Assessing the effect of advertising expenditures upon sales: A Bayesian structural time series model

We propose a robust implementation of the Nerlove‐Arrow model using a Bayesian structural time series model to explain the relationship between advertising expenditures of a countrywide fast‐food franchise network with its weekly sales. Due to the flexibility and modularity of the model, it is well suited to generalization to other markets or situations. Its Bayesian nature facilitates incorporating a priori information reflecting the manager's views, which can be updated with relevant data. This aspect of the model will be used to support the decision of the manager on the budget scheduling of the advertising firm across time and channels.     

Effect of the Substituents of the Neighboring Ring in the Conformational Equilibrium of Iduronate in Heparin‐like Trisaccharides

Based on the structure of the regular heparin, we have prepared a smart library of heparin‐like trisaccharides by incorporating some sulfate groups in the sequence α‐D ‐GlcNS‐ (1‐4)‐α‐L ‐Ido2S‐(1‐4)‐α‐D ‐GlcN. According to the 3D structure of heparin, which features one helix turn every four residues, this fragment corresponds to the minimum binding motif. We have performed a complete NMR study and found that the trisaccharides have a similar 3D structure to regular heparin itself, but their spectral properties are such that allow to extract very detailed information about distances and coupling constants as they are isotropic molecules. The characteristic conformational equilibrium of the central iduronate ring has been analyzed combining NMR and molecular dynamics and the populations of the conformers of the central iduronate ring have been calculated. We have found that in those compounds lacking the sulfate group at position 6 of the reducing end glucosamine, the population of ²S₀ of the central iduronate residue is sensitive to the temperature decreasing to 19 % at 278 K. On the contrary, the trisaccharides with 6‐O‐sulfate in the reducing end glucosamine keep the level of population constant with temperature circa 40 % of ²S₀ similar to that observed at room temperature. Another structural feature that has been revealed through this analysis is the larger flexibility of the L ‐IdoAS‐ D ‐GlcN glycosidic linkage, compared with the D ‐GlcNS‐L ‐IdoA. We propose that this is the point where the heparin chain is bended to form structures far from the regular helix known as kink that have been proposed to play an important role in the specificity of the heparin–protein interaction.     

sp2-Iminosugar O-, S-, and N-glycosides as conformational mimics of α-linked disaccharides; implications for glycosidase inhibition

The synthesis of mimics of the α(1→6)- and α(1→4)-linked disaccharides isomaltose and maltose featuring a bicyclic sp(2)-iminosugar nonreducing moiety O-, S-, or N-linked to a glucopyranoside residue is reported. The strong generalized anomeric effect operating in sp(2)-iminosugars determines the α-stereochemical outcome of the glycosylation reactions, independent of the presence or not of participating protecting groups and of the nature of the heteroatom. It also imparts chemical stability to the resulting aminoacetal, aminothioacetal, or gem-diamine functionalities. All the three isomaltose mimics behave as potent and very selective inhibitors of isomaltase and maltase, two α-glucosidases that bind the parent disaccharides either as substrate or inhibitor. In contrast, large differences in the inhibitory properties were observed among the maltose mimics, with the O-linked derivative being a more potent inhibitor than the N-linked analogue; the S-linked pseudodisaccharide did not inhibit either of the two target enzymes. A comparative conformational analysis based on NMR and molecular modelling revealed remarkable differences in the flexibility about the glycosidic linkage as a function of the nature of the linking atom in this series. Thus, the N-pseudodisaccharide is more rigid than the O-linked derivative, which exhibits conformational properties very similar to those of the natural maltose. The analogous pseudothiomaltoside is much more flexible than the N- or O-linked derivatives, and can access a broader area of the conformational space, which probably implies a strong entropic penalty upon binding to the enzymes. Together, the present results illustrate the importance of taking conformational aspects into consideration in the design of functional oligosaccharide mimetics.     

Integrated microring resonator sensor arrays for labs-on-chips

Planar waveguide optical ring resonators have shown great potential as compact and sensitive biochemical sensors. Advances in integrated optics based on Si technologies have allowed researchers to integrate multiple micron-sized ring resonator sensors with other optical and fluidic functions on Si chips using mass production techniques. Recent demonstrations of clinically relevant analyte detection by MRR sensor arrays have moved this technology closer to commercialization. Here, a survey of the development of microring sensor arrays for lab-on-a-chip applications is presented and illustrated with state-of-the-art examples.     

Insights into molecular recognition of Lewis(X) mimics by DC-SIGN using NMR and molecular modelling

In this work, we have studied in detail the binding of two α-fucosylamide-based mimics of Lewis(X) to DC-SIGN ECD (ECD = extracellular domain) using STD NMR and docking. We have concluded that the binding mode occurs mainly through the fucose moiety, in the same way as Lewis(X). Similarly to other mimics containing mannose or fucose previously studied, we have shown that both compounds bind to DC-SIGN ECD in a multimodal fashion. In this case, the main contact is the interaction of two hydroxyl groups one equatorial and the other one axial (O3 and O4) of the fucose with the Ca(2+) as Lewis(X) and similarly to mannose-containing mimics (in this case the interacting groups are both in the equatorial position). Finally, we have measured the K(D) of one mimic that was 0.4 mM. Competitive STD NMR experiments indicate that the aromatic moiety provides additional binding contacts that increase the affinity.     

Balanced split sets and Hamilton�CJacobi equations

We study the singular set of solutions to Hamilton?CJacobi equations with a Hamiltonian independent of u. In a previous paper, we proved that the singular set is what we called a balanced split locus. In this paper, we find and classify all balanced split loci, identifying the cases where the only balanced split locus is the singular locus, and the cases where this does not hold. This clarifies the relationship between viscosity solutions and the classical approach of characteristics, providing equations for the singular set. Along the way, we prove more structure results about the singular sets.     

Numerical schemes for a size-structured cell population model with equal fission

We study numerically the evolution of a size-structured cell population model, with finite maximum individual size and minimum size for mitosis. We formulate two schemes for the numerical solution of such a model. The schemes are analysed and optimal rates of convergence are derived. Some numerical experiments are also reported to demonstrate the predicted accuracy of the schemes. We also consider the behaviour of the methods with respect to the different discontinuities that appear in the solution to the problem and the stable size distribution. In addition, the numerical schemes are used to study asynchronous exponential growth.     

Unveiling the “Three‐Finger Pharmacophore” Required for p53–MDM2 Inhibition by Saturation‐Transfer Difference (STD) NMR Initial Growth‐Rates Approach

Inhibitors of the p53‐MDM2 protein–protein interaction are emerging as a new and validated approach to treating cancer. Herein, we describe the synthesis and inhibitory evaluation of a series of isoquinolin‐1‐one analogues, and highlight the utility of an initial growth‐rates saturation‐transfer difference (STD) NMR approach supported by protein–ligand docking to investigate p53‐MDM2 inhibition. The approach is illustrated by the study of compound 1 , providing key insights into the binding mode of this kind of MDM2 ligands and, more importantly, readily unveiling the previously proposed three‐finger pharmacophore requirement for p53‐MDM2 inhibition.     

sp2‐Iminosugar O‐, S‐, and N‐Glycosides as Conformational Mimics of α‐Linked Disaccharides; Implications for Glycosidase Inhibition

The synthesis of mimics of the α(1→6)‐ and α(1→4)‐linked disaccharides isomaltose and maltose featuring a bicyclic sp²‐iminosugar nonreducing moiety O‐, S‐, or N‐linked to a glucopyranoside residue is reported. The strong generalized anomeric effect operating in sp²‐iminosugars determines the α‐stereochemical outcome of the glycosylation reactions, independent of the presence or not of participating protecting groups and of the nature of the heteroatom. It also imparts chemical stability to the resulting aminoacetal, aminothioacetal, or gem‐diamine functionalities. All the three isomaltose mimics behave as potent and very selective inhibitors of isomaltase and maltase, two α‐glucosidases that bind the parent disaccharides either as substrate or inhibitor. In contrast, large differences in the inhibitory properties were observed among the maltose mimics, with the O‐linked derivative being a more potent inhibitor than the N‐linked analogue; the S‐linked pseudodisaccharide did not inhibit either of the two target enzymes. A comparative conformational analysis based on NMR and molecular modelling revealed remarkable differences in the flexibility about the glycosidic linkage as a function of the nature of the linking atom in this series. Thus, the N‐pseudodisaccharide is more rigid than the O‐linked derivative, which exhibits conformational properties very similar to those of the natural maltose. The analogous pseudothiomaltoside is much more flexible than the N‐ or O‐linked derivatives, and can access a broader area of the conformational space, which probably implies a strong entropic penalty upon binding to the enzymes. Together, the present results illustrate the importance of taking conformational aspects into consideration in the design of functional oligosaccharide mimetics.     

S-factor of 14N(p,γ)15O at astrophysical energies⋆

The astrophysical S(E) factor of ¹⁴N(p,γ)¹⁵O has been measured for effective center-of-mass energies between E _eff = 119 and 367 keV at the LUNA facility using TiN solid targets and Ge detectors. The data are in good agreement with previous and recent work at overlapping energies. R-matrix analysis reveals that due to the complex level structure of ¹⁵O the extrapolated S(0) value is model dependent and calls for additional experimental efforts to reduce the present uncertainty in S(0) to a level of a few percent as required by astrophysical calculations.