Normalization of bundle holomorphic contractions and applications to dynamics

We establish a Poincar\'e-Dulac theorem for sequences (G_n)_n of holomorphic contractions whose differentials d_0 G_n split regularly. The resonant relations determining the normal forms hold on the moduli of the exponential rates of contraction. Our results are actually stated in the framework of bundle maps. Such sequences of holomorphic contractions appear naturally as iterated inverse branches of endomorphisms of CP(k). In this context, our normalization result allows to precisely estimate the distortions of ellipsoids along typical orbits. As an application, we show how the Lyapunov exponents of the equilibrium measure are approximated in terms of the multipliers of the repulsive cycles.Comment: 29 pages, references added, to appear in Ann. Inst. Fourie

Effects of radio-frequency fields on bacterial cell membranes and nematode temperature-sensitive mutants

Membrane-related bioeffects have been reported in response to both radio-frequency (RF) and extremely low-frequency (ELF) electromagnetic fields (EMFs), particularly in neural cells. We have tested whether RF fields might cause inner membrane leakage in ML35 E. coli cells, which express β-galactosidase (lacZ) constitutively, but lack the lacY permease required for substrate entry. The activity of lacZ (indicating substrate leakage through the inner cell membrane) was increased only slightly by RF exposure (1 GHz, 0.5 W) over 45 min. Since lacZ activity showed no further increase with a longer exposure time of 90 min, this suggests that membrane permeability per se is not significantly affected by RF fields, and that slight heating (≤ 0.1°C) could account for this small difference. Temperature-sensitive (ts) mutants of the nematode, Caenorhabditis elegans, are wild-type at 15°C but develop the mutant phenotype at 25°C; an intermediate temperature of 21°C results in a reproducible mixture of both phenotypes. For two ts mutants affecting transmembrane receptors (TRA-2 and GLP-1), RF exposure for 24 h during the thermocritical phase strongly shifts the phenotype mix at 21°C towards the mutant end of the spectrum. For ts mutants affecting nuclear proteins, such phenotype shifts appear smaller (PHA-1) or non-significant (LIN-39), apparently confirming suggestions that RF power is dissipated mainly in the plasma membrane of cells. However, these phenotype shifts are no longer seen when microwave treatment is applied at 21°C in a modified exposure apparatus that minimises the temperature difference between sham and exposed conditions. Like other biological effects attributed to microwaves in the C. elegans system, phenotype shifts in ts mutants appear to be an artefact caused by very slight heating

Velocity profiles in shear-banding wormlike micelles

Using Dynamic Light Scattering in heterodyne mode, we measure velocity profiles in a much studied system of wormlike micelles (CPCl/NaSal) known to exhibit both shear-banding and stress plateau behavior. Our data provide evidence for the simplest shear-banding scenario, according to which the effective viscosity drop in the system is due to the nucleation and growth of a highly sheared band in the gap, whose thickness linearly increases with the imposed shear rate. We discuss various details of the velocity profiles in all the regions of the flow curve and emphasize on the complex, non-Newtonian nature of the flow in the highly sheared band.Comment: 4 pages, 5 figures, submitted to Phys. Rev. Let

Endothelial Cell Thrombin Receptors and PAR-2 TWO PROTEASE-ACTIVATED RECEPTORS LOCATED IN A SINGLE CELLULAR ENVIRONMENT

Human endothelial cells express thrombin receptors and PAR-2, the two known members of the family of protease-activated G protein-coupled receptors. Because previous studies have shown that the biology of the human thrombin receptor varies according to the cell in which it is expressed, we have taken advantage of the presence of both receptors in endothelial cells to examine the enabling and disabling interactions with candidate proteases likely to be encountered in and around the vascular space to compare the responses elicited by the two receptors when they are present in the same cell and to compare the mechanisms of thrombin receptor and PAR-2 clearance and replacement in a common cellular environment. Of the proteases that were tested, only trypsin activated both receptors. Cathepsin G, which disables thrombin receptors, had no effect on PAR-2, while urokinase, kallikrein, and coagulation factors IXa, Xa, XIa, and XIIa neither substantially activated nor noticeably disabled either receptor. Like thrombin receptors, activation of PAR-2 caused pertussis toxin-sensitive phospholipase C activation as well as activation of phospholipase A2, leading to the release of PGI2. Concurrent activation of both receptors caused a greater response than activation of either alone. It also abolished a subsequent response to the PAR-2 agonist peptide, SLIGRL, while only partially inhibiting the response to the agonist peptide, SFLLRN, which activates both receptors. After proteolytic or nonproteolytic activation, PAR-2, like thrombin receptors, was cleared from the endothelial cell surface and then rapidly replaced with new receptors by a process that does not require protein synthesis. Selective activation of either receptor had no effect on the clearance of the other. These results suggest that the expression of both thrombin receptors and PAR-2 on endothelial cells serves more to extend the range of proteases to which the cells can respond than it does to extend the range of potential responses. The results also show that proteases that can disable these receptors can distinguish between them, just as do most of the proteases that activate them. Finally, the residual response to SFLLRN after activation of thrombin receptors and PAR-2 raises the possibility that a third, as yet unidentified member of this family is expressed on endothelial cells, one that is activated by neither thrombin nor trypsin

Shear-melting of a hexagonal columnar crystal by proliferation of dislocations

A hexagonal columnar crystal undergoes a shear-melting transition above a critical shear rate or stress. We combine the analysis of the shear-thinning regime below the melting with that of synchrotron X-ray scattering data under shear and propose the melting to be due to a proliferation of dislocations, whose density is determined by both techniques to vary as a power law of the shear rate with a 2/3 exponent, as expected for a creep model of crystalline solids. Moreover, our data suggest the existence under shear of a line hexatic phase, between the columnar crystal and the liquid phase

Electrophoretic deposition of Sr-containing mesoporous bioactive glass particles produced by spray-drying

Introduction Mesoporous bioactive glasses (MBGs) are gaining increasing interest in the biomedical field thanks to their exceptional textural characteristics (high surface area, high pore volume and highly ordered mesoporosity). These properties lead to an improved apatite kinetics formation, which allow these glasses to be successfully applied in bone tissue regeneration [1]. In this work we adopted an aerosol-based spray drying process in order to have high control and reproducibility over the morphology of particles. In order to increase their regenerative potential, the particles have been doped with strontium, element known for its osteogenic and bone antiresorptive properties [2]. Later the particles have been deposed by electrophoretic deposition (EPD) on glass-ceramic scaffolds fabricated by the polymer sponge replication method. EPD is a versatile technique which allows an easy control of the thickness of the deposited film through simple adjustment of the applied voltage and the deposition time. The scaffolds, based on a quaternary silicate glass (SCNA, SiO2–CaO–Na2O–Al2O3 oxide system), have good mechanical properties but low bioactivity [3]. Thanks to MBG particle deposition, they acquire a pronounced bioactive behaviour, thus becoming an excellent solution for bone tissue regeneration. Results and Discussion MBGs synthesized with the aerosol-based spray-drying process have a basic composition on the SiO2-CaO system and have been doped with the 1% molar of strontium (SD_Sr1). FESEM image of particles shows micro-sized spherical particles, with size mostly ranging between 500 nm and 5 µm. N2 adsorption analysis gives back a high specific surface area value, 160 m2/g, and a pore size distribution between 5 and 9 nm, which confirms the mesoporosity of the sample. Strontium incorporation inside the binary composition does not modify the bioactive behaviour of the glass: after 14 days in SBF nanoparticles are completely covered by a layer of hydroxyapatite.The EDS quantitative analysis shows that the amount of strontium effectively incorporated in the microparticles was 70% of the theoretical one, probably because of the high dimension of the ion which hinders its entrance into the glass network. Nevertheless, most of the Sr incorporated has been released after 14 days of immersion in SBF, as the coupled plasma-atomic emission spectrometry (ICP-AES) reveals. On the basis of literature data, the released concentrations are suitable for inducing osteogenesis [4]. EPD has been performed in ethanol, applying a voltage of 120 V for 5 minutes. The scaffolds, being not conductive, have been suspended between two stainless steel electrodes through a clamp. A dispersant (TEA, triethanolamine) has been used to keep the particles in suspension during the whole deposition time. The deposited layer was abundant but not uniform on the scaffold surface. After immersion for 7 days in SBF, hydroxyapatite formation has been observed on the surface of the microparticles deposited on the scaffold struts. This demonstrates that MBGs not only maintain their bioactivity after deposition but also transfer this property to scaffolds. Conclusions MBGs synthetized with aerosol-based spray-drying process and doped with strontium have excellent textural properties and a bioactive behaviour. After electrophoretic deposition, they maintain these properties and consequently they improve the bioactivity of SCNA scaffolds, which initially are almost biologically inert. In this way we demonstrate that it is possible to obtain a successful construct for bone tissue engineering with both excellent regenerative and mechanical properties

Entropic phase separation of linked beads

We study theoretically a model system of a transient network of microemulsion droplets connected by telechelic polymers and explain recent experimental findings. Despite the absence of any specific interactions between either the droplets or polymer chains, we predict that as the number of polymers per drop is increased, the system undergoes a first order phase separation into a dense, highly connected phase, in equilibrium with dilute droplets, decorated by polymer loops. The phase transition is purely entropic and is driven by the interplay between the translational entropy of the drops and the configurational entropy of the polymer connections between them. Because it is dominated by entropic effects, the phase separation mechanism of the system is extremely robust and does not depend on the particlular physical realization of the network. The discussed model applies as well to other polymer linked particle aggregates, such as nano-particles connected with short DNA linkers