A novel mechanotactic 3D modeling of cell morphology.

Cell morphology plays a critical role in many biological processes, such as cell migration, tissue development, wound healing and tumor growth. Recent investigations demonstrate that, among other stimuli, cells adapt their shapes according to their substrate stiffness. Until now, the development of this process has not been clear. Therefore, in this work, a new three-dimensional (3D) computational model for cell morphology has been developed. This model is based on a previous cell migration model presented by the same authors. The new model considers that during cell-substrate interaction, cell shape is governed by internal cell deformation, which leads to an accurate prediction of the cell shape according to the mechanical characteristic of its surrounding micro-environment. To study this phenomenon, the model has been applied to different numerical cases. The obtained results, which are qualitatively consistent with well-known related experimental works, indicate that cell morphology not only depends on substrate stiffness but also on the substrate boundary conditions. A cell located within an unconstrained soft substrate (several kPa) with uniform stiffness is unable to adhere to its substrate or to send out pseudopodia. When the substrate stiffness increases to tens of kPa (intermediate and rigid substrates), the cell can adequately adhere to its substrate. Subsequently, as the traction forces exerted by the cell increase, the cell elongates and its shape changes. Within very stiff (hard) substrates, the cell cannot penetrate into its substrate or send out pseudopodia. On the other hand, a cell is found to be more elongated within substrates with a constrained surface. However, this elongation decreases when the cell approaches it. It can be concluded that the higher the net traction force, the greater the cell elongation, the larger the cell membrane area, and the less random the cell alignment.