The chromatic number of random Borsuk graphs

We study a model of random graph where vertices are n i.i.d. uniform random points on the unit sphere S^d in , and a pair of vertices is connected if the Euclidean distance between them is at least 2??. We are interested in the chromatic number of this graph as n tends to infinity. It is not too hard to see that if ?>0 is small and fixed, then the chromatic number is d+2 with high probability. We show that this holds even if ?→0 slowly enough. We quantify the rate at which ? can tend to zero and still have the same chromatic number. The proof depends on combining topological methods (namely the Lyusternik–Schnirelman–Borsuk theorem) with geometric probability arguments. The rate we obtain is best possible, up to a constant factor—if ?→0 faster than this, we show that the graph is (d+1)‐colorable with high probability.25     

A Novel [OSSO]-Type Chromium(III) Complex as a Versatile Catalyst for Copolymerization of Carbon Dioxide with Epoxides

A new chromium(III) complex, bearing a bis-thioether-diphenolate [OSSO]-type ligand, was found to be an efficient catalyst in the copolymerization of CO₂ and epoxides to achieve poly(propylene carbonate), poly(cyclohexene carbonate), poly(hexene carbonate) and poly(styrene carbonate), as well as poly(propylene carbonate)(cyclohexene carbonate) and poly(propylene carbonate)(hexene carbonate) terpolymers.     

Controlling the Length of Cooperative Supramolecular Polymers with Chain Cappers

The design and the characterization of supramolecular additives to control the chain length of benzene-1,3,5-tricarboxamide (BTA) cooperative supramolecular polymers under thermodynamic equilibrium is unraveled. These additives act as chain cappers of supramolecular polymers and feature one face as reactive as the BTA discotic to interact strongly with the polymer end, whereas the other face is nonreactive and therefore impedes further polymerization. Such a design requires fine tuning of the conformational preorganization of the amides and the steric hindrance of the motif. The chain cappers studied are monotopic derivatives of BTA, modified by partial N-methylation of the amides or by positioning of a bulky cyclotriveratrylene cage on one face of the BTA unit. This study not only clarifies the interplay between structural variations and supramolecular interactions, but it also highlights the necessity to combine orthogonal characterization methods, spectroscopy and light scattering, to elucidate the structures and compositions of supramolecular systems.     

Direct Synthesis of Peptide-Containing Silicones: A New Way to Bioactive Materials

A simple and efficient way to synthesize peptide-containing silicone materials is described. Silicone oils containing a chosen ratio of bioactive peptide sequences were prepared by acid-catalyzed copolymerization of dichlorodimethylsilane, hybrid dichloromethyl peptidosilane, and Si(vinyl)- or SiH-functionalized monomers. Functionalized silicone oils were first obtained and then, after hydrosilylation cross-linking, bioactive polydimethylsiloxane (PDMS)-based materials were straightforwardly obtained. The introduction of an antibacterial peptide yielded PDMS materials showing activity against Staphylococcus aureus. PDMS containing RGD ligands showed improved cell-adhesion properties. This generic method was fully compatible with the stability of peptides and thus opened the way to the synthesis of a wide range of biologically active silicones.     

MUC1 Aptamer-Capped Mesoporous Silica Nanoparticles for Navitoclax Resistance Overcoming in Triple-Negative Breast Cancer

Triple-negative breast cancer (TNBC) is the most aggressive breast cancer subtype. In the last years, navitoclax has emerged as a possible treatment for TNBC. Nevertheless, rapid navitoclax resistance onset has been observed thorough Mcl-1 overexpression. As a strategy to overcome Mcl-1-mediated resistance, herein we present a controlled drug co-delivery system based on mesoporous silica nanoparticles (MSNs) targeted to TNBC cells. The nanocarrier is loaded with navitoclax and the Mcl-1 inhibitor S63845 and capped with a MUC1-targeting aptamer ( apMUC1-MSNs(Nav/S63845) ). The apMUC1-capped nanoparticles effectively target TNBC cell lines and successfully induce apoptosis, overcoming navitoclax resistance. Moreover, navitoclax encapsulation protects platelets against apoptosis. These results point apMUC1-gated MSNs as suitable BH3 mimetics nanocarriers in the targeted treatment of MUC1-expressing TNBC.     

Janus Gold Nanostars–Mesoporous Silica Nanoparticles for NIR-Light-Triggered Drug Delivery

Janus gold nanostar–mesoporous silica nanoparticle ( AuNSt–MSNP ) nanodevices able to release an entrapped payload upon irradiation with near infrared (NIR) light were prepared and characterized. The AuNSt surface was functionalized with a thiolated photolabile molecule ( 5 ), whereas the mesoporous silica face was loaded with a model drug (doxorubicin) and capped with proton-responsive benzimidazole-β-cyclodextrin supramolecular gatekeepers ( N 1 ). Upon irradiation with NIR-light, the photolabile compound 5 photodissociated, resulting in the formation of succinic acid, which induced the opening of the gatekeeper and cargo delivery. In the overall mechanism, the gold surface acts as a photochemical transducer capable of transforming the NIR-light input into a chemical messenger (succinic acid) that opens the supramolecular nanovalve. The prepared hybrid nanoparticles were non-cytotoxic to HeLa cells, until they were irradiated with a NIR laser, which led to intracellular doxorubicin release and hyperthermia. This induced a remarkable reduction in HeLa cells viability.     

Single‐Site Zeolite‐Anchored Organoiridium Carbonyl Complexes: Characterization of Structure and Reactivity by Spectroscopy and Computational Chemistry

A family of HY zeolite‐supported cationic organoiridium carbonyl complexes was formed by reaction of Ir(CO)₂(acac) (acac=acetylacetonate) to form supported Ir(CO)₂ complexes, which were treated at 298 K and 1 atm with flowing gas‐phase reactants, including C₂H₄, H₂, ¹²CO, ¹³CO, and D₂O. Mass spectrometry was used to identify effluent gases, and infrared and X‐ray absorption spectroscopies were used to characterize the supported species, with the results bolstered by DFT calculations. Because the support is crystalline and presents a nearly uniform array of bonding sites for the iridium species, these were characterized by a high degree of uniformity, which allowed a precise determination of the species involved in the replacement, for example, of one CO ligand of each Ir(CO)₂ complex with ethylene. The supported species include the following: Ir(CO)₂, Ir(CO)(C₂H₄)₂, Ir(CO)(C₂H₄), Ir(CO)(C₂H₅), and (tentatively) Ir(CO)(H). The data determine a reaction network involving all of these species.     

Thioetherphenolate group 4 metal complexes in the ring opening polymerization of rac‐β‐Butyrolactone

Group 4 complexes 1 – 3 [ 1 = (t‐BuOS)₂Ti(O‐i‐Pr)₂; 2 = (t‐BuOS)₂Zr(O‐t‐Bu)₂; 3 = (t‐BuOS)₂Hf(O‐t‐Bu)₂] supported by two phenolate bidentate ligands (t‐BuOS‐H = 4,6‐di‐tert‐butyl‐2‐phenylsulfanylphenol) promote the well‐controlled ring opening polymerization of rac‐β‐butyrolactone. In presence of isopropanol, low dispersities and molecular weights proportional to the equivalents of isopropanol are achieved. Moreover, the zirconium complex is effective in the copolymerization of rac‐β‐butyrolactone with rac‐lactide. The 13 C nuclear magnetic resonance analysis revealed that the obtained copolymers have a tapered diblock microstructure consisting of an initial block composed of lactide sequences and a terminal block composed of butyrolactone sequences. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 3132–3139