Rhodium- and palladium-catalyzed 1,5-substitution reactions of 2-en-4-yne acetates and carbonates with organoboronic acids

Two methods involving the rhodium-catalyzed reaction of 2-en-4-yne acetates and the palladium-catalyzed reaction of 2-en-4-yne carbonates with organoboronic acids were investigated; both afforded exclusively the (E)-configured vinylallenes. The coordinative interaction of the rhodium with the acetate group promoted the δ-elimination of Rh(I)-OAc from the alkenylrhodium intermediate II in both syn and anti modes, with the syn-elimination being the major path. DFT calculations revealed that a conformer of this intermediate (II), which can lead to the (E)-configured vinylallene product via the syn-elimination mode, is energetically the most favorable conformer. The rhodium-catalyzed procedure is not applicable to reactions involving (E)-configured enyne acetates, because the geometry of the alkenylrhodium intermediate that is derived from the corresponding (E)-enyne acetate would not allow such coordinative interaction to occur. The palladium-catalyzed method, which proceeds through formation of the σ-vinylallenylpalladium intermediate, B, is suitable for both the (E)- and (Z)-configured enyne carbonates and appears to have a wider scope for both organoboronic acids and enyne substrates. The palladium-catalyzed reaction of an enantiomerically enriched enyne carbonate proceeded with racemization.     

Mechanical instability of amorphous polymeric networks: Asymmetric deformation under symmetric biaxial tension

Asymmetric deformation of a symmetrically loaded rubber sheet was observed, many years ago, by Treloar in his experiments on natural rubber. The problem has recently been studied by Kearsley, and the possibility of asymmetric deformations in an equi-biaxial state of force is predicted by the use of phenomenological constitutive relations. In the present study, the problem is analyzed in relation to the molecular constitution of rubber networks. It is shown that mechanical instability in symmetrically loaded networks may be possible only for limited choices of molecular parameters such as junction functionality, degree of crosslinking, and the degree of swelling during crosslinking and during deformation. Stability of multiple valued deformations is discussed by thermodynamic considerations of the elastic potential.     

Improved induced matchings in sparse graphs

An induced matching in a graph G=(V,E) is a matching M such that (V,M) is an induced subgraph of G. Clearly, among two vertices with the same neighbourhood (called twins) at most one is matched in any induced matching, and if one of them is matched then there is another matching of the same size that matches the other vertex. Motivated by this, Kanj et al. [10] studied induced matchings in twinless graphs. They showed that any twinless planar graph contains an induced matching of size at least and that there are twinless planar graphs that do not contain an induced matching of size greater than . We improve both these bounds to , which is tight up to an additive constant. This implies that the problem of deciding whether a planar graph has an induced matching of size k has a kernel of size at most 28k. We also show for the first time that this problem is fixed parameter tractable for graphs of bounded arboricity.Kanj et al. also presented an algorithm which decides in -time whether an n-vertex planar graph contains an induced matching of size k. Our results improve the time complexity analysis of their algorithm. However, we also show a more efficient -time algorithm. Its main ingredient is a new, O^∗(4^l)-time algorithm for finding a maximum induced matching in a graph of branch width at most l.     

Prediction of binding sites in receptor-ligand complexes with the Gaussian Network Model

Residues at the binding sites of the ligand and receptor of several enzyme-inhibitor and antibody-antigen complexes are predicted from the slowest (for the ligand) and fastest (for the receptor) modes of motion by the Gaussian Network Model applied to unbound molecules.     

VUV photoionisation of free azabenzenes: Pyridine, pyrazine, pyrimidine, pyridazine and s-triazine

Photoionisation mass spectrometry was used to obtain the fragmentation pathways of pyridine, pyridazine, pyrimidine, pyrazine and s-triazine molecules upon absorption of 23.0, 15.7 and 13.8 eV synchrotron photons. The ionic fragments observed vary from molecule to molecule, however C₂H₂⁺, HCN⁺and HCNH⁺ are common to all five molecules at the three photon energies. Furthermore, the presence of C₂H₂N₂⁺, C₃H₃N⁺ and C₄H₄⁺ in the spectra of some of the molecules suggests dissociation pathways via loss of HCN moieties. The respective parent cations, m/q=79, 80 and 81 have a greater yield at low photon energies when compared to the most intense fragment peak in each spectra. We recorded two of the fragment cation yields, as well as the parent photoion yield curves of pyridine, pyridazine, and pyrimidine in the 8–30 eV range. The formation of abundant cation fragments show a strong propensity of the molecules for dissociation after the absorption of VUV photons higher than 14 eV. The differences in relative fragment yields from molecule to molecule, and when changing the excitation energy, suggest significant bond rearrangements and nuclear motion during the dissociation time. Thus, bond cleavage is dependent on the photon energy deposited in the molecule and on intramolecular reactivity. With the aid of photoion yield curves and energy estimations we have assigned major peaks in the spectra and discussed their fragmentation pathways.     

Modelling of the blanking process of high-carbon steel using Lemaitre damage model

This paper presents a methodology to model a blanking process using a continuum mechanical damage model. A variant of the Lemaitre model, in which the quasi-unilateral conditions are taken into consideration to modify the damage behavior under compressive stress states, is selected as material model. S45C high-carbon steel is analyzed experimentally. To characterize the damage behavior of the material, notched round bar tensile tests with three different notch radii (6 mm, 10 mm, and 20 mm) using image analysis are performed. Using digital image processing, the strain at the deformation zone can be computed for the load–strain curves. Those curves are used as an objective function to determine the parameters of the Lemaitre damage model. The experimental results are compared with the results of the FE analysis of the tensile test. The identified model parameters are used in numerical investigations of axisymmetric blanking. The effect of the model's extension to quasi-unilateral damage evolution is discussed. The crack progress in high-carbon steel sheet during blanking and the final sheared part morphology are predicted and compared with the experimental results. Sheared surface and burr height obtained by the analysis coincide with the results of the blanking experiment.     

Optimum folding pathways of proteins: their determination and properties

We develop a dynamic optimization technique for determining optimum folding pathways of proteins starting from different initial configurations. A coarse-grained Go model is used. Forces acting on each bead are (i) the friction force, (ii) forces from bond length constraints, (iii) excluded volume constraints, and (iv) attractive forces between residue pairs that are in contact in the native state. An objective function is defined as the total attractive energy between nonbonded residues, which are neighbors in the native state. The objective function is minimized over all feasible paths, satisfying bond length and excluded volume constraints. The optimization problem is nonconvex and contains a large number of constraints. An augmented Lagrangian method with a penalty barrier function was used to solve the problem. The method is applied to a 36-residue protein, chicken villin headpiece. Sequences of events during folding of the protein are determined for various pathways and analyzed. The relative time scales are compared and scaled according to experimentally measured events. Formation times of the helices, turn, and the loop agree with experimental data. We obtain the overall folding time of the protein in the range of 600 ns-1.2 micros that is smaller than the experimental result of 4-5 micros, showing that the optimal folding times that we obtain may be possible lower bounds. Time dependent variables during folding and energies associated with short- and long-range interactions between secondary structures are analyzed in modal space using Karhunen-Loeve expansion.