Weighted Shift Matrices: Unitary Equivalence, Reducibility and Numerical Ranges

An $n$-by-$n$ ($n\ge 3$) weighted shift matrix $A$ is one of the form [{array}{cccc}0 & a_1 & & & 0 & \ddots & & & \ddots & a_{n-1} a_n & & & 0{array}], where the $a_j$'s, called the weights of $A$, are complex numbers. Assume that all $a_j$'s are nonzero and $B$ is an $n$-by-$n$ weighted shift matrix with weights $b_1,..., b_n$. We show that $B$ is unitarily equivalent to $A$ if and only if $b_1... b_n=a_1...a_n$ and, for some fixed $k$, $1\le k \le n$, $|b_j| = |a_{k+j}|$ ($a_{n+j}\equiv a_j$) for all $j$. Next, we show that $A$ is reducible if and only if $A$ has periodic weights, that is, for some fixed $k$, $1\le k \le \lfloor n/2\rfloor$, $n$ is divisible by $k$, and $|a_j|=|a_{k+j}|$ for all $1\le j\le n-k$. Finally, we prove that $A$ and $B$ have the same numerical range if and only if $a_1...a_n=b_1...b_n$ and $S_r(|a_1|^2,..., |a_n|^2)=S_r(|b_1|^2,..., |b_n|^2)$ for all $1\le r\le \lfloor n/2\rfloor$, where $S_r$'s are the circularly symmetric functions.Comment: 27 page

Autophagy and Coagulation in Liver Cancer and Disorders

The physiological role of autophagy in metabolism of the body involves both protein synthesis and degradation. The autophagy-lysosome and the ubiquitin-proteasome systems are the two major intracellular proteolytic mechanisms. Autophagy in hepatocytes is known to be quite active and contribute to its normal functions and the pathogenesis of liver diseases. The role of autophagy in liver diseases has been widely studied, and growing evidence has now shown that autophagy is involved in the pathogenesis of cirrhosis and hepatocellular carcinoma (HCC). However, the role of autophagy in the progression of liver fibrosis and prognosis of human HCC is not well known. Recent studies have demonstrated that tissue factor (TF) combined with coagulation factor VII (FVII) has a pathological role by activating a protease-activated receptor 2 (PAR2) for tumor growth. Autophagy-related LC3A/B-II formation induced by the inhibition of TF/FVII/PAR2 coagulation axis, particularly by FVII knockdown, was selectively mediated by the Atg7 induction. These results are consistent with clinical observations that indicate the important role of FVII activation in regulating autophagy in HCC. In this chapter, we discuss our findings in which FVII promotes growth and progression in HCC through ERK-TSC/mTOR signaling to repress autophagy and may play a pivotal role in conferring cirrhosis and other liver diseases

The nucleolar protein NIFK promotes cancer progression via CK1α/β-catenin in metastasis and Ki-67-dependent cell proliferation.

Nucleolar protein interacting with the FHA domain of pKi-67 (NIFK) is a Ki-67-interacting protein. However, its precise function in cancer remains largely uninvestigated. Here we show the clinical significance and metastatic mechanism of NIFK in lung cancer. NIFK expression is clinically associated with poor prognosis and metastasis. Furthermore, NIFK enhances Ki-67-dependent proliferation, and promotes migration, invasion in vitro and metastasis in vivo via downregulation of casein kinase 1α (CK1α), a suppressor of pro-metastatic TCF4/β-catenin signaling. Inversely, CK1α is upregulated upon NIFK knockdown. The silencing of CK1α expression in NIFK-silenced cells restores TCF4/β-catenin transcriptional activity, cell migration, and metastasis. Furthermore, RUNX1 is identified as a transcription factor of CSNK1A1 (CK1α) that is negatively regulated by NIFK. Our results demonstrate the prognostic value of NIFK, and suggest that NIFK is required for lung cancer progression via the RUNX1-dependent CK1α repression, which activates TCF4/β-catenin signaling in metastasis and the Ki-67-dependent regulation in cell proliferation

Increasing CD44+/CD24- tumor stem cells, and upregulation of COX-2 and HDAC6, as major functions of HER2 in breast tumorigenesis

<p>Abstract</p> <p>Background</p> <p>Cancer cells are believed to arise primarily from stem cells. CD44⁺/CD24^-have been identified as markers for human breast cancer stem cells. Although, HER2 is a well known breast cancer oncogene, the mechanisms of action of this gene are not completely understood. Previously, we have derived immortal (M13SV1), weakly tumorigenic (M13SV1R2) and highly tumorigenic (M13SV1R2N1) cell lines from a breast epithelial cell type with stem cell phenotypes after successive SV40 large T-antigen transfection, X-ray irradiation and ectopic expression of HER2/C-erbB2/neu. Recently, we found that M13SV1R2 cells became non-tumorigenic after growing in a growth factor/hormone-deprived medium (R2d cells).</p> <p>Results</p> <p>In this study, we developed M13SV1R2N1 under the same growth factor/hormone-deprived condition (R2N1d cells). This provides an opportunity to analyze HER2 effect on gene expression associated with tumorigenesis by comparative study of R2d and R2N1d cells with homogeneous genetic background except HER2 expression. The results reveal distinct characters of R2N1d cells that can be ascribed to HER2: 1) development of fast-growing tumors; 2) high frequency of CD44⁺/CD24^-cells (~50% for R2N1d vs. ~10% for R2d); 3) enhanced expression of COX-2, HDAC6 mediated, respectively, by MAPK and PI3K/Akt pathways, and many genes associated with inflammation, metastasis, and angiogenesis. Furthermore, HER2 expression can be down regulated in non-adhering R2N1d cells. These cells showed longer latent period and lower rate of tumor development compared with adhering cells.</p> <p>Conclusions</p> <p>HER2 may induce breast cancer by increasing the frequency of tumor stem cells and upregulating the expression of COX-2 and HDAC6 that play pivotal roles in tumor progression.</p

Highly sensitive analysis of the anti-tumor agent 1-[4-(furo[2,3-b]-quinolin-4-ylamino)phenyl]ethanone in rat plasma by high-performance liquid chromatography using electrochemical detection

Abstract A sensitive high-performance liquid chromatography method with electrochemical detection was developed for the purpose of determining the concentration of the new anti-tumor agent 1-[4-(furo[2,3-b]-quinolin-4-ylamino)phenyl]ethanone (FQPE) in rats. The plasma samples were spiked with the internal standard diclofenac and extracted using dichloromethane. A C 18 250 mm × 4 mm column was used for the separation of analyte with a mobile phase consisting of 50% acetonitrile and 50% pH 3.0 of sodium 1-pentansulfonate solution at a flow rate of 1.0 mL/min. FQPE was detected by electrochemical detector at 1.0 V and 20 nA. Intra-day and inter-day precision and accuracy were acceptable down to the limit of quantization of 1 ng/mL. The lower limit of detection (LOD) was 0.5 ng/mL. The pharmacokinetic parameters of FQPE in rats after intravenous administration of 2.1 and 4.2 mg/kg were determined. The apparent volume of distribution, half-life of elimination, and clearance showed no significant difference between the two dosages. The area under the plasma concentration time curve increased proportionally with dose. The half-life of FQPE was prolonged about 2.4-fold, compared with amsacrine

Direct Radiofrequency Application Improves Pain and Gait in Collagenase-Induced Acute Achilles Tendon Injury

Radiofrequency (RF) is often used as a supplementary and alternative method to alleviate pain for chronic tendinopathy. Whether or how it would work for acute tendon injury is not addressed in the literatures. Through detailed pain and gait monitoring, we hypothesized that collagenase-induce acute tendinopathy model may be able to answer these questions. Gait parameters, including time, distance, and range of motion, were recorded and analyzed using a walking track equipped with a video-based system. Expression of substance P (SP), calcitonin gene related peptide (CGRP), and galanin were used as pain markers. Beta-III tubulin and Masson trichrome staining were used as to evaluate nerve sprouting, matrix tension, and degeneration in the tendon. Of fourteen analyzed parameters, RF significantly improved stance phase, step length, preswing, and intermediary toe-spread of gait. Improved gait related to the expression of substance P, CGRP, and reduced nerve fiber sprouting and matrix tension, but not galanin. The study indicates that direct RF application may be a valuable approach to improve gait and pain in acute tendon injury. Altered gait parameters may be used as references to evaluate therapeutic outcomes of RF or other treatment plan for tendinopathy