Singular Sturm-Liouville problems whose coefficients depend rationally on the eigenvalue parameter

Let −Dω(·,z)D+q be a differential operator in L²(0,∞) whose leading coefficient contains the eigenvalue parameter z. For the case that ω(·,z) has the particular form

     

Simultaneous ejection of two molecular ions from keV gold atomic and polyatomic projectile impacts

We present the first experimental data on the simultaneous ejection of two molecular ions from the impact of Au(+)(n) (1< or =n< or =4) with energies ranging between 17 and 56 keV. The yields from single phenylalanine (Ph) emission, coemission of two Ph ions, and emission of the Ph dimer were measured. Large increases (1 to 2 orders of magnitude) in coemitted ion yields were observed with increasing projectile energy and complexity. Correlation coefficients were calculated for the coemission of two Ph ions; their behavior suggests differences in emission pathways for bombardment by atomic and polyatomic projectiles.     

Characterization of the first beta-class carbonic anhydrase from an arthropod (Drosophila melanogaster) and phylogenetic analysis of beta-class carbonic anhydrases in invertebrates

Background

The β-carbonic anhydrase (CA, EC 4.2.1.1) enzymes have been reported in a variety of organisms, but their existence in animals has been unclear. The purpose of the present study was to perform extensive sequence analysis to show that the β-CAs are present in invertebrates and to clone and characterize a member of this enzyme family from a representative model organism of the animal kingdom, e.g., Drosophila melanogaster.

Results

The novel β-CA gene, here named DmBCA, was identified from FlyBase, and its orthologs were searched and reconstructed from sequence databases, confirming the presence of β-CA sequences in 55 metazoan species. The corresponding recombinant enzyme was produced in Sf9 insect cells, purified, kinetically characterized, and its inhibition was investigated with a series of simple, inorganic anions. Holoenzyme molecular mass was defined by dynamic light scattering analysis and gel filtration, and the results suggested that the holoenzyme is a dimer. Double immunostaining confirmed predictions based on sequence analysis and localized DmBCA protein to mitochondria. The enzyme showed high CO₂ hydratase activity, with a k_cat of 9.5 × 10⁵ s^-1 and a k_cat/K_M of 1.1 × 10⁸ M^{- 1}s^{- 1}. DmBCA was appreciably inhibited by the clinically-used sulfonamide acetazolamide, with an inhibition constant of 49 nM. It was moderately inhibited by halides, pseudohalides, hydrogen sulfide, bisulfite and sulfate (K_I values of 0.67 - 1.36 mM) and more potently by sulfamide (K_I of 0.15 mM). Bicarbonate, nitrate, nitrite and phenylarsonic/boronic acids were much weaker inhibitors (K_Is of 26.9 - 43.7 mM).

Conclusions

The Drosophila β-CA represents a highly active mitochondrial enzyme that is a potential model enzyme for anti-parasitic drug development.     

On the viscous dissipation in the boundary layer of a high Prandtl number fluid in laminar flow over a flat plate

Summary An asymptotic expansion for large Prandtl number fluids has been obtained for the recovery factor in a laminar flow over flat plate. The expression underestimates the recovery factor by no more than 1% as long as the Prandtl number is greater than seven.

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Zusammenfassung Die adiabatische Oberflächentemperatur (recovery factor) für ein Fluid mit hoher Prandtl-Zahl wurde für laminare Strömung über eine ebene Platte mit Hilfe einer asymptotischen Entwicklung bestimmt. Der Ausdruck unterschätzt das genaue Resultat um weniger als 1 % für Prandtl-Zahlen höher als 7.

     

Error linearization as an effective tool for experimental analysis of the numerical stability of algorithms

After introducing briefly the principles of theerror linearization method, which is able to determine the coefficients of the first order error approximation, a collection of examples is presented to demonstrate its efficiency as a test bench for analyzing numerical algorithms. These examples illustrate the propagation of initial errors, the effect of cancellation, the easy location of the most unstable parts of an algorithm, calculation of condition numbers, approximating the statistical behavior of accumulated errors and the convergence of iterative methods.     

Atypical perceptual narrowing in prematurely born infants is associated with compromised language acquisition at 2 years of age

Background

Protein aggregation plays important roles in several neurodegenerative disorders. For instance, insoluble aggregates of phosphorylated tau and of Aβ peptides are cornerstones in the pathology of Alzheimer's disease. Soluble protein aggregates are therefore potential diagnostic and prognostic biomarkers for their cognate disorders. Detection of the aggregated species requires sensitive tools that efficiently discriminate them from monomers of the same proteins. Here we have established a proximity ligation assay (PLA) for specific and sensitive detection of Aβ protofibrils via simultaneous recognition of three identical determinants present in the aggregates. PLA is a versatile technology in which the requirement for multiple target recognitions is combined with the ability to translate signals from detected target molecules to amplifiable DNA strands, providing very high specificity and sensitivity.

Results

For specific detection of Aβ protofibrils we have used a monoclonal antibody, mAb158, selective for Aβ protofibrils in a modified PLA, where the same monoclonal antibody was used for the three classes of affinity reagents required in the assay. These reagents were used for detection of soluble Aβ aggregates in solid-phase reactions, allowing detection of just 0.1 pg/ml Aβ protofibrils, and with a dynamic range greater than six orders of magnitude. Compared to a sandwich ELISA setup of the same antibody the PLA increases the sensitivity of the Aβ protofibril detection by up to 25-fold. The assay was used to measure soluble Aβ aggregates in brain homogenates from mice transgenic for a human allele predisposing to Aβ aggregation.

Conclusions

The proximity ligation assay is a versatile analytical technology for proteins, which can provide highly sensitive and specific detection of Aβ aggregates - and by implication other protein aggregates of relevance in Alzheimer's disease and other neurodegenerative disorders.     

Boundary relations and their Weyl families

The concepts of boundary relations and the corresponding Weyl families are introduced. Let be a closed symmetric linear operator or, more generally, a closed symmetric relation in a Hilbert space , let be an auxiliary Hilbert space, let

and let be defined analogously. A unitary relation from the Krein space to the Krein space is called a boundary relation for the adjoint if . The corresponding Weyl family is defined as the family of images of the defect subspaces , , under . Here need not be surjective and is even allowed to be multi-valued. While this leads to fruitful connections between certain classes of holomorphic families of linear relations on the complex Hilbert space and the class of unitary relations , it also generalizes the notion of so-called boundary value space and essentially extends the applicability of abstract boundary mappings in the connection of boundary value problems. Moreover, these new notions yield, for instance, the following realization theorem: every -valued maximal dissipative (for ) holomorphic family of linear relations is the Weyl family of a boundary relation, which is unique up to unitary equivalence if certain minimality conditions are satisfied. Further connections between analytic and spectral theoretical properties of Weyl families and geometric properties of boundary relations are investigated, and some applications are given.