Ornstein-Uhlenbeck operator in convex domains of Banach spaces

Studiamo l'operatore di Ornstein-Uhlenbeck e il semigruppo di Ornstein-Uhlenbeck in un sottoinsieme aperto convesso $\Omega$ di uno spazio di Banach separabile $X$ dotato di una misura Gaussiana centrata non degnere $\gamma$. In particolare dimostriamo la disuguaglianza di Sobolev logaritmica e la disuguaglianza di Poincaré, e grazie a queste disuguaglianze deduciamo le proprietà spettrali dell'operatore di Ornstein-Uhlenbeck. Inoltre studiamo l'equazione ellittica $\lambdau+L^{\Omega}u=f$ in $\Omega$, dove $L^\Omega$ è l'operatore di Ornstein-Uhlenbeck. Dimostriamo che per $\lambda>0$ e $f\in L^2(\Omega,\gamma)$ la soluzione debole $u$ appartiene allo spazio di Sobolev $W^{2,2}(\Omega,\gamma)$. Inoltre dimostriamo che $u$ soddisfa la condizione di Neumann nel senso di tracce al bordo di $\Omega$. Questo viene fatto finita approssimazione dimensionale.

Transglutaminase 2 null macrophages respond to lipopolysaccharide stimulation by elevated proinflammatory cytokine production due to an enhanced αvβ3 integrin-induced Src tyrosine kinase signaling

Transglutaminase 2 (TG2) is a protein crosslinking enzyme with several additional biochemical functions. Loss of TG2 in vivo results in impaired phagocytosis of apoptotic cells and altered proinflammatory cytokine production by macrophages engulfing apoptotic cells leading to autoimmunity. It has been proposed that TG2 acts as an integrin ß(3) coreceptor in the engulfment process, while altered proinflammatory cytokine production is related to the lack of latent TGFß activation by TG2 null macrophages. Here we report that TG2 null macrophages respond to lipopolysaccharide treatment by elevated IL-6 and TNFa production. Though TGFß has been proposed to act as a feed back regulator of proinflammatory cytokine production in LPS-stimulated macrophages, this phenomenon is not related to the lack of active TGFß production. Instead, in the absence of TG2 integrin ß(3) maintains an elevated basal Src family kinase activity in macrophages, which leads to enhanced phosphorylation and degradation of the I?Ba. Low basal levels of I?Ba explain the enhanced sensitivity of TG2 null macrophages to signals that regulate NF-?B. Our data suggest that TG2 null macrophages bear a proinflammatory phenotype, which might contribute to the enhanced susceptibility of these mice to develop autoimmunity and atherosclerosis.

Sequential pyrolysis of willow SRC at low and high heating rates:implications for selective pyrolysis

The main aim of the work is to investigate sequential pyrolysis of willow SRC using two different heating rates (25 and 1500 °C/min) between 320 and 520 °C. Thermogravimetric analysis (TGA) and pyrolysis - gas chromatography - mass spectroscopy (Py-GC-MS) have been used for this analysis. In addition, laboratory scale processing has been undertaken to compare product distribution from fast and slow pyrolysis at 500 °C. Fast pyrolysis was carried out using a 1 kg/h continuous bubbling fluidized bed reactor, and slow pyrolysis using a 100 g batch reactor. Findings from this study show that heating rate and pyrolysis temperatures have a significant influence on the chemical content of decomposition products. From the analytical sequential pyrolysis, an inverse relationship was seen between the total yield of furfural (at high heating rates) and 2-furanmethanol (at low heating rates). The total yield of 1,2-dihydroxybenzene (catechol) was found to be significant higher at low heating rates. The intermediates of catechol, 2-methoxy-4-(2-propenyl)phenol (eugenol); 2-methoxyphenol (guaiacol); 4-Hydroxy-3,5-dimethoxybenzaldehyde (syringaldehyde) and 4-hydroxy-3-methoxybenzaldehyde (vanillin), were found to be highest at high heating rates. It was also found that laboratory scale processing alters the pyrolysis bio-oil chemical composition, and the proportions of pyrolysis product yields. The GC-MS/FID analysis of fast and slow pyrolysis bio-oils reveals significant differences. © 2011 Elsevier Ltd. All rights reserved.

The DHR1 domain of DOCK180 binds to SNX5 and regulates cation-independent mannose 6-phosphate receptor transport

DOCK180 is the archetype of the DOCK180-family guanine nucleotide exchange factor for small GTPases Rac1 and Cdc42. DOCK180-family proteins share two conserved domains, called DOCK homology region (DHR)-1 and -2. Although the function of DHR2 is to activate Rac1, DHR1 is required for binding to phosphoinositides. To better understand the function of DHR1, we searched for its binding partners by direct nanoflow liquid chromatography/tandem mass spectrometry, and we identified sorting nexins (SNX) 1, 2, 5, and 6, which make up a multimeric protein complex mediating endosome-to-trans-Golgi-network (TGN) retrograde transport of the cation-independent mannose 6-phosphate receptor (CI-MPR). Among these SNX proteins, SNX5 was coimmunoprecipitated with DOCK180 most efficiently. In agreement with this observation, DOCK180 colocalized with SNX5 at endosomes. The RNA interference-mediated knockdowns of SNX5 and DOCK180, but not Rac1, resulted in the redistribution of CI-MPR from TGN to endosomes. Furthermore, expression of the DOCK180 DHR1 domain was sufficient to restore the perturbed CI-MPR distribution in DOCK180 knockdown cells. These data suggest that DOCK180 regulates CI-MPR trafficking via SNX5 and that this function is independent of its guanine nucleotide exchange factor activity toward Rac1.

Multiple roles of charged amino acids in cytoplasmic loop 7 for expression and function of the multidrug and organic anion transporter MRP1 (ABCC1)

Multidrug resistance protein MRP1 mediates the ATP-dependent efflux of many chemotherapeutic agents and organic anions. MRP1 has two nucleotide binding sites (NBSs) and three membrane spanning domains (MSDs) containing 17 transmembrane helices linked by extracellular and cytoplasmic loops (CL). Homology models suggest that CL7 (amino acids 1141-1195) is in a position where it could participate in signaling between the MSDs and NBSs during the transport process. We have individually replaced eight charged residues in CL7 with Ala, and in some cases, an amino acid with the same charge, and then investigated the effects on MRP1 expression, transport activity, and nucleotide and substrate interactions. A triple mutant in which Glu(1169), Glu(1170), and Glu(1172) were all replaced with Ala was also examined. The properties of R1173A and E1184A were comparable with those of wild-type MRP1, whereas the remaining mutants were either poorly expressed (R1166A, D1183A) or exhibited reduced transport of one or more organic anions (E1144A, D1179A, K1181A, (1169)AAQA). Same charge mutant D1183E was also not expressed, whereas expression and activity of R1166K were similar to wild-type MRP1. The moderate substrate-selective changes in transport activity displayed by mutants E1144A, D1179A, K1181A, and (1169)AAQA were accompanied by changes in orthovanadate-induced trapping of [alpha-(32)P]azidoADP by NBS2 indicating changes in ATP hydrolysis or release of ADP. In the case of E1144A, estradiol glucuronide no longer inhibited trapping of azidoADP. Together, our results demonstrate the extreme sensitivity of CL7 to mutation, consistent with its critical and complex dual role in both the proper folding and transport activity of MRP1.

Identifying a novel functional domain within the p115 tethering factor required for Golgi ribbon assembly and membrane trafficking

The tethering factor p115 has been shown to facilitate Golgi biogenesis and membrane traffic in cells in culture. However, the role of p115 within an intact animal is largely unknown. Here, we document that RNAi-mediated depletion of p115 in C. elegans causes accumulation of the yolk protein (YP170) in body cavity and the retention of the yolk receptor RME-2 in the ER and the Golgi within oocytes.Structure-function analyses of p115 have identified two homology (H1-2) regions within the N-terminal globular head and the coiled-coil 1 (CC1) domain as essential for p115 function. We identify a novel C-terminal domain of p115 as necessary for Golgi ribbon formation and cargo trafficking. We show that p115 mutants lacking the fourth CC domain (CC4) act in a dominant negative manner to disrupt Golgi and prevent cargo trafficking in cells containing endogenous p115. Furthermore, using RNAi-mediated "replacement" strategy we show that CC4 is necessary for Golgi ribbon formation and membrane trafficking in cells depleted of endogenous p115.p115 has been shown to bind a subset of ER-Golgi SNAREs through CC1 and CC4 domains (Shorter et al., 2002). Our findings show that CC4 is required for p115 function and suggest that both the CC1 and the CC4 SNARE-binding motifs may participate in p115-mediated membrane tethering.

Identification of putative steroid-binding sites in human ABCB1 and ABCG2

Homology modelling was used to generate three-dimensional structures of the nucleotide-binding domains (NBDs) of human ABCB1 and ABCG2. Interactions between a series of steroidal ligands and transporter NBDs were investigated using an in silico docking approach. C-terminal ABCB1 NBD (ABCB1 NBD2) was predicted to bind steroids within a cavity formed partly by the P-Loop, Tyr1044 and Ile1050. The P-Loop within ABCG2 NBD was also predicted to be involved in steroid binding. No overlap between ATP- and RU-486-binding sites was predicted in either NBD, though overlaps between ATP- and steroid-binding sites were predicted in the vicinity of the P-Loop in both nucleotide-binding domains.

Emergence of equilibriumlike domains within nonequilibrium Ising spin systems

Many natural, technological and social systems are inherently not in equilibrium. We show, by detailed analysis of exemplar models, the emergence of equilibriumlike behavior in localized or nonlocalized domains within nonequilibrium Ising spin systems. Equilibrium domains are shown to emerge either abruptly or gradually depending on the system parameters and disappear, becoming indistinguishable from the remainder of the system for other parameter values. © 2013 American Physical Society.

Determining the temperature from Cauchy data in corner domains

We consider the problem of reconstruction of the temperature from knowledge of the temperature and heat flux on a part of the boundary of a bounded planar domain containing corner points. An iterative method is proposed involving the solution of mixed boundary value problems for the heat equation (with time-dependent conductivity). These mixed problems are shown to be well-posed in a weighted Sobolev space.

On an indirect integral equation approach for stationary heat transfer in semi-infinite layered domains in R3 with cavities

Regions containing internal boundaries such as composite materials arise in many applications.We consider a situation of a layered domain in IR3 containing a nite number of bounded cavities. The model is stationary heat transfer given by the Laplace equation with piecewise constant conductivity. The heat ux (a Neumann condition) is imposed on the bottom of the layered region and various boundary conditions are imposed on the cavities. The usual transmission (interface) conditions are satised at the interface layer, that is continuity of the solution and its normal derivative. To eciently calculate the stationary temperature eld in the semi-innite region, we employ a Green's matrix technique and reduce the problem to boundary integral equations (weakly singular) over the bounded surfaces of the cavities. For the numerical solution of these integral equations, we use Wienert's approach [20]. Assuming that each cavity is homeomorphic with the unit sphere, a fully discrete projection method with super-algebraic convergence order is proposed. A proof of an error estimate for the approximation is given as well. Numerical examples are presented that further highlights the eciency and accuracy of the proposed method.

An iterative method based on boundary integrals for elliptic Cauchy problems in semi-infinite domains

In this study, we investigate the problem of reconstruction of a stationary temperature field from given temperature and heat flux on a part of the boundary of a semi-infinite region containing an inclusion. This situation can be modelled as a Cauchy problem for the Laplace operator and it is an ill-posed problem in the sense of Hadamard. We propose and investigate a Landweber-Fridman type iterative method, which preserve the (stationary) heat operator, for the stable reconstruction of the temperature field on the boundary of the inclusion. In each iteration step, mixed boundary value problems for the Laplace operator are solved in the semi-infinite region. Well-posedness of these problems is investigated and convergence of the procedures is discussed. For the numerical implementation of these mixed problems an efficient boundary integral method is proposed which is based on the indirect variant of the boundary integral approach. Using this approach the mixed problems are reduced to integral equations over the (bounded) boundary of the inclusion. Numerical examples are included showing that stable and accurate reconstructions of the temperature field on the boundary of the inclusion can be obtained also in the case of noisy data. These results are compared with those obtained with the alternating iterative method.

The multiple pheromone ant clustering algorithm and its application to real world domains

The Multiple Pheromone Ant Clustering Algorithm (MPACA) models the collective behaviour of ants to find clusters in data and to assign objects to the most appropriate class. It is an ant colony optimisation approach that uses pheromones to mark paths linking objects that are similar and potentially members of the same cluster or class. Its novelty is in the way it uses separate pheromones for each descriptive attribute of the object rather than a single pheromone representing the whole object. Ants that encounter other ants frequently enough can combine the attribute values they are detecting, which enables the MPACA to learn influential variable interactions. This paper applies the model to real-world data from two domains. One is logistics, focusing on resource allocation rather than the more traditional vehicle-routing problem. The other is mental-health risk assessment. The task for the MPACA in each domain was to predict class membership where the classes for the logistics domain were the levels of demand on haulage company resources and the mental-health classes were levels of suicide risk. Results on these noisy real-world data were promising, demonstrating the ability of the MPACA to find patterns in the data with accuracy comparable to more traditional linear regression models. © 2013 Polish Information Processing Society.

Close contact fluctuations:the seeding of signalling domains in the immunological synapse

We analyse the size and density of thermally induced regions of close contact in cell : cell contact interfaces within a harmonic potential approximation, estimating these regions to be below one-tenth of a micron across. Our calculations indicate that as the distance between the close contact threshold depth and the mean membrane-membrane separation increases, the density of close contact patches decreases exponentially while there is only a minimal variation in their mean size. The technique developed can be used to calculate the probability of first crossing in reflection symmetry violating systems. © Europhysics Letters Association.

A procedure for the temperature reconstruction in corner domains from Cauchy data

An iterative procedure is proposed for the reconstruction of a stationary temperature field from Cauchy data given on a part of the boundary of a bounded plane domain where the boundary is smooth except for a finite number of corner points. In each step, a series of mixed well-posed boundary value problems are solved for the heat operator and its adjoint. Convergence is proved in a weighted L2-space. Numerical results are included which show that the procedure gives accurate and stable approximations in relatively few iterations.