Numerical Calibration of Steiner trees

In this paper we propose a variational approach to the Steiner tree problem, which is based on calibrations in a suitable algebraic environment for polyhedral chains which represent our candidates. This approach turns out to be very efficient from numerical point of view and allows to establish whether a given Steiner tree is optimal. Several examples are provided

Constraints, Histones, and the 30 Nanometer Spiral

We investigate the mechanical stability of a segment of DNA wrapped around a histone in the nucleosome configuration. The assumption underlying this investigation is that the proper model for this packaging arrangement is that of an elastic rod that is free to twist and that writhes subject to mechanical constraints. We find that the number of constraints required to stabilize the nuclesome configuration is determined by the length of the segment, the number of times the DNA wraps around the histone spool, and the specific constraints utilized. While it can be shown that four constraints suffice, in principle, to insure stability of the nucleosome, a proper choice must be made to guarantee the effectiveness of this minimal number. The optimal choice of constraints appears to bear a relation to the existence of a spiral ridge on the surface of the histone octamer. The particular configuration that we investigate is related to the 30 nanometer spiral, a higher-order organization of DNA in chromatin.Comment: ReVTeX, 15 pages, 18 figure

On a classical spectral optimization problem in linear elasticity

We consider a classical shape optimization problem for the eigenvalues of elliptic operators with homogeneous boundary conditions on domains in the $N$-dimensional Euclidean space. We survey recent results concerning the analytic dependence of the elementary symmetric functions of the eigenvalues upon domain perturbation and the role of balls as critical points of such functions subject to volume constraint. Our discussion concerns Dirichlet and buckling-type problems for polyharmonic operators, the Neumann and the intermediate problems for the biharmonic operator, the Lam\'{e} and the Reissner-Mindlin systems.Comment: To appear in the proceedings of the workshop `New Trends in Shape Optimization', Friedrich-Alexander Universit\"{a}t Erlangen-Nuremberg, 23-27 September 201

Phase field approach to optimal packing problems and related Cheeger clusters

In a fixed domain of $\Bbb{R}^N$ we study the asymptotic behaviour of optimal clusters associated to $\alpha$-Cheeger constants and natural energies like the sum or maximum: we prove that, as the parameter $\alpha$ converges to the "critical" value $\Big (\frac{N-1}{N}\Big ) _+$, optimal Cheeger clusters converge to solutions of different packing problems for balls, depending on the energy under consideration. As well, we propose an efficient phase field approach based on a multiphase Gamma convergence result of Modica-Mortola type, in order to compute $\alpha$-Cheeger constants, optimal clusters and, as a consequence of the asymptotic result, optimal packings. Numerical experiments are carried over in two and three space dimensions

Apoptotic HPV Positive Cancer Cells Exhibit Transforming Properties

Previous studies have shown that DNA can be transferred from dying engineered cells to neighboring cells through the phagocytosis of apoptotic bodies, which leads to cellular transformation. Here, we provide evidence of an uptake of apoptotic-derived cervical cancer cells by human mesenchymal cells. Interestingly, HeLa (HPV 18+) or Ca Ski (HPV16+) cells, harboring integrated high-risk HPV DNA but not C-33 A cells (HPV-), were able to transform the recipient cells. Human primary fibroblasts engulfed the apoptotic bodies effectively within 30 minutes after co-cultivation. This mechanism is active and involves the actin cytoskeleton. In situ hybridization of transformed fibroblasts revealed the presence of HPV DNA in the nucleus of a subset of phagocytosing cells. These cells expressed the HPV16/18 E6 gene, which contributes to the disruption of the p53/p21 pathway, and the cells exhibited a tumorigenic phenotype, including an increased proliferation rate, polyploidy and anchorage independence growth. Such horizontal transfer of viral oncogenes to surrounding cells that lack receptors for HPV could facilitate the persistence of the virus, the main risk factor for cervical cancer development. This process might contribute to HPV-associated disease progression in vivo

Detection of K-Ras mutations in tumour samples of patients with non-small cell lung cancer using PNA-mediated PCR clamping

Non-small cell lung cancers (NSCLC), in particular adenocarcinoma, are often mixed with normal cells. Therefore, low sensitivity of direct sequencing used for K-Ras mutation analysis could be inadequate in some cases. Our study focused on the possibility to increase the detection of K-Ras mutations in cases of low tumour cellularity. Besides direct sequencing, we used wild-type hybridisation probes and peptide-nucleic-acid (PNA)-mediated PCR clamping to detect mutations at codons 12 and 13, in 114 routine consecutive NSCLC frozen surgical tumours untreated by targeted drugs. The sensitivity of the analysis without or with PNA was 10 and 1% of tumour DNA, respectively. Direct sequencing revealed K-Ras mutations in 11 out of 114 tumours (10%). Using PNA-mediated PCR clamping, 10 additional cases of K-Ras mutations were detected (21 out of 114, 18%, P<0.005), among which five in samples with low tumour cellularity. In adenocarcinoma, K-Ras mutation frequency increased from 7 out of 55 (13%) by direct sequencing to 15 out of 55 (27%) by clamped-PCR (P<0.005). K-Ras mutations detected by these sensitive techniques lost its prognostic value. In conclusion, a rapid and sensitive PCR-clamping test avoiding macro or micro dissection could be proposed in routine analysis especially for NSCLC samples with low percentage of tumour cells such as bronchial biopsies or after neoadjuvant chemotherapy

In Vivo Chromatin Organization of Mouse Rod Photoreceptors Correlates with Histone Modifications

BACKGROUND: The folding of genetic information into chromatin plays important regulatory roles in many nuclear processes and particularly in gene transcription. Post translational histone modifications are associated with specific chromatin condensation states and with distinct transcriptional activities. The peculiar chromatin organization of rod photoreceptor nuclei, with a large central domain of condensed chromatin surrounded by a thin border of extended chromatin was used as a model to correlate in vivo chromatin structure, histone modifications and transcriptional activity. METHODOLOGY: We investigated the functional relationships between chromatin compaction, distribution of histone modifications and location of RNA polymerase II in intact murine rod photoreceptors using cryo-preparation methods, electron tomography and immunogold labeling. Our results show that the characteristic central heterochromatin of rod nuclei is organized into concentric domains characterized by a progressive loosening of the chromatin architecture from inside towards outside and by specific combinations of silencing histone marks. The peripheral heterochromatin is formed by closely packed 30 nm fibers as revealed by a characteristic optical diffraction signal. Unexpectedly, the still highly condensed most external heterochromatin domain contains acetylated histones, which are usually associated with active transcription and decondensed chromatin. Histone acetylation is thus not sufficient in vivo for complete chromatin decondensation. The euchromatin domain contains several degrees of chromatin compaction and the histone tails are hyperacetylated, enriched in H3K4 monomethylation and hypo trimethylated on H3K9, H3K27 and H4K20. The transcriptionally active RNA polymerases II molecules are confined in the euchromatin domain and are preferentially located at the vicinity of the interface with heterochromatin. CONCLUSIONS: Our results show that transcription is located in the most decondensed and highly acetylated chromatin regions, but since acetylation is found associated with compact chromatin it is not sufficient to decondense chromatin in vivo. We also show that a combination of histone marks defines distinct concentric heterochromatin domains

Preferential in vitro assembly of nucleosome cores on some AT-rich regions of SV40 DNA.

We have found that nucleosomes reconstituted from histone octamers and SV40 DNA Form I by progressively decreasing the salt concentration from 2 M NaCl are formed preferentially around 0.27, 0.37, 0.50 and 0.85 on SV40 DNA (relative to the EcoRI site). When SV40 DNA Form III is used, the nucleosomes form mainly at 0.28, 0.38, 0.61 and 0.83. These sites are very close to both the sites of RNA chain initiation by calf thymus RNA polymerase B on SV40 DNA Form I (0.25, 0.35, 0.42 and 0.88) and the regions of the supercoiled DNA which are readily denaturable by T4 gene 32 protein (0.25, 0.47 and 0.88), and correspond to AT-rich regions as deduced from the nucleotide sequence of SV40 DNA. The physiologically important region around 0.67 is an unfavourable site for all three types of proteins, and corresponds to a GC-rich region surrounding a 17 base pair AT cluster