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, align and elongate along 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 exerted by the cells' pulling on the ECM and shrink when the tension is released. In this study, we use mathematical modeling to study the hypothesis that mechanical reciprocity between cells and the ECM is sufficient for directing cell shape changes and orientation. We show that FAs are preferentially stabilized along the orientation of ECM fibers, where cells can generate higher tension than in directions perpendicular to the ECM fibers. We present a hybrid computational model coupling three mathematical approaches: first, the cellular Potts model (CPM) describes an individual contractile cell; second, molecular dynamics (MD) represent the ECM as a network of cross-linked, deformable fibers; third, a set of ordinary differential equations (ODEs) describes the dynamics of the cell's FAs, in terms of a balance between assembly and a mechanoresponsive disassembly. The resulting computational model shows that mechanical reciprocity suffices for stiffness-dependent cell spreading, local ECM remodeling, and ECM-alignment-dependent cell elongation. These combined effects are sufficient to explain how cell morphology is influenced by the local ECM structure and mechanics.