Density Estimation with Replicate Heteroscedastic Measurements

We present a deconvolution estimator for the density function of a random variable from a set of independent replicate measurements. We assume that measurements are made with normally distributed errors having unknown and possibly heterogeneous variances. The estimator generalizes well-known deconvoluting kernel density estimators, with error variances estimated from the replicate observations. We derive expressions for the integrated mean squared error and examine its rate of convergence as n → ∞ and the number of replicates is fixed. We investigate the finite-sample performance of the estimator through a simulation study and an application to real data.     

Discovery and assembly-line biosynthesis of the lymphostin pyrroloquinoline alkaloid family of mTOR inhibitors in Salinispora bacteria

The pyrroloquinoline alkaloid family of natural products, which includes the immunosuppressant lymphostin, has long been postulated to arise from tryptophan. We now report the molecular basis of lymphostin biosynthesis in three marine Salinispora species that maintain conserved biosynthetic gene clusters harboring a hybrid nonribosomal peptide synthetase-polyketide synthase that is central to lymphostin assembly. Through a series of experiments involving gene mutations, stable isotope profiling, and natural product discovery, we report the assembly-line biosynthesis of lymphostin and nine new analogues that exhibit potent mTOR inhibitory activity.     

Reactivity and selectivity of charged phenyl radicals toward amino acids in a Fourier transform ion cyclotron resonance mass spectrometer

The reactivity of 10 charged phenyl radicals toward several amino acids was examined in the gas phase in a dual-cell Fourier transform ion cyclotron resonance mass spectrometer. All radicals abstract a hydrogen atom from the amino acids, as expected. The most electrophilic radicals (with the greatest calculated vertical electron affinities (EA) at the radical site) also react with these amino acids via NH(2) abstraction (a nonradical nucleophilic addition-elimination reaction). Both the radical (hydrogen atom abstraction) and nonradical (NH(2) abstraction) reaction efficiencies were found to increase with the electrophilicity (EA) of the radical. However, NH(2) abstraction is more strongly influenced by EA. In contrast to an earlier report, the ionization energies of the amino acids do not appear to play a general reactivity-controlling role. Studies using several partially deuterium-labeled amino acids revealed that abstraction of a hydrogen atom from the α-carbon is only preferred for glycine; for the other amino acids, a hydrogen atom is preferentially abstracted from the side chain. The electrophilicity of the radicals does not appear to have a major influence on the site from which the hydrogen atom is abstracted. Hence, the regioselectivity of hydrogen atom abstraction appears to be independent of the structure of the radical but dependent on the structure of the amino acid. Surprisingly, abstraction of two hydrogen atoms was observed for the N-(3-nitro-5-dehydrophenyl)pyridinium radical, indicating that substituents on the radical not only influence the EA of the radical but also can be involved in the reaction. In disagreement with an earlier report, proline was found to display several unprecedented reaction pathways that likely do not proceed via a radical mechanism but rather by a nucleophilic addition-elimination mechanism. Both NH(2) and (15)NH(2) groups were abstracted from lysine labeled with (15)N on the side chain, indicating that NH(2) abstraction occurs both from the amino terminus and from the side chain. Quantum chemical calculations were employed to obtain insights into some of the reaction mechanisms.     

X-ray and NMR crystallography in an enzyme active site: the indoline quinonoid intermediate in tryptophan synthase

Chemical-level details such as protonation and hybridization state are critical for understanding enzyme mechanism and function. Even at high resolution, these details are difficult to determine by X-ray crystallography alone. The chemical shift in NMR spectroscopy, however, is an extremely sensitive probe of the chemical environment, making solid-state NMR spectroscopy and X-ray crystallography a powerful combination for defining chemically detailed three-dimensional structures. Here we adopted this combined approach to determine the chemically rich crystal structure of the indoline quinonoid intermediate in the pyridoxal-5'-phosphate-dependent enzyme tryptophan synthase under conditions of active catalysis. Models of the active site were developed using a synergistic approach in which the structure of this reactive substrate analogue was optimized using ab initio computational chemistry in the presence of side-chain residues fixed at their crystallographically determined coordinates. Various models of charge and protonation state for the substrate and nearby catalytic residues could be uniquely distinguished by their calculated effects on the chemical shifts measured at specifically (13)C- and (15)N-labeled positions on the substrate. Our model suggests the importance of an equilibrium between tautomeric forms of the substrate, with the protonation state of the major isomer directing the next catalytic step.     

In situ formation of N-trifluoroacetoxy succinimide (TFA-NHS): one-pot formation of succinimidyl esters, N-trifluoroacetyl amino acid succinimidyl esters, and N-maleoyl amino acid succinimidyl esters

A method for the in situ formation of N-trifluoroacetoxy succinimide (TFA-NHS) and its application in the formation of succinimidyl esters is presented. The developed method provides N-trifluoroacetyl and N-maleoyl amino acid succinimidyl esters from a variety of amino acids using a one-pot, high-yielding protocol. Investigations into the formation of an N-maleoyl amino acid succinimidyl ester supported the proposal of a revised reaction mechanism, and contributed to the optimization of the reaction conditions.     

Evaluating the electrochemical capacitance of surface-charged nanoparticle oxide coatings

While transition metal oxides have been thoroughly investigated as coatings for electrochemical capacitors due to their pseudocapacitance, little work has been done investigating other oxide coatings. There exists a whole class of nanoporous oxides typically synthesized by sol-gel chemistry techniques that have very high differential capacitance. This high differential capacitance has been attributed to the surface potential of these materials and the close approach of counterions near the surface of these oxides. This study focuses on investigating the electrochemical capacitance of non-transition metal oxide nanoparticle coatings when deposited on supporting electrodes. Here, we show that, by adding coatings of SiO(2), AlOOH, TiO(2), and ZrO(2) nanoparticles to graphite support electrodes, we can increase the electrochemical capacitance. We also show that the measured electrochemical capacitance of these oxide-coated electrodes directly relates to the electrophoretic mobility of these materials with the lowest values in capacitance occurring at or near the respective isoelectric pH (pH(IEP)) of each oxide.     

Volume in General Metric Spaces

A central question in the geometry of finite metric spaces is how well can an arbitrary metric space be “faithfully preserved” by a mapping into Euclidean space. In this paper we present an algorithmic embedding which obtains a new strong measure of faithful preservation: not only does it (approximately) preserve distances between pairs of points, but also the volume of any set of \(k\) points. Such embeddings are known as volume preserving embeddings. We provide the first volume preserving embedding that obtains constant average volume distortion for sets of any fixed size. Moreover, our embedding provides constant bounds on all bounded moments of the volume distortion while maintaining the best possible worst-case volume distortion. Feige, in his seminal work on volume preserving embeddings defined the volume of a set \(S = \{v_1, \ldots , v_k \}\) of points in a general metric space: the product of the distances from \(v_i\) to \(\{ v_1, \dots , v_{i-1} \}\) , normalized by \(\tfrac{1}{(k-1)!}\) , where the ordering of the points is that given by Prim’s minimum spanning tree algorithm. Feige also related this notion to the maximal Euclidean volume that a Lipschitz embedding of \(S\) into Euclidean space can achieve. Syntactically this definition is similar to the computation of volume in Euclidean spaces, which however is invariant to the order in which the points are taken. We show that a similar robustness property holds for Feige’s definition: the use of any other order in the product affects volume \(^{1/(k-1)}\) by only a constant factor. Our robustness result is of independent interest as it presents a new competitive analysis for the greedy algorithm on a variant of the online Steiner tree problem where the cost of buying an edge is logarithmic in its length. This robustness property allows us to obtain our results on volume preserving embedding.     

Model-based clustering of high-dimensional data: Variable selection versus facet determination

Variable selection is an important problem for cluster analysis of high-dimensional data. It is also a difficult one. The difficulty originates not only from the lack of class information but also the fact that high-dimensional data are often multifaceted and can be meaningfully clustered in multiple ways. In such a case the effort to find one subset of attributes that presumably gives the “best” clustering may be misguided. It makes more sense to identify various facets of a data set (each being based on a subset of attributes), cluster the data along each one, and present the results to the domain experts for appraisal and selection. In this paper, we propose a generalization of the Gaussian mixture models and demonstrate its ability to automatically identify natural facets of data and cluster data along each of those facets simultaneously. We present empirical results to show that facet determination usually leads to better clustering results than variable selection.     

Influence of applied potential on bradykinin adsorption onto Ag,Au, and Cu electrodes

Surface‐enhanced Raman scattering, electrochemistry, and generalized two‐dimensional correlation analysis (G2DCA) methods were used to characterize bradykinin (BK), a hormone which is known to be involved in small‐cell and non‐small‐cell lung carcinoma and prostate cancer. BK was deposited onto Ag, Au, and Cu electrode surfaces under different applied electrode potentials (−1.000 V to 0.200 V) in aqueous solutions. Based on the analysis of the enhancement, the broadening, and the shifts in the wavenumbers of individual bands, specific conclusions were drawn regarding the peptide geometry and changes in this geometry that occurred when the electrode type and applied electrode potential were varied. Briefly, BK deposited onto the Ag, Au, and Cu electrode surfaces showed bands that were due to the vibrations of moieties in contact with or in close proximity to the electrode surfaces and were thus located on the same side of the polypeptide backbone. These moieties included the Phe, Arg, and Pro residues. The findings for adsorbed BK were fully supported by G2DCA, which also allowed us to determine the order in which changes occurred when the electrode potential was changed. In addition, it was found that at negative electrode potentials, the Phe rings and methylene groups interact with Ag electrode surface. No such interaction was observed for Au and Cu electrodes. Copyright © 2013 John Wiley & Sons, Ltd.     

Perturbation theory and the excess properties of mixtures of simple liquids

One of the most successful theories of single-component simple liquids is perturbation theory which is based on the assumption that the structure of a liquid is primarily determined by the repulsive forces between its molecules, so that a liquid may be regarded as a system of hard spheres with the attractive forces providing a uniform background energy. Our earlier extension of these ideas to liquid mixtures was only partially successful. In this paper we show that this problem was due to the use of a somewhat unsatisfactory equation of state for the reference hard-sphere mixture. If a more satisfactory equation of state is used, perturbation theory yields results in close agreement with Monte Carlo and experimental results, even when the molecules of the mixture differ appreciably in size.