No abstract

We study and classify those tame irreducible elliptic quasi-simple Lie algebras which are simply laced and of rank l 3. The first step is to identify the core of such an algebra up to central isogeny by identifying the coordinates. When the type is D or E the coordinates are Laurent polynomials in & variables, while for type A the coordinates can be any quantum torus in & variables. The next step is to study the universal central extension as well as the derivation algebra of the core. These are related to the first Connes cyclic homology group of the coordinates. The final step is to use this information to give constructions of Lie algebras which we then prove yield representatives of all isomorphism classes of the above types of algebras.

Key pointsr Force production and maintenance in smooth muscle is largely controlled by myosin regulatory light chain (RLC) phosphorylation, which relies on a balance between Ca 2+ /calmodulindependent myosin light chain kinase (MLCK) and myosin light chain phosphatase (MLCP) activities.r MYPT1 is the regulatory subunit of MLCP that biochemically inhibits MLCP activity via T694 or T852 phosphorylation in vitro.r Here we separately investigated the contribution of these two phosphorylation sites in bladder smooth muscles by establishing two single point mutation mouse lines, T694A and T852A, and found that phosphorylation of MYPT1 T694, but not T852, mediates force maintenance via inhibition of MLCP activity and enhancement of RLC phosphorylation in vivo.r Our findings reveal the role of MYPT1 T694/T852 phosphorylation in vivo in regulation of smooth muscle contraction.Abstract Force production and maintenance in smooth muscle is largely controlled by different signalling modules that fine tune myosin regulatory light chain (RLC) phosphorylation, which relies on a balance between Ca 2+ /calmodulin-dependent myosin light chain kinase (MLCK) and myosin light chain phosphatase (MLCP) activities. To investigate the regulation of MLCP activity in vivo, we analysed the role of two phosphorylation sites on MYPT1 (regulatory subunit of MLCP) that biochemically inhibit MLCP activity in vitro. MYPT1 is constitutively phosphorylated at T694 by unidentified kinases in vivo, whereas the T852 site is phosphorylated by RhoA-associated protein kinase (ROCK). We established two mouse lines with alanine substitution of T694 or T852. Isolated bladder smooth muscle from T852A mice displayed no significant changes in RLC phosphorylation or force responses, but force was inhibited with a ROCK inhibitor. In contrast, smooth muscles containing the T694A mutation showed a significant reduction of force along with reduced RLC phosphorylation. The contractile responses of T694A mutant smooth muscle were also independent of ROCK activation. Thus, phosphorylation of MYPT1 T694, but not T852, is a primary mechanism contributing to inhibition of MLCP activity and enhancement of RLC phosphorylation in vivo. The constitutive phosphorylation of MYPT1 T694 may provide a mechanism for regulating force maintenance of smooth muscle.

We find the defining structures of two-parameter quantum groups U r,s (g) corresponding to the orthogonal and the symplectic Lie algebras, which are realized as Drinfel'd doubles. We further investigate the environment conditions upon which the Lusztig's symmetries exist between (U r,s (g), , ) and its associated object (U s −1 ,r −1 (g), | ).

No abstract

BackgroundMetabolic dysfunction and neuroinflammation are increasingly implicated in Parkinson’s disease (PD). The pentose phosphate pathway (PPP, a metabolic pathway parallel to glycolysis) converts glucose-6-phosphate into pentoses and generates ribose-5-phosphate and NADPH thereby governing anabolic biosynthesis and redox homeostasis. Brains and immune cells display high activity of glucose-6-phosphate dehydrogenase (G6PD), the rate-limiting enzyme of the PPP. A postmortem study reveals dysregulation of G6PD enzyme in brains of PD patients. However, spatial and temporal changes in activity/expression of G6PD in PD remain undetermined. More importantly, it is unclear how dysfunction of G6PD and the PPP affects neuroinflammation and neurodegeneration in PD.MethodsWe examined expression/activity of G6PD and its association with microglial activation and dopaminergic neurodegeneration in multiple chronic PD models generated by an intranigral/intraperitoneal injection of LPS, daily subcutaneous injection of 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP) for 6 days, or transgenic expression of A53T α-synuclein. Primary microglia were transfected with G6PD siRNAs and treated with lipopolysaccharide (LPS) to examine effects of G6PD knockdown on microglial activation and death of co-cultured neurons. LPS alone or with G6PD inhibitor(s) was administrated to mouse substantia nigra or midbrain neuron-glia cultures. While histological and biochemical analyses were conducted to examine microglial activation and dopaminergic neurodegeneration in vitro and in vivo, rotarod behavior test was performed to evaluate locomotor impairment in mice.ResultsExpression and activity of G6PD were elevated in LPS-treated midbrain neuron-glia cultures (an in vitro PD model) and the substantia nigra of four in vivo PD models. Such elevation was positively associated with microglial activation and dopaminergic neurodegeneration. Furthermore, inhibition of G6PD by 6-aminonicotinamide and dehydroepiandrosterone and knockdown of microglial G6PD attenuated LPS-elicited chronic dopaminergic neurodegeneration. Mechanistically, microglia with elevated G6PD activity/expression produced excessive NADPH and provided abundant substrate to over-activated NADPH oxidase (NOX2) leading to production of excessive reactive oxygen species (ROS). Knockdown and inhibition of G6PD ameliorated LPS-triggered production of ROS and activation of NF-кB thereby dampening microglial activation.ConclusionsOur findings indicated that G6PD-mediated PPP dysfunction and neuroinflammation exacerbated each other mediating chronic dopaminergic neurodegeneration and locomotor impairment. Insight into metabolic-inflammatory interface suggests that G6PD and NOX2 are potential therapeutic targets for PD.

Extended affine Lie algebras are higher nullity generalizations of finite dimensional simple Lie algebras and affine Kac Moody Lie algebras. In this paper we completely describe the structure of the core modulo its centre and the root system for extended affine Lie algebras of type B l (l ≥ 3), C l (l ≥ 2), F 4 and G 2 . MathematicsSubject Classification (2000). Primary 17B65; Secondary 17B60, 17B67, 17C50.Extended affine Lie algebras (or EALAs) were introduced in 1990 by Høegh-Krohn and Torresani [HT] as generalizations of finite dimensional simple Lie algebras and affine Kac-Moody Lie algebras. Another class of examples is the class of toroidal Lie algebras (with suitable derivations added). Toroidal Lie algebras are coordinatized by Laurent polynomials in several commuting variables and they are known to possess interesting vertex operator representations [Ya], [MRY].Although the axiom system for EALAs is simple and natural, it is strong enough to allow a detailed and deep structure theory for the algebras themselves and for their root systems.The structure of an EALA is understood by coordinatizing its core. The coordinate algebras that occur include infinite dimensional quantum versions of all noncommutative and nonassociative algebras that are used classically to construct finite dimensional simple Lie algebras. These can be thought of as noncommutative 1 The first author is grateful for the support of NSERC Grant #A8465 and the hospitality of the University of Ottawa during the preparation of this paper. 2 The second author acknowledges support from a research fellowship from the Alexander von Humboldt Foundation and thanks Peter Slodowy for his hospitality.

Different interacting signaling modules involving Ca2؉ / calmodulin-dependent myosin light chain kinase, Ca 2؉ -independent regulatory light chain phosphorylation, myosin phosphatase inhibition, and actin filament-based proteins are proposed as specific cellular mechanisms involved in the regulation of smooth muscle contraction. However, the relative importance of specific modules is not well defined. By using tamoxifen-activated and smooth muscle-specific knock-out of myosin light chain kinase in mice, we analyzed its role in tonic airway smooth muscle contraction. Knock-out of the kinase in both tracheal and bronchial smooth muscle significantly reduced contraction and myosin phosphorylation responses to K ؉ -depolarization and acetylcholine. Kinase-deficient mice lacked bronchial constrictions in normal and asthmatic airways, whereas the asthmatic inflammation response was not affected. These results indicate that myosin light chain kinase acts as a central participant in the contractile signaling module of tonic smooth muscle. Importantly, contractile airway smooth muscles are necessary for physiological and asthmatic airway resistance.