Empirical Orthogonal Functions: The Medium is the Message

Empirical orthogonal function (EOF) analysis is a powerful tool for data compression and dimensionality reduction used broadly in meteorology and oceanography. Often in the literature, EOF modes are interpreted individually, independent of other modes. In fact, it can be shown that no such attribution can generally be made. This review demonstrates that in general individual EOF modes (i) will not correspond to individual dynamical modes, (ii) will not correspond to individual kinematic degrees of freedom, (iii) will not be statistically independent of other EOF modes, and (iv) will be strongly influenced by the nonlocal requirement that modes maximize variance over the entire domain. The goal of this review is not to argue against the use of EOF analysis in meteorology and oceanography; rather, it is to demonstrate the care that must be taken in the interpretation of individual modes in order to distinguish the medium from the message.

BASIC HYPERGEOMETRIC FUNCTIONS and ORTHOGONAL LAURENT POLYNOMIALS

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Stieltjes functions and discrete classical orthogonal polynomials

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Reconstruction of spatiotemporal capture data by means of orthogonal functions: the case of skipjack tuna (Katsuwonus pelamis) in the central-east Atlantic

[EN] The information provided by the International Commission for the Conservation of Atlantic Tunas (ICCAT) on captures of skipjack tuna (Katsuwonus pelamis) in the central-east Atlantic has a number of limitations, such as gaps in the statistics for certain fleets and the level of spatiotemporal detail at which catches are reported. As a result, the quality of these data and their effectiveness for providing management advice is limited. In order to reconstruct missing spatiotemporal data of catches, the present study uses Data INterpolating Empirical Orthogonal Functions (DINEOF), a technique for missing data reconstruction, applied here for the first time to fisheries data. DINEOF is based on an Empirical Orthogonal Functions decomposition performed with a Lanczos method. DINEOF was tested with different amounts of missing data, intentionally removing values from 3.4% to 95.2% of data loss, and then compared with the same data set with no missing data. These validation analyses show that DINEOF is a reliable methodological approach of data reconstruction for the purposes of fishery management advice, even when the amount of missing data is very high.

A finite class of orthogonal functions generated by Routh-Romanovski polynomials

It is known that some orthogonal systems are mapped onto other orthogonal systems by the Fourier transform. In this article we introduce a finite class of orthogonal functions, which is the Fourier transform of Routh-Romanovski orthogonal polynomials, and obtain its orthogonality relation using Parseval identity.

Nuclear localization of NPR1 is required for activation of PR gene expression

Systemic acquired resistance (SAR) is a broad-spectrum resistance in plants that involves the upregulation of a battery of pathogenesis-related (PR) genes. NPR1 is a key regulator in the signal transduction pathway that leads to SAR. Mutations in NPR1 result in a failure to induce PR genes in systemic tissues and a heightened susceptibility to pathogen infection, whereas overexpression of the NPR1 protein leads to increased induction of the PR genes and enhanced disease resistance. We analyzed the subcellular localization of NPR1 to gain insight into the mechanism by which this protein regulates SAR. An NPR1–green fluorescent protein fusion protein, which functions the same as the endogenous NPR1 protein, was shown to accumulate in the nucleus in response to activators of SAR. To control the nuclear transport of NPR1, we made a fusion of NPR1 with the glucocorticoid receptor hormone binding domain. Using this steroid-inducible system, we clearly demonstrate that nuclear localization of NPR1 is essential for its activity in inducing PR genes.

Ideal threshold schemes from orthogonal arrays

The work investigates the design of ideal threshold secret sharing in the context of cheating prevention. We showed that each orthogonal array is exactly a defining matrix of an ideal threshold scheme. To prevent cheating, defining matrices should be nonlinear so both the cheaters and honest participants have the same chance of guessing of the valid secret. The last part of the work shows how to construct nonlinear secret sharing based on orthogonal arrays.

Orphan nuclear receptor subfamily NR4A their interplay with other nuclear receptors and functions in osteoblasts

Nurr1, NGFI-B and Nor1 (NR4A2, NR4A1 and NR4A3, respectively) belong to the NR4A subfamily of nuclear receptors. The NR4A receptors are orphan nuclear receptors which means that activating or repressing ligands for these receptors have not been found. NR4A expression is rapidly induced in response to various stimuli including growth factors and the parathyroid hormone (PTH). The studies concerning the NR4A receptors in the central nervous system have demonstrated that they have a major role in the development and function of the dopaminergic neurons of the midbrain and in regulating hypothalamus-pituitary-adrenal-axis. However, the peripheral functions of the NR4A family are largely unknown. Cultured mouse primary osteoblasts, a preosteoblastic cell line and several osteoblastic cell lines were used to investigate the role of NR4A receptors in osteoblasts. NR4A receptors were shown to directly bind to and activate the promoter of the osteopontin gene (OPN) in osteoblastic cells, thus regulating its expression. OPN is a major bone matrix protein expressed throughout the differentiation of preosteoblastic cells into osteoblasts. The activation of the OPN promoter was shown to be dependent on the activation function-1 located in the N-terminal part of Nurr1 and to occur in both monomeric and RXR heterodimeric forms of NR4A receptors. Furthermore, PTH was shown to upregulate OPN expression through the NR4A family. It was also demonstrated that the fibroblast growth factor-8b (FGF-8b) induces the expression of NR4A receptors in osteoblasts as immediate early genes. This induction involved phosphatidylinositol-3 kinase, protein kinase C, and mitogen activated protein kinase, which are all major pathways of FGF signalling. Nurr1 and NGFI-B were shown to induce the proliferation of preosteoblastic cells and to reduce their apoptosis. FGF-8b was shown to stimulate the proliferation of osteoblastic cells through the NR4A receptors. These results suggest that NR4A receptors have a role both in the differentiation of osteoblasts and in the proliferation and apoptosis of preosteoblast. The NR4A receptors were found to bind to the same response element on OPN as the members of the NR3B family of orphan receptors do. Mutual repression was observed between the NR4A receptors and the NR3B receptors. This repression was shown to be dependent on the DNA-binding domains of both receptor families, but to result neither from the competition of DNA binding nor from the competition for coactivators. As the repression was dependent on the relative expression levels of the NR4As and NR3Bs, it seems likely that the ratio of the receptors mediates their activity on their response elements. Rapid induction of the NR4As in response to various stimuli and differential expression of the NR3Bs can effectively control the gene activation by the NR4A receptors. NR4A receptors can bind DNA as monomers, and Nurr1 and NGFI-B can form permissive heterodimers with the retinoid X receptor (RXR). Permissive heterodimers can be activated with RXR agonists, unlike non-permissive heterodimers, which are formed by RXR and retinoic acid receptor or thyroid hormone receptor (RAR and TR, respectively). Non-permissive heterodimers can only be activated by the agonists of the heterodimerizing partner. The mechanisms behind differential response to RXR agonists have remained unresolved. As there are no activating or repressing ligands for the NR4A receptors, it would be important to find out, how they are regulated. Permissiviness of Nurr1/RXR heterodimers was linked to the N-terminal part of Nurr1 ligand-binding domain. This region has previously been shown to mediate the interaction between NRs and corepressors. Non-permissive RAR and TR, permissive Nurr1 and NGFI-B, and RXR were overexpressed with corepressors silencing mediator for retinoic acid and thyroid hormone receptors (SMRT), and with nuclear receptor corepressor in several cell lines. Nurr1 and NGFI-B were found to be repressed by SMRT. The interaction of RXR heterodimers with corepressors was weak in permissive heterodimers and much stronger in non-permissive heterodimers. Non-permissive heterodimers also released corepressors only in response to the agonist of the heterodimeric partner of RXR. In the permissive Nurr1/RXR heterodimer, however, SMRT was released following the treatment with RXR agonists. Corepressor release in response to ligands was found to differentiate permissive heterodimers from non-permissive ones. Corepressors were thus connected to the regulation of NR4A functions. In summary, the studies presented here linked the NR4A family of orphan nuclear receptors to the regulation of osteoblasts. Nurr1 and NGFI-B were found to control the proliferation and apoptosis of preosteoblasts. The studies also demonstrated that cross-talk with the NR3B receptors controls the activity of these orphan receptors. The results clarified the mechanism of permissiviness of RXR-heterodimers. New information was obtained on the regulation and functions of NR4A receptors, for which the ligands are unknown.

Latent TGF-beta Binding Proteins : Adhesive functions and matrix association of LTBP-2 and potential functions of LTBP-1 and LTBP-3 in mesothelioma

Latent transforming growth factor-beta (TGF-beta) binding proteins (LTBPs) -1, -3 and -4 are ECM components whose major function is to augment the secretion and matrix targeting of TGF-beta, a multipotent cytokine. LTBP-2 does not bind small latent TGF-beta but has suggested functions as a structural protein in ECM microfibrils. In the current work we focused on analyzing possible adhesive functions of LTBP-2 as well as on characterizing the kinetics and regulation of LTBP-2 secretion and ECM deposition. We also explored the role of TGF-beta binding LTBPs in endothelial cells activated to mimic angiogenesis as well as in malignant mesothelioma. We found that, unlike most adherent cells, several melanoma cell lines efficiently adhered to purified recombinant LTBP-2. Further characterization revealed that the adhesion was mediated by alpha3beta1 and alpha6beta1 integrins. Heparin also inhibited the melanoma cell adhesion suggesting a role for heparan sulphate proteoglycans. LTBP-2 was also identified as a haptotactic substrate for melanoma cell migration. We used cultured human embryonic lung fibroblasts to analyze the temporal and spatial association of LTBP-2 into ECM. By We found that LTBP-2 was efficiently assembled to the ECM only in confluent cultures following the deposition of fibronectin (FN) and fibrillin-1. In early, subconfluent cultures it remained primarily in soluble form after secretion. LTBP-2 colocalized transiently with FN and fibrillin-1. Silencing of fibrillin-1 expression by lentiviral shRNAs profoundly disrupted the deposition of LTBP-2 indicating that the ECM association of LTBP-2 depends on a pre-formed fibrillin-1 network. Considering the established role of TGF-beta as a regulator of angiogenesis we induced morphological activation of endothelial cells by phorbol 12-myristate 13-acetate (PMA) and followed the fate of LTBP-1 in the endothelial ECM. This resulted in profound proteolytic processing of LTBP-1 and release of latent TGF-beta complexes from the ECM. The processing was coupled with increased activation of MT-MMPs and specific upregulation of MT1-MMP. The major role of MT1-MMP in the proteolysis of LTBP-1 was confirmed by suppressing the expression with lentivirally induced short-hairpin RNAs as well as by various metalloproteinases inhibitors. TGF-beta can promote tumorigenesis of malignant mesothelioma (MM), which is an aggressive tumor of the pleura with poor prognosis. TGF-beta activity was analyzed in a panel of MM tumors by immunohistochemical staining of phosphorylated Smad-2 (P-Smad2). The tumor cells were strongly positive for P-Smad2 whereas LTBP-1 immunoreactivity was abundant in the stroma, and there was a negative correlation between LTBP-1 and P-Smad2 staining. In addition, the high P-Smad2 immunoreactivity correlated with shorter survival of patients. mRNA analysis revealed that TGF-beta1 was the most highly expressed isoform in both normal human pleura and MM tissue. LTBP-1 and LTBP-3 were both abundantly expressed. LTBP-1 was the predominant isoform in established MM cell lines whereas the expression of LTBP-3 was high in control cells. Suppression of LTBP-3 expression by siRNAs resulted in increased TGF-beta activity in MM cell lines accompanied by decreased proliferation. Our results suggest that decreased expression of LTBP-3 in MM could alter the targeting of TGF-beta to the ECM and lead to its increased activation. The current work emphasizes the coordinated process of the assembly and appropriate targeting of LTBPs with distinct adhesive or cytokine harboring properties into the ECM. The hierarchical assembly may have implications in the modulation of signaling events during morphogenesis and tissue remodeling.

Microbe-induced activation of inflammatory cytokine response in human cells

Human body is in continuous contact with microbes. Although many microbes are harmless or beneficial for humans, pathogenic microbes possess a threat to wellbeing. Antimicrobial protection is provided by the immune system, which can be functionally divided into two parts, namely innate and adaptive immunity. The key players of the innate immunity are phagocytic white blood cells such as neutrophils, monocytes, macrophages and dendritic cells (DCs), which constantly monitor the blood and peripheral tissues. These cells are armed for rapid activation upon microbial contact since they express a variety of microbe-recognizing receptors. Macrophages and DCs also act as antigen presenting cells (APCs) and play an important role in the development of adaptive immunity. The development of adaptive immunity requires intimate cooperation between APCs and T lymphocytes and results in microbe-specific immune responses. Moreover, adaptive immunity generates immunological memory, which rapidly and efficiently protects the host from reinfection. Properly functioning immune system requires efficient communication between cells. Cytokines are proteins, which mediate intercellular communication together with direct cell-cell contacts. Immune cells produce inflammatory cytokines rapidly following microbial contact. Inflammatory cytokines modulate the development of local immune response by binding to cell surface receptors, which results in the activation of intracellular signalling and modulates target cell gene expression. One class of inflammatory cytokines chemokines has a major role in regulating cellular traffic. Locally produced inflammatory chemokines guide the recruitment of effector cells to the site of inflammation during microbial infection. In this study two key questions were addressed. First, the ability of pathogenic and non-pathogenic Gram-positive bacteria to activate inflammatory cytokine and chemokine production in different human APCs was compared. In these studies macrophages and DCs were stimulated with pathogenic Steptococcus pyogenes or non-pathogenic Lactobacillus rhamnosus. The second aim of this thesis work was to analyze the role of pro-inflammatory cytokines in the regulation of microbe-induced chemokine production. In these studies bacteria-stimulated macrophages and influenza A virus-infected lung epithelial cells were used as model systems. The results of this study show that although macrophages and DCs share several common antimicrobial functions, these cells have significantly distinct responses against pathogenic and non-pathogenic Gram-positive bacteria. Macrophages were activated in a nearly similar fashion by pathogenic S. pyogenes and non-pathogenic L. rhamnosus. Both bacteria induced the production of similar core set of inflammatory chemokines consisting of several CC-class chemokines and CXCL8. These chemokines attract monocytes, neutrophils, dendritic cells and T cells. Thus, the results suggest that bacteria-activated macrophages efficiently recruit other effector cells to the site of inflammation. Moreover, macrophages seem to be activated by all bacteria irrespective of their pathogenicity. DCs, in contrast, were efficiently activated only by pathogenic S. pyogenes, which induced DC maturation and production of several inflammatory cytokines and chemokines. In contrast, L. rhamnosus-stimulated DCs matured only partially and, most importantly, these cells did not produce inflammatory cytokines or chemokines. L. rhamnosus-stimulated DCs had a phenotype of "semi-mature" DCs and this type of DCs have been suggested to enhance tolerogenic adaptive immune responses. Since DCs have an essential role in the development of adaptive immune response the results suggest that, in contrast to macrophages, DCs may be able to discriminate between pathogenic and non-pathogenic bacteria and thus mount appropriate inflammatory or tolerogenic adaptive immune response depending on the microbe in question. The results of this study also show that pro-inflammatory cytokines can contribute to microbe-induced chemokine production at multiple levels. S. pyogenes-induced type I interferon (IFN) was found to enhance the production of certain inflammatory chemokines in macrophages during bacterial stimulation. Thus, bacteria-induced chemokine production is regulated by direct (microbe-induced) and indirect (pro-inflammatory cytokine-induced) mechanisms during inflammation. In epithelial cells IFN- and tumor necrosis factor- (TNF-) were found to enhance the expression of PRRs and components of cellular signal transduction machinery. Pre-treatment of epithelial cells with these cytokines prior to virus infection resulted in markedly enhanced chemokine response compared to untreated cells. In conclusion, the results obtained from this study show that pro-inflammatory cytokines can enhance microbe-induced chemokine production during microbial infection by providing a positive feedback loop. In addition, pro-inflammatory cytokines can render normally low-responding cells to high chemokine producers via enhancement of microbial detection and signal transduction.

Neuromagnetic studies on cortical somatosensory functions in infants and children : Normal development and effect of early brain lesions

Until recently, objective investigation of the functional development of the human brain in vivo was challenged by the lack of noninvasive research methods. Consequently, fairly little is known about cortical processing of sensory information even in healthy infants and children. Furthermore, mechanisms by which early brain insults affect brain development and function are poorly understood. In this thesis, we used magnetoencephalography (MEG) to investigate development of cortical somatosensory functions in healthy infants, very premature infants at risk for neurological disorders, and adolescents with hemiplegic cerebral palsy (CP). In newborns, stimulation of the hand activated both the contralateral primary (SIc) and secondary somatosensory cortices (SIIc). The activation patterns differed from those of adults, however. Some of the earliest SIc responses, constantly present in adults, were completely lacking in newborns and the effect of sleep stage on SIIc responses differed. These discrepancies between newborns and adults reflect the still developmental stage of the newborns’ somatosensory system. Its further maturation was demonstrated by a systematic transformation of the SIc response pattern with age. The main early adult­like components were present by age two. In very preterm infants, at term age, the SIc and SIIc were activated at similar latencies as in healthy fullterm newborns, but the SIc activity was weaker in the preterm group. The SIIc response was absent in four out of the six infants with brain lesions of the underlying hemisphere. Determining the prognostic value of this finding remains a subject for future studies, however. In the CP adolescents with pure subcortical lesions, contrasting their unilateral symptoms, the SIc responses of both hemispheres differed from those of controls: For example the distance between SIc representation areas for digits II and V was shorter bilaterally. In four of the five CP patients with cortico­subcortical brain lesions, no normal early SIc responses were evoked by stimulation of the palsied hand. The varying differences in neuronal functions, underlying the common clinical symptoms, call for investigation of more precisely designed rehabilitation strategies resting on knowledge about individual functional alterations in the sensorimotor networks.

Intracellular Pathogen Sensor NOD2 Programs Macrophages to Trigger Notch1 Activation

Intracellular pathogen sensor, NOD2, has been implicated in regulation of wide range of anti-inflammatory responses critical during development of a diverse array of inflammatory diseases; however, underlying molecular details are still imprecisely understood. In this study, we demonstrate that NOD2 programs macrophages to trigger Notch1 signaling. Signaling perturbations or genetic approaches suggest signaling integration through cross-talk between Notch1-PI3K during the NOD2-triggered expression of a multitude of immunological parameters including COX-2/PGE(2) and IL-10. NOD2 stimulation enhanced active recruitment of CSL/RBP-Jk on the COX-2 promoter in vivo. Intriguingly, nitric oxide assumes critical importance in NOD2-mediated activation of Notch1 signaling as iNOS(-/-) macrophages exhibited compromised ability to execute NOD2-triggered Notch1 signaling responses. Correlative evidence demonstrates that this mechanism operates in vivo in brain and splenocytes derived from wild type, but not from iNOS(-/-) mice. Importantly, NOD2-driven activation of the Notch1-PI3K signaling axis contributes to its capacity to impart survival of macrophages against TNF-alpha or IFN-gamma-mediated apoptosis and resolution of inflammation. Current investigation identifies Notch1-PI3K as signaling cohorts involved in the NOD2-triggered expression of a battery of genes associated with anti-inflammatory functions. These findings serve as a paradigm to understand the pathogenesis of NOD2-associated inflammatory diseases and clearly pave a way toward development of novel therapeutics.

The Equations of Equilibrium in Orthogonal Curvilinear Reference Coordinates

Analytical solutions to problems in finite elasticity are most often derived using the semi-inverse approach along with the spatial form of the equations of motion involving the Cauchy stress tensor. This procedure is somewhat indirect since the spatial equations involve derivatives with respect to spatial coordinates while the unknown functions are in terms of material coordinates, thus necessitating the use of the chain rule. In this classroom note, we derive compact expressions for the components of the divergence, with respect to orthogonal material coordinates, of the first Piola-Kirchhoff stress tensor. The spatial coordinate system is also assumed to be an orthogonal curvilinear one, although, not necessarily of the same type as the material coordinate system. We show by means of some example applications how analytical solutions can be derived more directly using the derived results.

Pathogen-specific TLR2 Protein Activation Programs Macrophages to Induce Wnt-beta-Catenin Signaling

Innate immunity recognizes and resists various pathogens; however, the mechanisms regulating pathogen versus non-pathogen discrimination are still imprecisely understood. Here, we demonstrate that pathogen-specific activation of TLR2 upon infection with Mycobacterium bovis BCG, in comparison with other pathogenic microbes, including Salmonella typhimurium and Staphylococcus aureus, programs macrophages for robust up-regulation of signaling cohorts of Wnt-beta-catenin signaling. Signaling perturbations or genetic approaches suggest that infection-mediated stimulation of Wnt-beta-catenin is vital for activation of Notch1 signaling. Interestingly, inducible NOS (iNOS) activity is pivotal for TLR2-mediated activation of Wnt-beta-catenin signaling as iNOS(-/-) mice demonstrated compromised ability to trigger activation of Wnt-beta-catenin signaling as well as Notch1-mediated cellular responses. Intriguingly, TLR2-driven integration of iNOS/NO, Wnt-beta-catenin, and Notch1 signaling contributes to its capacity to regulate the battery of genes associated with T(Reg) cell lineage commitment. These findings reveal a role for differential stimulation of TLR2 in deciding the strength of Wnt-beta-catenin signaling, which together with signals from Notch1 contributes toward the modulation of a defined set of effector functions in macrophages and thus establishes a conceptual framework for the development of novel therapeutics.

ATP release and autocrine signaling through P2X4 receptors regulate gamma delta T cell activation

Purinergic signaling plays a key role in a variety of physiological functions, including regulation of immune responses. Conventional alpha beta T cells release ATP upon TCR cross-linking; ATP binds to purinergic receptors expressed by these cells and triggers T cell activation in an autocrine and paracrine manner. Here, we studied whether similar purinergic signaling pathways also operate in the ``unconventional'' gamma delta T lymphocytes. We observed that gamma delta T cells purified from peripheral human blood rapidly release ATP upon in vitro stimulation with anti-CD3/CD28-coated beads or IPP. Pretreatment of gamma delta T cells with (10)panx-1, CBX, or Bf A reversed the stimulation-induced increase in extracellular ATP concentration, indicating that panx-1, connexin hemichannels, and vesicular exocytosis contribute to the controlled release of cellular ATP. Blockade of ATP release with (10)panx-1 inhibited Ca2+ signaling in response to TCR stimulation. qPCR revealed that gamma delta T cells predominantly express purinergic receptor subtypes A2a, P2X1, P2X4, P2X7, and P2Y11. We found that pharmacological inhibition of P2X4 receptors with TNP-ATP inhibited transcriptional up-regulation of TNF-alpha and IFN-gamma in gamma delta T cells stimulated with anti-CD3/CD28-coated beads or IPP. Our data thus indicate that purinergic signaling via P2X4 receptors plays an important role in orchestrating the functional response of circulating human gamma delta T cells. J. Leukoc. Biol. 92: 787-794; 2012.