A matricial corona theorem II

We extend the ``matricial corona theorem' of M. Andersson to general algebras of functions which satisfy a corona theorem.

     

Synthesis and derivatization of ethynyl alpha,alpha-dibromomethyl ketones: formation of highly functionalized vinyl triflates

[reaction: see text] We describe the synthesis of alpha,alpha-dibromomethyl ynones (8) and their subsequent derivatization to vinyl acetates (10). These vinyl acetates feature a 1,1-dibromo-olefin moiety, which is readily exploited in palladium-catalyzed Sonogashira, Stille, and Suzuki cross-coupling reactions with alkynes, stannanes, and boronic acids, respectively. A novel one-pot process then directly converts the resulting vinyl acetates 11-13 to the vinyl triflate derivatives 14a-j.     

Synthesis of monofluorinated 1-(naphthalen-1-yl)piperazines

A series of regioisomerically monofluorinated 1-(naphthalen-1-yl)piperazines is described.     

Magic-angle spinning solid-state NMR spectroscopy of the beta1 immunoglobulin binding domain of protein G (GB1): 15N and 13C chemical shift assignments and conformational analysis

Magic-angle spinning solid-state NMR (SSNMR) studies of the beta1 immunoglobulin binding domain of protein G (GB1) are presented. Chemical shift correlation spectra at 11.7 T (500 MHz 1H frequency) were employed to identify signals specific to each amino acid residue type and to establish backbone connectivities. High sensitivity and resolution facilitated the detection and assignment of every 15N and 13C site, including the N-terminal (M1) 15NH3, the C-terminal (E56) 13C', and side-chain resonances from residues exhibiting fast-limit conformational exchange near room temperature. The assigned spectra lend novel insight into the structure and dynamics of microcrystalline GB1. Secondary isotropic chemical shifts report on conformation, enabling a detailed comparison of the microcrystalline state with the conformation of single crystals and the protein in solution; the consistency of backbone conformation in these three preparations is the best among proteins studied so far. Signal intensities and line widths vary as a function of amino acid position and temperature. High-resolution spectra are observed near room temperature (280 K) and at <180 K, whereas resolution and sensitivity greatly degrade substantially near 210 K; the magnitude of this effect is greatest among the side chains of residues at the intermolecular interface of the microcrystal lattice, which we attribute to intermediate-rate translational diffusion of solvent molecules near the glass transition. These features of GB1 will enable its use as an excellent model protein not only for SSNMR methods development but also for fundamental studies of protein thermodynamics in the solid state.     

A self-assembling protein template for constrained synthesis and patterning of nanoparticle arrays

Self-assembling biomolecules that form highly ordered structures have attracted interest as potential alternatives to conventional lithographic processes for patterning materials. Here, we introduce a general technique for patterning nanoparticle arrays using two-dimensional crystals of genetically modified hollow protein structures called chaperonins. Constrained chemical synthesis of transition metal nanoparticles is initiated using templates functionalized with polyhistidine sequences. These nanoparticles are ordered into arrays because the template-driven synthesis is constrained by the nanoscale structure of the crystallized protein. We anticipate that this system may be used to pattern different classes of nanoparticles based on the growing library of sequences shown to specifically bind or direct the growth of materials.     

Supramolecular assembly on surfaces: manipulating conductance in noncovalently modified mesoscale structures

Molecules capable of complementary hydrogen bonding were used to control the noncovalent self-assembly and electronic properties of a chemically well-defined surface mesostructure. In this work, we patterned a footprint region for molecular assembly on a surface and used moieties featuring complementary recognition to tune the current-voltage properties of the patterned region. With the appropriate functionalities on the complementary moieties, we were able to increase and decrease the observed conductance in surface-bound mesoscale structures imaged by scanning tunneling microscopy (STM).     

Maximal invariant subspaces for

We find the maximal invariant subspaces for on -valued Bergman-type spaces.