Density functional theory study of the mechanism of the proline-catalyzed intermolecular aldol reaction

Transition structures associated with the C-C bond-formation step of the proline-catalyzed intermolecular aldol reaction between acetone and isobutyraldehyde have been studies using density functional theory methods at the B3LYP/6-31G** computational level. A continuum model has been selected to represent solvent effects. For this step, which is the stereocontrolling and rate-determining step, four reactive channels corresponding to the syn and anti arrangement of the active methylene of the enamine relative to the carboxylic acid group of l-proline and the re and si attack modes to both faces of the aldehyde carbonyl group have been analyzed. The B3LYP/6-31G** energies are in good agreement with experiment, allowing us to explain the origin of the catalysis and stereoselectivity for these proline-catalyzed aldol reactions. Received: 2 April 2002 / Accepted: 18 July 2002 / Published online: 11 October 2002 Acknowledgements. This work was supported by research funds provided by the Ministerio de Educación y Cultura of the Spanish Government by DGICYT (project PB98–1429). All the calculations were performed on a Cray–Silicon Graphics Origin 2000 of the Servicio de Informática de la Universidad de Valencia. We are most indebted to this center for providing us with computer capabilities. Correspondence to: L. R. Domingo e-mail: domingo@utopia.uv.es     

Singularity spectrum of fractal signals from wavelet analysis: Exact results

The multifractal formalism for singular measures is revisited using the wavelet transform. For Bernoulli invariant measures of some expanding Markov maps, the generalized fractal dimensions are proved to be transition points for the scaling exponents of some partition functions defined from the wavelet transform modulus maxima. The generalization of this formalism to fractal signals is established for the class of distribution functions of these singular invariant measures. It is demonstrated that the Hausdorff dimensionD(h) of the set of singularities of Hölder exponenth can be directly determined from the wavelet transform modulus maxima. The singularity spectrum so obtained is shown to be not disturbed by the presence, in the signal, of a superimposed polynomial behavior of ordern, provided one uses an analyzing wavelet that possesses at leastN>n vanishing moments. However, it is shown that aC behavior generally induces a phase transition in theD(h) singularity spectrum that somewhat masks the weakest singularities. This phase transition actually depends on the numberN of vanishing moments of the analyzing wavelet; its observation is emphasized as a reliable experimental test for the existence of nonsingular behavior in the considered signal. These theoretical results are illustrated with numerical examples. They are likely to be valid for a large class of fractal functions as suggested by recent applications to fractional Brownian motions and turbulent velocity signals.     

Long time correlations in lagrangian dynamics: a key to intermittency in turbulence

Using a new experimental technique, based on the scattering of ultrasounds, we perform a direct measurement of particle velocities, in a fully turbulent flow. This allows us to approach intermittency in turbulence from a dynamical point of view and to analyze the Lagrangian velocity fluctuations in the framework of random walks. We find experimentally that the elementary steps in the walk have random uncorrelated directions but a magnitude that is extremely long range correlated in time. Theoretically, a Langevin equation is proposed and shown to account for the observed one- and two-point statistics. This approach connects intermittency to the dynamics of the flow.     

Intermittency of velocity time increments in turbulence

We analyze the statistics of turbulent velocity fluctuations in the time domain. Three cases are computed numerically and compared: (i) the time traces of Lagrangian fluid particles in a (3D) turbulent flow (referred to as the dynamic case); (ii) the time evolution of tracers advected by a frozen turbulent field (the static case); (iii) the evolution in time of the velocity recorded at a fixed location in an evolving Eulerian velocity field, as it would be measured by a local probe (referred to as the virtual probe case). We observe that the static case and the virtual probe cases share many properties with Eulerian velocity statistics. The dynamic (Lagrangian) case is clearly different; it bears the signature of the global dynamics of the flow.     

Theozyme for antibody aldolases. Characterization of the transition-state analogue

A theozyme for antibody aldolases has been studied at the MP2/6-31G** computational level. Formation of two cooperative hydrogen-bonds between the acidic hydrogen atoms of the enamine and of a methanol molecule with the oxygen atom of the aldol acceptor markedly favors the C-C bond-formation associated with the aldol reaction. A comparative analysis of the geometry, the charge distribution and the shape of the molecular electrostatic potential of the transition structure (TS) with the covalent adduct, resulting from the reaction of methylamine and the beta-diketone used as a hapten allows us to characterize the transition-state analogue (TSA) generated at immunization. This finding allows us to propose a hapten based on a chiral beta-ketosulfoxide that could give the formation of a TSA that addresses the tetrahedral geometry of the TS.     

Oscillating viscosity in a lyotropic lamellar phase under shear flow

We report some time-dependent behavior of lyotropic lamellar phase under shear flow. At fixed stress, near a layering instability, the system presents an oscillating shear rate. We build up a new stress versus shear rate diagram that includes temporal behavior. This diagram is made of two distinct branches of stationary states which correspond, respectively, to disordered and ordered multilamellar vesicle phases. When increasing the shear stress, prior to the transition to the ordered structural state, sustained oscillations of the viscosity are recorded. They correspond to periodic structural change of the entire sample between a disordered and a ordered state of multilamellar vesicles.     

Nucleotide composition effects on the long-range correlations in human genes

We use the wavelet transform to investigate the fractal scaling properties of coding and noncoding human DNA sequences. We find that the strength of the long-range correlations observed in the introns increases with the guanine-cytosine (GC) content, while coding sequences show no such correlations at any GC content. However, we demonstrate that long-range correlations can be detected when the coding sequences are undersampled by retaining the third base of each codon only. This strongly suggests that the observed correlations are not likely to be due to insertion-deletion mechanisms. We comment about the origin of these correlations in terms of putative dynamical processes that could produce the isochore structure of the human genome. Received: 18 August 1997 / Accepted: 29 October 1997