Résumé
One of the main difficulties in developing a mechanical model of living cells is to obtain realistic simulations when considering the shape-force relationship. A first numerical model has been developed with rigid grains and at-distance interactions for both cytoplasm and membrane. The network of cross-linking proteins is represented by a set of grains connected by interactions that mimic the cytoskeleton filaments. It allows proposing a form-finding method based on a calculated network of actin filaments and geometrically guided microtubules. The obtained numerical networks of tensile and compressive forces appear in good accordance with experimental observations of spatial distribution of f-actin and microtubules. As a next step, we present simulations representing mechanical tests such as those experimentally performed with "classical" techniques (e.g. magnetic twisting cytometry). The results are then compared to experimental data, particularly for the apparent elasticity modulus. Even if it shows that such an approach is promising, this model appears too static and cristallin: the cytoskeleton filament connectivity and spatial adaptation is still too restrained. Hence, we propose some features about the development of a more refined model able to take into account a non-cristallin structuration of the cytoskeleton, as well as to differentiate the respective role of the cell membrane with the actin cortex, the cytoskeleton filaments and the gel-like cytoplasm. The growth of filaments in this model is driven by mechanical parameters, mainly the tensile and compressive forces in the cytoplasm. The substrate characteristics can also vary (adhesive zones), leading to different scenarios for the cell adhesion.