Subset-Sum Representations of Domination Polynomials

The domination polynomial D(G, x) is the ordinary generating function for the dominating sets of an undirected graph G = (V, E) with respect to their cardinality. We consider in this paper representations of D(G, x) as a sum over subsets of the edge and vertex set of G. One of our main results is a representation of D(G, x) as a sum ranging over spanning bipartite subgraphs of G. Let d(G) be the number of dominating sets of G. We call a graph G conformal if all of its components are of even order. Let Con(G) be the set of all vertex-induced conformal subgraphs of G and let k(G) be the number of components of G. We show that $$d(G) = \sum \limits_{H\in{\rm Con}(G)}2^{k(H)}$$ .     

Determination of primary structure and microheterogeneity of a β-amyloid plaque-specific antibody using high-performance LC–tandem mass spectrometry

Using the bottom-up approach and liquid chromatography (LC) in combination with mass spectrometry, the primary structure and sequence microheterogeneity of a plaque-specific anti-β-amyloid (1–17) monoclonal antibody (clone 6E10) was characterized. This study describes the extent of structural information directly attainable by a high-performance LC–tandem mass spectrometric method in combination with both protein database searching and de novo sequence determination. Using trypsin and chymotrypsin for enzymatic digestion, 95% sequence coverage of the light chain and 82% sequence coverage of the heavy chain of the 6E10 antibody were obtained. The primary structure determination of a large number of peptides from the antibody variable regions was obtained through de novo interpretation of the data. In addition, N-terminal truncations of the heavy chain were identified as well as low levels of pyroglutamic acid formation. Surprisingly, pronounced sequence microheterogeneities were determined for the CDR 2 region of the light chain, indicating that changes at the protein level derived from somatic hypermutation of the Ig V_L genes in mature B-cells might contribute to unexpected structural diversity. Furthermore, the major glycoforms at the conserved heavy chain N-glycosylation site, Asn-292, were determined to be core-fucosylated, biantennary, complex-type structures containing zero to two galactose residues. Figure Primary structure and sequence microheterogeneities of a β-amyloid plaque-specific monoclonal antibody were identified by high-performance LC-tandem-mass spectrometry. Sequence heterogeneities of the light chain CDR2 reveal unexpected diversity from VL-gene hypermutations. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Capillary-zone electrophoresis/fast-atom bombardment mass spectrometry: design of an on-line coaxial continuous-flow interface

An on-line coaxial continuous-flow capillary-zone electrophoresis/fast-atom bombardment mass spectrometry (CZE/FAB-MS) interface is described. This interface is shown to be capable of acquiring mass spectra in an on-line fashion from low femtomole amounts of peptides while maintaining high (hundreds of thousands of plates) electrophoretic separation efficiencies. Active electrophoretic transport of the analytes directly to the FAB probe tip obviates the need for a transfer line from the end of the CZE capillary to this point, and thereby precludes the zone broadening that would otherwise occur both within such a transfer line and in the connections between the CZE column and the transfer line. The capability of acquiring an on-line tandem mass spectrometry (MS/MS) spectrum of an electrophoretically separated analyte using this interface is also demonstrated.     

Mass spectrometry in structural and stereochemical problems: CCXXXVI—corrected electron-impact-induced migratory aptitudes in aryl phenyl carbonates

Corrected relative migratory aptitudes for aryl groups in the electron-impact-induced rearrangement of aryl phenyl carbonates have been determined.     

Hydrogenation of arenes, alkenes and alkynes catalyzed by a sol–gel entrapped mixture of [Rh(cod)Cl]2 and Na[HRu3(CO)11]

A sol–gel entrapped 1:3 mixture of [Rh(cod)Cl]₂ and Na[HRu₃(CO)₁₁] catalyzes the hydrogenation of various unsaturated substrates by two distinguishable mechanisms. Under 13.8 bar H₂ and 20 °C methylated arenes react rapidly to give cycloalkane derivatives. XRD and TEM studies showed that under these conditions the hydrogenation proceeds without the generation of free metal particles. The hydrogenation of non-methylated arenes, as well as that of alkenes and alkynes, require a temperature of 80–120 °C at which the entrapped complexes form metallic nano-particles of 3–5 nm. Chloroarenes are also hydrodechlorinated at 120 °C, but require a hydrogen pressure of ≥25 bar. At both temperature ranges the catalysts are reusable at least four times. The high efficiency of the hydrogenation process at 20 °C is rationalized by a synergistic effect between the two different metal atoms of the combined catalyst. This may be related to a remote control model through a hydrogen spillover mechanism.     

Reactions of the transient species Cr(CO)5(cyclohexane) with C4HnE (n=4, 8; E=O, NH, S) studied by time-resolved IR absorption spectroscopy

Time-resolved IR absorption spectroscopy is used to investigate substitution of the cyclohexane (CyH) molecule of the photolytically generated alkane-solvated transient intermediate Cr(CO)5(CyH) by heterocyclic ligands C4HnE (n=4, 8; E=O, NH, S). From the concentration and temperature dependences of the pseudo-first order rate constants, we obtain activation parameters for the reactions, and find that they are consistent with an associative (A) or interchange (I) mechanism. As was the case with ligand substitution reactions at W(CO)5(CyH), a ligand's reactivity depends both on its electron-donating ability and on its polarizability. We also find that for a reaction with a given DeltaH, the activation entropy is higher for reaction of Cr(CO)5(CyH) than it is for reaction of W(CO)5(CyH). Comparison of the present results with ligand substitution reactions of W(CO)5(CyH), CpMn(CO)2(CyH), and Cr(CO)5(n-heptane) indicates that for ligand substitution reactions at alkane-solvated transition-metal intermediates, the solvent's effect upon the reaction rate is primarily entropic.     

DFT Study of the BH4− Hydrolysis on Au(111) Surface

The mechanism of the catalytic hydrolysis of BH₄⁻ on Au(111) as studied by DFT is reported. The results are compared to the analogous process on Ag(111) that was recently reported. It is found that the borohydride species are adsorbed stronger on the Au⁰-NP surface than on the Ag⁰-NP surface. The electron affinity of the Au is larger than that of Ag. The results indicate that only two steps of hydrolysis are happening on the Au(111) surface and the reaction mechanism differs significantly from that on the Ag(111) surface. These remarkable results were experimentally verified. Upon hydrolysis, only three hydrogens of BH₄⁻ are transferred to the Au surface, not all four, and H₂ generation is enhanced in the presence of surface H atoms. Thus, it is proposed that the BH₄⁻ hydrolysis and reduction mechanisms catalyzed by M⁰-NPs depend considerably on the nature of the metal.