On the minimum ropelength of knots and links

The ropelength of a knot is the quotient of its length by its thickness, the radius of the largest embedded normal tube around the knot. We prove existence and regularity for ropelength minimizers in any knot or link type; these are C ^1,1 curves, but need not be smoother. We improve the lower bound for the ropelength of a nontrivial knot, and establish new ropelength bounds for small knots and links, including some which are sharp. Oblatum 11-IV-2001 & 20-III-2002?Published online: 17 June 2002     

Manganese(I)‐Catalyzed C−H Activation: The Key Role of a 7‐Membered Manganacycle in H‐Transfer and Reductive Elimination

Manganese‐catalyzed C?H bond activation chemistry is emerging as a powerful and complementary method for molecular functionalization. A highly reactive seven‐membered Mn^I intermediate is detected and characterized that is effective for H‐transfer or reductive elimination to deliver alkenylated or pyridinium products, respectively. The two pathways are determined at Mn^I by judicious choice of an electron‐deficient 2‐pyrone substrate containing a 2‐pyridyl directing group, which undergoes regioselective C?H bond activation, serving as a valuable system for probing the mechanistic features of Mn C?H bond activation chemistry.     

Reagent‐Controlled α‐Selective Dehydrative Glycosylation of 2,6‐Dideoxy‐ and 2,3,6‐Trideoxy Sugars

We have found that activating either 2,3‐bis(2,3,4‐trimethoxyphenyl)cyclopropenone or 2,3‐bis(2,3,4‐trimethoxyphenyl)cyclopropene‐1‐thione with oxalyl bromide results in the formation of a species that promotes the glycosylation between 2,6‐dideoxy‐sugar hemiacetals and glycosyl acceptors in good yield and high α‐selectivity. Both reactions are mild and tolerate a number of sensitive functional groups including highly acid‐labile 2,3,6‐trideoxy‐sugar linkages.     

Amyloid Aggregates Arise from Amino Acid Condensations under Prebiotic Conditions

Current theories on the origin of life reveal significant gaps in our understanding of the mechanisms that allowed simple chemical precursors to coalesce into the complex polymers that are needed to sustain life. The volcanic gas carbonyl sulfide (COS) is known to catalyze the condensation of amino acids under aqueous conditions, but the reported di‐, tri‐, and tetra‐peptides are too short to support a regular tertiary structure. Here, we demonstrate that alanine and valine, two of the proteinogenic amino acids believed to have been among the most abundant on a prebiotic earth, can polymerize into peptides and subsequently assemble into ordered amyloid fibers comprising a cross‐β‐sheet quaternary structure following COS‐activated continuous polymerization of as little as 1 mm amino acid. Furthermore, this spontaneous assembly is not limited to pure amino acids, since mixtures of glycine, alanine, aspartate, and valine yield similar structures.     

Rearrangements in the Scholl oxidation: implications for molecular architectures

Rearrangements readily occur in Scholl oxidations and interfere with the construction of certain molecular architectures. 3,3?,4,4′,4″,4?,5′,5″-Octamethoxy-1,1′,2′,1″,2″,1?-quaterphenyl and 3,3?,4,4′,4′′,4?,5′,5′-octamethyl-1,1′,2′,1″,2″,1?-quaterphenyl, which were conceived as precursors to benzenoid strips, rearranged under Scholl conditions to the unexpected C_2v-substituted products 1,2,5,6,9,10,12,13-octamethoxydibenzo[fg,op]naphthacene and 1,2,5,6,9,10,12,13-octamethyldibenzo[fg,op]naphthacene. This corrects a widely propagated error in the literature in which the assignments of 1,2,5,6,9,10,12,13-octamethoxydibenzo[fg,op]naphthacene (C_2v) and 1,2,5,6,8,9,12,13-octamethoxydibenzo[fg,op] naphthacene (C_2h) are crossed. A mechanism involving the migration of an aryl ring on an arenium cation intermediate is proposed.     

Enantioselective total syntheses of nankakurines A and B: confirmation of structure and establishment of absolute configuration

Total syntheses of (+)-nankakurine A (2) and (+)-nankakurine B (3) were accomplished by a sequence that employs an intramolecular dipolar cycloaddition of an azomethine imine intermediate to form the azatricyclic moiety and establish the relative configuration of the spiropiperidine ring. These syntheses, together with the synthesis of the originally purported structure 1 of nankakurine A, rigorously establish the relative and absolute configuration of these structurally unusual Lycopodium alkaloids. The syntheses are sufficiently concise that gram quantities of (+)-nankakurine A (2) and (+)-nankakurine B (3) will be available for further biological studies.     

Photochemistry of adsorbed nitrate

In the atmosphere, gas-phase nitrogen oxides including nitric acid react with particle surfaces (e.g., mineral dust and sea salt aerosol) to yield adsorbed nitrate, yet little is known about the photochemistry of nitrate on the surface of these particles. In this study, nitrate adsorbed on alumina surfaces, a surrogate for mineral dust aerosol, is irradiated with broadband light (lambda > 300 nm) in the absence and presence of coadsorbed water, at <1% and 45 +/- 2% relative humidity (%RH), respectively, and molecular oxygen. Upon irradiation, the nitrate ion readily undergoes photolysis to yield nitrogen-containing gas-phase products, NO2, NO, and N2O. Although NO2, NO, and N2O form under the different conditions investigated, both coadsorbed water and molecular oxygen change the gas-phase product distribution, with NO being the major product under dry and humid conditions in the absence of molecular oxygen and NO2 the major product in the presence of molecular oxygen. To the best of our knowledge, this is the first study to investigate the role of solvation by coadsorbed water in the photochemistry of adsorbates at solid interfaces and the roles that molecular oxygen, adsorbed water, and relative humidity may have in photochemical processes on aerosol surfaces that have the potential to alter the chemical balance of the atmosphere.     

Direct site-selective covalent protein immobilization catalyzed by a phosphopantetheinyl transferase

Immobilization of proteins onto solid supports is important in the preparation of functional protein microarrays and in the development of bead-based bioassays, biosensors, and industrial biocatalysts. In order to generate the stable, functional, and homogeneous materials required for these applications, attention has focused on methods that enable the efficient and site-specific covalent immobilization of recombinant proteins onto a wide range of platforms. To this end, the phosphopantetheinyl transferase Sfp was employed to catalyze the direct immobilization of recombinant proteins bearing the small, genetically encoded ybbR tag onto surfaces functionalized with CoA. Using mass spectrometry, it was shown that the Sfp catalyzes immobilization of a model acyl carrier protein (ACP) onto CoA-derivatized PEGA resin beads through specific covalent bond formation. Luciferase (Luc) and glutathione-S-transferase (GST) ybbR-fusion proteins were similarly immobilized onto PEGA resin retaining high levels of enzyme activity. This strategy was also successfully applied for the immobilization of the ACP, as well as ybbR-Luc, -GST, and -thioredoxin fusion proteins, on hydrogel microarray slides. Overall, the Sfp-catalyzed surface ligation is mild, quantitative, and rapid, occurring in a single step without prior chemical modification of the target protein. Immobilization of the target proteins directly from a cell lysate mixture was also demonstrated.     

Separating chemical shift and quadrupolar anisotropies via multiple-quantum NMR spectroscopy

Chemical shift anisotropy (CSA) has been an invaluable probe of structure and dynamics for a variety of systems in NMR spectroscopy. Unfortunately, the presence of strong quadrupolar couplings has severely limited the ability to measure CSA in nuclei with spins I > 1/2. Here we show that these two interactions can be refocused at different times in a 2D multiple-quantum NMR experiment on polycrystalline samples. Combining this experiment with appropriate affine transformations allows these interactions to be cleanly separated into orthogonal dimensions. The 1D projection onto each axis can be fit to extract the respective principal tensor components. These components can then be used to fit the 2D spectrum for the relative orientation between the CSA and quadrupolar-coupling tensors. The necessary affine transformation parameters are given for all possible I values. Illustrative examples of spectra and analyses are given for 63Cu in K3[Cu(CN)4], 59Co in K3[Co(CN)6], and 87Rb in RbCrO4.     

Near-edge X-ray absorption fine structure spectroscopy of diamondoid thiol monolayers on gold

Diamondoids, hydrocarbon molecules with cubic-diamond-cage structures, have unique properties with potential value for nanotechnology. The availability and ability to selectively functionalize this special class of nanodiamond materials opens new possibilities for surface modification, for high-efficiency field emitters in molecular electronics, as seed crystals for diamond growth, or as robust mechanical coatings. The properties of self-assembled monolayers (SAMs) of diamondoids are thus of fundamental interest for a variety of emerging applications. This paper presents the effects of thiol substitution position and polymantane order on diamondoid SAMs on gold using near-edge X-ray absorption fine structure spectroscopy (NEXAFS) and X-ray photoelectron spectroscopy (XPS). A framework to determine both molecular tilt and twist through NEXAFS is presented and reveals highly ordered diamondoid SAMs, with the molecular orientation controlled by the thiol location. C 1s and S 2p binding energies are lower in adamantane thiol than alkane thiols on gold by 0.67 +/- 0.05 and 0.16 +/- 0.04 eV, respectively. These binding energies vary with diamondoid monolayer structure and thiol substitution position, consistent with different degrees of steric strain and electronic interaction with the substrate. This work demonstrates control over the assembly, in particular the orientational and electronic structure, providing a flexible design of surface properties with this exciting new class of diamond nanoparticles.