During this project we have developed a mathematical framework that captures cell-generated stresses and nonlinear deformations in the soft substrate. To do so, we have coupled Foppl-von Karman equations for thin plate deformation with a 3D phase-field model of a contractile cell. Our model accurately and efficiently reproduces wrinkling patterns that arise from cell-generated isotropic stresses. We have calibrated the model using wrinkle-force-microscopy single cell experimental data and performed an extensive sensitivity analysis, elucidating the roles of material properties of the substrate as well as cell properties, such as shape and cotnractility, on the wrinkle pattern formation.
Furthermore, by analysing experimental traction force microscopy data, we have explored different stress modes that cells exert on substrate and identified the importance of considering quadrupolar stresses. In order to understand the role of quadrupolar activity on the collective behaviour of active nematics, we have developed a corresponding continuum model and, together with newly established collaboration with experimentalists, uncovered new physical mechanism towards control of synthetic active materials, such as microtubule kinesin protein motors. We then took another step further and incorporated time-dependent changes coupling between active cells and their evironment (extracellular matrix) into continuum model to uncover the role of stress buildup during chick embryo muscle development, which led to another successful collaboration with experimentalists.
Finally, using the developed 3D model of a cell, we have investigated the role of contractility in the interactions between multiple cells and substrate. We have extended our novel model to the system of two cells and studied the emergent wrinkling patterns in soft deformable substrate. Moreover, we elucidated the role of cell contractility and cell-cell adhesion when cells reside on solid substrate with gaps, mimicking soft collagen substrates. This allowed us to determine which mechanical properties lead to apical versus basal extrusion in the monolayers of MDCK cells.
