Complete Systems of Hermite Associated Functions

It is proved that if the increasing sequence {kn} n=0..∞ n=0 of nonnegative integers has density greater than 1/2 and D is an arbitrary simply connected subregion of C\R then the system of Hermite associated functions Gkn(z) n=0..∞ is complete in the space H(D) of complex functions holomorphic in D.

Epidermal growth factor-induced ovarian carcinoma cell migration is associated with JAK2/STAT3 signals and changes in the abundance and localization of α6β1 integrin

Peritoneal dissemination of ovarian carcinoma is mediated by epithelial–mesenchymal interconversions leading to the disruption of cell–cell contact and modulation of cell–extracellular matrix (ECM) interactions. The present study was designed to evaluate the effects of epidermal growth factor (EGF) as a modulator of Janus kinase 2 (JAK2) and signal transducer and activator of transcription 3 (STAT3) signalling and changes in integrin expression during the process similar to EMT. A fibroblastic morphology with reduced intercellular cell contacts and increased cell motility was observed in ovarian cancer cell lines in response to EGF and was concomitant with the up regulation of EMT-associated N-cadherin and vimentin expression. These changes were accompanied by an increase in α2, α6 and β1 integrin subunits and activation of JAK2 and STAT3 signalling which was suppressed by a specific JAK2 inhibitor. Consistent with the suppression of STAT3 activity, N-cadherin and vimentin expression were abrogated and was coherent with the loss of cell motility and the expression of α6 and β1 integrin subunits. Neutralizing antibodies against α6 and β1 subunits inhibited cancer cell migration. A strong correlation between the expression of N-cadherin, vimentin and JAK2/STAT3 levels were detected in high-grade ovarian tumors and was consistent with the previously reported enhanced expression of α6 integrin subunit in advanced tumors [Ahmed N, Riley C, Oliva K, Rice G, Quinn M. Ascites induces modulation of α6β1 integrin and urokinase plasminogen activator receptor expression and associated functions in ovarian carcinoma. British Journal of Cancer 2005;92:1475–85]. Our data incorporating the clinical samples and the cancer cell lines is the first to demonstrate that JAK2/STAT3 pathway may be one of the downstream events in EMT-like process and α6β1 integrin-mediated signalling in ovarian carcinomas.

Zeros of Jacobi functions of second kind

The number of zeros in (- 1, 1) of the Jacobi function of second kind Q(n)((alpha, beta)) (x), alpha, beta > - 1, i.e. The second solution of the differential equation(1 - x(2))y (x) + (beta - alpha - (alpha + beta + 2)x)y' (x) + n(n + alpha + beta + 1)y(x) = 0,is determined for every n is an element of N and for all values of the parameters alpha > - 1 and beta > - 1. It turns out that this number depends essentially on alpha and beta as well as on the specific normalization of the function Q(n)((alpha, beta)) (x). Interlacing properties of the zeros are also obtained. As a consequence of the main result, we determine the number of zeros of Laguerre's and Hermite's functions of second kind. (c) 2005 Elsevier B.V. All rights reserved.

Outer Membrane Protease/Adhesin PgtE of Salmonella enterica: Role in Salmonella-Host Interaction

Salmonella enterica serovar Typhimurium is a common cause of gastroenteritis in humans and, occasionally, also causes systemic infection. During systemic infection an important characteristic of Salmonella is its ability to survive and replicate within macrophages. The outer membrane protease PgtE of S. enterica is a member of the omptin family of outer membrane aspartate proteases, which are beta-barrel proteins with five surface-exposed loops. The main goals of this study were to characterize biological substrates and pathogenesis-associated functions of PgtE and to determine the conditions where PgtE is fully active. In this study we found that PgtE requires rough lipopolysaccharide (LPS) to be functional but is sterically inhibited by the long O-antigen side chain in smooth LPS. Salmonella isolates normally are smooth with a long oligosaccharide O-antigen, and PgtE remains functionally cryptic in wild-type Salmonella cultivated in vitro. Interestingly, our results showed that due to increased expression of PgtE and to reduced length of the LPS O-antigen chains, the wild-type Salmonella expresses highly functional PgtE when isolated from mouse macrophage-like J774A.1 cells. Salmonella is thought to be continuously released from macrophages to infect new ones, and our results suggest that PgtE is functional during these transient extracellular growth phases. Six novel host protein substrates were identified for PgtE in this work. PgtE was previously known to activate human plasminogen (Plg) to plasmin, a broad-spectrum serine protease, and in this study PgtE was shown to interfere with the Plg system by inactivating the main inhibitor of plasmin, alpha2-antiplasmin. PgtE also interferes with another important proteolytic system of mammals by activating pro-matrix metalloproteinase-9 to an active gelatinase. PgtE also directly degrades gelatin, a component of extracellular matrices. PgtE also increases bacterial resistance against complement-mediated killing in human serum and enhances survival of Salmonella within murine macrophages as well as in the liver and spleen of intraperitoneally infected mice. Taken together, the results in this study suggest that PgtE is a virulence factor of Salmonella that has adapted to interfere with host proteolytic systems and to modify extracellular matrix; these features likely assist the migration of Salmonella during systemic salmonellosis.

Transverse mode formation in longitudinally pumped miniature slab lasers

The formation of transverse modes in longitudinally pumped miniature slab lasers is investigated theoretically and experimentally. The longitudinally non-uniform gain-guiding is studied by expanding the electric field into the Hermite-Gaussian functions that satisfy boundary conditions of the resonator. Non-Gaussian transversal beam profiles in the near field are found and the beam diameter is reduced when the pump spot becomes smaller. The experimental observation agrees with the theoretical calculation.

Spatial correlation of heat release rate and sound emission from turbulent premixed flames

The two-point spatial correlation of the rate of change of fluctuating heat release rate is central to the sound emission from open turbulent flames, and a few attempts have been made to address this correlation in recent studies. In this paper, the two-point correlation and its role in combustion noise are studied by analysing direct numerical simulation (DNS) data of statistically multi-dimensional turbulent premixed flames. The results suggest that this correlation function depends on the separation distance and direction but, not on the positions inside the flame brush. This correlation can be modelled using a combination of Hermite-Gaussian functions of zero and second order, i.e. functions of the form (1-Ax2)e-Bx2 for constants A and B, to include its possible negative values. The integral correlation volume obtained using this model is about 0.2δL3 with the length scale obtained from its cube root being about 0.6δ L, where δ L is the laminar flame thermal thickness. Both of the values are slightly larger than the values reported in an earlier study because of the anisotropy observed for the correlation. This model together with the turbulence-dependent parameter K, the ratio of the root-mean-square (RMS) value of the rate of change of reaction rate to the mean reaction rate, derived from the DNS data is applied to predict the far-field sound emitted from open flames. The calculated noise levels agree well with recently reported measurements and show a sensitivity to K values. © 2012 The Combustion Institute.

Research on the influence of fabrication parameters on the performance of buried ion-exchanged glass waveguides using the variational method

The variational method is proposed to analyze the influence of the fabrication parameters on the performance of buried K+-Na+ ion-exchanged Er3+-Yb3+ ions co-doped glass waveguide. The unknown parameters of the Hermite-Gaussian functions as the trial field distribution are determined based on the scalar variational principle. It is demonstrated that the results calculated in this paper agree with those measured in the experiment. The mode dimensions, the effective refractive index, and the overlap factor as the functions of the fabrication parameters are investigated. These results of the variational analysis are useful for the design and optimization of Er3+-Yb3+ ions co-doped waveguides.

Transform both sides model: A parametric approach

A parametric regression model for right-censored data with a log-linear median regression function and a transformation in both response and regression parts, named parametric Transform-Both-Sides (TBS) model, is presented. The TBS model has a parameter that handles data asymmetry while allowing various different distributions for the error, as long as they are unimodal symmetric distributions centered at zero. The discussion is focused on the estimation procedure with five important error distributions (normal, double-exponential, Student's t, Cauchy and logistic) and presents properties, associated functions (that is, survival and hazard functions) and estimation methods based on maximum likelihood and on the Bayesian paradigm. These procedures are implemented in TBSSurvival, an open-source fully documented R package. The use of the package is illustrated and the performance of the model is analyzed using both simulated and real data sets.

Biochemical Investigations on the Stability of Biological Membranes

In this project, an attempt has been made to study the stability of erythrocyte and lysosomal membranes biochemically. Erythrocytes were chosen for the study because of their ready availability and relative simplicity. Biological membranes forming closed boundaries between compartments of varying composition consist mainly of proteins and lipids. They are asymmetric, fluid structures that are thermodynamically stable and metabolically active. Normal cellular function begins with normal membrane structure and any variation in it may upset the normal functions. The degree of fluidity of a membrane depends on the chain length of its lipids and degree of unsaturation of constituent fatty acids. In response to environmental changes, many cells can regulate composition of their membranes to maintain the overall semi fluid environment necessary for many membrane associated functions. The assembly and Maintenance of membrane structures in cells is a dynamic process. The components are not only synthesized and inserted into a growing membrane but are also continuously degraded at a slower rate. This turnover process varies with each individual molecule.Lysosomes are important in the catabolic processes occurring in the cell. Lysosomes contain hydrolytic enzymes and are stable under normal conditions. In certain pathological conditions, the lysosomal membrane may rupture, releasing the hydrolytic enzymes into the cell and digestion of cell takes place as a whole. This is very dangerous. In normal life processes of multi cellular organisms, lysosomes rupture following the death of a cell and it may have some value as a built in mechanism for selfremoval of dead cells.An attempt has also been made in this project towards developing lysosome membrane stability as an index of fish spoilage during storage. Different membranes within the cell and between cells have different compositions as reflected in the ratio of protein to lipid. The difference is not surprising given the very different functions of membranes

Campanian crustacean burrow system from Israel with brood and nursery chambers representing communal organization

Phosphorite-filled crustacean burrows associated with a Campanian-age omission surface in the north-western Negev are described. The phosphatic burrow casts weather out displaying scratches (bioglyphs) and two types of local swellings (chambers), which are flattened normal to the course of the burrow. The more abundant chamber type is a flattened spheroid (diameter 45-50 mm) or a flattened, highly prolate ellipsoid of larger dimensions, with bioglyphs. The other type is a flattened spheroid (diameter 45 mm), gently rounded on the upper side and flat on the base. Rings of elevations on the cast (representing moats) form interconnected circlets, each capped by about eight rounded hemispherical tubercles (4 x 4 mm) (pits on original), the whole forming a discrete network. The first type of chamber may have hosted the young (nursery chamber) and/or stored food. The second type of cast replicates a chamber with a pitted floor, which may have formed a brood chamber for 60-70 spherical eggs, each about 3 mm in diameter. Brood chambers in crustacean burrow systems were previously suspected, but only at burrow terminations. The interpreted K-type breeding strategy, brood care and associated functions require a high degree of social organization, none of which has been observed in extant crustaceans, but all occur within social insects.

Spectral bounds and basis results for non-self-adjoint pencils, with an application to Hagen-Poiseuille flow

We obtain eigenvalue enclosures and basisness results for eigen- and associated functions of a non-self-adjoint unbounded linear operator pencil A−λBA−λB in which BB is uniformly positive and the essential spectrum of the pencil is empty. Both Riesz basisness and Bari basisness results are obtained. The results are applied to a system of singular differential equations arising in the study of Hagen–Poiseuille flow with non-axisymmetric disturbances.

Regulation of Alix by an autoinhibitory intramolecular interaction

In eukaryotic cells, the ESCRTs (endosomal sorting complexes required for transport) machinery is required for cellular processes such as endosomal sorting, retroviral budding and cytokinesis. The ALG-2 interacting protein Alix is a modular adaptor protein that is critically involved in these ESCRTs-associated cellular processes and consists of an N-terminal Bro1 domain, a middle V domain and C-terminal Pro-rich domain (PRD). In these cellular processes, Alix interacts with the ESCRT-III component CHMP4 at the Bro1 domain, with HIV-1 p6 Gag or EIAV p9Gag at the V domain, and with the ESCRT-I component TSG101 at the Pro-rich domain. Here we demonstrate that the N-terminal Bro1 domain forms an intramolecular interaction with C-terminal PRD within Alix. This Bro1-PRD intramolecular interaction forms a closed conformation of Alix that autoinhibits Alix interaction with all of these partner proteins. Moreover, the binding of Ca2+-activated ALG-2 to the PRD of Alix relieves the autoinhibitory intramolecular interaction, resulting in an open conformation of Alix which is able to interact with all of these partner proteins. The partner proteins bound to Alix in turn maintain Alix in the open conformation after ALG-2 dissociation with Alix. Consistent with the effect of Ca2+-activated ALG-2 on opening/activating Alix in these ESCRTs-associated functions, ALG-2 overexpression accelerates EGF-induced degradation of EGFR in an Alix-dependent manner. These findings discover an intrinsic autoinhibitory mechanism of Alix and a two-step process to activate/open Alix and then keep Alix active/open. This study has solved long-standing issues on the regulations of Alix in ESCRTs-associated functions and the role of ALG-2-Alix interaction, and may serve as the structural basis for further studies about Alix regulations. ^

Identification of a new mammalian centrin gene, more closely related to Saccharomyces cerevisiae CDC31 gene

Among the numerous centrin isoforms identified by two-dimensional gel electrophoresis in human cells, an acidic and slow-migrating isoform is particularly enriched in a centrosome fraction. We report here that this isoform specifically reacts with antibodies raised against Saccharomyces cerevisiae Cdc31p and is present, as other centrin isoforms, in the distal lumen of centrioles. It is encoded by a new centrin gene, which we propose to name HsCEN3 (Homo sapiens centrin gene 3). This gene is more closely related to the yeast CDC31 gene, and shares less identity with algae centrin than HsCEN1 and HsCEN2. A murine CDC31-related gene was also found that shows 98% identity and 100% similarity with HsCEN3, demonstrating a higher interspecies conservation than the murine centrin gene MmCEN1 (Mus musculus centrin gene 1) with either HsCEN1, or HsCEN2. Finally, immunological data suggest that a CDC31-related gene could exist in amphibians and echinoderms as well. All together, our data suggest the existence of two divergent protein subfamilies in the current centrin family, which might be involved in distinct centrosome-associated functions. The possible implication of this new mammalian centrin gene in centrosome duplication is discussed.

Functional Hierarchy of Simultaneously Expressed Adhesion Receptors: Integrin α2β1 but Not CD44 Mediates MV3 Melanoma Cell Migration and Matrix Reorganization within Three-dimensional Hyaluronan-containing Collagen MatricesV⃞

Haptokinetic cell migration across surfaces is mediated by adhesion receptors including β1 integrins and CD44 providing adhesion to extracellular matrix (ECM) ligands such as collagen and hyaluronan (HA), respectively. Little is known, however, about how such different receptor systems synergize for cell migration through three-dimensionally (3-D) interconnected ECM ligands. In highly motile human MV3 melanoma cells, both β1 integrins and CD44 are abundantly expressed, support migration across collagen and HA, respectively, and are deposited upon migration, whereas only β1 integrins but not CD44 redistribute to focal adhesions. In 3-D collagen lattices in the presence or absence of HA and cross-linking chondroitin sulfate, MV3 cell migration and associated functions such as polarization and matrix reorganization were blocked by anti-β1 and anti-α2 integrin mAbs, whereas mAbs blocking CD44, α3, α5, α6, or αv integrins showed no effect. With use of highly sensitive time-lapse videomicroscopy and computer-assisted cell tracking techniques, promigratory functions of CD44 were excluded. 1) Addition of HA did not increase the migratory cell population or its migration velocity, 2) blocking of the HA-binding Hermes-1 epitope did not affect migration, and 3) impaired migration after blocking or activation of β1 integrins was not restored via CD44. Because α2β1-mediated migration was neither synergized nor replaced by CD44–HA interactions, we conclude that the biophysical properties of 3-D multicomponent ECM impose more restricted molecular functions of adhesion receptors, thereby differing from haptokinetic migration across surfaces.

Adenylate kinase phosphotransfer communicates cellular energetic signals to ATP-sensitive potassium channels

Transduction of energetic signals into membrane electrical events governs vital cellular functions, ranging from hormone secretion and cytoprotection to appetite control and hair growth. Central to the regulation of such diverse cellular processes are the metabolism sensing ATP-sensitive K+ (KATP) channels. However, the mechanism that communicates metabolic signals and integrates cellular energetics with KATP channel-dependent membrane excitability remains elusive. Here, we identify that the response of KATP channels to metabolic challenge is regulated by adenylate kinase phosphotransfer. Adenylate kinase associates with the KATP channel complex, anchoring cellular phosphotransfer networks and facilitating delivery of mitochondrial signals to the membrane environment. Deletion of the adenylate kinase gene compromised nucleotide exchange at the channel site and impeded communication between mitochondria and KATP channels, rendering cellular metabolic sensing defective. Assigning a signal processing role to adenylate kinase identifies a phosphorelay mechanism essential for efficient coupling of cellular energetics with KATP channels and associated functions.