Amino acid catalyzed neogenesis of carbohydrates: a plausible ancient transformation

Hexose sugars play a fundamental role in vital biochemical processes and their biosynthesis is achieved through enzyme-catalyzed pathways. Herein we disclose the ability of amino acids to catalyze the asymmetric neogenesis of carbohydrates by sequential cross-aldol reactions. The amino acids mediate the asymmetric de novo synthesis of natural L- and D-hexoses and their analogues with excellent stereoselectivity in organic solvents. In some cases, the four new stereocenters are assembled with almost absolute stereocontrol. The unique feature of these results is that, when an amino acid is employed as the catalyst, a single reaction sequence can convert a protected glycol aldehyde into a hexose in one step. For example, proline and its derivatives catalyze the asymmetric neogenesis of allose with >99 % ee in one chemical manipulation. Furthermore, all amino acids tested catalyzed the asymmetric formation of natural sugars under prebiotic conditions, with alanine being the smallest catalyst. The inherent simplicity of this catalytic process suggests that a catalytic prebiotic "gluconeogenesis" may occur, in which amino acids transfer their stereochemical information to sugars. In addition, the amino acid catalyzed stereoselective sequential cross-aldol reactions were performed as a two-step procedure with different aldehydes as acceptors and nucleophiles. The employment of two different amino acids as catalysts for the iterative direct aldol reactions enabled the asymmetric synthesis of deoxysugars with >99 % ee. In addition, the direct amino acid catalyzed C(2)+C(2)+C(2) methodology is a new entry for the short, highly enantioselective de novo synthesis of carbohydrate derivatives, isotope-labeled sugars, and polyketide natural products. The one-pot asymmetric de novo syntheses of deoxy and polyketide carbohydrates involved a novel dynamic kinetic asymmetric transformation (DYKAT) mediated by an amino acid.     

Psychology and Mathematics Education

This article analyzes the relation between cognitive psychology, as a broad theoretical framework, and the psychology of mathematics education. It is argued that mathematics education should not simply “borrow” from cognitive psychology; rather, our discipline should provide its own psychological research problems, its adapted investigation strategies, and even, in certain circumstances, its adequate original concepts. It is argued that the didactical orientation of its research endeavors highlights new, original theoretical and applicative perspectives, perspectives that cognitive psychology cannot provide by itself. Some examples are described that emphasize the difference between the broad cognitive approach and that of the psychology of mathematics education.     

Influence of natural organic matter on the screening of pharmaceuticals in water by using liquid chromatography with full scan mass spectrometry

The influence of natural organic matter on the screening of pharmaceuticals in water was determined by using high resolution liquid chromatography (HRLC) combined with full scan mass spectrometry (MS) techniques like time of flight (ToF) or Orbitrap MS. Water samples containing different amount of natural organic matter (NOM) and residues of a set of 11 pharmaceuticals were analyzed by using Exactive Orbitrap? LC-MS. The samples were screened for residues of pharmaceuticals belonging to different classes like benzimidazoles, macrolides, penicillins, quinolones, sulfonamides, tetracyclines, tranquillizers, non-steroidal anti-inflammatory drugs (NSAIDs), anti-epileptics and lipid regulators. The method characteristics were established over a concentration range of 0.1-500 μg L(-1). The 11 pharmaceuticals were added to two effluent and two influent water samples. The NOM concentration within the samples ranged from 2 to 8 mg L(-1) of dissolved organic carbon. The HRLC-Exactive Orbitrap? LC-MS system was set at a resolution of 50,000 (FWHM) and this selection was found sufficient for the detection of the list of pharmaceuticals. With this resolution setting, accurate mass measurements with errors below 2 ppm were found, despite of the NOM concentration of the different types of water samples. The linearities were acceptable with correlation coefficients greater than 0.95 for 30 of the 51 measured linearities. The limit of detection varies between 0.1 μg L(-1)and 100 μg L(-1). It was demonstrated that sensitivity could be affected by matrix constituents in both directions of signal reduction or enhancement. Finally it was concluded that with direct shoot method used (no sample pretreatment) all compounds, were detected but LODs depend on matrix-analyte-concentration combination. No direct relation was observed between NOM concentration and method characteristics. For accurate quantification the use of internal standards and/or sample clean-up is necessary. The direct shoot method is only applicable for qualitative screening purposes. The use of full scan MS makes it possible to search for unknown contaminants. With the use of adequate software and a database containing more than 50,000 entries a tool is available to search for unknowns.     

Organocatalytic enantioselective (3+2) cycloaddition using stable azomethine ylides

We have developed a highly efficient procedure for carrying out the catalytic enantioselective (3+2) cycloaddition between enals and stable azomethine ylides such as isoquinolinium and phthalizinium methylides. Under the optimized reaction conditions highly substituted chiral pyrroloisoquinolines and pyrrolophthalazines have been obtained in high yields and excellent diastereo- and enantioselectivities.     

Poincaré type inequalities on the discrete cube and in the CAR algebra

We prove L ^p Poincaré inequalities with suitable dimension free constants for functions on the discrete cube {?1, 1} ⁿ . As well known, such inequalities for p an even integer allow to recover an exponential inequality hence the concentration phenomenon first obtained by Bobkov and Götze. We also get inequalities between the L ^p norms of $ \left\vert \nabla f\right\vert We prove L ^p Poincaré inequalities with suitable dimension free constants for functions on the discrete cube {−1, 1} ⁿ . As well known, such inequalities for p an even integer allow to recover an exponential inequality hence the concentration phenomenon first obtained by Bobkov and G?tze. We also get inequalities between the L ^p norms of and moreover L ^p spaces may be replaced by more general ones. Similar results hold true, replacing functions on the cube by matrices in the *-algebra spanned by n fermions and the L ^p norm by the Schatten norm C _p .     

Organocatalytic asymmetric synthesis of alpha,alpha-disubstituted alpha-amino acids and derivatives

It is shown that racemic oxazolones are excellent reagents for the synthesis of chiral quaternary amino acids and its derivatives by the diastereo- and enantioselective nucleophilic addition to alpha,beta-unsaturated aldehydes catalyzed by diarylprolinol silyl ethers. The scope of this new organocatalytic reaction is demonstrated for different oxazolones having aromatic and alkyl groups at the reactive carbon atom and different aromatic and aliphatic substituted alpha,beta-unsaturated aldehydes, for which the stereoselective reaction proceeds with good yield, moderate to good to very high diastereoselectivity, and very high enantioselectivity. The potential of the reaction is shown for the synthesis of optically active alpha,alpha-disubstituted alpha-amino acids, alpha-quaternary proline derivatives, amino alcohols, lactams, and tetrahydropyranes. Furthermore, we have calculated by DFT-methods the transition-state structures that account for both the diastereo- and enantioselectivity observed for the addition of oxazolones to the alpha,beta-unsaturated aldehydes. For one class of compounds, the stereoselectivity is controlled by a hydrogen-bonding interaction of the enolate-form of the oxazolone with an ortho-hydroxy-phenyl substituent of the alpha,beta-unsaturated aldehyde, whereas the benzhydryl-protecting group in the oxazolone determines the diastereo- and enantioselectivity in a more general manner for both aromatic and aliphatic alpha,beta-unsaturated aldehydes.     

Sturm's Method in Counting Roots of Random Polynomial Equations

The problem of finding the probability distribution of the number of zeros in some real interval of a random polynomial whose coefficients have a given continuous joint density function is considered. An algorithm which enables one to express this probability as a multiple integral is presented. Formulas for the number of zeros of random quadratic polynomials and random polynomials of higher order, some coefficients of which are non-random and equal to zero, are derived via use of the algorithm. Finally, the applicability of these formulas in numerical calculations is illustrated.     

Organocatalytic asymmetric michael addition of aldehydes to beta-nitroacroleine dimethyl acetal

[Structure: see text] The organocatalytic asymmetric Michael addition of aldehydes to beta-nitroacroleine dimethyl acetal has been studied in detail. The reaction took place with excellent yields and high stereoselectivities when a chiral beta-amino alcohol such as L-prolinol was employed as the catalyst, leaving a formation of highly functionalized enantioenriched compounds containing two differentiated formyl groups together with a nitro moiety.     

Improving bounds on the minimum Euclidean distance for block codes by inner distance measure optimization

The minimum Euclidean distance is a fundamental quantity for block coded phase shift keying (PSK). In this paper we improve the bounds for this quantity that are explicit functions of the alphabet size q, block length n and code size |C|. For q=8, we improve previous results by introducing a general inner distance measure allowing different shapes of a neighborhood for a codeword. By optimizing the parameters of this inner distance measure, we find sharper bounds for the outer distance measure, which is Euclidean.The proof is built upon the Elias critical sphere argument, which localizes the optimization problem to one neighborhood. We remark that any code with q=8 that fulfills the bound with equality is best possible in terms of the minimum Euclidean distance, for given parameters n and |C|. This is true for many multilevel codes.