Non-Commutative Harmonic and Subharmonic Polynomials

The paper introduces a notion of the Laplace operator of a polynomial p in noncommutative variables x = (x ₁,…, x _g ). The Laplacian Lap[p, h] of p is a polynomial in x and in a noncommuting variable h. When all variables commute we have Lap[p, h] = h ²Δ _x p where Δ _x p is the usual Laplacian. A symmetric polynomial in symmetric variables will be called harmonic if Lap[p, h] = 0 and subharmonic if the polynomial q(x, h) :=  Lap[p, h] takes positive semidefinite matrix values whenever matrices X ₁,…, X _g , H are substituted for the variables x ₁,…, x _g , h. In this paper we classify all homogeneous symmetric harmonic and subharmonic polynomials in two symmetric variables. We find there are not many of them: for example, the span of all such subharmonics of any degree higher than 4 has dimension 2 (if odd degree) and 3 (if even degree). Hopefully, the approach here will suggest ways of defining and analyzing other partial differential equations and inequalities. Dedicated to Israel Gohberg on the occasion of his 80^th birthday. All authors were partially supported by J.W. Helton’s grants from the NSF and the Ford Motor Co. and J. A. Hernandez was supported by a McNair Fellowship.     

Stereoselective synthesis of (Z)-alpha-halo-alpha,beta-unsaturated esters, and amides from aldehydes and trihaloesters or amides promoted by manganese

Preliminary results of a Mn-promoted sequential process directed toward the stereoselective synthesis of different (Z)-alpha-halo-alpha,beta-unsaturated compounds are described.     

Vibrational analysis of amino acids and short peptides in hydrated media. 3. Successive KL repeats induce highly stable beta-strands capable of forming non-H-bonded aggregates

Circular dichroism (CD) and Raman scattering were applied to the aqueous solution of minimalist LK peptides constructed with successive KL repeats leading to the following generic primary sequence: (KL)nK. Three peptides of this family, a 3-mer (n=1), a 9-mer (n=4), and a 15-mer (n=7), are analyzed in this report. Raman spectra of the 3-mer (KLK, a random chain) and its labile-hydrogen deuterated species yield a set of interesting information for analyzing longer peptides of this series. Although the CD spectrum of the 9-mer (KLKLKLKLK) reveals a signal traditionally assigned to a random structure, the corresponding Raman spectrum allows finding a mixture of conformations in solution, adopting predominantly beta-type structures. This fact proves the utility of Raman spectroscopy to eliminate eventual ambiguity concerning conformational assignments in peptides based only on the use of CD technique. Finally, the 15-mer (KLKLKLKLKLKLKLK) gives rise to CD and Raman spectra clearly assignable to a beta-type structure. On the basis of all the observed results on the 15-mer, we can confirm that this peptide may exist as isolated beta-strands at low concentration (sub-micromolar), flat-oriented at the air/water interface, whereas at high concentrations (millimolar), non-H-bonded immersible aggregates might be formed. A hypothetical model for these beta-strand aggregates could be proposed as stabilized by an interior hydrophobic core and a hydrophilic external face, formed by leucine and lysine side chains, respectively.     

Copper and palladium complexes with N-heterocyclic carbene ligands functionalised with carboxylate groups

The new imidazolium salts functionalised with the trimethylsilyl ester group 1a–c, were easily obtained by quaternisation of alkyl- or aryl-imidazoles with trimethylsilyl bromoacetate. Salt 1a was isolated and fully characterised. It reacted with mesityl copper (Cu₅Mes₅) under trimethylsilyl abstraction to form the complex 2. Methanolysis of 1a–c gave good yields of the carboxylic acid functionalised imidazolium salts 3a–c. Deprotonation of the latter in liquid ammonia led to the zwitterionic imidazolium carboxylates 4a–c. Reaction of 4a with (Cu₅Mes₅) gave solutions from which the insoluble polymeric 5a crystallised slowly. Generation of the carboxylate-functionalised NHC in situ followed by reaction with Pd(OOCCH₃)₂ gave the new complex 6a in which the NHC-carboxylate ligand is chelate bidentate.     

On the benefits of acquiring peptide fragment ions at high measured mass accuracy

The advantages and disadvantages of acquiring tandem mass spectra by collision-induced dissociation (CID) of peptides in linear ion trap Fourier-transform hybrid instruments are described. These instruments offer the possibility to transfer fragment ions from the linear ion trap to the FT-based analyzer for analysis with both high resolution and high mass accuracy. In addition, performing CID during the transfer of ions from the linear ion trap (LTQ) to the FT analyzer is also possible in instruments containing an additional collision cell (i.e., the "C-trap" in the LTQ-Orbitrap), resulting in tandem mass spectra over the full m/z range and not limited by the ejection q value of the LTQ. Our results show that these scan modes have lower duty cycles than tandem mass spectra acquired in the LTQ with nominal mass resolution, and typically result in fewer peptide identifications during data-dependent analysis of complex samples. However, the higher measured mass accuracy and resolution provides more specificity and hence provides a lower false positive ratio for the same number of true positives during database search of peptide tandem mass spectra. In addition, the search for modified and unexpected peptides is greatly facilitated with this data acquisition mode. It is therefore concluded that acquisition of tandem mass spectral data with high measured mass accuracy and resolution is a competitive alternative to "classical" data acquisition strategies, especially in situations of complex searches from large databases, searches for modified peptides, or for peptides resulting from unspecific cleavages.     

Xanthene-Based Nitric Oxide-Responsive Nanosensor for Photoacoustic Imaging in the SWIR Window

Shortwave infrared (SWIR) dyes are characterized by their ability to absorb light from 900 to 1400 nm, which is ideal for deep tissue imaging owing to minimized light scattering and interference from endogenous pigments. An approach to access such molecules is to tune the photophysical properties of known near-infrared dyes. Herein, we report the development of a series of easily accessible (three steps) SWIR xanthene dyes based on a dibenzazepine donor conjugated to thiophene ( SCR-1 ), thienothiophene ( SCR-2 ), or bithiophene ( SCR-3 ). We leverage the fact that SCR-1 undergoes a bathochromic shift when aggregated for in vivo studies by developing a ratiometric nanoparticle for NO ( rNP-NO ), which we employed to successfully visualize pathological levels of nitric oxide in a drug-induced liver injury model via deep tissue SWIR photoacoustic (PA) imaging. Our work demonstrates how easily this dye series can be utilized as a component in nanosensor designs for imaging studies.     

Towards a consistent mechanism of emulsion polymerization—new experimental details

The application of atypical experimental methods such as conductivity measurements, optical microscopy, and nonstirred polymerizations to investigations of the ‘classical’ batch ab initio emulsion polymerization of styrene revealed astonishing facts. The most important result is the discovery of spontaneous emulsification leading to monomer droplets even in the quiescent styrene in water system. These monomer droplets with a size between a few and some hundreds of nanometers, which are formed by spontaneous emulsification as soon as styrene and water are brought into contact, have a strong influence on the particle nucleation, the particle morphology, and the swelling of the particles. Experimental results confirm that micelles of low-molecular-weight surfactants are not a major locus of particle nucleation. Brownian dynamics simulations show that the capture of matter by the particles strongly depends on the polymer volume fraction and the size of the captured species (primary free radicals, oligomers, single monomer molecules, or clusters).     

Elaboration of monodisperse spherical hollow particles with ordered mesoporous silica shells via dual latex/surfactant templating: radial orientation of mesopore channels

Monodisperse spherical hollow nanoparticles of mesoporous silica featuring mesopores with a radial orientation in the silica shell were synthesized via a dual-templating method. Specifically designed polystyrene latexes with anionic or cationic surface charges acted as the core templates, while cetyltrimethylammonium bromide served as a co-template to structure the mesopore formation during tetraethoxysilane hydrolysis/condensation. The particles were well-separated and presented homogeneous mesoporous silica shells. Average particle diameters were less than 200 nm, and the particles displayed high values of specific surface area and pore volume. The shell thickness and the hollow core diameter could be tuned independently while the radial pore structure was preserved. A detailed analysis of the nitrogen adsorption-desorption isotherms proved that the central cavity was completely isolated from the external medium, that is, only accessible through the radial mesopores of the shell. Consequently, our particles gather the advantages of a well-defined structure, straight penetrating channels across the silica shell, and a high accessible porous volume of the central core. These properties make them far better candidates than simple mesoporous particles for any storage and/or controlled release applications.     

Toward [18F]-labeled aryltrifluoroborate radiotracers: in vivo positron emission tomography imaging of stable aryltrifluoroborate clearance in mice

The use of a boronic ester as a captor of aqueous [(18)F]-fluoride has been previously suggested as a means of labeling biomolecules in one step for positron emission tomography (PET) imaging. For this approach to be seriously considered, the [(18)F]-labeled trifluoroborate should be humorally stable such that it neither leaches free [(18)F]-fluoride to the bone nor accumulates therein. Herein, we have synthesized a biotinylated boronic ester that is converted to the corresponding trifluoroborate salt in the presence of aqueous [(18)F]-fluoride. In keeping with its in vitro aqueous kinetic stability at pH 7.5, the trifluoroborate appears to clear in vivo quite rapidly to the bladder as the stable trifluoroborate salt with no detectable leaching of free [(18)F]-fluoride to the bone. When this labeled biotin is preincubated with avidin, the pharmacokinetic clearance of the resulting complex is visibly altered. This work validates initial claims that boronic esters are potentially useful as readily labeled precursors to [(18)F]-PET reagents.