Optimality of Force Transmission in a Motor-Clutch Cellular Adhesion Model

Abstract

Microenvironmental mechanics play an important, but variable, role in determining cell morphology, traction, migration, proliferation, and differentiation with potential impacts on tumor development, growth, and invasion. Interestingly, some cell types have shown increasing migration and traction force as a function of substrate stiffness, while others have shown decreasing migration and traction force. These seemingly contradictory results may be explained by a motor-clutch model of cellular adhesion and force transmission which exhibits a maximum in traction force with respect to stiffness and may be tuned to different stiffness optima. Both stochastic and deterministic castings of the motor-clutch model provide a basis to explain the tuning of cells to different microenvironmental mechanics. A sensitivity analysis of the stochastic model suggests that molecular motors and adhesion clutches must approximately balance each other to achieve stiffness sensitivity. Consequently, individual parameters changes, which favor only the motors or the clutches, have little effect in shifting the stiffness optimum because the system loses stiffness sensitivity altogether. However, dual parameters changes, such that motors and clutches remain balanced, can shift the stiffness optimum over several orders of magnitude. This optimum occurs on the stiffness at which the time for all clutches to bind equals the cycle time of adhesion load and fail. At stiffnesses above this optimum, fewer than the maximum clutches bind, so the clutches are not utilized to their fullest extent. At stiffnesses below the optimum, clutches spontaneously fail at low loads because of the long cycle time, again resulting in an inefficient use of clutches. This determinant of the optimum stiffness was applied in conjunction with the deterministic motor-clutch model to derive a dimensionless quantity defining model behavior at any particular stiffness.