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

Novel Functional MAR Elements of Double Minute Chromosomes in Human Ovarian Cells Capable of Enhancing Gene Expression

Double minute chromosomes or double minutes (DMs) are cytogenetic hallmarks of extrachromosomal genomic amplification and play a critical role in tumorigenesis. Amplified copies of oncogenes in DMs have been associated with increased growth and survival of cancer cells but DNA sequences in DMs which are mostly non-coding remain to be characterized. Following sequencing and bioinformatics analyses, we have found 5 novel matrix attachment regions (MARs) in a 682 kb DM in the human ovarian cancer cell line, UACC-1598. By electrophoretic mobility shift assay (EMSA), we determined that all 5 MARs interact with the nuclear matrix in vitro. Furthermore, qPCR analysis revealed that these MARs associate with the nuclear matrix in vivo, indicating that they are functional. Transfection of MARs constructs into human embryonic kidney 293T cells showed significant enhancement of gene expression as measured by luciferase assay, suggesting that the identified MARS, particularly MARs 1 to 4, regulate their target genes in vivo and are potentially involved in DM-mediated oncogene activation

Centrosome clustering and Cyclin D1 gene amplification in double minutes are common events in chromosomal unstable bladder tumors

Background: Aneuploidy, centrosome abnormalities and gene amplification are hallmarks of chromosome instability (CIN) in cancer. Yet there are no studies of the in vivo behavior of these phenomena within the same bladder tumor. Methods: Twenty-one paraffin-embedded bladder tumors were analyzed by conventional comparative genome hybridization and fluorescence in situ hybridization (FISH) with a cyclin D1 gene (CCND1)/centromere 11 dual-color probe. Immunofluorescent staining of α, β and γ tubulin was also performed. Results: Based on the CIN index, defined as the percentage of cells not displaying the modal number for chromosome 11, tumors were classified as CIN-negative and CIN-positive. Fourteen out of 21 tumors were considered CIN-positive. All T1G3 tumors were included in the CIN-positive group whereas the majority of Ta samples were classified as CIN-negative tumors. Centrosome clustering was observed in six out of 12 CIN-positive tumors analyzed. CCND1 amplification in homogeneously staining regions was present in six out of 14 CIN-positive tumors; three of them also showed amplification of this gene in double minutes. Conclusions: Complex in vivo behavior of CCND1 amplicon in bladder tumor cells has been demonstrated by accurate FISH analysis on paraffin-embedded tumors. Positive correlation between high heterogeneity, centrosome abnormalities and CCND1 amplification was found in T1G3 bladder carcinomas. This is the first study to provide insights into the coexistence of CCND1 amplification in homogeneously staining regions and double minutes in primary bladder tumors. It is noteworthy that those patients whose tumors showed double minutes had a significantly shorter overall survival rate (p < 0.001)

Large-scale validation of methods for cytotoxic T-lymphocyte epitope prediction

<p>Abstract</p> <p>Background</p> <p>Reliable predictions of Cytotoxic T lymphocyte (CTL) epitopes are essential for rational vaccine design. Most importantly, they can minimize the experimental effort needed to identify epitopes. NetCTL is a web-based tool designed for predicting human CTL epitopes in any given protein. It does so by integrating predictions of proteasomal cleavage, TAP transport efficiency, and MHC class I affinity. At least four other methods have been developed recently that likewise attempt to predict CTL epitopes: EpiJen, MAPPP, MHC-pathway, and WAPP. In order to compare the performance of prediction methods, objective benchmarks and standardized performance measures are needed. Here, we develop such large-scale benchmark and corresponding performance measures and report the performance of an updated version 1.2 of NetCTL in comparison with the four other methods.</p> <p>Results</p> <p>We define a number of performance measures that can handle the different types of output data from the five methods. We use two evaluation datasets consisting of known HIV CTL epitopes and their source proteins. The source proteins are split into all possible 9 mers and except for annotated epitopes; all other 9 mers are considered non-epitopes. In the RANK measure, we compare two methods at a time and count how often each of the methods rank the epitope highest. In another measure, we find the specificity of the methods at three predefined sensitivity values. Lastly, for each method, we calculate the percentage of known epitopes that rank within the 5% peptides with the highest predicted score.</p> <p>Conclusion</p> <p>NetCTL-1.2 is demonstrated to have a higher predictive performance than EpiJen, MAPPP, MHC-pathway, and WAPP on all performance measures. The higher performance of NetCTL-1.2 as compared to EpiJen and MHC-pathway is, however, not statistically significant on all measures. In the large-scale benchmark calculation consisting of 216 known HIV epitopes covering all 12 recognized HLA supertypes, the NetCTL-1.2 method was shown to have a sensitivity among the 5% top-scoring peptides above 0.72. On this dataset, the best of the other methods achieved a sensitivity of 0.64. The NetCTL-1.2 method is available at <url>http://www.cbs.dtu.dk/services/NetCTL</url>.</p> <p>All used datasets are available at <url>http://www.cbs.dtu.dk/suppl/immunology/CTL-1.2.php</url>.</p

Characteristics of the Early Immune Response Following Transplantation of Mouse ES Cell Derived Insulin-Producing Cell Clusters

Background The fully differentiated progeny of ES cells (ESC) may eventually be used for cell replacement therapy (CRT). However, elements of the innate immune system may contribute to damage or destruction of these tissues when transplanted. Methodology/Principal Findings Herein, we assessed the hitherto ill-defined contribution of the early innate immune response in CRT after transplantation of either ESC derived insulin producing cell clusters (IPCCs) or adult pancreatic islets. Ingress of neutrophil or macrophage cells was noted immediately at the site of IPCC transplantation, but this infiltration was attenuated by day three. Gene profiling identified specific inflammatory cytokines and chemokines that were either absent or sharply reduced by three days after IPCC transplantation. Thus, IPCC transplantation provoked less of an early immune response than pancreatic islet transplantation. Conclusions/Significance Our study offers insights into the characteristics of the immune response of an ESC derived tissue in the incipient stages following transplantation and suggests potential strategies to inhibit cell damage to ensure their long-term perpetuation and functionality in CRT

Heterogeneous Response to a Quorum-Sensing Signal in the Luminescence of Individual Vibrio fischeri

The marine bacterium Vibrio fischeri regulates its bioluminescence through a quorum sensing mechanism: the bacterium releases diffusible small molecules (autoinducers) that accumulate in the environment as the population density increases. This accumulation of autoinducer (AI) eventually activates transcriptional regulators for bioluminescence as well as host colonization behaviors. Although V.fischeri quorum sensing has been extensively characterized in bulk populations, far less is known about how it performs at the level of the individual cell, where biochemical noise is likely to limit the precision of luminescence regulation. We have measured the time-dependence and AI-dependence of light production by individual V.fischeri cells that are immobilized in a perfusion chamber and supplied with a defined concentration of exogenous AI. We use low-light level microscopy to record and quantify the photon emission from the cells over periods of several hours as they respond to the introduction of AI. We observe an extremely heterogeneous response to the AI signal. Individual cells differ widely in the onset time for their luminescence and in their resulting brightness, even in the presence of high AI concentrations that saturate the light output from a bulk population. The observed heterogeneity shows that although a given concentration of quorum signal may determine the average light output from a population of cells, it provides far weaker control over the luminescence output of each individual cell

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

On the spontaneous stochastic dynamics of a single gene: complexity of the molecular interplay at the promoter

International audienceBACKGROUND: Gene promoters can be in various epigenetic states and undergo interactions with many molecules in a highly transient, probabilistic and combinatorial way, resulting in a complex global dynamics as observed experimentally. However, models of stochastic gene expression commonly consider promoter activity as a two-state on/off system. We consider here a model of single-gene stochastic expression that can represent arbitrary prokaryotic or eukaryotic promoters, based on the combinatorial interplay between molecules and epigenetic factors, including energy-dependent remodeling and enzymatic activities. RESULTS: We show that, considering the mere molecular interplay at the promoter, a single-gene can demonstrate an elaborate spontaneous stochastic activity (eg. multi-periodic multi-relaxation dynamics), similar to what is known to occur at the gene-network level. Characterizing this generic model with indicators of dynamic and steady-state properties (including power spectra and distributions), we reveal the potential activity of any promoter and its influence on gene expression. In particular, we can reproduce, based on biologically relevant mechanisms, the strongly periodic patterns of promoter occupancy by transcription factors (TF) and chromatin remodeling as observed experimentally on eukaryotic promoters. Moreover, we link several of its characteristics to properties of the underlying biochemical system. The model can also be used to identify behaviors of interest (eg. stochasticity induced by high TF concentration) on minimal systems and to test their relevance in larger and more realistic systems. We finally show that TF concentrations can regulate many aspects of the stochastic activity with a considerable flexibility and complexity. CONCLUSIONS: This tight promoter-mediated control of stochasticity may constitute a powerful asset for the cell. Remarkably, a strongly periodic activity that demonstrates a complex TF concentration-dependent control is obtained when molecular interactions have typical characteristics observed on eukaryotic promoters (high mobility, functional redundancy, many alternate states/pathways). We also show that this regime results in a direct and indirect energetic cost. Finally, this model can constitute a framework for unifying various experimental approaches. Collectively, our results show that a gene - the basic building block of complex regulatory networks - can itself demonstrate a significantly complex behavior

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

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