Bandwidth reduction in rectangular grids

We show that the bandwidth of a square twodimensional grid of arbitrary size can be reduced if two (but not less than two) edges are deleted. The two deleted edges may not be chosen arbitrarily, but they may be chosen to share a common endpoint or to be non-adjacent. We also show that the bandwidth of the rectangular n × m (n ≤ m) grid can be reduced by k, for all k that are sufficiently small, if m − n + 2k edges are deleted

Regulation of insulin-like growth factor-binding protein-5 by insulin-like growth factor I and interleukin-1alpha in ovine articular chondrocytes

Insulin-like growth factors (IGFs) contribute to the maintenance of the cartilage matrix by stimulating proteoglycan synthesis. In contrast, interleukin-1 (IL-1), an inflammatory cytokine, suppresses the synthesis of proteoglycans. In pathological conditions the chondrocytes’ responsiveness to IGF-I is decreased, and elevated levels of IGF-binding proteins (IGFBPs) have been implicated as a possible cause. The aim of this study was to investigate the effects of IGF-I and IL-1 on IGFBP production by ovine articular chondrocytes (OAC) and the roles of these IGFBPs in the regulation of proteoglycan synthesis. As revealed by Western ligand and immunoblotting, OACs secreted IGFBP-2 and a 24-kDa IGFBP in culture medium under basal conditions. Exposure of the cells to IGF-I for 48 h resulted in the appearance of IGFBP-5 in the medium. Des(1–3)IGF-I, an IGF-I analog with reduced affinity for IGFBPs, also increased the level of IGFBP-5, but to a lesser extent than IGF-I, whereas LR3IGF-I, which has virtually no affinity for IGFBPs, had no effect on IGFBP-5. Furthermore, IGFBP-5 underwent a time-dependent limited proteolysis when incubated with OAC-conditioned medium, degrading into 22- and 16-kDa fragments. The degradation of IGFBP-5 was significantly inhibited by IGF-I, but not by des(1–3)IGF-I or LR3IGF-I. Basic fibroblast growth factor, transforming growth factor-β, and platelet-derived growth factor had no effect on OAC IGFBPs. However, IL-1α increased the IGFBP-5 level in a dose-dependent manner, showing maximum activity at 200 U/ml. Furthermore, IL-1α, but not IGF-I, induced IGFBP-5 messenger RNA expression, as assessed by Northern blot analysis. Coincubation of IGF-I with IL-1α resulted in a substantially increased IGFBP-5 protein level, suggesting a synergism between the mechanisms of action of these two factors. Des(1–3)IGF-I and LR3IGF-I were 10 times more potent than IGF-I in stimulating proteoglycan synthesis, indicating inhibition of IGF-I activity by endogenous IGFBPs. IL-1α reduced the IGF-I bioactivity, but had no effect on the activities of the IGF-I analogs, thus implying that locally produced IGFBPs, particularly IGFBP-5, which was substantially increased when IGF-I and IL-1α were coincubated, mediated the reduction of the IGF-I activity. Our results demonstrate that IGF-I and IL-1α synergistically increase the level of IGFBP-5 in OAC by inhibiting the proteolysis and stimulating the expression of IGFBP-5, respectively. Furthermore, the attenuation of IGF-I-stimulated proteoglycan synthesis by IL-1α in OAC appears to be mediated by chondrocyte IGFBPs. We conclude that locally produced IGFBPs, in particular IGFBP-5, may play a critical role in the regulation of cartilage matrix degradation in inflammatory and degenerative arthritides.Damir Sunic, Julian D. McNeil, Timothy E. Rayner, Dennis L. Andress, and David A. Belfor

Benefits of Recombinant Adeno-Associated Virus (rAAV)-Mediated Insulinlike Growth Factor I (IGF-I) Overexpression for the Long-Term Reconstruction of Human Osteoarthritic Cartilage by Modulation of the IGF-I Axis

Administration of therapeutic genes to human osteoarthritic (OA) cartilage is a potential approach to generate effective, durable treatments against this slow, progressive disorder. Here, we tested the ability of recombinant adeno-associated virus (rAAV)-mediated overexpression of human insulinlike growth factor (hIGF)-I to reproduce an original surface in human OA cartilage in light of the pleiotropic activities of the factor. We examined the proliferative, survival and anabolic effects of the rAAV-hIGF-I treatment in primary human normal and OA chondrocytes in vitro and in explant cultures in situ compared with control (reporter) vector delivery. Efficient, prolonged IGF-I secretion via rAAV stimulated the biological activities of OA chondrocytes in all the systems evaluated over extended periods of time, especially in situ, where it allowed for the long-term reconstruction of OA cartilage (at least for 90 d). Remarkably, production of high, stable amounts of IGF-I in OA cartilage using rAAV advantageously modulated the expression of central effectors of the IGF-I axis by downregulating IGF-I inhibitors (IGF binding protein [IGFBP]-3 and IGFBP4) while up-regulating key potentiators (IGFBP5, the IGF-I receptor and downstream mitogen-activated protein kinase/extracellular signal–regulated kinase 1/2 [MAPK/ERK-1/2] and phosphatidylinisitol-3/Akt [PI3K/Akt] signal transduction pathways), probably explaining the enhanced responsiveness of OA cartilage to IGF-I treatment. These findings show the benefits of directly providing an IGF-I sequence to articular cartilage via rAAV for the future treatment of human osteoarthritis