Shearlet coorbit spaces and associated Banach frames

In this paper, we study the relationships of the newly developed continuous shearlet transform with the coorbit space theory. It turns out that all the conditions that are needed to apply the coorbit space theory can indeed be satisfied for the shearlet group. Consequently, we establish new families of smoothness spaces, the shearlet coorbit spaces. Moreover, our approach yields Banach frames for these spaces in a quite natural way. We also study the approximation power of best n-term approximation schemes and present some first numerical experiments.     

Classification of edges using compactly supported shearlets

We analyze the detection and classification of singularities of functions $f={\chi }_S$, where $S?{\mathbb{R}}^d$ and $d=2,3$. It will be shown how the set ?S can be extracted by a continuous shearlet transform associated with compactly supported shearlets. Furthermore, if ?S is a $d?1$ dimensional piecewise smooth manifold with $d=2$ or 3, we will classify smooth and non-smooth components of ?S. This improves previous results given for shearlet systems with a certain band-limited generator, since the estimates we derive are uniform. Moreover, we will show that our bounds are optimal. Along the way, we also obtain novel results on the characterization of wavefront sets in 3 dimensions by compactly supported shearlets. Finally, geometric properties of ?S such as curvature are described in terms of the continuous shearlet transform of f.     

Zeros of the Zak transform on locally compact Abelian groups

Let be a locally compact abelian group. The notion of Zak transform on extends to . Suppose that is compactly generated and its connected component of the identity is non-compact. Generalizing a classical result for , we then prove that if is such that its Zak transform is continuous on , then has a zero.

     

Quantitative Comparison of Tandem Mass Spectra Obtained on Various Instruments

The similarity between two tandem mass spectra, which were measured on different instruments, was compared quantitatively using the similarity index (SI), defined as the dot product of the square root of peak intensities in the respective spectra. This function was found to be useful for comparing energy-dependent tandem mass spectra obtained on various instruments. Spectral comparisons show the similarity index in a 2D “heat map”, indicating which collision energy combinations result in similar spectra, and how good this agreement is. The results and methodology can be used in the pharma industry to design experiments and equipment well suited for good reproducibility. We suggest that to get good long-term reproducibility, it is best to adjust the collision energy to yield a spectrum very similar to a reference spectrum. It is likely to yield better results than using the same tuning file, which, for example, does not take into account that contamination of the ion source due to extended use may influence instrument tuning. The methodology may be used to characterize energy dependence on various instrument types, to optimize instrumentation, and to study the influence or correlation between various experimental parameters.

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Amino acid cluster formation studied by electrospray ionization mass spectrometry

The association properties of natural and non-natural amino acids were studied in detail using electrospray ionization mass spectrometry. The results show a highly diverse cluster formation behavior of amino acids. There are differences regarding the degree of clustering (average cluster size), the presence or absence of one or several 'magic' clusters of special stability and the influence of chirality on cluster stability. Cluster formation does not show a good correlation with simple physico-chemical properties (such as solubility), indicating that it is a specific process and not only a simple aggregation during evaporation/ionization. A systematic study of cluster formation of serine derivatives reveals that all functional groups play a prominent role in the binding of the magic octamer. The results support the idea of the zwitterionic character of the octamer. Electrospray ionization of the side-chain acetylated serine shows the formation of a very stable tetramer with a strong preference for homochirality. The results suggest that Ser8 is made up of two tetramer subunits, held together by hydrogen bonds of the side-chain.     

Evaluation of Candidatus Liberibacter Asiaticus Efflux Pump Inhibition by Antimicrobial Peptides

Citrus greening, also known as Huanglongbing (HLB), is caused by the unculturable bacterium Candidatus Liberibacter spp. (e.g., CLas), and has caused a devastating decline in citrus production in many areas of the world. As of yet, there are no definitive treatments for controlling the disease. Antimicrobial peptides (AMPs) that have the potential to block secretion-dependent effector proteins at the outer-membrane domains were screened in silico. Predictions of drug-receptor interactions were built using multiple in silico techniques, including molecular docking analysis, molecular dynamics, molecular mechanics generalized Born surface area analysis, and principal component analysis. The efflux pump TolC of the Type 1 secretion system interacted with natural bacteriocin plantaricin JLA-9, blocking the β barrel. The trajectory-based principal component analysis revealed the possible binding mechanism of the peptides. Furthermore, in vitro assays using two closely related culturable surrogates of CLas (Liberibacter crescens and Rhizobium spp.) showed that Plantaricin JLA-9 and two other screened AMPs inhibited bacterial growth and caused mortality. The findings contribute to designing effective therapies to manage plant diseases associated with Candidatus Liberibacter spp.     

Optimum collision energies for proteomics: The impact of ion mobility separation

Ion mobility spectrometry (IMS) is a widespread separation technique used in various research fields. It can be coupled to liquid chromatography–mass spectrometry (LC–MS/MS) methods providing an additional separation dimension. During IMS, ions are subjected to multiple collisions with buffer gas, which may cause significant ion heating. The present project addresses this phenomenon from the bottom-up proteomics point of view. We performed LC–MS/MS measurements on a cyclic ion mobility mass spectrometer with varied collision energy (CE) settings both with and without IMS. We investigated the CE dependence of identification score, using Byonic search engine, for more than 1000 tryptic peptides from HeLa digest standard. We determined the optimal CE values—giving the highest identification score—for both setups (i.e., with and without IMS). Results show that lower CE is advantageous when IMS separation is applied, by 6.3 V on average. This value belongs to the one-cycle separation configuration, and multiple cycles may supposedly have even larger impact. The effect of IMS is also reflected in the trends of optimal CE values versus m/z functions. The parameters suggested by the manufacturer were found to be almost optimal for the setup without IMS; on the other hand, they are obviously too high with IMS. Practical consideration on setting up a mass spectrometric platform hyphenated to IMS is also presented. Furthermore, the two CID (collision induced dissociation) fragmentation cells of the instrument—located before and after the IMS cell—were also compared, and we found that CE adjustment is needed when the trap cell is used for activation instead of the transfer cell. Data have been deposited in the MassIVE repository (MSV000090944).     

Biomimetic oxidation of 3,5-di-tert-butylcatechol by dioxygen via Mn-enhanced base catalysis

The 6-coordinate dioximatomanganese(II) complex [Mn(HL)(CH3OH)]+ (2, where H2L is [HON=C(CH3)C(CH3)=NCH2CH2]2NH), formed by instant solvolysis of [Mn2(HL)2](BPh4)2 (1) in methanol, accelerates the triethylamine (TEA)-catalyzed oxidation of 3,5-di-tert-butylcatechol (H2dtbc) by O2 to the corresponding o-benzoquinone. Significantly, 2 alone has no catalytic effect. The observed rate increase can be explained by the interaction of 2 with the hydroperoxo intermediate HdtbcO2- formed from Hdtbc- and O2 in the TEA-catalyzed oxidation. The kinetics of the TEA-catalyzed and Mn-enhanced reaction has been studied by gas-volumetric monitoring of the amount of O2 consumed. The initial rate of O2 uptake (V(in)) shows a first-order dependence on the concentration of 2 and O2 and saturation kinetics with respect to both H2dtbc and TEA. The observed kinetic behavior is consistent with parallel TEA-catalyzed and Mn-enhanced oxidation paths. The 3,5-di-tert-butylsemiquinone anion radical is an intermediate detectable by electron spin resonance (ESR) spectroscopy. The dimeric catalyst precursor has been characterized by X-ray diffraction and electrospray ionization mass spectrometry and the monomeric catalyst by ESR spectroscopy.