A remark on a maximal function over a Cantor set of directions

LetM _e ⁰ be the maximal operator over segments of length 1 with directions belonging to a Cantor set. It has been conjectured that this operator is bounded onL ². We consider a sequence of operators over finite sets of directions converging toM _e ⁰ . We improve the previous estimate for the (L ²,L ²)-norm of these particular operators. We also prove thatM _e ⁰ is bounded from some subsets ofL ² toL ². These subsets are composed of positive functions whose Fourier transforms have a very weak decay or are supported in a vertical strip. Partially supported by Spanish DGICYT grant no. PB90-0187.     

Decay of geometry for Fibonacci critical covering maps of the circle

We study the growth of Dfⁿ(f(c)) when f is a Fibonacci critical covering map of the circle with negative Schwarzian derivative, degree d2 and critical point c of order ℓ>1. As an application we prove that f exhibits exponential decay of geometry if and only if ℓ2, and in this case it has an absolutely continuous invariant probability measure, although not satisfying the so-called Collet–Eckmann condition.     

P2Y12 Purinergic Receptor and Brain Tumors: Implications on Glioma Microenvironment

Gliomas are the most common malignant brain tumors in adults, characterized by a high proliferation and invasion. The tumor microenvironment is rich in growth-promoting signals and immunomodulatory pathways, which increase the tumor’s aggressiveness. In response to hypoxia and glioma therapy, the amounts of adenosine triphosphate (ATP) and adenosine diphosphate (ADP) strongly increase in the extracellular space, and the purinergic signaling is triggered by nucleotides’ interaction in P2 receptors. Several cell types are present in the tumor microenvironment and can facilitate tumor growth. In fact, tumor cells can activate platelets by the ADP-P2Y₁₂ engagement, which plays an essential role in the cancer context, protecting tumors from the immune attack and providing molecules that contribute to the growth and maintenance of a rich environment to sustain the protumor cycle. Besides platelets, the P2Y₁₂ receptor is expressed by some tumors, such as renal carcinoma, colon carcinoma, and gliomas, being related to tumor progression. In this context, this review aims to depict the glioma microenvironment, focusing on the relationship between platelets and tumor malignancy.     

Photochemistry and phototoxicity studies of flutamide, a phototoxic anti-cancer drug

The phototoxic anti-cancer drug flutamide is photolabile under UV-B light in either aerobic or anaerobic conditions. Irradiation of a methanol solution of this drug produces several photoproducts, one by photoreduction of the nitro group, one by rupture of the aromatic-NO2 bond of the parent compound, two as a result of the rupture of the CO-NH bond and one derived from the photoreduction product by scission of the aromatic-NH2 bond. Flutamide shows a photohemolytic effect on human erythrocytes and photoinduces lipid peroxidation. Studies on peripheral blood polymorphonuclear cells (neutrophils) demonstrated the phototoxicity of flutamide as well as inhibition of the cytotoxicity respiratory burst by the photoproduct derived from its photoreduction. The results suggest that the inhibition of the respiratory burst observed in phorbol myristate acetate (PMA)-activated cells is mediated by photosensitization and concomitant singlet oxygen production and/or formation of toxic photoproducts.     

Fluorescence-labelled DNA probes to detect complementary sequences in homogeneous media

Sensitive, safe and easy-to-use probes for the detection of nucleic acids are urgently called for. To this end we are in the process of developing a fluorescence-based technique to work in homogeneous assay media. We have examined pyrene and fluorescein as fluorescent labels for natural DNA probes. A fraction of the cytosine residues of a single-stranded cDNA was randomly labelled with either pyrene or fluorescein using the bisulfite-catalyzed diamine reaction. Both fluorophores showed fluorescence quenching when the labelled probe was hybridized with its complementary strand and we describe the changes in steady-state fluorescence intensity that occurred upon hybridization. Our results demonstrate that pyrene quenching is more efficient than fluorescein quenching and thus pyrene-labelled probes are more sensitive for detecting and quantifying DNA from natural sources.     

Magnetic properties of ferromagnetic quasi-1D copper-peptide compounds: exchange interactions and very low temperature phase transitions

The magnetic properties of the Cu(II)-peptide compounds (L-tyrosyl-L-leucinato)Cu(II) and (L-tryptophyl-glycinato)Cu(II), to be identified as Cu(II)Tyr-Leu and Cu(II)Trp-Gly, respectively, have been investigated by specific heat (0.08 < T < 28 K), dc magnetization (2 < T < 80 K, with B(0) = mu(o)H < or = 9 T), and ac magnetic susceptibility (with B(0) = 0 for 0.03 < T < 3 K and B(0) up to 9 T for 2 < T < 80 K) measurements. Above approximately 1 K, the specific heat and magnetization of both compounds display a ferromagnetic (FM) spin chain behavior sustained by syn-anti carboxylate bridges connecting equatorially Cu(II) ions at about 5 A. To model this behavior, we calculated the eigenvalues of Heisenberg chains with up to 20 spins 1/2 and used the method of Bonner and Fisher. A global fit of the model to the specific heat and magnetization data gives 2J(0)/k(B) = 3.60(5) K and 2.59(5) K for the intrachain exchange interactions in Cu(II)Tyr-Leu and Cu(II)Trp-Gly, respectively (H(ex)(i,j) = -2J(0) S(i).S(j)). These values of 2J(0) are discussed in terms of structural properties of the carboxylate bridges in the two compounds. Using the parameters obtained from the global fit, we calculated isothermal susceptibilities in agreement with the ac susceptibilities measured with small applied dc magnetic fields. However, the ac susceptibility measured with applied dc fields larger than 1 T lie between the values calculated for the isothermal and adiabatic susceptibilities. At 0.16 K for Cu(II)Tyr-Leu and 0.53 K for Cu(II)Trp-Gly, the observed specific heat and magnetic susceptibility display peaks associated to three-dimensional magnetic phase transitions. The interchain exchange couplings 2J(1) producing the 3D magnetic order are ferromagnetic and have magnitudes 2J(1)/k(B) approximately 0.015 and 0.073 K for Cu(II)Tyr-Leu and Cu(II)Trp-Gly, respectively.     

Theoretical and spectroscopic study of the effect of ring substitution on the adsorption of anisole on platinum

The adsorption of anisole, 3,5-dimethylanisole, and 3,5-bis-(trifluoromethyl)-anisole on Pt(111) was studied theoretically and compared to the adsorption of benzene using relativistically corrected density functional theory. A cluster of 31 platinum atoms was used to simulate the surface. The three anisoles were found to be less strongly adsorbed than the parent molecule benzene, 3,5-bis-(trifluoromethyl)-anisole showing weakest adsorption, with an adsorption energy of only one-third that of benzene. The theoretical study was complemented by in situ ATR-IR spectroscopy of the adsorption of the anisole derivatives on a polycrystalline Pt film. The spectroscopic study indicated that the adsorption strength of the anisoles follows the same order as predicted by the calculations. In addition, catalytic hydrogenation tests showed that the propensity to aromatic ring hydrogenation can also be correlated to the mode and strength of adsorption of the anisoles. The degree of saturation followed the same order as the adsorption strength found by the calculations and indicated by spectroscopy. Although 3,5-dimethyl substitution on anisole resulted in only a partial loss of adsorption energy and reactivity toward ring hydrogenation as compared to anisole, the substitution by CF(3) groups led to a large loss of adsorption energy and complete loss of reactivity toward aromatic ring saturation. Along with the study of the substituent effect on the adsorption of aromatic molecules, the correlation between adsorption and propensity to saturation of aromatic substrates could be corroborated.     

Theoretical study on the chemical fate of adducts formed through free radical addition reactions to carotenoids

It is well known that free radicals are responsible for oxidative stress and cause numerous health disorders. As a result, the study of molecules that can scavenge free radicals is significant. One of the most important classes of free radical scavengers are carotenoids (CAR). In this work, the effectiveness of the CAR in terms of the radical adduct formation (RAF) reaction is studied using density functional theory calculations (in polar and non-polar environments). The reactions between four CAR [β-carotene (BC), zeaxanthin (ZEA), canthaxanthin (CANTA) and astaxanthin (ASTA)] with eight different radicals (^?OH, ^?OOH, ^?CH₃, ^?O–CH₃, ^?OO–CH₃, ^?SH, ^?O–CH₂–CH=CH₂, and ^?OO–CH₂–CH=CH₂), as well as substantial further reactions involved in the radical chain propagation, are analyzed. According to our results, the RAF reactions are controlled to a larger extent by the nature of the free radical than by the particular CAR they are reacting with. Thermochemistry calculations predict that each CAR molecule is able to scavenge at least two free radicals, which would lead to the termination of the radical chain process. Epoxy and diepoxy CAR species can be formed, being epoxy molecules as good free radical scavengers as their parent CAR. ASTA and CANTA are predicted to be less reactive, when reacting through RAF mechanism, than BC and ZEA.     

Nitric oxide-dependent pigment migration induced by ultraviolet radiation in retinal pigment cells of the crab Neohelice granulata

The purpose of this study was to verify the occurrence of pigment dispersion in retinal pigment cells exposed to UVA and UVB radiation, and to investigate the possible participation of a nitric oxide (NO) pathway. Retinal pigment cells from Neohelice granulata were obtained by cellular dissociation. Cells were analyzed for 30 min in the dark (control) and then exposed to 1.1 and 3.3 J cm⁻² UVA, 0.07 and 0.9 J cm⁻² UVB, 20 n m β-PDH (pigment dispersing hormone) or 10 μ m SIN-1 (NO donor). Histological analyses were performed to verify the UV effect in vivo . Cultured cells were exposed to 250 μ m L-NAME (NO synthase blocker) and afterwards were treated with UVA, UVB or β-PDH. The retinal cells in culture displayed significant pigment dispersion in response to UVA, UVB and β-PDH. The same responses to UVA and UVB were observed in vivo . SIN-1 did not induce pigment dispersion in the cell cultures. l-NAME significantly decreased the pigment dispersion induced by UVA and UVB but not by β-PDH. All retinal cells showed an immunopositive reaction against neuronal nitric oxide synthases. Therefore, UVA and UVB radiation are capable of inducing pigment dispersion in retinal pigment cells of Neohelice granulata and this dispersion may be nitric oxide synthase dependent.     

Naphthocrown‐Strapped Calix[4]pyrroles: Formation of Self‐Assembled Structures by Ion‐Pair Recognition

A new approach to the construction of self‐assembled structures is reported that is based on ion‐pair recognition. Towards this end, the calix[4]pyrrole naphthocrown‐4 hybrid structures 2 and 3 were prepared. These multitopic receptors contain recognition sites for both anions and cations. On the basis of solution‐phase ¹H NMR spectroscopic analysis and solid‐state single‐crystal X‐ray diffraction structural studies, it was established that receptors 2 and 3 are able to bind specific ion pairs with high selectivity via different binding modes. In the case of CsF and CsCl, the ion‐pair complexes formed from receptors 2 and 3 were found to self‐assemble to produce either linear supramolecular polymeric crystalline solids or nanotube‐like cyclic hexamers depending on the specific choice of ion pairs and crystallization solvents. Proton NMR studies provided evidence for solution‐phase self‐association in organic media.