Generating Chordal Graphs with few Fill-in Edges: An Experimental Study

Graph Generation aids in analysis of graphs and their properties while insinuating conjectures via counterexamples and even generating test instances for other algorithms. In certain cases, a list of graphs will deliver numerical information for enumerative problems devoid of theoretical solutions, or even supply a source from which specimen graphs may be adopted. Any given graph can be embedded in a chordal graph by adding edges, and the resulting chordal graph is called a triangulation of the input graph i.e., contains no induced chordless cycle on four or more vertices. Triangulation is classified into Minimal and Minimum, where both the approach seems to minimize the number of edges added. A comparison has been drawn amongst LB-Triangulation, Lex-M and Minimum Degree Vertex (MDV) approaches to achieve triangulation with as few edges as possible along with respective run times. While LB-Triang and Lex-M algorithms provide minimal triangulation, MDV is an approximation for minimum triangulation. Determining the minimum number of edges that must be added to a bipartite graph to make it a chain graph is NP-complete. We exploit this reduction to propose a heuristic for obtaining a chain graph from a bipartite graph via a chordal graph using MDV. Dirac\u27s method of generating chordal graphs by the union is modified with the help of MDV. Nearly Chordal Graphs are generated using a novel heuristic from complete graphs. Recognition algorithm for nearly chordal graphs is introduced and the relationship between weakly chordal, nearly chordal and chordal graphs is established

Informing patients about their mutation tests : CDKN2A c.256G>A in melanoma as an example

Background When germline mutations are suspected as causal in cancer, patient DNA may be sequenced to detect variants in relevant genes. If a particular mutation has not been reported in reliable family studies, genetic counselors are facing a dilemma of appropriately informing patients. Many sequencing facilities provide an interpretation of the findings based on the available sequence databases or on prediction tools that are curated from bioinformatics and mechanistic datasets. The counseling dilemma is exacerbated if the pedigree data are not informative but the in silico predictions suggest pathogenicity. Methods We present here a real world example of the c.256G > ACDKN2Avariant, which was detected in one melanoma patient where two siblings were diagnosed with melanoma in situ. We investigated a detailed family history of the affected siblings in order to survey probability of the cancer risks within the context to this mutation. Results This c.256G > ACDKN2Avariant was detected in one of the brothers and in the melanoma-free mother while the other brother in the family tested negative. The variant had been previously described in one patient from a melanoma family. In the family under investigation, the mother's 16 first-and second-degree relatives had survived past the median onset age for melanoma and none presented melanoma. We tested the variant using multiple bioinformatic tools that all predicted deleteriousness of the variant. The genetic counseling report to the melanoma patient stated that theCDKN2Avariant was 'likely pathogenic' and the disease was defined as 'likely hereditary melanoma'. Conclusions The pedigree data showed at the most a low penetrance variant, which, if taken into consideration, might have altered the provided diagnosis. When dealing with 'practically' unknown variants the counselors would be advised to incorporate a detailed family history rather than basing predictions on functionality provided by sequencing facilities.Peer reviewe

Whole exome sequencing identifies APCDD1 and HDAC5 genes as potentially cancer predisposing in familial colorectal cancer

Germline mutations in predisposition genes account for only 20% of all familial colorectal cancers (CRC) and the remaining genetic burden may be due to rare high- to moderate-penetrance germline variants that are not explored. With the aim of identifying such potential cancer-predisposing variants, we performed whole exome sequencing on three CRC cases and three unaffected members of a Polish family and identified two novel heterozygous variants: a coding variant in APC downregulated 1 gene (APCDD1, p.R299H) and a non-coding variant in the 5' untranslated region (UTR) of histone deacetylase 5 gene (HDAC5). Sanger sequencing confirmed the variants segregating with the disease and Taqman assays revealed 8 additional APCDD1 variants in a cohort of 1705 familial CRC patients and no further HDAC5 variants. Proliferation assays indicated an insignificant proliferative impact for the APCDD1 variant. Luciferase reporter assays using the HDAC5 variant resulted in an enhanced promoter activity. Targeting of transcription factor binding sites of SNAI-2 and TCF4 interrupted by the HDAC5 variant showed a significant impact of TCF4 on promoter activity of mutated HDAC5. Our findings contribute not only to the identification of unrecognized genetic causes of familial CRC but also underline the importance of 5'UTR variants affecting transcriptional regulation and the pathogenesis of complex disorders.This article is based upon work from COST Action CA17118, supported by COST (European Cooperation in Science and Technology) and Transcan ERA-NET funding from the German Federal Ministry of Education and Research (BMBF). K.H. was supported from the EU Horizon 2020 program, grant No. 856620

Whole-exome sequencing identifies a novel germline variant in PTK7 gene in familial colorectal cancer

Colorectal cancer (CRC) is the third most frequently diagnosed malignancy worldwide. Only 5% of all CRC cases are due to germline mutations in known predisposition genes, and the remaining genetic burden still has to be discovered. In this study, we performed whole-exome sequencing on six members of a Polish family diagnosed with CRC and identified a novel germline variant in the protein tyrosine kinase 7 (inactive) gene (PTK7, ENST00000230419, V354M). Targeted screening of the variant in 1705 familial CRC cases and 1674 healthy elderly individuals identified the variant in an additional familial CRC case. Introduction of this variant in HT-29 cells resulted in increased cell proliferation, migration, and invasion; it also caused down-regulation of CREB, p21 and p53 mRNA and protein levels, and increased AKT phosphorylation. These changes indicated inhibition of apoptosis pathways and activation of AKT signaling. Our study confirmed the oncogenic function of PTK7 and supported its role in genetic predisposition of familial CRC

A Germline Mutation in the POT1 Gene Is a Candidate for Familial Non-Medullary Thyroid Cancer

Non-medullary thyroid cancer (NMTC) is a common endocrine malignancy with a genetic basis that has yet to be unequivocally established. In a recent whole-genome sequencing study of five families with occurrence of NMTCs, we shortlisted promising variants with the help of bioinformatics tools. Here, we report in silico analyses and in vitro experiments on a novel germline variant (p.V29L) in the highly conserved oligonucleotide/oligosaccharide binding domain of the Protection of Telomeres 1 (POT1) gene in one of the families. The results showed a reduction in telomere-bound POT1 levels in the mutant protein as compared to its wild-type counterpart. HEK293T cells carrying POT1 p.V29L showed increased telomere length in comparison to wild-type cells, suggesting that the mutation causes telomere dysfunction and may play a role in predisposition to NMTC in this family. While one germline mutation in POT1 has already been reported in a melanoma-prone family with prevalence of thyroid cancers, we report the first of such mutations in a family affected solely by NMTCs, thus expanding current knowledge on shelterin complex-associated cancers

Localization of Low Copy Number Plasmid pRC4 in Replicating Rod and Non-Replicating Cocci Cells of <i>Rhodococcus erythropolis</i> PR4

<div><p><i>Rhodococcus</i> are gram-positive bacteria, which can exist in two different shapes rod and cocci. A number of studies have been done in the past on replication and stability of small plasmids in this bacterium; however, there are no reports on spatial localization and segregation of these plasmids. In the present study, a low copy number plasmid pDS3 containing pRC4 replicon was visualized in growing cells of <i>Rhodococcus erythropolis</i> PR4 (NBRC100887) using P1 <i>parS</i>-ParB-GFP system. Cells were initially cocci and then became rod shaped in exponential phase. Cocci cells were found to be non-replicating as evident by the presence of single fluorescence focus corresponding to the plasmid and diffuse fluorescence of DnaB-GFP. Rod shaped cells contained plasmid either present as one fluorescent focus observed at the cell center or two foci localized at quarter positions. The results suggest that the plasmid is replicated at the cell center and then it goes to quarter position. In order to observe the localization of plasmid with respect to nucleoid, plasmid segregation was also studied in filaments where it was found to be replicated at the cell center in a nucleoid free region. To the best of our knowledge, this is the first report on segregation of small plasmids in <i>R</i>. <i>erythropolis</i>.</p></div

Localization of DnaB-GFP in cocci and rod shaped cells.

<p>A) Phase image and B) fluorescence image of cocci cells <i>of R</i>. <i>erythropolis</i> containing plasmid expressing DnaB-GFP. C) Phase image and D) shows fluorescence in rod shaped cells, Arrow shows one and four foci cells; E-H) Subcellular distribution of DnaB-GFP in <i>R</i>. <i>erythropolis</i> PR4 grown in LB medium at 30°C.</p

Localization of plasmid pRC4 in cocci cells.

<p>Representative images of cocci cells carrying plasmid pRC4 visualized using parS-ParB-GFP system. A) GFP fluorescence showing plasmid pRC4 B) nucleoid stained by DAPI and C) overlay of both plasmid and nucleoid.</p