Nonequilibrium-Driven Motion in Actin Networks: Comet Tails and Moving Beads

We present 3D dynamic Monte-Carlo simulations of the growth of an actin network close to an obstacle coated with Wiskott-Aldrich syndrome protein (WASP), an inducer of actin branching. Our simulations incorporate both elasticity and relaxation of the actin tail, thus allowing for local network compression. Whilst steady state motility derives mainly from polymerization at the leading edge, nonthermal stored elastic energy and retrograde flow are observed in a thin slab of material close to the obstacle. We observe a crossover from steady to hopping bead motion as the branching rate is decreased.

Figure 1

Actin tail for early (after ${10}^6$ MCS, (a)) and late (after $2.5\times {10}^7$ MCS, (b) and (c)) times. In (c) , only the network close to the obstacle is shown. Parameters were: $p_{\mathrm{cap}}/p_{\mathrm{pol}}=0.143$, $p_{\mathrm{br}}/p_{\mathrm{pol}}=0.2$, $p_{\mathrm{rip}}=0$, $p_{\mathrm{depol}}/p_{\mathrm{pol}}=0.013$, $2R=100\mathrm{nm}$, and $D_t=1.5\times {10}^{-6}$. A set of coordinate axes is shown for clarity. The dark (red, online) patches correspond to WASP covering.

Figure 2

(a) Plot of plate position vs time for 3DMC simulations of 4 networks. From top to bottom, persistence length is 17, 2.5, 0.25, and $0.1\mu \mathrm{m}$, respectively. Other parameters: $p_{\mathrm{cap}}/p_{\mathrm{pol}}=0.143$, $p_{\mathrm{br}}/p_{\mathrm{pol}}=0.125$, $p_{\mathrm{rip}}=0$, $p_{\mathrm{depol}}/p_{\mathrm{pol}}=0.013$, $2R=50\mathrm{nm}$, and $D_t=1.67\times {10}^{-7}$. (b) Plot of the number of monomers in the networks in (a) as a function of time for persistence lengths 17, 2.5, 0.25, and $0.1\mu \mathrm{m}$ from bottom to top (looking from the right). (c) Plot of density (solid line, monomer units) and stored elastic energy (dotted line, $k_{B}T$ units) as a function of $z$, for $2R=100\mathrm{nm}$, $p_{\mathrm{br}}/p_{\mathrm{pol}}=0.17$, $D_t=1.5{10}^{-6}$, and rest as in (a), after $\sim 0.2$ ${10}^7$ MCS (obstacle at 0). The dot-dashed line gives the density of a frozen network with the same parameters. (d) Same as (c) but after $\sim {10}^7$ MCS, (obstacle at 0). Going from (c) to (d), the plate has moved $\sim 115$ and $\sim 80$ units in the frozen and dynamic network simulation, respectively. (e) Plot of density (solid line, monomer units), stored elastic energy (dotted line, $k_{B}T$ units), numbers of pointed ends $n_p$ (dot-dashed line), as a function of $z$ (obstacle in 0), for a network with $p_{\mathrm{rip}}/p_{\mathrm{pol}}\simeq 0.01$, $p_{\mathrm{br}}/p_{\mathrm{pol}}=0.17$, $2R=100\mathrm{nm}$, $D_t\simeq 0.4\times {10}^{-7}$, and others as (c). (f) Plot of retrograde flow (solid line, in monomer per MCS, right $y$ axis), and stored elastic energy per cal (long dashed line, $k_{B}T$ units, left $y$ axis) for $2R=200\mathrm{nm}$, $p_{\mathrm{rip}}/p_{\mathrm{pol}}=0.0085$, and the rest as in (c) as a function of $z$ (obstacle in 0). (Quantities averaged over $>{10}^3$ statistically independent configurations.)

Figure 3

Snapshots corresponding to a bead undergoing “hopping” (a)–(d) and persistent (e)–(f) motion. Parameters were: for (a)–(d) $2R=50\mathrm{nm}$, $p_{\mathrm{cap}}/p_{\mathrm{pol}}=0.5$, $p_{\mathrm{br}}/p_{\mathrm{pol}}=0.067$, $p_{\mathrm{depol}}/p_{\mathrm{pol}}=0.013$, and $D_t=4.2\times {10}^{-6}$: for (e)–(f) $2R=100\mathrm{nm}$, $p_{\mathrm{cap}}/p_{\mathrm{pol}}=0.2$, $p_{\mathrm{br}}/p_{\mathrm{pol}}=0.2$, $p_{\mathrm{depol}}/p_{\mathrm{pol}}=0.013$, and $D_t=1.7\times {10}^{-6}$. Corresponding times (in MCS) are: (a) ${10}^6$, (b) $5\times {10}^6$, (c) ${10}^7$, (d) $2\times {10}^7$, (e) $4.25\times {10}^6$, (f) $1.125\times {10}^7$.