Many animal cells change their shape depending on the stiffness of the substrate on which they are cultured: they assume small, rounded shapes in soft ECMs, they elongate within stiffer ECMs, and flatten out on hard substrates. Cells tend to prefer stiffer parts of the substrate, a phenomenon known as durotaxis. Such mechanosensitive responses to ECM mechanics are key to understanding the regulation of biological tissues by mechanical cues, as it occurs, e.g., during angiogenesis and the alignment of cells in muscles and tendons. Although it is well established that the mechanical cell-ECM interactions are mediated by focal adhesions, the mechanosensitive molecular complexes linking the cytoskeleton to the substrate, it is poorly understood how the stiffness-dependent kinetics of the focal adhesions eventually produce the observed interdependence of substrate stiffness and cell shape and cell behavior. Here we show that the mechanosensitive behavior of single-focal adhesions, cell contractility and substrate adhesivity together suffice to explain the observed stiffness-dependent behavior of cells. We introduce a multiscale computational model that is based upon the following assumptions: (1) cells apply forces onto the substrate through FAs; (2) the FAs grow and stabilize due to these forces; (3) within a given time-interval, the force that the FAs experience is lower on soft substrates than on stiffer substrates due to the time it takes to reach mechanical equilibrium; and (4) smaller FAs are pulled from the substrate more easily than larger FAs. Our model combines the cellular Potts model for the cells with a finite-element model for the substrate, and describes each FA using differential equations. To-1 arXiv:1906.08962v1 [q-bio.CB] 21 Jun 2019 gether these assumptions provide a unifying model for cell spreading, cell elongation and durotaxis in response to substrate mechanics.
Significance statementBesides molecular signaling, mechanical cues coordinate cell behavior during embryonic development and wound healing; for example, in tendons cells and collagen fibers align to optimally support the forces that the tendon experiences. To this end, cells actively probe their environment and respond to its mechanics. Key building blocks for such active mechanosensing are the contractile actin cytoskeleton and the extracellular matrix (ECM), the matrix of fibrous proteins that glues cells together into tissues (e.g., collagen). Actin is linked to the ECM by structures called focal adhesions, which stabilize under force. Here we present a novel mathematical model that shows that these building blocks suffice to explain the cellular responses to ECM stiffness. The insights advance our understanding of cellular mechanobiology.3