Rank and biclique partitions of the complement of paths

The problem was posed of determining the biclique partition number of the complement of a Hamiltonian path (Monson, Rees, and Pullman, Bull. Inst. Combinatorics and Appl. 14 (1995), 17–86). We define the complement of a path P, denoted P , as the complement of P in K_m,n where P is a subgraph of K_m,n for some m and n. We give an exact formula for the biclique partition number of the complement of a path. In particular, we solve the problem posed in [9]. We also summarize our more general results on biclique partitions of the complement of forests. © 1998 John Wiley & Sons, Inc. J Graph Theory 27: 111–122, 1998     

SSPaQ: A Subtractive Segmentation Approach for the Exhaustive Parallel Quantification of the Extent of Protein Modification at Every Possible Site

Protein modifications, whether chemically induced or post-translational (PTMs), play an essential role for the biological activity of proteins. Understanding biological processes and alterations thereof will rely on the quantification of these modifications on individual residues. Here we present SSPaQ, a subtractive method for the parallel quantification of the extent of modification at each possible site of a protein. The method combines uniform isotopic labeling and proteolysis with MS, followed by a segmentation approach, a powerful tool to refine the quantification of the degree of modification of a peptide to a segment containing a single modifiable amino acid. The strength of this strategy resides in: (1) quantification of all modifiable sites in a protein without prior knowledge of the type(s) of modified residues; (2) insensitivity to changes in the solubility and ionization efficiency of peptides upon modification; and (3) detection of missed cleavages caused by the modification for mitigation. The SSPaQ method was applied to quantify modifications resulting from the interaction of human phosphatidyl ethanolamine binding protein 1 (hPEBP1), a metastasis suppressor gene product, with locostatin, a covalent ligand and antimigratory compound with demonstrated activity towards hPEBP1. Locostatin is shown to react with several residues of the protein. SSPaQ can more generally be applied to induced modification in the context of drugs that covalently bind their target protein. With an alternate front-end protocol, it could also be applied to the quantification of protein PTMs, provided a removal tool is available for that PTM.

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Biimidazol-2-yl–BF2 complexes

Nonfluorescent 4,4′,5,5′-tetramethyl- and 4,5,4′,5′-bistetramethylene biimidazol-2-yls 5 and 6 combined with boron trifluoride to give the tetramethyl and bistetramethylenebiimidazol-2-yl–BF₂ complexes 9 and 10 isolated as strongly fluorescent BF₃ salts, λ_f (dichloromethane): 377 nm Φ 0.93 and 386 nm Φ 0.90. Similarly, fluorescent bibenzimidazol-2-yl 7 , λ_f (ethanol), 370 nm Φ 0.14, gave a BF₂ complex 11 isolated as a BF₃ salt λ_f (ethanol), 417 nm Φ 0.68.     

Bimanes (1,5-diazabicyclo[3.3.0]octadienediones): Laser activity in syn-bimanes

The conversion of 3-methyl-4-benzyl-4-chloro-2-pyrazolin-5-one 10b was catalyzed by a mixture of potassium fluoride and alumina to give syn-(methyl, benzyl)bimane 6 (62%) without detectable formation of the anti isomer, A6 [a 1 : 1 mixture (87%) of the isomers 6 and A6 was obtained when the catalyst was potassium carbonate]. In a similar reaction syn-(methyl,carboethoxymethyl)bimane 7 (15%) with the anti isomer A7 (36%) was obtained from 3-methyl-4-carboethoxymethyl-4-chloro-2-pyrazolin-5-one 10c . syn-(Methyl, β-acetoxyethyl)bimane 8 (70%) was obtained from 3-methyl-4-β-acetoxyethyl-4-chloro-2-pyrazolin-5-one 10d (potassium carbonate catalysis) and was converted by hydrolysis to syn-(methyl, β-hydroxyethyl)bimane 9 (40%). Acetyl nitrate (nitric acid in acetic anhydride) converted anti-(amino,hydrogen)bimane 11 to anti-(amino,nitro)bimane 15 (91%), anti-(methyl,hydrogen)bimane 13 to anti-(methyl,nitro)(methyl,hydrogen)bimane 16 (57%), and degraded syn-(methyl,hydrogen)bimane 12 to an intractable mixture. Treatment with trimethyl phosphite converted syn-(bromomethyl,methyl)bimane 17 to syn-(dimethoxyphosphinylmethyl,methyl)bimane 18 (78%) that was further converted to syn-(styryl,methyl)bimane 19 (29%) in a condensation reaction with benzaldehyde. Treatment with acryloyl chloride converted syn-(hydroxymethyl,methyl)bimane 20 to its acrylate ester 21 (22%). Stoichiometric bromination of syn-(methyl,methyl)bimane 1 gave a monobromo derivative that was converted in situ by treatment with potassium acetate to syn-(acetoxymethyl,methyl)(methyl,methyl)bimane 47 . N-Amino-μ-amino-syn-(methylene,methyl)bimane 24 (68%) was obtained from a reaction between the dibromide 17 and hydrazine. Derivatives of the hydrazine 24 included a perchlorate salt and a hydrazone 25 derived from acetone. Dehydrogenation of syn-(tetramethylene)bimane 26 by treatment with dichlorodicyanobenzoquinone (DDQ) gave syn-(benzo,tetramethylene)bimane 27 (58%) and syn-(benzo)bimane 28 (29%). Bromination of the bimane 26 gave a dibromide 29 (92%) that was also converted by treatment with DDQ to syn-(benzo)bimane 28 . Treatment with palladium (10%) on charcoal dehydrogenated 5, 6, 10, 11-tetrahydro-7H,9H-benz [6, 7] indazol [1, 2a]benz[g]indazol-7,9-dione 35 to syn-(α-naphtho)bimane 36 (71%). The bimane 35 was prepared from 1,2,3,4-tetrahydro-1-oxo-2-naphthoate 37 by stepwise treatment with hydrazine to give 1,2,4,5-tetrahydro-3H-benz[g]indazol-3-one 38 , followed by chlorine to give 3a-chloro-2,3a,4,5-tetrahydro-3H-benz[g]indazol-3-one 39 , and base. Dehydrogenation over palladium converted the indazolone 34 to 1H-benz[g] indazol-3-ol 36 . Helicity for the hexacyclic syn-(α-naphtho)bimane 36 was confirmed by an analysis based on molecular modeling. The relative efficiencies (RE) for laser activity in the spectral region 500–530 nm were obtained for 37 syn-bimanes by reference to coumarin 30 (RE 100): RE > 80 for syn-bimanes 3, 5, 18 , and μ-(dicarbomethoxy)methylene-syn-(methylene,methyl)bimane 22 : RE 20–80: for syn-bimanes 1,2,4,20,24,26 , and μ-thia-syn-(methylene,methyl)bimane 50 : and RE 0-20 for 26 syn-bimanes. The bimane dyes tended to be more photostable and more water-soluble than coumarin 30. The diphosphonate 18 in dioxane showed laser activity at 438 nm and in water at 514 nm. Presumably helicity, that was demonstrated by molecular modeling, brought about a low fluorescence intensity for syn-(α-naphtho)bimane 36 , Φ0.1, considerably lower than obtained for syn-(benzo)bimane 28 , Φ0.9.     

A note on smooth toral reductions of spheres

In this paper we show that there exist mod 2 obstructions to the smoothness of 3-Sasakian reductions of spheres. Specifically, ifS is a smooth 3-Sasakian manifold obtained by reduction of the 3-Sasakian sphereS ⁴ⁿ⁻¹ by a torus, and if the second Betti numberb ₂(S)≥2 then dimS=7, 11, 15, whereas, ifb ₂ (S)≥5 then dimS=7. We also show that the above bounds are sharp, in that we construct explicit examples of 3-Sasakian manifolds in the cases not excluded by these bounds. During the preparation of this work the authors were partially supported by an NSF grant. This article was processed by the author using the L^AT_EX style file from Springer-Verlag.     

Dinoflagellate neurotoxins related to saxitoxin: Structures of toxins C3 and C4, and confirmation of the structure of neosaxitoxin

By x-ray crystallography of the 11β epimer, toxins C3 and C4 are shown to be 21-sulfo-N-1-hydroxysaxitoxin-11α- and 11β-hydroxysulfate, confirming the position and identity of the 3 substituents which, with the parent compound, form the array of 12 saxitoxins found in $\text{Protogonyaulax}$.     

Notiz zur Synthese Eines Optisch Aktiven Ace-Hemmers mit Amino-oxo-benzazepin-1-alkansäure-Struktur mittels enantiokonvergierender kristallisationsinduzierter Racemat-Trennung

Note on the Synthesis of an Optically Active ACE Inhibitor with Amino-oxo-benzazepine-1-alkanoic-Acid Structure by Means of an Enantioconvergent Crystallization-Based Resolution An enantioselective synthesis of the potent angiotensin-converting enzyme inhibitor (1′S,3S)-3-[(1′-(ethoxy-carbonyl)-3′-phenylpropyl)amino]-2,3,4,5-tetrahydro-2-oxo-1H-1-benzazepine-1-acetic acid hydrochloride ( 3 ) is described which user a crystallization-based resolution of a racemic amino intermediate with concomitant racemization of the unwanted enantiomer.     

High-brightness terawatt KrF* (248 nm) system

19 W/cm² range with improved shot-to-shot energy stability. This system gives a resulting brightness of ∼3.3×10²¹ W cm^-2 sr^-1. Received: 5 November 1996/Revised version: 29 November 1996