Emergent features of cell structural dynamics: a review of models based on tensegrity and nonlinear oscillations Philippe Tracqui 1 , Emmanuel Promayon 1 , Patrick Amar 3,4 , Nicolas Huc 1 , Vic Norris 2 and Jean-Louis Martiel 1 1 Laboratoire TIMC-IMAG, CNRS, Instut A. Bonniot, F-38706 La Tronche Cedex 2 Laboratoire des Processus intégratifs cellulaires, Faculté des Sciences et Techniques, Université de Rouen, F-76821 Mont-Saint-Aignan Cedex 3 Laboratoire de Recherches en Informatique, Université Paris Sud & CNRS UMR 8623, 15 avenue George Clémenceau, F-91405 Orsay Cedex 4 La.M.I. Université d’Évry Val d’Essonne & CNRS UMR 8042, Tour Évry 2, 523 Place des terrasses de l’agora, F-91000 Évry 1. Introduction The key role of the coupling between mechanical forces and tissue growth and remodelling was suggested nearly twenty years ago (Trinkhaus, 1984), especially in the field of bone formation and remodelling. However, it is only recently that a large body of experiments highlighted the effects of physical forces such as tension, compression, gravity or shear stress at the cell level (Edwards et al., 1999; Huang and Ingber, 1999; Kaspar et al., 2000; Tabony et al., 2002). Indeed, direct application of mechanical stresses to cultured cells can induce or modify cell differentiation, growth and migration as well as gene expression (Schmidt et al., 1998; Fujisawa et al., 1999; Wang et al., 2000; Meyer et al., 2000; Chen et al., 2001). Despite this progress, we do not fully understand how individual cells perceive and orchestrate mechanical signals to respond either individually at the level of the cell itself or collectively, via cooperative processes, at the level of the tissue. The challenge that confronts cells is how to integrate the information from many kinds of signals so as to permit a single appropriate response. Among these different cell signalling mechanisms, mechanotransduction, i.e. the conversion of a mechanical signal into a biological or biochemical response, enjoys a special status (Wang et al., 1993). This is because it relies on the structure of the cell, which is a global property, as opposed to its biochemistry, which is a local property (and which can be restricted for example, to the cytoplasmic membrane or an intracellular organelle). Mechanotransduction provides the only way to understand how many, simultaneous, extracellular, mechanical inputs (adhesion to extracellular matrix (ECM) proteins, junctions with other cells, …) combined with heterogeneous mechanical properties (local softening or hardening of the cytoskeleton) are integrated with other stimuli to allow a specific physiological or pathological cellular response (Lelièvre et al., 1996; Janmey, 1998). The importance of mechanotransduction makes it crucial to develop theoretical cytomechanical models of the living cell. We explore here some of these cytomechanical models and pay special attention to models of cell tensegrity, as proposed by Don Ingber (1993; 1997), although we also examine alternative models considering either the cell are a mechanical (viscoelastic) continuum, or more simply the spatio-temporal organization of structural elements of the cell cytoskeleton (CSK) like filamentous actin. All models should help to understand how the cell architectural properties are dynamically regulated and provided a support to the transduction of intracellular signals and mechanical forces that lead to a wide range of integrated cellular responses. These modelling approaches are based on the conviction that it is essential to model how cells dynamically stabilise and self-organise their structure and shape if we are to