Parity binomial edge ideals

Parity binomial edge ideals of simple undirected graphs are introduced. Unlike binomial edge ideals, they do not have square-free Gröbner bases and are radical if and only if the graph is bipartite or the characteristic of the ground field is not two. The minimal primes are determined and shown to encode combinatorics of even and odd walks in the graph. A mesoprimary decomposition is determined and shown to be a primary decomposition in characteristic two.     

The role of adsorbates in electrocatalytic systems: An analysis of model systems with single crystals

The use of single crystal electrodes as model catalysts has been widely applied for the study of several reactions. The known structure of the surface provides a system with controlled electronic properties that helps in the understanding of the mechanism of reactions. In this model system, any modification, including the adsorption of anions, organic molecules or foreign atoms, generate changes in the electronic properties of the surface and, thus, in the adsorption energy of the species involved in the studied reaction. The adsorbate can hinder the surface and diminish the activity or prevent the oxidation of the surface and improve the catalysis. The changes in electronic properties can modify the adsorption energy and enhance or worsen the catalytic activity. The effect of any adsorbed species will depend on the structure of the surface, the nature of the species and the studied reaction.     

Reversible linear differential equations

Let ? be a meromorphic connection on a vector bundle over a compact Riemann surface Γ. An automorphism $\sigma :\Gamma \to \Gamma$ is called a symmetry of ? if the pullback bundle and the pullback connection can be identified with ?. We study the symmetries by means of what we call the Fano group; and, under the hypothesis that ? has a unimodular reductive Galois group, we relate the differential Galois group, the Fano group and the symmetries by means of an exact sequence.     

Protonation/deprotonation effects on the stability of the Trp-cage miniprotein

The Trp-cage miniprotein is a 20 amino acid peptide that exhibits many of the properties of globular proteins. In this protein, the hydrophobic core is formed by a buried Trp side chain. The folded state is stabilized by an ion pair between aspartic acid and an arginine side chain. The effect of protonating the aspartic acid on the Trp-cage miniprotein folding/unfolding equilibrium is studied by explicit solvent molecular dynamics simulations of the protein in the charged and protonated Asp9 states. Unbiased Replica Exchange Molecular Dynamics (REMD) simulations, spanning a wide temperature range, are carried out to the microsecond time scale, using the AMBER99SB forcefield in explicit TIP3P water. The protein structural ensembles are studied in terms of various order parameters that differentiate the folded and unfolded states. We observe that in the folded state the root mean square distance (rmsd) from the backbone of the NMR structure shows two highly populated basins close to the native state with peaks at 0.06 nm and 0.16 nm, which are consistent with previous simulations using the same forcefield. The fraction of folded replicas shows a drastic decrease because of the absence of the salt bridge. However, significant populations of conformations with the arginine side chain exposed to the solvent, but within the folded basin, are found. This shows the possibility to reach the folded state without formation of the ion pair. We also characterize changes in the unfolded state. The equilibrium populations of the folded and unfolded states are used to characterize the thermodynamics of the system. We find that the change in free energy difference due to the protonation of the Asp amino acid is 3 kJ mol(-1) at 297 K, favoring the charged state, and resulting in ΔpK(1) = 0.5 units for Asp9. We also study the differences in the unfolded state ensembles for the two charge states and find significant changes at low temperature, where the protonated Asp side chain makes multiple hydrogen bonds to the protein backbone.     

Flexo-Ionic Effect of Ionic Liquid Crystal Elastomers

The first study of the flexo-ionic effect, i.e., mechanical deformation-induced electric signal, of the recently discovered ionic liquid crystal elastomers (iLCEs) is reported. The measured flexo-ionic coefficients were found to strongly depend on the director alignment of the iLCE films and can be over 200 µC/m. This value is orders of magnitude higher than the flexo-electric coefficient found in insulating liquid crystals and is comparable to the well-developed ionic polymers (iEAPs). The shortest response times, i.e., the largest bandwidth of the flexo-ionic responses, is achieved in planar alignment, when the director is uniformly parallel to the substrates. These results render high potential for iLCE-based devices for applications in sensors and wearable micropower generators.     

Force and Stress along Simulated Dissociation Pathways of Cucurbituril-Guest Systems

The field of host-guest chemistry provides computationally tractable yet informative model systems for biomolecular recognition. We applied molecular dynamics simulations to study the forces and mechanical stresses associated with forced dissociation of aqueous cucurbituril-guest complexes with high binding affinities. First, the unbinding transitions were modeled with constant velocity pulling (steered dynamics) and a soft spring constant, to model atomic force microscopy (AFM) experiments. The computed length-force profiles yield rupture forces in good agreement with available measurements. We also used steered dynamics with high spring constants to generate paths characterized by a tight control over the specified pulling distance; these paths were then equilibrated via umbrella sampling simulations and used to compute time-averaged mechanical stresses along the dissociation pathways. The stress calculations proved to be informative regarding the key interactions determining the length-force profiles and rupture forces. In particular, the unbinding transition of one complex is found to be a stepwise process, which is initially dominated by electrostatic interactions between the guest's ammoniums and the host's carbonyl groups, and subsequently limited by the extraction of the guest's bulky bicyclooctane moiety; the latter step requires some bond stretching at the cucurbituril's extraction portal. Conversely, the dissociation of a second complex with a more slender guest is mainly driven by successive electrostatic interactions between the different guest's ammoniums and the host's carbonyl groups. The calculations also provide information on the origins of thermodynamic irreversibilities in these forced dissociation processes.     

Structures of Two (<Emphasis Type="Italic">E</Emphasis>)-3-Substituted Cinnamoylbenzotriazole 1-Oxides

Abstract  

The molecule of (E)-3-(3-MeOC₆H₄CH=CHCO)-benzotriazole 1-oxide, 2, has a very near planar structure, while the 2-nitrophenyl ring is rotated out of the plane of the remaining atoms in (E)-3-(2-O₂NC₆H₄CH=CHCO)-benzotriazole 1-oxide, 1. The nitrogen oxide bond lengths in 1 and 2 are 1.258 (6) and 1.2683 (15) ?, respectively, and are in the region found for related compounds. There are no strong intermolecular hydrogen-bonds in either compound, instead there are weak C–H···O intermolecular hydrogen-bonds and π···π stacking interactions in 1, and C–H···O, C–H···π, and π···π stacking interactions in 2. Different three-dimensional arrays are generated in each case. Compound 1 crystallises in the orthorhombic space group Pna2₁, with a = 25.061 (2) ?, b = 3.6997 (2) ?, c = 14.2623 (12) ? and Z = 4. Compound 2 crystallises in the triclinic space group P-1, with a = 5.7297 (3) ?, b = 10.8440 (6) ?, c = 11.4965 (6) ?, α = 89.689 (3)°, β = 76.019 (3)°, γ = 75.047 (3)°, Z = 2.     

Axiomatizing core extensions

We give an axiomatization of the aspiration core on the domain of all TU-games using a relaxed feasibility condition, non-emptiness, individual rationality, and generalized versions of the reduced game property (consistency) and superadditivity. Our axioms also characterize the C-core (Guesnerie and Oddou, Econ Lett 3(4):301?C306, 1979; Sun et?al. J Math Econ 44(7?C8):853?C860, 2008) and the core on appropriate subdomains. The main result of the paper generalizes Peleg??s (J Math Econ 14(2):203?C214, 1985) core axiomatization to the entire family of TU-games.     

Insights into the interaction and binding mode of a set of antifungal azoles as inhibitors of potential fungal enzyme-based targets

Azole-containing compounds are a kind of chemical entities of natural and synthetic origin having a wide-range of activities. They are therefore considered as important moieties for fungicide development, mostly due to the possible action on several enzyme-based targets. As part of our research on fungicidal agents, the relationship between the ligand-enzyme affinities of several synthetic azole-containing compounds against a set of fungal enzyme-based targets was in silico evaluated through molecular docking. The affinity values of the test compounds were mostly higher than those of the respective test controls. Binding modes between enzymes and test compounds were firstly investigated through Vina scores and ligand–residue interactions. Furthermore, statistically relationships among docking scores were successfully found by multivariate analysis. They were mostly correlated with reported MIC₈₀ values, so it denoted an evident discrimination of the test compounds. Strong electron withdrawing groups on phenylacrylamide moiety were responsible for establishing stronger complexes with the enzyme targets, being trichodiene synthase and α-l-fucosidase the most important ones. Moreover, stability of a set of representative protein/ligand complexes was also analyzed by 10 ns molecular dynamics simulations (MD). Significant differences into the MD runs were detected and directly correlated to docking performances. Finally, docking affinity scores and HOMO–LUMO energy gaps resulted well predicted by comparative molecular field analysis (CoMFA) models, demonstrating the structure type is particularly associated with those calculated properties and these results were thus consistent with the respective validation parameters.