Figure 2. Principles of filament, motor and cross-link dynamics.

(a) Simultaneous polymerization at the plus end (incoming purple monomers) and depolymerization from the minus end (outgoing white monomers) induce a leftwards ‘treadmilling’ motion of the filament. The top and bottom images respectively correspond to times $t$ and $t+\mathrm{\Delta }t$. (b) Motors come on and off a pair of filaments with constant rates (on the left), and so do crosslinks (on the right). (c) In an assembly of identical filaments of mixed polarities where motors slide with a velocity $v_m$, a right-(left-)pointing filament moves with a velocity $v_m$ ($-v_m$) relative to any motor. Note that the coordinate $\xi$ is measured from the filament’s plus end. (d) Crosslinks that remain bound to two antiparallel filaments throughout this dynamics stretch with a velocity $2v_m$ (the top and bottom panels represent the same system with a time interval $\tau$).