Optimal cell traction forces in a generalized motor-clutch model

Abstract

Cells exert forces on mechanically compliant environments to sense stiffness, migrate, and remodel tissue. Cells can sense environmental stiffness via myosin-generated pulling forces acting on F-actin, which is in turn mechanically coupled to the environment via adhesive proteins, akin to a clutch in a drivetrain. In this "motor-clutch" framework, the force transmitted depends on the complex interplay of motor, clutch, and environmental properties. Previous mean-field analysis of the motor-clutch model identified the conditions for optimal stiffness for maximal force transmission via a dimensionless number that combines motor-clutch parameters. However, in this and other previous mean-field analyses, the motor-clutch system is assumed to have balanced motors and clutches and did not consider force-dependent clutch reinforcement and catch bond behavior. Here, we generalize the motor-clutch analytical framework to include imbalanced motor-clutch regimes, with clutch reinforcement and catch bonding, and investigate optimality with respect to all parameters. We found that traction force is strongly influenced by clutch stiffness, and we discovered an optimal clutch stiffness that maximizes traction force, suggesting that cells could tune their clutch mechanical properties to perform a specific function. The results provide guidance for maximizing the accuracy of cell-generated force measurements via molecular tension sensors by designing their mechanosensitive linker peptide to be as stiff as possible. In addition, we found that, on rigid substrates, the mean-field analysis identifies optimal motor properties, suggesting that cells could regulate their myosin repertoire and activity to maximize force transmission. Finally, we found that clutch reinforcement shifts the optimum substrate stiffness to larger values, whereas the optimum substrate stiffness is insensitive to clutch catch bond properties. Overall, our work reveals novel features of the motor-clutch model that can affect the design of molecular tension sensors and provide a generalized analytical framework for predicting and controlling cell adhesion and migration in immunotherapy and cancer.