Geometry over two Arbitrary Arithmetic Progressions

We consider quadrate matrices with elements of the first row members of an arithmetic progression and of the second row members of other arithmetic progression. We prove the set of these matrices is a group. Then we give a parameterization of this group and investigate about some invariants of the corresponding geometry. We find an invariant of any two points and an invariant of any sixth points. All calculations are made by Maple

Multiplication of non degenerated curves of second order

In this paper we introduce two operations in the set of non degenerated curves of second order: a) multiplication of curves and b) inversion of a curve. The main result is that this set with these two operations is a commutative and associative group. We prove also the multiplication of the curves is independent of the rotation of the coordinate system. All calculation are done using Computer System Maple. So we demonstrate the power of this system

Naturally Occurring Variants of Human Α9 Nicotinic Receptor Differentially Affect Bronchial Cell Proliferation and Transformation

Isolation of polyadenilated mRNA from human immortalized bronchial epithelial cell line BEP2D revealed the presence of multiple isoforms of RNA coded by the CHRNA9 gene for α9 nicotinic acetylcholine receptor (nAChR). BEP2D cells were homozygous for the rs10009228 polymorphism encoding for N442S amino acid substitution, and also contained mRNA coding for several truncated isoforms of α9 protein. To elucidate the biologic significance of the naturally occurring variants of α9 nAChR, we compared the biologic effects of overexpression of full-length α9 N442 and S442 proteins, and the truncated α9 variant occurring due to a loss of the exon 4 sequence that causes frame shift and early termination of the translation. These as well as control vector were overexpressed in the BEP2D cells that were used in the assays of proliferation rate, spontaneous vs. tobacco nitrosamine 4-(methylnitrosamino)-1-(3-pyridyl)-1-butanone (NNK)-induced cellular transformation, and tumorigenicity in cell culture and mice. Overexpression of the S442 variant significantly increased cellular proliferation, and spontaneous and NNK-induced transformation. The N442 variant significantly decreased cellular transformation, without affecting proliferation rate. Overexpression of the truncated α9 significantly decreased proliferation and suppressed cellular transformation. These results suggested that α9 nAChR plays important roles in regulation of bronchial cell growth by endogenous acetylcholine and exogenous nicotine, and susceptibility to NNK-induced carcinogenic transformation. The biologic activities of α9 nAChR may be regulated at the splicing level, and genetic polymorphisms in CHRNA9 affecting protein levels, amino acid sequence and RNA splicing may influence the risk for lung cancer

Inhibition of the Nicotinic Acetylcholine Receptors by Cobra Venom α-Neurotoxins: Is There a Perspective in Lung Cancer Treatment?

Nicotine exerts its oncogenic effects through the binding to nicotinic acetylcholine receptors (nAChRs) and the activation of downstream pathways that block apoptosis and promote neo-angiogenesis. The nAChRs of the α7 subtype are present on a wide variety of cancer cells and their inhibition by cobra venom neurotoxins has been proposed in several articles and reviews as a potential innovative lung cancer therapy. However, since part of the published results was recently retracted, we believe that the antitumoral activity of cobra venom neurotoxins needs to be independently re-evaluated

Nicotine Promotes Tumor Growth and Metastasis in Mouse Models of Lung Cancer

Nicotine is the major addictive component of tobacco smoke. Although nicotine is generally thought to have limited ability to initiate cancer, it can induce cell proliferation and angiogenesis in a variety of systems. These properties might enable nicotine to facilitate the growth of tumors already initiated. Here we show that nicotine significantly promotes the progression and metastasis of tumors in mouse models of lung cancer. This effect was observed when nicotine was administered through intraperitoneal injections, or through over-the-counter transdermal patches.In the present study, Line1 mouse adenocarcinoma cells were implanted subcutaneously into syngenic BALB/c mice. Nicotine administration either by intraperitoneal (i.p.) injection or transdermal patches caused a remarkable increase in the size of implanted Line1 tumors. Once the tumors were surgically removed, nicotine treated mice had a markedly higher tumor recurrence (59.7%) as compared to the vehicle treated mice (19.5%). Nicotine also increased metastasis of dorsally implanted Line1 tumors to the lungs by 9 folds. These studies on transplanted tumors were extended to a mouse model where the tumors were induced by the tobacco carcinogen, NNK. Lung tumors were initiated in A/J mice by i.p. injection of NNK; administration of 1 mg/kg nicotine three times a week led to an increase in the size and the number of tumors formed in the lungs. In addition, nicotine significantly reduced the expression of epithelial markers, E-Cadherin and beta-Catenin as well as the tight junction protein ZO-1; these tumors also showed an increased expression of the alpha(7) nAChR subunit. We believe that exposure to nicotine either by tobacco smoke or nicotine supplements might facilitate increased tumor growth and metastasis.Our earlier results indicated that nicotine could induce invasion and epithelial-mesenchymal transition (EMT) in cultured lung, breast and pancreatic cancer cells. This study demonstrates for the first time that administration of nicotine either by i.p. injection or through over-the-counter dermal patches can promote tumor growth and metastasis in immunocompetent mice. These results suggest that while nicotine has only limited capacity to initiate tumor formation, it can facilitate the progression and metastasis of tumors pre-initiated by tobacco carcinogens