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

International audienc

The enriched multinode Shepard collocation method for solving elliptic problems with singularities

In this paper, the multinode Shepard method is adopted for the first time to numerically solve a differential problem with a discontinuity in the boundary. Starting from previous studies on elliptic boundary value problems, here the Shepard method is employed to catch the singularity on the boundary. Enrichments of the functional space spanned by the multinode cardinal Shepard basis functions are proposed to overcome the difficulties encountered. The Motz's problem is considered as numerical benchmark to assess the method. Numerical results are presented to show the effectiveness of the proposed approach

Explicit polynomial expansions of regular real functions by means of even order Bernoulli polynomials and boundary values

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Numerical approximation of Fredholm integral equation by the constrained mock-Chebyshev least squares operator

In this paper, we propose two numerical approaches for approximating the solution of the following kind of integral equation f(y)−μ∫−11f(x)k(x,y)w(x)dx=g(y),y∈[−1,1],where f is the unknown solution, μ∈R∖{0}, k,g are given functions not necessarily known in the analytical form, and w is a Jacobi weight. The proposed projection methods are based on the constrained mock-Chebyshev least squares polynomials, and starting from data known at equally spaced points, provide a fine approximation of the solution. Such peculiarity can be helpful in all cases we deal with experimental data, typically measured at equispaced points. We prove the introduced methods are stable and convergent in some Sobolev subspace of C[−1,1]. Several numerical tests confirm the theoretical estimates and numerical effectiveness of the proposed method

Product integration rules by the constrained mock-Chebyshev least squares operator

In this paper we consider the problem of the approximation of definite integrals on finite intervals for integrand functions showing some kind of "pathological" behavior, e.g. "nearly" singular functions, highly oscillating functions, weakly singular functions, etc. In particular, we introduce and study a product rule based on equally spaced nodes and on the constrained mock-Chebyshev least squares operator. Like other polynomial or rational approximation methods, this operator was recently introduced in order to defeat the Runge phenomenon that occurs when using polynomial interpolation on large sets of equally spaced points. Unlike methods based on piecewise approximation functions, mainly used in the case of equally spaced nodes, our product rule offers a high efficiency, with performances slightly lower than those of global methods based on orthogonal polynomials in the same spaces of functions. We study the convergence of the product rule and provide error estimates in subspaces of continuous functions. We test the effectiveness of the formula by means of several examples, which confirm the theoretical estimates

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

Sortilin Is Upregulated in Osteoarthritis-Dependent Cartilage Calcification and Associated with Cellular Senescence.

Osteoarthritis (OA) is a chronic joint disease characterized by articular cartilage calcification, loss of articular cartilage, bone changes, pain, and disability. Cartilage calcification is one hallmark of OA and is predominantly caused by basic calcium crystals formed due to an imbalance of the pyrophosphate pathway. Sortilin is a transmembrane protein that contributes to vascular calcification in atherosclerosis by externalizing alkaline phosphatase (ALP)-containing vesicles. Calcification in atherosclerosis and osteoarthritis has been associated with cellular senescence. The aim of this study was to investigate the potential role of sortilin and senescence in osteoarthritis-dependent cartilage calcification. Osteoarthritic cartilage from human knee joints was collected after joint replacement, and samples were analyzed by immunohistochemistry and quantitative RT-PCR analysis. Human chondrocytes were treated with osteogenic medium for up to 21 days to induce calcification. Western blots for sortilin and ALP, as well as an ALP activity assay, were performed. Human chondrocytes were treated with mitomycin C to induce senescence, and sortilin expression was quantified at the protein and gene levels. Sections of knee joints from a murine model of osteoarthritis were stained for sortilin and p16 and analyzed by immunohistochemistry. Treatment of wild-type chondrocytes using an osteogenic medium similar to human chondrocytes was performed. Osteoarthritic cartilage from mouse and human knee joints showed an increased number of sortilin and p16-positive chondrocytes compared to healthy cartilage. This observation was corroborated by increased gene expression of sortilin and p16 in mild and moderate osteoarthritic cartilage samples. To investigate the mechanism of sortilin regulation, human chondrocytes were treated with osteogenic medium to induce calcification. Sortilin protein levels and expression were increased after 7 days of stimulation, whereas ALP levels and activity were upregulated after 21 days of stimulation. Similar observations were made in a murine osteoarthritis model. Mechanistically, senescent chondrocytes induced by mitomycin C showed an upregulation of sortilin and ALP gene expression compared to non-senescent chondrocytes. Our data indicate that sortilin and ALP are upregulated during cartilage calcification, which is associated with chondrocyte senescence and thus might contribute to the pathogenesis of osteoarthritis. Cellular senescence seems to induce sortilin expression

Activation of WNT and BMP signaling in adult human articular cartilage following mechanical injury

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