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Didier G.,CNRS Luminy Institute of Mathematics (IML) | Remy E.,CNRS Luminy Institute of Mathematics (IML) | Chaouiya C.,Instituto Gulbenkian Of Cicncia | Chaouiya C.,French Institute of Health and Medical Research
Journal of Theoretical Biology | Year: 2011

This paper deals with the generalized logical framework defined by René Thomas in the 70's to qualitatively represent the dynamics of regulatory networks. In this formalism, a regulatory network is represented as a graph, where nodes denote regulatory components (basically genes) and edges denote regulations between these components. Discrete variables are associated to regulatory components accounting for their levels of expression. In most cases, Boolean variables are enough, but some situations may require further values. Despite this fact, the majority of tools dedicated to the analysis of logical models are restricted to the Boolean case. A formal Boolean mapping of multivalued logical models is a natural way of extending the applicability of these tools.Three decades ago, a multivalued to Boolean variable mapping was proposed by P. Van Ham. Since then, all works related to multivalued logical models and using a Boolean representation rely on this particular mapping. We formally show in this paper that this mapping is actually the sole, up to cosmetic changes, that could preserve the regulatory structures of the underlying graphs as well as their dynamical behaviours. © 2010 Elsevier Ltd. Source


Rifes P.,University of Lisbon | Rifes P.,Instituto Gulbenkian Of Cicncia | Thorsteinsdottir S.,University of Lisbon | Thorsteinsdottir S.,Instituto Gulbenkian Of Cicncia
Developmental Biology | Year: 2012

The extracellular matrix (ECM) is a major player in the microenvironment governing morphogenesis. However, much is yet to be known about how matrix composition and architecture changes as it influences major morphogenetic events. Here we performed a detailed, 3D analysis of the distribution of two ECM components, fibronectin and laminin, during the development of the chick paraxial mesoderm. By resorting to whole mount double immunofluorescence and confocal microscopy, we generated a detailed 3D map of the two ECM components, revealing their supra-cellular architecture in vivo, while simultaneously retaining high resolution cellular detail. We show that fibronectin assembly occurs at the surface of the presomitic mesoderm (PSM), where a gradual increase in the complexity of the fibronectin matrix accompanies PSM maturation. In the rostral PSM, where somites form, fibronectin fibrils are thick and densely packed and some occupy the cleft which comes to separate the newly formed somite from the PSM. Our 3D approach revealed that laminin matrix assembly starts at the PSM surface as small dispersed patches, which are always localized closer to cells than the fibronectin matrix. These patches gradually grow and coalesce with neighboring patches, but do not generate a continuous laminin sheet, not even on epithelial somites and dermomyotome, suggesting that these epithelia develop in contact with a fenestrated laminin matrix. Unexpectedly, as the somite differentiates, its fibronectin and laminin matrices are maintained, thus initially containing both the epithelial dermomyotome and the mesenchymal sclerotome within the somite segment. Our analysis provides unprecedented details of the progressive in vivo assembly and 3D architecture of fibronectin and laminin matrices during paraxial mesoderm development. These data are consistent with the hypothesis that progressive ECM assembly and subsequent 3D organization are active driving and containing forces during tissue development. © 2012 Elsevier Inc. Source

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