Carlos Tenreiro

Role of glucose as a modulator of anabolic and catabolic gene expression in normal and osteoarthritic human chondrocytes.

Cartilage matrix homeostasis involves a dynamic balance between numerous signals that modulate chondrocyte functions. This study aimed at elucidating the role of the extracellular glucose concentration in modulating anabolic and catabolic gene expression in normal and osteoarthritic (OA) human chondrocytes and its ability to modify the gene expression responses induced by pro‐anabolic stimuli, namely Transforming Growth Factor‐β (TGF). For this, we analyzed by real time RT‐PCR the expression of articular cartilage matrix‐specific and non‐specific genes, namely collagen types II and I, respectively. The expression of the matrix metalloproteinases (MMPs)‐1 and ‐13, which plays a major role in cartilage degradation in arthritic conditions, and of their tissue inhibitors (TIMP) was also measured. The results showed that exposure to high glucose (30 mM) increased the mRNA levels of both MMPs in OA chondrocytes, whereas in normal ones only MMP‐1 increased. Collagen II mRNA was similarly increased in normal and OA chondrocytes, but the increase lasted longer in the later. Exposure to high glucose for 24 h prevented TGF‐induced downregulation of MMP‐13 gene expression in normal and OA chondrocytes, while the inhibitory effect of TGF on MMP‐1 expression was only partially reduced. Other responses were not significantly modified. In conclusion, exposure of human chondrocytes to high glucose, as occurs in vivo in diabetes mellitus patients and in vitro for the production of engineered cartilage, favors the chondrocyte catabolic program. This may promote articular cartilage degradation, facilitating OA development and/or progression, as well as compromise the quality and consequent in vivo efficacy of tissue engineered cartilage. J. Cell. Biochem. 112: 2813–2824, 2011.

On the choice of the smoothing parameter for the BHEP goodness-of-fit test

The BHEP (Baringhaus-Henze-Epps-Pulley) test for assessing univariate and multivariate normality has shown itself to be a relevant test procedure, recommended in some recent comparative studies. It is well known that the finite sample behaviour of the BHEP goodness-of-fit test strongly depends on the choice of a smoothing parameter h. A theoretical and finite sample based description of the role played by the smoothing parameter in the detection of departures from the null hypothesis of normality is given. Additionally, the results of a Monte Carlo study are reported in order to propose an easy-to-use rule for choosing h. In the important multivariate case, and contrary to the usual choice of h, the BHEP test with the proposed smoothing parameter presents a comparatively good performance against a wide range of alternative distributions. In practice, if no relevant information about the tail of the alternatives is available, the use of this new bandwidth is strongly recommended. Otherwise, new choices of h which are suitable for short tailed and long tailed alternative distributions are also proposed.

Expression and function of the insulin receptor in normal and osteoarthritic human chondrocytes: modulation of anabolic gene expression, glucose transport and GLUT-1 content by insulin

OBJECTIVE Chondrocytes respond to insulin, but the presence and role of the specific high affinity insulin receptor (InsR) has never been demonstrated. This study determined whether human chondrocytes express the InsR and compared its abundance and function in normal and osteoarthritis (OA) human chondrocytes. DESIGN Cartilage sections were immunostained for detection of the InsR. Non-proliferating chondrocyte cultures from normal and OA human cartilage were treated with 1nM or 10nM insulin for various periods. InsR, insulin-like growth factor receptor (IGFR), aggrecan and collagen II mRNA levels were assessed by real time RT-PCR. InsR, glucose transporter (GLUT)-1, phospho-InsRbeta and phospho-Akt were evaluated by western blot and immunofluorescence. Glucose transport was measured as the uptake of [3H]-2-Deoxy-d-Glucose (2-DG). RESULTS Chondrocytes staining positively for the InsR were scattered throughout the articular cartilage. The mRNA and protein levels of the InsR in OA chondrocytes were approximately 33% and 45%, respectively, of those found in normal chondrocytes. Insulin induced the phosphorylation of the InsRbeta subunit. Akt phosphorylation and 2-DG uptake increased more intensely in normal than OA chondrocytes. Collagen II mRNA expression increased similarly in normal and OA chondrocytes while aggrecan expression remained unchanged. The Phosphoinositol-3 Kinase (PI3K)/Akt pathway was required for both basal and insulin-induced collagen II expression. CONCLUSIONS Human chondrocytes express functional InsR that respond to physiologic insulin concentrations. The InsR seems to be more abundant in normal than in OA chondrocytes, but these still respond to physiologic insulin concentrations, although some responses are impaired while others appear fully activated. Understanding the mechanisms that regulate the expression and function of the InsR in normal and OA chondrocytes can disclose new targets for the development of innovative therapies for OA.

An affine invariant multiple test procedure for assessing multivariate normality

A multiple test procedure for assessing multivariate normality (MVN) is proposed. The new test combines a finite set of affine invariant test statistics for MVN through an improved Bonferroni method. The usefulness of such an approach is illustrated by a multiple test including the Mardia and BHEP (Baringhaus-Henze-Epps-Pulley) tests that are among the most recommended procedures for testing MVN. A simulation study carried out for a wide range of alternative distributions, in order to analyze the finite sample power behavior of the proposed multiple test procedure, indicates that the new test demonstrates a good overall performance against other highly recommended MVN tests.

Fourier series-based direct plug-in bandwidth selectors for kernel density estimation

A class of Fourier series-based direct plug-in bandwidth selectors for kernel density estimation is considered in this paper. The proposed bandwidth estimators have a relative convergence rate n −1/2 whenever the underlying density is smooth enough and the simulation results testify that they present a very good finite sample performance against the most recommended bandwidth selection methods in the literature.

On the asymptotic normality of multistage integrated density derivatives kernel estimators

The estimation of integrated density derivatives is a crucial problem which arises in data-based methods for choosing the bandwidth of kernel and histogram estimators. In this paper, we establish the asymptotic normality of a multistage kernel estimator of such quantities, by showing that under some regularity conditions on the underlying density function and on the kernels used on the multistage estimation procedure, the multistage kernel estimator with at least one step of estimation is asymptotically equivalent in probability to the kernel estimator with associated optimal bandwidth. An application to kernel density bandwidth selection is also presented. In particular, we conclude that the common used plug-in bandwidth do not attempt the optimal rate of convergence to the optimal bandwidth.

On the asymptotic behaviour of the integrated square error of kernel density estimators with data-dependent bandwidth

In this paper, we consider the integrated square error where f is the common density function of the independent and identically distributed random vectors X1,...,Xn and is the kernel estimator with a data-dependent bandwidth. Using the approach introduced by Hall (J. Multivariate Anal. 14 (1984) 1), and under some regularity conditions, we derive the L2 consistency in probability of and we establish an asymptotic expansion in probability and a central limit theorem for Jn.

On the Finite Sample Behavior of Fixed Bandwidth Bickel–Rosenblatt Test for Univariate and Multivariate Uniformity

The Bickel–Rosenblatt (BR) goodness-of-fit test with fixed bandwidth was introduced by Fan in 1998. Although its asymptotic properties have been studied by several authors, little is known about its finite sample performance. Restricting our attention to the test of uniformity in the d-unit cube for d ≥ 1, we present in this article a description of the finite sample behavior of the BR test as a function of the bandwidth h. For d = 1 our analysis is based not only on empirical power results but also on the Bahadurs concept of efficiency. The numerical evaluation of the Bahadur local slopes of the BR test statistic for different values of h for a set of Legendre and trigonometric alternatives give us some additional insight about the role played by the smoothing parameter in the detection of departures from the null hypothesis. For d > 1 we develop a Monte-Carlo study based on a set of meta-type uniforme alternative distributions and a rule-of-thumb for the practical choice of the bandwidth is proposed. For both univariate and multivariate cases, comparisons with existing uniformity tests are presented. The BR test reveals an overall good comparative performance, being clearly superior to the considered competiting tests for bivariate data.

On the asymptotic behaviour of the ISE for automatic kernel distribution estimators

In this paper we give an asymptotic expansion in probability for the integrated square error J˜ n  = ∫{[Ftilde] n (x) − F(x)}2 dF(x) (ISE), where F is the common distribution function of the independent and identically distributed real random variables X 1, …, X n , and [Ftilde] n is the kernel estimator of F with random bandwidth. This expansion enables us to describe the asymptotic behaviour in probability of J˜ n , and to present an asymptotic comparison, in the sense of ISE, of some distribution function estimators. These results, which extend the conclusions of Shirahata and Chu (1992) to the context of automatic estimators, give us, at least from an asymptotic point of view, a theoretical justification for the natural conjecture that the choice of the bandwidth in the distribution function estimation has not the main role as in the probability density estimation context. Some numerical results, for finite sample sizes, are also presented.

Asymptotic behaviour of multistage plug-in bandwidth selections for kernel distribution function estimators

Given X 1, …, X n independent real random variables with common but unknown absolutely continuous distribution function F, we study the asymptotic behaviour of two classes of multistage plug-in bandwidth selectors for the kernel distribution function estimator F¯ n , on the basis of two asymptotic approximations of the optimal bandwidth h MISE that minimizes the mean integrated square error E∫{F¯ n (x)−F(x)}2 dx. The second asymptotic approximation we consider is, to our knowledge, new in the literature. Although a better rate of convergence for h MISE could be obtained by a multistage plug-in procedure based on this new asymptotic approximation, we prove that, from an asymptotic point of view, there is not a substantial difference between the two classes of associated kernel distribution function estimators in the sense of the integrated square error. For finite sample sizes, a simulation study indicates that the plug-in methods based on the new asymptotic approximation of the optimal bandwidth are superior to the corresponding one based on the asymptotic approximation usually considered in the literature. Some comparisons with the cross-validation procedure proposed by Bowman et al. [Bowman, A., Hall, P. and Prvan, T., 1998, Bandwidth selection for the smoothing of distribution functions. Biometrika, 85, 799–808.] are also presented.