Adjoint modular Galois representations and their Selmer groups

In the last 15 years, many class number formulas and main conjectures have been proven. Here, we discuss such formulas on the Selmer groups of the three-dimensional adjoint representation ad(φ) of a two-dimensional modular Galois representation φ. We start with the p-adic Galois representation φ0 of a modular elliptic curve E and present a formula expressing in terms of L(1, ad(φ0)) the intersection number of the elliptic curve E and the complementary abelian variety inside the Jacobian of the modular curve. Then we explain how one can deduce a formula for the order of the Selmer group Sel(ad(φ0)) from the proof of Wiles of the Shimura–Taniyama conjecture. After that, we generalize the formula in an Iwasawa theoretic setting of one and two variables. Here the first variable, T, is the weight variable of the universal p-ordinary Hecke algebra, and the second variable is the cyclotomic variable S. In the one-variable case, we let φ denote the p-ordinary Galois representation with values in GL2(Zp[[T]]) lifting φ0, and the characteristic power series of the Selmer group Sel(ad(φ)) is given by a p-adic L-function interpolating L(1, ad(φk)) for weight k + 2 specialization φk of φ. In the two-variable case, we state a main conjecture on the characteristic power series in Zp[[T, S]] of Sel(ad(φ) ⊗ ν−1), where ν is the universal cyclotomic character with values in Zp[[S]]. Finally, we describe our recent results toward the proof of the conjecture and a possible strategy of proving the main conjecture using p-adic Siegel modular forms.

Deforming semistable Galois representations

Let V be a p-adic representation of Gal(Q̄/Q). One of the ideas of Wiles’s proof of FLT is that, if V is the representation associated to a suitable autromorphic form (a modular form in his case) and if V′ is another p-adic representation of Gal(Q̄/Q) “closed enough” to V, then V′ is also associated to an automorphic form. In this paper we discuss which kind of local condition at p one should require on V and V′ in order to be able to extend this part of Wiles’s methods.

On degree 2 Galois representations over

We discuss proofs of some new special cases of Serre’s conjecture on odd, degree 2 representations of Gℚ.

Controlling cell attachment on contoured surfaces with self-assembled monolayers of alkanethiolates on gold.

This paper describes a method based on experimentally simple techniques--microcontact printing and micromolding in capillaries--to prepare tissue culture substrates in which both the topology and molecular structure of the interface can be controlled. The method combines optically transparent contoured surfaces with self-assembled monolayers (SAMs) of alkanethiolates on gold to control interfacial characteristics; these tailored interfaces, in turn, control the adsorption of proteins and the attachment of cells. The technique uses replica molding in poly(dimethylsiloxane) molds having micrometer-scale relief patterns on their surfaces to form a contoured film of polyurethane supported on a glass slide. Evaporation of a thin (< 12 nm) film of gold on this surface-contoured polyurethane provides an optically transparent substrate, on which SAMs of terminally functionalized alkanethiolates can be formed. In one procedure, a flat poly(dimethylsiloxane) stamp was used to form a SAM of hexadecanethiolate on the raised plateaus of the contoured surface by contact printing hexadecanethiol [HS(CH2)15CH3]; a SAM terminated in tri(ethylene glycol) groups was subsequently formed on the bare gold remaining in the grooves by immersing the substrate in a solution of a second alkanethiol [HS(CH2)11(OCH2CH2)3OH]. Then this patterned substrate was immersed in a solution of fibronectin, the protein adsorbed only on the methyl-terminated plateau regions of the substrate [the tri(ethylene glycol)-terminated regions resisted the adsorption of protein]; bovine capillary endothelial cells attached only on the regions that adsorbed fibronectin. A complementary procedure confined protein adsorption and cell attachment to the grooves in this substrate.

Culture as shared cognitive representations.

Culture consists of shared cognitive representations in the minds of individuals. This paper investigates the extent to which English speakers share the "same" semantic structure of English kinship terms. The semantic structure is defined as the arrangement of the terms relative to each other as represented in a metric space in which items judged more similar are placed closer to each other than items judged as less similar. The cognitive representation of the semantic structure, residing in the mind of an individual, is measured by judged similarity tasks involving comparisons among terms. Using six independent measurements, from each of 122 individuals, correspondence analysis represents the data in a common multidimensional spatial representation. Judged by a variety of statistical procedures, the individuals in our sample share virtually identical cognitive representations of the semantic structure of kinship terms. This model of culture accounts for 70-90% of the total variability in these data. We argue that our findings on kinship should generalize to all semantic domains--e.g., animals, emotions, etc. The investigation of semantic domains is important because they may reside in localized functional units in the brain, because they relate to a variety of cognitive processes, and because they have the potential to provide methods for diagnosing individual breakdowns in the structure of cognitive representations typical of such ailments as Alzheimer disease.

Numerical representations in primates.

Research has demonstrated that human infants and nonhuman primates have a rudimentary numerical system that enables them to count objects or events. More recently, however, studies using a preferential looking paradigm have suggested that preverbal human infants are capable of simple arithmetical operations, such as adding and subtracting a small number of visually presented objects. These findings implicate a relatively sophisticated representational system in the absence of language. To explore the evolutionary origins of this capacity, we present data from an experiment with wild rhesus monkeys (Macaca mulatta) that methodologically mirrors those conducted on human infants. Results suggest that rhesus monkeys detect additive and subtractive changes in the number of objects present in their visual field. Given the methodological and empirical similarities, it appears that nonhuman primates such as rhesus monkeys may also have access to arithmetical representations, although alternative explanations must be considered for both primate species.

Helicobacter pylori attachment to gastric cells induces cytoskeletal rearrangements and tyrosine phosphorylation of host cell proteins.

The consequences of Helicobacter pylori attachment to human gastric cells were examined by transmission electron microscopy and immunofluorescence microscopy. H. pylori attachment resulted in (i) effacement of microvilli at the site of attachment, (ii) cytoskeletal rearrangement directly beneath the bacterium, and (iii) cup/pedestal formation at the site of attachment. Double-immunofluorescence studies revealed that the cytoskeletal components actin, alpha-actinin, and talin are involved in the process. Immunoblot analysis showed that binding of H. pylori to AGS cells induced tyrosine phosphorylation of two host cell proteins of 145 and 105 kDa. These results indicate that attachment of H. pylori to gastric epithelial cells resembles that of enteropathogenic Escherichia coli. Coccoid H. pylori, which are thought to be terminally differentiated bacterial forms, are capable of binding and inducing cellular changes of the same sort as spiral H. pylori, including tyrosine phosphorylation of host proteins.

Using in vitro selection to direct the covalent attachment of human immunodeficiency virus type 1 Rev protein to high-affinity RNA ligands.

We have used an in vitro selection procedure called crosslinking SELEX (SELEX = systematic evolution of ligands by exponential enrichment) to identify RNA sequences that bind with high affinity and crosslink to the Rev protein from human immunodeficiency virus type 1 (HIV-1). A randomized RNA library substituted with the photoreactive chromophore 5-iodouracil was irradiated with monochromatic UV light in the presence of Rev. Those sequences with the ability to photocrosslink to Rev were partitioned from the rest of the RNA pool, amplified, and used for the next round of selection. Rounds of photocrosslinking selection were alternated with rounds of selection for RNA sequences with high affinity to Rev. This iterative, dual-selection method yielded RNA molecules with subnanomolar dissociation constants and high efficiency photocrosslinking to Rev. Some of the RNA molecules isolated by this procedure form a stable complex with Rev that is resistant to denaturing gel electrophoresis in the absence of UV irradiation. In vitro selection of nucleic acids by using modified nucleotides allows the isolation of nucleic acid molecules with potentially limitless chemical capacities to covalently attack a target molecule.

Mutagenesis of the human apolipoprotein B gene in a yeast artificial chromosome reveals the site of attachment for apolipoprotein(a).

Lipoprotein(a) [Lp(a)] is a lipoprotein formed by the disulfide linkage of apolipoprotein (apo) B100 of a low density lipoprotein particle to apolipoprotein(a). Prior studies have suggested that one of the C-terminal Cys residues of apo-B100 is involved in the disulfide linkage of apo-B100 to apo(a). To identify the apo-B100 Cys residue involved in the formation of Lp(a), we constructed a yeast artificial chromosome (YAC) spanning the human apo-B gene and used gene-targeting techniques to change Cys-4326 to Gly. The mutated YAC DNA was used to generate transgenic mice expressing the mutant human apo-B100 (Cys4326Gly). Unlike the wild-type human apo-B100, the mutant human apo-B100 completely lacked the ability to bind to apo(a) and form Lp(a). This study demonstrates that apo-B100 Cys-4326 is required for the assembly of Lp(a) and shows that gene targeting in YACs, followed by the generation of transgenic mice, is a useful approach for analyzing the structure of large proteins coded for by large genes.

Alpha 1(E)-catenin is an actin-binding and -bundling protein mediating the attachment of F-actin to the membrane adhesion complex.

Calcium-dependent homotypic cell-cell adhesion, mediated by molecules such as E-cadherin, guides the establishment of classical epithelial cell polarity and contributes to the control of migration, growth, and differentiation. These actions involve additional proteins, including alpha- and beta-catenin (or plakoglobin) and p120, as well as linkage to the cortical actin cytoskeleton. The molecular basis for these interactions and their hierarchy of interaction remain controversial. We demonstrate a direct interaction between F-actin and alpha (E)-catenin, an activity not shared by either the cytoplasmic domain of E-cadherin or beta-catenin. Sedimentation assays and direct visualization by transmission electron microscopy reveal that alpha 1(E)-catenin binds and bundles F-actin in vitro with micromolar affinity at a catenin/G-actin monomer ratio of approximately 1:7 (mol/mol). Recombinant human beta-catenin can simultaneously bind to the alpha-catenin/actin complex but does not bind actin directly. Recombinant fragments encompassing the amino-terminal 228 residues of alpha 1(E)-catenin or the carboxyl-terminal 447 residues individually bind actin in cosedimentation assays with reduced affinity compared with the full-length protein, and neither fragment bundles actin. Except for similarities to vinculin, neither region contains sequences homologous to established actin-binding proteins. Collectively these data indicate that alpha 1 (E)-catenin is a novel actin-binding and -bundling protein and support a model in which alpha 1(E)-catenin is responsible for organizing and tethering actin filaments at the zones of E-cadherin-mediated cell-cell contact.

Surfactant protein a promotes attachment of Mycobacterium tuberculosis to alveolar macrophages during infection with human immunodeficiency virus.

The incidence of tuberculosis is increasing on a global scale, in part due to its strong association with human immunodeficiency virus (HIV) infection. Attachment of Mycobacterium tuberculosis to its host cell, the alveolar macrophage (AM), is an important early step in the pathogenesis of infection. Bronchoalveolar lavage of HIV-infected individuals demonstrated the presence of a factor which significantly enhances the attachment of tubercle bacilli to AMs 3-fold relative to a normal control population. This factor is surfactant protein A (SP-A). SP-A levels are increased in the lungs of HIV-infected individuals. SP-A levels and attachment of M. tuberculosis to AMs inversely correlate with peripheral blood CD4 lymphocyte counts. Elevated concentrations of SP-A during the progression of HIV infection may represent an important nonimmune risk factor for acquiring tuberculosis, even before significant depletion of CD4 lymphocytes in the peripheral blood occurs.