Similarity Measures for Convex Polyhedra Based on Minkowski Addition

In this paper we introduce and investigate similarity measures for convex polyhedra based on Minkowski addition and inequalities for the mixed volume, volume and surface area related to the Brunn-Minkowski theory. All measures considered are invariant under translations; furthermore, they may also be invariant under subgroups of the affine transformation group. For the case of rotation and scale invariance, we prove that to obtain the measures based on (mixed) volume, it is sufficient to compute certain functionals only for a finite number of critical rotations. Extensive use is made of the slope diagram representation of convex polyhedra. AMS Subject Classification (1991): 52A38, 52B15, 68T10, 68U05 Keywords & Phrases: similarity measure, convex set, convex polyhedron, Minkowski addition, slope diagram representation, affine transformation, rotation, reflection, multiplication, similitude, volume, mixed volume, Brunn-Minkowski inequality, critical rotation, critical angle. 1 Introdu..

Biantennary oligoglycines and glyco-oligoglycines self-associating in aqueous medium

Oligoglycines designed in a star-like fashion, so-called tri- and tetraantennary molecules, were found to form highly ordered supramers in aqueous medium. The formation of these supramers occurred either spontaneously or due to the assistance of a mica surface. The driving force of the supramer formation is hydrogen bonding, the polypeptide chain conformation is related to the folding of helical polyglycine II (PG II). Tri- and tetraantennary molecules are capable of association if the antenna length reach 7 glycine (Gly) residues. Properties of similar biantennary molecules have not been investigated yet, and we compared their self-aggregating potency with similar tri- and tetraantennary analogs. Here, we synthesized oligoglycines of the general formula R-Glyn-Х-Glyn-R (X = -HN-(СН2)m-NH-, m = 2, 4, 10; n = 1–7) without pendant ligands (R = H) and with two pendant sialoligands (R = sialic acid or sialooligosaccharide). Biantennary oligoglycines formed PG II aggregates, their properties, however, differ from those of the corresponding tri- and tetraantennary oligoglycines. In particular, the tendency to aggregate starts from Gly4 motifs instead of Gly7. The antiviral activity of end-glycosylated peptides was studied, and all capable of assembling glycopeptides demonstrated an antiviral potency which was up to 50 times higher than the activity of peptide-free glycans

6-sulfo sialyl Lewis X is the common receptor determinant recognized by H5, H6, H7 and H9 influenza viruses of terrestrial poultry-2

3N8) [], A/Turkey/Italy/02 (H7N1) [] and A/Swine/Hong Kong/9/98 (H9N2) []. The fucose moiety and the sulfo group of Su-SLeare shown as mesh surfaces. Amino acid residues described in the text are numbered.<p><b>Copyright information:</b></p><p>Taken from "6-sulfo sialyl Lewis X is the common receptor determinant recognized by H5, H6, H7 and H9 influenza viruses of terrestrial poultry"</p><p>http://www.virologyj.com/content/5/1/85</p><p>Virology Journal 2008;5():85-85.</p><p>Published online 24 Jul 2008</p><p>PMCID:PMC2515299.</p><p></p

6-sulfo sialyl Lewis X is the common receptor determinant recognized by H5, H6, H7 and H9 influenza viruses of terrestrial poultry-5

Espond to lower binding affinities. The data were averaged from 3 sets of experiments. Standard errors did not exceed 50% of the mean values. Viruses labelled with asterisk were kindly provided by Dr. S. Yamnikova, the Ivanovsky Institute of Virology, Moscow, Russia. Colours depict relative levels of binding for each individual virus: red – maximal binding; yellow – good binding; pale cyan – weak binding; blue – no detectable binding.<p><b>Copyright information:</b></p><p>Taken from "6-sulfo sialyl Lewis X is the common receptor determinant recognized by H5, H6, H7 and H9 influenza viruses of terrestrial poultry"</p><p>http://www.virologyj.com/content/5/1/85</p><p>Virology Journal 2008;5():85-85.</p><p>Published online 24 Jul 2008</p><p>PMCID:PMC2515299.</p><p></p

6-sulfo sialyl Lewis X is the common receptor determinant recognized by H5, H6, H7 and H9 influenza viruses of terrestrial poultry-4

Ng structural formulas are given in the Table 1. The figures were generated using Discovery Studio ViewerPro5.0 software (Accelrys Inc.).<p><b>Copyright information:</b></p><p>Taken from "6-sulfo sialyl Lewis X is the common receptor determinant recognized by H5, H6, H7 and H9 influenza viruses of terrestrial poultry"</p><p>http://www.virologyj.com/content/5/1/85</p><p>Virology Journal 2008;5():85-85.</p><p>Published online 24 Jul 2008</p><p>PMCID:PMC2515299.</p><p></p

6-sulfo sialyl Lewis X is the common receptor determinant recognized by H5, H6, H7 and H9 influenza viruses of terrestrial poultry-3

, and 226 are highlighted. The figure was generated with GeneDoc 2.6 software [].<p><b>Copyright information:</b></p><p>Taken from "6-sulfo sialyl Lewis X is the common receptor determinant recognized by H5, H6, H7 and H9 influenza viruses of terrestrial poultry"</p><p>http://www.virologyj.com/content/5/1/85</p><p>Virology Journal 2008;5():85-85.</p><p>Published online 24 Jul 2008</p><p>PMCID:PMC2515299.</p><p></p

6-sulfo sialyl Lewis X is the common receptor determinant recognized by H5, H6, H7 and H9 influenza viruses of terrestrial poultry-1

Espond to lower binding affinities. The data were averaged from 3 sets of experiments. Standard errors did not exceed 50% of the mean values. Viruses labelled with asterisk were kindly provided by Dr. S. Yamnikova, the Ivanovsky Institute of Virology, Moscow, Russia. Colours depict relative levels of binding for each individual virus: red – maximal binding; yellow – good binding; pale cyan – weak binding; blue – no detectable binding.<p><b>Copyright information:</b></p><p>Taken from "6-sulfo sialyl Lewis X is the common receptor determinant recognized by H5, H6, H7 and H9 influenza viruses of terrestrial poultry"</p><p>http://www.virologyj.com/content/5/1/85</p><p>Virology Journal 2008;5():85-85.</p><p>Published online 24 Jul 2008</p><p>PMCID:PMC2515299.</p><p></p

6-sulfo sialyl Lewis X is the common receptor determinant recognized by H5, H6, H7 and H9 influenza viruses of terrestrial poultry-0

Ng structural formulas are given in the Table 1. The figures were generated using Discovery Studio ViewerPro5.0 software (Accelrys Inc.).<p><b>Copyright information:</b></p><p>Taken from "6-sulfo sialyl Lewis X is the common receptor determinant recognized by H5, H6, H7 and H9 influenza viruses of terrestrial poultry"</p><p>http://www.virologyj.com/content/5/1/85</p><p>Virology Journal 2008;5():85-85.</p><p>Published online 24 Jul 2008</p><p>PMCID:PMC2515299.</p><p></p

Identification of the mycobacterial carbohydrate structure that binds the C-type lectins DC-SIGN, L-SIGN and SIGNR1

Mycobacterium tuberculosis represents a worldwide health risk and although macrophages are primarily infected, dendritic cells (DC) are important in inducing cellular immune responses against M. tuberculosis. Recent studies have demonstrated that M. tuberculosis targets the DC-specific C-type lectin DC-SIGN to inhibit the immuno-stimulatory function of DC through the interaction of the mycobacterial mannosylated lipoarabinomannan (ManLAM) to DC-SIGN, which prevents DC maturation and induces the immuno-suppressive cytokine IL-10. This may contribute to survival and persistence of M. tuberculosis. Here, we have identified the specific pathogen-derived carbohydrate structure on ManLAM that is recognized by DC-SIGN. We have synthesized the mannose-cap oligosaccharides man-ara, (man)2-ara and (man)3-ara, and demonstrate that these neoglycoconjugates are specifically bound by DC-SIGN. Moreover, we demonstrate that the human and murine DC-SIGN homologue L-SIGN and SIGNR1, respectively, also interact with mycobacteria through ManLAM. Both homologues have the highest affinity for the (man)3-ara structure, similar to DC-SIGN. This study provides information about the specific carbohydrate structures on pathogens that are recognized by DC-SIGN, and may provide strategies to develop vaccines against these pathogens. Moreover, the identification of SIGNR1 as a receptor for ManLAM will enable in vivo studies to investigate the role of DC-SIGN in M. tuberculosis pathogenesi