Supplementary material from "Multiscale mechanics and remodelling of focal adhesions and the extracellular matrix"

We present a multiscale continuum framework predicting the mechanical behaviour of focal adhesions (FAs) in response to the interactions exchanged with the extra-cellular matrix (ECM) and living cells. Our study, in particular, focuses on the time-dependent remodelling of both FAs and the ECM induced by cell stimuli and incorporates the effect of microscale heterogeneities characterizing their architecture. Using a one-dimensional model of shear-lag type, we describe FAs as a layered assembly composed of three key elements: the adhesion plaque, integrin receptors and the surrounding ECM. The adhesion plaque and ECM are modelled as linearly elastic fibres undergoing axial deformation, while integrins are treated as mechanical connectors capable of transmitting both elastic and non-elastic forces. In extending previous models available in the existing literature, we emphasize that the entire analysis is grounded in biological evidence and supported by experimental studies. The resulting multiscale approach, based on asymptotic homogenization, leads to the computation of elastic effective coefficients in closed form, and they are employed to solve numerically a benchmark problem representing cell-matrix systems mediated by FAs, whose key insights are discussed.