Krull’s theory for the double gamma function

The Barnes’ G-function G(x) = 1/Γ₂, satisfies the functional equation logG(x + 1) − logG(x) = logΓ(x). We complement W. Krull’s work in Bemerkungen zur Differenzengleichung g(x + 1) − g(x) = φ(x), Math. Nachrichten 1 (1948), 365-376 with additional results that yield a different characterization of the function G, new expansions and sharp bounds for G on x > 0 in terms of Gamma and Digamma functions, a new expansion for the Gamma function and summation formulae with Polygamma functions.     

Electrochemically controlled formation/dissociation of phosphonate-cavitand/methylpyridinium complexes

The phosphorus-bridged cavitand 1 self-assembles very efficiently in CH2Cl2 with either the monopyridinium guest 2+ or the bispyridinium guest 3(2+). In the first case a 1:1 complex is obtained, whereas in the second case both 1:1 and 2:1 host-guest complexes are observed. The association between 1 and either one of the guests causes the quenching of the cavitand fluorescence; in the case of the adduct between 1 and 3(2+), the fluorescence of the latter is also quenched. Cavitand complexation is found to affect the reduction potential values of the electroactive guests. Voltammetric and spectroelectrochemical measurements show that upon one-electron reduction both guests are released from the cavity of 1. Owing to the chemical reversibility of such redox processes, the supramolecular complexes can be re-assembled upon removal of the extra electron from the guest. Systems of this kind are promising for the construction of switchable nanoscale devices and self-assembling supramolecular materials, the structure and properties of which can be reversibly controlled by electrochemical stimuli.     

One pot grafting of tetrairon(III) single molecule magnets on silicon

Herein we report on the Si grafting of two Fe₄ derivatives, [Fe₄(Lⁱ)₂(tmhd)₆], in which tmhd is 2,2,6,6-tetramethylheptane-3,5-dionate and H₃Lⁱ = R–C(CH₂OH)₃ is a tripodal ligand with R = CH₂CH–CH₂–O–CH₂ (H₃L¹) and CH₂CH–(CH₂)₉–O–CH₂ (H₃L²). These complexes were specifically designed to be directly anchored on the H-terminated silicon surface via the hydrosilylation reaction. The complexes were grafted by a one pot route based on the photoinduced hydrosilylation followed by a ligand exchange step in the same reaction solution. The resulting decorated surfaces were characterized using X-ray photoelectron spectroscopy (XPS), attenuated total reflection infrared spectroscopy (ATR-IR) and atomic force microscopy (AFM).     

Controlling the electrophoretic mobility of single-walled carbon nanotubes: a comparison of theory and experiment

The electrophoretic mobilities of single-walled carbon nanotubes (SWNTs) in agarose gels subjected to negatively charged covalent functionalization and noncovalent anionic surfactant adsorption are compared using a simplified hydrodynamic model. Net charges are calculated on the basis of estimated friction coefficients for cylindrical rodlike particles. The effects of functionalization with negatively charged 4-hydroxybenzene diazonium and anionic sodium cholate are quantified and compared with model predictions. The adsorption of Na+ counterions into the nonionic surfactant layer adsorbed on SWNTs (Triton-X-405) is shown to induce a positive charge and reverse the mobility under select conditions. This effect has not been identified or quantified for nanoparticle systems and may be important in the processing of these systems.     

Effect of bending and torsion rigidity on self-diffusion in polymer melts: a molecular-dynamics study

Extensive molecular-dynamics simulations have been performed to study the effect of chain conformational rigidity, controlled by bending and torsion potentials, on self-diffusion in polymer melts. The polymer model employs a novel torsion potential that avoids computational singularities without the need to impose rigid constraints on the bending angles. Two power laws are traditionally used to characterize the dependence of the self-diffusion coefficient on polymer length: D proportional to N(-nu) with nu=1 for NNe (reptation regime), Ne being the entanglement length. Our simulations, at constant temperature and density, up to N=250 reveal that, as the chain rigidity increases, the exponent nu gradually increases towards nu=2.0 for NNe. The value of Ne is slightly increased from 70 for flexible chains, up to the point where the crossover becomes undefined. This behavior is confirmed also by an analysis of the bead mean-square displacement. Subsequent investigations of the Rouse modes, dynamical structure factor, and chain trajectories indicate that the pre-reptation regime, for short stiff chains, is a modified Rouse regime rather than reptation.     

Supramolecular architectures of streptavidin on biotinylated self-assembled monolayers. Tracking biomolecular reorganization after bioconjugation

In this work we have studied the supramolecular bioconjugation of streptavidin (SAv) on biotinylated self-assembled monolayers. By using the quartz crystal microbalance technique with dissipation we were able to follow in real time the biomolecular reorganization within the film. The overall process could be described as an early stage involving a significant increase in surface coverage followed by another stage where the SAv layer slowly reached the asymptotic coverage. Finally, a reorganization process takes place in the bioconjugated film. These results on the kinetics of biomolecular reorganization can be described in terms of the Lifshitz-Slyozov law. These are the first experimental results demonstrating the complexity and the different time scales involved on the bioconjugation of SAv at solid-liquid interfaces. We consider that these findings could have strong implications on the molecular design of biosensing platforms.     

Combined Short-Term Glucose Starvation and Chemotherapy in 3D Colorectal Cancer Cell Culture Decreases 14-3-3 Family Protein Expression and Phenotypic Response to Therapy

Short-term glucose starvation prior to chemotherapy has the potential to preferentially weaken cancer cells, making them more likely to succumb to treatment, while protecting normal cells. In this study, we used 3D cell cultures of colorectal cancer and assessed the effects of short-term glucose starvation and chemotherapy compared to treatment of either individually. We evaluated both phenotypic changes and protein expression levels. Our findings indicate that the combined treatment results in more significant phenotypic responses, including decreased cell viability and clonogenicity. These phenotypic responses can be explained by the decreased expression of LDHA and 14-3-3 family proteins, which were found only in the combined treatment groups. This study indicates that short-term glucose starvation has the potential to increase the efficacy of current cancer treatment regimes.

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Perfluoroaryl Bicyclic Cell‐Penetrating Peptides for Delivery of Antisense Oligonucleotides

Exon‐skipping antisense oligonucleotides are effective treatments for genetic diseases, yet exon‐skipping activity requires that these macromolecules reach the nucleus. While cell‐penetrating peptides can improve delivery, proteolytic instability often limits efficacy. It is hypothesized that the bicyclization of arginine‐rich peptides would improve their stability and their ability to deliver oligonucleotides into the nucleus. Two methods were introduced for the synthesis of arginine‐rich bicyclic peptides using cysteine perfluoroarylation chemistry. Then, the bicyclic peptides were covalently linked to a phosphorodiamidate morpholino oligonucleotide (PMO) and assayed for exon skipping activity. The perfluoroaryl cyclic and bicyclic peptides improved PMO activity roughly 14‐fold over the unconjugated PMO. The bicyclic peptides exhibited increased proteolytic stability relative to the monocycle, demonstrating that perfluoroaryl bicyclic peptides are potent and stable delivery agents.     

Styrene copolymers as pollutant adsorbents : Safe sampling volume determination

The determination of safe sampling volumes of benzene and acetone on air samplers filled with Porapak Q, Chromosorb 101, 102 and 103 is described. Two direct methods are employed; one method is based on frontal chromatography, while the second one is a concentration method followed by thermal desorption. The results are compared to those determined by the indirect pulse chromatographic method. The safe sampling volumes determined by the direct methods were in accordance. The indirect method gives slightly different values; however, this procedure is carried out at "infinite dilution". The effect of the pollutant concentration on the safe sampling volumes was also examined. The values decrease with increasing pollutant concentration.     

Brownmillerites CaFeO2.5 and SrFeO2.5 as Catalyst Support for CO Oxidation

The support material can play an important role in oxidation catalysis, notably for CO oxidation. Here, we study two materials of the Brownmillerite family, CaFeO_2.5 and SrFeO_2.5, as one example of a stoichiometric phase (CaFeO_2.5, CFO) and one existing in different modifications (SrFeO_2.75, SrFeO_2.875 and SrFeO₃, SFO). The two materials are synthesized using two synthesis methods, one bottom-up approach via a complexation route and one top-down method (electric arc fusion), allowing to study the impact of the specific surface area on the oxygen mobility and catalytic performance. CO oxidation on ¹⁸O-exchanged materials shows that oxygen from SFO participates in the reaction as soon as the reaction starts, while for CFO, this onset takes place 185 °C after reaction onset. This indicates that the structure of the support material has an impact on the catalytic performance. We report here on significant differences in the catalytic activity linked to long-term stability of CFO and SFO, which is an important parameter not only for possible applications, but equally to better understand the mechanism of the catalytic activity itself.