Generalized Newton's Method based on Graphical Derivatives

This paper concerns developing a numerical method of the Newton type to solve systems of nonlinear equations described by nonsmooth continuous functions. We propose and justify a new generalized Newton algorithm based on graphical derivatives, which have never been used to derive a Newton-type method for solving nonsmooth equations. Based on advanced techniques of variational analysis and generalized differentiation, we establish the well-posedness of the algorithm, its local superlinear convergence, and its global convergence of the Kantorovich type. Our convergence results hold with no semismoothness assumption, which is illustrated by examples. The algorithm and main results obtained in the paper are compared with well-recognized semismooth and $B$-differentiable versions of Newton's method for nonsmooth Lipschitzian equations

Utilising the left-helical conformation of L-DNA for analysing different marker types on a single universal microarray platform

L-DNA is the perfect mirror-image form of the naturally occurring d-conformation of DNA. Therefore, L-DNA duplexes have the same physical characteristics in terms of solubility, duplex stability and selectivity as D-DNA but form a left-helical double-helix. Because of its chiral difference, L-DNA does not bind to its naturally occurring D-DNA counterpart, however. We analysed some of the properties that are typical for L-DNA. For all the differences, L-DNA is chemically compatible with the D-form of DNA, so that chimeric molecules can be synthesized. We take advantage of the characteristics of L-DNA toward the establishment of a universal microarray that permits the analysis of different kinds of molecular diagnostic information in a single experiment on a single platform, in various combinations. Typical results for the measurement of transcript level variations, genotypic differences and DNA–protein interactions are presented. However, on the basis of the characteristic features of L-DNA, also other applications of this molecule type are discussed

Fabrication of adhesive lenses using free surface shaping

Two approaches for fabricating polymer lenses are presented in this paper. Both are based on filling circular holes with UV curing adhesives. Initially, the viscous adhesive material creates a liquid and spherical free surface due to its own surface tension. This shape is then preserved by curing with UV-hardening light. For the first approach, the holes are generated in a 4 inch Si-wafer by deep reactive ion etching (DRIE) and for the second, a polydimethylsiloxane (PDMS) mould is manufactured. Three types of UV-curing adhesives are investigated (NOA 61, NOA 88 and NEA 121 by Norland Products). Preliminary to the determination of the lens curvature, a contact angle goniometer is used for taking side view images of the lenses. The radius of curvature is then extracted via image processing with the software MATLAB®. Furthermore, the surface roughness of the PDMS mould and the generated lenses is measured with a white light interferometer to characterize the casting process. The resolution power of the generated lenses is evaluated by measurement of their point spread functions (psf) and modulation transfer functions (mtf), respectively

An integrated gene annotation and transcriptional profiling approach towards the full gene content of the Drosophila genome

BACKGROUND: While the genome sequences for a variety of organisms are now available, the precise number of the genes encoded is still a matter of debate. For the human genome several stringent annotation approaches have resulted in the same number of potential genes, but a careful comparison revealed only limited overlap. This indicates that only the combination of different computational prediction methods and experimental evaluation of such in silico data will provide more complete genome annotations. In order to get a more complete gene content of the Drosophila melanogaster genome, we based our new D. melanogaster whole-transcriptome microarray, the Heidelberg FlyArray, on the combination of the Berkeley Drosophila Genome Project (BDGP) annotation and a novel ab initio gene prediction of lower stringency using the Fgenesh software. RESULTS: Here we provide evidence for the transcription of approximately 2,600 additional genes predicted by Fgenesh. Validation of the developmental profiling data by RT-PCR and in situ hybridization indicates a lower limit of 2,000 novel annotations, thus substantially raising the number of genes that make a fly. CONCLUSIONS: The successful design and application of this novel Drosophila microarray on the basis of our integrated in silico/wet biology approach confirms our expectation that in silico approaches alone will always tend to be incomplete. The identification of at least 2,000 novel genes highlights the importance of gathering experimental evidence to discover all genes within a genome. Moreover, as such an approach is independent of homology criteria, it will allow the discovery of novel genes unrelated to known protein families or those that have not been strictly conserved between species

DNA Methylation of the ABO Promoter Underlies Loss of ABO Allelic Expression in a Significant Proportion of Leukemic Patients

Background: Loss of A, B and H antigens from the red blood cells of patients with myeloid malignancies is a frequent occurrence. Previously, we have reported alterations in ABH antigens on the red blood cells of 55% of patients with myeloid malignancies. Methodology/Principal Findings: To determine the underlying molecular mechanisms of this loss, we assessed ABO allelic expression in 21 patients with ABH antigen loss previously identified by flow cytometric analysis as well as an additional 7 patients detected with ABH antigen changes by serology. When assessing ABO mRNA allelic expression, 6/12 (50%) patients with ABH antigen loss detected by flow cytometry and 5/7 (71%) of the patients with ABH antigen loss detected by serology had a corresponding ABO mRNA allelic loss of expression. We examined the ABO locus for copy number and DNA methylation alterations in 21 patients, 11 with loss of expression of one or both ABO alleles, and 10 patients with no detectable allelic loss of ABO mRNA expression. No loss of heterozygosity (LOH) at the ABO locus was observed in these patients. However in 8/11 (73%) patients with loss of ABO allelic expression, the ABO promoter was methylated compared with 2/10 (20%) of patients with no ABO allelic expression loss (P = 0.03). Conclusions/Significance: We have found that loss of ABH antigens in patients with hematological malignancies is associated with a corresponding loss of ABO allelic expression in a significant proportion of patients. Loss of ABO allelic expression was strongly associated with DNA methylation of the ABO promoter.Tina Bianco-Miotto, Damian J. Hussey, Tanya K. Day, Denise S. O'Keefe and Alexander Dobrovi

Sdhd and Sdhd/H19 Knockout Mice Do Not Develop Paraganglioma or Pheochromocytoma

BACKGROUND: Mitochondrial succinate dehydrogenase (SDH) is a component of both the tricarboxylic acid cycle and the electron transport chain. Mutations of SDHD, the first protein of intermediary metabolism shown to be involved in tumorigenesis, lead to the human tumors paraganglioma (PGL) and pheochromocytoma (PC). SDHD is remarkable in showing an 'imprinted' tumor suppressor phenotype. Mutations of SDHD show a very high penetrance in man and we postulated that knockout of Sdhd would lead to the development of PGL/PC, probably in aged mice. METHODOLOGY/PRINCIPAL FINDINGS: We generated a conventional knockout of Sdhd in the mouse, removing the entire third exon. We also crossed this mouse with a knockout of H19, a postulated imprinted modifier gene of Sdhd tumorigenesis, to evaluate if loss of these genes together would lead to the initiation or enhancement of tumor development. Homozygous knockout of Sdhd results in embryonic lethality. No paraganglioma or other tumor development was seen in Sdhd KO mice followed for their entire lifespan, in sharp contrast to the highly penetrant phenotype in humans. Heterozygous Sdhd KO mice did not show hyperplasia of paraganglioma-related tissues such as the carotid body or of the adrenal medulla, or any genotype-related pathology, with similar body and organ weights to wildtype mice. A cohort of Sdhd/H19 KO mice developed several cases of profound cardiac hypertrophy, but showed no evidence of PGL/PC. CONCLUSIONS: Knockout of Sdhd in the mouse does not result in a disease phenotype. H19 may not be an initiator of PGL/PC tumorigenesis

Assessment and optimisation of normalisation methods for dual-colour antibody microarrays

<p>Abstract</p> <p>Background</p> <p>Recent advances in antibody microarray technology have made it possible to measure the expression of hundreds of proteins simultaneously in a competitive dual-colour approach similar to dual-colour gene expression microarrays. Thus, the established normalisation methods for gene expression microarrays, e.g. loess regression, can in principle be applied to protein microarrays. However, the typical assumptions of such normalisation methods might be violated due to a bias in the selection of the proteins to be measured. Due to high costs and limited availability of high quality antibodies, the current arrays usually focus on a high proportion of regulated targets. Housekeeping features could be used to circumvent this problem, but they are typically underrepresented on protein arrays. Therefore, it might be beneficial to select invariant features among the features already represented on available arrays for normalisation by a dedicated selection algorithm.</p> <p>Results</p> <p>We compare the performance of several normalisation methods that have been established for dual-colour gene expression microarrays. The focus is on an invariant selection algorithm, for which effective improvements are proposed. In a simulation study the performances of the different normalisation methods are compared with respect to their impact on the ability to correctly detect differentially expressed features. Furthermore, we apply the different normalisation methods to a pancreatic cancer data set to assess the impact on the classification power.</p> <p>Conclusions</p> <p>The simulation study and the data application demonstrate the superior performance of the improved invariant selection algorithms in comparison to other normalisation methods, especially in situations where the assumptions of the usual global loess normalisation are violated.</p