On the constrained mock-Chebyshev least-squares

The algebraic polynomial interpolation on uniformly distributed nodes is affected by the Runge phenomenon, also when the function to be interpolated is analytic. Among all techniques that have been proposed to defeat this phenomenon, there is the mock-Chebyshev interpolation which is an interpolation made on a subset of the given nodes whose elements mimic as well as possible the Chebyshev-Lobatto points. In this work we use the simultaneous approximation theory to combine the previous technique with a polynomial regression in order to increase the accuracy of the approximation of a given analytic function. We give indications on how to select the degree of the simultaneous regression in order to obtain polynomial approximant good in the uniform norm and provide a sufficient condition to improve, in that norm, the accuracy of the mock-Chebyshev interpolation with a simultaneous regression. Numerical results are provided.Comment: 17 pages, 9 figure

Adjustment curves for binary responses associated to stochastic processes

Functional Data, Random Multiplicative Cascade, Adjustment Curve, Stochastic Process

PPAR gamma/mTOR signalling: striking the right balance in cartilage homeostasis

This is an Open Access article distributed in accordance with the terms of the Creative Commons Attribution (CC BY 4.0) license, which permits others to distribute, remix, adapt and build upon this work, for commercial use, provided the original work is properly cited. See: http://creativecommons.org/licenses/by/4.0http://dx.doi.org/10.1136/annrheumdis-2014-20574

Culture expansion in low-glucose conditions preserves chondrocyte differentiation and enhances their subsequent capacity to form cartilage tissue in three-dimensional culture.

Culture conditions that preserve a stable chondrocyte phenotype are desirable in cell-based cartilage repair to maximize efficacy and clinical outcome. This study investigates whether low-glucose conditions will preserve the chondrocyte phenotype during culture expansion. Articular chondrocytes were culture-expanded in media supplemented with either low (1 mM) or high (10 mM) glucose. The metabolic phenotype, reactive oxygen species generation, and mRNA expression of markers of differentiation or catabolism were assessed by reverse-transcription quantitative polymerase chain reaction after four population doublings (PDs) and subsequent tissue formation capacity determined using pellet cultures. Continuous monolayer culture was used to determine the population doubling limit. After expansion in monolayer for four PDs, chondrocytes expanded in low-glucose conditions exhibited higher expression of the differentiation markers SOX9 and COL2A1 and reduced expression of the catabolic metalloproteinase matrix metallopeptidase 13. When chondrocytes expanded in low glucose were cultured in micropellets, they consistently generated more cartilaginous extracellular matrix than those expanded in high glucose, as evaluated by wet weight, sulfated glycosaminoglycan content, and hydroxyproline assay for collagen content. The same pattern was observed whether high or low glucose was used during the pellet culture. During expansion, chondrocytes in high-glucose generated 50% more reactive oxygen species than low-glucose conditions, despite a lower dependence on oxidative phosphorylation for energy. Furthermore low-glucose cells exhibited >30% increased population doubling limit. These data suggests that low-glucose expansion conditions better preserve the expression of differentiation markers by chondrocytes and enhance their subsequent capacity to form cartilage in vitro. Therefore, low glucose levels should be considered for the expansion of chondrocytes intended for tissue engineering applications.This study was funded by the Medical Research Council/Engineering and Physical Sciences Research Council (EPSRC) discipline bridging initiative grant PPA026, EPSRC Platform Grant EP/E046975/1; Human Frontier Science Program Grant RGP0025/2009-C and Arthritis Research U.K. grants 19654 and 19344

A homeostatic function of CXCR2 signalling in articular cartilage

Funding This work was funded by Arthritis Research UK (grants 17859, 17971, 19654), INNOCHEM EU FP6 (grant LSHB-CT-2005-51867), MRC (MR/K013076/1) and the William Harvey Research FoundationPeer reviewedPublisher PD

Agrin mediates chondrocyte homeostasis and requires both LRP4 and alpha-dystroglycan to enhance cartilage formation in vitro and in vivo

Objectives Osteoarthritis (OA) is a leading cause of disability for which there is no cure. The identification of molecules supporting cartilage homeostasis and regeneration is therefore a major pursuit in musculoskeletal medicine. Agrin is a heparan sulfate proteoglycan which, through binding to low-density lipoprotein receptor-related protein 4 (LRP4), is required for neuromuscular synapse formation. In other tissues, it connects the cytoskeleton to the basement membrane through binding to α-dystroglycan. Prompted by an unexpected expression pattern, we investigated the role and receptor usage of agrin in cartilage. Methods Agrin expression pattern was investigated in human osteoarthritic cartilage and following destabilisation of the medial meniscus in mice. Extracellular matrix (ECM) formation and chondrocyte differentiation was studied in gain and loss of function experiments in vitro in three-dimensional cultures and gain of function in vivo, using an ectopic cartilage formation assay in nude mice. Receptor usage was investigated by disrupting LRP4 and α-dystroglycan by siRNA and blocking antibodies respectively. Results Agrin was detected in normal cartilage but was progressively lost in OA. In vitro, agrin knockdown resulted in reduced glycosaminoglycan content, downregulation of the cartilage transcription factor SOX9 and other cartilage-specific ECM molecules. Conversely, exogenous agrin supported cartilage differentiation in vitro and ectopic cartilage formation in vivo. In the context of cartilage differentiation, agrin used an unusual receptor repertoire requiring both LRP4 and α-dystroglycan. Conclusions We have discovered that agrin strongly promotes chondrocyte differentiation and cartilage formation in vivo. Our results identify agrin as a novel potent anabolic growth factor with strong therapeutic potential in cartilage regeneration

Pharmacological blockade of the WNT-beta-catenin signaling: a possible first-in-kind DMOAD.

International audienc

Polynomial approximation of derivatives by the constrained mock-Chebyshev least squares operator

The constrained mock-Chebyshev least squares operator is a linear approximation operator based on an equispaced grid of points. Like other polynomial or rational approximation methods, it was recently introduced in order to defeat the Runge phenomenon that occurs when using polynomial interpolation on large sets of equally spaced points. The idea is to improve the mock-Chebyshev subset interpolation, where the considered function $f$ is interpolated only on a proper subset of the uniform grid, formed by nodes that mimic the behavior of Chebyshev--Lobatto nodes. In the mock-Chebyshev subset interpolation all remaining nodes are discarded, while in the constrained mock-Chebyshev least squares interpolation they are used in a simultaneous regression, with the aim to further improving the accuracy of the approximation provided by the mock-Chebyshev subset interpolation. The goal of this paper is two-fold. We discuss some theoretical aspects of the constrained mock-Chebyshev least squares operator and present new results. In particular, we introduce explicit representations of the error and its derivatives. Moreover, for a sufficiently smooth function $f$ in $[-1,1]$, we present a method for approximating the successive derivatives of $f$ at a point $x\in [-1,1]$, based on the constrained mock-Chebyshev least squares operator and provide estimates for these approximations. Numerical tests demonstrate the effectiveness of the proposed method.Comment: 17 pages, 23 figure

Preconditioning of mesenchymal stromal cells with low-intensity ultrasound: influence on chondrogenesis and directed SOX9 signaling pathways

Background: Continuous low-intensity ultrasound (cLIUS) facilitates the chondrogenic differentiation of human mesenchymal stromal cells (MSCs) in the absence of exogenously added transforming growth factor-beta (TGFβ) by upregulating the expression of transcription factor SOX9, a master regulator of chondrogenesis. The present study evaluated the molecular events associated with the signaling pathways impacting SOX9 gene and protein expression under cLIUS. Methods: Human bone marrow-derived MSCs were exposed to cLIUS stimulation at 14 kPa (5 MHz, 2.5 Vpp) for 5 min. The gene and protein expression of SOX9 was evaluated. The specificity of SOX9 upregulation under cLIUS was determined by treating the MSCs with small molecule inhibitors of select signaling molecules, followed by cLIUS treatment. Signaling events regulating SOX9 expression under cLIUS were analyzed by gene expression, immunofluorescence staining, and western blotting. Results: cLIUS upregulated the gene expression of SOX9 and enhanced the nuclear localization of SOX9 protein when compared to non-cLIUS-stimulated control. cLIUS was noted to enhance the phosphorylation of the signaling molecule ERK1/2. Inhibition of MEK/ERK1/2 by PD98059 resulted in the effective abrogation of cLIUS-induced SOX9 expression, indicating that cLIUS-induced SOX9 upregulation was dependent on the phosphorylation of ERK1/2. Inhibition of integrin and TRPV4, the upstream cell-surface effectors of ERK1/2, did not inhibit the phosphorylation of ERK1/2 and therefore did not abrogate cLIUS-induced SOX9 expression, thereby suggesting the involvement of other mechanoreceptors. Consequently, the effect of cLIUS on the actin cytoskeleton, a mechanosensitive receptor regulating SOX9, was evaluated. Diffused and disrupted actin fibers observed in MSCs under cLIUS closely resembled actin disruption by treatment with cytoskeletal drug Y27632, which is known to increase the gene expression of SOX9. The upregulation of SOX9 under cLIUS was, therefore, related to cLIUS-induced actin reorganization. SOX9 upregulation induced by actin reorganization was also found to be dependent on the phosphorylation of ERK1/2. Conclusions: Collectively, preconditioning of MSCs by cLIUS resulted in the nuclear localization of SOX9, phosphorylation of ERK1/2 and disruption of actin filaments, and the expression of SOX9 was dependent on the phosphorylation of ERK1/2 under cLIUS