A quadratic programming approach to the Randić index

Let G(k, n) be the set of connected graphs without multiple edges or loops which have n vertices and the minimum degree of vertices is k. The Randi? index χ = χ(G) of a graph G   is defined by χ(G)=_∑(uv)(_δuδv)^-1/2$\chi (G)={\sum }_{(\mathit{uv})}({\delta }_u{\delta }_v{)}^{-1/2}$, where δ_u is the degree of vertex u and the summation extends over all edges (uv) of G. Caporossi et al. [G. Caporossi, I. Gutman, P. Hansen, Variable neighborhood search for extremal graphs IV: Chemical trees with extremal connectivity index, Computers and Chemistry 23 (1999) 469–477] proposed the use of linear programming as one of the tools for finding the extremal graphs. In this paper we introduce a new approach based on quadratic programming for finding the extremal graphs in G(k, n) for this index. We found the extremal graphs or gave good bounds for this index when the number n_k of vertices of degree k is between n − k and n. We also tried to find the graphs for which the Randi? index attained its minimum value with given k (k ? n/2) and n. We have solved this problem partially, that is, we have showed that the extremal graphs must have the number n_k of vertices of degree k less or equal n − k and the number of vertices of degree n − 1 less or equal k.     

Dibromo(pyridoxal semicarbazone‐κ3N1,O3,O3′)copper(II)

The title compound, di­bromo(3‐hydroxy‐5‐hydroxy­methyl‐2‐methyl‐4‐pyridine­carbox­aldehyde semicarbazone‐κ³N¹,O³,O^3′)copper(II), [CuBr₂(C₉H₁₂N₄O₃)], consists of discrete complex units with the tridentate pyridoxal semicarbazone ligand as a zwitterion in an almost planar configuration. The Cu^II ions are in a distorted square‐pyramidal coordination, with the equatorial Br atom at a distance of 2.4017 (6) Å and the apical Br atom at a distance of 2.6860 (6) Å.     

Chemometrically Assisted Development and Validation of LC for Simultaneous Determination of Carbamazepine and Its Impurities Iminostilbene and Iminodibenzyl in Solid Dosage Form

A chemometrical approach was applied to develop a reversed-phase liquid chromatographic method for simultaneous determination of carbamazepine and its impurities iminostilbene and iminodibenzyl in solid dosage form. According to contemporary literature, no method was developed for simultaneous determination of carbamazepine and these impurities by chemometrical approach. The fractional factorial design was used for selection of variables significantly influencing the chromatographic separation of the investigated substances. The investigated variables were: temperature of the column, the percentage of organic modifier, the acetate buffer concentration and pH of water phase. The first three variables were proved to be significant and were optimized by face centered, central composite design. Investigation was performed using C18 XBridge Shield analytical column (50 mm × 4.6 mm i.d., particle size 3.5 µm). The optimal conditions for the separation were established with the mobile phase composition of methanol–10 mM acetate buffer (pH adjusted to 2.21 with glacial acetic acid) (50:50, v/v) at a flow rate of 1.5 mL min^?1, 25 °C column temperature and detection at 260 nm. Total analysis time was shortened to about 8 min. Finally, the method was successfully validated and subsequently applied to the analysis of commercially available carbamazepine tablets.     

Apoenzyme Reconstitution as a Chemical Tool for Structural Enzymology and Biotechnology

Enzymes with artificial cofactors : Nondiffusible organic cofactors of enzymes can often be replaced by artifical analogues to generate semisynthetic enzymes (see scheme). This approach can be used to study structure–function relationships in enzymology and to produce novel enzymes with enhanced or even entirely new functions that are useful for biosensing, biocatalysis, and materials science applications.

     

Surface-enhanced Raman scattering as a tool to probe cytochrome P450-catalysed substrate oxidation

Surface-enhanced Raman scattering was used as a spectroscopic tool to investigate the changes brought upon cytochrome P450BSß after fatty acid binding. Differences in the spectra of substrate-free and substrate-bound enzyme were observed indicating the potential for this method to be used in the screening of P450 substrates. In particular, the binding characteristics of myristic acid, an inherent substrate, and hydroxylauric acid, a product of fatty acid oxidation, towards P450BSß in the presence of H₂O₂ were investigated. Specific spectral changes could be assigned to changes in the heme environment only for myristic acid, indicating an occurrence of oxidation process characteristic for the enzymatic substrate.     

Pressure limited sustained off-resonance irradiation for collision-activated dissociation in Fourier transform mass spectrometry

A theoretical evaluation of the sustained off-resonance irradiation of ions (SORI) in the presence of a collisional buffer gas in a Fourier transform ion cyclotron resonance mass spectrometer is presented. It is shown that there is an optimal pressure for a given set of irradiation parameters corresponding to the most effective dissociation. Theoretical predictions are compared with experimental results for the dissociation of electrosprayed biopolymer ions and with previously accepted view of the SORI process.     

21 Tesla Fourier Transform Ion Cyclotron Resonance Mass Spectrometer Greatly Expands Mass Spectrometry Toolbox

We provide the initial performance evaluation of a 21 Tesla Fourier transform ion cyclotron resonance mass spectrometer operating at the Environmental Molecular Sciences Laboratory at the Pacific Northwest National Laboratory. The spectrometer constructed for the 21T system employs a commercial dual linear ion trap mass spectrometer coupled to a FTICR spectrometer designed and built in-house. Performance gains from moving to higher magnetic field strength are exemplified by the measurement of peptide isotopic fine structure, complex natural organic matter mixtures, and large proteins. Accurate determination of isotopic fine structure was demonstrated for doubly charged Substance P with minimal spectral averaging, and 8158 molecular formulas assigned to Suwannee River Fulvic Acid standard with root-mean-square (RMS) error of 10 ppb. We also demonstrated superior performance for intact proteins; namely, broadband isotopic resolution of the entire charge state distribution of apo-transferrin (78 kDa) and facile isotopic resolution of monoclonal antibody under a variety of acquisition parameters (e.g., 6 s time-domains with absorption mode processing yielded resolution of approximately 1 M at m/z?=?2700).

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Utilizing a Robotic Sprayer for High Lateral and Mass Resolution MALDI FT-ICR MSI of Microbial Cultures

The ability to visualize biochemical interactions between microbial communities using MALDI MSI has provided tremendous insights into a variety of biological fields. Matrix application using a sieve proved to be incredibly useful, but it has many limitations that include uneven matrix coverage and limitation in the types of matrices that could be employed in studies. Recently, there has been a concerted effort to improve matrix application for studying agar plated microbial cultures, many of which utilized automated matrix sprayers. Here, we describe the usefulness of using a robotic sprayer for matrix application. The robotic sprayer has two-dimensional control over where matrix is applied, and a heated capillary that allows for rapid drying of the applied matrix. This method provided a significant increase in MALDI sensitivity over the sieve method, as demonstrated by FT-ICR MS analysis, facilitating the ability to gain higher lateral resolution MS images of Bacillus subtilis than previously reported. This method also allowed for the use of different matrices to be applied to the culture surfaces.

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Collisional activation of ions in RF ion traps and ion guides: The effective ion temperature treatment

Ion transfer and storage using inhomogeneous radio frequency (RF) electric fields in combination with gas-assisted ion cooling and focusing constitutes one of the basic techniques in mass spectrometry today. The RF motion of ions in the bath gas environment involves a large number of ion-neutral collisions that leads to the internal activation of ions and their effective "heating" (when a thermal distribution of internal energies results). The degree of ion activation required in various applications may range from a minimum level (e.g., slightly raising the average internal energy) to an intense level resulting in ion fragmentation. Several research groups proposed using the effective temperature as a measure of ion activation under conditions of multiple ion-neutral collisions. Here we present approximate relationships for the effective ion temperature relevant to typical operation modes of RF multipole devices. We show that RF ion activation results in near-thermal energies for ions occupying an equilibrium position at the center of an RF trap, whereas increased ion activation can be produced by shifting ions off-center, e.g., by means of an external DC electric field. The ion dissociation in the linear quadrupole ion trap using the dipolar DC ion activation has been observed experimentally and interpreted in terms of the effective ion temperature.