Independent systems of representatives in weighted graphs

The following conjecture may have never been explicitly stated, but seems to have been floating around: if the vertex set of a graph with maximal degree Δ is partitioned into sets V _i of size 2Δ, then there exists a coloring of the graph by 2Δ colors, where each color class meets each V _i at precisely one vertex. We shall name it the strong 2Δ-colorability conjecture. We prove a fractional version of this conjecture. For this purpose, we prove a weighted generalization of a theorem of Haxell, on independent systems of representatives (ISR’s). En route, we give a survey of some recent developments in the theory of ISR’s. The research of the first author was supported by grant no 780/04 from the Israel Science Foundation, and grants from the M. & M. L. Bank Mathematics Research Fund and the fund for the promotion of research at the Technion. The research of the third author was supported by the Sacta-Rashi Foundation.     

The Max-Flow Min-Cut theorem for countable networks

We prove a strong version of the Max-Flow Min-Cut theorem for countable networks, namely that in every such network there exist a flow and a cut that are “orthogonal” to each other, in the sense that the flow saturates the cut and is zero on the reverse cut. If the network does not contain infinite trails then this flow can be chosen to be mundane, i.e. to be a sum of flows along finite paths. We show that in the presence of infinite trails there may be no orthogonal pair of a cut and a mundane flow. We finally show that for locally finite networks there is an orthogonal pair of a cut and a flow that satisfies Kirchhoff's first law also for ends.     

Studies of Hindered Rotation and Magnetic Anisotropy by 1H, 13C and 19F NMR. The Diels-Alder Adduct of N- Pentafluorophenylmaleimide and Phencyclone: A Model for Drugs.

The potent Diels-Alder diene, phencyclone, 1, reacts with N-pentafluorophenylmaleimide, 2, to form an adduct, 3, characterized by ¹H, ¹³C, and ¹⁹F NMR at 300, 75 and 282 MHz, respectively. The one-dimensional (1D) and two-dimensional (2D) ¹H and ¹³C NMR spectra of 3 at ambient temperatures imply a slow exchange limit (SEL) regime with respect to rotation of the unsubstituted bridgehead phenyl groups about severely hindered C(sp²)-C(sp³) bonds. Major non-bonded interactions are expected between the ortho protons of the C₆H₅ groups and H-1, 8 of the phenanthrenoid moiety of 3. ¹⁹F 1D and 2D (COSY) NMR spectra show that the SEL regime also obtains for rotation about the N-C₆F₅ bond of 3, with five separate fluorine signals seen, consistent with a preferred conformation in which the C₆F₅ may lie roughly perpendicular to the plane of the pyrrolidinedione moiety, and may be in the mirror symmetry plane of 3. The results are considered relevant to hindered aryl rotations in numerous Pharmaceuticals. Selected spectral data for 2 and precursors are also presented.     

The antioxidant tempamine: in vitro antitumor and neuroprotective effects and optimization of liposomal encapsulation and release

The piperidine nitroxide tempamine (TMN) is a cell-permeable, stable radical having antioxidant, anticancer, and proapoptotic and/or pronecrotic activities, as was demonstrated by us in cell cultures. We also demonstrated synergism between TMN and doxorubicin in doxorubicin-sensitive and doxorubicin-resistant cell lines. Treatment of the C26 mouse colon carcinoma model in vivo also demonstrated synergism between TMN and doxorubicin in sterically stabilized liposomes (SSLs) containing TMN (SSL-TMN) and those containing doxorubicin. The above effects of TMN and SSL-TMN motivated us to develop and optimize the SSL-TMN formulation so that it will be able to reach the disease site with a sufficiently high TMN level and a release rate needed to achieve a therapeutic effect. Because TMN is an amphipathic weak base, it was remote loaded by an intraliposome high/extraliposome low transmembrane ammonium sulfate gradient. The kinetics and level of TMN loading were monitored by cyclic voltammetry (CV) and electron paramagnetic resonance (EPR); the latter also indicates TMN precipitation in the intraliposomal aqueous phase. The regeneration of the original CV and EPR signals by the ionophore nigericin indicates that TMN remained fully intact during loading and release. The cardinal role of the transmembrane ammonium ion gradient in the loading process was proven by the use of the selective ionophores nonactin (for NH4+) and nigericin (for H+). The anion of the ammonium salts affects loading stability and the rate of TMN release, both mediated through the TMN state of aggregation in the intraliposomal aqueous phase. The greater the TMN salt precipitation, the slower the TMN release rate. This was supported by measurement of osmolality, which is inversely related to TMN salt precipitate. Precipitation is in the order SO4(-2)>Cl-1>glucuronate-1. Liposome lipid composition, magnitude of the transmembrane ammonium ion gradient, and type of anion of the ammonium salt determine the amount of TMN loaded and its release rate.     

Aromatic Polynitro Ether Derivatives of Cellulose

The nucleophilic reaction of sodium cellulosate in the form of membrane or cotton fabric with 2, 4-dinitrohalo-benzenes, 2, 4, 6-trinitrochlorobenzene, 2, 4, 6-trinitrobenzyl bromide, and 2, 4, 6-trinitrostyrene was investigated. The degree of substitution attained with the dinitroaryl derivatives was much higher than that with the trinitroaryl derivatives. The reaction proceeded through Meisen-heimer complexes, which in the case of the trinitro derivatives could be isolated. The ability of the polynitro phenyl ether derivatives of the cellulose to form n- and π-complexes was investigated using naphthalene and p-toluidine. No -π- complex was formed with the former, and the latter gave complexes only with the 2, 4, 6-trinitrobenzyl or -phenethyl cellulose derivatives but not with the trinitrophenyl. The results were explained as due to steric hindrance from the polymeric cellulosic backbone.     

Maximum feasibility guideline in the design and analysis of protein folding potentials

Protein folding potentials are expected to have the lowest energy for the native shape. The Linear Programming (LP) approach achieves exactly that goal for a training set, or indicates that this goal is impossible to obtain. If a solution cannot be found (i.e., the problem is infeasible) two possible routes are possible: (a) choosing a new functional form for the potential, (b) finding the best potential with a feasible subset of the data, and (or) detecting inconsistent subset of the data in the training set. Here, we explore option (b). A simple heuristic for finding an approximate solution to an infeasible set of linear inequalities is outlined. An approximately feasible solution is obtained iteratively, starting from a certain initial guess, by computing a series of analytic centers of the polyhedra defined by all the inequalities satisfied at the subsequent iterations. Standard interior point algorithms for Linear Programming can be used to compute efficiently the analytic center of a polyhedron. We demonstrate how this procedure can be used for the design of folding potentials that are linear in their parameters. The procedure shows an improvement in the quality of the potentials and sometimes points to flaws in the original data.     

Solution equilibria of aromatic dinitroso compounds: a combined NMR and DFT study

Solution-state nitroso monomer-azodioxide equilibria and conformational freedom of several aromatic dinitroso derivatives, differing in the spacer group between the aromatic rings, were studied by one- and two-dimensional variable temperature ¹H NMR spectroscopy and by quantum chemical calculations. The proton signals of nitroso monomer-azodioxide mixtures revealed by low-temperature NMR were assigned and validated using B3LYP-D3/6-311+G(2d,p)/SMD level of theory. In almost all cases, a preference towards the formation of only one azodioxy isomer of aromatic dinitroso compounds was found, which was assigned to Z-dimer according to computational data. Nevertheless, the computed small energy difference between the Z- and E-isomer could not account for the extreme preference for Z-dimer formation, indicating an influence of entropic or solvent effects. The formation of shorter oligomers in solution was excluded based on integrated ¹H NMR signal intensities. The experimental results indicated an average dimerization Gibbs energy of about ??5 kJ/mol at 223 K and were found to be in very good correlation with dimerization energies obtained by solution-phase optimization.

     

Characterization of phosphopeptides from protein digests using matrix-assisted laser desorption/ionization time-of-flight mass spectrometry and nanoelectrospray quadrupole time-of-flight mass spectrometry

A two-step mass spectrometric method for characterization of phosphopeptides from peptide mixtures is presented. In the first step, phosphopeptide candidates were identified by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOFMS) based on their higher relative intensities in negative ion MALDI spectra than in positive ion MALDI spectra. The detection limit for this step was found to be 18 femtomoles or lower in the case of unfractionated in-solution digests of a model phosphoprotein, beta-casein. In the second step, nanoelectrospray tandem mass (nES-MS/MS) spectra of doubly or triply charged precursor ions of these candidate phosphopeptides were obtained using a quadrupole time-of-flight (Q-TOF) mass spectrometer. This step provided information about the phosphorylated residues, and ruled out nonphosphorylated candidates, for these peptides. After [(32)P] labeling and reverse-phase high-performance liquid chromatography (RP-HPLC) to simplify the mixtures and to monitor the efficiency of phosphopeptide identification, we used this method to identify multiple autophosphorylation sites on the PKR-like endoplasmic reticulum kinase (PERK), a recently discovered mammalian stress-response protein.     

Synthesis of the C1-side chain of zaragozic acid D and progress towards a total synthesis

A synthesis of a 1,3-dithiane corresponding to the C1-side chain of zaragozic acid D is described. An aldol reaction using an Evans oxazolidinone is the key step in controlling stereochemistry. Metallation of the derived dithiane monosulfoxide and coupling to an aldehyde effected construction of the C1-C7 bond. Subsequent steps are also reported, including acid-mediated ketalization resulting in formation of an advanced synthetic intermediate containing the bicyclic ketal core of the natural product.