Dynamics of Folding in Semiflexible Filaments

The dynamics of a single semiflexible filament under the action of a compressing force is simulated. We find that the filament folds asymmetrically with a folding length which depends only on the bending stiffness $\kappa$ and the applied force $f$. It is shown that this behavior can be attributed to the exponentially falling tension profile in the filament. While the folding time ${\tau }_0$ depends on the initial configuration, the distance moved by the terminal point of the filament and the length of the fold scales as ${\tau }^{1/2}$ at $\tau \gg {\tau }_0$ and is independent of the initial configuration.