Analysis of the importance of the metallo-beta-lactamase active site loop in substrate binding and catalysis

The role of the mobile loop comprising residues 60-66 in metallo-beta-lactamases has been studied by site-directed mutagenesis, determination of kinetic parameters for six substrates and two inhibitors, pre-steady-state characterization of the interaction with chromogenic nitrocefin, and molecular modeling. The W64A mutation was performed in IMP-1 and BcII (after replacement of the BcII 60-66 peptide by that of IMP-1) and always resulted in increased K(i) and K(m) and decreased k(cat)/K(m) values, an effect reinforced by complete deletion of the loop. k(cat) values were, by contrast, much more diversely affected, indicating that the loop does not systematically favor the best relative positioning of substrate and enzyme catalytic groups. The hydrophobic nature of the ligand is also crucial to strong interactions with the loop, since imipenem was almost insensitive to loop modifications.     

Synthesis and characterization of nanoapatites organofunctionalized with aminotriphosphonate agents

Organofunctionalized apatite nanoparticles were prepared using a one step process involving dissolution/precipitation of natural phosphate rock and covalent grafting of nitrilotris(methylene)triphosphonate (NTP). The synthesized materials were characterized by Brunauer–Emmett–Teller (BET) surface measurement, thermogravimetry, inductively coupled plasma emission spectroscopy (ICP–ES), elemental analysis, multinuclear solid state cross-polarization/magic angle spinning (CP/MAS) and single-pulse NMR spectroscopy, transmission electron microscopy (TEM) and energy dispersive X-ray analysis (EDXA). After grafting BET measurements yielded particle specific surface areas ranging from 88 to 193 m² g^?1 depending on the grafted phosphonate. The results show that the surfaces of the nanoapatite particles can be covered with functional groups bound through a variable number of R–P–O–Ca bonds to render them organoapatites.     

A new branching strategy for time constrained routing problems with application to backhauling

In this paper, we explore a new branching strategy for branch-and-bound approaches based on column generation for the vehicle routing problems with time windows. This strategy involves branching on resource variables (time or capacity) rather than on network flow variables. We also examine criteria for selecting network nodes for branching. To test the effectiveness of the branching strategy, we conduct computational experiments on time window constrained vehicle routing problems where backhauling is permitted only after all the shipments to clients have been made. The branching method proved very effective. In cases where time was the more binding constraint, time-based branching succeeded in decreasing the number of nodes explored by two thirds and the total computation time by more than half when compared to flow-based branching. The computational results also show that the overall algorithm was successful in optimally solving problems with up to 100 customers. It produced an average cost decrease of almost 7% when backhauling was permitted as compared to the cost involved when the client and the distributor routes were distinct.     

Quasi-stationary distributions for structured birth and death processes with mutations

We study the probabilistic evolution of a birth and death continuous time measure-valued process with mutations and ecological interactions. The individuals are characterized by (phenotypic) traits that take values in a compact metric space. Each individual can die or generate a new individual. The birth and death rates may depend on the environment through the action of the whole population. The offspring can have the same trait or can mutate to a randomly distributed trait. We assume that the population will be extinct almost surely. Our goal is the study, in this infinite dimensional framework, of the quasi-stationary distributions of the process conditioned on non-extinction. We first show the existence of quasi-stationary distributions. This result is based on an abstract theorem proving the existence of finite eigenmeasures for some positive operators. We then consider a population with constant birth and death rates per individual and prove that there exists a unique quasi-stationary distribution with maximal exponential decay rate. The proof of uniqueness is based on an absolute continuity property with respect to a reference measure.     

Comportement électrochimique des faces vicinales de Au(111) ; surfaces à marches {111}

Electrochemical behaviour of the Au(111) vicinal faces; {111} stepped surfaces. The Au(332) and Au(776) facets forming on Au(554) and Au(775) faceted vicinal faces have different electrochemical behaviours. The electrochemical study in NaF solutions of the Au(776) face reveals that the whole of the {111} steps of an Au(776) surface have the same electrochemical behaviour as the Au(332) face. On the other hand, the (111) terraces of Au(776) behave differently from the large (111) terraces of an Au(111) single-crystal electrode. The atomic reconstruction of the (111) terraces of the Au(776) facets, observed by vacuum STM, completely disappears in contact with the solution, whereas the reconstruction of the wide (111) terraces of a Au(111) single-crystal does not disappear completely. Measurements of the differential capacity C(E) also showed that faceted or non-faceted surfaces of Au(554) and Au(775) faces had the same electrochemical behaviour. This implies that non-faceted surfaces consist of Au(332) and Au(111)(1 × 1) domains that have independent electrochemical behaviours.     

An extension to overpartitions of the Rogers-Ramanujan identities for even moduli

We study a class of well-poised basic hypergeometric series , interpreting these series as generating functions for overpartitions defined by multiplicity conditions on the number of parts. We also show how to interpret the as generating functions for overpartitions whose successive ranks are bounded, for overpartitions that are invariant under a certain class of conjugations, and for special restricted lattice paths. We highlight the cases (a,q)→(1/q,q), (1/q,q²), and (0,q), where some of the functions become infinite products. The latter case corresponds to Bressoud's family of Rogers-Ramanujan identities for even moduli.     

The regularity of the Stokes operator and the Fujita-Kato approach to the Navier-Stokes initial value problem in Lipschitz domains

We study the regularity of the Navier-Stokes equations in arbitrary Lipschitz domains.     

A Probabilistic Approach for Nonlinear Equations Involving the Fractional Laplacian and a Singular Operator

We consider a class of nonlinear integro-differential equations involving a fractional power of the Laplacian and a nonlocal quadratic nonlinearity represented by a singular integral operator. Initially, we introduce cut-off versions of this equation, replacing the singular operator by its Lipschitz continuous regularizations. In both cases we show the local existence and global uniqueness in L¹L^p. Then we associate with each regularized equation a stable-process-driven nonlinear diffusion; the law of this nonlinear diffusion has a density which is a global solution in L¹ of the cut-off equation. In the next step we remove the cut-off and show that the above densities converge in a certain space to a solution of the singular equation. In the general case, the result is local, but under a more stringent balance condition relating the dimension, the power of the fractional Laplacian and the degree of the singularity, it is global and gives global existence for the original singular equation. Finally, we associate with the singular equation a nonlinear singular diffusion and prove propagation of chaos to the law of this diffusion for the related cut-off interacting particle systems. Depending on the nature of the singularity in the drift term, we obtain either a strong pathwise result or a weak convergence result. Mathematics Subject Classifications (2000) 60K35, 35S10.