Covariant q-differential operators and unitary highest weight representations for U_q su(n,n)

We investigate a one-parameter family of quantum Harish-Chandra modules of U_q sl(2n). This family is an analog of the holomorphic discrete series of representations of the group SU(n,n) for the quantum group U_q su(n, n). We introduce a q-analog of "the wave" operator (a determinant-type differential operator) and prove certain covariance property of its powers. This result is applied to the study of some quotients of the above-mentioned quantum Harish-Chandra modules. We also prove an analog of a known result by J.Faraut and A.Koranyi on the expansion of reproducing kernels which determines the analytic continuation of the holomorphic discrete series.Comment: 26 page

On the Two q-Analogue Logarithmic Functions

There is a simple, multi-sheet Riemann surface associated with e_q(z)'s inverse function ln_q(w) for 0< q < 1. A principal sheet for ln_q(w) can be defined. However, the topology of the Riemann surface for ln_q(w) changes each time "q" increases above the collision point of a pair of the turning points of e_q(x). There is also a power series representation for ln_q(1+w). An infinite-product representation for e_q(z) is used to obtain the ordinary natural logarithm ln{e_q(z)} and the values of sum rules for the zeros "z_i" of e_q(z). For |z|<|z_1|, e_q(z)=exp{b(z)} where b(z) is a simple, explicit power series in terms of values of these sum rules. The values of the sum rules for the q-trigonometric functions, sin_q(z) and cos_q(z), are q-deformations of the usual Bernoulli numbers.Comment: This is the final version to appear in J.Phys.A: Math. & General. Some explict formulas added, and to update the reference

Discrete series representations for sl(2|1), Meixner polynomials and oscillator models

We explore a model for the one-dimensional quantum oscillator based upon the Lie superalgebra sl(2|1). For this purpose, a class of discrete series representations of sl(2|1) is constructed, each representation characterized by a real number beta>0. In this model, the position and momentum operators of the oscillator are odd elements of sl(2|1) and their expressions involve an arbitrary parameter gamma. In each representation, the spectrum of the Hamiltonian is the same as that of the canonical oscillator. The spectrum of the momentum operator can be continuous or infinite discrete, depending on the value of gamma. We determine the position wavefunctions both in the continuous and discrete case, and discuss their properties. In the discrete case, these wavefunctions are given in terms of Meixner polynomials. From the embedding osp(1|2)\subset sl(2|1), it can be seen why the case gamma=1 corresponds to the paraboson oscillator. Consequently, taking the values (beta,gamma)=(1/2,1) in the sl(2|1) model yields the canonical oscillator.Comment: (some minor misprints were corrected in this version

Cytokeratin 18 in plasma of patients with gastrointestinal adenocarcinoma as a biomarker of tumour response

BACKGROUND: Plasma biomarkers may be particularly useful as a predictor or early marker of clinical response to treatment in addition to radiological imaging. Cytokeratin 18 (CK18) is an epithelial-specific cytokeratin that undergoes cleavage by caspases during apoptosis. Measurement of caspase-cleaved (CK18-Asp396) or total cytokeratin 18 (CK18) from epithelial-derived tumours could be a simple, non-invasive way to monitor or predict responses to treatment. METHODS: Soluble plasma CK18-Asp396 and CK18 were measured by ELISA from 73 patients with advanced gastrointestinal adenocarcinomas before treatment and during chemotherapy, as well as 100 healthy volunteers. RESULTS: Both CK18-Asp396 and total CK18 plasma levels were significantly higher in patients compared with the healthy volunteers (P = 0.015, P &lt; 0.001). The total CK18 baseline plasma levels before treatment were significantly higher (P = 0.009) in patients who develop progressive disease than those who achieve partial response or stable disease and this correlation was confirmed in an independent validation set. The peak plasma levels of CK18 occurring in any cycle following treatment were also found to be associated with tumour response, but peak levels of CK18-Asp396 did not reach significance (P = 0.01, and P = 0.07, respectively). CONCLUSION: Plasma levels CK18 are a potential marker of tumour response in patients with advanced gastrointestinal malignancy

Clinical significance of stromal apoptosis in colorectal cancer

BackgroundEpithelial and stromal cells play an important role in the development of colorectal cancer (CRC). We aimed to determine the prognostic significance of both epithelial and stromal cell apoptosis in CRC.MethodsTotal apoptosis was determined by caspase-3 activity measurements in protein homogenates of CRC specimens and adjacent normal mucosa of 211 CRC patients. Epithelial apoptosis was determined by an ELISA specific for a caspase-3-degraded cytokeratin 18 product, the M30 antigen. Stromal apoptosis was determined from the ratio between total and epithelial apoptosis.ResultsEpithelial and stromal apoptosis, as well as total apoptosis, were significantly higher in CRC compared with corresponding adjacent normal mucosa. Low total tumour apoptosis (&lt; or = median caspase-3 activity) was associated with a significantly worse disease recurrence (hazard ratio (HR), 95% confidence interval (95% CI): 1.77 (1.05-3.01)), independent of clinocopathological parameters. Epithelial apoptosis was not associated with clinical outcome. In contrast, low stromal apoptosis (&lt; or = median caspase-3/M30) was found to be an independent prognostic factor for overall survival, disease-free survival and disease recurrence, with HRs (95% CI) of 1.66 (1.17-2.35), 1.62 (1.15-2.29) and 1.69 (1.01-2.85), respectively.InterpretationStromal apoptosis, in contrast to epithelial apoptosis, is an important factor with respect to survival and disease-recurrence in CRC

Agarose Spot as a Comparative Method for in situ Analysis of Simultaneous Chemotactic Responses to Multiple Chemokines

yesWe describe a novel protocol to quantitatively and simultaneously compare the chemotactic responses of cells towards different chemokines. In this protocol, droplets of agarose gel containing different chemokines are applied onto the surface of a Petri dish, and then immersed under culture medium in which cells are suspended. As chemokine molecules diffuse away from the spot, a transient chemoattractant gradient is established across the spots. Cells expressing the corresponding cognate chemokine receptors migrate against this gradient by crawling under the agarose spots towards their centre. We show that this migration is chemokine-specific; meaning that only cells that express the cognate chemokine cell surface receptor, migrate under the spot containing its corresponding chemokine ligand. Furthermore, we show that migration under the agarose spot can be modulated by selective small molecule antagonists present in the cell culture medium

5-aminosalicylic acid inhibits stem cell function in human adenoma derived cells: Implications for chemoprophylaxis in colorectal tumorigenesis

Background: Most colorectal cancers (CRC) arise sporadically from precursor lesions: colonic polyps. Polyp resection prevents progression to CRC. Risk of future polyps is proportional to the number and size of polyps detected at screening, allowing identification of high-risk individuals who may benefit from effective chemoprophylaxis. We aimed to investigate the potential of 5-aminosalicylic acid (5-ASA), a medication used in the treatment of ulcerative colitis, as a possible preventative agent for sporadic CRC. Methods: Human colorectal adenoma (PC/AA/C1, S/AN/C1 and S/RG/C2), transformed adenoma PC/AA/C1/SB10 and carcinoma cell lines (LS174T and SW620) were treated with 5-ASA. The effect on growth in two- and three-dimensional (3D) culture, β-catenin transcriptional activity and on cancer stemness properties of the cells were investigated. Results: 5-ASA was shown, in vitro, to inhibit the growth of adenoma cells and suppress β-catenin transcriptional activity. Downregulation of β-catenin was found to repress expression of stem cell marker LGR5 (leucine-rich G protein-coupled receptor-5) and functionally suppress stemness in human adenoma and carcinoma cells using 3D models of tumorigenesis. Conclusions: 5-ASA can suppress the cancer stem phenotype in adenoma-derived cells. Affordable and well-tolerated, 5-ASA is an outstanding candidate as a chemoprophylactic medication to reduce the risk of colorectal polyps and CRC in those at high risk