Representation theory of 2-groups on Kapranov and Voevodsky's 2-vector spaces

In this paper the representation theory of 2-groups in 2-categories is considered, focusing the attention on the 2-category Rep2MatK(G) of representations of a 2-group G in (a version of) Kapranov and Voevodsky's 2-category of 2-vector spaces over a field K. The set of equivalence classes of such representations is computed in terms of the invariants π₀(G), π₁(G) and [α]∈H³(π₀(G),π₁(G)) classifying G, and the categories of intertwiners are described in terms of categories of vector bundles endowed with a projective action. In particular, it is shown that the monoidal category of finite dimensional linear representations (more generally, the category of [z]-projective representations, for any given cohomology class [z]∈H²(π₀(G),K^∗)) of the first homotopy group π₀(G) as well as its category of representations on finite sets both live in Rep2MatK(G), the first as the monoidal category of endomorphisms of the trivial representation (more generally, as the category of intertwiners between suitable 1-dimensional representations) and the second as a non-full subcategory of the homotopy category of Rep2MatK(G).     

The shape of the Sc2(μ2-S) unit trapped in C82: crystallographic, computational, and electrochemical studies of the isomers, Sc2(μ2-S)@C(s)(6)-C82 and Sc2(μ2-S)@C(3v)(8)-C82

Single-crystal X-ray diffraction studies of Sc(2)(μ(2)-S)@C(s)(6)-C(82)·Ni(II)(OEP)·2C(6)H(6) and Sc(2)(μ(2)-S)@C(3v)(8)-C(82)·Ni(II)(OEP)·2C(6)H(6) reveal that both contain fully ordered fullerene cages. The crystallographic data for Sc(2)(μ(2)-S)@C(s)(6)-C(82)·Ni(II)(OEP)·2C(6)H(6) show two remarkable features: the presence of two slightly different cage sites and a fully ordered molecule Sc(2)(μ(2)-S)@C(s)(6)-C(82) in one of these sites. The Sc-S-Sc angles in Sc(2)(μ(2)-S)@C(s)(6)-C(82) (113.84(3)°) and Sc(2)(μ(2)-S)@C(3v)(8)-C(82) differ (97.34(13)°). This is the first case where the nature and structure of the fullerene cage isomer exerts a demonstrable effect on the geometry of the cluster contained within. Computational studies have shown that, among the nine isomers that follow the isolated pentagon rule for C(82), the cage stability changes markedly between 0 and 250 K, but the C(s)(6)-C(82) cage is preferred at temperatures ≥250 °C when using the energies obtained with the free encapsulated model (FEM). However, the C(3v)(8)-C(82) cage is preferred at temperatures ≥250 °C using the energies obtained by rigid rotor-harmonic oscillator (RRHO) approximation. These results corroborate the fact that both cages are observed and likely to trap the Sc(2)(μ(2)-S) cluster, whereas earlier FEM and RRHO calculations predicted only the C(s)(6)-C(82) cage is likely to trap the Sc(2)(μ(2)-O) cluster. We also compare the recently published electrochemistry of the sulfide-containing Sc(2)(μ(2)-S)@C(s)(6)-C(82) to that of corresponding oxide-containing Sc(2)(μ(2)-O)@C(s)(6)-C(82).     

Hierarchical chiral expression from the nano- to mesoscale in synthetic supramolecular helical fibers of a nonamphiphilic C3-symmetrical π-functional molecule

The controlled preparation of chiral structures is a contemporary challenge for supramolecular science because of the interesting properties that can arise from the resulting materials, and here we show that a synthetic nonamphiphilic C(3) compound containing π-functional tetrathiafulvalene units can form this kind of object. We describe the synthesis, characterization, and self-assembly properties in solution and in the solid state of the enantiopure materials. Circular dichroism (CD) measurements show optical activity resulting from the presence of twisted stacks of preferential helicity and also reveal the critical importance of fiber nucleation in their formation. Molecular mechanics (MM) and molecular dynamics (MD) simulations combined with CD theoretical calculations demonstrate that the (S) enantiomer provides the (M) helix, which is more stable than the (P) helix for this enantiomer. This relationship is for the first time established in this family of C(3) symmetric compounds. In addition, we show that introduction of the "wrong" enantiomer in a stack decreases the helical reversal barrier in a nonlinear manner, which very probably accounts for the absence of a "majority rules" effect. Mesoscopic chiral fibers, which show inverted helicity, i.e. (P) for the (S) enantiomer and (M) for the (R) one, have been obtained upon reprecipitation from dioxane and analyzed by optical and electronic microscopy. The fibers obtained with the racemic mixture present, as a remarkable feature, opposite homochiral domains within the same fiber, separated by points of helical reversal. Their formation can be explained through an "oscillating" crystallization mechanism. Although C(3) symmetric disk-shaped molecules containing a central benzene core substituted in the 1,3,5 positions with 3,3'-diamido-2,2'-bipyridine based wedges have shown peculiar self-assembly properties for amphiphilic derivatives, the present result shows the benefits of reducing the nonfunctional part of the molecule, in our case with short chiral isopentyl chains. The research reported herein represents an important step toward the preparation of functional mesostructures with controlled helical architectures.     

On the regular representation of an (essentially) finite 2-group

The regular representation of an essentially finite 2-group G in the 2-category 2Vectk of (Kapranov and Voevodsky) 2-vector spaces is defined and cohomology invariants classifying it are computed. It is next shown that all hom-categories in Rep2Vectk(G) are 2-vector spaces under quite standard assumptions on the field k, and a formula giving the corresponding “intertwining numbers” is obtained which proves they are symmetric. Finally, it is shown that the forgetful 2-functor ω:Rep2Vectk(G)→2Vectk is representable with the regular representation as representing object. As a consequence we obtain a k-linear equivalence between the 2-vector space of functors from the underlying groupoid of G to Vectk, on the one hand, and the k-linear category End(ω) of pseudonatural endomorphisms of ω, on the other hand. We conclude that End(ω) is a 2-vector space, and we (partially) describe a basis of it.     

Forchlorfenuron-mimicking haptens: from immunogen design to antibody characterization by hierarchical clustering analysis

To obtain highly-specific and selective forchlorfenuron binders, a collection of functionalized derivatives with different spacer arm locations and lengths was prepared. By immunization with target-mimicking haptens, a large battery of monoclonal and polyclonal antibodies against this synthetic cell regulator was produced and exhaustively characterized in two immunoassay formats using homologous and heterologous conjugates. Antibodies with IC(50) values lower than 0.3 nM were successfully raised from the prepared immunogens, thus evidencing the efficacy of the explored strategies. In order to identify significant epitopes in the antibody-antigen interaction, a series of new chemical forchlorfenuron analogues, with slight modifications at both rings of the target molecule, were synthesized and evaluated in competitive assays. As a novel approach in hapten recognition studies, data processing was performed by computational classification methods based on hierarchical clustering. This strategy was shown to be highly valuable for a straightforward profiling of antibodies according to analogue recognition patterns. A relationship could be established between the antigen binding properties of antibodies and the structure of the immunogen. Whereas antibodies with equivalent affinities had been obtained from all of the derivatives, their specificity was found to be largely influenced by the differential exposition of the molecule to the immune system.     

Synthesis of site-heterologous haptens for high-affinity anti-pyraclostrobin antibody generation

The design and synthesis of functional chemical derivatives of small organic molecules is usually a key step for the intricate production of a variety of bioconjugates. In this respect, the derivatization site at which the spacer arm is introduced in immunizing conjugates constitutes a highly critical parameter for the generation of high-affinity and selective antibodies. However, due to the usual complexity of the required synthetic procedures, the appropriate comparison of alternative tethering positions has often been neglected. In the present study, meticulous strategies were followed to prepare synthetic derivatives of pyraclostrobin with the same linkers located at diverse rationally-chosen sites. Activity appraisal of antibodies and bioconjugates was carried out by bidimensional competitive direct and indirect immunoassays, and a superior performance of two of the three synthesized haptens was found. Finally, a detailed analysis of the conformations of the target molecule and the synthesized haptens in aqueous solution was done using computer assisted molecular modeling techniques. This study suggested that the lower titers and affinities of one set of antibodies are most probably due to conformational effects of the spacer arm in the immunizing bioconjugate.     

Development of a methodology to quantify tamoxifen and endoxifen in breast cancer patients by micellar liquid chromatography and validation according to the ICH guidelines

A simple micellar liquid chromatographic procedure is described to determine tamoxifen and endoxifen in plasma. For the analysis, tamoxifen and endoxifen solutions were diluted in water and UV-irradiated for 20 min to form the photocycled derivative with a phenanthrene core which shows intense fluorescence. Samples were then directly injected, thus avoiding long extraction and experimental procedures. The resolution from the matrix was performed using a mobile phase containing 0.15 mol L⁻¹ SDS-7% n-butanol at pH 3, running at 1.5 mL min⁻¹ through a C18 column at 40 °C. Detection was carried out by fluorescence, and the excitation and emission wavelengths were 260 and 380 nm, respectively. The chromatographic analysis time was 20 min. The analytical methodology was validated following the International Conference on Harmonisation of Technical Requirements for Registration of Pharmaceuticals for Human Use (ICH) guidelines. The response of the drugs in plasma was linear in the 0.5-15 μg mL⁻¹ range, with r² > 0.99. Accuracy and precision were <14% in both cases. Limits of detection and quantification (ng mL⁻¹) in plasma were 75 and 250 for endoxifen, and 50 and 150 in tamoxifen. The method developed herein does not show interferences by endogenous compounds. Finally the analytical method was used to determine the amount of tamoxifen and endoxifen in several plasma samples of breast cancer patients from a local hospital.     

Tribological evaluation of HVOF thermal‐spray coatings as a hard chrome replacement

Hard chrome plating has been used in several different applications in industries that require abrasive sliding wear resistance, such as hydraulic pistons, shafts or bearings. However, the increasing environmental and worker safety pressures on electrolytic hard chrome are leading companies to adopt alternatives. The improvements of the high‐velocity‐oxy‐fuel (HVOF) thermal spray process allow the chromium coating replacement with a comparable or superior surface treatment and are more environmentally friendly. This HVOF process, as a flexible dry‐coating technology, avoids high‐volume waste streams and enables a flexible choice of coating material for each application. The cobalt–chromium‐cemented tungsten carbides are some of the easiest materials to spray and the WC‐10Co‐4Cr coatings have demonstrated superior performance over hard chrome with regard to mechanical and tribological properties. In this work, this coating has been deposited with a Sulzer Metco WokaJet‐400 kerosene fuel spray gun, and the spray conditions have been optimized in order to ensure the best properties of the coatings. The mechanical and tribological properties have been evaluated in coatings sprayed with four deposition conditions that involve different gas flow rates. The most wear‐resistant coating is obtained with those HVOF parameters that prevent decarburization of WC particles and, at the same time, allow an adequate agglomerate melting giving a good intersplat adhesion. The results indicate that HVOF‐sprayed WC‐CoCr coatings are a reliable alternative to electrolytic hard chrome (EHC) in the aeronautical industry to coat landing gear components. In particular, in the dry wear tests, the WC‐CoCr coatings outperform hard chrome coatings in wear resistance. Copyright © 2010 John Wiley & Sons, Ltd.