Anomalous Diffusion Probes Microstructure Dynamics of Entangled F-Actin Networks

We study the thermal motion of colloidal tracer particles in entangled actin filament (F-actin) networks, where the particle radius is comparable to the mesh size of the F-actin network. In this regime, the ensemble-averaged mean-squared displacement of the particles is proportional to ${\tau }^{\gamma }$, where $0<\gamma <1$ from $0.1<\tau <100\mathrm{s}$ and depends only on the ratio of the probe radius to mesh size. By directly imaging hundreds of particles over 20 min, we determine this anomalous subdiffusion is due to the dynamics of infrequent and large jumps particles make between distinct pores in the network.

Figure 1

MSD of $0.25\mu \mathrm{m}$ spheres in F-actin with $\xi =0.79\mu \mathrm{m}$ (open triangles), $0.55\mu \mathrm{m}$ (solid circles), $0.30\mu \mathrm{m}$ (solid squares), $0.25\mu \mathrm{m}$ (solid triangles), and $0.17\mu \mathrm{m}$ (open squares). The solid line indicates a linear fit, $⟨\Delta x^2(\tau )⟩\sim \tau$.

Figure 2

(a) Representative constrained $x\mathrm{\text{−}}y$ trajectory of a $0.25\mu \mathrm{m}$ particle in $0.9\mathrm{mg}/\mathrm{mL}$ ($\xi =0.31\mu \mathrm{m}$) F-actin over 600 s. (b) The $y$ coordinate of (a) as a function of time. (c) Representative jumping $x\mathrm{\text{−}}y$ trajectory from same sample. (d) The $y$ coordinate in (c) as a function of time.

Figure 3

(a) MSD of $0.25\mu \mathrm{m}$ particles in $0.9\mathrm{mg}/\mathrm{mL}$ F-actin (triangles). The solid line indicates a power-law fit ${\tau }^{\gamma }$, where $\gamma =0.32$. The MSD of constrained particles (line) and caged portions of jumping particles (open circles) agree well. (b) Histogram of cage times for jumping $0.25\mu \mathrm{m}$ particles in $0.9\mathrm{mg}/\mathrm{mL}$ F-actin (squares). The dashed line indicates a power-law fit, $P({\tau }_c)\sim {\tau }_c^{-\nu }$, with $\nu =1.33\pm 0.04$.

Figure 4

The scaling of the diffusive exponent, $\gamma$, as a function of $a/\xi$ for several particle radii, $a$: $0.25\mu \mathrm{m}$ (open squares), $0.32\mu \mathrm{m}$ (diamonds), and $0.5\mu \mathrm{m}$ (triangles). Error bars indicate measured sample-to-sample variation.