On a new conformal functional for simplicial surfaces

We introduce a smooth quadratic conformal functional and its weighted version $$W_2=\sum_e \beta^2(e)\quad W_{2,w}=\sum_e (n_i+n_j)\beta^2(e),$$ where $\beta(e)$ is the extrinsic intersection angle of the circumcircles of the triangles of the mesh sharing the edge $e=(ij)$ and $n_i$ is the valence of vertex $i$. Besides minimizing the squared local conformal discrete Willmore energy $W$ this functional also minimizes local differences of the angles $\beta$. We investigate the minimizers of this functionals for simplicial spheres and simplicial surfaces of nontrivial topology. Several remarkable facts are observed. In particular for most of randomly generated simplicial polyhedra the minimizers of $W_2$ and $W_{2,w}$ are inscribed polyhedra. We demonstrate also some applications in geometry processing, for example, a conformal deformation of surfaces to the round sphere. A partial theoretical explanation through quadratic optimization theory of some observed phenomena is presented.Comment: 14 pages, 8 figures, to appear in the proceedings of "Curves and Surfaces, 8th International Conference", June 201

Existence of immersed spheres minimizing curvature functionals in compact 3-manifolds

We study curvature functionals for immersed 2-spheres in a compact, three-dimensional Riemannian manifold M. Under the assumption that the sectional curvature of M is strictly positive, we prove the existence of a smoothly immersed sphere minimizing the L^{2} integral of the second fundamental form. Assuming instead that the sectional curvature is less than or equal to 2, and that there exists a point in M with scalar curvature bigger than 6, we obtain a smooth 2-sphere minimizing the integral of 1/4|H|^{2} +1, where H is the mean curvature vector

Existence of Integral mm-Varifolds minimizing ∫∣A∣p\int |A|^p and ∫∣H∣p\int |H|^p, p>mp>m, in Riemannian Manifolds

We prove existence and partial regularity of integral rectifiable $m$-dimensional varifolds minimizing functionals of the type $\int |H|^p$ and $\int |A|^p$ in a given Riemannian $n$-dimensional manifold $(N,g)$, $2\leq mm$, under suitable assumptions on $N$ (in the end of the paper we give many examples of such ambient manifolds). To this aim we introduce the following new tools: some monotonicity formulas for varifolds in $\mathbb{R}^S$ involving $\int |H|^p$, to avoid degeneracy of the minimizer, and a sort of isoperimetric inequality to bound the mass in terms of the mentioned functionals.Comment: 33 pages; this second submission corresponds to the published version of the paper, minor typos are fixe

High resolution melting analysis for rapid and sensitive EGFR and KRAS mutation detection in formalin fixed paraffin embedded biopsies

<p>Abstract</p> <p>Background</p> <p>Epithelial growth factor receptor (<it>EGFR</it>) and <it>KRAS </it>mutation status have been reported as predictive markers of tumour response to <it>EGFR </it>inhibitors. High resolution melting (HRM) analysis is an attractive screening method for the detection of both known and unknown mutations as it is rapid to set up and inexpensive to operate. However, up to now it has not been fully validated for clinical samples when formalin-fixed paraffin-embedded (FFPE) sections are the only material available for analysis as is often the case.</p> <p>Methods</p> <p>We developed HRM assays, optimised for the analysis of FFPE tissues, to detect somatic mutations in <it>EGFR </it>exons 18 to 21. We performed HRM analysis for <it>EGFR </it>and <it>KRAS </it>on DNA isolated from a panel of 200 non-small cell lung cancer (NSCLC) samples derived from FFPE tissues.</p> <p>Results</p> <p>All 73 samples that harboured <it>EGFR </it>mutations previously identified by sequencing were correctly identified by HRM, giving 100% sensitivity with 90% specificity. Twenty five samples were positive by HRM for <it>KRAS </it>exon 2 mutations. Sequencing of these 25 samples confirmed the presence of codon 12 or 13 mutations. <it>EGFR </it>and <it>KRAS </it>mutations were mutually exclusive.</p> <p>Conclusion</p> <p>This is the first extensive validation of HRM on FFPE samples using the detection of <it>EGFR </it>exons 18 to 21 mutations and <it>KRAS </it>exon 2 mutations. Our results demonstrate the utility of HRM analysis for the detection of somatic <it>EGFR </it>and <it>KRAS </it>mutations in clinical samples and for screening of samples prior to sequencing. We estimate that by using HRM as a screening method, the number of sequencing reactions needed for <it>EGFR </it>and <it>KRAS </it>mutation detection can be reduced by up to 80% and thus result in substantial time and cost savings.</p

The human epidermal growth factor receptor (EGFR) gene in European patients with advanced colorectal cancer harbors infrequent mutations in its tyrosine kinase domain

ABSTRACT: BACKGROUND: The epidermal growth factor receptor (EGFR), a member of the ErbB family of receptors, is a transmembrane tyrosine kinase (TK) activated by the binding of extracellular ligands of the EGF-family and involved in triggering the MAPK signaling pathway, which leads to cell proliferation. Mutations in the EGFR tyrosine kinase domain are frequent in non-small-cell lung cancer (NSCLC). However, to date, only very few, mainly non-European, studies have reported rare EGFR mutations in colorectal cancer (CRC). METHODS: We screened 236 clinical tumor samples from European patients with advanced CRC by direct DNA sequencing to detect potential, as yet unknown mutations, in the EGFR gene exons 18 to 21, mainly covering the EGFR TK catalytic domain. RESULTS: EGFR sequences showed somatic missense mutations in exons 18 and 20 at a frequency of 2.1% and 0.4% respectively. Somatic SNPs were also found in exons 20 and 21 at a frequency of about 3.1% and 0.4% respectively. Of these mutations, four have not yet been described elsewhere. CONCLUSIONS: These mutation frequencies are higher than in a similarly sized population characterized by Barber and colleagues, but still too low to account for a major role played by the EGFR gene in CRC.Peer reviewe

Detection of Somatic Mutations by High-Resolution DNA Melting (HRM) Analysis in Multiple Cancers

Identification of somatic mutations in cancer is a major goal for understanding and monitoring the events related to cancer initiation and progression. High resolution melting (HRM) curve analysis represents a fast, post-PCR high-throughput method for scanning somatic sequence alterations in target genes. The aim of this study was to assess the sensitivity and specificity of HRM analysis for tumor mutation screening in a range of tumor samples, which included 216 frozen pediatric small rounded blue-cell tumors as well as 180 paraffin-embedded tumors from breast, endometrial and ovarian cancers (60 of each). HRM analysis was performed in exons of the following candidate genes known to harbor established commonly observed mutations: PIK3CA, ERBB2, KRAS, TP53, EGFR, BRAF, GATA3, and FGFR3. Bi-directional sequencing analysis was used to determine the accuracy of the HRM analysis. For the 39 mutations observed in frozen samples, the sensitivity and specificity of HRM analysis were 97% and 87%, respectively. There were 67 mutation/variants in the paraffin-embedded samples, and the sensitivity and specificity for the HRM analysis were 88% and 80%, respectively. Paraffin-embedded samples require higher quantity of purified DNA for high performance. In summary, HRM analysis is a promising moderate-throughput screening test for mutations among known candidate genomic regions. Although the overall accuracy appears to be better in frozen specimens, somatic alterations were detected in DNA extracted from paraffin-embedded samples

Sensitivity of epidermal growth factor receptor and ErbB2 exon 20 insertion mutants to Hsp90 inhibition

The mature epidermal growth factor receptor (EGFR) neither associates with nor requires the molecular chaperone heat-shock protein 90 (Hsp90). Mutations in EGFR exons 18, 19, and 21 confer Hsp90 chaperone dependence. In non-small cell lung cancer (NSCLC), these mutations are associated with enhanced sensitivity to EGFR inhibitors in vitro and with clinical response in vivo. Although less prevalent, insertions in EGFR exon 20 have also been described in NSCLC. These mutations, however, confer resistance to EGFR inhibitors. In NSCLC, exon 20 insertions have also been identified in the EGFR family member ErbB2. Here, we examined the sensitivity of exon 20 insertion mutants to an Hsp90 inhibitor currently in the clinic. Our data demonstrate that both EGFR and ErbB2 exon 20 insertion mutants retain dependence on Hsp90 for stability and downstream-signalling capability, and remain highly sensitive to Hsp90 inhibition. Use of Hsp90 inhibitors should be considered in NSCLC harbouring exon 20 insertions in either EGFR or ErbB2

‘Classical' but not ‘other' mutations of EGFR kinase domain are associated with clinical outcome in gefitinib-treated patients with non-small cell lung cancer

‘Classical' mutations in the EGFR tyrosine kinase domain (exons 18, 19 and 21) have been associated with sensitivity to tyrosine kinase inhibitors (TKIs) in patients with NSCLC. The aim of the current study was to evaluate whether other than the classical G719X, DEL19 and L858R mutations of EGFR confer sensitivity to TKIs. Genomic DNA was extracted from microdissected formalin-fixed paraffin-embedded tumour tissue from 86 patients treated with gefitinib. Exons 18, 19 and 21 were amplified and subjected to direct sequencing. Eleven (13%) patients harboured the classical exon's 18, 19 and 21 mutations, while 14 (16%) had ‘other' variants. There was a significantly higher percentage of ‘never-smoker' patients with ‘classical' EGFR mutations (P=0.002). Among patients with ‘classical' mutations 3 patients achieved PR and 7 SD, while in the ‘other' mutations group 10 patients had SD as best response. In the wild-type group, there were 3 patients with PR and 25 with SD. Median TTP was 16, 64 (P=0.002) and 21 weeks and median survival was 36, 78 and 67 weeks for patients with wild-type, ‘classical' and ‘other' EGFR mutations, respectively. The clinical relevance of ‘other' EGFR mutation variants remains uncertain and requires further assessment in a prospective study