Koen AE Keijzer ¹ Erika Tsingos ¹ Roeland MH Merks ^1,2*

• ¹ Mathematical Institute, Faculty of Science, Leiden University, Leiden, Netherlands
• ² Institute of Biology, Faculty of Science, Leiden University, Leiden, Netherlands

Many mammalian cells, including endothelial cells and fibroblasts, tend to 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 due to the cells' pulling on the ECM, and shrink when the tension is released. Here we use mathematical modeling to study the hypothesis that mechanical reciprocity between cells and the ECM suffices for directing cell shape changes and cell orientation. 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, computational model coupling three mathematical approaches. Firstly, the cellular Potts model describes an individual, contractile cell; secondly, molecular dynamics describe the ECM that is represented as a network of cross-linked deformable fibers; thirdly, a set of 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 effects combined suffice to explain how cell morphology is determined by local ECM structure and mechanics.