Two-Time-Scale Relaxation Towards Thermal Equilibrium of the Enigmatic Piston

We investigate the evolution of a system composed of N non-interacting point particles of mass m in a container divided into two chambers by a movable adiabatic piston of mass Mm. Using a two-time-scale perturbation approach in terms of the small parameter =2m/(M+m), we show that the evolution towards thermal equilibrium proceeds in two stages. The first stage is a fast, deterministic, adiabatic relaxation towards mechanical equilibrium. The second stage, which takes place at times (M), is a slow fluctuation-driven, diathermic relaxation towards thermal equilibrium. A very simple equation is derived which shows that in the second stage, the position of the piston is given by X _M (t)= L[1/2–(t)] where the function is independent of M. Numerical simulations support the assumptions underlying our analytical derivations and illustrate the large mass range in which the picture holds.     

Correlation des effets (α-Me) en RMN13C: modele topologique par difference lineaire DARC-PULFO.

Variations from deshielding to shielding α-Me. effects (+ 11,7 to ? 9 ppm for alkylketones) are accounted for by a general and heuristic model. Connectivity variation action is measured by the difference between linear equations expressing the shifts of an sp³¹³C in terms of its organized alkyl environment.     

Functionalisation of saturated hydrocarbons. Part 9. Oxidation of patchouli alcohol by the ‘gif system’: Isolation and organoleptic properties of three new ketonic derivatives

Oxidation of patchouli alcohol ( 1 ) using the ‘Gif system’ afforded as major isolated products three new ketonic derivatives 16–18 . The structures of these compounds were established by spectral techniques including 2D-NMR. Ketones 16–18 display interesting organoleptic properties.     

A method to investigate intervertebral disc morphology from MRI in early idiopathic scoliosis: a preliminary evaluation in a group of 14 patients

The aim of the study was to implement a methodology to quantify in vivo and from magnetic resonance imaging (MRI) the 3D geometrical properties of intervertebral discs (IVDs) in early idiopathic scoliosis with small curves. MRI data were posttreated using a custom-made image processing software to semiautomatically determine the location of disc centres, the location of the nucleus pulposus (NP) and the ratio between the NP volume and the disc volume. MRI was performed in a clinical protocol involving 14 patients having an early idiopathic scoliosis. First, the 3D reconstruction errors were quantified using a reproducibility test (intraoperator and interoperator) in one IVD (L5-S1). The maximal errors in location were 0.79 mm in the frontal plane, 1.84 mm in the sagittal plane and 0.76 mm in the vertical plane. The maximal error in relative volume was 42%. Second, the nucleus migration and relative volume were quantified in discs T5-T6 to L5-S1. No significant relative volume variation was detected. Concerning the disc migration, no significant differences were found in the sagittal and axial planes. In the frontal plane, significant differences were observed at the apex of the scoliotic curvature when the Cobb angle was > or =20 degrees . This innovative study in early scoliosis showed reproducible preliminary results, and its application to improve diagnosis and follow-up will be established in an enlarged patient database.     

Theoretical evaluation of pK(a) in phosphoranes: implications for phosphate ester hydrolysis

Knowledge of the pK(a) of phosphoranes is important for the interpretation of phosphate ester hydrolysis. Calculated pK(a)'s of the model phosphorane, ethylene phosphorane, are reported. The method of calculation is based on the use of dimethyl phosphate as a reference state for evaluating relative pK(a) values, and on the optimization of the oxygen and acidic hydrogen van der Waals radii to give reasonable pK(1)(a), pK(2)(a), and pK(3)(a) for phosphoric acid in solution. Density functional theory is employed to calculate the gas-phase protonation energies, and continuum dielectric methods are used to determine the solvation corrections. The calculated pK(1)(a) and p(2)(a) for the model phosphorane are 7.9 and 14.3, respectively. These values are within the range of proposed experimental values, 6.5-11.0 for pK(1)(a), and 11.3-15.0 for pK(2)(a). The mechanistic implications of the calculated pK(a)'s are discussed.     

Protein/ligand binding free energies calculated with quantum mechanics/molecular mechanics

The calculation of binding affinities for flexible ligands has hitherto required the availability of reliable molecular mechanics parameters for the ligands, a restriction that can in principle be lifted by using a mixed quantum mechanics/molecular mechanics (QM/MM) representation in which the ligand is treated quantum mechanically. The feasibility of this approach is evaluated here, combining QM/MM with the Poisson-Boltzmann/surface area model of continuum solvation and testing the method on a set of 47 benzamidine derivatives binding to trypsin. The experimental range of the absolute binding energy (DeltaG = -3.9 to -7.6 kcal/mol) is reproduced well, with a root-mean-square (RMS) error of 1.2 kcal/mol. When QM/MM is applied without reoptimization to the very different ligands of FK506 binding protein the RMS error is only 0.7 kcal/mol. The results show that QM/MM is a promising new avenue for automated docking and scoring of flexible ligands. Suggestions are made for further improvements in accuracy.     

Reduction electrochimique des derives carbonyles insatures : IX. Indanones et tetralones : electrolyses mixtes en presence d'electrophiles

It is shown that activated cyclic carbonyl compounds, such as tetralones and indanones, can behave in a particular manner when they are reduced in presence of electrophiles. Two classes of electrophiles were chosen : alkyl halides and carbon dioxide. The reactivity (alkylation and carboxylation) often depends on the nature of the activated ketone used as a substrate.     

Ditopic Ligands. The Synthesis of a Series of Phosphine-Functionalised Macrocycles

The synthesis of a series of phosphine-functionalised macrocycles, 1–6 , is described. The combination of N-and O-sites with P- and S-sites provides ligands which may bind transition or non-transition metal ions; as a consequence, they give access to dinuclear complexes containing both a Lewis acid and a redox metallic site. Compounds 1,2 and 6 are heterodinucleating ligands capable of binding two dissimilar metals in proximity. Macrocycles 3–5 are homotopic ligands which may form homodinuclear complexes of transition metals.     

Reactions des derives du phosphore trivalent avec les composes a halogene positif—XI : Action des phosphines sur les cyano-3 dichloro-1,3 pyrrolidinediones-2,5 disubstituees en 4

Treatment of 3-cyano 1,3-dichloropyrrolidine-2,5-diones with two equivalents of a phosphine, PY₃, affords an ion pair, then a salt consisting of a dianion and two halophosphonium cations. This salt gives Cl₂PY₃ and a phosphobetaïne 6 which carries a P-O bond. Rearrangement of the phosphobetaïne 6, Y=Ph or p-MeC₆H₄, catalysed by halide ions, gives a ne? phosphobetaine 7 which is carrying a P-N bond.