Multiple loop structures critical for ligand binding of the integrin α4 subunit in the upper face of the β-propeller mode 1

A non-I-domain integrin, α4β1, recognizes vascular cell adhesion molecule 1 (VCAM-1) and the IIICS portion of fibronectin. To localize regions of α4 critical for ligand binding, we swapped several predicted loops within or near the putative ligand-binding site of α4 (which spans repeats 2–5 of the seven N-terminal repeats) with the corresponding regions of α5. Swapping residues 112–131 in repeat 2, or residues 237–247 in repeat 4, completely blocked adhesion to immobilized VCAM-1 and connecting segment 1 (CS-1) peptide. However, swapping residues 40–52 in repeat 1, residues 151–164 in repeat 3, or residues 282–288 (which contain a putative cation binding motif) in repeat 5 did not affect or only slightly reduced adhesion to these ligands. The binding of several function-blocking antibodies is blocked by swapping residues 112–131, 151–164, and 186–191 (which contain previously identified residues critical for ligand binding, Tyr-187 and Gly-190). These results are consistent with the recently published β-propeller folding model of the integrin α4 subunit [Springer, T. A. (1997) Proc. Natl. Acad. Sci. USA 94, 65–72], in which seven four-stranded β-sheets are arranged in a torus around a pseudosymmetric axis. The regions of α4 critical for ligand binding are adjacent to each other and are located in the upper face, the predicted ligand-binding site, of the β-propeller model, although they are not adjacent in the primary structure.

Equilibrium distributions of topological states in circular DNA: Interplay of supercoiling and knotting

Two variables define the topological state of closed double-stranded DNA: the knot type, K, and ΔLk, the linking number difference from relaxed DNA. The equilibrium distribution of probabilities of these states, P(ΔLk, K), is related to two conditional distributions: P(ΔLk|K), the distribution of ΔLk for a particular K, and P(K|ΔLk) and also to two simple distributions: P(ΔLk), the distribution of ΔLk irrespective of K, and P(K). We explored the relationships between these distributions. P(ΔLk, K), P(ΔLk), and P(K|ΔLk) were calculated from the simulated distributions of P(ΔLk|K) and of P(K). The calculated distributions agreed with previous experimental and theoretical results and greatly advanced on them. Our major focus was on P(K|ΔLk), the distribution of knot types for a particular value of ΔLk, which had not been evaluated previously. We found that unknotted circular DNA is not the most probable state beyond small values of ΔLk. Highly chiral knotted DNA has a lower free energy because it has less torsional deformation. Surprisingly, even at |ΔLk| > 12, only one or two knot types dominate the P(K|ΔLk) distribution despite the huge number of knots of comparable complexity. A large fraction of the knots found belong to the small family of torus knots. The relationship between supercoiling and knotting in vivo is discussed.

Occurrence of two somatostatin variants in the frog brain: characterization of the cDNAs, distribution of the mRNAs, and receptor-binding affinities of the peptides.

In tetrapods, only one gene encoding a somatostatin precursor has been identified so far. The present study reports the characterization of the cDNA clones that encode two distinct somatostatin precursors in the brain of the frog Rana ridibunda. The cDNAs were isolated by using degenerate oligonucleotides based on the sequence of the central region of somatostatin to screen a frog brain cDNA library. One of the cDNAs encodes a 115-amino acid protein (prepro-somatostatin-14; PSS1) that exhibits a high degree of structural similarity with the mammalian somatostatin precursor. The other cDNA encodes a 103-amino acid protein (prepro-[Pro2, Met13]somatostatin-14; PSS2) that contains the sequence of the somatostatin analog (peptide SS2) at its C terminus, but does not exhibit appreciable sequence similarity with PSS1 in the remaining region. In situ hybridization studies indicate differential expression of the PSS1 and PSS2 genes in the septum, the lateral part of the pallium, the amygdaloid complex, the posterior nuclei of the thalamus, the ventral hypothalamic nucleus, the torus semicircularis and the optic tectum. The somatostatin variant SS2 was significantly more potent (4-6 fold) than somatostatin itself in displacing [125I-Tyr0, D-Trp8] somatostatin-14 from its specific binding sites. The present study indicates that the two somatostatin variants could exert different functions in the frog brain and pituitary. These data also suggest that distinct genes encoding somatostatin variants may be expressed in the brain of other tetrapods.

Active site topology and reaction mechanism of GTP cyclohydrolase I.

GTP cyclohydrolase I of Escherichia coli is a torus-shaped homodecamer with D5 symmetry and catalyzes a complex ring expansion reaction conducive to the formation of dihydroneopterin triphosphate from GTP. The x-ray structure of a complex of the enzyme with the substrate analog, dGTP, bound at the active site was determined at a resolution of 3 A. In the decamer, 10 equivalent active sites are present, each of which contains a 10-A deep pocket formed by surface areas of 3 adjacent subunits. The substrate forms a complex hydrogen bond network with the protein. Active site residues were modified by site-directed mutagenesis, and enzyme activities of the mutant proteins were measured. On this basis, a mechanism of the enzyme-catalyzed reaction is proposed. Cleavage of the imidazole ring is initiated by protonation of N7 by His-179 followed by the attack of water at C8 of the purine system. Cystine Cys-110 Cys-181 may be involved in this reaction step. Opening of the imidazole ring may be in concert with cleavage of the furanose ring to generate a Schiff's base from the glycoside. The gamma-phosphate of GTP may be involved in the subsequent Amadori rearrangement of the carbohydrate side chain by activating the hydroxyl group of Ser-135.

The case for unification.

I investigate the issue of whether the various subclasses of radio-loud galaxies are intrinsically the same but have been classified differently mainly due to their being viewed from different directions. Evidence for the two key elements of this popular version of the "unified scheme (US)," relativistic jets and nuclear tori, is updated. The case for the torus opening angle increasing with the radio luminosity of the active galactic nucleus (AGN) is freshly argued. Radio-loud AGN are particularly suited for testing the US, since their structures and polarization properties on different scales, as well as their overall radio sizes, provide useful statistical indicators of the relative orientations of their various subclasses. I summarize recent attempts to bring under a single conceptual framework the USs developed for radio-moderate [Fanaroff-Riley type I (FRI)] and radio-powerful (FRII) AGN. By focusing on FRII radio sources, I critically examine the recent claims of conflict with the US, based on the statistics of radio-size measurements for large, presumably orientation-independent, samples with essentially complete optical identifications. Possible ways of reconciling these results, and also the ones based on very-long-baseline radio interferometry polarimetric observations, with the US are pointed out. By incorporating a highly plausible temporal evolution of radio source properties into the US, I outline a scenario that allows the median linear size of quasars to approach, or even exceed, that of radio galaxies, as samples with decreasing radio luminosity are observed. Thus, even though a number of issues remain to be fully resolved, the scope of unified models continues to expand.

Difficulties with unification.

The difficulties perceived in the orientation-based unified scheme models, when confronted with the observational data, are pointed out. It is shown that in meter-wavelength selected samples, which presumably are largely free of an orientation bias, the observed numbers of quasars versus radio galaxies are not in accordance with the expectations of the unified scheme models. The observed number ratios seem to depend heavily on the redshift, fluxdensity, or radio luminosity levels of the selected sample. This cannot be explained within the simple orientation-based unified scheme with a fixed average value of the half-opening angle (c approximately 45 degrees ) for the obscuring torus that supposedly surrounds the nuclear optical continuum and the broad-line regions. Further, the large differences seen between radio galaxies and quasars in their size distributions in the luminosity-redshift plane could not be accommodated even if I were to postulate some suitable cosmological evolution of the opening angle of the torus. Some further implications of these observational results for the recently proposed modified versions of the unified scheme model are pointed out.

The supergiant B[e] star LHA 115-S 18 - binary and/or luminous blue variable?

Context. The mechanism by which supergiant (sg)B[e] stars support cool, dense dusty discs/tori and their physical relationship with other evolved, massive stars such as luminous blue variables is uncertain. Aims. In order to investigate both issues we have analysed the long term behaviour of the canonical sgB[e] star LHA 115-S 18. Methods. We employed the OGLE II-IV lightcurve to search for (a-)periodic variability and supplemented these data with new and historic spectroscopy. Results. In contrast to historical expectations for sgB[e] stars, S18 is both photometrically and spectroscopically highly variable. The lightcurve is characterised by rapid aperiodic ` aring' throughout the 16 years of observations. Changes in the high excitation emission line component of the spectrum imply evolution in the stellar temperature - as expected for luminous blue variables - although somewhat surprisingly, spectroscopic and photometric variability appears not to be correlated. Characterised by emission in low excitation metallic species, the cool circumstellar torus appears largely unaffected by this behaviour. Finally, in conjunction with intense, highly variable He ii emission, X-ray emission implies the presence of an unseen binary companion. Conclusions. S18 provides observational support for the putative physical association of (a subset of) sgB[e] stars and luminous blue variables. Given the nature of the circumstellar environment of S18 and that luminous blue variables have been suggested as SN progenitors, it is tempting to draw a parallel to the progenitors of SN1987A and SN2009ip. Moreover the likely binary nature of S18 strengthens the possibility that the dusty discs/tori that characterise sgB[e] stars are the result of binary-driven mass-loss; consequently such stars may provide a window on the short lived phase of mass-transfer in massive compact binaries.

On the chaotic rotation of a liquid-filled gyrostat via the Melnikov-Holmes-Marsden integral

The non-linear motions of a gyrostat with an axisymmetrical, fluid-filled cavity are investigated. The cavity is considered to be completely filled with an ideal incompressible liquid performing uniform rotational motion. Helmholtz theorem, Euler's angular momentum theorem and Poisson equations are used to develop the disturbed Hamiltonian equations of the motions of the liquid-filled gyrostat subjected to small perturbing moments. The equations are established in terms of a set of canonical variables comprised of Euler angles and the conjugate angular momenta in order to facilitate the application of the Melnikov-Holmes-Marsden (MHM) method to investigate homoclinic/heteroclinic transversal intersections. In such a way, a criterion for the onset of chaotic oscillations is formulated for liquid-filled gyrostats with ellipsoidal and torus-shaped cavities and the results are confirmed via numerical simulations. (c) 2006 Elsevier Ltd. All rights reserved.

Canonical solution groups of a homomorphism : manipulator kinematics, nonparametric regression and distributed object systems

The kinematic mapping of a rigid open-link manipulator is a homomorphism between Lie groups. The homomorphisrn has solution groups that act on an inverse kinematic solution element. A canonical representation of solution group operators that act on a solution element of three and seven degree-of-freedom (do!) dextrous manipulators is determined by geometric analysis. Seven canonical solution groups are determined for the seven do! Robotics Research K-1207 and Hollerbach arms. The solution element of a dextrous manipulator is a collection of trivial fibre bundles with solution fibres homotopic to the Torus. If fibre solutions are parameterised by a scalar, a direct inverse funct.ion that maps the scalar and Cartesian base space coordinates to solution element fibre coordinates may be defined. A direct inverse pararneterisation of a solution element may be approximated by a local linear map generated by an inverse augmented Jacobian correction of a linear interpolation. The action of canonical solution group operators on a local linear approximation of the solution element of inverse kinematics of dextrous manipulators generates cyclical solutions. The solution representation is proposed as a model of inverse kinematic transformations in primate nervous systems. Simultaneous calibration of a composition of stereo-camera and manipulator kinematic models is under-determined by equi-output parameter groups in the composition of stereo-camera and Denavit Hartenberg (DH) rnodels. An error measure for simultaneous calibration of a composition of models is derived and parameter subsets with no equi-output groups are determined by numerical experiments to simultaneously calibrate the composition of homogeneous or pan-tilt stereo-camera with DH models. For acceleration of exact Newton second-order re-calibration of DH parameters after a sequential calibration of stereo-camera and DH parameters, an optimal numerical evaluation of DH matrix first order and second order error derivatives with respect to a re-calibration error function is derived, implemented and tested. A distributed object environment for point and click image-based tele-command of manipulators and stereo-cameras is specified and implemented that supports rapid prototyping of numerical experiments in distributed system control. The environment is validated by a hierarchical k-fold cross validated calibration to Cartesian space of a radial basis function regression correction of an affine stereo model. Basic design and performance requirements are defined for scalable virtual micro-kernels that broker inter-Java-virtual-machine remote method invocations between components of secure manageable fault-tolerant open distributed agile Total Quality Managed ISO 9000+ conformant Just in Time manufacturing systems.

The interaction of fast neutrons with shielding and fusion blanket materials

In the present work the neutron emission spectra from a graphite cube, and from natural uranium, lithium fluoride, graphite, lead and steel slabs bombarded with 14.1 MeV neutrons were measured to test nuclear data and calculational methods for D - T fusion reactor neutronics. The neutron spectra measured were performed by an organic scintillator using a pulse shape discrimination technique based on a charge comparison method to reject the gamma rays counts. A computer programme was used to analyse the experimental data by the differentiation unfolding method. The 14.1 MeV neutron source was obtained from T(d,n)4He reaction by the bombardment of T - Ti target with a deuteron beam of energy 130 KeV. The total neutron yield was monitored by the associated particle method using a silicon surface barrier detector. The numerical calculations were performed using the one-dimensional discrete-ordinate neutron transport code ANISN with the ZZ-FEWG 1/ 31-1F cross section library. A computer programme based on Gaussian smoothing function was used to smooth the calculated data and to match the experimental data. There was general agreement between measured and calculated spectra for the range of materials studied. The ANISN calculations carried out with P3 - S8 calculations together with representation of the slab assemblies by a hollow sphere with no reflection at the internal boundary were adequate to model the experimental data and hence it appears that the cross section set is satisfactory and for the materials tested needs no modification in the range 14.1 MeV to 2 MeV. Also it would be possible to carry out a study on fusion reactor blankets, using cylindrical geometry and including a series of concentric cylindrical shells to represent the torus wall, possible neutron converter and breeder regions, and reflector and shielding regions.

N–Dimensional Orthogonal Tile Sizing Problem

AMS subject classification: 68Q22, 90C90

Double complexes and vanishing of Novikov cohomology

2010 Mathematics Subject Classification: Primary 18G35; Secondary 55U15.