Figure 1

Illustration of tube extraction. Molecular motors are attached to the membrane and can bind and unbind from the microtubule. Two frames of reference are used in the text: the “tip frame” is comoving with the tip, with site labels increasing toward the vesicle; the “lab frame” where the vesicle is stationary and the site labels increase towards the tip.Reuse & Permissions

Figure 2

Possible phase diagrams depending on the value of the ratio $d/a$ of detachment to attachment rate. The axes represent the densities (${\tau }_t$, ${\tau }_v$) of bound motors in the tip and vesicle plateaux. (a) $1/4\le d/a$. The system presents either shock or inverse-shock profiles. (b) $1/8<d/a<1/4$. The tip phase appears inside the shock region. (c) $d/a\le 1/8$. The boundary of the tip phase moves into the inverse-shock region. In cases (b) and (c), reentrant transitions are possible, e.g., along the vertical blue (or gray) line.Reuse & Permissions

Figure 3

Coupled lattice model for the bulk dynamics. The sites are labeled in the lab frame. The bottom and top lattices represent bound and unbound motors, respectively. Possible transitions of motors in the bulk are illustrated by arrows in the left panel. The right panel shows how extension and retraction of the tube drag the unbound motors in the bulk.Reuse & Permissions

Figure 4

Shock profiles obtained from numerics ($p=1$, $d=.08$, $a=1$, $D=1$, $\mu =9$, $\gamma =0.45$, ${\tau }_0=0.2$). Data are averaged over a short time window ($\Delta t=1000$) and then over 100 simulations. Left panel: Bound (upper) and unbound (lower) motor densities along the tube, in the tip frame, at time $t=60000$. Black lines correspond to MF predictions (5), with $v_{\mathrm{tip}}$ obtained from the simulation. Right panel: Density of motors (black) at fixed time intervals ($t=4\times {10}^4$; $8\times {10}^4$; $12\times {10}^4$) in the lab frame. Tubes are color-coded, with light and dark blue (or gray) representing low and high density. Note that the tip moves faster than the shock.Reuse & Permissions

Figure 5

Left panel: Different profiles are illustrated as in Fig. 4, but with $t=120000$, $d=0.11$, and ${\tau }_0=0.3$, 0.6, 0.9. Note that the length of the lattice, hence the tube velocity, is independent of ${\tau }_0$. Right panel: Numerical value of $\Delta$ (crosses) along the vertical blue (or gray) line of Fig. 2. When ${\tau }_0$ goes from 0 to 1, the average density of bound motors is first lower than that of the tip plateau ($\Delta <0$, shock), then equals it ($\Delta =0$, tip phase), and last overcomes it ($\Delta =0$, inverse shock). The vertical blue (or gray) lines correspond to the predicted boundaries of the tip phase (9). There is thus a reentrant phase transition from the kink phase to the tip phase and back into the kink phase, whose boundaries are accurately predicted by the MF theory.Reuse & Permissions