Numerical integration of fully nonlinear size-structured population models

Characteristics' schemes of second order are introduced for the numerical solution of size-structured population models. The models are fully nonlinear: all the vital functions (growth, mortality and fertility rates) depend on the total population. The schemes are completely analysed: consistency, stability, existence and convergence are established. Some numerical experiments are also reported in order to show numerically the results proved in our analysis and to study the efficiency of a selection nodes technique.     

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.     

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.     

Fluoronucleosides, isothiocyanato C-nucleosides, and thioureylene di-C-nucleosides via cyclic sulfates

Cyclic sulfates of N- and C-nucleosides (D-ribo and D-erythro configurations, respectively) are used to prepare 3'-fluoro and 3'-azido D-xylo N-nucleosides and L-threo C-nucleosides. The reduction of the 3'-azido C-nucleosides (furan, imidazoline-2-thione, and pyrrole derivatives) gives 3'-amino C-nucleosides, which, by reaction with thiocarbonyldiimidazole, are transformed into 3'-isothiocyanato C-nucleosides. Reaction of the 3'-amino with the 3'-isothiocyanato C-nucleosides gives thioureylene di-C-nucleosides, a type of nucleotide analogue with a nonionic bridge isosteric of the phosphate group.     

Low-energy measurement of the 7Be(p,gamma)8B cross section

We have measured the cross section of the 7Be(p,gamma)8B reaction for E(c.m.) = 185.8, 134.7, and 111.7 keV using a radioactive 7Be target (132 mCi). Single and coincidence spectra of beta+ and alpha particles from 8B and 8Be* decay, respectively, were measured using a large acceptance spectrometer. The zero energy S factor inferred from these data is 18.5+/-2.4 eV b and a weighted mean value of 18.8+/-1.7 eV b (theoretical uncertainty included) is deduced when combining this value with our previous results at higher energies.     

Inference in lognormal multidimensional diffusion processes with exogenous factors: Application to modelling in economics

The multidimensional lognormal diffusion process with exogenous factors is treated using the Kolmogorov equations, and the mean vector and covariance matrix are estimated using discrete sampling by the maximum-likelihood method. Also, this process is constructed as a solution of a multidimensional stochastic differential equation, and an estimation is made through the maximum-likelihood method to infer the parameters of the exogenous factors, this time using continuous sampling. Finally, a test for a hypothesis based on these parameters is constructed.     

Structural properties of reciprocal form factor in neutral atoms and singly charged ions

Structural characteristics of the spherically averaged internally folded density or reciprocal form factor Br are studied within the Hartree-Fock framework for 103 neutral atoms, 54 singly charged cations, and 43 anions in their ground state. The function Br is classified throughout the Periodic Table into three types: (i) monotonic decrease from the origin, (ii) maximum at r=0 and a negative minimum at r>0, and (iii) a local maximum at r=0 and a pair maximum-minimum out of the origin. A detailed study of the corresponding properties for individual subshells as well as their relative weight for the total Br is also carried out. For completeness, the analytical Br for hydrogenlike atoms in both ground and excited states is also analyzed.