A general fractional porous medium equation

A general fractional porous medium equation

An introduction to flow and transport in fractal models of porous media: Part I

This special issue gathers together a number of recent papers on fractal geometry and its applications to the modeling of flow and transport in porous media. The aim is to provide a systematic approach for analyzing the statics and dynamics of fluids in fractal porous media by means of theory, modeling and experimentation. The topics covered include lacunarity analyses of multifractal and natural grayscale patterns, random packing's of self-similar pore/particle size distributions, Darcian and non-Darcian hydraulic flows, diffusion within fractals, models for the permeability and thermal conductivity of fractal porous media and hydrophobicity and surface erosion properties of fractal structures.

Design, Technology and Characterization of Micromechanised Sensors and Actuators for Harsh Environments

Los sistemas micro electro mecánicos (MEMS) han demostrado ser una exitosa familia de dispositivos que pueden usarse como plataforma para el desarrollo de dispositivos con aplicaciones en óptica, comunicaciones, procesado de señal y sensorización. Los dispositivos MEMS estándar suelen estar fabricados usando tecnología de silicio. Sin embargo, el rendimiento de estos MEMS se puede mejorar si se usan otros materiales. Por ejemplo, el diamante nanocristalino (NCD) ofrece unas excelentes propiedades mecánicas, transparencia y una superficie fácil de funcionalizar. Por otro lado, el sistema de materiales (In; Ga; Al)N, los materiales IIIN, se pueden usar para producir estructuras monocristalinas con alta sensibilidad mecánica y química. Además, el AlN se puede depositar por pulverización catódica reactiva sobre varios substratos, incluyendo NCD, para formar capas policristalinas orientadas con alta respuesta piezoeléctrica. Adicionalmente, tanto el NCD como los materiales III-N muestran una gran estabilidad térmica y química, lo que los hace una elección idónea para desarrollar dispositivos para aplicaciones para alta temperatura, ambientes agresivos e incluso para aplicaciones biocompatibles. En esta tesis se han usado estos materiales para el diseño y medición de demostradores tecnológicos. Se han perseguido tres objetivos principales: _ Desarrollo de unos procesos de fabricación apropiados. _ Medición de las propiedades mecánicas de los materiales y de los factores que limitan el rendimiento de los dispositivos. _ Usar los datos medidos para desarrollar dispositivos demostradores complejos. En la primera parte de esta tesis se han estudiado varias técnicas de fabricación. La estabilidad de estos materiales impide el ataque y dificulta la producción de estructuras suspendidas. Los primeros capítulos de esta disertación se dedican al desarrollo de unos procesos de transferencia de patrones por ataque seco y a la optimización del ataque húmedo sacrificial de varios substratos propuestos. Los resultados de los procedimientos de ataque se presentan y se describe la optimización de las técnicas para la fabricación de estructuras suspendidas de NCD y materiales III-N. En un capítulo posterior se estudia el crecimiento de AlN por pulverización catódica. Como se ha calculado en esta disertación para obtener una actuación eficiente de MEMS, las capas de AlN han de ser finas, típicamente d < 200 nm, lo que supone serias dificultades para la obtención de capas orientadas con respuesta piezoeléctrica. Las condiciones de depósito se han mapeado para identificar las fronteras que proporcionan el crecimiento de material orientado desde los primeros pasos del proceso. Además, durante la optimización de los procesos de ataque se estudió un procedimiento para fabricar películas de GaN nanoporoso. Estas capas porosas pueden servir como capas sacrificiales para la fabricación de estructuras suspendidas de GaN con baja tensión residual o como capas para mejorar la funcionalización superficial de sensores químicos o biológicos. El proceso de inducción de poros se discutirá y también se presentarán experimentos de ataque y funcionalización. En segundo lugar, se han determinado las propiedades mecánicas del NCD y de los materiales III-N. Se han fabricado varias estructuras suspendidas para la medición del módulo de Young y de la tensión residual. Además, las estructuras de NCD se midieron en resonancia para calcular el rendimiento de los dispositivos en términos de frecuencia y factor de calidad. Se identificaron los factores intrínsecos y extrínsecos que limitan ambas figuras de mérito y se han desarrollado modelos para considerar estas imperfecciones en las etapas de diseño de los dispositivos. Por otra parte, los materiales III-N normalmente presentan grandes gradientes de deformación residual que causan la deformación de las estructuras al ser liberadas. Se han medido y modelado estos efectos para los tres materiales binarios del sistema para proporcionar puntos de interpolación que permitan predecir las características de las aleaciones del sistema III-N. Por último, los datos recabados se han usado para desarrollar modelos analíticos y numéricos para el diseño de varios dispositivos. Se han estudiado las propiedades de transducción y se proporcionan topologías optimizadas. En el último capítulo de esta disertación se presentan diseños optimizados de los siguientes dispositivos: _ Traviesas y voladizos de AlN=NCD con actuación piezoeléctrica aplicados a nanoconmutadores de RF para señales de alta potencia. _ Membranas circulares de AlN=NCD con actuación piezoeléctrica aplicadas a lentes sintonizables. _ Filtros ópticos Fabry-Pérot basados en cavidades aéreas y membranas de GaN actuadas electrostáticamente. En resumen, se han desarrollado unos nuevos procedimientos optimizados para la fabricación de estructuras de NCD y materiales III-N. Estas técnicas se han usado para producir estructuras que llevaron a la determinación de las principales propiedades mecánicas y de los parámetros de los dispositivos necesarios para el diseño de MEMS. Finalmente, los datos obtenidos se han usado para el diseño optimizado de varios dispositivos demostradores. ABSTRACT Micro Electro Mechanical Systems (MEMS) have proven to be a successful family of devices that can be used as a platform for the development of devices with applications in optics, communications, signal processing and sensorics. Standard MEMS devices are usually fabricated using silicon based materials. However, the performance of these MEMS can be improved if other material systems are used. For instance, nanocrystalline diamond (NCD) offers excellent mechanical properties, optical transparency and ease of surface functionalization. On the other hand, the (In; Ga; Al)N material system, the III-N materials, can be used to produce single crystal structures with high mechanical and chemical sensitivity. Also, AlN can be deposited by reactive sputtering on various substrates, including NCD, to form oriented polycrystalline layers with high piezoelectric response. In addition, both NCD and III-N materials exhibit high thermal and chemical stability, which makes these material the perfect choice for the development of devices for high temperatures, harsh environments and even biocompatible applications. In this thesis these materials have been used for the design and measurement of technological demonstrators. Three main objectives have been pursued: _ Development of suitable fabrication processes. _ Measurement of the material mechanical properties and device performance limiting factors. _ Use the gathered data to design complex demonstrator devices. In a first part of the thesis several fabrication processes have been addressed. The stability of these materials hinders the etching of the layers and hampers the production of free standing structures. The first chapters of this dissertation are devoted to the development of a dry patterning etching process and to sacrificial etching optimization of several proposed substrates. The results of the etching processes are presented and the optimization of the technique for the manufacturing of NCD and III-N free standing structures is described. In a later chapter, sputtering growth of thin AlN layers is studied. As calculated in this dissertation, for efficient MEMS piezoelectric actuation the AlN layers have to be very thin, typically d < 200 nm, which poses serious difficulties to the production of c-axis oriented material with piezoelectric response. The deposition conditions have been mapped in order to identify the boundaries that give rise to the growth of c-axis oriented material from the first deposition stages. Additionally, during the etching optimization a procedure for fabricating nanoporous GaN layers was also studied. Such porous layers can serve as a sacrificial layer for the release of low stressed GaN devices or as a functionalization enhancement layer for chemical and biological sensors. The pore induction process will be discussed and etching and functionalization trials are presented. Secondly, the mechanical properties of NCD and III-N materials have been determined. Several free standing structures were fabricated for the measurement of the material Young’s modulus and residual stress. In addition, NCD structures were measured under resonance in order to calculate the device performance in terms of frequency and quality factor. Intrinsic and extrinsic limiting factors for both figures were identified and models have been developed in order to take into account these imperfections in the device design stages. On the other hand, III-N materials usually present large strain gradients that lead to device deformation after release. These effects have been measured and modeled for the three binary materials of the system in order to provide the interpolation points for predicting the behavior of the III-N alloys. Finally, the gathered data has been used for developing analytic and numeric models for the design of various devices. The transduction properties are studied and optimized topologies are provided. Optimized design of the following devices is presented at the last chapter of this dissertation: _ AlN=NCD piezoelectrically actuated beams applied to RF nanoswitches for large power signals. _ AlN=NCD piezoelectrically actuated circular membranes applied to tunable lenses. _ GaN based air gap tunable optical Fabry-Pérot filters with electrostatic actuation. On the whole, new optimized fabrication processes has been developed for the fabrication of NCD and III-N MEMS structures. These processing techniques was used to produce structures that led to the determination of the main mechanical properties and device parameters needed for MEMS design. Lastly, the gathered data was used for the design of various optimized demonstrator devices.

Binary metal oxides for composite ultrafiltration membranes

A new ultrafiltration membrane was developed by the incorporation of binary metal oxides inside polyethersulfone. Physico-chemical characterization of the binary metal oxides demonstrated that the presence of Ti in the TiO2?ZrO2 system results in an increase of the size of the oxides, and also their dispersity. The crystalline phases of the synthesized binary metal oxides were identified as srilankite and zirconium titanium oxide. The effect of the addition of ZrO2 can be expressed in terms of the inhibition of crystal growth of anocrystalline TiO2 during the synthesis process. For photocatalytic applications the band gap of the synthesized semiconductors was determined, confirming a gradual increase (blue shift) in the band gap as the amount of Zr loading increases. Distinct distributions of binary metal oxides were found along the permeation axis for the synthesized membranes. Particles with Ti are more uniformly dispersed throughout the membrane cross-section. The physico-chemical characterization of membranes showed a strong correlation between some key membrane properties and the spatial particle distribution in the membrane structure. The proximity of metal oxide fillers to the membrane surface determines the hydrophilicity and porosity of modified membranes. Membranes incorporating binary metal oxides were found to be promising candidates for wastewater treatment by ultrafiltration, considering the observed improvement influx and anti-fouling properties of doped membranes. Multi-run fouling tests of doped membranes confirmed the stability of permeation through membranes embedded with binary TiO2?ZrO2 particles.

The helical domain of intestinal fatty acid binding protein is critical for collisional transfer of fatty acids to phospholipid membranes

Fatty acid binding proteins (FABPs) exhibit a β-barrel topology, comprising 10 antiparallel β-sheets capped by two short α-helical segments. Previous studies suggested that fatty acid transfer from several FABPs occurs during interaction between the protein and the acceptor membrane, and that the helical domain of the FABPs plays an important role in this process. In this study, we employed a helix-less variant of intestinal FABP (IFABP-HL) and examined the rate and mechanism of transfer of fluorescent anthroyloxy fatty acids (AOFA) from this protein to model membranes in comparison to the wild type (wIFABP). In marked contrast to wIFABP, IFABP-HL does not show significant modification of the AOFA transfer rate as a function of either the concentration or the composition of the acceptor membranes. These results suggest that the transfer of fatty acids from IFABP-HL occurs by an aqueous diffusion-mediated process, i.e., in the absence of the helical domain, effective collisional transfer of fatty acids to membranes does not occur. Binding of wIFABP and IFABP-HL to membranes was directly analyzed by using a cytochrome c competition assay, and it was shown that IFABP-HL was 80% less efficient in preventing cytochrome c from binding to membranes than the native IFABP. Collectively, these results indicate that the α-helical region of IFABP is involved in membrane interactions and thus plays a critical role in the collisional mechanism of fatty acid transfer from IFABP to phospholipid membranes.

Inhibition of the electrostatic interaction between β-amyloid peptide and membranes prevents β-amyloid-induced toxicity

The accumulation of β-amyloid peptides (Aβ) into senile plaques is one of the hallmarks of Alzheimer disease. Aggregated Aβ is toxic to cells in culture and this has been considered to be the cause of neurodegeneration that occurs in the Alzheimer disease brain. The discovery of compounds that prevent Aβ toxicity may lead to a better understanding of the processes involved and ultimately to possible therapeutic drugs. Low nanomolar concentrations of Aβ1-42 and the toxic fragment Aβ25-35 have been demonstrated to render cells more sensitive to subsequent insults as manifested by an increased sensitivity to formazan crystals following MTT (3-[4,5-dimethylthiazol-2-yl]-2,5-diphenyltetrazolium bromide) reduction. Formation of the toxic β-sheet conformation by Aβ peptides is increased by negatively charged membranes. Here we demonstrate that phloretin and exifone, dipolar compounds that decrease the effective negative charge of membranes, prevent association of Aβ1-40 and Aβ25-35 to negatively charged lipid vesicles and Aβ induced cell toxicity. These results suggest that Aβ toxicity is mediated through a nonspecific physicochemical interaction with cell membranes.

Role of lipid polymorphism in G protein-membrane interactions: Nonlamellar-prone phospholipids and peripheral protein binding to membranes

Heterotrimeric G proteins (peripheral proteins) conduct signals from membrane receptors (integral proteins) to regulatory proteins localized to various cellular compartments. They are in excess over any G protein-coupled receptor type on the cell membrane, which is necessary for signal amplification. These facts account for the large number of G protein molecules bound to membrane lipids. Thus, the protein-lipid interactions are crucial for their cellular localization, and consequently for signal transduction. In this work, the binding of G protein subunits to model membranes (liposomes), formed with defined membrane lipids, has been studied. It is shown that although G protein α-subunits were able to bind to lipid bilayers, the presence of nonlamellar-prone phospholipids (phosphatidylethanolamines) enhanced their binding to model membranes. This mechanism also appears to be used by other (structurally and functionally unrelated) peripheral proteins, such as protein kinase C and the insect protein apolipophorin III, indicating that it could constitute a general mode of protein-lipid interactions, relevant in the activity and translocation of some peripheral (amphitropic) proteins from soluble to particulate compartments. Other factors, such as the presence of cholesterol or the vesicle surface charge, also modulated the binding of the G protein subunits to lipid bilayers. Conversely, the binding of G protein-coupled receptor kinase 2 and the G protein β-subunit to liposomes was not increased by hexagonally prone lipids. Their distinct interactions with membrane lipids may, in part, explain the different cellular localizations of all of these proteins during the signaling process.

High-frequency, spin-label EPR of nonaxial lipid ordering and motion in cholesterol-containing membranes

The EPR spectra of spin-labeled lipid chains in fully hydrated bilayer membranes of dimyristoyl phosphatidylcholine containing 40 mol % of cholesterol have been studied in the liquid-ordered phase at a microwave radiation frequency of 94 GHz. At such high field strengths, the spectra should be optimally sensitive to lateral chain ordering that is expected in the formation of in-plane domains. The high-field EPR spectra from random dispersions of the cholesterol-containing membranes display very little axial averaging of the nitroxide g-tensor anisotropy for lipids spin labeled toward the carboxyl end of the sn-2 chain (down to the 8-C atom). For these positions of labeling, anisotropic 14N-hyperfine splittings are resolved in the gzz and gyy regions of the nonaxial EPR spectra. For positions of labeling further down the lipid chain, toward the terminal methyl group, the axial averaging of the spectral features systematically increases and is complete at the 14-C atom position. Concomitantly, the time-averaged 〈Azz〉 element of the 14N-hyperfine tensor decreases, indicating that the axial rotation at the terminal methyl end of the chains arises from correlated torsional motions about the bonds of the chain backbone, the dynamics of which also give rise to a differential line broadening of the 14N-hyperfine manifolds in the gzz region of the spectrum. These results provide an indication of the way in which lateral ordering of lipid chains in membranes is induced by cholesterol.

In vivo zippering of inner and outer mitochondrial membranes by a stable translocation intermediate

It was previously assumed that the import of cytoplasmically synthesized precursor proteins into mitochondria occurs through a single structure spanning both outer and inner membranes at contact sites. Based on recent findings, however, the two membranes appear to contain independent translocation elements that reversibly cooperate during protein import. This feature makes it difficult to generate a means of isolating a fully integrated and functional translocation complex. To study these independent translocases in vitro and in vivo, we have constructed a chimeric protein consisting of an N-terminal authentic mitochondrial precursor (delta1-pyrroline-5-carboxylate dehydrogenase) linked, through glutathione S-transferase, to IgG binding domains derived from staphylococcal protein A. This construct becomes trapped en route to the matrix, spanning both outer and inner membranes in such a way that the entire signal-less delta1-pyrroline-5-carboxylate dehydrogenase moiety reaches the matrix, while only the folded protein A domain remains outside. During in vivo import of this precursor, outer and inner membranes of yeast mitochondria become progressively “zippered” together, forming long stretches of close contact. Using this novel intermediate, the outer and inner mitochondrial membrane channels, which normally interact only transiently, can be tightly joined (both in vitro and in vivo), forming a stable association. This suggests a method for isolating the functional translocation complex as a single entity.

The dimensions of the protein import channels in the outer and inner mitochondrial membranes

Most mitochondrial proteins are imported into mitochondria through transmembrane channels composed largely, and perhaps exclusively, of proteins. We have determined the effective internal diameter of the protein import channel in the mitochondrial outer membrane to be between 20 Å and 26 Å during translocation. The diameter of the import channel in the inner membrane is smaller than the diameter of the outer membrane import channel. These results were obtained by measuring the effect of rigid steric bulk introduced into precursor proteins on import.

Specific binding of proinsulin C-peptide to human cell membranes

Recent reports have demonstrated beneficial effects of proinsulin C-peptide in the diabetic state, including improvements of kidney and nerve function. To examine the background to these effects, C-peptide binding to cell membranes has been studied by using fluorescence correlation spectroscopy. Measurements of ligand–membrane interactions at single-molecule detection sensitivity in 0.2-fl confocal volume elements show specific binding of fluorescently labeled C-peptide to several human cell types. Full saturation of the C-peptide binding to the cell surface is obtained at low nanomolar concentrations. Scatchard analysis of binding to renal tubular cells indicates the existence of a high-affinity binding process with Kass > 3.3 × 109 M−1. Addition of excess unlabeled C-peptide is accompanied by competitive displacement, yielding a dissociation rate constant of 4.5 × 10−4 s−1. The C-terminal pentapeptide also displaces C-peptide bound to cell membranes, indicating that the binding occurs at this segment of the ligand. Nonnative d-C-peptide and a randomly scrambled C-peptide do not compete for binding with the labeled C-peptide, nor were crossreactions observed with insulin, insulin-like growth factor (IGF)-I, IGF-II, or proinsulin. Pretreatment of cells with pertussis toxin, known to modify receptor-coupled G proteins, abolishes the binding. It is concluded that C-peptide binds to specific G protein-coupled receptors on human cell membranes, thus providing a molecular basis for its biological effects.

Network formation of lipid membranes: Triggering structural transitions by chain melting

Phospholipids when dispersed in excess water generally form vesicular membrane structures. Cryo-transmission and freeze-fracture electron microscopy are combined here with calorimetry and viscometry to demonstrate the reversible conversion of phosphatidylglycerol aqueous vesicle suspensions to a three-dimensional structure that consists of extended bilayer networks. Thermodynamic analysis indicates that the structural transitions arise from two effects: (i) the enhanced membrane elasticity accompanying the lipid state fluctuations on chain melting and (ii) solvent-associated interactions (including electrostatics) that favor a change in membrane curvature. The material properties of the hydrogels and their reversible formation offer the possibility of future applications, for example in drug delivery, the design of structural switches, or for understanding vesicle fusion or fission processes.

The terminal tail region of a yeast myosin-V mediates its attachment to vacuole membranes and sites of polarized growth

The Saccharomyces cerevisiae myosin-V, Myo2p, has been implicated in the polarized movement of several organelles and is essential for yeast viability. We have shown previously that Myo2p is required for the movement of a portion of the lysosome (vacuole) into the bud and consequently for proper inheritance of this organelle during cell division. Class V myosins have a globular carboxyl terminal tail domain that is proposed to mediate localization of the myosin, possibly through interaction with organelle-specific receptors. Here we describe a myo2 allele whose phenotypes support this hypothesis. vac15–1/myo2–2 has a single mutation in this globular tail domain, causing defects in vacuole movement and inheritance. Although a portion of wild-type Myo2p fractionates with the vacuole, the myo2–2 gene product does not. In addition, the mutant protein does not concentrate at sites of active growth, the predominant location of wild-type Myo2p. Although deletion of the tail domain is lethal, the myo2–2 gene product retains the essential functions of Myo2p. Moreover, myo2–2 does not cause the growth defects and lethal genetic interactions seen in myo2–66, a mutant defective in the actin-binding domain. These observations suggest that the myo2–2 mutation specifically disrupts interactions with selected myosin receptors, namely those on the vacuole membrane and those at sites of polarized growth.

ADP-ribosylation factor and phosphatidic acid levels in Golgi membranes during budding of coatomer-coated vesicles

The finding that ADP-ribosylation factor (ARF) can activate phospholipase D has led to debate as to whether ARF recruits coat proteins through direct binding or indirectly by catalytically increasing phosphatidic acid production. Here we test critical aspects of these hypotheses. We find that Golgi membrane phosphatidic acid levels do not rise—in fact they decline—during cell-free budding reactions. We confirm that the level of membrane-bound ARF can be substantially reduced without compromising coat assembly [Ktistakis, N. T., Brown, H. A., Waters, M. G., Sternweis, P. C. & Roth, M. G. (1996) J. Cell Biol. 134, 295–306], but find that under all conditions, ARF is present on the Golgi membrane in molar excess over bound coatomer. These results do not support the possibility that the activation of coat assembly by ARF is purely catalytic, and they are consistent with ARF forming direct interactions with coatomer. We suggest that ARF, like many other G proteins, is a multifunctional protein with roles in trafficking and phospholipid signaling.

Peroxynitrite rapidly permeates phospholipid membranes

Peroxynitrite (ONOO−) is a potent oxidant implicated in a number of pathophysiological processes. The activity of ONOO− is related to its accessibility to biological targets before its spontaneous decomposition (t1/2 ≈ 1 s at pH 7.4, 37°C). Using model phospholipid vesicular systems and manganese porphyrins as reporter molecules, we demonstrated that ONOO− freely crosses phospholipid membranes. The calculated permeability coefficient for ONOO− is ≈8.0 × 10−4 cm⋅s−1, which compares well with that of water and is ≈400 times greater than that of superoxide. We suggest that ONOO− is a significant biological effector molecule not only because of its reactivity but also because of its high diffusibility.