Effective Symmetries of the Minimal Supermultiplet of N = 8 Extended Worldline Supersymmetry

A minimal representation of the N = 8 extended worldline supersymmetry, known as the `ultra-multiplet', is closely related to a family of supermultiplets with the same, E(8) chromotopology. We catalogue their effective symmetries and find a Spin(4) x Z(2) subgroup common to them all, which explains the particular basis used in the original construction. We specify a constrained superfield representation of the supermultiplets in the ultra-multiplet family, and show that such a superfield representation in fact exists for all adinkraic supermultiplets. We also exhibit the correspondences between these supermultiplets, their Adinkras and the E(8) root lattice bases. Finally, we construct quadratic Lagrangians that provide the standard kinetic terms and afford a mixing of an even number of such supermultiplets controlled by a coupling to an external 2-form of fluxes.Comment: 13 Figure

Codes and Supersymmetry in One Dimension

Adinkras are diagrams that describe many useful supermultiplets in D=1 dimensions. We show that the topology of the Adinkra is uniquely determined by a doubly even code. Conversely, every doubly even code produces a possible topology of an Adinkra. A computation of doubly even codes results in an enumeration of these Adinkra topologies up to N=28, and for minimal supermultiplets, up to N=32.Comment: 48 pages, a new version that combines arXiv:0811.3410 and parts of arXiv:0806.0050, for submission for publicatio

A Superfield for Every Dash-Chromotopology

The recent classification scheme of so-called adinkraic off-shell supermultiplets of N-extended worldline supersymmetry without central charges finds a combinatorial explosion. Completing our earlier efforts, we now complete the constructive proof that all of these trillions or more of supermultiplets have a superfield representation. While different as superfields and supermultiplets, these are still super-differentially related to a much more modest number of minimal supermultiplets, which we construct herein.Comment: 13 pages, integrated illustration

Independent Interactions of Phosphorylated β-Catenin with E-Cadherin at Cell-Cell Contacts and APC at Cell Protrusions

BACKGROUND: The APC tumour suppressor functions in several cellular processes including the regulation of β-catenin in Wnt signalling and in cell adhesion and migration. FINDINGS: In this study, we establish that in epithelial cells N-terminally phosphorylated β-catenin specifically localises to several subcellular sites including cell-cell contacts and the ends of cell protrusions. N-terminally phosphorylated β-catenin associates with E-cadherin at adherens junctions and with APC in cell protrusions. We isolated APC-rich protrusions from stimulated cells and detected β-catenin, GSK3β and CK1α, but not axin. The APC/phospho-β-catenin complex in cell protrusions appears to be distinct from the APC/axin/β-catenin destruction complex. GSK3β phosphorylates the APC-associated population of β-catenin, but not the cell junction population. β-catenin associated with APC is rapidly phosphorylated and dephosphorylated. HGF and wound-induced cell migration promote the localised accumulation of APC and phosphorylated β-catenin at the leading edge of migrating cells. APC siRNA and analysis of colon cancer cell lines show that functional APC is required for localised phospho-β-catenin accumulation in cell protrusions. CONCLUSIONS: We conclude that N-terminal phosphorylation of β-catenin does not necessarily lead to its degradation but instead marks distinct functions, such as cell migration and/or adhesion processes. Localised regulation of APC-phospho-β-catenin complexes may contribute to the tumour suppressor activity of APC

The Influence of Sequence Variability and Dimerization on Mannose Binding in Monocot Mannose Binding Lectins

Abstract Motivation. A model of the lectin from Aloe arborescens was built by homology modeling. Docking studies with mannose were performed on this model and the known crystal structures of monocot mannose binding lectins from snowdrop and garlic. On the basis of these results association of monomers to form dimers is found to be necessary for successful binding of mannose by site III of these lectins, by providing the fourth strand of the -sheet that is a supporting edge for the site. From an analysis of the carbohydrate binding sites (I, II and III) of the above lectins and the docking studies, the mannose binding site I of aloe lectin is predicted to retain the ability to bind mannose with all of the key residues involved in binding unchanged. Site II and III lose residues specific for hydrogen bonding and are predicted to be unable to bind mannose. Aloe lectin monomers are shown to be able to associate as dimers but docking is still unsuccessful in site III. Method. Protein homology modeling and AutoDock docking studies were used in this study. Results. A homology model of aloe lectin was created by both manual and automatic methods and its ability to bind the natural substrate mannose was assessed by docking studies using the genetic algorithm approach in the AutoDock program. The results of the docking studies were correlated with those on lectins for which X-ray crystal data is known and rationalized in terms of specific mutations in the aloe lectin binding sites. Conclusions. Aloe lectin is predicted to be able to bind mannose in its site I binding site, unable to bind in site II because of key residue mutations and also unable to bind in site III

On Graph-Theoretic Identifications of Adinkras, Supersymmetry Representations and Superfields

In this paper we discuss off-shell representations of N-extended supersymmetry in one dimension, ie, N-extended supersymmetric quantum mechanics, and following earlier work on the subject codify them in terms of certain graphs, called Adinkras. This framework provides a method of generating all Adinkras with the same topology, and so also all the corresponding irreducible supersymmetric multiplets. We develop some graph theoretic techniques to understand these diagrams in terms of a relatively small amount of information, namely, at what heights various vertices of the graph should be "hung". We then show how Adinkras that are the graphs of N-dimensional cubes can be obtained as the Adinkra for superfields satisfying constraints that involve superderivatives. This dramatically widens the range of supermultiplets that can be described using the superspace formalism and organizes them. Other topologies for Adinkras are possible, and we show that it is reasonable that these are also the result of constraining superfields using superderivatives. The family of Adinkras with an N-cubical topology, and so also the sequence of corresponding irreducible supersymmetric multiplets, are arranged in a cyclical sequence called the main sequence. We produce the N=1 and N=2 main sequences in detail, and indicate some aspects of the situation for higher N.Comment: LaTeX, 58 pages, 52 illustrations in color; minor typos correcte