Fig. 4.

MSD of the end-to-end distance of a filament, $\delta R^2\left(t\right)=\langle {\left[R\left(t\right)-R\left(0\right)\right]}^2\rangle$ (rescaled by $1/L^2$) vs. time t (rescaled by $v/L$). (A) Experiments were performed for filaments with the length range 3–8 μm. To achieve sufficient statistical power, we averaged over a large number of filaments and, in addition, performed a moving time average (Materials and Methods). The typical relaxation time is 0.5 s, which implies for a filament speed of 6 μm/s that the filament must move approximately half its length before bending modes are relaxed. (B) Results obtained from the computational model for different values of $L/{\ell }_p$ as indicated in the graph. Experiment and computer simulations both show that relaxation of bending modes for active filaments is independent of filament length L, and that $\delta R^2\left(t\right)\propto t^{\alpha }$ with an exponent $\alpha =1$, which significantly deviates from Brownian scaling with $\alpha =3/4$. There are differences in the absolute scale, which we attributed to the simplification of the motor dynamics and the motor-filament interaction. Parameters: $c=1.5\cdot {10}^3{\mu \text{m}}^{-2}$ corresponding to a linear motor density of $60/{\ell }_p$.