Robust exponential attractors for singularly perturbed Hodgkin-Huxley equations

Here we consider a singular perturbation of the Hodgkin-Huxley system which is derived from the Lieberstein's model. We study the associated dynamical system on a suitable bounded phase space, when the perturbation parameter ε (i.e., the axon specific inductance) is sufficiently small. We prove the existence of bounded absorbing sets as well as of smooth attracting sets. We deduce the existence of a smooth global attractor Aε. Finally we prove the main result, that is, the existence of a family of exponential attractors {Eε} which is Hölder continuous with respect to ε.     

Recent advances in linear analysis of convergence for splittings for solving ODE problems

In the nineties, Van der Houwen et al. (see, e.g., [P.J. van der Houwen, B.P. Sommeijer, J.J. de Swart, Parallel predictor–corrector methods, J. Comput. Appl. Math. 66 (1996) 53–71; P.J. van der Houwen, J.J.B. de Swart, Triangularly implicit iteration methods for ODE-IVP solvers, SIAM J. Sci. Comput. 18 (1997) 41–55; P.J. van der Houwen, J.J.B. de Swart, Parallel linear system solvers for Runge–Kutta methods, Adv. Comput. Math. 7 (1–2) (1997) 157–181]) introduced a linear analysis of convergence for studying the properties of the iterative solution of the discrete problems generated by implicit methods for ODEs. This linear convergence analysis is here recalled and completed, in order to provide a useful quantitative tool for the analysis of splittings for solving such discrete problems. Indeed, this tool, in its complete form, has been actively used when developing the computational codes BiM and BiMD [L. Brugnano, C. Magherini, The BiM code for the numerical solution of ODEs, J. Comput. Appl. Math. 164–165 (2004) 145–158. Code available at: http://www.math.unifi.it/~brugnano/BiM/index.html; L. Brugnano, C. Magherini, F. Mugnai, Blended implicit methods for the numerical solution of DAE problems, J. Comput. Appl. Math. 189 (2006) 34–50]. Moreover, the framework is extended for the case of special second order problems. Examples of application, aimed to compare different iterative procedures, are also presented.     

Contribution of the Adenosine 2A Receptor to Behavioral Effects of Tetrahydrocannabinol,Cannabidiol and PECS-101

The cannabis-derived molecules, ∆⁹ tetrahydrocannabinol (THC) and cannabidiol (CBD), are both of considerable therapeutic interest for a variety of purposes, including to reduce pain and anxiety and increase sleep. In addition to their other pharmacological targets, both THC and CBD are competitive inhibitors of the equilibrative nucleoside transporter-1 (ENT-1), a primary inactivation mechanism for adenosine, and thereby increase adenosine signaling. The goal of this study was to examine the role of adenosine A2A receptor activation in the effects of intraperitoneally administered THC alone and in combination with CBD or PECS-101, a 4′-fluorinated derivative of CBD, in the cannabinoid tetrad, elevated plus maze (EPM) and marble bury assays. Comparisons between wild-type (WT) and A2AR knock out (A2AR-KO) mice were made. The cataleptic effects of THC were diminished in A2AR-KO; no other THC behaviors were affected by A2AR deletion. CBD (5 mg/kg) potentiated the cataleptic response to THC (5 mg/kg) in WT but not A2AR-KO. Neither CBD nor THC alone affected EPM behavior; their combination produced a significant increase in open/closed arm time in WT but not A2AR-KO. Both THC and CBD reduced the number of marbles buried in A2AR-KO but not WT mice. Like CBD, PECS-101 potentiated the cataleptic response to THC in WT but not A2AR-KO mice. PECS-101 also reduced exploratory behavior in the EPM in both genotypes. These results support the hypothesis that CBD and PECS-101 can potentiate the cataleptic effects of THC in a manner consistent with increased endogenous adenosine signaling.     

Contact and Frobenius solvable Lie algebras with abelian nilradical

The aim of this work is to characterize the families of Frobenius (respectively, contact) solvable Lie algebras that satisfies the following condition: 𝔤 = 𝔥?V, where 𝔥?𝔤𝔩(V), |dim V?dim 𝔤|≤1 and NilRad(𝔤) = V, V being a finite dimensional vector space. In particular, it is proved that every complex Frobenius solvable Lie algebra is decomposable, whereas that in the real case there are only two indecomposable Frobenius solvable Lie algebras.     

Rhodococcus as Biofactories for Microbial Oil Production

Bacteria belonging to the Rhodococcus genus are frequent components of microbial communities in diverse natural environments. Some rhodococcal species exhibit the outstanding ability to produce significant amounts of triacylglycerols (TAG) (>20% of cellular dry weight) in the presence of an excess of the carbon source and limitation of the nitrogen source. For this reason, they can be considered as oleaginous microorganisms. As occurs as well in eukaryotic single-cell oil (SCO) producers, these bacteria possess specific physiological properties and molecular mechanisms that differentiate them from other microorganisms unable to synthesize TAG. In this review, we summarized several of the well-characterized molecular mechanisms that enable oleaginous rhodococci to produce significant amounts of SCO. Furthermore, we highlighted the ability of these microorganisms to degrade a wide range of carbon sources coupled to lipogenesis. The qualitative and quantitative oil production by rhodococci from diverse industrial wastes has also been included. Finally, we summarized the genetic and metabolic approaches applied to oleaginous rhodococci to improve SCO production. This review provides a comprehensive and integrating vision on the potential of oleaginous rhodococci to be considered as microbial biofactories for microbial oil production.     

Microwave-assisted Suzuki reaction catalyzed by Pd(0)-PVP nanoparticles

Suzuki cross-coupling reaction was successfully carried out in ethanol utilizing a palladium colloidal solution stabilized by polyvinylpyrrolidone (PVP). High isolated yields (75-97%) to biaryls were obtained using different bases, aryl halides, and aryl boronic acids with a small loading of the palladium catalyst. Pd(0)-PVP nanoparticles with 3-6 nm of medium diameter were prepared from Pd(OAc)₂ in the presence of the stabilizer PVP using methanol as the reducing agent.     

An expanded halogen bonding scale using astatine

As a non-covalent interaction, halogen bonding is now acknowledged to be useful in all fields where the control of intermolecular recognition plays a pivotal role. Halogen-bond basicity scales allow quantification of the halogen bonding of referential donors with organic functional groups from a thermodynamic point of view. Herein we present the pK_BAtI basicity scale to provide the community an overview of halogen-bond acceptor strength towards astatine, the most potent halogen-bond donor element. This experimental scale is erected on the basis of complexation constants measured between astatine monoiodide (AtI) and sixteen selected Lewis bases. It spans over 6 log units and culminates with a value of 5.69 ± 0.32 for N,N,N′,N′-tetramethylthiourea. On this scale, the carbon π-bases are the weakest acceptors, the oxygen derivatives cover almost two-thirds of the scale, and sulphur bases exhibit the highest AtI basicity. Regarding the applications of ²¹¹At in targeted radionuclide therapy, stronger labelling of carrier agents could be envisaged on the basis of the pK_BAtI scale.

Based on the halogen bonding between astatine monoiodide (AtI) and 16 Lewis bases, the newly established pK_BAtI scale indicates that the halogen bond basicity of AtI follows the order C ≤ O ≤ S ≈ Se for the acceptor atomic site.     

Growth of Escherichia coli under extremely low-frequency electromagnetic fields

The inflence of extremely low-frequency (ELF) electromagnetic fields on Escherichia coli cultures in submerse fermentation was studied. The fermentation processes were carried out recycling the culture medium externally through a stainless steel tube inserted in a magnetic field generator (solenoid). The exposure time and electromagnetic induction were varied in a range of 1 to 12 h and 0.010 to 0.10 T, respectively, according to a Box-Wilson Central Composite Designs of face centered with five central points. Growth of E. coli could be altered (stimulated or inhibited) under magnetic fieldinduced effects. E. coli culturesexposed at 0.1 T during 6.5 h exhibited changes in its viability compared to unexposed cells, which was 100 times higher than the control. The magnetic field generator associated with the cellular suspension recycle is a new way of magnetic treatment in fermentation processes and could be appropriate to industrial scale up.     

The smart Petri dish: a nanostructured photonic crystal for real-time monitoring of living cells

The intensity of light scattered from a porous Si photonic crystal is used to monitor physiological changes in primary rat hepatocytes. The cells are seeded on the surface of a porous Si photonic crystal that has been filled with polystyrene and treated with an O2 plasma. Light resonant with the photonic crystal is scattered by the cell layer and detected as an optical peak with a charge-coupled-device spectrometer. It is demonstrated that exposure of hepatocytes to the toxins cadmium chloride or acetaminophen leads to morphology changes that cause a measurable increase in scattered intensity. The increase in signal occurs before traditional assays are able to detect a decrease in viability, demonstrating the potential of the technique as a complementary tool for cell viability studies. The scattering method presented here is noninvasive and can be performed in real time, representing a significant advantage compared to other techniques for in vitro monitoring of cell morphology.     

Nonradical mechanisms for the uncatalyzed thermal functionalization of silicon surfaces by alkenes and alkynes: a density functional study

We propose a new concerted mechanism for the uncatalyzed hydrosilylation of terminal alkenes and alkynes, alternative to the conventional radical-based mechanism. Density functional calculations have been carried out on these and on previously proposed alternative mechanisms for the hydrosilylation of ethylene and acetylene by suitable finite size clusters as models of the thermal functionalization of -SiH3, =SiH2, and [triple bound] SiH groups in flat Si(100) and Si(111) and porous silicon surfaces by alkenes and alkynes. For each step involved in the considered hydrosilylation pathways, we optimized the geometries of reactants and products and located the corresponding transition states. The calculated activation energies for the concerted pathways of ethylene and acetylene are, respectively, 57.6 and 60.9 kcal mol(-1) on -SiH3 and in the ranges 62-63 and 58-61 kcal mol-1 on =SiH2 and 64-66 and 56-61 kcal mol(-1) on SiH. These values are much lower than the activation energies calculated for the corresponding homolytic dissociation of the Si-H bond, which is the preliminary step in the radical path, 85.6, 82-83, and 79-81 kcal mol(-1), respectively, for -SiH3, =SiH2, and [triple bound] SiH groups. Our results thus suggest that the thermal hydrosilylation of alkenes and alkynes on silicon surfaces, for which a radical-based mechanism is currently accepted, may occur through a concerted mechanism.