Analyticity and criticality results for the eigenvalues of the biharmonic operator

We consider the eigenvalues of the biharmonic operator subject to several homogeneous boundary conditions (Dirichlet, Neumann, Navier, Steklov). We show that simple eigenvalues and elementary symmetric functions of multiple eigenvalues are real analytic, and provide Hadamard-type formulas for the corresponding shape derivatives. After recalling the known results in shape optimization, we prove that balls are always critical domains under volume constraint.Comment: To appear on the proceedings of the conference "Geometric Properties for Parabolic and Elliptic PDE's - 4th Italian-Japanese Workshop" held in Palinuro (Italy), May 25-29, 201

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

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

Amplification of a Zygosaccharomyces bailii DNA Segment in Wine Yeast Genomes by Extrachromosomal Circular DNA Formation

We recently described the presence of large chromosomal segments resulting from independent horizontal gene transfer (HGT) events in the genome of Saccharomyces cerevisiae strains, mostly of wine origin. We report here evidence for the amplification of one of these segments, a 17 kb DNA segment from Zygosaccharomyces bailii, in the genome of S. cerevisiae strains. The copy number, organization and location of this region differ considerably between strains, indicating that the insertions are independent and that they are post-HGT events. We identified eight different forms in 28 S. cerevisiae strains, mostly of wine origin, with up to four different copies in a single strain. The organization of these forms and the identification of an autonomously replicating sequence functional in S. cerevisiae, strongly suggest that an extrachromosomal circular DNA (eccDNA) molecule serves as an intermediate in the amplification of the Z. bailii region in yeast genomes. We found little or no sequence similarity at the breakpoint regions, suggesting that the insertions may be mediated by nonhomologous recombination. The diversity between these regions in S. cerevisiae represents roughly one third the divergence among the genomes of wine strains, which confirms the recent origin of this event, posterior to the start of wine strain expansion. This is the first report of a circle-based mechanism for the expansion of a DNA segment, mediated by nonhomologous recombination, in natural yeast populations