Monotone iterative procedure and systems of a finite number of nonlinear fractional differential equations

The aim of the paper is to present a nontrivial and natural extension of the comparison result and the monotone iterative procedure based on upper and lower solutions, which were recently established in (Wang et al. in Appl. Math. Lett. 25:1019-1024, 2012), to the case of any finite number of nonlinear fractional differential equations.The author is very grateful to the reviewers for the remarks, which improved the final version of the manuscript. This article was financially supported by University of Łódź as a part of donation for the research activities aimed at the development of young scientists, grant no. 545/1117

β2-Adrenoceptor Deficiency Results in Increased Calcified Cartilage Thickness and Subchondral Bone Remodeling in Murine Experimental Osteoarthritis

Purpose: Recent studies demonstrated a contribution of adrenoceptors (ARs) to osteoarthritis (OA) pathogenesis. Several AR subtypes are expressed in joint tissues and the β2-AR subtype seems to play a major role during OA progression. However, the importance of β2-AR has not yet been investigated in knee OA. Therefore, we examined the development of knee OA in β2-AR-deficient (Adrb2-/- ) mice after surgical OA induction. Methods: OA was induced by destabilization of the medial meniscus (DMM) in male wildtype (WT) and Adrb2-/- mice. Cartilage degeneration and synovial inflammation were evaluated by histological scoring. Subchondral bone remodeling was analyzed using micro-CT. Osteoblast (alkaline phosphatase - ALP) and osteoclast (cathepsin K - CatK) activity were analyzed by immunostainings. To evaluate β2-AR deficiency-associated effects, body weight, sympathetic tone (splenic norepinephrine (NE) via HPLC) and serum leptin levels (ELISA) were determined. Expression of the second major AR, the α2-AR, was analyzed in joint tissues by immunostaining. Results: WT and Adrb2-/- DMM mice developed comparable changes in cartilage degeneration and synovial inflammation. Adrb2-/- DMM mice displayed elevated calcified cartilage and subchondral bone plate thickness as well as increased epiphyseal BV/TV compared to WTs, while there were no significant differences in Sham animals. In the subchondral bone of Adrb2-/- mice, osteoblasts activity increased and osteoclast activity deceased. Adrb2-/- mice had significantly higher body weight and fat mass compared to WT mice. Serum leptin levels increased in Adrb2-/- DMM compared to WT DMM without any difference between the respective Shams. There was no difference in the development of meniscal ossicles and osteophytes or in the subarticular trabecular microstructure between Adrb2-/- and WT DMM as well as Adrb2-/- and WT Sham mice. Number of α2-AR-positive cells was lower in Adrb2-/- than in WT mice in all analyzed tissues and decreased in both Adrb2-/- and WT over time. Conclusion: We propose that the increased bone mass in Adrb2-/- DMM mice was not only due to β2-AR deficiency but to a synergistic effect of OA and elevated leptin concentrations. Taken together, β2-AR plays a major role in OA-related subchondral bone remodeling and is thus an attractive target for the exploration of novel therapeutic avenues