From exponential to linear growth in polyelectrolyte multilayers

There exist two types of polyelectrolyte multilayers: those whose thickness increases linearly with the number of deposition steps, which are nicely structured, and those whose thickness increases exponentially, which resembles hydrogels. This simple picture has recently slightly evolved with the finding that some exponentially growing films enter into a linear growth phase after a certain number of deposition steps. In this study, we investigate the buildup process of hyaluronic acid/poly(L-lysine) (HA/PLL) multilayers that constitute one of the best known exponentially growing systems. The films are built by using two deposition methods: the well-known dipping method and the more recent spraying method where the polyelectrolyte solutions are sprayed alternately onto a vertical substrate. The goal of this study is twofold. First, we investigate the influence of the main parameters (i.e., spraying rate and spraying time) of the spraying method on the film growth process. We find that, as for the dipping method, the film thickness first evolves exponentially with the number of deposition steps, and after a given number of deposition steps, it follows a linear evolution. We find that similar behavior is observed with the dipping method. Second, because the spraying method allows the very fine variation of the different parameters of the buildup, we use this method to investigate the exponential-to-linear transition. We find that this transition always takes place after about 12 deposition steps whatever the values of the parameters controlling the deposition process. We discuss our results in light of a model proposed by Hübsch et al. (Hübsch, E.; Ball, V.; Senger, B.; Decher, G.; Voegel, J. C.; Schaaf, P. Langmuir 2004, 20, 1980-1985) and later by Salom?ki et al. (Salom?ki, M.; Vinokurov, I. A.; Kankare, J. Langmuir 2005, 21, 11232-11240) in which it is assumed that the exponential-to-linear transition is due to a film restructuring that progressively forbids the diffusion of one of the polyelectrolytes constituting the film over part of the film. This "forbidden" zone then grows with the number of deposition steps so that the outer zone of the film that is still concerned with diffusion keeps a constant thickness and moves upward as the total film thickness increases.     

Convergence to equilibrium for delay-diffusion equations with small delay

It is shown that for scalar dissipative delay-diffusion equationsu _t–u=f(u(t),u(t–)) with a small delay, all solutions are asymptotic to the set of equilibria ast tends to infinity.     

Local lagrange interpolation with cubic splines on tetrahedral partitions

We describe an algorithm for constructing a Lagrange interpolation pair based on C¹ cubic splines defined on tetrahedral partitions. In particular, given a set of points , we construct a set P containing and a spline space based on a tetrahedral partition whose set of vertices include such that interpolation at the points of P is well-defined and unique. Earlier results are extended in two ways: (1) here we allow arbitrary sets , and (2) the method provides optimal approximation order of smooth functions.     

Study of the development of chemoresistance in melanoma cell lines using proteome analysis

Malignant melanomas have poor prognosis since treatment with anti-neoplastic agents is mostly ineffective. The biological mechanisms of this strong intrinsic therapy resistance are unknown. In order to identify new molecular factors potentially associated with the drug-resistant phenotype of malignant melanoma, a panel of human melanoma cell variants exhibiting low and high levels of resistance to four commonly used anticancer drugs in melanoma treatment, i.e., vindesine, etoposide, cisplatin, and fotemustine, was characterized using proteomic tools (two-dimensional electrophoresis for protein fractionation and matrix assisted laser desorption/ionization-time of flight (MALDI-TOF)-mass spectrometry for protein identification). In the neutral and weak acidic milieu (pH 4.0-8.0) a total number of 14 proteins showed alterations in expression whereas 20 proteins were differentially expressed in the basic milieu (pH 8.0-11.0). Besides proteins with unknown physiologic function, several factors were identified that show chaperone activity. Moreover, proteins involved in drug detoxification, metabolism, and regulation of apoptotic pathways could be identified. The possible role of these proteins in the development of chemoresistance is discussed, although detailed functional tests with these proteins have still to be performed. Nevertheless, it is clear that this proteomic approach for studying chemoresistance phenomena is a prerequisite before further investigation can yield insight into the biology and development of drug resistance in malignant melanoma.     

Direct Microfabrication of Topographical and Chemical Cues for the Guided Growth of Neural Cell Networks on Polyamidoamine Hydrogels

Cell patterning is an important tool for organizing cells in surfaces and to reproduce in a simple way the tissue hierarchy and complexity of pluri‐cellular life. The control of cell growth, proliferation and differentiation on solid surfaces is consequently important for prosthetics, biosensors, cell‐based arrays, stem cell therapy and cell‐based drug discovery concepts. We present a new electron beam lithography method for the direct and simultaneous fabrication of sub‐micron topographical and chemical patterns, on a biocompatible and biodegradable PAA hydrogel. The localized e‐beam modification of a hydrogel surface makes the pattern able to adsorb proteins in contrast with the anti‐fouling surface. By also exploiting the selective attachment, growth and differentiation of PC12 cells, we fabricated a neural network of single cells connected by neuritis extending along microchannels. E‐beam microlithography on PAA hydrogels opens up the opportunity of producing multifunctional microdevices incorporating complex topographies, allowing precise control of the growth and organization of individual cells.

     

Derivation of nonlinear bending theory for shells from three-dimensional nonlinear elasticity by Gamma-convergence

We show that the nonlinear bending theory of shells arises as a Γ-limit of three-dimensional nonlinear elasticity. To cite this article: G. Friesecke et al., C. R. Acad. Sci. Paris, Ser. I 336 (2003).