Linear-time certifying algorithms for near-graphical sequences

A sequence 〈d₁,d₂,…,d_n〉 of non-negative integers is graphical if it is the degree sequence of some graph, that is, there exists a graph G on n vertices whose ith vertex has degree d_i, for 1≤i≤n. The notion of a graphical sequence has a natural reformulation and generalization in terms of factors of complete graphs.If H=(V,E) is a graph and g and f are integer-valued functions on the vertex set V, then a (g,f)-factor of H is a subgraph G=(V,F) of H whose degree at each vertex v∈V lies in the interval [g(v),f(v)]. Thus, a (0,1)-factor is just a matching of H and a (1, 1)-factor is a perfect matching of H. If H is complete then a (g,f)-factor realizes a degree sequence that is consistent with the sequence of intervals 〈[g(v₁),f(v₁)],[g(v₂),f(v₂)],…,[g(v_n),f(v_n)]〉.Graphical sequences have been extensively studied and admit several elegant characterizations. We are interested in extending these characterizations to non-graphical sequences by introducing a natural measure of “near-graphical”. We do this in the context of minimally deficient (g,f)-factors of complete graphs. Our main result is a simple linear-time greedy algorithm for constructing minimally deficient (g,f)-factors in complete graphs that generalizes the method of Hakimi and Havel (for constructing (f,f)-factors in complete graphs, when possible). It has the added advantage of producing a certificate of minimum deficiency (through a generalization of the Erdös-Gallai characterization of (f,f)-factors in complete graphs) at no additional cost.     

Characterization of the interaction of hypericin with protein kinase C in U-87 MG human glioma cells

A fluorescence imaging technique was used to monitor intracellular localization of protein kinase C (PKC) in U-87 MG human glioma cells in the presence of hypericin (Hyp) and phorbol 12-myristate-13-acetate (PMA). It is shown that PKC localization, which reflects its activity, is influenced by Hyp and this influence is different from that observed for PMA which acts as PKC activator. Fluorescence binding experiments were used to determine the binding constants of Hyp to several isoforms of PKC. The obtained values of K(d)s (approximately 100 nM) suggest that Hyp binds with high affinity to PKC. Finally, molecular modeling was used to compare structural models of the interaction of C1B domain of PKC (PKC isoforms alpha, delta, gamma) with Hyp and our previously published model of the (C1B domain PKCgamma)/PMA complex. The influence of Hyp on PKC translocation in U-87 MG cells in comparison with PMA, colocalization fluorescence pattern of Hyp and PKC, the higher binding affinity of Hyp to PKC in comparison with known binding constants of phorbol esters, as well as the binding mode of Hyp and PMA to the C1B domain of PKC suggested by molecular modeling, support the idea that Hyp and PMA might competitively bind to the regulatory domain of PKC.     

Stability of homomorphisms in the compact-open topology

We will prove a kind of stability result for homomorphisms from locally compact to completely regular topological universal algebras with respect to the compact-open topology on the space of all continuous functions between them. More precisely, given such algebras A and B and two additional set-valued mappings controlling the continuity of (partial) functions g from A to B and the range of the sets g(a) for individual elements ${a \in A}$ , every “controlled” partial function behaving almost like a homomorphism on a sufficiently big compact subset of A is arbitrarily close to a continuous homomorphism A → B on a compact set given in advance. We will give some counterexamples, showing the necessity of the assumptions, and discuss some special cases, among them a purely algebraic problem of extendability of finite partial functions to homomorphisms.     

Determination of beer aroma compounds using headspace solid-phase microcolumn extraction

A rapid sampling technique for the analysis of beer aroma compounds is described. The headspace (10 ml) is passed through the microcolumn filled with 5 mg of Tenax TA and thermally desorbed in a modified GC inlet (modification is described). Eight compounds (from acetaldehyde to 2-phenylethanol) in four beer samples were analyzed. The correlation coefficients (r²), repeatability (RSD) and limits of detection (LOD) were 0.9973-0.9994, 2.1-6.9% and 0.00002-0.13 mg/l, respectively. The methodology can be useful for routine beer sample analysis.     

A facile route to phenyl, phenylsulfanyl and phenylselanyl substituted pyrano[3,2-c]chromenes

The synthesis of phenyl, phenylsulfanyl and phenylselanyl substituted pyrano[3,2-c]chromenes 4 is accomplished via cyclocondensation of 4-oxo-4H-chromen-3-carbaldehydes 1 with appropriately substituted acetic acids 2 under mild conditions. Further treatment of 4 with alcohol or water led to 5-alkoxy- and 5-hydroxy-2H,5H-pyrano[3,2-c]chromen-2-ones 5 and 6, respectively. Acid and thermal catalysed rearrangement of 4-6 gave 5-hydroxypyrano[2,3-b]chromen-2(10aH)-ones 7 and their subsequent substitution led to 5-alkoxyderivatives 8. Reaction of 4 with amides led to 5-acylamino or 5-phenylsulfonamino substituted 2H,5H-pyrano[3,2-c]chromen-2-ones 9. Reactions were performed under heating or microwave irradiation.     

Glycation sites in neoglycoglycoconjugates from the terminal monosaccharide antigen of the O‐PS of Vibrio cholerae O1, serotype Ogawa,and BSA revealed by matrix‐assisted laser desorption–ionization tandem mass spectrometry

We present the MALDI‐TOF/TOF‐MS analyses of various hapten–bovine serum albumin (BSA) neoglycoconjugates obtained by squaric acid chemistry coupling of the spacer‐equipped, terminal monosaccharide of the O‐specific polysaccharide of Vibrio cholerae O1, serotype Ogawa, to BSA. These analyses allowed not only to calculate the molecular masses of the hapten–BSA neoglycoconjugates with different hapten–BSA ratios (4.3, 6.6 and 13.2) but, more importantly, also to localize the covalent linkages (conjugation sites) between the hapten and the carrier protein. Determination of the site of glycation was based on comparison of the MALDI‐TOF/TOF‐MS analysis of the peptides resulting from the digestion of BSA with similar data resulting from the digestion of BSA glycoconjugates, followed by sequencing by MALDI‐TOF/TOF‐MS/MS of the glycated peptides. The product‐ion scans of the protonated molecules were carried out with a MALDI‐TOF/TOF‐MS/MS tandem mass spectrometer equipped with a high‐collision energy cell. The high‐energy collision‐induced dissociation (CID) spectra afforded product ions formed by fragmentation of the carbohydrate hapten and amino acid sequences conjugated with fragments of the carbohydrate hapten. We were able to identify three conjugation sites on lysine residues (Lys235, Lys437 and Lys455). It was shown that these lysine residues are very reactive and bind lysine specific reagents. We presume that these Lys residues belong to those that are considered to be sterically more accessible on the surface of the tridimensional structure. The identification of the y‐series product ions was very useful for the sequencing of various peptides. The series of a‐ and b‐product ions confirmed the sequence of the conjugated peptides. Copyright © 2010 John Wiley & Sons, Ltd.     

Condensed lamellar phase in ternary DNA-DLPC-cationic gemini surfactant system: a small-angle synchrotron X-ray diffraction study

We report on a small-angle synchrotron X-ray diffraction study of dilauroylphosphatidylcholine (DLPC) liposomes aggregated with high molecular DNA in the presence of 1,4-butanediammonium-N,N'-dilauryl-N,N,N',N'-tetramethyl gemini surfactant cations (C12GS). The aggregates prepared at the DLPC/C12GS/DNA phosphate group=2:1:1.6 molar ratio in 0.0015 mol x l(-1) NaCl aqueous solution exhibit Bragg reflections due to lamellar lipid bilayer stacking and the Bragg reflection typical of one-dimensional DNA lattice with parallel strands intercalated between lipid bilayers. In this condensed fluid lamellar L(alpha)(c) phase, the interactions between DNA and charged bilayers damp the thermally induced bilayer undulations. The diffraction data obtained with the mixture of DLPC liposomes and DNA (at DNA phosphate group/DLPC=0.8:1 molar ratio) indicate a DNA-lipid interaction in the absence of C12GS.     

Spectroscopic study of 2-[2-(4-cyclaminophenyl)ethen-1-yl] benzothiazoles and their N-allylbenzothiazolium bromides. Solvent and substituent effects on their ultraviolet-visible and fluorescence spectra.

UV-vis and fluorescence spectra of 2-[2-(4-cyclaminophenyl)ethen-1-yl] benzothiazoles 1 and their N-allylbenzothiazolium bromides 2 have been measured and interpreted. The substitution and solvent effects on electronic structure and spectra have been investigated. The benzothiazolium salts substituted with saturated cyclamines show strong push-pull character and can be used as potential NLO materials. Formation of aggregated structures was observed at higher concentrations of the benzothiazolium bromides.