658 research outputs found

    Complex WKB Analysis of a PT Symmetric Eigenvalue Problem

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    The spectra of a particular class of PT symmetric eigenvalue problems has previously been studied, and found to have an extremely rich structure. In this paper we present an explanation for these spectral properties in terms of quantisation conditions obtained from the complex WKB method. In particular, we consider the relation of the quantisation conditions to the reality and positivity properties of the eigenvalues. The methods are also used to examine further the pattern of eigenvalue degeneracies observed by Dorey et al. in [1,2].Comment: 22 pages, 13 figures. Added references, minor revision

    The cost of reducing starting RNA quantity for Illumina BeadArrays: a bead-level dilution experiment.

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    BACKGROUND: The demands of microarray expression technologies for quantities of RNA place a limit on the questions they can address. As a consequence, the RNA requirements have reduced over time as technologies have improved. In this paper we investigate the costs of reducing the starting quantity of RNA for the Illumina BeadArray platform. This we do via a dilution data set generated from two reference RNA sources that have become the standard for investigations into microarray and sequencing technologies. RESULTS: We find that the starting quantity of RNA has an effect on observed intensities despite the fact that the quantity of cRNA being hybridized remains constant. We see a loss of sensitivity when using lower quantities of RNA, but no great rise in the false positive rate. Even with 10 ng of starting RNA, the positive results are reliable although many differentially expressed genes are missed. We see that there is some scope for combining data from samples that have contributed differing quantities of RNA, but note also that sample sizes should increase to compensate for the loss of signal-to-noise when using low quantities of starting RNA. CONCLUSIONS: The BeadArray platform maintains a low false discovery rate even when small amounts of starting RNA are used. In contrast, the sensitivity of the platform drops off noticeably over the same range. Thus, those conducting experiments should not opt for low quantities of starting RNA without consideration of the costs of doing so. The implications for experimental design, and the integration of data from different starting quantities, are complex.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are

    Spike-in validation of an Illumina-specific variance-stabilizing transformation

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    BACKGROUND: Variance-stabilizing techniques have been used for some time in the analysis of gene expression microarray data. A new adaptation, the variance-stabilizing transformation (VST), has recently been developed to take advantage of the unique features of Illumina BeadArrays. VST has been shown to perform well in comparison with the widely-used approach of taking a log2 transformation, but has not been validated on a spike-in experiment. We apply VST to the data from a recently published spike-in experiment and compare it both to a regular log2 analysis and a recently recommended analysis that can be applied if all raw data are available. FINDINGS: VST provides more power to detect differentially expressed genes than a log2 transformation. However, the gain in power is roughly the same as utilizing the raw data from an experiment and weighting observations accordingly. VST is still advantageous when large changes in expression are anticipated, while a weighted log2 approach performs better for smaller changes. CONCLUSION: VST can be recommended for summarized Illumina data regardless of which Illumina pre-processing options have been used. However, using the raw data is still encouraged whenever possible

    PMC42, a breast progenitor cancer cell line, has normal-like mRNA and microRNA transcriptomes.

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    INTRODUCTION: The use of cultured cell lines as model systems for normal tissue is limited by the molecular alterations accompanying the immortalisation process, including changes in the mRNA and microRNA (miRNA) repertoire. Therefore, identification of cell lines with normal-like expression profiles is of paramount importance in studies of normal gene regulation. METHODS: The mRNA and miRNA expression profiles of several breast cell lines of cancerous or normal origin were measured using printed slide arrays, Luminex bead arrays, and real-time reverse transcription-polymerase chain reaction. RESULTS: We demonstrate that the mRNA expression profiles of two breast cell lines are similar to that of normal breast tissue: HB4a, immortalised normal breast epithelium, and PMC42, a breast cancer cell line that retains progenitor pluripotency allowing in-culture differentiation to both secretory and myoepithelial fates. In contrast, only PMC42 exhibits a normal-like miRNA expression profile. We identified a group of miRNAs that are highly expressed in normal breast tissue and PMC42 but are lost in all other cancerous and normal-origin breast cell lines and observed a similar loss in immortalised lymphoblastoid cell lines compared with healthy uncultured B cells. Moreover, like tumour suppressor genes, these miRNAs are lost in a variety of tumours. We show that the mechanism leading to the loss of these miRNAs in breast cancer cell lines has genomic, transcriptional, and post-transcriptional components. CONCLUSION: We propose that, despite its neoplastic origin, PMC42 is an excellent molecular model for normal breast epithelium, providing a unique tool to study breast differentiation and the function of key miRNAs that are typically lost in cancer.RIGHTS : This article is licensed under the BioMed Central licence at http://www.biomedcentral.com/about/license which is similar to the 'Creative Commons Attribution Licence'. In brief you may : copy, distribute, and display the work; make derivative works; or make commercial use of the work - under the following conditions: the original author must be given credit; for any reuse or distribution, it must be made clear to others what the license terms of this work are

    The Dispersion Interaction between Quantum Mechanics and Effective Fragment Potential Molecules

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    A method for calculating the dispersion energy between molecules modeled with the general effective fragment potential (EFP2) method and those modeled using a full quantum mechanics (QM) method, e.g., Hartree-Fock (HF) or second-order perturbation theory, is presented. C6dispersion coefficients are calculated for pairs of orbitals using dynamic polarizabilities from the EFP2 portion, and dipole integrals and orbital energies from the QM portion of the system. Dividing by the sixth power of the distance between localized molecular orbital centroids yields the first term in the commonly employed London series expansion. A C 8 term is estimated from the C 6 term to achieve closer agreement with symmetry adapted perturbation theory values. Two damping functions for the dispersion energy are evaluated. By using terms that are already computed during an ordinary HF or EFP2 calculation, the new method enables accurate and extremely rapid evaluation of the dispersioninteraction between EFP2 and QM molecules

    A re-annotation pipeline for Illumina BeadArrays: improving the interpretation of gene expression data.

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    Illumina BeadArrays are among the most popular and reliable platforms for gene expression profiling. However, little external scrutiny has been given to the design, selection and annotation of BeadArray probes, which is a fundamental issue in data quality and interpretation. Here we present a pipeline for the complete genomic and transcriptomic re-annotation of Illumina probe sequences, also applicable to other platforms, with its output available through a Web interface and incorporated into Bioconductor packages. We have identified several problems with the design of individual probes and we show the benefits of probe re-annotation on the analysis of BeadArray gene expression data sets. We discuss the importance of aspects such as probe coverage of individual transcripts, alternative messenger RNA splicing, single-nucleotide polymorphisms, repeat sequences, RNA degradation biases and probes targeting genomic regions with no known transcription. We conclude that many of the Illumina probes have unreliable original annotation and that our re-annotation allows analyses to focus on the good quality probes, which form the majority, and also to expand the scope of biological information that can be extracted

    Identification and correction of previously unreported spatial phenomena using raw Illumina BeadArray data

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    <p>Abstract</p> <p>Background</p> <p>A key stage for all microarray analyses is the extraction of feature-intensities from an image. If this step goes wrong, then subsequent preprocessing and processing stages will stand little chance of rectifying the matter. Illumina employ random construction of their BeadArrays, making feature-intensity extraction even more important for the Illumina platform than for other technologies. In this paper we show that using raw Illumina data it is possible to identify, control, and perhaps correct for a range of spatial-related phenomena that affect feature-intensity extraction.</p> <p>Results</p> <p>We note that feature intensities can be unnaturally high when in the proximity of a number of phenomena relating either to the images themselves or to the layout of the beads on an array. Additionally we note that beads neighbour beads of the same type more often than one might expect, which may cause concern in some models of hybridization. We highlight issues in the identification of a bead's location, and in particular how this both affects and is affected by its intensity. Finally we show that beads can be wrongly identified in the image on either a local or array-wide scale, with obvious implications for data quality.</p> <p>Conclusions</p> <p>The image processing issues identified will often pass unnoticed by an analysis of the standard data returned from an experiment. We detail some simple diagnostics that can be implemented to identify problems of this nature, and outline approaches to correcting for such problems. These approaches require access to the raw data from the arrays, not just the summarized data usually returned, making the acquisition of such raw data highly desirable.</p

    The pitfalls of platform comparison: DNA copy number array technologies assessed

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    <p>Abstract</p> <p>Background</p> <p>The accurate and high resolution mapping of DNA copy number aberrations has become an important tool by which to gain insight into the mechanisms of tumourigenesis. There are various commercially available platforms for such studies, but there remains no general consensus as to the optimal platform. There have been several previous platform comparison studies, but they have either described older technologies, used less-complex samples, or have not addressed the issue of the inherent biases in such comparisons. Here we describe a systematic comparison of data from four leading microarray technologies (the Affymetrix Genome-wide SNP 5.0 array, Agilent High-Density CGH Human 244A array, Illumina HumanCNV370-Duo DNA Analysis BeadChip, and the Nimblegen 385 K oligonucleotide array). We compare samples derived from primary breast tumours and their corresponding matched normals, well-established cancer cell lines, and HapMap individuals. By careful consideration and avoidance of potential sources of bias, we aim to provide a fair assessment of platform performance.</p> <p>Results</p> <p>By performing a theoretical assessment of the reproducibility, noise, and sensitivity of each platform, notable differences were revealed. Nimblegen exhibited between-replicate array variances an order of magnitude greater than the other three platforms, with Agilent slightly outperforming the others, and a comparison of self-self hybridizations revealed similar patterns. An assessment of the single probe power revealed that Agilent exhibits the highest sensitivity. Additionally, we performed an in-depth visual assessment of the ability of each platform to detect aberrations of varying sizes. As expected, all platforms were able to identify large aberrations in a robust manner. However, some focal amplifications and deletions were only detected in a subset of the platforms.</p> <p>Conclusion</p> <p>Although there are substantial differences in the design, density, and number of replicate probes, the comparison indicates a generally high level of concordance between platforms, despite differences in the reproducibility, noise, and sensitivity. In general, Agilent tended to be the best aCGH platform and Affymetrix, the superior SNP-CGH platform, but for specific decisions the results described herein provide a guide for platform selection and study design, and the dataset a resource for more tailored comparisons.</p
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