Boundary value problems for third-order linear PDEs in time-dependent domains

We present the extension of a methodology to solve moving boundary value problems from the second-order case to the case of the third-order linear evolution PDE qt + qxxx = 0. This extension is the crucial step needed to generalize this methodology to PDEs of arbitrary order. The methodology is based on the derivation of inversion formulae for a class of integral transforms that generalize the Fourier transform and on the analysis of the global relation associated with the PDE. The study of this relation and its inversion using the appropriate generalized transform are the main elements of the proof of our results.

Nerve terminal GABAA receptors activate Ca2+/calmodulin-dependent signaling to inhibit voltage-gated Ca2+ influx and glutamate release

-Aminobutyric acid type A (GABAA) receptors, a family of Cl-permeable ion channels, mediate fast synaptic inhibition as postsynaptically enriched receptors for -aminobutyric acid at GABAergic synapses. Here we describe an alternative type of inhibition mediated byGABAA receptors present on neocortical glutamatergic nerve terminals and examine the underlying signaling mechanism(s). By monitoring the activity of the presynaptic CaM kinase II/synapsin I signaling pathway in isolated nerve terminals, we demonstrate that GABAA receptor activation correlated with an increase in basal intraterminal [Ca2]i. Interestingly, this activation of GABAA receptors resulted in a reduction of subsequent depolarization-evoked Ca2 influx, which thereby led to an inhibition of glutamate release. To investigate how the observed GABAA receptor-mediated modulation operates, we determined the sensitivity of this process to the Na-K-2Cl cotransporter 1 antagonist bumetanide, as well as substitution of Ca2 with Ba2, or Ca2/calmodulin inhibition by W7. All of these treatments abolished the modulation by GABAA receptors. Application of selective antagonists of voltage-gated Ca2 channels (VGCCs) revealed that the GABAA receptor-mediated modulation of glutamate release required the specific activity of L- and R-type VGCCs. Crucially, the inhibition of release by these receptors was abolished in terminals isolated from R-type VGCC knock-out mice. Together, our results indicate that a functional coupling between nerve terminal GABAA receptors and L- or R-type VGCCs is mediated by Ca2/calmodulin-dependent signaling. This mechanism provides a GABA-mediated control of glutamatergic synaptic activity by a direct inhibition of glutamate release.

The relationship between diffuse spectral reflectance of the soil and its cation exchange capacity is scale-dependent

Diffuse reflectance spectroscopy (DRS) is increasingly being used to predict numerous soil physical, chemical and biochemical properties. However, soil properties and processes vary at different scales and, as a result, relationships between soil properties often depend on scale. In this paper we report on how the relationship between one such property, cation exchange capacity (CEC), and the DRS of the soil depends on spatial scale. We show this by means of a nested analysis of covariance of soils sampled on a balanced nested design in a 16 km × 16 km area in eastern England. We used principal components analysis on the DRS to obtain a reduced number of variables while retaining key variation. The first principal component accounted for 99.8% of the total variance, the second for 0.14%. Nested analysis of the variation in the CEC and the two principal components showed that the substantial variance components are at the > 2000-m scale. This is probably the result of differences in soil composition due to parent material. We then developed a model to predict CEC from the DRS and used partial least squares (PLS) regression do to so. Leave-one-out cross-validation results suggested a reasonable predictive capability (R2 = 0.71 and RMSE = 0.048 molc kg− 1). However, the results from the independent validation were not as good, with R2 = 0.27, RMSE = 0.056 molc kg− 1 and an overall correlation of 0.52. This would indicate that DRS may not be useful for predictions of CEC. When we applied the analysis of covariance between predicted and observed we found significant scale-dependent correlations at scales of 50 and 500 m (0.82 and 0.73 respectively). DRS measurements can therefore be useful to predict CEC if predictions are required, for example, at the field scale (50 m). This study illustrates that the relationship between DRS and soil properties is scale-dependent and that this scale dependency has important consequences for prediction of soil properties from DRS data

Sex-dependent age modulation of frontostriatal and temporo-parietal activation during cognitive control

Developmental functional imaging studies of cognitive control show progressive age-related increase in task-relevant fronto-striatal activation in male development from childhood to adulthood. Little is known, however, about how gender affects this functional development. In this study, we used event related functional magnetic resonance imaging to examine effects of sex, age, and their interaction on brain activation during attentional switching and interference inhibition, in 63 male and female adolescents and adults, aged 13 to 38. Linear age correlations were observed across all subjects in task-specific frontal, striatal and temporo-parietal activation. Gender analysis revealed increased activation in females relative to males in fronto-striatal areas during the Switch task, and laterality effects in the Simon task, with females showing increased left inferior prefrontal and temporal activation, and males showing increased right inferior prefrontal and parietal activation. Increased prefrontal activation clusters in females and increased parietal activation clusters in males furthermore overlapped with clusters that were age-correlated across the whole group, potentially reflecting more mature prefrontal brain activation patterns for females, and more mature parietal activation patterns for males. Gender by age interactions further supported this dissociation, revealing exclusive female-specific age correlations in inferior and medial prefrontal brain regions during both tasks, and exclusive male-specific age correlations in superior parietal (Switch task) and temporal regions (Simon task). These findings show increased recruitment of age-correlated prefrontal activation in females, and of age-correlated parietal activation in males, during tasks of cognitive control. Gender differences in frontal and parietal recruitment may thus be related to gender differences in the neurofunctional maturation of these brain regions.

The Klein-Gordon equation in a domain with time-dependent boundary

We solve a Dirichlet boundary value problem for the Klein–Gordon equation posed in a time-dependent domain. Our approach is based on a general transform method for solving boundary value problems for linear and integrable nonlinear PDE in two variables. Our results consist of the inversion formula for a generalized Fourier transform, and of the application of this generalized transform to the solution of the boundary value problem.

Integrable evolution equations in time-dependent domains

We discuss the implementation of a method of solving initial boundary value problems in the case of integrable evolution equations in a time-dependent domain. This method is applied to a dispersive linear evolution equation with spatial derivatives of arbitrary order and to the defocusing nonlinear Schrödinger equation, in the domain l(t)

Singular vector ensemble forecasting systems and the prediction of flow dependent uncertainty

The ECMWF ensemble weather forecasts are generated by perturbing the initial conditions of the forecast using a subset of the singular vectors of the linearised propagator. Previous results show that when creating probabilistic forecasts from this ensemble better forecasts are obtained if the mean of the spread and the variability of the spread are calibrated separately. We show results from a simple linear model that suggest that this may be a generic property for all singular vector based ensemble forecasting systems based on only a subset of the full set of singular vectors.

Syk-Dependent Cytokine Induction by Dectin-1 Reveals a Novel Pattern Recognition Pathway for C Type Lectins

Pattern-recognition receptors (PRRs) detect molecular signatures of microbes and initiate immune responses to infection. Prototypical PRRs such as Toll-like receptors (TLRs) signal via a conserved pathway to induce innate response genes. In contrast, the signaling pathways engaged by other classes of putative PRRs remain ill defined. Here, we demonstrate that the β-glucan receptor Dectin-1, a yeast binding C type lectin known to synergize with TLR2 to induce TNFα and IL-12, can also promote synthesis of IL-2 and IL-10 through phosphorylation of the membrane proximal tyrosine in the cytoplasmic domain and recruitment of Syk kinase. syk−/− dendritic cells (DCs) do not make IL-10 or IL-2 upon yeast stimulation but produce IL-12, indicating that the Dectin-1/Syk and Dectin-1/TLR2 pathways can operate independently. These results identify a novel signaling pathway involved in pattern recognition by C type lectins and suggest a potential role for Syk kinase in regulation of innate immunity.

Overproduction, purification and preliminary X-ray diffraction analysis of YncE, an iron-regulated Sec-dependent periplasmic protein from Escherichia coli

The yncE gene of Escherichia coli encodes a predicted periplasmic protein of unknown function. The gene is de-repressed under iron restriction through the action of the global iron regulator Fur. This suggests a role in iron acquisition, which is supported by the presence of the adjacent yncD gene encoding a potential TonB-dependent outer-membrane transporter. Here, the preliminary crystallographic structure of YncE is reported, revealing that it consists of a seven-bladed beta-propeller which resembles the corresponding domain of the `surface-layer protein' of Methanosarcina mazei. A full structure determination is under way in order to provide insight into the function of this protein.

Bone morphogenetic protein-6 enhances gonadotrophin-dependent progesterone and inhibin secretion and expression of rnRNA transcripts encoding gonadotrophin receptors and inhibin/activin subunits in chicken granulosa cells

The aims were to examine ovarian expression of bone morphogenetic protein (BMP) ligands/receptor mRNAs in the chicken and to test the hypothesis that theca-derived BMP(s) modulates granulosa cell function in a paracrine manner. RT-PCR revealed expression of multiple BMPs in granulosa and theca cells from prehierarchical and preovulatory follicles with greater expression in theca cells; both cell types expressed BMP receptors-1A, -1B and -II consistent with tissue responsiveness. Preovulatory granulosa cells F1, F2 and F3/4) were cultured with BMP-6 (expressed by theca but not granulosa) in the presence/absence of LH, FSH or 8-Br-cAMP. RMP-6 increased 'basal' and gonadotrophin-induced inhibin-A and progesterone secretion by each cell type but did not enhance the effect of 8-Br-cAMP. This indicates that the observed synergism between BMP-6 and gonadotrophin might involve BMP-induced up-regulation of gonadotrophin receptors. In support of this, BMP-6 alone increased LH-receptor (LHR) mRNA in F1 cells and FSH-receptor (FSHR) mRNA in F1, F2 and F3/4 cells. RMP-6 also enhanced LH/FSH-induced LHR transcript amount in each cell type but did not raise FSHR transcript amounts above those induced by BMP-6 alone. To further explore BMP6 action on inhibin-A secretion, we quantified inhibin/activin subunits (alpha, beta(A), beta(B)) mRNAs. Consistent with its effect on inhibin-A secretion, BMP-6 enhanced 'basal' expression of alpha- and beta(A)-Subunit mRNA in F1, F2 and F3/4 cells, and beta(B)-subunit mRNA in F3/4 cells. BMP-6 markedly enhanced FSH/LH-induced expression of alpha-subunit in all follicles and FSH-induced beta(A)-subunit in F2 and F3/4 follicles but not in F1 follicles. Neither BMP-6 alone, nor FSH/LH alone, affected 'basal' OB mRNA abundance. However, co-treatment with gonadotrophin and BMP-6 greatly increased beta(B)-subunit expression, the response being lowest in F1 follicles and greatest in F3/4 follicles. Collectively, these results support the hypothesis that intra-ovarian OMPs of thecal origin have a paracrine role in modulating granulosa cell function in the chicken in a preovulatory stage-dependent manner.

Agonist-dependent internalization of D2 receptors: imaging quantification by confocal microscopy

In positron emission tomography and single photon emission computed tomography studies using D2 dopamine (DA) receptor radiotracers, a decrease in radiotracer binding potential (BP) is usually interpreted in terms of increased competition with synaptic DA. However, some data suggest that this signal may also reflect agonist (DA)-induced increases in D2 receptor (D2R) internalization, a process which would presumably also decrease the population of receptors available for binding to hydrophilic radioligands. To advance interpretation of alterations in D2 radiotracer BP, direct methods of assessment of D2R internalization are required. Here, we describe a confocal microscopy-based approach for the quantification of agonist-dependent receptor internalization. The method relies upon double-labeling of the receptors with antibodies directed against intracellular as well as extracellular epitopes. Following agonist stimulation, DA D2R internalization was quantified by differentiating, in optical cell sections, the signal due to the staining of the extracellular from intracellular epitopes of D2Rs. Receptor internalization was increased in the presence of the D2 agonists DA and bromocriptine, but not the D1 agonist SKF38393. Pretreatment with either the D2 antagonist sulpiride, or inhibitors of internalization (phenylarsine oxide and high molarity sucrose), blocked D2-agonist induced receptor internalization, thus validating this method in vitro. This approach therefore provides a direct and streamlined methodology for investigating the pharmacological and mechanistic aspects of D2R internalization, and should inform the interpretation of results from in vivo receptor imaging studies.

Mapping the Sinorhizobium meliloti 1021 solute-binding protein-dependent transportome

The number of solute-binding protein-dependent transporters in rhizobia is dramatically increased compared with the majority of other bacteria so far sequenced. This increase may be due to the high affinity of solute-binding proteins for solutes, permitting the acquisition of a broad range of growth-limiting nutrients from soil and the rhizosphere. The transcriptional induction of these transporters was studied by creating a suite of plasmid and integrated fusions to nearly all ATP-binding cassette (ABC) and tripartite ATP-independent periplasmic (TRAP) transporters of Sinorhizobium meliloti. In total, specific inducers were identified for 76 transport systems, amounting to approximate to 47% of the ABC uptake systems and 53% of the TRAP transporters in S. meliloti. Of these transport systems, 64 are previously uncharacterized in Rhizobia and 24 were induced by solutes not known to be transported by ABC- or TRAP-uptake systems in any organism. This study provides a global expression map of one of the largest transporter families (transportome) and an invaluable tool to both understand their solute specificity and the relationships between members of large paralogous families.