Prognostic prediction and expression validation of NSD3 in pan-cancer analyses

Background:Nuclear receptor binding SET domain protein-3(NSD3)is a histone lysine methyltransferase and a crucial regulator of carcinogenesis in several cancers.We aimed to investigate the prognostic value and potential function of NSD3 in 33 types of human cancer.Methods:The data were obtained from The Cancer Genome Atlas.Kaplan-Meier analysis,CIBERSORT,gene set enrichment analysis,and gene set variation analysis were performed.The expression of NSD3 was measured using quantitative real-time polymerase chain reaction and western blot.Results:The expression of NSD3 was altered in pan-cancer samples.Patients with higher levels of NDS3 generally had shorter overall survival and disease-specific survival.Levels of NSD3 were positively correlated with DNA copy number variation(CNV)in pan-cancer.NSD3 expression was also associated with tumor mutation burden and microsatellite instability.The levels of immune-cell infiltration differed significantly between high and low NSD3 expression.NSD3 negatively correlated with levels of CD8+T cells.Functional enrichment analysis showed that while NSD3 expression was positively associated with several immune cell-related and histone methylation-related pathways,it was negatively correlated with cell metabolism-related,drug transport-related,and drug metabolismrelated pathways.NSD3 levels in the cell lines tested were significantly different.In U251 and NCI-H23 cells,silencing NSD3 inhibited cell proliferation and promoted apoptosis.Conclusions:NSD3 expression was changed in pan-cancer samples that was also verified in cell lines.NSD3 was associated with CNV and immune-cell infiltration.A poor prognosis was predicted in patients with high expression of NSD3.NSD3 might hence be a potential marker for predicting tumor prognosis.

Gauss-Bonnet-Chern mass and Alexandrov-Fenchel inequality

This is a survey about our recent works on the Gauss-Bonnet-Chern （GBC） mass for asymptotically flat and asymptotically hyperbolic manifolds. We first introduce the GBC mass, a higher order mass, for asymptotically flat and for asymptotically hyperbolic manifolds, respectively, by using a higher order scalar curvature. Then we prove its positivity and the Penrose inequality for graphical manifolds. One of the crucial steps in the proof of the Penrose inequality is the use of an Alexandrov-Fenchel inequality, which is a classical^inequality in the Euclidean space. In the hyperbolic space, we have established this new Alexandrov-Fenchel inequality. We also have a similar work for asymptotically locally hyperbolic manifolds. At the end, we discuss the relation between the GBC mass and Chern＇s magic form.