Multicuts in unweighted graphs and digraphs with bounded degree and bounded tree-width

The Multicut problem can be defined as: given a graph G and a collection of pairs of distinct vertices {s_i,t_i} of G, find a minimum set of edges of G whose removal disconnects each s_i from the corresponding t_i. Multicut is known to be NP-hard and Max SNP-hard even when the input graph is restricted to being a tree. The main result of the paper is a polynomial-time approximation scheme (PTAS) for Multicut in unweighted graphs with bounded degree and bounded tree-width. That is, for any ε>0, we present a polynomial-time (1+ε)-approximation algorithm. In the particular case when the input is a bounded-degree tree, we have a linear-time implementation of the algorithm. We also provide some hardness results: we prove that Multicut is still NP-hard for binary trees and that it is Max SNP-hard if we drop any of the three conditions (unweighted, bounded-degree, bounded tree-width). Finally we show that some of these results extend to the vertex version of Multicut and to a directed version of Multicut.     

Disjoint bases in a polymatroid

Let f : 2^N → ⁺ be a polymatroid (an integer‐valued non‐decreasing submodular set function with f(??) = 0). We call S ? N a base if f(S) = f(N). We consider the problem of finding a maximum number of disjoint bases; we denote by m* be this base packing number. A simple upper bound on m* is given by k* = max{k : Σ_iεNf_A(i) ≥ kf_A(N),?A ? N} where f_A(S) = f(A ∪ S) ‐ f(A). This upper bound is a natural generalization of the bound for matroids where it is known that m* = k*. For polymatroids, we prove that m* ≥ (1 ? o(1))k*/lnf(N) and give a randomized polynomial time algorithm to find (1 ? o(1))k*/lnf(N) disjoint bases, assuming an oracle for f. We also derandomize the algorithm using minwise independent permutations and give a deterministic algorithm that finds (1 ? ε)k*/lnf(N) disjoint bases. The bound we obtain is almost tight because it is known there are polymatroids for which m* < (1 + o(1))k*/lnf(N). Moreover it is known that unless NP ? DTIME(n^{log log n}), for any ε > 0, there is no polynomial time algorithm to obtain a (1 + ε)/lnf(N)‐approximation to m*. Our result generalizes and unifies two results in the literature. © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2009     

CO rebinding to protoheme: investigations of the proximal and distal contributions to the geminate rebinding barrier

The rebinding kinetics of CO to protoheme (FePPIX) in the presence and absence of a proximal imidazole ligand reveals the magnitude of the rebinding barrier associated with proximal histidine ligation. The ligation states of the heme under different solvent conditions are also investigated using both equilibrium and transient spectroscopy. In the absence of imidazole, a weak ligand (probably water) is bound on the proximal side of the FePPIX-CO adduct. When the heme is encapsulated in micelles of cetyltrimethylammonium bromide (CTAB), photolysis of FePPIX-CO induces a complicated set of proximal ligation changes. In contrast, the use of glycerol-water solutions leads to a simple two-state geminate kinetic response with rapid (10-100 ps) CO recombination and a geminate amplitude that can be controlled by adjusting the solvent viscosity. By comparing the rate of CO rebinding to protoheme in glycerol solution with and without a bound proximal imidazole ligand, we find the enthalpic contribution to the proximal rebinding barrier, H(p), to be 11 +/- 2 kJ/mol. Further comparison of the CO rebinding rate of the imidazole bound protoheme with the analogous rate in myoglobin (Mb) leads to a determination of the difference in their distal free energy barriers: DeltaG(D) approximately 12 +/- 1 kJ/mol. Estimates of the entropic contributions, due to the ligand accessible volumes in the distal pocket and the xenon-4 cavity of myoglobin ( approximately 3 kJ/mol), then lead to a distal pocket enthalpic barrier of H(D) approximately 9 +/- 2 kJ/mol. These results agree well with the predictions of a simple model and with previous independent room-temperature measurements of the enthalpic MbCO rebinding barrier (18 +/- 2 kJ/mol).     

Bioactive microparticles (10): thermal and oxidative stability of nicotine and its complex with β-cyclodextrin

The paper presents a comparative thermal and oxidative stability study between nicotine/β-cyclodextrin microparticles and commercial nicotine. It is well known that the nicotine is the bioactive compound in formulations used for smoking cessation and no studies among the stability of nicotine in cyclodextrin-containing formulations were reported. The non-enzymatic and enzymatic oxidation of nicotine can lead to cotinine (an alkaloid/metabolite with a lower toxicity), but another way is the obtaining of the cancerigene N-nitroso-nicotine derivatives by nornicotine derivative intermediates (like nornicotine and myosmine). The present study demonstrates the protecting capacity of β-cyclodextrin for commercial nicotine against thermal and oxidative factors: for the non-complexed nicotine the thermal and oxidative degradation led to a decrease of the relative concentration of nicotine from 96 to 92% for an increasing temperature from 30 to 90 °C (in the presence of air at normal pressure), with an increase of the relative concentration of the corresponding oxidized compounds (like cotinine and furthermore myosmine up to 0.7%, and up to 4.7%, respectively). For the nicotine/β-cyclodextrin complex the interaction selectivity was higher for nicotine and the stability of this bioactive compound against oxidation was also higher in comparison with the non-complexed nicotine (around 98% in all cases).     

Characterization of Phenolics in Lavandula angustifolia

ABSTRACT

The lavender flowers and their essential oil are widely used in therapy in Romania and the European Community. Since the European Pharmacopoeia only allows the use of Lavandula sp flowers for medicinal purposes, the objective of this study was to investigate the chemical composition of Lavandula angustifolia extracts obtained by ultrasound-assisted extraction, rapid pressurized extraction at 6.7?bar, and subcritical fluid extraction. The solvents used for the first two methods were mixtures of water and alcohol, glycerin, and propylene glycol. These extracts were analyzed by high-performance thin-layer chromatography, infrared spectroscopy with attenuated total reflectance, and Raman spectroscopy. The total phenolics were evaluated using a modified Folin–Ciocalteu method. The primary phenolics were chlorogenic acid, gallic acid, umbelliferone, luteolin 7-O-glucoside, vitexin, and isoquercitroside. The extracts were variable in composition, with the highest yield by subcritical fluid extraction, followed by extraction at 6.7?bar. The infrared and Raman spectroscopy results confirmed the chromatography measurements.     

Coherence spectroscopy investigations of the low-frequency vibrations of heme: effects of protein-specific perturbations

Femtosecond coherence spectroscopy is used to probe the low-frequency (20-200 cm(-1)) vibrational modes of heme proteins in solution. Horseradish peroxidase (HRP), myoglobin (Mb), and Campylobacter jejuni globin (Cgb) are compared and significant differences in the coherence spectra are revealed. It is concluded that hydrogen bonding and ligand charge do not strongly affect the low-frequency coherence spectra and that protein-specific deformations of the heme group lower its symmetry and control the relative spectral intensities. Such deformations potentially provide a means for proteins to tune heme reaction coordinates, so that they can perform a broad array of specific functions. Native HRP displays complex spectral behavior above approximately 50 cm(-1) and very weak activity below approximately 50 cm(-1). Binding of the substrate analog, benzhydroxamic acid, leads to distinct changes in the coherence and Raman spectra of HRP that are consistent with the stabilization of a heme water ligand. The CN derivatives of the three proteins are studied to make comparisons under conditions of uniform heme coordination and spin-state. MbCN is dominated by a doming mode near 40 cm(-1), while HRPCN displays a strong oscillation at higher frequency (96 cm(-1)) that can be correlated with the saddling distortion observed in the X-ray structure. In contrast, CgbCN displays low-frequency coherence spectra that contain strong modes near 30 and 80 cm(-1), probably associated with a combination of heme doming and ruffling. HRPNO displays a strong doming mode near 40 cm(-1) that is activated by photolysis. The damping of the coherent motions is significantly reduced when the heme is shielded from solvent fluctuations by the protein material and reduced still further when T approximately < 50 K, as pure dephasing processes due to the protein-solvent phonon bath are frozen out.     

A Better Approximation Algorithm for Finding Planar Subgraphs

The MAXIMUM PLANAR SUBGRAPH problem—given a graphG, find a largest planar subgraph ofG—has applications in circuit layout, facility layout, and graph drawing. No previous polynomial-time approximation algorithm for this NP-Complete problem was known to achieve a performance ratio larger than 1/3, which is achieved simply by producing a spanning tree ofG. We present the first approximation algorithm for MAXIMUM PLANAR SUBGRAPH with higher performance ratio (4/9 instead of 1/3). We also apply our algorithm to find large outerplanar subgraphs. Last, we show that both MAXIMUM PLANAR SUBGRAPH and its complement, the problem of removing as few edges as possible to leave a planar subgraph, are Max SNP-Hard.     

Low-frequency mode activity of heme: femtosecond coherence spectroscopy of iron porphine halides and nitrophorin

The low-frequency mode activity of metalloporphyrins has been studied for iron porphine-halides (Fe(P)(X), X = Cl, Br) and nitrophorin 4 (NP4) using femtosecond coherence spectroscopy (FCS) in combination with polarized resonance Raman spectroscopy and density functional theory (DFT). It is confirmed that the mode symmetry selection rules for FCS are the same as for Raman scattering and that both Franck-Condon and Jahn-Teller mode activities are observed for Fe(P)(X) under Soret resonance conditions. The DFT-calculated low-frequency (20-400 cm (-1)) modes, and their frequency shifts upon halide substitution, are in good agreement with experimental Raman and coherence data, so that mode assignments can be made. The doming mode is located at approximately 80 cm (-1) for Fe(P)(Cl) and at approximately 60 cm (-1) for Fe(P)(Br). NP4 is also studied with coherence techniques, and the NO-bound species of ferric and ferrous NP4 display a mode at approximately 30-40 cm (-1) that is associated with transient heme doming motion following NO photolysis. The coherence spectra of three ferric derivatives of NP4 with different degrees of heme ruffling distortion are also investigated. We find a mode at approximately 60 cm (-1) whose relative intensity in the coherence spectra depends quadratically on the magnitude of the ruffling distortion. To quantitatively account for this correlation, a new "distortion-induced" Raman enhancement mechanism is presented. This mechanism is unique to low-frequency "soft modes" of the molecular framework that can be distorted by environmental forces. These results demonstrate the potential of FCS as a sensitive probe of dynamic and functionally important nonplanar heme vibrational excitations that are induced by the protein environmental forces or by the chemical reactions in the aqueous phase.     

The antioxidant response induced by Lonicera caerulaea berry extracts in animals bearing experimental solid tumors

Lonicera caerulea is a species of bush native to the Kamchatka Peninsula (Russian Far East) whose berries have been extensively studied due to their potential high antioxidant activity. The aim of our work was to investigate the in vivo effects of the antioxidant action of Lonicera caerulea berry extracts on the dynamics of experimentally-induced tumors. Our data showed that aqueous Lonicera caerulaea extracts reduced the tumor volume when administered continuously during the tumor growth and development stages, but augmented the tumor growth when the administration of extracts started three weeks before tumor grafting. Prolonged administration of Lonicera caerulaea berry extracts induced the antioxidant defense mechanism in the tumor tissues, while surprisingly amplifying the peripheral oxidative stress.