On dual molecules and convolution-dominated operators

We show that sampling or interpolation formulas in reproducing kernel Hilbert spaces can be obtained by reproducing kernels whose dual systems form molecules, ensuring that the size profile of a function is fully reflected by the size profile of its sampled values. The main tool is a local holomorphic calculus for convolution-dominated operators, valid for groups with possibly non-polynomial growth. Applied to the matrix coefficients of a group representation, our methods improve on classical results on atomic decompositions and bridge a gap between abstract and concrete methods.     

Polymer escape from a metastable Kramers potential: path integral hyperdynamics study

We study the dynamics of flexible, semiflexible, and self-avoiding polymer chains moving under a Kramers metastable potential. Due to thermal noise, the polymers, initially placed in the metastable well, can cross the potential barrier, but these events are extremely rare if the barrier is much larger than thermal energy. To speed up the slow rate processes in computer simulations, we extend the recently proposed path integral hyperdynamics method to the cases of polymers. We consider the cases where the polymers' radii of gyration are comparable to the distance between the well bottom and the barrier top. We find that, for a flexible polymers, the crossing rate (R) monotonically decreases with chain contour length (L), but with the magnitude much larger than the Kramers rate in the globular limit. For a semiflexible polymer, the crossing rate decreases with L but becomes nearly constant for large L. For a fixed L, the crossing rate becomes maximum at an intermediate bending stiffness. For the self-avoiding chain, the rate is a nonmonotonic function of L, first decreasing with L, and then, above a certain length, increasing with L. These findings can be instrumental for efficient separation of biopolymers.     

Atomic‐Level Elucidation of the Initial Stages of Self‐Assembled Monolayer Metallization and Nanoparticle Formation

The development of high‐performance molecular electronics and nanotech applications requires deep understanding of atomic level structural, electronic, and magnetic properties of electrode/molecular interfaces. Recent electrochemical experiments on self‐assembled monolayers (SAMs) have identified highly practical means to generate nanoparticles and metal monolayers suspended above substrate surfaces through SAM metallizations. A rational basis why this process is even possible is not yet well‐understood. To clarify the initial stages of interface formation during SAM metallization, we used first‐principles spin‐polarized density functional theory (DFT) calculations to study Pd diffusion on top of 4‐mercaptopyridine (4MP) SAMs on Au(111). After distinguishing potential‐energy surfaces (PESs) for different spin configurations for transition metal atoms on the SAM, we find adatom diffusion is not possible over the clean 4MP–SAM surface. Pre‐adsorption of transition‐metal atoms, however, facilitates atomic diffusion that appears to explain multiple reports on experimentally observed island and monolayer formation on top of SAMs. Furthermore, these diffusions most likely occur by moving across low‐lying and intersecting PESs of different spin states, opening the possibility of magnetic control over these systems. Vertical diffusion processes were also investigated, and the electrolyte was found to play a key role in preventing metal permeation through the SAM to the substrate.     

Masking effect of anti-androgens on androgenic activity in European river sediment unveiled by effect-directed analysis

This study shows that the androgen receptor agonistic potency is clearly concealed by the effects of androgen receptor antagonists in a total sediment extract, demonstrating that toxicity screening of total extracts is not enough to evaluate the full in vitro endocrine disrupting potential of a complex chemical mixture, as encountered in the environment. The anti-androgenic compounds were masking the activity of androgenic compounds in the extract with relatively high anti-androgenic potency, equivalent to 200 nmol flutamide equivalents/g dry weight. A two-step serial liquid chromatography fractionation of the extract successfully separated anti-androgenic compounds from androgenic compounds, resulting in a total androgenic potency of 3,820 pmol dihydrotestosterone equivalents/g dry weight. The fractionation simplified the chemical identification analysis of the original complex sample matrix. Seventeen chemical structures were tentatively identified. Polyaromatic hydrocarbons, a technical mixture of nonylphenol and dibutyl phthalate were identified to contribute to the anti-androgenic potency observed in the river sediment sample. With the GC/MS screening method applied here, no compounds with AR agonistic disrupting potencies could be identified. Seventy-one unidentified peaks, which represent potentially new endocrine disrupters, have been added to a database for future investigation.     

The transfer of tin and germanium atoms from N-heterocyclic stannylenes and germylenes to diazadienes

New N-heterocyclic stannylenes and germylenes were synthesized by transamination of E[N(SiMe3)2] (E = Ge, Sn) with alpha-amino-aldimines or ethylidene-1,2-diamines and were characterized by spectroscopic methods and in the case of the germylene 10 g by X-ray diffraction. The reactions of several germylenes and stannylenes with diazadienes were studied by using dynamic NMR and computational methods. Experimental and theoretical studies confirmed that metathesis with exchange of the Group 14 atom is feasible for both stannylenes and germylenes, with exchange rates being generally higher for stannylenes. The metathesis of the diazadiene 3 b and the stannylene 1 b follows second-order kinetics and exhibits a sizeable negative entropy of activation. The transfer reaction is inhibited by bulky substituents in both reactants and surprisingly coincides with a suppression of the fragmentation of the stannylene into tin and diazadiene. A connection between oxidative addition and ring fragmentation was also observed in the reaction of 1 f with sulfur. Density functional theory (DFT) calculations suggest that all metathesis reactions proceed via transient spirocyclic [1+4] cycloaddition products, the formation of which is generally endothermic and endergonic. The spirostannanes display a distorted Psi-tbp geometry at the tin atom and their cycloreversion requires low or nearly negligible activation energies; spirogermanes exhibit distorted tetrahedral central atoms and sizeable energy barriers with respect to the same reaction. Complementary studies of cycloadditions of diazadienes to triplet germylenes or stannylenes indicate that these reactions are exothermic. The lowest triplet state in the carbene homologues results from promotion of an electron from an n(N) orbital with pi character rather than the n(C)-sigma orbital as in carbenes, and singlet-triplet excitation energies decrease from carbon to tin. Spirostannanes exhibit a triplet ground-state multiplicity that implies that the energy hypersurfaces for the reactions of singlet and triplet stannylenes with diazadienes intersect; for germylenes, the singlet hypersurface is always lower in energy. A reaction mechanism explaining the different thermal stabilities of N-heterocyclic germylenes and stannylenes, and the coincidence between ring metathesis and thermal decomposition of the latter, is proposed based on the different separation of the singlet and triplet energy hypersurfaces.     

Simultaneous analysis of prostanoids using liquid chromatography/high-field asymmetric waveform ion mobility spectrometry/tandem mass spectrometry

A liquid chromatography/high-field asymmetric waveform ion mobility spectrometry/tandem mass spectrometry (LC-FAIMS-MS/MS) semi-quantitative method was developed for the simultaneous determination of prostaglandin (PG) E2, PGD2, PGF(2alpha), 6-keto-PGF(1alpha), and thromboxane (TX) B2. Diluted samples containing these prostanoids and their tetra-deuterium-substituted internal standards were analyzed by LC followed by either selected reaction monitoring (LC-SRM) or FAIMS and selected reaction monitoring (LC-FRM). FAIMS reduced background noise, separated the isobaric ions PGE2 and PGD2, and separated dynamically interchanging TXB2 anomers. This is the first report of the separation of interconverting anomers by FAIMS. Generally, the LC-FRM chromatograms were more selective than the LC-SRM chromatograms. Its potential was demonstrated by analysis of prostanoids in guinea pig lumbar spinal cord homogenate.     

Heterologous expression of photoactivated adenylyl cyclase (PAC) genes from the flagellate Euglena gracilis in insect cells

The unicellular, green flagellate wild-type Euglena gracilis (strain Z) possesses two genes of the photoactivated adenylyl cyclase (PAC) family. The corresponding gene products were found to be responsible for step-up (but not step-down) photophobic responses as well as both positive and negative phototaxis. The proteins consist of two PACalpha (Mr 105 kDa) and two PACbeta (90 kDa) subunits. In an effort to produce sufficient amounts of PAC proteins, several routes of over-expression have been tried including homologous expression in Euglena and heterologous expression in Escherichia coli. All these approaches were hampered by low yield or formation of inclusion bodies. Therefore we decided to attempt a heterologous expression in an insect cell line. PACalpha and PACbeta were separately cloned in the transfer vector pBacPAK9 with a His tag attached. The transfer vector was subsequently cotransfected via baculovirus into the insect cells and amplified. For the expression both recombinant viruses (containing PACbeta and PACbeta, respectively) were cotransfected simultaneously into insect cells. The expressed proteins were analyzed in Western blots using PACalpha and PACbeta antibodies. Most of the proteins were found to be in soluble form in high yield. The recombinant PAC proteins were purified via their attached His tag on an anti-His resin. Adenylyl cyclase activity was quantified after blue-light excitation using a cAMP enzyme immunoassay kit.