Geometric methods on low-rank matrix and tensor manifolds

In this chapter we present numerical methods for low-rank matrix and tensor problems that explicitly make use of the geometry of rank constrained matrix and tensor spaces. We focus on two types of problems: The first are optimization problems, like matrix and tensor completion, solving linear systems and eigenvalue problems. Such problems can be solved by numerical optimization for manifolds, called Riemannian optimization methods. We will explain the basic elements of differential geometry in order to apply such methods efficiently to rank constrained matrix and tensor spaces. The second type of problem is ordinary differential equations, defined on matrix and tensor spaces. We show how their solution can be approximated by the dynamical low-rank principle, and discuss several numerical integrators that rely in an essential way on geometric properties that are characteristic to sets of low rank matrices and tensors

Growth arrest-specific transcript 5 associated snoRNA levels are related to p53 expression and DNA damage in colorectal cancer

BACKGROUND The growth arrest-specific transcript 5 gene (GAS5) encodes a long noncoding RNA (lncRNA) and hosts a number of small nucleolar RNAs (snoRNAs) that have recently been implicated in multiple cellular processes and cancer. Here, we investigate the relationship between DNA damage, p53, and the GAS5 snoRNAs to gain further insight into the potential role of this locus in cell survival and oncogenesis both in vivo and in vitro. METHODS We used quantitative techniques to analyse the effect of DNA damage on GAS5 snoRNA expression and to assess the relationship between p53 and the GAS5 snoRNAs in cancer cell lines and in normal, pre-malignant, and malignant human colorectal tissue and used biological techniques to suggest potential roles for these snoRNAs in the DNA damage response. RESULTS GAS5-derived snoRNA expression was induced by DNA damage in a p53-dependent manner in colorectal cancer cell lines and their levels were not affected by DICER. Furthermore, p53 levels strongly correlated with GAS5-derived snoRNA expression in colorectal tissue. CONCLUSIONS In aggregate, these data suggest that the GAS5-derived snoRNAs are under control of p53 and that they have an important role in mediating the p53 response to DNA damage, which may not relate to their function in the ribosome. We suggest that these snoRNAs are not processed by DICER to form smaller snoRNA-derived RNAs with microRNA (miRNA)-like functions, but their precise role requires further evaluation. Furthermore, since GAS5 host snoRNAs are often used as endogenous controls in qPCR quantifications we show that their use as housekeeping genes in DNA damage experiments can lead to inaccurate results

Expression of high p53 levels in colorectal cancer: a favourable prognostic factor

The expression of p53 protein was examined in a series of 111 colorectal cancer adenocarcinomas with a long follow-up. A quantitative luminometric immunoassay (LIA) was used for the measurement of wild-type and mutant p53 protein in extracts from colorectal tumour cytosols, p53 being detected in 42% of the samples (range 0.0–52 ng mg−1). Using an arbitrary cut-off value of 2.7 ng mg−1, 25% of the tumours were classified as manifesting high p53 levels. There was no association of p53 expression with patient age, sex, serum preoperative carcinoembryonic antigen (CEA) levels, tumour site and size, nodal status or TNM stage. Significant and independent correlation was found to exist between high p53 levels and prolonged disease-free survival (P = 0.05) at a median follow-up of 60 months. This survival advantage was most apparent among stage III cancer patients. The results from this study would suggest that expression of high p53 levels appear to be useful in selecting a group of colorectal cancer patients with a better prognosis. © 1999 Cancer Research Campaig

Prognostic Significance and Gene Expression Profiles of p53 Mutations in Microsatellite-Stable Stage III Colorectal Adenocarcinomas

Although the prognostic value of p53 abnormalities in Stage III microsatellite stable (MSS) colorectal cancers (CRCs) is known, the gene expression profiles specific to the p53 status in the MSS background are not known. Therefore, the current investigation has focused on identification and validation of the gene expression profiles associated with p53 mutant phenotypes in MSS Stage III CRCs. Genomic DNA extracted from 135 formalin-fixed paraffin-embedded tissues, was analyzed for microsatellite instability (MSI) and p53 mutations. Further, mRNA samples extracted from five p53-mutant and five p53-wild-type MSS-CRC snap-frozen tissues were profiled for differential gene expression by Affymetrix Human Genome U133 Plus 2.0 arrays. Differentially expressed genes were further validated by the high-throughput quantitative nuclease protection assay (qNPA), and confirmed by quantitative real-time polymerase chain reaction (qRT-PCR) and by immunohistochemistry (IHC). Survival rates were estimated by Kaplan-Meier and Cox regression analyses. A higher incidence of p53 mutations was found in MSS (58%) than in MSI (30%) phenotypes. Both univariate (log-rank, P = 0.025) and multivariate (hazard ratio, 2.52; 95% confidence interval, 1.25–5.08) analyses have demonstrated that patients with MSS-p53 mutant phenotypes had poor CRC-specific survival when compared to MSS-p53 wild-type phenotypes. Gene expression analyses identified 84 differentially expressed genes. Of 49 down-regulated genes, LPAR6, PDLIM3, and PLAT, and, of 35 up-regulated genes, TRIM29, FUT3, IQGAP3, and SLC6A8 were confirmed by qNPA, qRT-PCR, and IHC platforms. p53 mutations are associated with poor survival of patients with Stage III MSS CRCs and p53-mutant and wild-type phenotypes have distinct gene expression profiles that might be helpful in identifying aggressive subsets

Changes in the status of p53 affect drug sensitivity to thymidylate synthase (TS) inhibitors by altering TS levels

Colorectal cancer (CRC) resistance to fluoropyrimidines and other inhibitors of thymidylate synthase (TS) is a serious clinical problem often associated with increased intracellular levels of TS. Since the tumour suppressor gene p53, which is mutated in 50% of CRC, regulates the expression of several genes, it may modulate TS activity, and changes in the status of p53 might be responsible for chemoresistance. Therefore, this study was aimed to investigate TS levels and sensitivity to TS inhibitors in wild-type (wt) and mutant (mt) p53 CRC cells, Lovo and WiDr, respectively, transfected with mt and wt p53. Lovo 175X2 cells (transfected with mt p53) were more resistant to 5-fluorouracil (5-FU; 2-fold), nolatrexed (3-fold), raltitrexed (3-fold) and pemetrexed (10-fold) in comparison with the wt p53 parental cells Lovo 92. Resistance was associated with an increase in TS protein expression and catalytic activity, which might be caused by the loss of the inhibitory effect on the activity of TS promoter or by the lack of TS mRNA degradation, as suggested by the reversal of TS expression to the levels of Lovo 92 cells by adding actinomycin. In contrast, Lovo li cells, characterized by functionally inactive p53, were 3-13-fold more sensitive to nolatrexed, raltitrexed and pemetrexed, and had a lower TS mRNA, protein expression and catalytic activity than Lovo 92. However, MDM-2 expression was significantly higher in Lovo li, while no significant differences were observed in Lovo 175X2 cells with respect to Lovo 92. Finally, mt p53 WiDr transfected with wt p53 were not significantly different from mt p53 WiDr cells with respect to sensitivity to TS inhibitors or TS levels. Altogether, these results indicate that changes in the status of p53, can differently alter sensitivity to TS inhibitors by affecting TS levels, depending on activity or cell line, and might explain the lack of clear correlation between mutations in p53 and clinical outcome after chemotherapy with TS inhibitors

Mutations in APC, CTNNB1 and K-ras genes and expression of hMLH1 in sporadic colorectal carcinomas from the Netherlands Cohort Study

BACKGROUND: The early to intermediate stages of the majority of colorectal tumours are thought to be driven by aberrations in the Wnt (APC, CTNNB1) and Ras (K-ras) pathways. A smaller proportion of cancers shows mismatch repair deficiency. The aim of this study was to analyse the co-occurrence of these genetic alterations in relation to tumour and patient characteristics. METHODS: In a group of 656 unselected sporadic colorectal cancer patients, aberrations in the APC, K-ras, CTNNB1 genes, and expression of hMLH1 were investigated. Additionally, tumours were divided in groups based on molecular features and compared with respect to patient's age at diagnosis, sex, family history of colorectal cancer, tumour sub-localisation, Dukes' stage and differentiation. RESULTS: Mutations at the phosphorylation sites (codons 31, 33, 37, and 45) in the CTNNB1 gene were observed in tumours from only 5/464 patients. Tumours with truncating APC mutations and activating K-ras mutations in codons 12 and 13 occurred at similar frequencies (37% (245/656) and 36% (235/656), respectively). Seventeen percent of tumours harboured both an APC and a K-ras mutation (109/656). Nine percent of all tumours (58/656) lacked hMLH1 expression. Patients harbouring a tumour with absent hMLH1 expression were older, more often women, more often had proximal colon tumours that showed poorer differentiation when compared to patients harbouring tumours with an APC and/or K-ras mutation. CONCLUSION: CTNNB1 mutations seem to be of minor importance in sporadic colorectal cancer. The main differences in tumour and patient characteristics are found between groups of patients based on mismatch repair deficiency

Poorer outcome in stromal HIF-2α- and CA9-positive colorectal adenocarcinomas is associated with wild-type TP53 but not with BNIP3 promoter hypermethylation or apoptosis

Stromal expression of hypoxia inducible factor 2α (HIF-2α) and carbonic anhydrase 9 (CA9) are associated with a poorer prognosis in colorectal cancer (CRC). Tumour cell death, regulated by a hypoxic stromal microenvironment, could be of importance in this respect. Therefore, we correlated apoptosis, TP53 mutational status and BNIP3 promoter hypermethylation of CRC cells with HIF-2α- and CA9-related poor outcome. In a series of 195 CRCs, TP53 mutations in exons 5–8 were analysed by direct sequencing, and promoter hypermethylation of BNIP3 was determined by methylation-specific PCR. Expressions of HIF-2α, CA9, p53, BNIP3 and M30 were analysed immunohistochemically. Poorer survival of HIF-2α and CA9 stromal-positive CRCs was associated with wild-type TP53 (P=0.001 and P=0.0391), but not with BNIP3 methylation. Furthermore, apoptotic levels were independent of the TP53 status, but lower in unmethylated BNIP3 CRCs (P=0.004). It appears that wild-type TP53 in CRC cells favours the progression of tumours expressing markers for hypoxia in their stroma, rather than in the epithelial compartment. Preserved BNIP3 function in CRC cells lowers apoptosis, and may thus be involved in alternative cell death pathways, such as autophagic cell death. However, BNIP3 silencing in tumour cells does not impact on hypoxia-driven poorer prognosis

p53 status and response to radiotherapy in rectal cancer: a prospective multilevel analysis

The aim of this study was to evaluate, in a prospective study, the predictive role of p53 status analysed at four different levels in identifying the response to preoperative radiotherapy in rectal adenocarcinoma. Before treatment, 70 patients were staged and endoscopic forceps biopsies from the tumour area were taken. p53 status was assessed by total cDNA sequencing, allelic loss analysis, immunohistochemistry, and p53 antibodies. Neoadjuvant treatment was based on preoperative radiotherapy or radiochemotherapy. Response to therapy was evaluated after surgery by both pathologic downstaging and histologic tumour regression grade. In all, 35 patients (50.0%) had p53 gene mutations; 44.4% of patients had an allelic loss; nuclear p53 overexpression was observed in 39 patients (55.7%); and p53 antibodies were detected in 11 patients (16.7%). In the multilevel analysis of p53 status, gene mutations correlated with both nuclear protein overexpression (P<0.0001) and loss of heterozygosity (P=0.013). In all, 29 patients (41.4%) were downstaged by pathologic analysis, and 19 patients (29.2%) were classified as tumour regression grade 1. Whatever the method of evaluation of treatment response, no correlation between p53 alterations and response to radiotherapy was observed. Our results do not support the use of p53 alterations alone as a predictive marker for response to radiotherapy in rectal carcinoma