Pharmacophore model for bile acids recognition by the FPR receptor

Formyl-peptide receptors (FPRs) belong to the family A of the G-protein coupled receptor superfamily and include three subtypes: FPR, FPR-like-1 and FPR-like-2. They have been involved in the control of␣many inflammatory processes promoting the recruitment and infiltration of leukocytes in regions of inflammation through the molecular recognition of chemotactic factors. A large number of structurally diverse chemotypes modulate the activity of FPRs. Newly identified antagonists include bile acids deoxycholic acid (DCA) and chenodeoxycholic acid (CDCA). The molecular recognition of these compounds at FPR receptor was computationally investigated using both ligand- and structure-based approaches. Our findings suggest that all antagonists bind at the first third of the seven helical bundles. A closer inspection of bile acid interaction reveals a number of unexploited anchor points in the binding site that may be used to aid the design of new potent and selective bile acids derivatives at FPR.     

Detection of bias errors in ETAAS Determination of copper in beer and wine samples

A method that evidences changes in the shape of the absorbance profiles obtained by graphite furnace atomic absorption spectrometry (ETAAS) is proposed. The method is based upon the apparent content curves model previously described for molecular spectroscopy and it permits the detection of possible sources of bias errors. Moreover, a procedure that allows to detect the existence of constant and/or proportional errors is also described. Both models has been applied to the determination of copper in wine and beer samples with and without pre-treatment of the samples. Results obtained evidence the usefulness of the proposed models.     

Capturing molecules with templated materials--analysis and rational design of molecularly imprinted polymers

The creation of synthetic tailor-made receptors capable of recognizing desired molecular targets with high affinity and selectivity is a persistent long-term goal for researchers in the fields of chemical, biological, and pharmaceutical research. Compared to biomacromolecular receptors, these synthetic receptors promise simplified production and processing, less costs, and more robust receptor architectures. During recent decades, molecularly imprinted polymers (MIPs) are widely considered mimics of natural molecular receptors suitable for a diversity of applications ranging from biomimetic sensors, to separations and biocatalysis.A remaining challenge for the next generation of MIPs is the synthesis of deliberately designed and highly efficient receptor architectures suitable for recognizing biologically relevant molecules, for which natural receptors are either not prevalent, or difficult to isolate and utilize. Hence, this review discusses recent advances in synthetic receptor technology for biomolecules (e.g. drugs, amino acids, steroids, proteins, entire cells, etc.) via molecular imprinting techniques. Surface imprinting methods and epitope imprinting approaches have been introduced for protein recognition at imprinted surfaces. Imprinting techniques in aqueous solution or organic-water co-solvents have been introduced avoiding denaturation of biomolecules during MIP synthesis. In addition, improved bioreactivity of entire enzyme or active site mimics generated by molecular imprinting will be highlighted. Finally, the emerging importance of molecular modeling and molecular dynamics studies detailing the intermolecular interactions between the template species, the porogenic solvent molecules, and the involved monomer and cross-linker in the pre-polymerization solution will be addressed yielding a rational approach toward next-generation MIP technology.     

Symmetric Stable Processes on Unbounded Domains

Let be a symmetric -stable process in , , . We give necessary and sufficient condition under which the expectation of a very general function of the exit time from horns is finite. These domains include the symmetric domains given by increasing functions studied earlier by various authors. Our methods differ from those in earlier papers in that we obtain our results from estimates on the transition densities instead of harmonic measure. Some of this estimates are of independent interest.Supported in part by NSF grant #9700585-DMS and RTN Harmonic Analysis and Related Problems contract HPRN-CT-2001-00273-HARP.     

A Low-Memory Algorithm for Point Counting on Picard Curves

Combining the ideas of Bauer, Teske and Weng, [1] and Gaudry, Schost [3], we give a low memory algorithm for computing the number of points on the Jacobian of a Picard curve. It is efficient enough to handle Picard curves over finite prime fields , where p is a prime with 58 bits. We present an example where the Jacobian has a prime group order of size 2¹⁷⁴     

Stable manifolds for all monic supercritical focusing nonlinear Schrödinger equations in one dimension

Standing wave solutions of the one-dimensional nonlinear Schrödinger equation

with are well known to be unstable. In this paper we show that asymptotic stability can be achieved provided the perturbations of these standing waves are small and chosen to belong to a codimension one Lipschitz surface. Thus, we construct codimension one asymptotically stable manifolds for all supercritical NLS in one dimension. The considerably more difficult -critical case, for which one wishes to understand the conditional stability of the pseudo-conformal blow-up solutions, is studied in the authors' companion paper Non-generic blow-up solutions for the critical focusing NLS in 1-d, preprint, 2005.

     

Poisson geometry of differential invariants of curves in some nonsemisimple homogeneous spaces

In this paper we describe a family of compatible Poisson structures defined on the space of coframes (or differential invariants) of curves in flat homogeneous spaces of the form where is semisimple. This includes Euclidean, affine, special affine, Lorentz, and symplectic geometries. We also give conditions on geometric evolutions of curves in the manifold so that the induced evolution on their differential invariants is Hamiltonian with respect to our main Hamiltonian bracket.

     

Limit Laws for Norms of IID Samples with Weibull Tails

We are concerned with the limit distribution of l _t -norms (of order t) of samples of i.i.d. positive random variables, as N→∞, t→∞. The problem was first considered by Schlather [(2001), Ann. Probab. 29, 862–881], but the case where {X _i } belong to the domain of attraction of Gumbel’s double exponential law (in the sense of extreme value theory) has largely remained open (even for an exponential distribution). In this paper, it is assumed that the log-tail distribution function is regularly varying at infinity with index . We proceed from studying the limit distribution of the sums , which is of interest in its own right. A proper growth scale of N relative to t appears to be of the form (). We show that there are two critical points, α₁ = 1 and α₂ = 2, below which the law of large numbers and the central limit theorem, respectively, break down. For α < 2, under a slightly stronger condition of normalized regular variation of h, we prove that the limit laws for S _N (t) are stable, with characteristic exponent and skewness parameter . A complete picture of the limit laws for the norms R _N (t) = S _N (t)^1/t is then derived. In particular, our results corroborate a conjecture in Schlather [(2001), Ann. Probab. 29, 862–881] regarding the “endpoints” , α→ 0.      

Module supersingulier et homologie des courbes modulaires

We study here the free group generated by isomorphism classes of supersingular elliptic curves in positive characteristic. We compare this -module to the homology of the modular curve X₀(p). We give an interpretation of Gross formula for special values of L-functions of modular forms in this context. As an application, we obtain a formula for the sum of the squares of the optimal embeddings numbers of quadratic orders in a definite quaternion algebra.     

Improvement of Newman inequality

Let . Newman inequality is