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The mechanical response of a contractile cell anchored to the substrate through focal adhesions is studied by means of an asymmetric pre-strained tensegrity structure obeying a neo-Hookean stress–strain law. The aim is to assess the influence of overall asymmetric contraction on the cell durotaxis and on the growth of the focal adhesion plaque. The asymmetric kinematics of the system is obtained in two ways, that is by assuming a gradient of the substrate stiffness and through asymmetric buckling. Equivalent springs are purposely considered to represent the stiffness of the ensemble formed by the substrate, the focal adhesion plaque and the integrin ligands. Then, contraction results from elastic strains induced by competing polymerization and actomyosin contraction. The cell mechanical response in terms of durotaxis and its coupling with focal adhesion plaque growth is finally analysed with respect to the effects of asymmetry, gaining some insights into how this asymmetry could participate to redirect cell migration, both in terms of durotaxis and mollitaxis.

We demonstrate that several key aspects of the contractile activity of a cell interacting with the substrate can be captured by means of a non linear elastic tensegrity mechanical system made of a tensile element in parallel with a buckling-prone component, and exchanging forces with the surroundings through an extracellular matrix-focal adhesion complex. Mechanosensitivity of the focal adhesion plaque is triggered by pre-strain-driven buckling of the system induced either by pre-contraction or pre-polymerization of the constituents. The impact of pre-polymerization on the mechanical force and the implications of using linear and nonlinear elasticity for the focal adhesion plaque are assessed.