Elucidating the Origin of Heterogeneous Anomalous Diffusion in the Cytoplasm of Mammalian Cells

Diffusion of tracer particles in the cytoplasm of mammalian cells is often anomalous with a marked heterogeneity even within individual particle trajectories. Despite considerable efforts, the mechanisms behind these observations have remained largely elusive. To tackle this problem, we performed extensive single-particle tracking experiments on quantum dots in the cytoplasm of living mammalian cells at varying conditions. Analyses of the trajectories reveal a strong, microtubule-dependent subdiffusion with antipersistent increments and a substantial heterogeneity. Furthermore, particles stochastically switch between different mobility states, most likely due to transient associations with the cytoskeleton-shaken endoplasmic reticulum network. Comparison to simulations highlight that all experimental observations can be fully described by an intermittent fractional Brownian motion, alternating between two states of different mobility.

Figure 1

The PDF of anomaly exponents $\alpha$, obtained from individual TA-MSDs ($N=100$), shows a broad variation around a mean $⟨\alpha ⟩=0.59$ in untreated cells (black histogram). Nocodazole-treated cells have a similarly broad PDF (red histogram) with a significantly lower mean (cf. Table 1). Similar results are found for longer trajectories [Fig. S1(a) in [34] ]. Using a bootstrapping approach with geometric averaging (diamonds; full lines are Gaussian fits) resulted in narrower PDFs with the same mean, $⟨\alpha ⟩$.

Figure 2

Rescaled normalized VACFs [Eq. (2)] of all experimental trajectories with $N=100$ at different $\delta t$ agree with the analytical prediction for FBM [full lines, Eq. (3)], without treatment (grey symbols) and after nocodazole treatment (red symbols). For better visibility, untreated cell data have been shifted upwards. No significant differences are seen for longer trajectories [Fig. S3(a) in [34] ]. An estimate of $⟨\alpha ⟩$ can be directly obtained from the VACF minimum, $C_v(\xi =1)=2^{\alpha -1}-1$. VACF minima for untreated and nocodazole-treated cells yield $\alpha =0.58\pm 0.01$ and $\alpha =0.38\pm 0.02$, respectively, in favorable agreement with our MSD results. Inset: VACFs of simulated intermittent FBM trajectories ($N=100$, anomaly parameter ${\alpha }_0$) also agree with Eq. (3) (full lines).

Figure 3

(a) PDFs of normalized increments (time lag $\delta t=\mathrm{\Delta }t$, shown here as moduli, $|\chi |$) follow the anticipated Gaussian (green dashed line) for small $|\chi |$ but show significant deviations for $|\chi |>3.5$, indicating a heterogeneous process (black circles and red crosses: untreated and nocodazole-treated cells). These data are in excellent agreement with simulations of an intermittent FBM model (${\alpha }_0=0.5$ and ${\alpha }_0=0.3$: coinciding light and dark blue lines). (b) Representative trajectory (color-coded successive positions) with a local convex hull (LCH) at $t=28\mathrm{\Delta }t$ highlighted in grey. The corresponding time series of largest LCH diameters, $S_d(t)$, shows considerable fluctuations. Values $S_d(t)\ge \mu +\sigma$ (dashed horizontal line) are rated to be in the more mobile “off” state. (c) Residence times in the low- and high-mobility state, extracted from individual trajectories (threshold $\theta =\mu +\sigma$) feature exponential PDFs (full black lines) with a substantially longer mean residence time in the “on” state. No substantial differences are seen for nocodazole treatment or when choosing a threshold $\theta =\mu +2\sigma$ [Fig. S6(c) in [34] ]. (d) The fraction of trajectories without any switching rises when successively increasing the threshold value to $\theta =\mu +4\sigma$. No significant differences are seen between untreated (black horizontal stripes) and nocodazole-treated cells (filled red circles). In contrast, trajectories from filipin-treated cells (open blue squares) feature a much stronger increase (highlighted by dashed lines), indicating that ER structures are required for the mobility switching.

Figure 4

Representative fluorescence images of the ER in (a) untreated, (b) filipin-treated, and (c) osmotically shocked cells. In line with previous reports [55, 56], the ER network of untreated cells is completely fragmented after filipin treatment or osmotic shock. Scale bars: $10\mu \mathrm{m}$.