Figure 3.

Traction force transmission is maximum at intermediate values of clutch stiffness. (A and B) Dimensionless time-averaged traction force ${\overline{\mathrm{T}}}^{\ast }$ as a function of the clutch stiffness parameter ${\beta }_{\mathrm{c}}$ (notice that ${\kappa }_{\mathrm{c}}\propto {\beta }_{\mathrm{c}}$) for different values of the clutch kinetic parameter $\tau$ and for two values of the substrate stiffness parameter $K^{\prime }$ ($\mathrm{K}={\mathrm{K}}^{\prime }/{\beta }_{\mathrm{c}})$: (A) ${\mathrm{K}}^{\prime }=0.01$ and (B) ${\mathrm{K}}^{\prime }=1$. Cellular traction forces on rigid substrates are very sensitive to clutch stiffness. The optimum clutch stiffness (optimum ${\beta }_{\mathrm{c}}$) increases with the value of the clutch kinetic parameter. Parameter values: $\mathrm{F}=1$, ${\omega }^{\prime }=200$ ($\omega ={\omega }^{\prime }{\beta }_{\mathrm{c}})$. (C) Time evolution of traction force for four different values of the clutch stiffness parameter. Parameter values: $\mathrm{F}=1$, ${\omega }^{\prime }=200,{\mathrm{K}}^{\prime }=0.01,\tau =1$. (D) Dimensionless time-averaged traction force as a function of the effective clutch stiffness parameter for three different values of the myosin activity parameter $\mathrm{F}$. Parameter values: ${\omega }^{\prime }=200$, ${\mathrm{K}}^{\prime }=1$, $\tau =10$. Solid lines correspond to the numerical solution of the mean-field model (Eqs. 3 and 4), and symbols correspond to the numerical solution of the stochastic motor-clutch model. To see this figure in color, go online.