Traction Forces During Cell Migration Predicted by the Multiphysics Model

Abstract

Cells rely on traction forces in order to crawl across a substrate. These traction forces come from dynamic changes in focal adhesions, cytoskeletal structures, and chemical and mechanical signals from the extracellular matrix. Several computational models have been developed that help explain the trajectory or accumulation of cells during migration, but little attention has been placed on traction forces during this process. Here, we investigated the spatial and temporal dynamics of traction forces by using a multiphysics model that describes the cycle of steps for a migrating cell on an array of posts. The migration cycle includes extension of the leading edge, formation of new adhesions at the front, contraction of the cytoskeleton, and the release of adhesions at the rear. In the model, an activation signal triggers the assembly of actin and myosin into a stress fiber, which generates a cytoskeletal tension in a manner similar to Hill’s muscle model. In addition, the role that adhesion dynamics has in regulating cytoskeletal tension has been added to the model. The multiphysics model was simulated in Matlab for 1-D simulations, and in Comsol for 2-D simulations. The model was able to predict the spatial distribution of traction forces observed with previous experiments in which large forces were seen at the leading and trailing edges. The large traction force at the trailing edge during the extension phase likely contributes to detachment of the focal adhesion by overcoming its adhesion strength with the post. Moreover, the model found that the mechanical work of a migrating cell underwent a cyclic relationship that rose with the formation of a new adhesion and fell with the release of an adhesion at its rear. We applied a third activation signal at the time of release and found it helped to maintain a more consistent level of work during migration. Therefore, the results from both our 1-D and 2-D migration simulations strongly suggest that cells use biochemical activation to supplement the loss in cytoskeletal tension upon adhesion release.