The role of cannabinoid receptors, G alpha z, and B cell receptor in lymphoma pathobiology with focus on chemotaxis

Mantle cell lymphoma (MCL) and chronic lymphocytic leukaemia (CLL) are two incurable B cell malignancies, with an overall survival of 5 to 8 years and 6 to 10 years, respectively. Therapies are available but are often very aggressive, and patients relapse due to minimal residual disease. Minimal residual disease is defined by the presence of few malignant cells that escaped from therapy, mainly due to the survival signals provided by non-malignant cells from the tissue environment, in lymph nodes and in bone marrow. Alternative and targeted therapies are under investigation to increase patient overall survival and to reduce the risks of relapses. However, some patients do not respond to these treatments, as malignant cells develop mechanisms that prevent the drug efficacy. Many factors have already been depicted to contribute to MCL pathogenesis, and in this thesis, a new potential actor in MCL pathobiology is described, the protein G alpha z (Gαz). The gene encoding for Gαz, GNAZ is overexpressed in most MCL cases compared to B lymphocytes from reactive lymph nodes. It was found that GNAZ expression correlates with lymphocytosis, and inversely correlates with the cannabinoid receptor type 1 previously described as a receptor potentially involved in the egress and/or retention of MCL cells within the tissue. Although the downregulation of GNAZ did not affect cell survival, proliferation or chemotaxis in vitro, its potential role in MCL pathobiology is of interest and needs further investigation. Moreover, we characterize a co-culture in vitro system of MCL cell lines with mesenchymal stromal cells that permitted to identify differentially expressed genes between cells from different tissue origin. The JeKo-1 MCL cell line from peripheral blood origin, utilized the BCR signalling pathway to adhere to stromal cells, while the Rec-1 MCL cell line from lymph node origin did not, which conferred resistance to BCR targeted therapies. This system could be useful for testing patient samples to determinate a potential resistance before treatment decision. Finally, the endocannabinoid system has been previously identified as dysregulated in both MCL and CLL. Here, we provide a new role of the endogenous cannabinoid 2-arachidonoylglycerol in chemotaxis of malignant B cells, regulated by both cannabinoid receptors type 1 and type 2. This endocannabinoid did not only induce chemotaxis by itself but also modulated the chemotaxis towards the chemokine CXCL12. In addition, a single administration of the natural cannabinoids, THC and CBD, in lymphoma patients promoted the redistribution of malignant cells from peripheral blood, and also affected non-malignant immune cells in blood. This potential negative effect of cannabinoids on the immune cells should be taken into consideration, knowing that around 25% o

C1C^1 Interpolatory Subdivision with Shape Constraints for Curves

International audienceWe derive two reformulations of the $C^1$ Hermite subdivision scheme introduced in [12]. One where we separate computation of values and derivatives and one based of refinement of a control polygon. We show that the latter leads to a subdivision matrix which is totally positive. Based on this we give algorithms for constructing subdivision curves that preserve positivity, monotonicity, and convexity

Hermite Subdivision Schemes and Taylor Polynomials

International audienceWe propose a general study of the convergence of a Hermite subdivision scheme $\mathcal H$ of degree $d>0$ in dimension 1. This is done by linking Hermite subdivision schemes and Taylor polynomials and by associating a so-called Taylor subdivision (vector) scheme $\cal S$. The main point of investigation is a spectral condition. If the subdivision scheme of the finite differences of $\mathcal S$ is contractive, then $\mathcal S$ is $C^0$ and $\mathcal H$ is $C^d$. We apply this result to two families of Hermite subdivision schemes, the first one is interpolatory, the second one is a kind of corner cutting, both of them use Obreshkov interpolation polynomial

Extended Hermite Subdivision Schemes

International audienceSubdivision schemes are efficient tools for building curves and surfaces. For vector subdivision schemes, it is not so straightforward to prove more than the Hölder regularity of the limit function. On the other hand, Hermite subdivision schemes produce function vectors that consist of derivatives of a certain function, so that the notion of convergence automatically includes regularity of the limit. In this paper, we establish an equivalence betweena spectral condition and operator factorizations, then we study how such schemes with smooth limit functions can be extended into ones with higher regularity. We conclude by pointing out this new approach applied to cardinal splines

From Hermite to stationary subdivision schemes in one and several variables

International audienceVector and Hermite subdivision schemes both act on vector data, but since the latter one interprets the vectors as function values and consecutive derivatives they differ by the "renormalization" of the Hermite scheme in any step. In this paper we give an algebraic factorization method in one and several variables to relate any Hermite subdivision scheme that satisfies the so-called spectral condition to a vector subdivision scheme. These factorizations are natural extensions of the "zero at π" condition known for the masks of refinable functions. Moreover, we show how this factorization can be used to investigate different forms of convergence of the Hermite scheme and why the multivariate situation is conceptionally more intricate than the univariate one. Finally, we give some examples of such factorizations

Hermite Subdivision with Shape Constraints on a Rectangular Mesh

International audienceWe study a two parameter version of the Hermite subdivision scheme introduced in [7], wish gives $C^1$ interpolants on rectangular meshes. We prove $C^1$-convergence for a range of the two parameters. By introducing a control grid we can choose the parameters in the scheme so that the interpolant inherits positivity and/or directional monotonicity from the initial data. Several examples are given showing that a desired shape can be achieved even if we use only very crude estimates for the initial slopes

Dual Hermite subdivision schemes of de Rham-type

International audienceThough a Hermite subdivision scheme is non-stationary by nature, its non-stationarity can be of two types, making useful the distinction between Inherently Stationary and Inherently Non-Stationary Hermite subdivision schemes. This paper focuses on the class of inherently stationary, dual non-interpolatory Hermite subdivision schemes that can be obtained from known Hermite interpolatory ones, by applying a generalization of the de Rham corner cutting strategy. Exploiting specific tools for the analysis of inherently stationary Hermite subdivision schemes we show that, giving up the interpolation condition, the smoothness of the associated basic limit function can be increased by one, while its support width is only enlarged by one. To accomplish the analysis of de Rham-type Hermite subdivision schemes two new theoretical results are derived and the new notion of HC-convergence is introduced. It allows the construction of Hermite-type subdivision schemes of order d + 1 with the first element of the vector valued limit function having regularity ≥ d