Filament Depolymerization by Motor Molecules

Motor proteins that specifically interact with the ends of cytoskeletal filaments can induce filament depolymerization. A phenomenological description of this process is presented. We show that under certain conditions motors dynamically accumulate at the filament ends. We compare simulations of two microscopic models to the phenomenological description. The depolymerization rate can exhibit maxima and dynamic instabilities as a function of the bulk motor density for processive depolymerization. We discuss our results in relation to experimental studies of Kin-13 family motor proteins.

Figure 1

Regimes of accumulation and depletion of motors at the shrinking filament end as a function of the coefficient ${\Omega }_2^{*}={\Omega }_2{\rho }_{\mathrm{m}\mathrm{a}\mathrm{x}}/(D{\omega }_{\mathrm{d}}{)}^{1/2}$ and the bulk motor concentration $c^{*}={\omega }_{\mathrm{a}}c/{\omega }_{\mathrm{d}}{\rho }_{\mathrm{m}\mathrm{a}\mathrm{x}}$ for $J_0={\Omega }_0=J_2=0$ and $J_1/(D{\omega }_{\mathrm{d}}{)}^{1/2}=-0.1$, ${\Omega }_1/(D{\omega }_{\mathrm{d}}{)}^{1/2}=0.45$. Accumulation occurs above the solid line, depletion occurs below. The gray area indicates the region of physical interest. Above this area, $p_{\mathrm{e}\mathrm{f}\mathrm{f}}({\rho }_{\mathrm{m}\mathrm{a}\mathrm{x}})>0$ which is forbidden by steric exclusion of particles. Below this area, filaments polymerize at high motor concentration.

Figure 2

Discrete model of motor-induced filament depolymerization. Motors attach to empty sites at rate ${\overline{\omega }}_{\mathrm{a}}c$ and detach with rate ${\overline{\omega }}_{\mathrm{d}}$. The hopping rate to free neighboring sites is ${\overline{\omega }}_{\mathrm{h}}$. Occupied sites are removed from the end with rate $\overline{\Omega }$. With probability $\overline{p}$, the particle remains attached to the end when a subunit is removed.

Figure 3

The velocity $v_{\mathrm{d}}^{*}=v_{\mathrm{d}}/a({\overline{\omega }}_{\mathrm{h}}{\overline{\omega }}_{\mathrm{d}}{)}^{1/2}$ of depolymerization as a function of the bulk motor concentration $c^{*}={\overline{\omega }}_{\mathrm{a}}c/{\overline{\omega }}_{\mathrm{d}}$ obtained in simulations of model A for different values of the processivity $\overline{p}=0$, 0.9, and 1 (symbols). For comparison the corresponding solutions of the phenomenological equations are displayed (lines). Inset: The accumulation of motors, characterized by the ratio ${\rho }_0/{\rho }_{\infty }$ of motor density at the end and far from the end is shown as a function of $c^{*}$ for the same situations. Parameter values are ${\overline{\omega }}_{\mathrm{a}}={\overline{\Omega }}_{\mathrm{a}}$, ${\overline{\omega }}_{\mathrm{d}}={\overline{\Omega }}_{\mathrm{d}}=0.008{\overline{\omega }}_{\mathrm{h}}$, and $\overline{\Omega }=4{\overline{\omega }}_{\mathrm{h}}$.