On the index of length four minimal zero-sum sequences

Let $G$ be a finite cyclic group. Every sequence $S$ over $G$ can be written in the form $S=(n_1g)\cdot\ldots\cdot(n_lg)$ where $g\in G$ and n_1, \ldots, n_l\in[1, \ord(g)], and the index \ind(S) of $S$ is defined to be the minimum of (n_1+\cdots+n_l)/\ord(g) over all possible $g\in G$ such that $\langle g \rangle =G$. A conjecture on the index of length four sequences says that every minimal zero-sum sequence of length 4 over a finite cyclic group $G$ with $\gcd(|G|, 6)=1$ has index 1. The conjecture was confirmed recently for the case when $|G|$ is a product of at most two prime powers. However, the general case is still open. In this paper, we make some progress towards solving the general case. Based on earlier work on this problem, we show that if $G=\langle g\rangle$ is a finite cyclic group of order $|G|=n$ such that $\gcd(n,6)=1$ and $S=(x_1g)(x_2g)(x_3g)(x_4g)$ is a minimal zero-sum sequence over $G$ such that $x_1,\cdots,x_4\in[1,n-1]$ with $\gcd(n,x_1,x_2,x_3,x_4)=1$, and $\gcd(n,x_i)>1$ for some $i\in[1,4]$, then \ind(S)=1. By using an innovative method developed in this paper, we are able to give a new (and much shorter) proof to the index conjecture for the case when $|G|$ is a product of two prime powers

The Role of Long Non-Coding RNAs in Epithelial-Mesenchymal Transition-Related Signaling Pathways in Prostate Cancer

Prostate cancer (PCa) is one of the most common male malignancies with frequent remote invasion and metastasis, leading to high mortality. Epithelial-mesenchymal transition (EMT) is a fundamental process in embryonic development and plays a key role in tumor proliferation, invasion and metastasis. Numerous long non-coding RNAs (lncRNAs) could regulate the occurrence and development of EMT through various complex molecular mechanisms involving multiple signaling pathways in PCa. Given the importance of EMT and lncRNAs in the progression of tumor metastasis, we recapitulate the research progress of EMT-related signaling pathways regulated by lncRNAs in PCa, including AR signaling, STAT3 signaling, Wnt/β-catenin signaling, PTEN/PI3K/AKT signaling, TGF-β/Smad and NF-κB signaling pathways. Furthermore, we summarize four modes of how lncRNAs participate in the EMT process of PCa via regulating relevant signaling pathways

Development and validation of prognostic dynamic nomograms for hepatitis B Virus-related hepatocellular carcinoma with microvascular invasion after curative resection

Background and AimThe prediction models of postoperative survival for hepatitis B virus-related hepatocellular carcinoma (HBV-HCC) with microvascular invasion (MVI) have not been well established. The study objective was the development of nomograms to predict disease recurrence and overall survival (OS) in these patients.MethodsData were obtained from 1046 HBV-related MVI-positive HCC patients who had undergone curative resection from January 2014 to December 2017. The study was approved by the Eastern Hepatobiliary Surgery Hospital and Jinling Hospital ethics committee, and patients provided informed consent for the use of their data. Nomograms for recurrence and OS were created by Cox regression model in the training cohort (n=530). The modes were verified in an internal validation cohort (n= 265) and an external validation cohort (n= 251).ResultsThe nomograms of recurrence and OS based on preoperative serological indicators (HBV-DNA, neutrophil-lymphocyte ratio, a-fetoprotein), tumor clinicopathologic features (diameter, number), surgical margin and postoperative adjuvant TACE achieved high C-indexes of 0.722 (95% confidence interval [CI], 0.711-0.732) and 0.759 (95% CI, 0.747-0.771) in the training cohort, respectively, which were significantly higher than conventional HCC staging systems (BCLC, CNLC, HKLC).The nomograms were validated in the internal validation cohort (0.747 for recurrence, 0.758 for OS) and external validation cohort(0.719 for recurrence, 0.714 for OS) had well-fitted calibration curves. Our nomograms accurately stratified patients with HBV-HCC with MVI into low-, intermediate- and high-risk groups of postsurgical recurrence and mortality. Prediction models for recurrence-free survival (https://baishileiehbh.shinyapps.io/HBV-MVI-HCC-RFS/) and OS (https://baishileiehbh.shinyapps.io/HBV-MVI-HCC-OS/) were constructed.ConclusionsThe two nomograms showed good predictive performance and accurately distinguished different recurrence and OS by the nomograms scores for HBV-HCC patients with MVI after resection

A Residue at the Cytoplasmic Entrance of BK-Type Channels Regulating Single-Channel Opening by Its Hydrophobicity

Single large-conductance calcium-activated K+ (BK) channels encoded by the mSlo gene usually have synchronous gating, but a Drosophila dSlo (A2/C2/E2/G5/10) splice variant (dSlo1A) exhibits very flickery openings. To probe this difference in gating, we constructed a mutant I323T. This channel exhibits four subconductance levels similar to those of dSlo1A. Rectification of the single-channel current-voltage relation of I323T decreased as [Ca2+ ]in increased from 10 to 300 μM. Mutagenesis suggests that the hydrophobicity of the residue at the position is important for the wild-type gating; i.e., increasing hydrophobicity prolongs open duration. Molecular dynamics simulation suggests that four hydrophobic pore-lining residues at position 323 of mSlo act cooperatively in a “shutter-like” mechanism gating the permeation of K+ ions. Rate-equilibrium free energy relations analysis shows that the four I323 residues in an mSlo channel have a conformation 65% similar to the closed conformation during gating. Based on these observations, we suggest that the appearance of rectification and substates of BK-type channels arise from a reduction of the cooperativity among these four residues and a lower probability of being open

CCCCC pentadentate chelates with planar Möbius aromaticity and unique properties

本课题充分发挥了厦门大学多学科协同研究优势，通讯作者为夏海平教授（合成、表征）、刘刚教授（生物医学应用）和吕鑫教授（理论计算）。合成实验和结构表征由朱从青（第一作者，目前在麻省理工学院、2005年诺贝尔化学奖得主Richard Schrock教授课题组从事博士后研究）完成；生物医学应用由杨彩霞（共同第一作者）、林凎、杨宇惠、王晓勇合作完成；理论计算由朱军、王永恒、朱从青完成。美国NIH的陈小元教授参与了生物医学应用的讨论。该研究工作得到国家自然科学基金委、科技部项目的支持。The coordinating atoms in polydentate chelates are primarily heteroatoms. We present the first examples of pentadentate chelates with all binding atoms of the chelating agent being carbon atoms, denoted as CCCCC chelates. Having up to five metal-carbon bonds in the equatorial plane has not been previously observed in transition metal chemistry. Density functional theory calculations showed that the planar metallacycle has extended Craig-Möbius aromaticity arising from 12-center–12-electron dπ-pπ π-conjugation. These planar chelates have broad absorption in the ultraviolet-visible–near-infrared region and, thus, notable photothermal performance upon irradiation by an 808-nm laser, indicating that these chelates have potential applications in photothermal therapy. The combination of facile synthesis, high stability, and broad absorption of these complexes could make the polydentate carbon chain a novel building block in coordination chemistry.the National Basic Research Program of China (nos. 2012CB821600 and 2014CB744503) , the National Science Foundation of China (nos. 21332002, 81422023, 51273165, 21490573, and 21573179)

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