Computing the vertices of tropical polyhedra using directed hypergraphs

We establish a characterization of the vertices of a tropical polyhedron defined as the intersection of finitely many half-spaces. We show that a point is a vertex if, and only if, a directed hypergraph, constructed from the subdifferentials of the active constraints at this point, admits a unique strongly connected component that is maximal with respect to the reachability relation (all the other strongly connected components have access to it). This property can be checked in almost linear-time. This allows us to develop a tropical analogue of the classical double description method, which computes a minimal internal representation (in terms of vertices) of a polyhedron defined externally (by half-spaces or hyperplanes). We provide theoretical worst case complexity bounds and report extensive experimental tests performed using the library TPLib, showing that this method outperforms the other existing approaches.Comment: 29 pages (A4), 10 figures, 1 table; v2: Improved algorithm in section 5 (using directed hypergraphs), detailed appendix; v3: major revision of the article (adding tropical hyperplanes, alternative method by arrangements, etc); v4: minor revisio

Evidence for classification of c.1852_1853AA>GC in MLH1 as a neutral variant for Lynch syndrome

Background: Lynch syndrome (LS) is an autosomal dominant inherited cancer syndrome characterized by early onset cancers of the colorectum, endometrium and other tumours. A significant proportion of DNA variants in LS patients are unclassified. Reports on the pathogenicity of the c.1852_1853AA>GC (p.Lys618Ala) variant of the MLH1 gene are conflicting. In this study, we provide new evidence indicating that this variant has no significant implications for LS. Methods: The following approach was used to assess the clinical significance of the p.Lys618Ala variant: frequency in a control population, case-control comparison, co-occurrence of the p.Lys618Ala variant with a pathogenic mutation, co-segregation with the disease and microsatellite instability in tumours from carriers of the variant. We genotyped p.Lys618Ala in 1034 individuals (373 sporadic colorectal cancer [CRC] patients, 250 index subjects from families suspected of having LS [revised Bethesda guidelines] and 411 controls). Three well-characterized LS families that fulfilled the Amsterdam II Criteria and consisted of members with the p.Lys618Ala variant were included to assess co-occurrence and co-segregation. A subset of colorectal tumour DNA samples from 17 patients carrying the p.Lys618Ala variant was screened for microsatellite instability using five mononucleotide markers. Results: Twenty-seven individuals were heterozygous for the p.Lys618Ala variant; nine had sporadic CRC (2.41%), seven were suspected of having hereditary CRC (2.8%) and 11 were controls (2.68%). There were no significant associations in the case-control and case-case studies. The p.Lys618Ala variant was co-existent with pathogenic mutations in two unrelated LS families. In one family, the allele distribution of the pathogenic and unclassified variant was in trans, in the other family the pathogenic variant was detected in the MSH6 gene and only the deleterious variant co-segregated with the disease in both families. Only two positive cases of microsatellite instability (2/17, 11.8%) were detected in tumours from p.Lys618Ala carriers, indicating that this variant does not play a role in functional inactivation of MLH1 in CRC patients. Conclusions: The p.Lys618Ala variant should be considered a neutral variant for LS. These findings have implications for the clinical management of CRC probands and their relatives.Generalitat Valenciana in Spain (AP140/08) and the Biomedical Research Foundation from the Hospital of Elche, Spain (FIBElx0902). Conselleria de Educació (Generalitat Valenciana); Fundacion Juan Peran-Pikolinos; Fundacion Carolina-BBVA and Fondo Investigación Sanitaria (FI07/00303). Instituto de Salud Carlos III (INT09/208)

Search for Specific Biomarkers of IFNβ Bioactivity in Patients with Multiple Sclerosis

Myxovirus A (MxA), a protein encoded by the MX1 gene with antiviral activity, has proven to be a sensitive measure of IFNβ bioactivity in multiple sclerosis (MS). However, the use of MxA as a biomarker of IFNβ bioactivity has been criticized for the lack of evidence of its role on disease pathogenesis and the clinical response to IFNβ. Here, we aimed to identify specific biomarkers of IFNβ bioactivity in order to compare their gene expression induction by type I IFNs with the MxA, and to investigate their potential role in MS pathogenesis. Gene expression microarrays were performed in PBMC from MS patients who developed neutralizing antibodies (NAB) to IFNβ at 12 and/or 24 months of treatment and patients who remained NAB negative. Nine genes followed patterns in gene expression over time similar to the MX1, which was considered the gold standard gene, and were selected for further experiments: IFI6, IFI27, IFI44L, IFIT1, HERC5, LY6E, RSAD2, SIGLEC1, and USP18. In vitro experiments in PBMC from healthy controls revealed specific induction of selected biomarkers by IFNβ but not IFNγ, and several markers, in particular USP18 and HERC5, were shown to be significantly induced at lower IFNβ concentrations and more selective than the MX1 as biomarkers of IFNβ bioactivity. In addition, USP18 expression was deficient in MS patients compared with healthy controls (p = 0.0004). We propose specific biomarkers that may be considered in addition to the MxA to evaluate IFNβ bioactivity, and to further explore their implication in MS pathogenesis

MRPS18CP2 alleles and DEFA3 absence as putative chromosome 8p23.1 modifiers of hearing loss due to mtDNA mutation A1555G in the 12S rRNA gene

<p>Abstract</p> <p>Background</p> <p>Mitochondrial DNA (mtDNA) mutations account for at least 5% of cases of postlingual, nonsyndromic hearing impairment. Among them, mutation A1555G is frequently found associated with aminoglycoside-induced and/or nonsyndromic hearing loss in families presenting with extremely variable clinical phenotypes. Biochemical and genetic data have suggested that nuclear background is the main factor involved in modulating the phenotypic expression of mutation A1555G. However, although a major nuclear modifying locus was located on chromosome 8p23.1 and regardless intensive screening of the region, the gene involved has not been identified.</p> <p>Methods</p> <p>With the aim to gain insights into the factors that determine the phenotypic expression of A1555G mutation, we have analysed in detail different genetic and genomic elements on 8p23.1 region (<it>DEFA3 </it>gene absence, <it>CLDN23 </it>gene and <it>MRPS18CP2 </it>pseudogene) in a group of 213 A1555G carriers.</p> <p>Results</p> <p>Family based association studies identified a positive association for a polymorphism on <it>MRPS18CP2 </it>and an overrepresentation of <it>DEFA3 </it>gene absence in the deaf group of A1555G carriers.</p> <p>Conclusion</p> <p>Although none of the factors analysed seem to have a major contribution to the phenotype, our findings provide further evidences of the involvement of 8p23.1 region as a modifying locus for A1555G 12S rRNA gene mutation.</p