ZX-Calculus: Cyclotomic Supplementarity and Incompleteness for Clifford+T quantum mechanics

The ZX-Calculus is a powerful graphical language for quantum mechanics and quantum information processing. The completeness of the language -- i.e. the ability to derive any true equation -- is a crucial question. In the quest of a complete ZX-calculus, supplementarity has been recently proved to be necessary for quantum diagram reasoning (MFCS 2016). Roughly speaking, supplementarity consists in merging two subdiagrams when they are parameterized by antipodal angles. We introduce a generalised supplementarity -- called cyclotomic supplementarity -- which consists in merging n subdiagrams at once, when the n angles divide the circle into equal parts. We show that when n is an odd prime number, the cyclotomic supplementarity cannot be derived, leading to a countable family of new axioms for diagrammatic quantum reasoning.We exhibit another new simple axiom that cannot be derived from the existing rules of the ZX-Calculus, implying in particular the incompleteness of the language for the so-called Clifford+T quantum mechanics. We end up with a new axiomatisation of an extended ZX-Calculus, including an axiom schema for the cyclotomic supplementarity.Comment: Mathematical Foundations of Computer Science, Aug 2017, Aalborg, Denmar

IKKβ programs to turn on the GADD45α–MKK4–JNK apoptotic cascade specifically via p50 NF-κB in arsenite response

Cross talk between NF-κB and c-Jun N-terminal kinases (JNKs) has been implicated in the cell life and death decision under various stresses. Functional suppression of JNK activation by NF-κB has recently been proposed as a key cellular survival mechanism and contributes to cancer cells escaping from apoptosis. We provide a novel scenario of the proapoptotic role of IκB kinase β (IKKβ)–NF-κB, which can act as the activator of the JNK pathway through the induction of GADD45α for triggering MKK4/JNK activation, in response to the stimulation of arsenite, a cancer therapeutic reagent. This effect of IKKβ–NF-κB is dependent on p50 but not the p65/relA NF-κB subunit, which can increase the stability of GADD45α protein through suppressing its ubiquitination and proteasome-dependent degradation. IKKβ–NF-κB can therefore either activate or suppress the JNK cascade and consequently mediate pro- or antiapoptotic effects, depending on the manner of its induction. Furthermore, the NF-κB p50 subunit can exert a novel regulatory function on protein modification independent of the classical NF-κB transcriptional activity

Genomic analysis of oesophageal squamous-cell carcinoma identifies alcohol drinking-related mutation signature and genomic alterations

Approximately half of the world's 500,000 new oesophageal squamous-cell carcinoma (ESCC) cases each year occur in China. Here, we show whole-genome sequencing of DNA and RNA in 94 Chinese individuals with ESCC. We identify six mutational signatures (E1–E6), and Signature E4 is unique in ESCC linked to alcohol intake and genetic variants in alcohol-metabolizing enzymes. We discover significantly recurrent mutations in 20 protein-coding genes, 4 long non-coding RNAs and 10 untranslational regions. Functional analyses show six genes that have recurrent copy-number variants in three squamous-cell carcinomas (oesophageal, head and neck and lung) significantly promote cancer cell proliferation, migration and invasion. The most frequently affected genes by structural variation are LRP1B and TTC28. The aberrant cell cycle and PI3K-AKT pathways seem critical in ESCC. These results establish a comprehensive genomic landscape of ESCC and provide potential targets for precision treatment and prevention of the cancer

Aurora-A Interacts with AP-2α and Down Regulates Its Transcription Activity

Aurora-A is a serine/threonine protein kinase and plays an important role in the control of mitotic progression. Dysregulated expression of Aurora-A impairs centrosome separation and maturation, which lead to disrupted cell cycle progression and tumorigenesis. However, the molecular mechanism by which Aurora-A causes cell malignant transformation remains to be further defined. In this report, using transcription factors array and mRNA expression profiling array, we found that overexpression of Aurora-A suppressed transcription activity of AP-2α, a tumor suppressor that is often downregulated in variety of tumors, and inhibited expression of AP-2α-regulated downstream genes. These array-based observations were further confirmed by microwell colorimetric TF assay and luciferase reporter assay. Downregulated transcription activity of AP-2α by Aurora-A was found to be associated with reduced AP-2α protein stability, which appeared to be mediated by Aurora-A enhanced ubiquitin-dependent proteasomal degradation of AP-2α protein. Interestingly, Aurora-A-mediated AP-2α degradation was likely dependent Aurora-A kinase activity since inhibition of Aurora-A kinase activity was able to rescue Aurora-A-induced degradation of AP-2α. Moreover, we defined a physical interaction between Aurora-A and AP-2α, and such interaction might bridge the suppressive effect of Aurora-A on AP-2α protein stability. These findings provide new insights into molecular mechanism by which Aurora-A acts as an oncogenic molecule in tumor occurrence and malignant development

Genomic Analyses Reveal Mutational Signatures and Frequently Altered Genes in Esophageal Squamous Cell Carcinoma

Esophageal squamous cell carcinoma (ESCC) is one of the most common cancers worldwide and the fourth most lethal cancer in China. However, although genomic studies have identified some mutations associated with ESCC, we know little of the mutational processes responsible. To identify genome-wide mutational signatures, we performed either whole-genome sequencing (WGS) or whole-exome sequencing (WES) on 104 ESCC individuals and combined our data with those of 88 previously reported samples. An APOBEC-mediated mutational signature in 47% of 192 tumors suggests that APOBEC-catalyzed deamination provides a source of DNA damage in ESCC. Moreover, PIK3CA hotspot mutations (c.1624G>A [p.Glu542Lys] and c.1633G>A [p.Glu545Lys]) were enriched in APOBEC-signature tumors, and no smoking-associated signature was observed in ESCC. In the samples analyzed by WGS, we identified focal (<100 kb) amplifications of CBX4 and CBX8. In our combined cohort, we identified frequent inactivating mutations in AJUBA, ZNF750, and PTCH1 and the chromatin-remodeling genes CREBBP and BAP1, in addition to known mutations. Functional analyses suggest roles for several genes (CBX4, CBX8, AJUBA, and ZNF750) in ESCC. Notably, high activity of hedgehog signaling and the PI3K pathway in approximately 60% of 104 ESCC tumors indicates that therapies targeting these pathways might be particularly promising strategies for ESCC. Collectively, our data provide comprehensive insights into the mutational signatures of ESCC and identify markers for early diagnosis and potential therapeutic targets

Joint analysis of three genome-wide association studies of esophageal squamous cell carcinoma in Chinese populations

We conducted a joint (pooled) analysis of three genome-wide association studies (GWAS) 1-3 of esophageal squamous cell carcinoma (ESCC) in ethnic Chinese (5,337 ESCC cases and 5,787 controls) with 9,654 ESCC cases and 10,058 controls for follow-up. In a logistic regression model adjusted for age, sex, study, and two eigenvectors, two new loci achieved genome-wide significance, marked by rs7447927 at 5q31.2 (per-allele odds ratio (OR) = 0.85, 95% CI 0.82-0.88; P=7.72x10−20) and rs1642764 at 17p13.1 (per-allele OR= 0.88, 95% CI 0.85-0.91; P=3.10x10−13). rs7447927 is a synonymous single nucleotide polymorphism (SNP) in TMEM173 and rs1642764 is an intronic SNP in ATP1B2, near TP53. Furthermore, a locus in the HLA class II region at 6p21.32 (rs35597309) achieved genome-wide significance in the two populations at highest risk for ESSC (OR=1.33, 95% CI 1.22-1.46; P=1.99x10−10). Our joint analysis identified new ESCC susceptibility loci overall as well as a new locus unique to the ESCC high risk Taihang Mountain region

Cancer Research in 2021

Cancer research has been severely impacted by COVID-19. What does the future of cancer research look like in the new year after the pandemic