K-duality for stratified pseudomanifolds

This paper is devoted to the study of Poincar\'e duality in K-theory for general stratified pseudomanifolds. We review the axiomatic definition of a smooth stratification \fS of a topological space $X$ and we define a groupoid T^{\fS}X, called the \fS-tangent space. This groupoid is made of different pieces encoding the tangent spaces of the strata, and these pieces are glued into the smooth noncommutative groupoid T^{\fS}X using the familiar procedure introduced by A. Connes for the tangent groupoid of a manifold. The main result is that C^{*}(T^{\fS}X) is Poincar\'e dual to $C(X)$, in other words, the \fS-tangent space plays the role in $K$-theory of a tangent space for $X$

Index theory and Groupoids

This paper collects the notes of a serie of lectures given by the two authors during the summer school "Geometric and topological methods for Quantum Field Theory" at Villa de Leyva, Colombia, summer 2007. These lecture notes are mainly devoted to a proof using groupoids and $KK$-theory of Atiyah-Singer index theorem on compact smooth manifolds. We will present an elementary introduction to groupoids, $C^*$-algebras, $KK$-theory and pseudodifferential calculus on groupoids. We will finish by showing that the point of view adopted here generalizes to the case of conical pseudo-manifolds

Pseudodifferential operators on manifolds with fibred corners

International audienc

Large scale analysis of routine dose adjustments of mycophenolate mofetil based on global exposure in renal transplant patients.

International audienceBACKGROUND: : We report a feasibility study based on our large-scale experience with mycophenolate mofetil dose adjustment based on mycophenolic acid interdose area under the curve (AUC) in renal transplant patients. METHODS: : Between 2005 and 2010, 13,930 requests for 7090 different patients (outside any clinical trial) were posted by more than 30 different transplantation centers on a free, secure web site for mycophenolate mofetil dose recommendations using three plasma concentrations and Bayesian estimation. RESULTS: : This retrospective study showed that 1) according to a consensually recommended 30- to 60-mg*h/L target, dose adjustment was needed for approximately 35% of the patients, 25% being underexposed with the highest proportion observed in the first weeks after transplantation; 2) when dose adjustment had been previously proposed, the subsequent AUC was significantly more often in the recommended range if the dose was applied than not at all posttransplantation periods (72-80% vs. 43-54%); and 3) the interindividual AUC variability in the "respected-dose" group was systematically lower than that in the "not respected-dose" group (depending on the posttransplantation periods; coefficient of variation %, 31-41% vs 49-70%, respectively). Further analysis suggested that mycophenolic acid AUC should best be monitored at least every 2 weeks during the first month, every 1 to 3 months between months 1 and 12, whereas in the stable phase, the odds to be still in the 30- to 60-mg*h/L range on the following visit was still 75% up to 1 year after the previous dose adjustment. CONCLUSION: : This study showed that the monitoring of mycophenolate mofetil on the basis of AUC measurements is a clinically feasible approach, apparently acceptable by the patients, the nurses, and the physicians owing to its large use in routine clinics

Pharmacokinetic modelling and development of Bayesian estimators for therapeutic drug monitoring of mycophenolate mofetil in reduced-intensity haematopoietic stem cell transplantation.

International audienceBACKGROUND: Mycophenolate mofetil, a prodrug of mycophenolic acid (MPA), is used during non-myeloablative and reduced-intensity conditioning haematopoetic stem cell transplantation (HCT) to improve engraftment and reduce graft-versus-host disease (GVHD). However, information about MPA pharmacokinetics is sparse in this context and its use is still empirical. OBJECTIVES: To perform a pilot pharmacokinetic study and to develop maximum a posteriori Bayesian estimators (MAP-BEs) for the estimation of MPA exposure in HCT. PATIENTS AND METHODS: Fourteen patients administered oral mycophenolate mofetil 15 g/kg three times daily were included. Two consecutive 8-hour pharmacokinetic profiles were performed on the same day, 3 days before and 4 days after the HCT. One 8-hour pharmacokinetic profile was performed on day 27 after transplantation. For these 8-hour pharmacokinetic profiles, blood samples were collected predose and 20, 40, 60, 90 minutes and 2, 4, 6 and 8 hours post-dose. Using the iterative two-stage (ITS) method, two different one-compartment open pharmacokinetic models with first-order elimination were developed to describe the data: one with two gamma laws and one with three gamma laws to describe the absorption phase. For each pharmacokinetic profile, the Akaike information criterion (AIC) was calculated to evaluate model fitting. On the basis of the population pharmacokinetic parameters, MAP-BEs were developed for the estimation of MPA pharmacokinetics and area under the plasma concentration-time curve (AUC) from 0 to 8 hours at the different studied periods using a limited-sampling strategy. These MAP-BEs were then validated using a data-splitting method. RESULTS: The ITS approach allowed the development of MAP-BEs based either on 'double-gamma' or 'triple-gamma' models, the combination of which allowed correct estimation of MPA pharmacokinetics and AUC on the basis of a 20 minute-90 minute-240 minute sampling schedule. The mean bias of the Bayesian versus reference (trapezoidal) AUCs was 20%. AIC was systematically calculated for the choice of the most appropriate model fitting the data. CONCLUSION: Pharmacokinetic models and MAP-BEs for mycophenolate mofetil when administered to HCT patients have been developed. In the studied population, they allowed the estimation of MPA exposure based on three blood samples, which could be helpful in conducting clinical trials for the optimization of MPA in reduced-intensity HCT. However, prior studies will be needed to validate them in larger populations

Groupoids and an index theorem for conical pseudo-manifolds

We define an analytical index map and a topological index map for conical pseudomanifolds. These constructions generalize the analogous constructions used by Atiyah and Singer in the proof of their topological index theorem for a smooth, compact manifold $M$. A main ingredient is a non-commutative algebra that plays in our setting the role of $C_0(T^*M)$. We prove a Thom isomorphism between non-commutative algebras which gives a new example of wrong way functoriality in $K$-theory. We then give a new proof of the Atiyah-Singer index theorem using deformation groupoids and show how it generalizes to conical pseudomanifolds. We thus prove a topological index theorem for conical pseudomanifolds

Temperature dependence of binding and catalysis for human serum arylesterase/paraoxonase.

International audience: The influence of temperature upon the hydrolysis of phenyl acetate, catalysed by purified human serum arylesterase/paraoxonase (E. C. 3.1.8.1), was studied in the temperature range 10 °C-40 °C by spectrophotometry in TRIS buffer, pH 8.0, using both initial rate analysis and progress curve analysis. The kinetic parameters (catalytic constant kcat; Michaelis constant Km; product inhibition constant Kp) were determined by nonlinear regression. All parameters increased with temperature, but the ratios kcat/Km and Kp/Km remained practically constant. Binding of both substrate and reaction product (phenol) was exothermic. A negative entropic term accounted for about 50% of the enthalpy change for both the binding and catalytic steps. Thermodynamic analysis suggested that: (1) the rate-limiting step is the nucleophilic attack of the carbonyl group of the substrate by a water molecule, (2) the active site is preorganized with no induced fit, (3) the enzyme-bound calcium plays an important role in stabilizing both the substrate and the transition state. The practical implications of these results are discussed