Azasugar inhibitors as pharmacological chaperones for Krabbe disease

Krabbe disease is a devastating neurodegenerative disorder characterized by rapid demyelination of nerve fibers. This disease is caused by defects in the lysosomal enzyme β-galactocerebrosidase (GALC), which hydrolyzes the terminal galactose from glycosphingolipids. These lipids are essential components of eukaryotic cell membranes: substrates of GALC include galactocerebroside, the primary lipid component of myelin, and psychosine, a cytotoxic metabolite. Mutations of GALC that cause misfolding of the protein may be responsive to pharmacological chaperone therapy (PCT), whereby small molecules are used to stabilize these mutant proteins, thus correcting trafficking defects and increasing residual catabolic activity in cells. Here we describe a new approach for the synthesis of galacto-configured azasugars and the characterization of their interaction with GALC using biophysical, biochemical and crystallographic methods. We identify that the global stabilization of GALC conferred by azasugar derivatives, measured by fluorescence-based thermal shift assays, is directly related to their binding affinity, measured by enzyme inhibition. X-ray crystal structures of these molecules bound in the GALC active site reveal which residues participate in stabilizing interactions, show how potency is achieved and illustrate the penalties of aza/iminosugar ring distortion. The structure–activity relationships described here identify the key physical properties required of pharmacological chaperones for Krabbe disease and highlight the potential of azasugars as stabilizing agents for future enzyme replacement therapies. This work lays the foundation for new drug-based treatments of Krabbe disease.     

Gabor Frames in $${\ell }^2({\mathbb {Z}})$$ ℓ 2 ( Z ) and Linear Dependence

We prove that an overcomplete Gabor frame in \({\ell }^2({\mathbb {Z}})\) generated by a finitely supported sequence is always linearly dependent. This is a particular case of a general result about linear dependence versus independence for Gabor systems in \({\ell }^2({\mathbb {Z}})\) with modulation parameter 1 / M and translation parameter N for some \(M,N\in {\mathbb {N}},\) and generated by a finite sequence g in \({\ell }^2({\mathbb {Z}})\) with K nonzero entries.

     

Frame properties of systems arising via iterated actions of operators

Motivated by recent progress in dynamical sampling we prove that every frame which is norm-bounded below can be represented as a finite union of sequences ${\{{(T_j)}^n{\phi }_j\}}_{n=0}^{\infty },j=1,\dots ,J$ for some bounded operators $T_j$ and elements ${\phi }_j$ in the underlying Hilbert space. The result is optimal, in the sense that it turns out to be problematic to replace the collection of generators ${\phi }_1,\dots ,{\phi }_J$ by a singleton: indeed, for linearly independent frames we prove that we can represent the frame in terms of just one system ${\{T^n\phi \}}_{n=0}^{\infty }$, but unfortunately this representation often forces the operator T to be unbounded. Several examples illustrate the connection of the results to typical frames like Gabor frames and wavelet frames, as well as generic constructions in arbitrary separable Hilbert spaces.     

Characterizations of modalities and lex modalities

A reflective subuniverse in homotopy type theory is an internal version of the notion of a localization in topology or in the theory of ∞-categories. Working in homotopy type theory, we give new characterizations of the following conditions on a reflective subuniverse L: (1) the associated subuniverse $L^{\prime }$ of L-separated types is a modality; (2) L is a modality; (3) L is a lex modality; and (4) L is a cotopological modality. In each case, we give several necessary and sufficient conditions. Our characterizations involve various families of maps associated to L, such as the L-étale maps, the L-equivalences, the L-local maps, the L-connected maps, the unit maps ${\eta }_X$, and their left and/or right orthogonal complements. More generally, our main theorem gives an overview of how all of these classes related to each other. We also give examples that show that all of the inclusions we describe between these classes of maps can be strict.     

Explicit constructions and properties of generalized shift-invariant systems in $L^{2}(\mathbb {R})$

Generalized shift-invariant (GSI) systems, originally introduced by Hernández et al. and Ron and Shen, provide a common frame work for analysis of Gabor systems, wavelet systems, wave packet systems, and other types of structured function systems. In this paper we analyze three important aspects of such systems. First, in contrast to the known cases of Gabor frames and wavelet frames, we show that for a GSI system forming a frame, the Calderón sum is not necessarily bounded by the lower frame bound. We identify a technical condition implying that the Calderón sum is bounded by the lower frame bound and show that under a weak assumption the condition is equivalent with the local integrability condition introduced by Hernández et al. Second, we provide explicit and general constructions of frames and dual pairs of frames having the GSI-structure. In particular, the setup applies to wave packet systems and in contrast to the constructions in the literature, these constructions are not based on characteristic functions in the Fourier domain. Third, our results provide insight into the local integrability condition (LIC).     

Anthracene-Porphyrin Nanoribbons

π-Conjugated nanoribbons attract interest because of their unusual electronic structures and charge-transport behavior. Here, we report the synthesis of a series of fully edge-fused porphyrin-anthracene oligomeric ribbons (dimer and trimer), together with a computational study of the corresponding infinite polymer. The porphyrin dimer and trimer were synthesized in high yield, via oxidative cyclodehydrogenation of singly linked precursors, using 2,3-dichloro-5,6-dicyano-1,4-benzoquinone (DDQ) and trifluoromethanesulfonic acid (TfOH). The crystal structure of the dimer shows that the central π-system is flat, with a slight S-shaped wave distortion at each porphyrin terminal. The extended π-conjugation causes a dramatic red-shift in the absorption spectra: the absorption maxima of the fused dimer and trimer appear at 1188 nm and 1642 nm, respectively (for the nickel complexes dissolved in toluene). The coordinated metal in the dimer was changed from Ni to Mg, using p-tolylmagnesium bromide, providing access to free-base and Zn complexes. These results open a versatile avenue to longer π-conjugated nanoribbons with integrated metalloporphyrin units.     

An improved scheme for determining heat transfer correlations from heat exchanger regression models with three unknowns

A nonlinear regression scheme for determining heat transfer correlations from overall heat exchanger measurements is presented. The proposed scheme is valid for any two-fluid heat exchanger data where only one fluid's thermal resistance varies. The resulting regression model has three unknowns; two are associated with the variable resistance, and the third is the sum of all other resistances. The model can be analyzed only by using nonlinear regression because it cannot be transformed into linear form. Unlike existing approximate methods of analysis (known as modified Wilson plots), the proposed scheme is guaranteed to converge if a solution exists. The scheme was successfully tested by analyzing data collected on a tube-fin heat exchanger with continuous plain fins.     

单矢量水听器估计目标方位的方法与实验

为评估基于单矢量水听器的方位估计能力,在黄海海域对矢量水听器进行实验。矢量水听器吊放于接收船尾部,采用平均声强器和复声强器方位估计方法,并提出以概率密度值最大的方位角作为目标方位估计值的具体处理准则,对恒定方向、匀速行驶的目标船方位进行估计,并求出两种方法的方位估计误差。结果表明,水听器布放深度10 m时,对正横距离为0.42 km的航速10 kn的目标船,平均声强器方法的水平方位角估计误差18°,极角估计误差为5°,可以在离目标船最远1.17 km处估计其方位;复声强法的水平方位角估计误差为13°,极角估计误差为8°,可以在离目标船最远2.35 km处估计其方位。在有接收船的噪声干扰情况下,复声强器比平均声强器方法估计的方位更准确,可以对更远处的噪声源进行方位估计。