An exact sequence for contact- and symplectic homology

A symplectic manifold $W$ with contact type boundary $M = \partial W$ induces a linearization of the contact homology of $M$ with corresponding linearized contact homology $HC(M)$. We establish a Gysin-type exact sequence in which the symplectic homology $SH(W)$ of $W$ maps to $HC(M)$, which in turn maps to $HC(M)$, by a map of degree -2, which then maps to $SH(W)$. Furthermore, we give a description of the degree -2 map in terms of rational holomorphic curves with constrained asymptotic markers, in the symplectization of $M$.Comment: Final version. Changes for v2: Proof of main theorem supplemented with detailed discussion of continuation maps. Description of degree -2 map rewritten with emphasis on asymptotic markers. Sec. 5.2 rewritten with emphasis on 0-dim. moduli spaces. Transversality discussion reorganized for clarity (now Remark 9). Various other minor modification

Symplectic cohomology and q-intersection numbers

Given a symplectic cohomology class of degree 1, we define the notion of an equivariant Lagrangian submanifold. The Floer cohomology of equivariant Lagrangian submanifolds has a natural endomorphism, which induces a grading by generalized eigenspaces. Taking Euler characteristics with respect to the induced grading yields a deformation of the intersection number. Dehn twists act naturally on equivariant Lagrangians. Cotangent bundles and Lefschetz fibrations give fully computable examples. A key step in computations is to impose the "dilation" condition stipulating that the BV operator applied to the symplectic cohomology class gives the identity. Equivariant Lagrangians mirror equivariant objects of the derived category of coherent sheaves.Comment: 32 pages, 9 figures, expanded introduction, added details of example 7.5, added discussion of sign

Échange international et distorsions internes:Comment gouverner la globalisation ?

La concurrence des pays émergents de la taille de la Chine ou de l’Inde fait resurgir avec force le débat qui oppose partisans et adversaires du libre-échange au sein même des pays développés. Pour les premiers, la croissance du commerce international est forcément bénéficiaire pour tous. Pour les seconds, elle est la cause de tous les maux et en particulier du chômage. Les choses sont pourtant bien différentes et beaucoup moins simples. Les changements dans le commerce international, comme d’ailleurs le progrès technique, créent inévitablement des distorsions qui perturbent le fonctionnement de l’économie. Ces distorsions ne sont pas réductibles à des dysfonctionnements des marchés des biens ou du travail. Elles ne peuvent donc pas être éliminées ab initio en choisissant des institutions optimales. Pour autant, des restrictions au commerce international ne sont pas une solution car elles risquent de créer d’autres distorsions qui viennent s’ajouter aux premières. Des distorsions avant tout intérieures appellent des solutions intérieures. Pour explorer ces solutions, il faut retenir une analyse conçue pour étudier, non les propriétés des positions d’équilibre avant et après l’ouverture à l’échange, mais les caractéristiques d’un processus de transition dont le succès n’est pas assuré. Ce type d’analyse permet de mettre en évidence la nécessité d’introduire une forme d’inertie dans les mécanismes d’ajustement. Si une relative flexibilité des salaires est encore possible quand l’intensité du changement est limitée, une certaine viscosité est requise dans le cas contraire, et un accès facilité aux ressources financières externes est nécessaire. Ce résultat pourrait aider à formuler les choix institutionnels et organisationnels à mettre en œuvre dans les économies qui veulent tirer avantage du commerce international et de la globalisation.Changes in the pattern of international trade inevitably create distortions that perturb the functioning of the economy. These distortions may not be reduced to malfunctioning goods or labour markets, and hence cannot be eliminated by simply choosing the optimal institutions. Domestic distortions call for domestic solutions. To explore these solutions it is useless to analyze the properties of equilibria before and after the opening to trade. Rather, we need to build an analytical framework suited to investigate the characteristics of a transition process whose success is not guaranteed ex ante. it appears that wage rigidity and an easy access to external financial resources are necessary in presence of fast pace of change, while if change is sufficiently slow the standard recipe of wage flexibility may be appropriate. These results may help in the institutional and organizational choices to be implemented in economies willing to profit from international trade and globalization

Photoswitchable diacylglycerols enable optical control of protein kinase C.

Increased levels of the second messenger lipid diacylglycerol (DAG) induce downstream signaling events including the translocation of C1-domain-containing proteins toward the plasma membrane. Here, we introduce three light-sensitive DAGs, termed PhoDAGs, which feature a photoswitchable acyl chain. The PhoDAGs are inactive in the dark and promote the translocation of proteins that feature C1 domains toward the plasma membrane upon a flash of UV-A light. This effect is quickly reversed after the termination of photostimulation or by irradiation with blue light, permitting the generation of oscillation patterns. Both protein kinase C and Munc13 can thus be put under optical control. PhoDAGs control vesicle release in excitable cells, such as mouse pancreatic islets and hippocampal neurons, and modulate synaptic transmission in Caenorhabditis elegans. As such, the PhoDAGs afford an unprecedented degree of spatiotemporal control and are broadly applicable tools to study DAG signaling

Structural arrangement of the transmission interface in the antigen ABC transport complex TAP

The transporter associated with antigen processing (TAP) represents a focal point in the immune recognition of virally or malignantly transformed cells by translocating proteasomal degradation products into the endoplasmic reticulum–lumen for loading of MHC class I molecules. Based on a number of experimental data and the homology to the bacterial ABC exporter Sav1866, we constructed a 3D structural model of the core TAP complex and used it to examine the interface between the transmembrane and nucleotide-binding domains (NBD) by cysteine-scanning and cross-linking approaches. Herein, we demonstrate the functional importance of the newly identified X-loop in the NBD in coupling substrate binding to downstream events in the transport cycle. We further verified domain swapping in a heterodimeric ABC half-transporter complex by cysteine cross-linking. Strikingly, either substrate binding or translocation can be blocked by cross-linking the X-loop to coupling helix 2 or 1, respectively. These results resolve the structural arrangement of the transmission interface and point to different functions of the cytosolic loops and coupling helices in substrate binding, signaling, and transport

Properties of metabolic graphs: biological organization or representation artifacts?

<p>Abstract</p> <p>Background</p> <p>Standard graphs, where each edge links two nodes, have been extensively used to represent the connectivity of metabolic networks. It is based on this representation that properties of metabolic networks, such as hierarchical and small-world structures, have been elucidated and null models have been proposed to derive biological organization hypotheses. However, these graphs provide a simplistic model of a metabolic network's connectivity map, since metabolic reactions often involve more than two reactants. In other words, this map is better represented as a hypergraph. Consequently, a question that naturally arises in this context is whether these properties truly reflect biological organization or are merely an artifact of the representation.</p> <p>Results</p> <p>In this paper, we address this question by reanalyzing topological properties of the metabolic network of <it>Escherichia coli </it>under a hypergraph representation, as well as standard graph abstractions. We find that when clustering is properly defined for hypergraphs and subsequently used to analyze metabolic networks, the scaling of clustering, and thus the hierarchical structure hypothesis in metabolic networks, become unsupported. Moreover, we find that incorporating the distribution of reaction sizes into the null model further weakens the support for the scaling patterns.</p> <p>Conclusions</p> <p>These results combined suggest that the reported scaling of the clustering coefficients in the metabolic graphs and its specific power coefficient may be an artifact of the graph representation, and may not be supported when biochemical reactions are atomically treated as hyperedges. This study highlights the implications of the way a biological system is represented and the null model employed on the elucidated properties, along with their support, of the system.</p