted preparation of a copper lanthanum binuclear complex. The dark purple crystals are monoclinic, space group P2₁/n, with 4 molecules per unit cell; dimensions a = 13.961(5), b = tl.787(3), c = 11.622(3) Å and β = 113.09(2)°. The final R was 0.046 for the 2062 reflections used in the analysis. The Cu atom in the N₂O₂ cavity is five coordinate with CuN distances of 1.879 and 1.880 Å and CuO distances of 1.898 and 1.900 Å. A water molecule at 2.557 Å completes the square pyramidal arrangement. The second Cu in the O₄ cavity is square planar, with CuO distances to the bridging oxygens of 1.914 and 1.909 Å and to the carboxy oxygens of 1.871 and 1.882 Å. A survey of copper complexes in a square planar N₂O₂ arrangement has led to the equation δCu from the N₂O₂ plane = 0.822 – 0.275 (CuO axial distance) with a correlation coefficient of 0.98 for the 12 structures in which the Cu atom is bonded to a fifth oxygen atom. A model for the transition from square planar to square pyramidal geometry is proposed.     

Characterization of a mononuclear copper carboxylate complex: Bis(acetylsalicylato)bis(pyridine)copper(II)

The preparation, spectral properties, and crystal structure of a mononuclear copper(II) complex of acetylsalicylate and pyridine are reported. The complex exists as bis(acetylsalicylato)bis(pyridine)copper(II) both in the solid state and in chloroform solution. The crystal is monoclinic, space group P2₁/n, with a = 17.823(5), b = 10.903(4), c = 6.598(2) Å, β = 95.74(2)°. The final refinement used 1472 observed reflections and gave an R of 0.046. The copper atom is surrounded by four atoms in a trans square planar arrangement with two short CuO distances of 1.949(3) Å and two CuN distances of 2.003(4) Å. Two longer CuO distances of 2.623(3) Å are made with the remaining oxygen atoms of the aspirin carboxylate groups.     

X-ray absorption fine-structure spectroscopy studies of Fe sites in natural human neuromelanin and synthetic analogues.

X-ray absorption fine-structure spectroscopy is used to study the local environment of the iron site in natural (human) neuromelanin extracted from substantia nigra tissue and in various synthetic neuromelanins. All the materials show Fe centered in a nearest neighbor sixfold (distorted) oxygen octahedron; the Fe-O distances, while slightly different in the natural and synthetic neuromelanin, are both approximately 2.0 A. Appreciable differences arise, however, in the second (and higher) coordination shells. In this case the synthetic melanin has the four planar oxygens bound to carbon rings with Fe-C distances of approximately 2.82 and 4.13 A; the human sample does not show the 2.82 A link but instead indicates a double shell at approximately 3.45 and 3.78 A.     

Planar polarity and actin dynamics in the epidermis of Drosophila

Dorsal closure is a morphogenetic process involving the coordinated convergence of two epithelial sheets to enclose the Drosophila melanogaster embryo. Specialized populations of cells at the edges of each epithelial sheet, the dorsal-most epidermal cells, emit actin-based processes that are essential for the proper enclosure of the embryo. Here we show that actin dynamics at the leading edge is preceded by a planar polarization of the dorsal-most epidermal cells associated with a reorganization of the cytoskeleton. An important consequence of this planar polarization is the formation of actin-nucleating centres at the leading edge, which are important in the dynamics of actin. We show that Wingless (Wg) signalling and Jun amino-terminal kinase (JNK) signalling have overlapping but different roles in these events.     

Effects of Experimentally Achievable Improvements in the Quality of NMR Distance Constraints on the Accuracy of Calculated Protein Structures

New methods for collecting cross-relaxation data from proteins and nucleic acids make it possible to improve the accuracy and precision of interproton distance measurements used as input for NMR solution structure determinations. It thus is of interest to determine whether such experimentally achievable improvements in input distance constraints have significant effects on the precision and accuracy of the resulting structures. To answer this question, we have turned to a computational procedure involving the use of data simulated from a known structure, in order to allow unambiguous assessments of accuracy. The approach to improved distances evaluated here is that afforded by magnetization exchange network editing (MENE); MENE pulse sequences break the network of cross-relaxation interactions into regions that are manipulated so as to defeat certain spin-diffusion terms. A target structure was prepared from the X-ray structure of a small protein, turkey ovomucoid third domain (OMTKY3). A normal NOESY spectrum and two varieties of MENE spectra, BD-NOESY and CBD-NOESY, were simulated by means of complete relaxation matrix analysis. These results were used to create different input data sets with the same number of constraints (perfectly accurate distances derived from the target structure, more accurate distances derived from the MENE simulations, and less accurate distances derived from the NOESY simulation), and these, interpreted at different levels of precision, were used as input for solution structure calculations. The results showed that the use of more precise input data measurably improves the local precision and accuracy of calculated structures, but only if the more precise data include the actual target distance. Incorporation of the experimentally achievable, accurate distances with higher precision afforded by the MENE pulse sequences into the set of input distances was found to improve the accuracy of the resulting structures, particularly in terms of side-chain conformation.     

Dispersal of potato tuber moth estimated using field application of Bt for mark-capture techniques

A new mark-capture technique involving field applications of Bacillus thuringiensis Berliner (Bt) to study the dispersal of potato tuber moth, Phthorimaea operculella (Zeller) (Lepidoptera: Gelechiidae), was investigated as a tool to improve information on the potential impact of insect pest dispersal on crop infestation and insecticide resistance. The acquisition and persistence of Bt on moths were characterized and potential contamination of moths from naturally occurring Bts was examined. This mark-capture technique was developed to mark larger numbers of moths than had been previously achieved with laboratory marking using fluorescent dyes in mark-release-recapture experiments. Applications of commercial preparations of Bt to 0.3 and 1.0 ha potato fields were estimated to have marked ca. 50 000 moths in each experiment. Pheromone trap catches of potato tuber moths in the Bt-sprayed fields and in potato fields at distances of ca. 80, 200, 350, and 750 m were assayed for the Bt marker using selective microbiological media and identification of characteristic Bt crystal inclusions. Marking rates of moths were 78–100% in the sprayed fields and, compared with our previous mark-release-recapture studies, marking at ca. 200 m was increased by 15–18-fold to >3.0 moths per trap. This capture rate allowed the calculation of a dispersal curve that improved the reliability of estimates of movement at farm-scale distances. These estimates indicated that 10% of the population dispersed to 240 m in 3 days, and suggested that moths can potentially disperse throughout a typical potato-growing area in one growing season. This level of dispersal has implications for the spread and management of potato tuber moth populations, especially if insecticide resistance is present.     

Assessing phylogenetic signal with measurement error: a comparison of mantel tests, blomberg et Al.'s k, and phylogenetic distograms

In macroevolutionary studies, different approaches are commonly used to measure phylogenetic signal-the tendency of related taxa to resemble one another-including the K statistic and the Mantel test. The latter was recently criticized for lacking statistical power. Using new simulations, we show that the power of the Mantel test depends on the metrics used to define trait distances and phylogenetic distances between species. Increasing power is obtained by lowering variance and increasing negative skewness in interspecific distances, as obtained using Euclidean trait distances and the complement of Abouheif proximity as a phylogenetic distance. We show realistic situations involving "measurement error" due to intraspecific variability where the Mantel test is more powerful to detect a phylogenetic signal than a permutation test based on the K statistic. We highlight limitations of the K-statistic (univariate measure) and show that its application should take into account measurement errors using repeated measures per species to avoid estimation bias. Finally, we argue that phylogenetic distograms representing Euclidean trait distance as a function of the square root of patristic distance provide an insightful representation of the phylogenetic signal that can be used to assess both the impact of measurement error and the departure from a Brownian evolution model.