A note on the arithmetic of differential equations

In this note we give a method for computing the differential Galois group of some linear second-order ordinary differential equations using arithmetic information, namely the p-curvatures.     

Effect of the oxygen transfer coefficient on xylitol production from sugarcane bagasse hydrolysate by continuous stirred-tank reactor fermentation

The effect of the oxygen transfer coefficient on the production of xylitol by biocon version of xylose present in sugarcane bagasse hemicellulosic hydrolysate using the yeast Candiada guilliermondii was investigated. Continuous cultivation was carried out in a 1.25-L fermentor at 30°C, pH 5.5, 300 rpm, and a dilution rate of 0.03/h, using oxygen transfer coefficients of 10,20, and 30/h. The results showed that the microbial xylitol production (11 g/L) increased by 108% with the decrease in the oxygen volumetric transfer coefficient from 30 to 20/h. The maximum values of xylitol productivity (0.7g/[L…h]) and yield (0.58 g/g) were obtained at k _L a 20/h.     

Synthesis, Characterization, and Fluxional Behaviour of Binuclear Palladium Complexes with a Half-A-Frame Structure

 Partial removal of chloride anions from the dimer [Pd(η³-2-CH₃*C₃H₄)(μ-Cl)]₂ with AgTf(Tf = CF₃SO₃) followed by addition of dppm affords [Pd₂(η³-Me*C₃H₄)₂(μ-Cl)(μ-dppm)]Tf (1). The substitution of Cl⁻ by X⁻ (X = pz, SC₆F₅, S _py ) using the appropriate salts yields the new derivatives [Pd₂(η³-Me*C₃H₄)₂(μ-X)(μ-dppm)]Tf (2–4). All complexes exhibit a dinuclear half-A-frame structure with two isomers present in solution. The isomers differ in the relative orientation of the two allyl groups (cis or trans). The isomer interconversion was studied by variable temperature ¹H NMR spectroscopy. The molecular structures of 2 and 4 were solved by X-ray diffraction studies. A distorted boat conformation of the seven- or six-membered metallacycle was found in both cases.     

Evaluation of the Use of Elicitors for the Production of Antioxidant Compounds in Liquid Cultures of Ganoderma curtisii from Costa Rica

The use of substances or conditions as elicitors can significantly increase the production of secondary metabolites. In this research, the effects of different elicitors on the production of antioxidant secondary metabolites were evaluated in a strain of Ganoderma sp. The elicitors tested were pH changes in different growth phases of the fungus (pH 3, 5.5 and 8), different concentrations of peptone as a nitrogen source (1 g/L and 10 g/L), and the addition of chemical agents to the culture medium (ethanol, growth regulators, and salts). The alkaline pH during the stationary phase and the high availability of nitrogen were effective elicitors, producing cultures with higher antioxidant activity (37.87 g/L and 43.13 g/L dry biomass) although there were no significant differences with other treatments.     

Bond Length Alternation Observed Experimentally: The Case of 1H-Indazole

Bond length alternation is a chemical phenomenon in benzene rings fused to other rings, which has been mainly predicted theoretically. Its physical origin is still not clear and has generated discussion. Here, by using a strategy that combines microwave spectroscopy, custom-made synthesis and high-level ab initio calculations, we demonstrate that this phenomenon is clearly observed in the prototype indazole molecule isolated in the gas phase. The 1H-indazole conformer was detected by rotational spectroscopy, and its 17 isotopologues resulting from single and double heavy atom substitution (¹³C and ¹⁵N) were also unambiguously observed. Several experimental structures were determined and, in particular, the most useful semi-experimental equilibrium structure (r_e^SE), allowed determination of the heavy atom bond lengths to milli-Ångstrom precision. The experimentally determined bond length alternation is estimated to correspond to 60:40 contributions from the two resonant forms of 1H-indazole.     

Enzyme-Decorated Covalent Organic Frameworks as Nanoporous Platforms for Heterogeneous Biocatalysis

Sustainability in chemistry heavily relies on heterogeneous catalysis. Enzymes, the main catalyst for biochemical reactions in nature, are an elegant choice to catalyze reactions due to their high activity and selectivity, although they usually suffer from lack of robustness. To overcome this drawback, enzyme-decorated nanoporous heterogeneous catalysts were developed. Three different approaches for Candida antarctica lipase B (CAL-B) immobilization on a covalent organic framework (PPF-2) were employed: physical adsorption on the surface, covalent attachment of the enzyme in functional groups on the surface and covalent attachment into a linker added post-synthesis. The influence of the immobilization strategy on the enzyme uptake, specific activity, thermal stability, and the possibility of its use through multiple cycles was explored. High specific activities were observed for PPF-2-supported CAL-B in the esterification of oleic acid with ethanol, ranging from 58 to 283 U mg⁻¹, which was 2.6 to 12.7 times greater than the observed for the commercial Novozyme 435.     

Full-Atom Model of the Agonist LPS-Bound Toll-like Receptor 4 Dimer in a Membrane Environment

The Toll-like receptor 4 (TLR4)/myeloid differentiation factor 2 (MD-2) innate immunity system is a membrane receptor of paramount importance as therapeutic target. Its assembly, upon binding of Gram-negative bacteria lipopolysaccharide (LPS), and also dependent on the membrane composition, finally triggers the immune response cascade. We have combined ab-initio calculations, molecular docking, all-atom molecular dynamics simulations, and thermodynamics calculations to provide the most realistic and complete 3D models of the active full TLR4 complex embedded into a realistic membrane to date. Our studies give functional and structural insights into the transmembrane domain behavior in different membrane environments, the ectodomain bouncing movement, and the dimerization patterns of the intracellular Toll/Interleukin-1 receptor domain. Our work provides TLR4 models as reasonable 3D structures for the (TLR4/MD-2/LPS)₂ architecture accounting for the active (agonist) state of the TLR4, and pointing to a signal transduction mechanism across cell membrane. These observations unveil relevant molecular aspects involved in the TLR4 innate immune pathways and will promote the discovery of new TLR4 modulators.     

General formulas for the smoothed analysis of condition numbers

We provide estimates on the volume of tubular neighborhoods around a subvariety Σ of real projective space, intersected with a disk of radius σ. The bounds are in terms of σ, the dimension of the ambient space, and the degree of equations defining Σ. We use these bounds to obtain smoothed analysis estimates for some conic condition numbers. To cite this article: P. Bürgisser et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

Fonctions de Nash sur les variétés affines

Sans résuméPartiellement subventioné par C.A.I.C.yT. 2280/83