Model-based Traction Force Microscopy Reveals Differential Tension in Cellular Actin Bundles

Adherent cells use forces at the cell-substrate interface to sense and respond to the physical properties of their environment. These cell forces can be measured with traction force microscopy which inverts the equations of elasticity theory to calculate them from the deformations of soft polymer substrates. We introduce a new type of traction force microscopy that in contrast to traditional methods uses additional image data for cytoskeleton and adhesion structures and a biophysical model to improve the robustness of the inverse procedure and abolishes the need for regularization. We use this method to demonstrate that ventral stress fibers of U2OS-cells are typically under higher mechanical tension than dorsal stress fibers or transverse arcs.Author Summary: Adherent cells respond very sensitively not only to biochemical, but also to physical properties of their environment. For example, it has been shown that stem cell differentiation can be guided by substrate rigidity, which is sensed by cells by actively pulling on their environment with actomyosin-generated forces. A commonly used method to measure cell forces during essential biological processes is traction force microscopy, which uses the deformations of a soft elastic substrate to calculate cell forces. However, the standard setup for traction force microscopy suffers from mathematical limitations in calculating forces from displacements. In order to improve this method, we combine image data and biophysical modelling to arrive at a procedure which is more robust and in addition allows us to make statements about the force distribution not only at the cell-substrate interface, but also inside the cell. Here we demonstrate this approach for the contractility of actin stress fibers, which we investigate experimentally with U2OS-cells and theoretically with an active cable network model.