On the role of friction and remodelling in cell–matrix interactions: A continuum mechanical model

We discuss a mathematical model addressing the mechanical interactions exchanged between living cells and the extra-cellular environment, by specialising our study to focal adhesions. Many biological functions, such as cell locomotion, proliferation or orientation, require living cells to establish stable connections with the extra-cellular matrix. In this respect, focal adhesions anchor cells to the extra-cellular matrix and regulate the transmission of signals in response to internal or external stimuli. Within the adopted mechanical setting, both the focal adhesion and the extra-cellular matrix are described as rectified elastic fibres, subjected to a system of elastic forces. Moreover, the proposed model relies upon two peculiar features. The former aspect concerns the characterisation of a friction-like interaction between the focal adhesion complex and the extra-cellular matrix. Friction does, indeed, play a role in determining stability and growth of focal adhesion. The latter phenomenon considered in the present model is remodelling. Here, remodelling is understood as the occurrence and development of irreversible, plastic-like distortions related to the internal structure of both the focal adhesion complex and the extra-cellular matrix. The obtained formulation encompasses and generalises a class of models formerly proposed in the literature to the case where friction-like interactions and remodelling of both focal adhesion and substratum are taken into account. The reported numerical results illustrate the influence of both friction and remodelling on the distribution of tractions, displacements and effective stiffness of the ensemble comprising focal adhesion, extra-cellular-matrix and interacting cells.