Discrete linear stability and sensitivity analysis of fluid flows

Este trabajo presenta un método discreto para el cálculo de estabilidad hidrodinámica y análisis de sensibilidad a perturbaciones externas para ecuaciones diferenciales y en particular para las ecuaciones de Navier-Stokes compressible. Se utiliza una aproximación con variable compleja para obtener una precisión analítica en la evaluación de la matriz Jacobiana. Además, mapas de sensibilidad para la sensibilidad a las modificaciones del flujo de base y a una fuerza constante permiten identificar las regiones del campo fluido donde una modificacin (ej. fuerza puntual) tiene un efecto estabilizador del flujo. Se presentan cuatro casos de prueba: (1) un caso analítico para comprobar la derivación discreta, (2) una cavidad cerrada a bajo Reynolds para mostrar la mayor precisión en el cálculo de los valores propios con la aproximación de paso complejo, (3) flujo 2D en un cilindro circular para validar la metodología, y (4) flujo en un cavidad abierta, presentado para validar el método en casos de inestabilidades convectivamente inestables. Los tres últimos casos mencionados (2-4) se resolvieron con las ecuaciones de Navier-Stokes compresibles, utilizando un método Discontinuous Galerkin Spectral Element Method. Se obtuvo una buena concordancia para el caso de validación (3), cuando se comparó el nuevo método con resultados de la literatura. Además, este trabajo muestra que para el cálculo de los modos propios directos y adjuntos, así como para los mapas de sensibilidad, el uso de variables complejas es de suprema importancia para obtener una predicción precisa. El método descrito es aplicado al análisis para la estabilización de la estela generada por un disco actuador, que representa un modelo sencillo para hélices, rotores de helicópteros o turbinas eólicas. Se explora la primera bifurcación del flujo para un disco actuador, y se sugiere que está asociada a una inestabilidad de tipo Kelvin-Helmholtz, cuya estabilidad se controla con en el número de Reynolds y en la resistencia del disco actuador (o fuerza resistente). En primer lugar, se verifica que la disminución de la resistencia del disco tiene un efecto estabilizador parecido a una disminución del Reynolds. En segundo lugar, el análisis hidrodinmico discreto identifica dos regiones para la colocación de una fuerza puntual que controle las inestabilidades, una cerca del disco y otra en una zona aguas abajo. En tercer lugar, se muestra que la inclusión de un forzamiento localizado cerca del actuador produce una estabilización más eficiente que al forzar aguas abajo. El análisis de los campos de flujo controlados confirma que modificando el gradiente de velocidad cerca del actuador es más eficiente para estabilizar la estela. Estos resultados podrían proporcionar nuevas directrices para la estabilización de la estela de turbinas de viento o de marea cuando estén instaladas en un parque eólico y minimizar las interacciones no estacionarias entre turbinas. ABSTRACT A discrete framework for computing the global stability and sensitivity analysis to external perturbations for any set of partial differential equations is presented. In particular, a complex-step approximation is used to achieve near analytical accuracy for the evaluation of the Jacobian matrix. Sensitivity maps for the sensitivity to base flow modifications and to a steady force are computed to identify regions of the flow field where an input could have a stabilising effect. Four test cases are presented: (1) an analytical test case to prove the theory of the discrete framework, (2) a lid-driven cavity at low Reynolds case to show the improved accuracy in the calculation of the eigenvalues when using the complex-step approximation, (3) the 2D flow past a circular cylinder at just below the critical Reynolds number is used to validate the methodology, and finally, (4) the flow past an open cavity is presented to give an example of the discrete method applied to a convectively unstable case. The latter three (2–4) of the aforementioned cases were solved with the 2D compressible Navier–Stokes equations using a Discontinuous Galerkin Spectral Element Method. Good agreement was obtained for the validation test case, (3), with appropriate results in the literature. Furthermore, it is shown that for the calculation of the direct and adjoint eigenmodes and their sensitivity maps to external perturbations, the use of complex variables is paramount for obtaining an accurate prediction. An analysis for stabilising the wake past an actuator disc, which represents a simple model for propellers, helicopter rotors or wind turbines is also presented. We explore the first flow bifurcation for an actuator disc and it suggests that it is associated to a Kelvin- Helmholtz type instability whose stability relies on the Reynolds number and the flow resistance applied through the disc (or actuator forcing). First, we report that decreasing the disc resistance has a similar stabilising effect to an decrease in the Reynolds number. Second, a discrete sensitivity analysis identifies two regions for suitable placement of flow control forcing, one close to the disc and one far downstream where the instability originates. Third, we show that adding a localised forcing close to the actuator provides more stabilisation that forcing far downstream. The analysis of the controlled flow fields, confirms that modifying the velocity gradient close to the actuator is more efficient to stabilise the wake than controlling the sheared flow far downstream. An interesting application of these results is to provide guidelines for stabilising the wake of wind or tidal turbines when placed in an energy farm to minimise unsteady interactions.

The C-terminal SET domains of ALL-1 and TRITHORAX interact with the INI1 and SNR1 proteins, components of the SWI/SNF complex

The ALL-1 gene was discovered by virtue of its involvement in human acute leukemia. Its Drosophila homolog trithorax (trx) is a member of the trx-Polycomb gene family, which maintains correct spatial expression of the Antennapedia and bithorax complexes during embryogenesis. The C-terminal SET domain of ALL-1 and TRITHORAX (TRX) is a 150-aa motif, highly conserved during evolution. We performed yeast two hybrid screening of Drosophila cDNA library and detected interaction between a TRX polypeptide spanning SET and the SNR1 protein. SNR1 is a product of snr1, which is classified as a trx group gene. We found parallel interaction in yeast between the SET domain of ALL-1 and the human homolog of SNR1, INI1 (hSNF5). These results were confirmed by in vitro binding studies and by demonstrating coimmunoprecipitation of the proteins from cultured cells and/or transgenic flies. Epitope-tagged SNR1 was detected at discrete sites on larval salivary gland polytene chromosomes, and these sites colocalized with around one-half of TRX binding sites. Because SNR1 and INI1 are constituents of the SWI/SNF complex, which acts to remodel chromatin and consequently to activate transcription, the interactions we observed suggest a mechanism by which the SWI/SNF complex is recruited to ALL-1/trx targets through physical interactions between the C-terminal domains of ALL-1 and TRX and INI1/SNR1.

Examining the relationship between daily changes in support and smoking around a self-set quit date

This study was funded by the Swiss National Foundation (100014_124516). We would like to thank all students who helped with data collection.

Tumor necrosis factor (TNF)-mediated kinase cascades: Bifurcation of Nuclear Factor-κB and c-jun N-terminal kinase (JNK/SAPK) pathways at TNF receptor-associated factor 2

TNF-induced activation of the transcription factor NF-κB and the c-jun N-terminal kinase (JNK/SAPK) requires TNF receptor-associated factor 2 (TRAF2). The NF-κB-inducing kinase (NIK) associates with TRAF2 and mediates TNF activation of NF-κB. Herein we show that NIK interacts with additional members of the TRAF family and that this interaction requires the conserved “WKI” motif within the TRAF domain. We also investigated the role of NIK in JNK activation by TNF. Whereas overexpression of NIK potently induced NF-κB activation, it failed to stimulate JNK activation. A kinase-inactive mutant of NIK was a dominant negative inhibitor of NF-κB activation but did not suppress TNF- or TRAF2-induced JNK activation. Thus, TRAF2 is the bifurcation point of two kinase cascades leading to activation of NF-κB and JNK, respectively.

O apelo ao legislador : apellentscheidung, na praxis da Corte Constitucional Federal Alemã / Gilmar Ferreira Mendes. --Tribunal Constitucional Alemão e o apelo ao legislador : "appelentscheidung" ; na praxis da Corte Constitucional Federal Alemã. Revista de Direito Público, vol 25 n 99 p 32 a 53 jul/set 1991."

Variação do título : Apelo ao legislador na Corte Constitucional Federal Alemã. Revista Trimestral de Direito Público, n 10 p 33 a 51 1995.

sqv-3, -7, and -8, a set of genes affecting morphogenesis in Caenorhabditis elegans, encode enzymes required for glycosaminoglycan biosynthesis

sqv (squashed vulva) genes comprise a set of eight independent loci in Caenorhabditis elegans required zygotically for the invagination of vulval epithelial cells and maternally for normal oocyte formation and embryogenesis. Sequencing of sqv-3, sqv-7, and sqv-8 suggested a role for the encoded proteins in glycolipid or glycoprotein biosynthesis. Using a combination of in vitro analysis of SQV enzymatic activities, sqv+-mediated rescue of vertebrate cell lines, and biochemical characterization of sqv mutants, we show that sqv-3, -7, and -8 all affect the biosynthesis of glycosaminoglycans and therefore compromise the function of one specific class of glycoconjugates, proteoglycans. These findings establish the importance of proteoglycans and their associated glycosaminoglycans in epithelial morphogenesis and patterning during C. elegans development.

“Coarse” stability and bifurcation analysis using time-steppers: A reaction-diffusion example

Evolutionary, pattern forming partial differential equations (PDEs) are often derived as limiting descriptions of microscopic, kinetic theory-based models of molecular processes (e.g., reaction and diffusion). The PDE dynamic behavior can be probed through direct simulation (time integration) or, more systematically, through stability/bifurcation calculations; time-stepper-based approaches, like the Recursive Projection Method [Shroff, G. M. & Keller, H. B. (1993) SIAM J. Numer. Anal. 30, 1099–1120] provide an attractive framework for the latter. We demonstrate an adaptation of this approach that allows for a direct, effective (“coarse”) bifurcation analysis of microscopic, kinetic-based models; this is illustrated through a comparative study of the FitzHugh-Nagumo PDE and of a corresponding Lattice–Boltzmann model.

Delineating developmental and metabolic pathways in vivo by expression profiling using the RIKEN set of 18,816 full-length enriched mouse cDNA arrays

We have systematically characterized gene expression patterns in 49 adult and embryonic mouse tissues by using cDNA microarrays with 18,816 mouse cDNAs. Cluster analysis defined sets of genes that were expressed ubiquitously or in similar groups of tissues such as digestive organs and muscle. Clustering of expression profiles was observed in embryonic brain, postnatal cerebellum, and adult olfactory bulb, reflecting similarities in neurogenesis and remodeling. Finally, clustering genes coding for known enzymes into 78 metabolic pathways revealed a surprising coordination of expression within each pathway among different tissues. On the other hand, a more detailed examination of glycolysis revealed tissue-specific differences in profiles of key regulatory enzymes. Thus, by surveying global gene expression by using microarrays with a large number of elements, we provide insights into the commonality and diversity of pathways responsible for the development and maintenance of the mammalian body plan.

A minimal gene set for cellular life derived by comparison of complete bacterial genomes.

The recently sequenced genome of the parasitic bacterium Mycoplasma genitalium contains only 468 identified protein-coding genes that have been dubbed a minimal gene complement [Fraser, C.M., Gocayne, J.D., White, O., Adams, M.D., Clayton, R.A., et al. (1995) Science 270, 397-403]. Although the M. genitalium gene complement is indeed the smallest among known cellular life forms, there is no evidence that it is the minimal self-sufficient gene set. To derive such a set, we compared the 468 predicted M. genitalium protein sequences with the 1703 protein sequences encoded by the other completely sequenced small bacterial genome, that of Haemophilus influenzae. M. genitalium and H. influenzae belong to two ancient bacterial lineages, i.e., Gram-positive and Gram-negative bacteria, respectively. Therefore, the genes that are conserved in these two bacteria are almost certainly essential for cellular function. It is this category of genes that is most likely to approximate the minimal gene set. We found that 240 M. genitalium genes have orthologs among the genes of H. influenzae. This collection of genes falls short of comprising the minimal set as some enzymes responsible for intermediate steps in essential pathways are missing. The apparent reason for this is the phenomenon that we call nonorthologous gene displacement when the same function is fulfilled by nonorthologous proteins in two organisms. We identified 22 nonorthologous displacements and supplemented the set of orthologs with the respective M. genitalium genes. After examining the resulting list of 262 genes for possible functional redundancy and for the presence of apparently parasite-specific genes, 6 genes were removed. We suggest that the remaining 256 genes are close to the minimal gene set that is necessary and sufficient to sustain the existence of a modern-type cell. Most of the proteins encoded by the genes from the minimal set have eukaryotic or archaeal homologs but seven key proteins of DNA replication do not. We speculate that the last common ancestor of the three primary kingdoms had an RNA genome. Possibilities are explored to further reduce the minimal set to model a primitive cell that might have existed at a very early stage of life evolution.

Perspectives on archaeal diversity, thermophily and monophyly from environmental rRNA sequences.

Phylogenetic analysis of ribosomal RNA sequences obtained from uncultivated organisms of a hot spring in Yellowstone National Park reveals several novel groups of Archaea, many of which diverged from the crenarchaeal line of descent prior to previously characterized members of that kingdom. Universal phylogenetic trees constructed with the addition of these sequences indicate monophyly of Archaea, with modest bootstrap support. The data also show a specific relationship between low-temperature marine Archaea and some hot spring Archaea. Two of the environmental sequences are enigmatic: depending upon the data set and analytical method used, these sequences branch deeply within the Crenarchaeota, below the bifurcation between Crenarchaeota and Euryarchaeota, or even as the sister group to Eukaryotes. If additional data confirm either of the latter two placements, then the organisms represented by these ribosomal RNA sequences would merit recognition as a new kingdom, provisionally named "Korarchaeota."

The C-terminal domain of the largest subunit of RNA polymerase II interacts with a novel set of serine/arginine-rich proteins.

Although transcription and pre-mRNA processing are colocalized in eukaryotic nuclei, molecules linking these processes have not previously been described. We have identified four novel rat proteins by their ability to interact with the repetitive C-terminal domain (CTD) of RNA polymerase II in a yeast two-hybrid assay. A yeast homolog of one of the rat proteins has also been shown to interact with the CTD. These CTD-binding proteins are all similar to the SR (serine/arginine-rich) family of proteins that have been shown to be involved in constitutive and regulated splicing. In addition to alternating Ser-Arg domains, these proteins each contain discrete N-terminal or C-terminal CTD-binding domains. We have identified SR-related proteins in a complex that can be immunoprecipitated from nuclear extracts with antibodies directed against RNA polymerase II. In addition, in vitro splicing is inhibited either by an antibody directed against the CTD or by wild-type but not mutant CTD peptides. Thus, these results suggest that the CTD and a set of CTD-binding proteins may act to physically and functionally link transcription and pre-mRNA processing.

Membrane lipid perturbation modifies the set point of the temperature of heat shock response in yeast.

Addition of a saturated fatty acid (SFA) induced a strong increase in heat shock (HS) mRNA transcription when cells were heat-shocked at 37 degrees C, whereas treatment with an unsaturated fatty acid (UFA) reduced or eliminated the level of HS gene transcription at 37 degrees C. Transcription of the delta 9-desaturase gene (Ole1) of Histoplasma capsulatum, whose gene product is responsible for the synthesis of UFA, is up-regulated in a temperature-sensitive strain. We show that when the L8-14C mutant of Saccharomyces cerevisiae, which has a disrupted Ole1 gene, is complemented with its own Ole1 coding region under control of its own promoter or Ole1 promoters of H. capsulatum, the level of HS gene transcription depends on the activity of the promoters. Fluorescence anisotropy of mitochondrial membranes of completed strains corresponded to the different activity of the Ole1 promoter used. We propose that the SFA/UFA ratio and perturbation of membrane lipoprotein complexes are involved in the perception of rapid temperature changes and under HS conditions disturbance of the preexisting membrane physical state causes transduction of a signal that induces transcription of HS genes.

POU domain factor Brn-3b is required for the development of a large set of retinal ganglion cells.

The three members of the Brn-3 family of POU domain transcription factors are found in highly restricted sets of central nervous system neurons. Within the retina, these factors are present only within subsets of ganglion cells. We show here that in the developing mouse retina, Brn-3b protein is first observed in presumptive ganglion cell precursors as they begin to migrate from the zone of dividing neuroblasts to the future ganglion cell layer, and that targeted disruption of the Brn-3b gene leads in the homozygous state to a selective loss of 70% of retinal ganglion cells. In Brn-3b (-/-) mice other neurons within the retina and brain are minimally or not at all affected. These experiments indicate that Brn-3b plays an essential role in the development of specific ganglion cell types.