Unfolded singularities of analytic differential equations

La thèse est composée d’un chapitre de préliminaires et de deux articles sur le sujet du déploiement de singularités d’équations différentielles ordinaires analytiques dans le plan complexe. L’article Analytic classification of families of linear differential systems unfolding a resonant irregular singularity traite le problème de l’équivalence analytique de familles paramétriques de systèmes linéaires en dimension 2 qui déploient une singularité résonante générique de rang de Poincaré 1 dont la matrice principale est composée d’un seul bloc de Jordan. La question: quand deux telles familles sontelles équivalentes au moyen d’un changement analytique de coordonnées au voisinage d’une singularité? est complètement résolue et l’espace des modules des classes d’équivalence analytiques est décrit en termes d’un ensemble d’invariants formels et d’un invariant analytique, obtenu à partir de la trace de la monodromie. Des déploiements universels sont donnés pour toutes ces singularités. Dans l’article Confluence of singularities of non-linear differential equations via Borel–Laplace transformations on cherche des solutions bornées de systèmes paramétriques des équations non-linéaires de la variété centre de dimension 1 d’une singularité col-noeud déployée dans une famille de champs vectoriels complexes. En général, un système d’ÉDO analytiques avec une singularité double possède une unique solution formelle divergente au voisinage de la singularité, à laquelle on peut associer des vraies solutions sur certains secteurs dans le plan complexe en utilisant les transformations de Borel–Laplace. L’article montre comment généraliser cette méthode et déployer les solutions sectorielles. On construit des solutions de systèmes paramétriques, avec deux singularités régulières déployant une singularité irrégulière double, qui sont bornées sur des domaines «spirals» attachés aux deux points singuliers, et qui, à la limite, convergent vers une paire de solutions sectorielles couvrant un voisinage de la singularité confluente. La méthode apporte une description unifiée pour toutes les valeurs du paramètre.

Differential induction, isolation, physicochemical and molecular characterization of temperate phages of environmental Vibrio cholerae as evidence of phage mediated Horizontal Gene Transfer

The resurgence of the enteric pathogen Vibrio cholerae, the causative organism of epidemic cholera, remains a major health problem in many developing countries like India. The southern Indian state of Kerala is endemic to cholera. The outbreaks of cholera follow a seasonal pattern in regions of endemicity. Marine aquaculture settings and mangrove environments of Kerala serve as reservoirs for V. cholerae. The non-O1/non-O139 environmental isolates of V. cholerae with incomplete ‘virulence casette’ are to be dealt with caution as they constitute a major reservoir of diverse virulence genes in the marine environment and play a crucial role in pathogenicity and horizontal gene transfer. The genes coding cholera toxin are borne on, and can be infectiously transmitted by CTXΦ, a filamentous lysogenic vibriophages. Temperate phages can provide crucial virulence and fitness factors affecting cell metabolism, bacterial adhesion, colonization, immunity, antibiotic resistance and serum resistance. The present study was an attempt to screen the marine environments like aquafarms and mangroves of coastal areas of Alappuzha and Cochin, Kerala for the presence of lysogenic V. cholerae, to study their pathogenicity and also gene transfer potential. Phenotypic and molecular methods were used for identification of isolates as V. cholerae. The thirty one isolates which were Gram negative, oxidase positive, fermentative, with or without gas production on MOF media and which showed yellow coloured colonies on TCBS (Thiosulfate Citrate Bile salt Sucrose) agar were segregated as vibrios. Twenty two environmental V. cholerae strains of both O1 and non- O1/non-O139 serogroups on induction with mitomycin C showed the presence of lysogenic phages. They produced characteristic turbid plaques in double agar overlay assay using the indicator strain V. cholerae El Tor MAK 757. PCR based molecular typing with primers targeting specific conserved sequences in the bacterial genome, demonstrated genetic diversity among these lysogen containing non-O1 V. cholerae . Polymerase chain reaction was also employed as a rapid screening method to verify the presence of 9 virulence genes namely, ctxA, ctxB, ace, hlyA, toxR, zot,tcpA, ninT and nanH, using gene specific primers. The presence of tcpA gene in ALPVC3 was alarming, as it indicates the possibility of an epidemic by accepting the cholera. Differential induction studies used ΦALPVC3, ΦALPVC11, ΦALPVC12 and ΦEKM14, underlining the possibility of prophage induction in natural ecosystems, due to abiotic factors like antibiotics, pollutants, temperature and UV. The efficiency of induction of prophages varied considerably in response to the different induction agents. The growth curve of lysogenic V. cholerae used in the study drastically varied in the presence of strong prophage inducers like antibiotics and UV. Bacterial cell lysis was directly proportional to increase in phage number due to induction. Morphological characterization of vibriophages by Transmission Electron Microscopy revealed hexagonal heads for all the four phages. Vibriophage ΦALPVC3 exhibited isometric and contractile tails characteristic of family Myoviridae, while phages ΦALPVC11 and ΦALPVC12 demonstrated the typical hexagonal head and non-contractile tail of family Siphoviridae. ΦEKM14, the podophage was distinguished by short non-contractile tail and icosahedral head. This work demonstrated that environmental parameters can influence the viability and cell adsorption rates of V. cholerae phages. Adsorption studies showed 100% adsorption of ΦALPVC3 ΦALPVC11, ΦALPVC12 and ΦEKM14 after 25, 30, 40 and 35 minutes respectively. Exposure to high temperatures ranging from 50ºC to 100ºC drastically reduced phage viability. The optimum concentration of NaCl required for survival of vibriophages except ΦEKM14 was 0.5 M and that for ΦEKM14 was 1M NaCl. Survival of phage particles was maximum at pH 7-8. V. cholerae is assumed to have existed long before their human host and so the pathogenic clones may have evolved from aquatic forms which later colonized the human intestine by progressive acquisition of genes. This is supported by the fact that the vast majority of V. cholerae strains are still part of the natural aquatic environment. CTXΦ has played a critical role in the evolution of the pathogenicity of V. cholerae as it can transmit the ctxAB gene. The unusual transformation of V. cholerae strains associated with epidemics and the emergence of V. cholera O139 demonstrates the evolutionary success of the organism in attaining greater fitness. Genetic changes in pathogenic V. cholerae constitute a natural process for developing immunity within an endemically infected population. The alternative hosts and lysogenic environmental V. cholerae strains may potentially act as cofactors in promoting cholera phage ‘‘blooms’’ within aquatic environments, thereby influencing transmission of phage sensitive, pathogenic V. cholerae strains by aquatic vehicles. Differential induction of the phages is a clear indication of the impact of environmental pollution and global changes on phage induction. The development of molecular biology techniques offered an accessible gateway for investigating the molecular events leading to genetic diversity in the marine environment. Using nucleic acids as targets, the methods of fingerprinting like ERIC PCR and BOX PCR, revealed that the marine environment harbours potentially pathogenic group of bacteria with genetic diversity. The distribution of virulence associated genes in the environmental isolates of V. cholerae provides tangible material for further investigation. Nucleotide and protein sequence analysis alongwith protein structure prediction aids in better understanding of the variation inalleles of same gene in different ecological niche and its impact on the protein structure for attaining greater fitness of pathogens. The evidences of the co-evolution of virulence genes in toxigenic V. cholerae O1 from different lineages of environmental non-O1 strains is alarming. Transduction studies would indicate that the phenomenon of acquisition of these virulence genes by lateral gene transfer, although rare, is not quite uncommon amongst non-O1/non-O139 V. cholerae and it has a key role in diversification. All these considerations justify the need for an integrated approach towards the development of an effective surveillance system to monitor evolution of V. cholerae strains with epidemic potential. Results presented in this study, if considered together with the mechanism proposed as above, would strongly suggest that the bacteriophage also intervenes as a variable in shaping the cholera bacterium, which cannot be ignored and hinting at imminent future epidemics.

Differential changes in transforming growth factor β isoform expression during postnatal cardiac growth

Transforming growth factor-β (TGF-β) is synthesised as an inactive precursor protein; this is cleaved to produce the mature peptide and a latency associated protein (LAP), which remains associated with the mature peptide until activation by LAP degradation. Isoform specific antibodies raised against the LAPs for TGF-β2and -β3were used to determine the myocardial levels of LAP (activatable TGF-β) and full length precursor (inactive TGF-β) forms during post-natal development in the rat. TGF-β2was present predominantly as the precursor in 2 day old myocardium. There was an age-dependent shift from precursor protein to LAP between 2 and 28 days. A corresponding increase in the level of mature (activatable) TGF-β2was found. TGF-β3was detected in significant quantities only as LAP. However, a four-fold increase in the expression of TGF-β3LAP was observed between 2 and 28 days. The substantial increases in activatable forms of TGF-β2and -β3that occur in myocardium during the first 28 days of life in the rat support a role for these proteins in post-natal cardiac development.

Physiological and morphological adaptations of herbaceous perennial legumes allow differential access to sources of varyingly soluble phosphate

The aim of this study was to investigate the capacity of three perennial legume species to access sources of varyingly soluble phosphorus (P) and their associated morphological and physiological adaptations. Two Australian native legumes with pasture potential (Cullen australasicum and Kennedia prostrata) and Medicago sativa cv. SARDI 10 were grown in sand under two P levels (6 and 40 µg P g−1) supplied as Ca(H2PO4)2·H2O (Ca-P, highly soluble, used in many fertilizers) or as one of three sparingly soluble forms: Ca10(OH)2(PO4)6 (apatite-P, found in relatively young soils; major constituent of rock phosphate), C6H6O24P6Na12 (inositol-P, the most common form of organic P in soil) and FePO4 (Fe-P, a poorly-available inorganic source of P). All species grew well with soluble P. When 6 µg P g−1 was supplied as sparingly soluble P, plant dry weight (DW) and P uptake were very low for C. australasicum and M. sativa (0.1–0.4 g DW) with the exception of M. sativa supplied with apatite-P (1.5 g). In contrast, K. prostrata grew well with inositol-P (1.0 g) and Fe-P (0.7 g), and even better with apatite-P (1.7 g), similar to that with Ca-P (1.9 g). Phosphorus uptake at 6 µg P g−1 was highly correlated with total root length, total rhizosphere carboxylate content and total rhizosphere acid phosphatase (EC 3.1.3.2) activity. These findings provide strong indications that there are opportunities to utilize local Australian legumes in low P pasture systems to access sparingly soluble soil P and increase perennial legume productivity, diversity and sustainability.

Crosstalk between oestrogen receptors and thyroid hormone receptor isoforms results in differential regulation of the preproenkephalin gene

Nuclear receptors are ligand-activated transcription factors, which have the potential to integrate internal metabolic events in an organism, with consequences for control of behaviour. Previous studies from this laboratory have shown that thyroid hormone receptor (TR) isoforms can inhibit oestrogen receptor (ER)alpha-mediated induction of preproenkephalin (PPE) gene expression in the hypothalamus. Also, thyroid hormone administration inhibits lordosis, a behaviour facilitated by PPE expression. We have examined the effect of multiple ligand-binding TR isoforms on the ER-mediated induction of the PPE gene in transient transfection assays in CV-1 cells. On a natural PPE gene promoter fragment containing two putative oestrogen response elements (EREs), both ER alpha and beta isoforms mediate a four to five-fold induction by oestrogen. Cotransfection of TR alpha 1 along with ER alpha inhibited the ER alpha transactivation of PPE by approximately 50%. However, cotransfection with either TR beta 1 or TR beta 2 expression plasmids produced no effect on the ER alpha or ER beta mediated induction of PPE. Therefore, under these experimental conditions, interactions with a single ER isoform are specific to an individual TR isoform. Transfection with a TR alpha 1 DNA-binding mutant could also inhibit ER alpha transactivation, suggesting that competition for binding on the ERE may not be the exclusive mechanism for inhibition. Data with the coactivator, SRC-1, suggested that coactivator squelching may participate in the inhibition. In dramatic contrast, when ER beta is cotransfected, TR alpha 1 stimulated ER beta-mediated transactivation of PPE by approximately eight-fold over control levels. This is the first study revealing specific interactions among nuclear receptor isoforms on a neuroendocrine promoter. These data also suggest that the combinatorics of ER and TR isoforms allow multiple forms of flexible gene regulations in the service of neuroendocrine integration.

INDEX OF AN IMPLICIT DIFFERENTIAL EQUATION

In this paper we introduce the concept of the index of an implicit differential equation F(x,y,p) = 0, where F is a smooth function, p = dy/dx, F(p) = 0 and F(pp) = 0 at an isolated singular point. We also apply the results to study the geometry of surfaces in R(5).

Protein variation in blood-dwelling schistosome worms generated by differential splicing of micro-exon gene transcripts

Schistosoma mansoni is a well-adapted blood-dwelling parasitic helminth, persisting for decades in its human host despite being continually exposed to potential immune attack. Here, we describe in detail micro-exon genes (MEG) in S. mansoni, some present in multiple copies, which represent a novel molecular system for creating protein variation through the alternate splicing of short (<= 36 bp) symmetric exons organized in tandem. Analysis of three closely related copies of one MEG family allowed us to trace several evolutionary events and propose a mechanism for micro-exon generation and diversification. Microarray experiments show that the majority of MEGs are up-regulated in life cycle stages associated with establishment in the mammalian host after skin penetration. Sequencing of RT-PCR products allowed the description of several alternate splice forms of micro-exon genes, highlighting the potential use of these transcripts to generate a complex pool of protein variants. We obtained direct evidence for the existence of such pools by proteomic analysis of secretions from migrating schistosomula and mature eggs. Whole-mount in situ hybridization and immunolocalization showed that MEG transcripts and proteins were restricted to glands or epithelia exposed to the external environment. The ability of schistosomes to produce a complex pool of variant proteins aligns them with the other major groups of blood parasites, but using a completely different mechanism. We believe that our data open a new chapter in the study of immune evasion by schistosomes, and their ability to generate variant proteins could represent a significant obstacle to vaccine development.

Drug Excipient Interaction Study with Polymorphic Forms of Tibolone

Powder mixtures (1:1) of tibolone polymorphic forms I (monoclinic) and II (triclinic) and excipients have been prepared and compacted. The samples were stored at 50 degrees C and 90% RH for one month and subsequently were evaluated using differential scanning calorimetry (DSC) and high-performance liquid chromatography (HPLC). The results indicate that during the compaction, the applied pressure reduced the chemical stability of tibolone in both polymorph forms. The triclinic form was more chemically unstable, both pure and in contact with excipients, than the monoclinic form. Lactose monohydrate was shown to reduce chemical degradation for both forms. Ascorbyl palmitate was shown to affect the tibolone stability differently depending on the polymorphic form used.

Differential gene expression analysis of Paracoccidioides brasiliensis during keratinocyte infection

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Differential antibody isotype expression to the major Paracoccidioides brasiliensis antigen in juvenile and adult form paracoccidioidomycosis

We investigated the relationship between antibody response to the major Paracoccidioides brasiliensis antigen, a 43-kDa glycoprotein, and the two paracoccidioidomycosis (PCM) clinical presentations, the juvenile and the adult forms. Total immunoglobulin G (IgG), IgG isotypes, and IgA anti-gp43 antibodies were determined by enzyme-linked immunosorbent assay in patients' sera. Juvenile PCM patients had higher (P =.003) IgG anti-gp43 levels than adult form patients. IgG1 subclass levels, however, were comparable between the two clinical forms. Patients with the juvenile form had higher (P <.001) IgG4, but lower(P =.03) IgG2 levels than patients with the adult form. The IgG4 isotype, regulated by interleukin 4, was found in all juvenile form patients but in only 12% of the adult form patients. In contrast, high levels of the IgG2 isotype, regulated by interferon-gamma, were found in 41% of the adult PCM patients, mainly those with a more benign disease, but in only 12% of the juvenile patients. IgG3 was either absent or detected at low levels. These results demonstrate, for the first time, specific IgG4 antibodies in the humoral immune response of patients with an endemic deep mycosis and suggest that the switch to the IgG subclasses in PCM is regulated by the patients' T-helper subset (Th-l or Th-2) dominant cytokine profile. A possible role for IgG4 in the immunopathogenesis of the juvenile, more severe form of the disease is discussed. Finally, IgA was found mainly in adult form patients, probably as a result of the chronic mucosal antigenic stimulation characteristic of this form. (C) Elsevier, Paris.

Phosphate forms in plant and their internal buffering in five soybean cultivars

Diferenças inter e intra-específicas na habilidade de suportar períodos de estresse nutricional podem dever-se à capacidade de armazenar e liberar íons dos vacúolos, e, ou, à intensidade de retranslocação de nutrientes em tais condições. Neste trabalho, pretendeu-se avaliar diferenças varietais quanto ao tamanho do pool não-metabólico de Pi; velocidade de liberação do Pi previamente armazenado (VLPi), quando o P citoplasmático cai a um valor limite; capacidade de transportar Pi de regiões menos ativas para aquelas mais ativas metabolicamente e definir compartimentos que são preferencialmente fontes e os que são preferencialmente drenos para o Pi, em condições de absorção limitada de P. Avaliaram-se a produção de matéria seca e os teores internos de Pi, orgânico (Po) e total solúvel em ácido (Pts), de diferentes órgãos de plantas dos cultivares de soja (Glycine max L. Merrill) Santa Rosa, Uberaba, IAC8, Doko e UFV1, submetidos a oito dias de omissão do elemento. A VLPi foi estimada como tangente às equações obtidas para Pi como função do perído de omissão no ponto médio do período de omissão em que houve maior decréscimo em Pi (zero a quatro dias de omissão de P), t = dois dias, considerando-se que -deltaPi/deltat expressa a velocidade de liberação de Pi. A capacidade interna de tamponamento de Pi (CTIPi) foi calculada como o inverso da VLPi. O cultivar Santa Rosa apresentou maior capacidade de armazenar Pi, quando o suprimento externo foi alto, liberando-o mais intensamente sob condições de baixo suprimento de P que os cultivares IAC8 e UFV1. O cultivar Uberaba mostrou-se superior ao Doko em sua habilidade de armazenar e utilizar o Pi. Folhas superiores mostraram ser o principal dreno para o Pi armazenado em folhas medianas e inferiores, seguidas por raízes e caules. Raízes comportaram-se como fontes ou drenos para o Pi. Raízes e folhas superiores apresentaram maiores (VLPi) e menores valores de CTIPi que folhas medianas e folhas inferiores, sendo o caule o compartimento com menor VLPi e maior CTIPi. Dentre as variedades, as diferenças foram pequenas, destacando-se a maior VLPi e menor CTIPi do cultivar Santa Rosa. O cultivar Doko apresentou a menor VLPi e maior CTIPi, enquanto Uberaba, IAC8 e UFV1 ocuparam posição intermediária quanto a essas características.

Differential alterations in the activity of matrix metalloproteinases within the nervous tissue of dogs in distinct manifestations of visceral leishmaniasis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Differential MMP-2 and MMP-9 Activity and Collagen Distribution in Skeletal Muscle from pacu (Piaractus mesopotamicus) During Juvenile and Adult Growth Phases

Here, we evaluated collagen distribution and matrix metalloproteinases (MMPs) MMP-2 and MMP-9 activities in skeletal muscle of pacu (Piaractus mesopotamicus) during juvenile and adult growth phases. Muscle samples from juvenile and adult fishes were processed by histochemistry for collagen system fibers and for gelatin-zymography for MMP-2 and MMP-9 activities analysis. Picrosirius staining revealed a myosept, endomysium, and perimysium-like structures in both growth phases and muscle types, with increased areas of collagen fibers in adults, mainly in red muscle. Reticulin staining showed that reticular fibers in the endomysium-like structure were thinner and discontinuous in the red muscle fibers. The zymography revealed clear bands of the pro-MMP-9, active-MMP-9, intermediate-MMP-2, and active-MMP-2 forms in red and white muscle in both growth phases. MMP-2 activity was more intense in juvenile than adult muscle fibers. Comparing the red and white muscle types, MMP-2 activity was significantly higher in red muscle in adult phase only. The activity of MMP-9 forms was similar in juvenile red and white muscles and in the adult red muscle, without any activity in adult white muscle. In conclusion, our results show that, in pacu, the higher activities of MMP-2 and -9 are associated with the rapid muscle growth in juvenile age and in adult fish, these activities are related with a different red and white muscle physiology. This study may contribute to the understanding muscle growth mechanisms and may also contribute to analyse red and the white muscle parameters of firmness and softness, respectively, of the commercial product. Anat Rec, 292:387-395, 2009. (C) 2009 Wiley-Liss, Inc.

Voltammetric assay of albendazole in pharmaceutical dosage forms

A simple, rapid inexpensive voltammetric method have been developed for the quantitative determination of albendazole (ABZ) as the pure assay, by direct dissolution of commercial tablets in HCl solutions. Studies with linear sweep (LSV), square-wave (SWV) and differential pulse voltammetry (DPV) were carried out ABZ in aqueous medium at a glassy carbon electrode. A well defined irreversible oxidation peak current was obtained at 1,00V vs. SCE. The method permits a precise quantitative determination of ABZ using the standard addition method. The detection limits for the three voltammetric techniques were found to be 3.0 x 10(-5) M (LSV), 6.2 x 10(-5) M (SWV) and 4.0 x 10(-5) M (DPV).

Plane waves in noncommutative fluids

We study the dynamics of the noncommutative fluid in the Snyder space perturbatively at the first order in powers of the noncommutative parameter. The linearized noncommutative fluid dynamics is described by a system of coupled linear partial differential equations in which the variables are the fluid density and the fluid potentials. We show that these equations admit a set of solutions that are monochromatic plane waves for the fluid density and two of the potentials and a linear function for the third potential. The energy-momentum tensor of the plane waves is calculated. © 2013 Elsevier B.V.