Influence of nucleus deformability on cell entry into cylindrical structures.

The mechanical properties of cell nuclei have been demonstrated to play a fundamental role in cell movement across extracellular networks and micro-channels. In this work, we focus on a mathematical description of a cell entering a cylindrical channel composed of extracellular matrix. An energetic approach is derived in order to obtain a necessary condition for which cells enter cylindrical structures. The nucleus of the cell is treated either (i) as an elastic membrane surrounding a liquid droplet or (ii) as an incompressible elastic material with Neo-Hookean constitutive equation. The results obtained highlight the importance of the interplay between mechanical deformability of the nucleus and the capability of the cell to establish adhesive bonds and generate active forces in the cytoskeleton due to myosin action.

Modelling the compression and reorganization of cell aggregates.

In this paper, we study the mechanical behaviour of multicellular aggregates using the notion of multiple natural configurations. In particular, we extend the elasto-visco-plastic model proposed in Preziosi et al. (2010, An elasto-visco-plastic model of cell aggregates. J. Theor. Biol., 262, 35-47) taking into account the liquid constituent present in cellular spheroids. Aggregates are treated as porous materials, composed of cells and filled with water. The cellular constituent is responsible for the elastic and the plastic behaviour of the material. The plastic component is due to the rearrangement of adhesion bonds between cells and it is translated into the existence of a yield stress in the macroscopic constitutive equation. On the other hand, the liquid constituent is responsible for the viscous-like response during deformation. The general framework is then applied to describe uniaxial homogeneous compression both when a constant load is applied and when a fixed deformation is imposed and subsequently released. We compare the results of the model with the dynamics observed during the experiments in Forgacs et al. (1998, Viscoelastic properties of living embryonic tissues: a quantitative study. Biophys. J., 74, 2227-2234).