Retention of stereochemistry in the microwave assisted synthesis of 1H-tetrazole bioisosteric moiety from chiral phenyl-acetic acid derivatives

Chiral substituted phenylethyl-1H-tetrazoles were built-up from the corresponding carboxylic acid derivatives by a useful three-step synthesis. The procedure, that preserves the chiral center from racemization, was successfully applied to a selection of several hit compounds by conversion of the carboxylic acid moiety to the nitrile derivatives and subsequent reaction with trimethylstannyl azide, under microwave conditions. A useful application to the corresponding tetrazole analogue has been found also in the conversion of the aminoacidic moiety like (R)-N-Cbz-phenylglycine showing a wide potential synthetic application.     

Almost periodic invariant tori for the NLS on the circle

In this paper we study the existence and linear stability of almost periodic solutions for a NLS equation on the circle with external parameters. Starting from the seminal result of Bourgain in [15] on the quintic NLS, we propose a novel approach allowing to prove in a unified framework the persistence of finite and infinite dimensional invariant tori, which are the support of the desired solutions. The persistence result is given through a rather abstract “counter-term theorem” à la Herman, directly in the original elliptic variables without passing to action-angle ones. Our framework allows us to find “many more” almost periodic solutions with respect to the existing literature and consider also non-translation invariant PDEs.     

KAM Theory in Configuration Space and Cancellations in the Lindstedt Series

The KAM theorem for analytic quasi-integrable anisochronous Hamiltonian systems yields that the perturbation expansion (Lindstedt series) for any quasi-periodic solution with Diophantine frequency vector converges. If one studies the Lindstedt series by following a perturbation theory approach, one finds that convergence is ultimately related to the presence of cancellations between contributions of the same perturbation order. In turn, this is due to symmetries in the problem. Such symmetries are easily visualised in action-angle coordinates, where the KAM theorem is usually formulated by exploiting the analogy between Lindstedt series and perturbation expansions in quantum field theory and, in particular, the possibility of expressing the solutions in terms of tree graphs, which are the analogue of Feynman diagrams. If the unperturbed system is isochronous, Moser’s modifying terms theorem ensures that an analytic quasi-periodic solution with the same Diophantine frequency vector as the unperturbed Hamiltonian exists for the system obtained by adding a suitable constant (counterterm) to the vector field. Also in this case, one can follow the alternative approach of studying the perturbation expansion for both the solution and the counterterm, and again convergence of the two series is obtained as a consequence of deep cancellations between contributions of the same order. In this paper, we revisit Moser’s theorem, by studying the perturbation expansion one obtains by working in Cartesian coordinates. We investigate the symmetries giving rise to the cancellations which makes possible the convergence of the series. We find that the cancellation mechanism works in a completely different way in Cartesian coordinates, and the interpretation of the underlying symmetries in terms of tree graphs is much more subtle than in the case of action-angle coordinates.     

Rapid activation of the melibiose permease MelB immobilized on a solid-supported membrane

Rapid solution exchange on a solid-supported membrane (SSM) is investigated using fluidic structures and a solid-supported membrane of 1 mm diameter in wall jet geometry. The flow is analyzed with a new technique based on specific ion interactions with the surface combined with an electrical measurement. The critical parameters affecting the time course of the solution exchange and the transfer function describing the time resolution of the SSM system are determined. The experimental data indicate that solution transport represents an intermediate situation between the plug flow and the Hagen-Poiseuille laminar flow regime. However, to a good approximation the rise of the surface concentration can be described by Hagen-Poiseuille flow with ideal mixing at the surface of the SSM. Using an improved cuvette design, solution exchange as fast as 2 ms was achieved at the surface of a solid-supported membrane. As an application of the technique, the rate constant of a fast electrogenic reaction in the melibiose permease MelB, a bacterial ( Escherichia coli) sugar transporter, is determined. For comparison, the kinetics of a conformational transition of the same transporter was measured using stopped-flow tryptophan fluorescence spectroscopy. The relaxation time constant obtained for the charge displacement agrees with that determined in the stopped-flow experiments. This demonstrates that upon sugar binding MelB undergoes an electrogenic conformational transition with a rate constant of k approximately 250 s (-1).     

Nanoaggregates of copper porphyrazine in floating layers and Langmuir-Schaefer films

Aggregation behavior of unsubstituted copper porphyrazine (CuPaz) on the water surface was studied by analysis of compression curves, Brewster angle microscopy (BAM), and optical spectroscopy. The structure and stability of the CuPaz aqua aggregates in the floating layers are determined by hydration degree that depends on initial surface concentration and surface pressure. Langmuir-Schaefer (LS) films of CuPaz were prepared by deposition of the variously structured floating layers and studied by X-ray scattering technique and optical spectroscopy. Stable and labile structures were detected and compared with the floating CuPaz aqua aggregates. Conditions of formation of the stable four-stacked nanoaggregates in LS films were determined. A model comprising both nucleation of CuPaz on the water surface and structural transformations in the solid films is proposed.     

Determination of aliphatic amines by cation‐exchange chromatography with suppressed conductivity detection after solid phase extraction*

A sensitive method for the determination of underivatized aliphatic amines based on cation exchange chromatography coupled with suppressed conductivity detection scheme and solid phase extraction (SPE) procedure has been developed. A surface modified styrene divinylbenzene polymeric sorbent, based on a reversed‐phase (RP) and strong cation exchange (SCX) mixed mode was used as an active material for the SPE of amines. The conductometric capabilities of several aliphatic mono‐ and polyamines, expressed in terms of molar sensitivity (nS/μM), were determined. The LODs, obtained without the SPE treatment, ranged between 20 and 65 nM for putrescine and 2‐butylamine, respectively. The resulting calibration plots for the aliphatic amines were generally linear over about three orders of magnitude, with correlation coefficients >0.98. The LODs of amines decreased generally by one factor when SPE procedure, using BaCl₂/H₂SO₄ eluents, has been adopted. The proposed SPE procedure, seems to offer good results in terms of preconcentration, recoveries and cleanup of samples. The proposed methodology was successfully tested for the quantitative determination of some biogenic amines in beer and tuna.     

Compactness and existence results in weighted Sobolev spaces of radial functions. Part II: existence

We apply the compactness results obtained in the first part of this work, to prove existence and multiplicity results for finite energy solutions to the nonlinear elliptic equation

$$-\triangle u + V \left(\left|x\right|\right) u = g \left(\left|x\right|, u\right) \quad {\rm in} \Omega \subseteq \mathbb{R}^{N},\,N \geq 3,$$

where \({\Omega}\) is a radial domain (bounded or unbounded) and u satisfies u =  0 on \({\partial\Omega}\) if \({\Omega \neq\mathbb{R}^{N}}\) and \({u \rightarrow 0}\) as \({\left|x\right| \rightarrow \infty}\) if \({\Omega}\) is unbounded. The potential V may be vanishing or unbounded at zero or at infinity and the nonlinearity g may be superlinear or sublinear. If g is sublinear, the case with a forcing term \({g\left(\left|\cdot\right|, 0\right) \neq 0}\) is also considered. Our results allow to deal with V and g exhibiting behaviours at zero or at infinity which are new in the literature and, when \({\Omega = \mathbb{R}^{N}}\), do not need to be compatible with each other.

     

Readily Accessible Bulky Iron Catalysts exhibiting Site Selectivity in the Oxidation of Steroidal Substrates

Bulky iron complexes are described that catalyze the site‐selective oxidation of alkyl C?H bonds with hydrogen peroxide under mild conditions. Steric bulk at the iron center is introduced by appending trialkylsilyl groups at the meta‐position of the pyridines in tetradentate aminopyridine ligands, and this effect translates into high product yields, an enhanced preferential oxidation of secondary over tertiary C?H bonds, and the ability to perform site‐selective oxidation of methylenic sites in terpenoid and steroidal substrates. Unprecedented site selective oxidation at C6 and C12 methylenic sites in steroidal substrates is shown to be governed by the chirality of the catalysts.