The basic construction from the conditional expectation on the quantum double of a finite group

summary:Let $G$ be a finite group and $H$ a subgroup. Denote by $D(G;H)$ (or $D(G)$) the crossed product of $C(G)$ and $\Bbb {C}H$ (or $\Bbb {C}G$) with respect to the adjoint action of the latter on the former. Consider the algebra $\langle D(G), e\rangle$ generated by $D(G)$ and $e$, where we regard $E$ as an idempotent operator $e$ on $D(G)$ for a certain conditional expectation $E$ of $D(G)$ onto $D(G;H)$. Let us call $\langle D(G), e\rangle$ the basic construction from the conditional expectation $E\colon D(G)\rightarrow D(G;H)$. The paper constructs a crossed product algebra $C(G/H\times G)\rtimes \Bbb {C}G$, and proves that there is an algebra isomorphism between $\langle D(G),e\rangle$ and $C(G/H\times G)\rtimes \Bbb {C}G$

Expressions of Carbohydrate Response Element Binding Protein and Glucose Transporters in Liver Cancer and Clinical Significance

Carbohydrate response element binding protein (ChREBP) is a glucose-sensing transcription factor that mediates the induction of glycolytic and lipogenic genes in response to glucose. We investigated the expression patterns of ChREBP and glucose transporters (GLUTs) in human hepatocellular carcinoma (HCC) and their association with HCC progression. ChREBP, GLUT2 and GLUT1 immunohistochemistry were performed on liver tissue array containing normal liver tissue, HCC adjacent tissue and cancer tissue of different HCC stages. The effect of HCC malignancy on protein expression was analyzed with one-way ANOVA. The correlations between protein expressions were analyzed with Pearson Correlation test. We found that ChREBP protein expression tended to be positively correlated to liver malignancy. GLUT2 protein expression was significantly reduced in human HCC as compared to normal liver tissue and its expression in HCC was inversely associated to malignancy (p <0.001). In contrast, GLUT1 was significantly increased in cancer cells and its expression was positively correlated to malignancy (p <0.001). Furthermore, GLUT1 expression was positively associated to ChREBP expression (r = 0.481, p <0.0001, n = 70) but negatively correlated to GLUT2 expression (r = -0.320, p = 0.007, n = 70). Notably, ChREBP-expressing hepatocytes did not express GLUT2 but GLUT1. This is the first report unveiling expressions of ChREBP and GLUT2/GLUT1 and their relations in HCC. The expression patterns are related to malignancy and this information would facilitate evaluation of clinical behavior and treatment of HCC

BmC/EBPZ gene is essential for the larval growth and development of silkworm, Bombyx mori

The genetic male sterile line (GMS) of the silkworm Bombyx mori is a recessive mutant that is naturally mutated from the wild-type 898WB strain. One of the major characteristics of the GMS mutant is its small larvae. Through positional cloning, candidate genes for the GMS mutant were located in a region approximately 800.5 kb long on the 24th linkage group of the silkworm. One of the genes was Bombyx mori CCAAT/enhancer-binding protein zeta (BmC/EBPZ), which is a member of the basic region-leucine zipper transcription factor family. Compared with the wild-type 898WB strain, the GMS mutant features a 9 bp insertion in the 3′end of open reading frame sequence of BmC/EBPZ gene. Moreover, the high expression level of the BmC/EBPZ gene in the testis suggests that the gene is involved in the regulation of reproduction-related genes. Using the CRISPR/Cas9-mediated knockout system, we found that the BmC/EBPZ knockout strains had the same phenotypes as the GMS mutant, that is, the larvae were small. However, the larvae of BmC/EBPZ knockout strains died during the development of the third instar. Therefore, the BmC/EBPZ gene was identified as the major gene responsible for GMS mutation

FBXO5 acts as a novel prognostic biomarker for patients with cervical cancer

Background: Cervical cancer (CC) remains one of the most common and deadly malignancies in women worldwide. FBXO5, a protein-coding gene, is highly expressed in a variety of primary tumors and promotes tumor progression, however, its role and prognostic value in CC remain largely unknown.Methods: A key differential gene, FBXO5, was screened according to WGCNA based on immunohistochemical assays of clinical samples, multiple analyses of the Cancer Genome Atlas (TCGA) and Genotype-Tissue Expression (GTEx) databases, including survival analysis, tumor mutational burden, GO, KEGG, tumor immune infiltration, and chemotherapeutic drug sensitivity, to explore the expression and prognostic value of FBXO5 in CC. The migration and invasiveness of cervical cancer cells following FBXO5 knockdown and overexpression were examined using wound healing and transwell assays, and the viability of cancer cells was assessed using CCK8 and EdU assays.Results:FBXO5 was discovered to be substantially expressed in CC tissues using data from our CC cohort and the TCGA database, and a survival analysis indicated FBXO5 as a predictive factor for poor overall survival in CC patients. In vitro, CC cells were more inclined to proliferate, migrate, and invade when FBXO5 was upregulated as opposed to when it was knocked down

Transient receptor potential channels’ genes forecast cervical cancer outcomes and illuminate its impact on tumor cells

Introduction: In recent years, there has been a strong association between transient receptor potential (TRP) channels and the development of various malignancies, drug resistance, and resistance to radiotherapy. Consequently, we have investigated the relationship between transient receptor potential channels and cervical cancer from multiple angles.Methods: Patients’ mRNA expression profiles and gene variants were obtained from the TCGA database. Key genes in transient receptor potential channel prognosis-related genes (TRGs) were screened using the least absolute shrinkage and selection operator (LASSO) regression method, and a risk signature was constructed based on the expression of key genes. Various analyses were performed to evaluate the prognostic significance, biological functions, immune infiltration, and response to immunotherapy based on the risk signature.Results: Our research reveals substantial differences between high and low-risk groups in prognosis, tumor microenvironment, tumor mutational load, immune infiltration, and response to immunotherapy. Patients in the high-risk group exhibited poorer prognosis, lower tumor microenvironment scores and reduced response to immunotherapy while showing increased sensitivity to specific targeted drugs. In vitro experiments further illustrated that inhibiting transient receptor potential channels effectively decreased the proliferation, invasion, and migration of cervical cancer cells.Discussion: This study highlights the significant potential of transient receptor potential channels in cervical cancer, emphasizing their crucial role in prognostic prediction and personalized treatment strategies. The combination of TRP inhibitors with immunotherapy and targeted drugs may offer promise for individuals affected by cervical cancer