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.

The structure of Selmer groups

The purpose of this article is to describe certain results and conjectures concerning the structure of Galois cohomology groups and Selmer groups, especially for abelian varieties. These results are analogues of a classical theorem of Iwasawa. We formulate a very general version of the Weak Leopoldt Conjecture. One consequence of this conjecture is the nonexistence of proper Λ-submodules of finite index in a certain Galois cohomology group. Under certain hypotheses, one can prove the nonexistence of proper Λ-submodules of finite index in Selmer groups. An example shows that some hypotheses are needed.

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.

Contact interactions between epitheliocytes and fibroblasts: Formation of heterotypic cadherin-containing adhesion sites is accompanied by local cytoskeletal reorganization

Contact interactions between different cell types play a number of important roles in development, for example in cell sorting, tissue organization, and ordered migration of cells. The nature of such heterocellular interactions, in contrast to interactions between cells of the same type, remains largely unknown. In this report, we present experimental data examining the dynamics of heterocellular interactions between epitheliocytes and fibroblasts, which express different cadherin cell adhesion molecules and possess different actin cytoskeletal organizations. Our analysis revealed two striking features of heterocellular contact. First, the active free edge of an epitheliocyte reorganizes its actin cytoskeleton after making contact with a fibroblast. Upon contact with the leading edge of a fibroblast, epitheliocytes disassemble their marginal bundle of actin filaments and reassemble actin filaments into a geometric organization more typical of a fibroblast lamella. Second, epitheliocytes and fibroblasts form cell–cell adhesion structures that have an irregular organization and are associated with components of cell adhesion complexes. The structural organization of these adhesions is more closely related to the type of contacts formed between fibroblasts rather than to those between epitheliocytes. Heterotypic epithelio-fibroblastic contacts, like homotypic contacts between fibroblasts, are transient and do not lead to formation of stable contact interactions. We suggest that heterocellular contact interactions in culture may be regarded as models of how tissue systems consisting of epithelia and mesenchyme interact and become organized in vivo.

Gene recognition via spliced sequence alignment.

Gene recognition is one of the most important problems in computational molecular biology. Previous attempts to solve this problem were based on statistics, and applications of combinatorial methods for gene recognition were almost unexplored. Recent advances in large-scale cDNA sequencing open a way toward a new approach to gene recognition that uses previously sequenced genes as a clue for recognition of newly sequenced genes. This paper describes a spliced alignment algorithm and software tool that explores all possible exon assemblies in polynomial time and finds the multiexon structure with the best fit to a related protein. Unlike other existing methods, the algorithm successfully recognizes genes even in the case of short exons or exons with unusual codon usage; we also report correct assemblies for genes with more than 10 exons. On a test sample of human genes with known mammalian relatives, the average correlation between the predicted and actual proteins was 99%. The algorithm correctly reconstructed 87% of genes and the rare discrepancies between the predicted and real exon-intron structures were caused either by short (less than 5 amino acids) initial/terminal exons or by alternative splicing. Moreover, the algorithm predicts human genes reasonably well when the homologous protein is nonvertebrate or even prokaryotic. The surprisingly good performance of the method was confirmed by extensive simulations: in particular, with target proteins at 160 accepted point mutations (PAM) (25% similarity), the correlation between the predicted and actual genes was still as high as 95%.

Binding of a hairpin polyamide in the minor groove of DNA: sequence-specific enthalpic discrimination.

Hairpin polyamides are synthetic ligands for sequence-specific recognition in the minor groove of double-helical DNA. A thermodynamic characterization of the DNA-binding properties exhibited by a six-ring hairpin polyamide, ImPyPy-gamma-PyPyPy-beta-Dp (where Im = imidazole, Py = pyrrole, gamma = gamma-aminobutyric acid, beta = beta-alanine, and Dp = dimethylaminopropylamide), reveals an approximately 1-2 kcal/mol greater affinity for the designated match site, 5'-TGTTA-3', relative to the single base pair mismatch sites, 5'-TGGTA-3' and 5'-TATTA-3'. The enthalpy and entropy data at 20 degrees C reveal this sequence specificity to be entirely enthalpic in origin. Correlations between the thermodynamic driving forces underlying the sequence specificity exhibited by ImPyPy-gamma-PyPyPy-beta-Dp and the structural properties of the heterodimeric complex of PyPyPy and ImPyPy bound to the minor groove of DNA provide insight into the molecular forces that govern the affinity and specificity of pyrrole-imidazole polyamides.

Dynamic friction and the origin of the complexity of earthquake sources.

We study a simple antiplane fault of finite length embedded in a homogeneous isotropic elastic solid to understand the origin of seismic source heterogeneity in the presence of nonlinear rate- and state-dependent friction. All the mechanical properties of the medium and friction are assumed homogeneous. Friction includes a characteristic length that is longer than the grid size so that our models have a well-defined continuum limit. Starting from a heterogeneous initial stress distribution, we apply a slowly increasing uniform stress load far from the fault and we simulate the seismicity for a few 1000 events. The style of seismicity produced by this model is determined by a control parameter associated with the degree of rate dependence of friction. For classical friction models with rate-independent friction, no complexity appears and seismicity is perfectly periodic. For weakly rate-dependent friction, large ruptures are still periodic, but small seismicity becomes increasingly nonstationary. When friction is highly rate-dependent, seismicity becomes nonperiodic and ruptures of all sizes occur inside the fault. Highly rate-dependent friction destabilizes the healing process producing premature healing of slip and partial stress drop. Partial stress drop produces large variations in the state of stress that in turn produce earthquakes of different sizes. Similar results have been found by other authors using the Burridge and Knopoff model. We conjecture that all models in which static stress drop is only a fraction of the dynamic stress drop produce stress heterogeneity.

The invariant system of coordinates of antibody molecules: prediction of the "standard" C alpha framework of VL and VH domains.

A new approach of comparing protein structures that does not involve the procedure of superposition is suggested. An invariant system of coordinates for immunoglobulin molecules that is based on the geometrical symmetry inherent to the variable domain light-chain (VL)-heavy-chain (VH) complex is described. The coordinates of the Calpha atoms in 22 immunoglobulin structures are calculated in the invariant system of coordinates. We found that 76 identical positions in this Calpha framework are symmetrical about the twofold axis. Comparison of the identical positions in these molecules allows us to select 96 positions in the light chains and 87 positions in the heavy chains whose Calpha atom coordinates are approximately the same. To check whether the average coordinates of Calpha atoms in these positions complies with the stereochemical requirements, we calculated Calpha-Calpha distances. Seventy-three positions of the light chains and 72 positions of the heavy chains satisfy the Calpha-Calpha distance criterion. The Calpha atoms in these positions are used for constructing the "standard" Calpha framework of VL and VH complexes. The average coordinates of Calpha atoms are presented.

Hyperplane arrangements, interval orders, and trees.

A hyperplane arrangement is a finite set of hyperplanes in a real affine space. An especially important arrangement is the braid arrangement, which is the set of all hyperplanes xi - xj = 1, 1

Analysis of the relation between the sequence and secondary and three-dimensional structures of immunoglobulin molecules.

Methods of structural and statistical analysis of the relation between the sequence and secondary and three-dimensional structures are developed. About 5000 secondary structures of immunoglobulin molecules from the Kabat data base were predicted. Two statistical analyses of amino acids reveal 47 universal positions in strands and loops. Eight universally conservative positions out of the 47 are singled out because they contain the same amino acid in > 90% of all chains. The remaining 39 positions, which we term universally alternative positions, were divided into five groups: hydrophobic, charged and polar, aromatic, hydrophilic, and Gly-Ala, corresponding to the residues that occupied them in almost all chains. The analysis of residue-residue contacts shows that the 47 universal positions can be distinguished by the number and types of contacts. The calculations of contact maps in the 29 antibody structures revealed that residues in 24 of these 47 positions have contacts only with residues of antiparallel beta-strands in the same beta-sheet and residues in the remaining 23 positions always have far-away contacts with residues from other beta-sheets as well. In addition, residues in 6 of the 47 universal positions are also involved in interactions with residues of the other variable or constant domains.

Seven newly discovered intron positions in the triose-phosphate isomerase gene: evidence for the introns-late theory.

The gene encoding the glycolytic enzyme triose-phosphate isomerase (TPI; EC 5.3.1.1) has been central to the long-standing controversy on the origin and evolutionary significance of spliceosomal introns by virtue of its pivotal support for the introns-early view, or exon theory of genes. Putative correlations between intron positions and TPI protein structure have led to the conjecture that the gene was assembled by exon shuffling, and five TPI intron positions are old by the criterion of being conserved between animals and plants. We have sequenced TPI genes from three diverse eukaryotes--the basidiomycete Coprinus cinereus, the nematode Caenorhabditis elegans, and the insect Heliothis virescens--and have found introns at seven novel positions that disrupt previously recognized gene/protein structure correlations. The set of 21 TPI introns now known is consistent with a random model of intron insertion. Twelve of the 21 TPI introns appear to be of recent origin since each is present in but a single examined species. These results, together with their implication that as more TPI genes are sequenced more intron positions will be found, render TPI untenable as a paradigm for the introns-early theory and, instead, support the introns-late view that spliceosomal introns have been inserted into preexisting genes during eukaryotic evolution.

Photolabeling reveals the proximity of the alpha-neurotoxin binding site to the M2 helix of the ion channel in the nicotinic acetylcholine receptor.

A photoactivatable derivative of neurotoxin II from Naja naja oxiana containing a 125I-labeled p-azidosalicylamidoethyl-1,3'-dithiopropyl label at Lys-25 forms a photo-induced cross-link with the delta subunit of the membrane-bound Torpedo californica nicotinic acetylcholine receptor (AChR). The cross-linked radioactive receptor peptide was isolated by reverse-phase HPLC after tryptic digestion of the labeled delta subunit. The sequence of this peptide, delta-(260-277), and the position of the label at Ala-268 were established by matrix-assisted laser-desorption-ionization mass spectrometry based on the molecular mass and on post-source decay fragment analysis. With the known dimensions of the AChR molecule, of the photolabel, and of alpha-neurotoxin, finding the cross-link at delta Ala-268 (located in the upper part of the channel-forming transmembrane helix M2) means that the center of the alpha-neurotoxin binding site is situated at least approximately 40 A from the extracellular surface of the AChR, proximal to the channel axis.

Dynamics of active lamellae in cultured epithelial cells: effects of expression of exogenous N-ras oncogene.

We examined the functional consequences of cellular transformation of rat IAR-2 epithelial cells, by a mutant N-ras oncogene, on the dynamics of active lamellae, structures that play an important role in cell motility, adhesion, and surface-receptor capping. Lamellar activity was assessed by measuring the rate of outer-edge pseudopodial activity and by analyzing the motility of Con A-coated beads placed on lamellar surfaces with optical tweezers. Although transformation dramatically affected the shape and size of active cellular lamellae, there was little detectable effect on either pseudopodial activity or bead movement. To investigate the potential relationship between functional lamellar activity and the microtubule cytoskeleton, lamellar activity was examined in nontransformed and transformed cells treated with the microtubule-disrupting drug nocodazole. In the absence of microtubules, transformed cells were less polarized and possessed decreased rates of pseudopodial and bead motility. On the basis of these observations, it is suggested that ras-induced transformation of epithelial cells consists of two cytoskeletal modifications: overall diminished actin cytoskeletal dynamics in lamellae and reorganization of the microtubule cytoskeleton that directs pseudopodial activity to smaller polarized lamellae.

Equações de quarta ordem na modelagem de oscilações de pontes

Equações diferenciais de quarta ordem aparecem naturalmente na modelagem de oscilações de estruturas elásticas, como aquelas observadas em pontes pênseis. São considerados dois modelos que descrevem as oscilações no tabuleiro de uma ponte. No modelo unidimensional estudamos blow up em espaço finito de soluções de uma classe de equações diferenciais de quarta ordem. Os resultados apresentados solucionam uma conjectura apresentada em [F. Gazzola and R. Pavani. Wide oscillation finite time blow up for solutions to nonlinear fourth order differential equations. Arch. Ration. Mech. Anal., 207(2):717752, 2013] e implicam a não existência de ondas viajantes com baixa velocidade de propagação em uma viga. No modelo bidimensional analisamos uma equação não local para uma placa longa e fina, suportada nas extremidades menores, livre nas demais e sujeita a protensão. Provamos existência e unicidade de solução fraca e estudamos o seu comportamento assintótico sob amortecimento viscoso. Estudamos ainda a estabilidade de modos simples de oscilação, os quais são classificados como longitudinais ou torcionais.

Desenvolvimento da modelagem de turbulência e interação fluido-estrutura para as vibrações induzidas por vórtices de cilindro rígido.

Esta tese apresenta o desenvolvimento e aplicação de modelos de turbulência, transição laminar-turbulenta e de interações fluido-estrutura ao escoamento externo em cilindro rígido estacionário e em vibrações induzidas por vórtices. Tais desenvolvimentos foram realizados no código ReFRESCO, baseado em técnicas de dinâmica de fluidos computacional (CFD). Realizou-se um estudo quanto ao desempenho do modelo k- SST em extensa faixa de números de Reynolds, segundo o qual se identificaram as deficiências de modelagem para este escoamento. A modelagem adaptativa das escalas (SAS) e o modelo de transição por correlações locais (LCTM), ambos combinados ao SST, melhoraram a aderência aos resultados experimentais para este escoamento, em uma contribuição original deste trabalho. A aplicação de técnicas de verificação e validação possibilitou a estimação de incertezas e erros para os modelos e números de Reynolds e também de identificada como outra contribuição deste trabalho. A combinação da modelagem em SST, SAS e LCTM com movimentos impostos de realizada para números de Reynolds moderados, diferentes frequências e amplitudes de vibração, algo que poucas publicações abordam em detalhes. Com relação aos movimentos livres, este trabalho traz contribuições com a aplicação dos modelos SST e SAS ao estudo de vibrações induzidas por vórtices em dois graus de liberdade, baixa razão de massa e números de Reynolds moderados, mais altos do que normalmente observados na literatura. Por fim, a investigação da importância relativa de efeitos da turbulência aos casos de movimentos livres e impostos, com relação ao caso de cilindro estacionário, comprovou a conjetura formulada na parte inicial deste trabalho, no que tange à escolha do modelo de turbulência em determinadas aplicações. Tal escolha mostrou-se menos decisiva no caso do cilindro em movimento imposto e ainda menos nos movimentos livres, em comparação ao caso estacionário, uma vez que a resposta em movimentos do corpo filtra grande parte dos efeitos turbulentos de ordem superior. Esta observação mostra-se relevante, uma vez que pode permitir simplificações na modelagem e aplicação de ferramentas de CFD em uma classe importante de projetos de engenharia.