“Optimality of motor and clutch mechanical properties in a generalized model for cell traction forces”

The mechanical properties of the extracellular environment influence cell behavior, such as cell morphogenesis, cell migration and cell fate. During the cell migration cycle, cells extend plasma membrane protrusions via actin polymerization, actin filaments move retrogradely via myosin motors and actin polymerization, and the formation of adhesion complexes commonly called clutches mediate the production of traction forces on the extracellular microenvironment allowing the cell to move forward. In this study, we revisited the motor-clutch model for cell migration and derived its mean-field counterpart to study force production of cellular protrusions on compliant substrates. We derived an analytical expression for the optimum substrate stiffness that maximizes force transmission, without unknown adjustable parameters that is valid for all motor-clutch ratio regimes; and determined the required conditions for the protrusion to operate in the clutch-dominated “stalled” regime, the motor-clutch “balanced” regime and motor-dominated “free flowing” regime. We explored these regimes theoretically and obtained an analytical expression for the traction force produced in the limits of low and high myosin activity. We discovered the existence of an optimum clutch stiffness for maximal cellular traction force and identified a biphasic dependence of traction force produced by protrusions on rigid substrates on motor activity and unloaded myosin motor velocity, results that could be tested via novel molecular tension sensor experiments. We additionally showed that clutch reinforcement shifts the optimum substrate and clutch stiffnesses to larger values whereas the optimum substrate stiffness is found to be insensitive to changes in clutch catch bond properties. Overall, our work reveals that altering cell adhesion levels, actomyosin activity and rigidity of clutches and extracellular matrix can cause nontrivial traction force changes and modulated cell migration capabilities that provide insights to effectively design novel cell and stromal-based therapies to treat development and human diseases, such as cancer invasion and metastasis. STATEMENT OF SIGNIFICANCE Adherent cells produce mechanical forces on their environment that critically regulate cell adhesion, signaling and function, essential during developmental events and human disease. Despite recent progress, cell-generated force measurements across a wide range of extracellular stiffnesses and cell states have faced numerous technical challenges. Our mean-field study provides a new generalized analysis of regulation of force transmission by modulation of cellular components and extracellular rigidity. We identify the existence of an intermediate stiffness of cell adhesion complexes for maximum force transmission and find that effective force transmission on rigid environments reduces to a competition between cell adhesion reinforcement and load-dependent dissociation kinetics. The developed model provides important insights to aid design of novel therapeutic strategies for cancers and other diseases. ### Competing Interest Statement Dr. Provenzano is a member of the Scientific Advisory Board for Parthenon Therapeutics. The other authors declare no competing interests.