Eigenvalue Problem in Two Dimensions for an Irregular Boundary II: Neumann Condition

We formulate a systematic elegant perturbative scheme for determining the eigenvalues of the Helmholtz equation (\bigtriangledown^{2} + k^{2}){\psi} = 0 in two dimensions when the normal derivative of {\psi} vanishes on an irregular closed curve. Unique feature of this method, unlike other perturbation schemes, is that it does not require a separate formalism to treat degeneracies. Degenerate states are handled equally elegantly as the non-degenerate ones. A real parameter, extracted from the parameters defining the irregular boundary, serves as a perturbation parameter in this scheme as opposed to earlier schemes where the perturbation parameter is an artificial one. The efficacy of the proposed scheme is gauged by calculating the eigenvalues for elliptical and supercircular boundaries and comparing with the results obtained numerically. We also present a simple and interesting semi-empirical formula, determining the eigenspectrum of the 2D Helmholtz equation with the Dirichlet or the Neumann condition for a supercircular boundary. A comparison of the eigenspectrum for several low-lying modes obtained by employing the formula with the corresponding numerical estimates shows good agreement for a wide range of the supercircular exponent.Comment: 26 pages, 12 figure

Detecção de anticorpos para Anaplasma sp. em pequenos ruminantes no semi-árido do estado de Pernambuco, Brasil

Neste trabalho é descrita a detecção de anticorpos para Anaplasma sp. em caprinos e ovinos da região do semi-árido do Estado de Pernambuco, Brasil, utilizando-se um ensaio de imunoadsorção enzimática baseado em MSP5 recombinante de Anaplasma marginale. Foram analisados soros de 243 caprinos e 68 ovinos provenientes do município de Ibimirim, e observadas freqüências de anticorpos de 11,93% (29/243) e 16,17% (11/68) para caprinos e ovinos, respectivamente. A importância epidemiológica dos achados foi discutida.This paper reports the detection of antibodies against Anaplasma sp. in goats and sheep from the semi-arid region from Pernambuco State, Brazil, using an enzyme-linked immunosorbent assay with recombinant MSP5 of Anaplasma marginale. Sera from 243 goats and 68 sheep from Ibimirim municipality were analyzed and frequencies of antibodies of 11.93% (29/243) and 16.17% (11/68) were found for goats and sheep, respectively. The epidemiological relevance of the findings was discussed

Point Mutations in c-Myc Uncouple Neoplastic Transformation from Multiple Other Phenotypes in Rat Fibroblasts

Deregulation of c-Myc (Myc) occurs in many cancers. In addition to transforming various cell types, Myc also influences additional transformation-associated cellular phenotypes including proliferation, survival, genomic instability, reactive oxygen species production, and metabolism. Although Myc is wild type in most cancers (wtMyc), it occasionally acquires point mutations in certain lymphomas. Some of these mutations confer a survival advantage despite partially attenuating proliferation and transformation. Here, we have evaluated four naturally-occurring or synthetic point mutations of Myc for their ability to affect these phenotypes, as well as to promote genomic instability, to generate reactive oxygen species and to up-regulate aerobic glycolysis and oxidative phosphorylation. Our findings indicate that many of these phenotypes are genetically and functionally independent of one another and are not necessary for transformation. Specifically, the higher rate of glucose metabolism known to be associated with wtMyc deregulation was found to be independent of transformation. One mutation (Q131R) was greatly impaired for nearly all of the studied Myc phenotypes, yet was able to retain some ability to transform. These findings indicate that, while the Myc phenotypes examined here make additive contributions to transformation, none, with the possible exception of increased reliance on extracellular glutamine for survival, are necessary for achieving this state

Septin 9 isoform expression, localization and epigenetic changes during human and mouse breast cancer progression

International audienceABSTRACT: INTRODUCTION: Altered expression of Septin 9 (SEPT9), a septin coding for multiple isoform variants, has been observed in several carcinomas including colorectal, head and neck, ovarian and breast, compared to normal tissue. Mechanisms regulating its expression during tumor initiation and progression in vivo and the oncogenic function of its different isoforms remain elusive. METHODS: Using an integrative approach, we investigated SEPT9 at the genetic, epigenetic, mRNA, and protein levels in breast cancer. We analyzed a panel of breast cancer cell lines, human primary tumors and corresponding tumor-free areas, normal breast from reduction mammoplasty patients, as well as primary mammary gland adenocarcinomas derived from the Polyoma Virus Middle T antigen mouse model (PyMT). MCF7 clones expressing individual GFP-tagged SEPT9 isoforms were used to determine their respective intracellular distribution and affect on cell migration. RESULTS: An overall increase in gene amplification and altered expression of SEPT9 was observed during breast tumorigenesis. We identified an intragenic alternative promoter whose methylation regulates SEPT9_v3 expression. Transfection of specific GFP-SEPT9 isoforms in MCF7 cells indicates that these isoforms exhibit differential localization and affect migration rates. Additionally, the loss of an uncharacterized SEPT9 nucleolar localization is observed during tumorigenesis. CONCLUSIONS: In this study we found conserved in vivo changes of SEPT9 gene amplification and overexpression during human and mouse breast tumorigenesis. We show that DNA methylation is a prominent mechanism responsible for regulating differential SEPT9 isoform expression and that breast tumor samples exhibit distinctive SEPT9 intracellular localization. Together, these findings support the significance of SEPT9 as a promising tool in breast cancer detection and further emphasize the importance of analyzing and targeting SEPT9 isoform specific expression and function

A cytomorphological and immunohistochemical profile of aggressive B-cell lymphoma: high clinical impact of a cumulative immunohistochemical outcome predictor score

We analyzed morphological and immunohistochemical features in 174 aggressive B-cell lymphomas of nodal and extranodal origin. Morphological features included presence or absence of a follicular component and cytologic criteria according to the Kiel classification, whereas immunohistochemical studies included expression of CD10, BCL-2, BCL-6, IRF4/MUM1, HLA-DR, p53, Ki-67 and the assessment of plasmacytoid differentiation. Patients were treated with a CHOP-like regimen. While the presence or absence of either CD10, BCL-6 and IRF4/MUM1 reactivity or plasmacytoid differentiation did not identify particular cytomorphologic or site-specific subtypes, we found that expression of CD10 and BCL-6, and a low reactivity for IRF4/MUM1 were favourable prognostic indicators. In contrast, BCL-2 expression and presence of a monotypic cytoplasmic immunoglobulin expression was associated with an unfavourable prognosis in univariate analyses. Meta-analysis of these data resulted in the development of a cumulative immunohistochemical outcome predictor score (CIOPS) enabling the recognition of four distinct prognostic groups. Multivariate analysis proved this score to be independent of the international prognostic index. Such a cumulative immunohistochemical scoring approach might provide a valuable alternative in the recognition of defined risk types of aggressive B-cell lymphomas

A mathematical model of quorum sensing regulated EPS production in biofilm communities

<p>Abstract</p> <p>Background</p> <p>Biofilms are microbial communities encased in a layer of extracellular polymeric substances (EPS). The EPS matrix provides several functional purposes for the biofilm, such as protecting bacteria from environmental stresses, and providing mechanical stability. Quorum sensing is a cell-cell communication mechanism used by several bacterial taxa to coordinate gene expression and behaviour in groups, based on population densities.</p> <p>Model</p> <p>We mathematically model quorum sensing and EPS production in a growing biofilm under various environmental conditions, to study how a developing biofilm impacts quorum sensing, and conversely, how a biofilm is affected by quorum sensing-regulated EPS production. We investigate circumstances when using quorum-sensing regulated EPS production is a beneficial strategy for biofilm cells.</p> <p>Results</p> <p>We find that biofilms that use quorum sensing to induce increased EPS production do not obtain the high cell populations of low-EPS producers, but can rapidly increase their volume to parallel high-EPS producers. Quorum sensing-induced EPS production allows a biofilm to switch behaviours, from a colonization mode (with an optimized growth rate), to a protection mode.</p> <p>Conclusions</p> <p>A biofilm will benefit from using quorum sensing-induced EPS production if bacteria cells have the objective of acquiring a thick, protective layer of EPS, or if they wish to clog their environment with biomass as a means of securing nutrient supply and outcompeting other colonies in the channel, of their own or a different species.</p