Duality for the Jordanian Matrix Quantum Group GLg,h(2)GL_{g,h}(2)

We find the Hopf algebra $U_{g,h}$ dual to the Jordanian matrix quantum group $GL_{g,h}(2)$. As an algebra it depends only on the sum of the two parameters and is split in two subalgebras: $U'_{g,h}$ (with three generators) and $U(Z)$ (with one generator). The subalgebra $U(Z)$ is a central Hopf subalgebra of $U_{g,h}$. The subalgebra $U'_{g,h}$ is not a Hopf subalgebra and its coalgebra structure depends on both parameters. We discuss also two one-parameter special cases: $g =h$ and $g=-h$. The subalgebra $U'_{h,h}$ is a Hopf algebra and coincides with the algebra introduced by Ohn as the dual of $SL_h(2)$. The subalgebra $U'_{-h,h}$ is isomorphic to $U(sl(2))$ as an algebra but has a nontrivial coalgebra structure and again is not a Hopf subalgebra of $U_{-h,h}$.Comment: plain TeX with harvmac, 16 pages, added Appendix implementing the ACC nonlinear ma

Overexpression of Chitinase 3-Like 1/YKL-40 in Lung-Specific IL-18-Transgenic Mice, Smokers and COPD

We analyzed the lung mRNA expression profiles of a murine model of COPD developed using a lung-specific IL-18-transgenic mouse. In this transgenic mouse, the expression of 608 genes was found to vary more than 2-fold in comparison with control WT mice, and was clustered into 4 groups. The expression of 140 genes was constitutively increased at all ages, 215 genes increased gradually with aging, 171 genes decreased gradually with aging, and 82 genes decreased temporarily at 9 weeks of age. Interestingly, the levels of mRNA for the chitinase-related genes chitinase 3-like 1 (Chi3l1), Chi3l3, and acidic mammalian chitinase (AMCase) were significantly higher in the lungs of transgenic mice than in control mice. The level of Chi3l1 protein increased significantly with aging in the lungs and sera of IL-18 transgenic, but not WT mice. Previous studies have suggested Chi3l3 and AMCase are IL-13-driven chitinase-like proteins. However, IL-13 gene deletion did not reduce the level of Chi3l1 protein in the lungs of IL-18 transgenic mice. Based on our murine model gene expression data, we analyzed the protein level of YKL-40, the human homolog of Chi3l1, in sera of smokers and COPD patients. Sixteen COPD patients had undergone high resolution computed tomography (HRCT) examination. Emphysema was assessed by using a density mask with a cutoff of −950 Hounsfield units to calculate the low-attenuation area percentage (LAA%). We observed significantly higher serum levels in samples from 28 smokers and 45 COPD patients compared to 30 non-smokers. In COPD patients, there was a significant negative correlation between serum level of YKL-40 and %FEV1. Moreover, there was a significant positive correlation between the serum levels of YKL-40 and LAA% in COPD patients. Thus our results suggest that chitinase-related genes may play an important role in establishing pulmonary inflammation and emphysematous changes in smokers and COPD patients

An Order of Magnitude Faster AIP1-Associated Actin Disruption than Nucleation by the Arp2/3 Complex in Lamellipodia

The mechanism of lamellipod actin turnover is still under debate. To clarify the intracellular behavior of the recently-identified actin disruption mechanism, we examined kinetics of AIP1 using fluorescent single-molecule speckle microscopy. AIP1 is thought to cap cofilin-generated actin barbed ends. Here we demonstrate a reduction in actin-associated AIP1 in lamellipodia of cells overexpressing LIM-kinase. Moreover, actin-associated AIP1 was rapidly abolished by jasplakinolide, which concurrently blocked the F-actin-cofilin interaction. Jasplakinolide also slowed dissociation of AIP1, which is analogous to the effect of this drug on capping protein. These findings provide in vivo evidence of the association of AIP1 with barbed ends generated by cofilin-catalyzed filament disruption. Single-molecule observation found distribution of F-actin-associated AIP1 throughout lamellipodia, and revealed even faster dissociation of AIP1 than capping protein. The estimated overall AIP1-associated actin disruption rate, 1.8 µM/s, was one order of magnitude faster than Arp2/3 complex-catalyzed actin nucleation in lamellipodia. This rate does not suffice the filament severing rate predicted in our previous high frequency filament severing-annealing hypothesis. Our data together with recent biochemical studies imply barbed end-preferred frequent filament disruption. Frequent generation of AIP1-associated barbed ends and subsequent release of AIP1 may be the mechanism that facilitates previously observed ubiquitous actin polymerization throughout lamellipodia