The splitting number of the complete graph

If a given graphG can be obtained bys vertex identifications from a suitable planar graph ands is the minimum number for which this is possible thens is called the splitting number ofG. Here a formula for the splitting number of the complete graph is derived.     

Enzymatic amplification in a bioinspired, autonomous signal cascade

A two-step reaction cascade is applied to the sequence-specific detection of DNA by enzymatic amplification of the molecular into an optical signal.     

Three-center-two-electron and four-center-four-electron bonds. A study by electron charge density over the structure of methonium cations

We study the electronic density charge topology of CH(5)(+) species 1 (C(s)()), 2 (C(s)()), and 3 (C(2)(v)) at ab initio level using the theory of atoms in molecules developed by Bader. Despite the reports of previous studies concerning carbocationic species, the methane molecule is protonated at the carbon atom, which clearly shows its pentacoordination. In addition to the fact that hydrogen atoms in the methonium molecule behave in a very fluxional fashion and that the energy difference among the species 1, 2, and 3 are very low, is important to point out that two different topological situations can be defined on the basis of our study of the topology of the electronic charge density. Then, the species 1 and 2 present a three-center-two-electron (3c-2e) bond of singular characteristics as compared with other carbocationic species, but in the species 3, the absence of a 3c-2e bond is noteworthy. This structure can be characterized through the three bond critical points found, corresponding to saddle points on the path bonds between the C-H(2,3,5) that lie in the same plane. These nuclei define a four-center interaction where the electronic delocalization produced among the sigma(C-H) bonds provide a stabilization of the three C-H bonds involved in this interaction (the remaining two C-H bonds are similar to those belonging to the nonprotonated species). Our results show that bonding situations with a higher number of atom arrays are possible in protonated hydrocarbons.     

Hinge peptide combinatorial libraries for inhilbitors of botulinum neurotoxins and saxitoxin: Deconvolution strategy

Combinatorial library screening offers a rapid process for identifying potential therapies to toxins. Hinge peptide libraries, which rely on conformational diversity rather than traditional molecular diversity, reduce the need for huge numbers of syntheses and screening steps and greatly expedite the discovery process of active molecules. Hinge peptide libraries having the structures: Acetyl-X₁–X₂–hinge–X₃–X₄–NH₂ (capped) and X₁–hinge–X₂–X₃ (uncapped), where X₁ through X₄ are near-equimolar mixtures of twelve L-amino acids and hinge = 4-aminobutyric acid, were screened for inhibitory activity in bioassays for botulinum neurotoxins A and B (BoNT/A, BoNT/B) and saxitoxin. The zinc protease activity of the reduced light chains of BoNT/A and /B was assayed by measuring the cleavage of synthetic substrates. Saxitoxin activity was measured by the restoration of the viability of neuroblastoma cells treated with ouabain and veratridine. Deconvolution of libraries was accomplished by fixing one position at a time beginning with the C-terminus. Primary library subsets in which position 4 was fixed showed moderate levels of inhibition for BoNT/A. Secondary library subsets showed stronger inhibition in the bioassays. In each of the bioassays, inhibitory potency was stronger when the second position to be fixed was on the opposite side of the hinge, rather than on the same side with respect to the C-terminus, suggesting that the hinge facilitates the interaction of side chains. Inhibitors for all three of the toxins studied were discovered within library subsets, although not necessarily in primary subsets. These studies demonstrate that (1) the best strategy for deconvoluting hinge peptide libraries is by fixing residues alternately on each side of the hinge moiety, and (2) it is essential to investigate secondary subsets even when primary subsets are inactive. The present findings support the concept that the increased flexibility imposed by the inclusion of a central hinge residue in small peptides increases the opportunity for side chain interactions, providing a distinct advantage for hinge peptide libraries over conventional peptide libraries. Hinge peptide libraries are a rich source of novel ligands for modulation of biomechanisms. The library subsets uncovered in this study may possess peptides that will lead to effective therapies to neurotoxin poisoning.     

A new inertial-type hybrid projection-proximal algorithm for monotone inclusions

This paper investigates an enhanced proximal algorithm with interesting practical features and convergence properties for solving non-smooth convex minimization problems, or approximating zeroes of maximal monotone operators, in Hilbert spaces. The considered algorithm involves a recent inertial-type extrapolation technique, the use of enlargement of operators and also a recently proposed hybrid strategy, which combines inexact computation of the proximal iteration with a projection. Compared to other existing related methods, the resulting algorithm inherits the good convergence properties of the inertial-type extrapolation and the relaxed projection strategy. It also inherits the relative error tolerance of the hybrid proximal-projection method. As a special result, an update of inexact Newton-proximal method is derived and global convergence results are established.     

Enhancing high-order above-threshold dissociation of H2+ beams with few-cycle laser pulses

High-order (three-photon or more) above-threshold dissociation (ATD) of H(2)(+) has generally not been observed using 800 nm light. We demonstrate a strong enhancement of its probability using intense 7 fs laser pulses interacting with beams of H(2)(+), HD(+), and D(2)(+) ions. The mechanism invokes a dynamic control of the dissociation pathway. These measurements are supported by theory that additionally reveals, for the first time, an unexpectedly large contribution to ATD from highly excited electronic states.     

The daguerreotype surface as a SERS substrate: characterization of image deterioration in plates from the 19th century studio of Southworth & Hawes

Dramatic condition changes were noted in a group of daguerreotypes during a 10 month‐long exhibition featuring masterworks of the prominent Boston‐based studio of Southworth & Hawes. The changes took the form of a hazy, extended white surface layer and of white spots that partially obscured the images after between four weeks and 10 months of exhibition. Raman spectroscopy, complemented by in situ scanning electron microscopy–energy dispersive X‐ray spectrometry (SEM–EDS), was used to nondestructively characterize this form of image deterioration in eight representative daguerreotypes from the studio. Raman proved to be a sensitive technique to noninvasively identify the compounds on the plates due to the fact that their Ag surfaces behave as surface‐enhanced Raman scattering (SERS) substrates. A band at ca 242 cm⁻¹ assigned to the Ag Cl stretching mode was observed in the areas where a white surface layer or white spots are present. In some of the areas probed, substituted aromatic compounds were also detected. The presence of Ag Cl bonds on daguerreotype surfaces has profound implications for their exhibition and preservation due to the photosensitivity of silver chloride in the ultraviolet–visible range, which can generate metallic silver that would redeposit on the surfaces. The possible sources of the compounds detected on the surfaces of the plates are discussed. Copyright © 2008 John Wiley & Sons, Ltd.     

Chalcedony (a crystalline variety of silica): biogenic origin in electric organs from living Psammobatis extenta (family Rajidae)

The electric organs of electric fish have been used extensively for the study of peripheral cholinergic synapses. Aluminum and silicon have been observed in the electrocytes of Psammobatis extenta, a fish belonging to the family Rajidae, using a combination of scanning electron microscopy and X-ray spectrometry. Based on this evidence, the presence of silica minerals has been documented by means of mineralogical techniques. Electric organ cryostat sections and subcellular fractions were observed using a Leica DMLP mineralogical microscope. The shape, size and color, among other properties, were analyzed in plane-polarized light, while birefringence and the extinction angle, which allow for mineral identification, were observed through crossed-polarized illumination. The distribution of chalcedony, an oxide silicon mineral, in the sections and all the fractions of the electric organ was recorded. X-ray diffraction analysis of the electric organ segments showed a similar result, with a low-quartz variety. Chalcedony precipitation occurred at a specific pH (7-8) and oxidation potential (Eh; 0.0 to -0.2). This observation supports the important role played by pH and Eh conditions in silica precipitation in electrocytes, as has been reported in geological environments. It is possible that silica formation and silica degradation in electric organs are also related to the enzymes, silicatein and silicase, that direct the polymerization and depolymerization of amorphous silica in sponges. Carbonic anhydrases (silicase) are involved in physiological pH regulation. Crystallization of chalcedony via spiral growth from a partially polymerized fluid is consistent with processes known to occur in organic systems. This is the first time that a biogenically produced crystalline mineral phase (i.e., chalcedony) has been observed in the electrocytes and cholinergic nerves from living electric fish.