Counting and effective rigidity in algebra and geometry

The purpose of this article is to produce effective versions of some rigidity results in algebra and geometry. On the geometric side, we focus on the spectrum of primitive geodesic lengths (resp., complex lengths) for arithmetic hyperbolic 2-manifolds (resp., 3-manifolds). By work of Reid, this spectrum determines the commensurability class of the 2-manifold (resp., 3-manifold). We establish effective versions of these rigidity results by ensuring that, for two incommensurable arithmetic manifolds of bounded volume, the length sets (resp., the complex length sets) must disagree for a length that can be explicitly bounded as a function of volume. We also prove an effective version of a similar rigidity result established by the second author with Reid on a surface analog of the length spectrum for hyperbolic 3-manifolds. These effective results have corresponding algebraic analogs involving maximal subfields and quaternion subalgebras of quaternion algebras. To prove these effective rigidity results, we establish results on the asymptotic behavior of certain algebraic and geometric counting functions which are of independent interest.Comment: v.2, 39 pages. To appear in Invent. Mat

iNOS Ablation Does Not Improve Specific Force of the Extensor Digitorum Longus Muscle in Dystrophin-Deficient mdx4cv Mice

Nitrosative stress compromises force generation in Duchenne muscular dystrophy (DMD). Both inducible nitric oxide synthase (iNOS) and delocalized neuronal NOS (nNOS) have been implicated. We recently demonstrated that genetic elimination of nNOS significantly enhanced specific muscle forces of the extensor digitorum longus (EDL) muscle of dystrophin-null mdx4cv mice (Li D et al J. Path. 223:88–98, 2011). To determine the contribution of iNOS, we generated iNOS deficient mdx4cv mice. Genetic elimination of iNOS did not alter muscle histopathology. Further, the EDL muscle of iNOS/dystrophin DKO mice yielded specific twitch and tetanic forces similar to those of mdx4cv mice. Additional studies suggest iNOS ablation did not augment nNOS expression neither did it result in appreciable change of nitrosative stress markers in muscle. Our results suggest that iNOS may play a minor role in mediating nitrosative stress-associated force reduction in DMD

HIV-1 gp120 Induces Expression of IL-6 through a Nuclear Factor-Kappa B-Dependent Mechanism: Suppression by gp120 Specific Small Interfering RNA

In addition to its role in virus entry, HIV-1 gp120 has also been implicated in HIV-associated neurocognitive disorders. However, the mechanism(s) responsible for gp120-mediated neuroinflammation remain undefined. In view of increased levels of IL-6 in HIV-positive individuals with neurological manifestations, we sought to address whether gp120 is involved in IL-6 over-expression in astrocytes. Transfection of a human astrocyte cell line with a plasmid encoding gp120 resulted in increased expression of IL-6 at the levels of mRNA and protein by 51.3±2.1 and 11.6±2.2 fold respectively; this effect of gp120 on IL-6 expression was also demonstrated using primary human fetal astrocytes. A similar effect on IL-6 expression was observed when primary astrocytes were treated with gp120 protein derived from different strains of X4 and R5 tropic HIV-1. The induction of IL-6 could be abrogated by use of gp120-specific siRNA. Furthermore, this study showed that the NF-κB pathway is involved in gp120-mediated IL-6 over-expression, as IKK-2 and IKKβ inhibitors inhibited IL-6 expression by 56.5% and 60.8%, respectively. These results were also confirmed through the use of NF-κB specific siRNA. We also showed that gp120 could increase the phosphorylation of IκBα. Furthermore, gp120 transfection in the SVGA cells increased translocation of NF-κB from cytoplasm to nucleus. These results demonstrate that HIV-1 gp120-mediated over-expression of IL-6 in astrocytes is one mechanism responsible for neuroinflammation in HIV-infected individuals and this is mediated by the NF-κB pathway

Quantitative evaluation of the beneficial effects in the mdx mouse of epigallocatechin gallate, an antioxidant polyphenol from green tea

In two separate previous studies, we reported that subcutaneous (sc) or oral administration of (−)-epigallocatechin-3-gallate (EGCG) limited the development of muscle degeneration of mdx mice, a mild phenotype model for Duchenne muscular dystrophy (DMD). However, it was not possible to conclude which was the more efficient route of EGCG administration because different strains of mdx mice, periods of treatment and methods of assessment were used. In this study, we investigated which administration routes and dosages of EGCG are the most effective for limiting the onset of dystrophic lesions in the same strain of mdx mice and applying the same methods of assessment. Three-week-old mdx mice were injected sc for 5 weeks with either saline or a daily average of 3 or 6 mg/kg EGCG. For comparison, age-matched mdx mice were fed for 5 weeks with either a diet containing 0.1% EGCG or a control diet. The effects of EGCG were assessed quantitatively by determining the activities of serum muscle-derived creatine kinase, isometric contractions of triceps surae muscles, integrated spontaneous locomotor activities, and oxidative stress and fibrosis in selected muscles. Oral administration of 180 mg/kg/day EGCG in the diet was found the most effective for significantly improving several parameters associated with muscular dystrophy. However, the improvements were slightly less than those observed previously for sc injection started immediately after birth. The efficacy of EGCG for limiting the development of dystrophic muscle lesions in mice suggests that EGCG may be of benefit for DMD patients