Lagrangian matching invariants for fibred four-manifolds: I

In a pair of papers, we construct invariants for smooth four-manifolds equipped with `broken fibrations' - the singular Lefschetz fibrations of Auroux, Donaldson and Katzarkov - generalising the Donaldson-Smith invariants for Lefschetz fibrations. The `Lagrangian matching invariants' are designed to be comparable with the Seiberg-Witten invariants of the underlying four-manifold. They fit into a field theory which assigns Floer homology groups to fibred 3-manifolds. The invariants are derived from moduli spaces of pseudo-holomorphic sections of relative Hilbert schemes of points on the fibres, subject to Lagrangian boundary conditions. Part I is devoted to the symplectic geometry of these Lagrangians.Comment: 72 pages, 4 figures. v.2 - numerous small corrections and clarification

Differential hydrophobicity drives self-assembly in Huntington's disease

Identifying the driving forces and the mechanism of association of huntingtin-exon1, a close marker for the progress of Huntington's disease, is an important prerequisite towards finding potential drug targets, and ultimately a cure. We introduce here a modelling framework based on a key analogy of the physico-chemical properties of the exon1 fragment to block copolymers. We use a systematic mesoscale methodology, based on Dissipative Particle Dynamics, which is capable of overcoming kinetic barriers, thus capturing the dynamics of significantly larger systems over longer times than considered before. Our results reveal that the relative hydrophobicity of the poly-glutamine block as compared to the rest of the (proline-based) exon1 fragment, ignored to date, constitutes a major factor in the initiation of the self-assembly process. We find that the assembly is governed by both the concentration of exon1 and the length of the poly-glutamine stretch, with a low length threshold for association even at the lowest volume fractions we considered. Moreover, this self-association occurs irrespective of whether the glutamine stretch is in random coil or hairpin configuration, leading to spherical or cylindrical assemblies, respectively. We discuss the implications of these results for reinterpretation of existing research within this context, including that the routes towards aggregation of exon1 may be distinct to those of the widely studied homopolymeric poly-glutamine peptides

Photochemistry of transition metal hydrides

Photochemical reactivity associated with metal-hydrogen bonds is widespread among metal hydride complexes and has played a critical part in opening up C-H bond activation. It has been exploited to design different types of photocatalytic reactions and to obtain NMR spectra of dilute solutions with a single pulse of an NMR spectrometer. Because photolysis can be performed on fast time scales and at low temperature, metal-hydride photochemistry has enabled determination of the molecular structure and rates of reaction of highly reactive intermediates. We identify five characteristic photoprocesses of metal monohydride complexes associated with the M-H bond, of which the most widespread are M-H homolysis and R-H reductive elimination. For metal dihydride complexes, the dominant photoprocess is reductive elimination of H2. Dihydrogen complexes typically lose H2 photochemically. The majority of photochemical reactions are likely to be dissociative, but hydride complexes may be designed with equilibrated excited states that undergo different photochemical reactions, including proton transfer or hydride transfer. The photochemical mechanisms of a few reactions have been analyzed by computational methods, including quantum dynamics. A section on specialist methods (time-resolved spectroscopy, matrix isolation, NMR, and computational methods) and a survey of transition metal hydride photochemistry organized by transition metal group complete the Review

A Diffusion-Based Approach to Geminate Recombination of Heme Proteins with Small Ligands

A model of postphotodissociative monomolecular (geminate) recombination of heme proteins with small ligands (NO, O2 or CO) is represented. The non-exponential decay with time for the probability to find a heme in unbound state is interpreted in terms of diffusion-like migration of ligabs physics/0212040 and between protein cavities. The temporal behavior for the probability is obtained from numerical simulation and specified by two parameters: the time \tau_{reb} of heme-ligand rebinding for the ligand localized inside the heme pocket and the time \tau_{esc} of ligand escape from the pocket. The model is applied in the analysis of available experimental data for geminate reoxygenation of human hemoglobin HbA. Our simulation is in good agreement with the measurements. The analysis shows that the variation in pH of the solution (6.0<pH<9.4) results in considerable changes for \tau_{reb} from 0.36 ns (at pH=8.5) up to 0.5 ns (pH=6.0) but effects slightly on the time \tau_{esc} (\tau_{esc} ~ 0.88 ns).Comment: 8 pages with 4 figures, submitted to Chem. Phy

Tribute to Daedalus: Fertile mind that led to unexpected places

Tribute to Daedalus, David E.H. Jones

A solvent-resistant halogen bond

The effect of solvent on the stabilities of complexes involving a single H-bond or halogen-bond (X-bond) has been quantified. Association constants for binary complexes of 4-(phenylazo)phenol, molecular iodine, tetramethylurea and tetramethylthiourea have been measured in fifteen different solvents by UV/vis absorption and 1H NMR titration experiments. The stabilities of the H-bonded complexes decrease by more than three orders of magnitude with increasing solvent polarity. In contrast, the X-bonded complex of molecular iodine with tetramethylthiourea is remarkably insensitive to the nature of the solvent (association constants measured in alkanes and alcohols are similar). The results suggest that, in contrast to H-bonds, where electrostatics determine thermodynamic stability, charge-transfer interactions make a major contribution to the stability of these X-bonded complexes rendering them resistant to increases in solvent polarity