Close-packed floating clusters: granular hydrodynamics beyond the freezing point?

Monodisperse granular flows often develop regions with hexagonal close packing of particles. We investigate this effect in a system of inelastic hard spheres driven from below by a "thermal" plate. Molecular dynamics simulations show, in a wide range of parameters, a close-packed cluster supported by a low-density region. Surprisingly, the steady-state density profile, including the close-packed cluster part, is well described by a variant of Navier-Stokes granular hydrodynamics (NSGH). We suggest a simple explanation for the success of NSGH beyond the freezing point.     

Enantioselective [6pi]-photocyclization reaction of an acrylanilide mediated by a chiral host. Interplay between enantioselective ring closure and enantioselective protonation

The [6pi]-photocyclization of the anilides 1a and 5 was studied in the absence and in the presence of the enantiomerically pure chiral lactam 4. The relative configuration of the products was unambiguously established by single-crystal X-ray crystallography and by NMR spectroscopy. A significant enantiomeric excess was observed upon reaction of compound 1a to its photocyclization products at -55 degrees C employing lactam 4 as a chiral complexing agent in toluene as the solvent (66% yield). The trans product ent-3a was obtained in 57% ee, and the minor diastereoisomer (trans/cis = 73/27), cis product ent-2a, was obtained in 30% ee. DFT calculations were conducted modeling the complexation of intermediates 8 and ent-8 to host 4. In agreement with steric arguments concerning the conrotatory ring closure of 1a, the formation of ent-8 is favored leading to the more stable complex 4.ent-8 as compared to 4.8. Whereas the enantioselectivity in the photocyclization to trans compound ent-3a increased upon reduction in the reaction temperature, the enantiomeric excess in the formation of cis compound ent-2a went through a maximum at -15 degrees C (45% ee) and decreased at lower temperatures. Deuteration experiments conducted with the pentadeuterated analogue of 1a, d(5)-1a, revealed that the protonation of the intermediates 8 and ent-8 is influenced by chiral amide 4. In the formation of ent-3a/3a, both the enantioselective ring closure and the enantioselective protonation by amide 4 favor the observed (6aS,10aS)-configuration of the major enantiomer ent-3a. In the formation of ent-2a/2a, the enantioselective ring closure (and the subsequent diastereoselective protonation) favors the (6aR,10aS)-configuration that is found in compound 2a. Contrary to that, the enantioselective protonation by amide 4 shows a preference for ent-2a with the (6aS,10aR)-configuration.     

Discovery of aminoglycoside mimetics by NMR-based screening of Escherichia coli A-site RNA

A method is described for the NMR-based screening for the discovery of aminoglycoside mimetics that bind to Escherichia coli A-site RNA. Although aminoglycosides are clinically useful, they exhibit high nephrotoxicity and ototoxicity, and their overuse has led to the development of resistance to important microbial pathogens. To identify a new series of aminoglycoside mimetics that could potentially overcome the problems associated with toxicities and resistance development observed with the aminoglycosides, we have prepared large quantities of E. coli 16 S A-site RNA and conducted an NMR-based screening of our compound library in search for small-molecule RNA binders against this RNA target. From these studies, several classes of compounds were identified as initial hits with binding affinities in the range of 70 microM to 3 mM. Lead optimization through synthetic modifications of these initial hits led to the discovery of several small-molecule aminoglycoside mimetics that are structurally very different from the known aminoglycosides. Structural models of the A-site RNA/ligand complexes were prepared and compared to the three-dimensional structures of the RNA/aminoglycoside complexes.     

On approximation of affine Baire-one functions

It is known (G. Choquet, G. Mokobodzki) that a Baire-one affine function on a compact convex set satisfies the barycentric formula and can be expressed as a pointwise limit of a sequence of continuous affine functions. Moreover, the space of Baire-one affine functions is uniformly closed. The aim of this paper is to discuss to what extent analogous properties are true in the context of general function spaces. In particular, we investigate the function spaceH(U), consisting of the functions continuous on the closure of a bounded open setU⊂ℝ ^m and harmonic onU, which has been extensively studied in potential theory. We demonstrate that the barycentric formula does not hold for the spaceB ₁ ^b (H(U)) of bounded functions which are pointwise limits of functions from the spaceH(U) and thatB ₁ ^b (H(U)) is not uniformly closed. On the other hand, every Baire-oneH(U)-affine function (in particular a solution of the generalized Dirichlet problem for continuous boundary data) is a pointwise limit of a bounded sequence of functions belonging toH(U). It turns out that such a situation always occurs for simplicial spaces whereas it is not the case for general function spaces. The paper provides several characterizations of those Baire-one functions which can be approximated pointwise by bounded sequences of elements of a given function space. Research supported in part by grants GA ČR No. 201/00/0767 from the Grant Agency of the Czech Republic, GA UK 165/99 from the Grant Agency of Charles University, and in part by grant number MSM 113200007 from the Czech Ministry of Education.     

Holographic interference microscope for laboratory studies

A digital holographic interference microscope is designed that allows real-time 3D imaging of phase microobjects and measurement of their morphological parameters. The instrument may find application in medical institutions and research laboratories.