Platonic polyhedra,topological constraints and periodic solutions of the classical <Emphasis Type="Italic">N</Emphasis>-body problem

We prove the existence of a number of smooth periodic motions u _∗ of the classical Newtonian N-body problem which, up to a relabeling of the N particles, are invariant under the rotation group R\mathcal{R} of one of the five Platonic polyhedra. The number N coincides with the order |R||\mathcal{R}| of R\mathcal{R} and the particles have all the same mass. Our approach is variational and u _∗ is a minimizer of the Lagrangian action A\mathcal{A} on a suitable subset K\mathcal{K} of the H ¹ T-periodic maps u:ℝ→ℝ^3N . The set K{\mathcal {K}} is a cone and is determined by imposing on u both topological and symmetry constraints which are defined in terms of the rotation group R\mathcal{R}. There exist infinitely many such cones K{\mathcal {K}}, all with the property that A|_K{\mathcal {A}}|_{{\mathcal {K}}} is coercive. For a certain number of them, using level estimates and local deformations, we show that minimizers are free of collisions and therefore classical solutions of the N-body problem with a rich geometric–kinematic structure.     

A regularization for discontinuous differential equations with application to state-dependent delay differential equations of neutral type

We consider a regularization for a class of discontinuous differential equations arising in the study of neutral delay differential equations with state dependent delays. For such equations the possible discontinuity in the derivative of the solution at the initial point may propagate along the integration interval giving rise to so-called “breaking points”, where the solution derivative is again discontinuous. Consequently, the problem of continuing the solution in a right neighborhood of a breaking point is equivalent to a Cauchy problem for an ode with a discontinuous right-hand side (see e.g. Bellen et al., 2009 [4]). Therefore a classical solution may cease to exist.The regularization is based on the replacement of the vector-field with its time average over an interval of length ε>0. The regularized solution converges as ε→⁰⁺ to the classical Filippov solution (Filippov, 1964, 1988 [13] and [14]). Several properties of the solutions corresponding to small ε>0 are presented.     

Selective synthesis of hydroxy analogues of valinomycin using dioxiranes

A synthesis of representative monohydroxy derivatives of valinomycin (VLM) was achieved under mild conditions by direct hydroxylation at the side chains of the macrocyclic substrate using dioxiranes. Results demonstrate that the powerful methyl(trifluoromethyl)dioxirane 1b should be the reagent of choice to carry out these key transformations. Thus, a mixture of compounds derived from the direct dioxirane attack at the β-(CH(3))(2)C-H alkyl chain of one Hyi residue (compound 3a) or of one Val moiety (compounds 3b and 3c) could be obtained. Following convenient mixture separation, each of the new oxyfunctionalized macrocycles became completely characterized.     

Supramolecular synthons in fluorinated and nitrogen-rich <Emphasis Type="Italic">ortho</Emphasis>-diaminotriazoles

5-Substituted 3,4-diamino-1,2,4-triazoles can be obtained in moderate to good yields in a one-pot reaction starting from a carboxylic acid and dimethylaminoguanidine monohydrochloride in polyphosphoric acid (PPA) at 120 °C. Several triazoles and bistriazoles have been prepared in this way, with substituents ranging from alkyl to aryl, including perfluoroaryl or perfluoroalkyl substituents. The crystal structure analysis of three perfluorinated diaminotriazoles has evidenced a most stable R₂² (8) R_{2}^{2} (8) H bonding synthon, involving the amino CNH₂ donor and the adjacent nitrogen ring acceptor; additionally, two new synthons consisting of chains of rings have been identified. The relevance of the short F⋯F intermolecular contacts found in the structures is also discussed.     

Effect of serum proteins on polystyrene nanoparticle uptake and intracellular trafficking in endothelial cells

The physico-chemical properties of nanoparticles (NPs), such as small dimensions, surface charge and surface functionalization, control their capability to interact with cells and, in particular, with sub-cellular components. This interaction can be also influenced by the adsorption of molecules present in biological fluids, like blood, on NP surface. Here, we analysed the effect of serum proteins on 49 and 100 nm red fluorescent polystyrene NP uptake in porcine aortic endothelial (PAE) cells, as a model for vascular transport. To this aim, NP uptake kinetic, endocytic pathway and intracellular trafficking were studied by monitoring NPs inside cells through confocal microscopy and multiple particle tracking (MPT). We demonstrated that NPs are rapidly internalized by cells in serum-free (SF) medium, according to a saturation kinetic. Conversely, in 10% foetal bovine serum-enriched (SE) medium, NP uptake rate results drastically reduced. Moreover, NP internalization depends on an active endocytic mechanism that does not involve clathrin- and caveolae-mediated vesicular transport, in both SE and SF media. Furthermore, MPT data indicate that NP intracellular trafficking is unaffected by protein presence. Indeed, approximately 50–60% of internalized NPs is characterized by a sub-diffusive behaviour, whereas the remaining fraction shows an active motion. These findings demonstrate that the unspecific protein adsorption on NP surface can affect cellular uptake in terms of internalization kinetics, but it is not effective in controlling active and cellular-mediated uptake mechanisms of NPs and their intracellular routes.     

A New Butyrate Releaser Exerts a Protective Action against SARS-CoV-2 Infection in Human Intestine

Butyrate is a major gut microbiome metabolite that regulates several defense mechanisms against infectious diseases. Alterations in the gut microbiome, leading to reduced butyrate production, have been reported in patients with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection. A new butyrate releaser, useful for all the known applications of butyrate, presenting physiochemical characteristics suitable for easy oral administration, (N-(1-carbamoyl-2-phenyl-ethyl) butyramide (FBA), has been recently developed. We investigated the protective action of FBA against SARS-CoV-2 infection in the human small intestine and enterocytes. Relevant aspects of SARS-CoV-2 infection were assessed: infectivity, host functional receptor angiotensin-converting enzyme-2 (ACE2), transmembrane protease serine 2 (TMPRSS2), neuropilin-1 (NRP1), pro-inflammatory cytokines expression, genes involved in the antiviral response and the activation of Nf-kB nuclear factor (erythroid-derived 2-like) 2 (Nfr2) pathways. We found that FBA positively modulates the crucial aspects of the infection in small intestinal biopsies and human enterocytes, reducing the expression of ACE2, TMPRSS2 and NRP1, pro-inflammatory cytokines interleukin (IL)-15, monocyte chemoattractant protein-1 (MCP-1) and TNF-α, and regulating several genes involved in antiviral pathways. FBA was also able to reduce the number of SARS-CoV-2-infected cells, and ACE2, TMPRSS2 and NRP1 expression. Lastly, through the inhibition of Nf-kB and the up-regulation of Nfr2, it was also able to reduce the expression of pro-inflammatory cytokines IL-15, MCP-1 and TNF-α in human enterocytes. The new butyrate releaser, FBA, exerts a preventive action against SARS-CoV-2 infection. It could be considered as an innovative strategy to limit COVID-19.     

Thermodynamics of the early stages in homogeneous ziegler-natta polymerization: Density functional calculations on model systems TiCl2R+ and ZrCl2R+

The ethylene polymerization enthalpy, calculated through quantum-mechanical ab-initio methods on model systems of homogeneous Ziegler-Natta cationic catalysts, is reported to be from two to three times greater than the experimental value of 22,3 kcal/mol. In this paper we analyze the origin of this discrepancy and show that it is mainly due to the intrisnic instability of the cationic system in vacuum. We also demonstrate that the growing polymer chain can act as a quite efficient stabilizing agent. We examined, through density functional calculations, the model systems MCl₂R⁺, where M = Ti, Zr and R = CH₃, C₃H₇, C₅H₁₁, C₇H₁₅ and their analogues obtained by neutralizing the positive charge with a chloride anion. On the basis of our computational results, we found that: (i) for the ideal reaction of ethane with ethylene to give butane, considered as a thermodynamical model of the single insertion step, the calculated enthalpy value of 35,6 kcal/mol is in closer agreement with the experimental value and is taken as theoretical reference value; (ii) the same value is obtained also for the neutral systems MCl₃R independently of the nature of the metal and of the alkyl chain length; (iii) for cationic systems, when R = CH₃, high insertion enthalpies are obtained in agreement with the calculated values reported in literature, but, for R = C₃H₇, C₅H₁₁ and C₇H₁₅, the insertion enthalpy remarkably decreases converging towards the theoretical reference value. We conclude that the high enthalpy value obtained for the first monomer insertion is not only a mere consequence of the computational method, but is mainly due to the weak stabilizing effect of the methyl group. A longer alkyl chain produces a stabilization of the cationic system through the inductive effect as well as through formation of agostic bonds. This leads us to formulate the hypothesis that, in real polymerization conditions, the role of a stabilizing agent, which is mainly played by the counterion in the early stages of the propagation reaction, could be performed by the growing chain as the polymerization proceeds.     

Syndiotactic Polymerization of Propylene: Single‐Site Vanadium Catalysts in Comparison with Zirconium and Nickel

The syndiotactic‐specific polymerization of propylene can be promoted by single‐site catalysts based on vanadium, nickel and group IV metals. The polymerization mechanisms are reasonably well established for nickel and group IV metals. For vanadium catalysts the polymerization mechanisms reported in the literature are still debatable, since the stereochemistry of the monomer insertion is well known, but the active species have never been isolated. In this paper the mechanisms concerning Ni and group IV metal catalysts are briefly summarized and proposed mechanisms concerning vanadium are compared within one another.     

The NE detector for a long baseline neutrino oscillation experiment

The project of a large underground experiment, N^OE (Neutrino Oscillation Experiment), composed by modules of scintillating fiber calorimeter interleaved with TRD modules, total weight 6.7 ktons, is presented. This apparatus has been optimized for long baseline neutrino oscillation studies, in particular to be sensitive in the region of sin² 2θ and Δm² suggested by the atmospheric neutrino anomaly (fig. 3).     

Molecular dynamics simulation of semirigid polymers

The chain rigidity of poly(p-hydroxybenzoate) was estimated through the theoretical evaluation of its persistence length (L_p). A non-Brownian molecular dynamics (MD) simulation of an isolated chain with 20 monomeric units was performed. The sampled conformational population was analyzed and the orientational correlation function between monomeric units along the chain was calculated. An algorithm based on the worm-like chain model was applied to evaluate the persistence length. The results were compared with those obtained from equilibrium models like the freely-rotating-chain and the rotational-matrix method with fluctuations. Equilibrium models give different results depending on the degree of accuracy used in describing the monomeric unit. The inclusion of thermal fluctuations is crucial to obtain realistic results. These coincide with those given by MD simulation when only nearest-neighbour orientational correlations are taken into account: inclusion of higher-order correlation terms leads to lower values of the persistence length. The origin of this discrepancy was investigated. The MD simulation results are characterized by an overrepresentation of conformations with a short end-to-end distance resulting from an anomalous energy concentration in the first bending mode of the chain. In analogy with previous simulation results from systems characterized by a week coupling amoung their degrees of freedom, failure in the energy equipartition is proposed as a likely explanation of the anomalous dynamical behaviour.