Sensing and modelling mechanical response in large deformation indentation of adherent cell using atomic force microscopy

The mechanical behaviour of adherent cells when subjected to the local indentation can be modelled via various approaches. Specifically, the tensegrity structure has been widely used in describing the organization of discrete intracellular cytoskeletal components, including microtubules (MTs) and microfilaments. The establishment of a tensegrity model for adherent cells has generally been done empirically, without a mathematically demonstrated methodology. In this study, a rotationally symmetric prism-shaped tensegrity structure is introduced, and it forms the basis of the proposed multi-level tensegrity model. The modelling approach utilizes the force density method to mathematically assure self-equilibrium. The proposed multi-level tensegrity model was developed by densely distributing the fundamental tensegrity structure in the intracellular space. In order to characterize the mechanical behaviour of the adherent cell during the atomic force microscopy (AFM) indentation with large deformation, an integrated model coupling the multi-level tensegrity model with a hyperelastic model was also established and applied. The coefficient of determination between the computational force-distance (F-D) curve and the experimental F-D curve was found to be at 0.977 in the integrated model on average. In the simulation range, along with the increase in the overall deformation, the local stiffness contributed by the cytoskeletal components decreased from 75% to 45%, while the contribution from the hyperelastic components increased correspondingly.