Computational models for simulating the bio-chemo-mechanical response of the cells in diverse extra-cellular settings are developed in this research. First, we consider the viability of a cytoskeletal model composed of cable-like fibrils as a statically determinate structure. We find that the discrete model of stress fibers lacks the features essential for capturing various aspect of cell behavior. We develop a finite element model based on a continuum mechanics grounded bio-chemo-mechanical model for cytoskeletal contractility and focal adhesion formation. We extend this model to two-dimensional situations and simulate the behavior of cells adhered to flat substrates as well as micro-posts. This modeling scheme is shown to capture a variety of key experimental observations including: (i) high concentrations of stress-fibers and focal adhesions at the periphery of ligand patterns; (ii) high focal adhesion concentrations along the edges of the V, T, Y and U-shaped concave ligand patterns; and (iii) highly aligned stress-fibers along the non-adhered edges of cells. We also use this model to simulate the cell response to varying substrate stiffness, substrate architecture and cell size. Both for flat gel substrates and micro-posts, cell contractility and focal adhesion concentration are shown to be higher for stiffer adhered substrate, which matches with experimental results in the literature. Lastly, we devise a new signaling model for the pathway where a Ca2+ signal originates from focal adhesions growth and activates the intracellular acto-myosin contractile machinery. A one dimensional cell attached to a rigid ligand patch and pulled at one end is utilized to demonstrate the response of a cell having the signaling, stress fiber and focal adhesion models.
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