On the topology of compact smooth three-dimensional Levi-flat hypersurfaces

We study topological conditions that must be satisfied by a compactC ^∞ Levi-flat hypersurface in a two-dimensional complex manifold, as well as related questions about the holonomy of Levi-flat hypersurfaces. As a consequence of our work, we show that no two-dimensional complex manifold admits a subdomain Ω with compact nonemptyC ^∞ boundary such that Ω ? ?².     

Perturbation theory for kinds

In this paper we prove the validity of formal asymptotic results on perturbation theory for kind solutions of the sine-Gordon equation, originally obtained by McLaughlin and Scott. We prove that for appropriate perturbations, of size in an appropriate norm, slowly varying in time in the rest frame of the kink, the shape of the kink is unaltered in theL norm toO() for a time ofO(1/). The kink parameters, which represent its velocity and centre, evolve slowly in time in the way predicted by the asymptotics. The method of proof uses an orthogonal decomposition of the solution into an oscillatory part and a one-dimensional zero-mode term. The slow evolution of the kink parameters is chosen so as to suppress secular evolution of the zero-mode.Partially supported as a graduate student at Princeton University of NSF grant 215 6211     

Non-smoothness of event horizons of Robinson-Trautman black holes

It is shown that generic small data Robinson-Trautman space-times cannot beC ¹²³ extended beyond the r=2m Schwarzschild-like event horizon. This implies that an observer living in such a space-time can determine by local measurements whether or not he has crossed the event-horizon of the black-hole.     

Phase separation dynamics in driven diffusive systems

We study phase separation dynamics in a driven diffusive system. Our simulations are based on the Cahn-Hilliard equation with an additional flux term due to an external field. We study the dynamical scaling parallel and perpendicular to the field. A crossover is observed from isotropic domains at early times to extremely anisotropic domains at later times. We find that the inverse interfacial density (an isotropic measure of the domain size) increases ast , with =1/3, from early times independent of the field strength, even though we do not observe dynamical scaling during these times. Our results indicate that a growth exponent =1/3 may be more universal than previously expected. We analyze the dynamics in terms of surface driven instabilities and one-dimensional solitary waves.     

Kinetic energy dependence of the reactions of N+ and N2+ with molybdenum

Mass-selected beams of N⁺ and N₂⁺ in the energy range 5–50 eV react with molybdenum to produce a surface nitride. The relative reaction cross section for N⁺ reaction is higher than that of N₂⁺ in the range 5–25 eV and N₂⁺ exhibits a reaction threshold near 7 eV. The N₂⁺ threshold suggests collisional dissociation prior to reaction.     

Complementary kinetic and thermodynamic resolution of a chiral biaryl axis

The condensation of 2′-formylbiphenyl-2-carboxylic acid 4 with (S)-valinol proceeds under kinetic control to give a major product, (4bR,7S,aS)-6,7-dihydro-7-isopropyldibenz[c,e]oxazolo[3,2-a]azepin-9(4bH)-one 6a (84%), in which the biaryl axis has the (S)-configuration. Heating 6a at 140°C with a catalytic amount of acid gives rise to an equilibrium dominated by the diastereoisomeric (4bS,7S)-lactam 6b (6a:6b ratio 27:73), in which the biaryl unit has the (R)-configuration. The structures of both lactams were established by X-ray crystallography; no other diastereoisomers were obtained.     

Validation of an empirical RNA-ligand scoring function for fast flexible docking using RiboDock®

We report the design and validation of a fast empirical function for scoring RNA-ligand interactions, and describe its implementation within RiboDock, a virtual screening system for automated flexible docking. Building on well-known protein-ligand scoring function foundations, features were added to describe the interactions of common RNA-binding functional groups that were not handled adequately by conventional terms, to disfavour non-complementary polar contacts, and to control non-specific charged interactions. The results of validation experiments against known structures of RNA-ligand complexes compare favourably with previously reported methods. Binding modes were well predicted in most cases and good discrimination was achieved between native and non-native ligands for each binding site, and between native and non-native binding sites for each ligand. Further evidence of the ability of the method to identify true RNA binders is provided by compound selection ('enrichment factor') experiments based around a series of HIV-1 TAR RNA-binding ligands. Significant enrichment in true binders was achieved amongst high scoring docking hits, even when selection was from a library of structurally related, positively charged molecules. Coupled with a semi-automated cavity detection algorithm for identification of putative ligand binding sites, also described here, the method is suitable for the screening of very large databases of molecules against RNA and RNA-protein interfaces, such as those presented by the bacterial ribosome.     

Enantioselective synthesis of epoxides by alpha-deprotonation--electrophile trapping of achiral epoxides

Enantioselective alpha-deprotonation of achiral epoxides 1, 21, and 26 using organolithiums in the presence of (-)-sparteine 2 and subsequent electrophile trapping gives access to enantioenriched trisubstituted epoxides 9-17, 22, 23, 27 and 28 (in up to 86% ee).     

Assay development and high-throughput screening of caspases in microfluidic format

Caspase proteases are familiar targets in drug discovery. A common format for screening to identify caspase inhibitors employs fluorogenic or colorimetric tetra-peptide substrates in 96, 384, or 1536 -well microtiter plates. The primary motivation for increasing the number of wells per plate is to reduce the reagent cost per test and increase the throughput of HTS operations. There are significant challenges, however, to moving into or beyond the 1536-well format, such as submicroliter liquid handling, liquid evaporation, increased surface area-to-volume ratios, and the potential for artifacts and interference from small air-borne particles such as lint. Therefore, HTS scientists remain keenly interested in technologies that offer alternatives to the ever-shrinking microtiter plate well. Microfluidic assay technology represents an attractive option that, in theory, consumes only subnanoliter volumes of reagents per test. We have successfully employed a microfluidic assay technology in fluorogenic screening assays for several caspase isoforms utilizing the Caliper Technologies Labchip platform. Caspase-3 is used as a representative case to describe microfluidic assay development and initial high-throughput screening results. In addition, microfluidic screening and plate-based screening are compared in terms of reagent consumption, data quality, and ease of operation.