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.     

Rapid convergence of a Galerkin projection of the KdV equation

In this Note, it is shown that a Fourier Galerkin approximation of the Korteweg–de Vries equation with periodic boundary conditions converges exponentially fast if the initial data can be continued analytically to a strip about the real axis. To cite this article: H. Kalisch, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

On-line cysteine modification for protein analysis: new probes for electrochemical tagging nanospray mass spectrometry

A series of electrogenerated selective electrophiles based on substituted benzoquinones has been characterized as tags for l-cysteine and cysteine residues in proteins. The electrophiles are generated electrochemically from the corresponding hydroquinones. It is shown from mass spectrometry analysis that the electrogenerated benzoquinone can tag the biomolecules. The rate constants pertaining to the addition of l-cysteine onto the electrogenerated benzoquinones have been determined using electrochemical techniques. The substitution patterns have been unraveled leading to the assessment of site-specific rate constants. It is shown that the rate constants are primarily dependent on the electronic nature of the substituents as expressed by the Hammett substitution constant. The apparent tagging yields observed for l-cysteine in nanospray mass spectrometry experiments do not correspond to the yields expected from the electrochemical study, as the ionisation efficiencies are highly dependent on the tag. Finally, the on-line tagging has been tested using β-lactoglobulin A and myoglobin. Based on these results, it is concluded that the tagging reaction is selective towards cysteine when it takes place in the nanospray interface. The results show that the methodology presented can be used for a rapid characterization and identification of reactive sites in biomolecules.     

Non-perturbative approach to high-index-contrast variations in electromagnetic systems

We present a method that formally calculates exact frequency shifts of an electromagnetic field for arbitrary changes in the refractive index. The possible refractive index changes include both anisotropic changes and boundary shifts. Degenerate eigenmode frequencies pose no problems in the presented method. The approach relies on operator algebra to derive an equation for the frequency shifts, which eventually turn out in a simple and physically sound form. Numerically the equations are well-behaved, easy implementable, and can be solved very fast. Like in perturbation theory a reference system is first considered, which then subsequently is used to solve another related, but different system. For our method precision is only limited by the reference system basis functions and the error induced in frequency is of second order for first-order basis set error. As an example we apply our method to the problem of variations in the air-hole diameter in a photonic crystal fiber.     

Evolution in complex systems

What features characterize complex system dynamics? Power laws and scale invariance of fluctuations are often taken as the hallmarks of complexity, drawing on analogies with equilibrium critical phenomena. Here we argue that slow, directed dynamics, during which the system's properties change significantly, is fundamental. The underlying dynamics is related to a slow, decelerating but spasmodic release of an intrinsic strain or tension. Time series of a number of appropriate observables can be analyzed to confirm this effect. The strain arises from local frustration. As the strain is released through “quakes,” some system variable undergoes record statistics with accompanying log‐Poisson statistics for the quake event times. We demonstrate these phenomena via two very different systems: a model of magnetic relaxation in type II superconductors and the Tangled Nature model of evolutionary ecology and show how quantitative indications of aging can be found. © 2004 Wiley Periodicals, Inc. Complexity 10: 49–56, 2004     

Solutions of the WDVV Equations and Integrable Hierarchies of KP Type

We show that reductions of KP hierarchies related to the loop algebra of SL_n with homogeneous gradation give solutions of the Darboux-Egoroff system of PDE's. Using explicit dressing matrices of the Riemann-Hilbert problem generalized to include a set of commuting additional symmetries, we construct solutions of the Witten– Dijkgraaf–E. Verlinde–H. Verlinde equations.     

Representations, convolution square roots and spherical vectors

We extend results on square integrable representations of a locally compact group to subrepresentations of a representations induced from a character of a closed subgroup. We do so working in the framework of quotient representations of ∗-algebras.