How cells align to structured collagen fibrils: A hybrid cellular Potts and molecular dynamics model with dynamic mechanosensitive focal adhesions.

Many mammalian cells, including endothelial cells and fibroblasts, tend to align and elongate with the orientation of extracellular matrix (ECM) fibers in a gel when cultured in vitro. During cell elongation, clusters of focal adhesions (FAs) form near the poles of the elongating cells. FAs are mechanosensitive clusters of adhesions that grow under mechanical tension due to the cells pulling on the ECM, and shrink when the tension is released. Using a mathematical modeling approach, we study the hypothesis that reciprocity between cells and the ECM drives cell shape changes. We show that FAs are preferentially stabilized along the orientation of ECM fibers, where the cells can generate more tension than perpendicular to the ECM fibers. We present a hybrid cellular Potts model that represents the ECM as an off-the-lattice network of cross-linked deformable fibers, whereas the cell is represented on the lattice. Multiple FAs are modeled individually by an independent rate of FA assembly and a mechanoresponsive FA disassembly. The resulting computational model predicts stiffness-dependent cell spreading and local ECM remodelling, and ECM-alignment dependent cell elongation. The effects combined suffice to explain how cell morphology is determined by local ECM structure and mechanics.