Mechanochemical model of cell migration on substrates of varying stiffness

Cells propel themselves along a substrate by organizing structures at the leading edge called lamellipodia that contain the actin network, myosin, integrin, and other proteins. In this article, we describe a quantitative model that couples the response of stretch-sensitive proteins in the lamellipodia to the dynamics of the actin cytoskeleton, therefore allowing the cell to respond to different substrate stiffnesses. Using this model, we predict the various phases of dynamics possible, including continuous protrusion, unstable retractions leading to ruffling, and periodic protrusion-retraction cycles. We explain the necessary conditions for each type of migratory behavior to occur. In particular, we show that, for periodic protrusion-retraction cycles to occur, the stiffness of the substrate must be high, the myosin-dependent maturation rate of nascent to focal adhesions must be high, and the myosin-independent integrin activation rate must be low. In addition, we also predict the dynamics expected at a given substrate stiffness, leading to a quantitative explanation of experimental data that showed that periodic protrusion-retraction cycles disappear when cells are placed on soft substrates. We also suggest experiments with downregulating α actinin and/or talin and upregulating p130Cas and make predictions on what types of migratory dynamics will be observed.