Schreier rewriting beyond the classical setting

Using actions of free monoids and free associative algebras, we establish some Schreier-type formulas involving the ranks of actions and the ranks of subactions in free actions or Grassmann-type relations for the ranks of intersections of subactions of free actions. The coset action of the free group is used to establish the generalization of the Schreier formula to the case of subgroups of infinite index. We also study and apply large modules over free associative algebras in the spirit of the paper Olshanskii, A. Yu.; Osin, D.V., Large groups and their periodic quotients, Proc. Amer. Math. Soc., 136 (2008), 753 - 759.Comment: 17 page

Thymosin Beta 4 Prevents Oxidative Stress by Targeting Antioxidant and Anti-Apoptotic Genes in Cardiac Fibroblasts

Thymosin beta-4 (Tβ4) is a ubiquitous protein with diverse functions relating to cell proliferation and differentiation that promotes wound healing and modulates inflammatory responses. The effecter molecules targeted by Tβ4 for cardiac protection remains unknown. The purpose of this study is to determine the molecules targeted by Tβ4 that mediate cardio-protection under oxidative stress.Rat neonatal fibroblasts cells were exposed to hydrogen peroxide (H(2)O(2)) in presence and absence of Tβ4 and expression of antioxidant, apoptotic and pro-fibrotic genes was evaluated by quantitative real-time PCR and western blotting. Reactive oxygen species (ROS) levels were estimated by DCF-DA using fluorescent microscopy and fluorimetry. Selected antioxidant and antiapoptotic genes were silenced by siRNA transfections in cardiac fibroblasts and the effect of Tβ4 on H(2)O(2)-induced profibrotic events was evaluated.Pre-treatment with Tβ4 resulted in reduction of the intracellular ROS levels induced by H(2)O(2) in the cardiac fibroblasts. This was associated with an increased expression of antioxidant enzymes Cu/Zn superoxide dismutase (SOD) and catalase and reduction of Bax/Bcl(2) ratio. Tβ4 treatment reduced the expression of pro-fibrotic genes [connective tissue growth factor (CTGF), collagen type-1 (Col-I) and collagen type-3 (Col-III)] in the cardiac fibroblasts. Silencing of Cu/Zn-SOD and catalase gene triggered apoptotic cell death in the cardiac fibroblasts, which was prevented by treatment with Tβ4.This is the first report that exhibits the targeted molecules modulated by Tβ4 under oxidative stress utilizing the cardiac fibroblasts. Tβ4 treatment prevented the profibrotic gene expression in the in vitro settings. Our findings indicate that Tβ4 selectively targets and upregulates catalase, Cu/Zn-SOD and Bcl(2), thereby, preventing H(2)O(2)-induced profibrotic changes in the myocardium. Further studies are warranted to elucidate the signaling pathways involved in the cardio-protection afforded by Tβ4