Model for how retrograde actin flow regulates adhesion traction stresses

Cells from animals adhere to and exert mechanical forces on their surroundings. Cells must control these forces for many biological processes, and dysfunction can lead to pathologies. How the actions of molecules within a cell are coordinated to regulate the adhesive interaction with the extracellular matrix remains poorly understood. It has been observed that cytoplasmic proteins that link integrin cell-surface receptors with the actin cytoskeleton flow with varying rates from the leading edge toward the center of a cell. Here, we explore theoretically how measurable subcellular traction stresses depend on the local speed of retrograde actin flow. In the model, forces result from the stretching of molecular complexes in response to the drag from the flow; because these complexes break with extension-dependent kinetics, the flow results in a decrease in their number when sufficiently large. Competition between these two effects naturally gives rise to a clutch-like behavior and a nonmonotonic trend in the measured stresses, consistent with recent data for epithelial cells. We use this basic framework to evaluate slip and catch bond mechanisms for integrins; better fits of experimental data are obtained with a catch bond representation. Extension of the model to one comprising multiple molecular interfaces shifts the peak stress to higher speeds. Connections to other models and cell movement are discussed.