Let Ln6,6 be the molecular graph of the linear [n]phenylene with n hexagons and n − 1 squares, and let Ln4,4 be the graph obtained by attaching four‐membered rings to the terminal hexagons of Ln6,6. In this article, the normalized Laplacian spectrum of Ln6,6 consisting of the eigenvalues of two symmetric tridiagonal matrices of order 3n is determined. An explicit closed‐form formula of the multiplicative degree‐Kirchhoff index (respectively the number of spanning trees) of Ln6,6 is derived. Similarly, explicit closed‐form formulas of the multiplicative degree‐Kirchhoff index and the number of spanning trees of Ln4,4 are obtained. It is interesting to see that the multiplicative degree‐Kirchhoff index of Ln6,6 (respectively Ln4,4) is approximately to one half of its Gutman index.
Apoptosis is closely associated with the development of various cancers, including lung adenocarcinoma (LUAD). However, the prognostic value of apoptosis-related lncRNAs (ApoRLs) in LUAD has not been fully elucidated. In the present study, we screened 2, 960 ApoRLs by constructing a co-expression network of mRNAs-lncRNAs associated with apoptosis, and identified 421 ApoRLs that were differentially expressed between LUAD samples and normal lung samples. Sixteen differentially expressed apoptosis-related lncRNAs (DE-ApoRLs) with prognostic relevance to LUAD patients were screened using univariate Cox regression analysis. An apoptosis-related lncRNA signature (ApoRLSig ) containing 10 ApoRLs was constructed by applying the Least Absolute Shrinkage and Selection Operator (LASSO) Cox regression method, and all LUAD patients in the TCGA cohort were divided into high or low risk groups. Moreover, patients in the high-risk group had a worse prognosis (p < 0.05). When analyzed in conjunction with clinical features, we found ApoRLSig to be an independent predictor of LUAD patients and established a prognostic nomogram combining ApoRLSig and clinical features. Gene set enrichment analysis (GSEA) revealed that ApoRLSig is involved in many malignancy-associated immunomodulatory pathways. In addition, there were significant differences in the immune microenvironment and immune cells between the high-risk and low-risk groups. Further analysis revealed that the expression levels of most immune checkpoint genes (ICGs) were higher in the high-risk group, which suggested that the immunotherapy effect was better in the high-risk group than in the low-risk group. And we found that the high-risk group was also better than the low-risk group in terms of chemotherapy effect. In conclusion, we successfully constructed an ApoRLSig which could predict the prognosis of LUAD patients and provide a novel strategy for the antitumor treatment of LUAD patients.
Background: P-element induced wimpy testis (PIWI)-interacting RNAs (piRNAs) are the most mysterious class of small non-coding RNAs. They limit gene expression in gonads and sequence diversity. Dysregulated piRNAs can led to all kinds of cancers. Recently, piRNAs were postulated to be potentially useful biomarkers for tumor diagnosis and prognosis. However, there lack a systematic review of prognostic and diagnostic piRNAs in neoplasms. The study aimed to decipher the relationships between piRNAs expression, diagnostic and prognostic outcome in tumors. Methods: This study systematically searched Google Scholar, MEDLINE, Scopus, PubMed, Embase, ScienceDirect, Ovid-Medline, Chinese National Knowledge Infrastructure, WanFang and SinoMed databases for relevant articles published before July 13, 2022. The study is registered in PROSPERO (CRD42020208717). Results: Thirty relevant studies were included in the meta-analysis: 19 on diagnosis and 23 on prognosis. The pooled adds ratio, 95% confidence intervals (Cl) and hazard ratios (HR) of the studies were used to investigate the clinical parameters and overall survival (OS) of cancer patients. The area under the curve (AUC), sensitivity, and specificity was 0.82, 79%, and 77% in tumors, respectively. Though abnormally expressed piRNAs were associated with poor and unfavorable impacts on the OS time of cancer patients (HR=1.00, 95% Cl: 1.00-1.00, P<0.00001). Meanwhile, piRNAs in the breast cancer had favorable impacts on the OS (HR=0.70, 95% CI:0.45-1.09). However, the piRNAs in cell renal cell carcinoma, colorectal cancer, diffuse large B-cell lymphoma and gastric cancer had bad favorable impacts on the OS (HR=1.46, 95% CI:1.37-1.55; HR=1.56, 95% CI:1.24 -1.95; HR=2.19, 95% CI:1.25-3.86; HR=1.01, 95% CI:0.97-1.04, respectively). Conclusions: The results strongly suggested that piRNAs were potential novel prognostic and diagnostic indicators in tumors.
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