A mathematical model of anorexia and bulimia

In this paper, we propose a mathematical model to study the dynamics of anorexic and bulimic populations. The model proposed takes into account, among other things, the effects of peers' influence, media influence, and education. We prove the existence of three possible equilibria that without media influences are disease‐free, bulimic‐endemic, and endemic. Neglecting media and education effects, we investigate the stability of such equilibria, and we prove that under the influence of media, only one of such equilibria persists and becomes a global attractor. Which of the three equilibria becomes global attractor depends on the other parameters. Copyright © 2014 John Wiley & Sons, Ltd.     

On the Ekman Equations for Ocean Currents Driven by a Stochastic Wind

The basic assumptions for the depth-dependent Ekman equations are presented. An analysis of three wind stress time series, from different geographical locations, is performed: The results lead to interpret the wind stress as a stochastic process, with components fluctuating with deterministic frequencies. The stochastic equations coupling wind stress and ocean currents are formulated; their solutions are stochastically bounded. Results of numerical simulations are given to show the main behaviors of the system.     

Fluxional rearrangement in congested ruthenium(II) complexes containing pyrimidine- and/or pyridine-based dithioether ligands

The solvento species obtained by the treatment of cis-RuCl₂(N,N-L)₂ [L = di-2-pyridyl sulfide (dps), di-2-pyrimidyl sulfide (dprs)] with AgPF₆, reacted with dithioethers L′ [L′ = 2,6-bis(2-pyridylthiomethyl)pyridine (pytmp), 2,6-bis(2-pyrimidylthiomethyl)pyridine (prtmp) and 2,6-bis{2-(4-methyl)pyrimidylthiomethyl} pyridine (mprtmp)] to afford the compounds [Ru(N,N-L)₂(N,S-L′)][PF₆]₂. The ¹H NMR spectra indicate that L′ is chelated through S and N atoms with the formation of a four-membered ring. As a consequence, the ruthenium and sulfur atoms are stereogenic centers with ∆ and Λ and (R) and (S) configurations, respectively. NMR spectra, at low temperatures, show that two invertomers, of similar abundance, as enantiomeric couples ∆S, ΛR and ∆R, ΛS are present. In the methylene region, four AB systems are observed that in both the species contain two non-equivalent methylene groups. Variable-temperature NMR spectra and EXSY experiments show that the sulfur inversion produces an exchange between the invertomers. The one-dimensional band-shape analysis of the exchanging methylene signals showed that the energy barriers for the process are in the 43–52 kJ mol⁻¹ range. The possible mechanisms of the sulfur inversion are discussed.     

Probing the internal environment of PVP networks generated by irradiation with different sources

Poly(N-vinyl-2-pyrrolidone) (PVP) hydrogels have been synthesised from the aqueous solutions of the same linear polymer by two different radiation sources: electron beams and UV rays. The present investigation couples conventional hydrogel characterisation techniques with the study of the partition equilibria, fluorescence behaviour and release of two different molecular probes, 1-anilino-8-naphthalene sulphonate (ANS) and Thioflavin T (ThT). The two probes have comparable molecular weight and different structural and optical properties. The ‘chemical’ networks produced upon irradiation in different experimental conditions presented quite distinctive mechanical spectra, yielded to different porous solids upon freeze-drying and showed specific rehydration ratios when ‘equilibrated’ in water. More interestingly, they offered ‘hydrophobic pockets’ to host the ANS molecules in a way that the probe is completely occluded from water, making it fluoresce. Conversely, the generated PVP networks did not show any specific affinity towards the hydrophilic ThT that was only barely untaken.     

Well-defined transition metal complexes with phosphorus and nitrogen ligands for 1,3-dienes polymerization

This article provides an overview on recent progress in the polymerization of 1,3-dienes catalyzed by transition metal complexes with phosphorus and nitrogen ligands. Polymers having different microstructures (cis-1,4; 1,2; mixed cis-1,4/1,2) and tacticity (iso- or syndiotactic) were obtained from various 1,3-dienes (1,3-butadiene, isoprene, 1,3-pentadienes, 1,3-hexadienes) depending on the catalyst used, clearly suggesting that the catalyst structure (i.e. metal nature, type of ligand) strongly affects the polymerization chemo- and stereoselectivity. However, as indicated by the results obtained in the polymerization of substituted butadienes, a fundamental role in determining the selectivity is also played by the type of monomer: polymers with different structure, some of them completely new, were obtained from different monomers with the same catalyst. All these observations permitted to confirm, and in some cases to improve, the knowledge on the diene polymerization mechanism.     

Epimerization and hydrolysis of 3,6-dimethyl-2,3,5,6-tetrahydro[1,2,4]thiadiazino[6,5,4-hi]indole 1,1-dioxide

In this study, configurational and chemical stability of (R,R),(S,S),(R,S),(S,R)-3,6-dimethyl-2,3,5,6-tetrahydro[1,2,4]thiadiazino[6,5,4-hi]indole 1,1-dioxide (1) were investigated by dynamic and stopped-flow HPLC methods. Single epimeric mixtures (R,R),(R,S)-1 and (S,S),(S,R)-1 were obtained combining synthetic and chromatographic strategies. Separation of (R,R)-1 and (R,S)-1 was achieved by chiral chromatography and absolute configuration of eluted epimers has been assigned basing on molecular modelling calculations. Epimerization and hydrolysis of (R,R),(R,S)-1 have been studied by classical off-column, dynamic HPLC and stopped-flow HPLC methods. The influence of different parameters, such as temperature, pH and dielectric constant was evaluated. The data obtained indicate that (R,R),(R,S)-1 undergoes to a rapid epimerization in aqueous solvent and hydrolysis in acidic conditions. Moreover, epimerization and hydrolysis were investigated in presence of an artificial membrane and in physiological buffers (pH 2.2 and 7.0 at 37.5°C) to simulate in vivo conditions.     

Antioxidant and spectroscopic studies of crosslinked polymers synthesized by grafting polymerization of ferulic acid

A novel, simple synthetic strategy for the preparation of crosslinked polymers with significant antioxidant properties is proposed. Ferulic acid (FA), a well‐known antioxidant compound, due to its reactivity toward free radical process, was inserted into a polymeric network with methacrylic acid (MAA) and ethylene glycole dimethacrylate acting as comonomer and crosslinker, respectively. All the reactants were simultaneously mixed in the polymerization feed and one‐pot radical reaction was carried out. Irregular microparticles were prepared by bulk polymerization and microspheres by precipitation polymerization. The materials were characterized by nuclear magnetic resonance–magic angle spinning (NMR‐MAS) studies, to verify effective FA insertion into polymeric networks, and by morphological, dimensional analyses, and water absorption measurement to study their superficial and swelling properties, respectively. Antioxidant properties of materials were evaluated by linoleic acid emulsion system–thiocyanate assay, determination of scavenging activity on DPPH radicals, determination of available phenolic groups in polymeric matrices, and determination of total antioxidant capacity. Copyright © 2009 John Wiley & Sons, Ltd.     

On the molecular origin of cold denaturation of globular proteins

A polypeptide chain can adopt very different conformations, a fundamental distinguishing feature of which is the water accessible surface area, WASA, that is a measure of the layer around the polypeptide chain where the center of water molecules cannot physically enter, generating a solvent-excluded volume effect. The large WASA decrease associated with the folding of a globular protein leads to a large decrease in the solvent-excluded volume, and so to a large increase in the configurational/translational freedom of water molecules. The latter is a quantity that depends upon temperature. Simple calculations over the -30 to 150 °C temperature range, where liquid water can exist at 1 atm, show that such a gain decreases significantly on lowering the temperature below 0 °C, paralleling the decrease in liquid water density. There will be a temperature where the destabilizing contribution of the polypeptide chain conformational entropy exactly matches the stabilizing contribution of the water configurational/translational entropy, leading to cold denaturation.     

Dynamics of hyaluronan aqueous solutions as assessed by fast field cycling NMR relaxometry

Fast field cycling (FFC) NMR relaxometry has been used to study the conformational properties of aqueous solutions of hyaluronan (HYA) at three concentrations in the range 10 to 25 mg mL^–1. Results revealed that, irrespective of the solution concentration, three different hydration layers surround hyaluronan. The inner layer consists of water molecules strongly retained in the proximity of the HYA surface. Because of their strong interactions with HYA, water molecules in this inner hydration layer are subject to very slow dynamics and have the largest correlation times. The other two hydration layers are made of water molecules which are located progressively further from the HYA surface. As a result, decreasing correlation times caused by faster molecular motion were measured. The NMRD profiles obtained by FFC-NMR relaxometry also showed peaks attributable to ¹H–¹⁴N quadrupole interactions. Changes in intensity and position of the quadrupolar peaks in the NMRD profiles suggested that with increasing concentration the amido group is progressively involved in the formation of weak and transient intramolecular water bridging adjacent hyaluronan chains. In this work, FFC-NMR was used for the first time to obtain deeper insight into HYA–water interactions and proved itself a powerful and promising tool in hyaluronan chemistry.