Bounds relating the weakly connected domination number to the total domination number and the matching number

Let G=(V,E) be a connected graph. A dominating set S of G is a weakly connected dominating set of G if the subgraph (V,E∩(S×V)) of G with vertex set V that consists of all edges of G incident with at least one vertex of S is connected. The minimum cardinality of a weakly connected dominating set of G is the weakly connected domination number, denoted . A set S of vertices in G is a total dominating set of G if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set of G is the total domination number γ_t(G) of G. In this paper, we show that . Properties of connected graphs that achieve equality in these bounds are presented. We characterize bipartite graphs as well as the family of graphs of large girth that achieve equality in the lower bound, and we characterize the trees achieving equality in the upper bound. The number of edges in a maximum matching of G is called the matching number of G, denoted α^′(G). We also establish that , and show that for every tree T.     

New ring-linear codes from dualization in projective Hjelmslev geometries

In this article, several new constructions for ring-linear codes are given. The class of base rings are the Galois rings of characteristic 4, which include ${\mathbb {Z}_4}$ as its smallest and most important member. Associated with these rings are the Hjelmslev geometries, and the central tool for the construction is geometric dualization. Applying it to the ${\mathbb {Z}_4}$ -preimages of the Kerdock codes and a related family of codes we will call Teichmüller codes, we get two new infinite series of codes and compute their symmetrized weight enumerators. In some cases, residuals of the original code give further interesting codes. The generalized Gray map translates our codes into ordinary, generally non-linear codes in the Hamming space. The obtained parameters include (58, 2⁷, 28)₂, (60, 2⁸, 28)₂, (114, 2⁸, 56)₂, (372, 2¹⁰, 184)₂ and (1988, 2¹², 992)₂ which provably have higher minimum distance than any linear code of equal length and cardinality over an alphabet of the same size (better-than-linear, BTL), as well as (180, 2⁹, 88)₂, (244, 2⁹, 120)₂, (484, 2¹⁰, 240)₂ and (504, 4⁶, 376)₄ where no comparable (in the above sense) linear code is known (better-than-known-linear, BTKL).     

Optical Control of Acetylcholinesterase with a Tacrine Switch

Photochromic ligands have been used to control a variety of biological functions, especially in neural systems. Recently, much effort has been invested in the photocontrol of ion channels and G‐protein coupled receptors found in the synapse. Herein, we describe the expansion of our photopharmacological approach toward the remote control of an enzyme. Building on hallmark studies dating from the late 1960s, we evaluated photochromic inhibitors of one of the most important enzymes in synaptic transmission, acetylcholinesterase (AChE). Using structure‐based design, we synthesized several azobenzene analogues of the well‐known AChE inhibitor tacrine (THA) and determined their effects on enzymatic activity. One of our compounds, AzoTHA, is a reversible photochromic blocker of AChE in vitro and ex vivo with high affinity and fast kinetics. As such, AzoTHA can be used to control synaptic transmission on the neuromuscular endplate based on the light‐dependent clearance of a neurotransmitter.     

Carpet Beater Molecules: Synthesis and Characterization of Functional Hexa-peri-benzocoronene–Alkyne Coupling Products

Within the scope of this paper, nine π-expanded mono-substituted 5,8,11,14,17-pentakis-(tert-butyl)-hexa-peri-hexabenzocoronenes (HBC) are introduced. 2-Iodo-5,8,11,14,17-pentakis-(tert-butyl)-hexa-peri-hexabenzocoronene served as precursor and was reacted with ethynyltrimethylsilane in a Sonogashira coupling reaction. The acetylene unit is used as a linker and can undergo another Sonogashira coupling reaction combining different phenyl coupling partners with the HBC core. The electron-withdrawing groups such as nitrile, pyridine and carbonyl species (aldehyde, methylester, carboxylic acid) as well as the three quinoxaline based species (diphenylquinoxaline, dibenzo[a,c]phenazine, phenanthro[4’,5’-a,b,c]phenazine) serve as substitution moieties. Their influence on the optoelectronic properties were investigated by UV/Vis absorption spectroscopy demonstrating a maximum redshift of 7 nm compared to starting compound 2-Iodo-5,8,11,14,17-pentakis-(tert-butyl) HBC. As for the phenanthro[4’,5’-a,b,c]phenazine substituted HBC a dramatic decrease in the intensity of the absorption of the UV/Vis spectrum was observed. The fluorescence spectroscopy pointed out that the dibenzo[a,c]phenazine and phenanthro[4’,5’-a,b,c]phenazine substitution changed the spectra to one broad peak departing from the characteristic HBC-like emission pattern.     

Cross-docking of inhibitors into CDK2 structures. 1

Predicting protein/ligand binding affinity is one of the most challenging computational chemistry tasks. Numerous methods have been developed to address this challenge, but they all have limitations. Failure to account for protein flexibility has been a shortcoming of many methods. In this cross-docking study the data set comprised 150 inhibitor complexes of the protein kinase CDK2. Gold and Glide performed well in terms of docking accuracy. The chance of cross-docking a ligand within a 2 A RMSD of its experimental pose was found to be 50%. Relative binding potency was not properly predicted from scoring functions, even though cross-docking of each inhibitor into each protein structure was performed and only scores of correctly docked ligands were considered. An accompanying paper (Voigt, J. H.; Elkin, C.; Madison, V. S. Duca, J. S. J. Chem. Inf. Model. 2008, 48, 669-678) covers cross-docking and docking accuracy from the perspective of using multiple protein structures.     

Do hydroxyl radical-water clusters, OH(H2O)n, n = 1-5, exist in the atmosphere?

It has been speculated that the presence of OH(H2O)n clusters in the troposphere could have significant effects on the solar absorption balance and the reactivity of the hydroxyl radical. We have used the G3 and G3B3 model chemistries to model the structures and predict the frequencies of hydroxyl radical/water clusters containing one to five water molecules. The reaction between hydroxyl radical clusters and methane was examined as a function of water cluster size to gain an understanding of how cluster size affects the hydroxyl radical reactivity.     

Raman scattering studies of the Ba2MnWO6 and Sr2MnWO6 double perovskites

Polycrystalline Ba2MnWO6 (BMW) and Sr2MnWO6 (SMW) samples were studied between 80 and 1200 K by Raman scattering spectroscopy. In the case of BMW (space group Fmm), four Raman active vibrational modes, predicted by factor group analysis, were identified. Raman scattering studies with different wavelengths revealed a resonant bands between 300 and 800 cm-1. The origin of these bands was related to the Franck-Condon process. Line broadening versus temperature and phonon frequency were studied, and a qualitative explanation was proposed. SMW samples had considerably more complex Raman spectra. It was found that SMW transformed from tetragonal (room-temperature space group P42/n) to the cubic phase between 670 and 690 K; the phase transition temperature was dependent on sample preparation conditions, and it was considerably lower than in the case of large grain size powders. The role of grain size in phase transition is discussed. Mn ions were found to have a crucial role in the lattice dynamics of both materials.     

Theoretical evaluation of structural models of the S2 state in the oxygen evolving complex of Photosystem II: protonation states and magnetic interactions

Protonation states of water ligands and oxo bridges are intimately involved in tuning the electronic structures and oxidation potentials of the oxygen evolving complex (OEC) in Photosystem II, steering the mechanistic pathway, which involves at least five redox state intermediates S(n) (n = 0-4) resulting in the oxidation of water to molecular oxygen. Although protons are practically invisible in protein crystallography, their effects on the electronic structure and magnetic properties of metal active sites can be probed using spectroscopy. With the twin purpose of aiding the interpretation of the complex electron paramagnetic resonance (EPR) spectroscopic data of the OEC and of improving the view of the cluster at the atomic level, a complete set of protonation configurations for the S(2) state of the OEC were investigated, and their distinctive effects on magnetic properties of the cluster were evaluated. The most recent X-ray structure of Photosystem II at 1.9 ? resolution was used and refined to obtain the optimum structure for the Mn(4)O(5)Ca core within the protein pocket. Employing this model, a set of 26 structures was constructed that tested various protonation scenarios of the water ligands and oxo bridges. Our results suggest that one of the two water molecules that are proposed to coordinate the outer Mn ion (Mn(A)) of the cluster is deprotonated in the S(2) state, as this leads to optimal experimental agreement, reproducing the correct ground state spin multiplicity (S = 1/2), spin expectation values, and EXAFS-derived metal-metal distances. Deprotonation of Ca(2+)-bound water molecules is strongly disfavored in the S(2) state, but dissociation of one of the two water ligands appears to be facile. The computed isotropic hyperfine couplings presented here allow distinctions between models to be made and call into question the assumption that the largest coupling is always attributable to Mn(III). The present results impose limits for the total charge and the proton configuration of the OEC in the S(2) state, with implications for the cascade of events in the Kok cycle and for the water splitting mechanism.