REGULAR ARTICLE A General Formalism for Tissue Morphogenesis Based on Cellular Dynamics and Control System Interactions Loı ¨c Forest Æ Jacques Demongeot Received: 19 December 2007 / Accepted: 19 December 2007 / Published online: 15 February 2008 Ó Springer Science+Business Media B.V. 2008 Abstract Morphogenesis is a key process in developmental biology. An important issue is the understanding of the generation of shape and cellular organisation in tissues. Despite of their great diversity, morphogenetic processes share common features. This work is an attempt to describe this diversity using the same formalism based on a cellular description. Tissue is seen as a multi-cellular system whose behaviour is the result of all constitutive cells dynamics. Morphogenesis is then considered as a spatiotemporal organization of cells activities. We show how this formalism relies on Reaction–Diffusion/Positional Information approach and how it permits to generalize its modelling possibilities. Three quite different applications for concrete morphogenetic processes are presented. The first one is a model for epithelial invagination, the second is a model of cellular differentiation by local cell–cell signalling. The last example is the secondary radial growth of conifer trees. From the mathematical point of view, different modelling tools are used according to the specificity of each process. L. Forest (&) Laboratoire de Mathe ´matiques, INSA de Rouen, B.P. 8, 76131 Mont-Saint-Aignan cedex, France e-mail: forest@insa-rouen.fr J. Demongeot Laboratoire Techniques de l’Inge ´nierie Me ´dicale et de la Complexite ´ – Informatique, Mathe ´matiques et Applications de Grenoble (TIMC-IMAG UMR CNRS Universite ´ Joseph Fourier 5525), Institut d’Inge ´nierie de l’Information de Sante ´, Pavillon Taillefer, Faculte ´ de Me ´decine, 38706 La Tronche cedex, France J. Demongeot Institut Universitaire de France, Paris, France 123 Acta Biotheor (2008) 56:51–74 DOI 10.1007/s10441-008-9030-4