Anomalous intracellular transport phases depend on cytoskeletal network features

Intracellular transport in eukaryotic cells consists of phases of passive, diffusion-based transport and active, motor-driven transport along filaments that make up the cell's cytoskeleton. The interplay between superdiffusive transport along cytoskeletal filaments and the anomalous nature of subdiffusion in the bulk can lead to novel effects in transport behavior at the cellular scale. Here we develop a computational model of the process with cargo being ballistically transported along explicitly modeled cytoskeletal filament networks and passively transported in the cytoplasm by a subdiffusive continuous-time random walk (CTRW). We show that, over a physiologically relevant range of filament lengths and numbers, the network introduces a filament-length sensitive superdiffusive phase at early times which crosses over to a phase where the CTRW is dominant and produces subdiffusion at late times. We apply our approach to the problem of insulin secretion from cells and show that the superdiffusive phase introduced by the filament network manifests as a peak in the secretion at early times followed by an extended sustained release phase that is dominated by the CTRW process at late times. Our results are consistent with in vivo observations of insulin transport in healthy cells and shed light on the potential for the cell to tune functionally important transport phases by altering its cytoskeletal network.

Figure 1

(a) The initial state of the system. Cargos [shown as (red) circles] start near the nucleus. Randomly placed filaments (straight lines) model the cytoskeleton. Each filament has a fixed polarization. (b) The final state of the simulation. Cargos alternate between passive and active phases of transport until they reach the outer cell membrane. Individual trajectories are denoted by thin (red) curves traced out by the cargos. (c) The ensemble-average MSD for a system of 1000 cargos, with no filaments present (CTRW only). The smooth (blue) curve going through the data is a power-law fit with an exponent $\alpha =0.8$. (d) TA-MSD for the same system for a constant measuring time, $t$, as a function of a sliding time window $\mathrm{\Delta }$. Inset, upper left shows the TA-MSD for constant time windows (1 s, 2 s, and 3 s, from top to bottom), as a function of measuring time. Inset, lower right, shows the ergodicity-breaking parameter plotted as $\mathrm{EB}/\mathrm{\Delta }$ as a function of $\mathrm{\Delta }$ (dashed line shows $1/\mathrm{\Delta }$).

Figure 2

(a) A log-log plot of an ensemble-average MSD in the presence of filaments (1500 filaments, $5\mu \mathrm{m}$ each) compared to MSD for CTRW only [lower set of data points (blue symbols)]. Dashed lines show fits to different power-law behaviors for short and long times for the MSD data with filaments and over the entire time range for the control CTRW-only case. The measured long- (b) and short-time (c) power-law exponents as a function of filament length and number. In panel (c) lines of constant mass are in white. (d) MSD short-time exponents as a function of filament length for different total filament masses. Averaging is over $N=10000$ cargo in all cases. Error in the measured exponents due to fitting is less than $6\%$ over the parameter range explored.

Figure 3

(a) Ensemble-average MSD as a function of time for different values of $\alpha$ ($N=100$ cargo) (b) MSD as a function of time for 100 cargos over five different networks at fixed $\alpha =0.8$. Normalized standard deviation of MSD (averaged over 100 cargo and 100 different networks) at 10 s (c) and 100 s (d) as a function of filament length and number.

Figure 4

(a) FPTDs for networks comprising 300 filaments, with varying lengths. (b) The second phase of the FPTD for different values of $\alpha$. (c) Strength of FPTD decay as a function of filament length and number. Lines of constant mass are in white. (d) FPTD decay exponent as a function of filament length for different filament masses. FPTDs are for 100 cargo over 100 different networks. Error in measured exponents due to fitting is less than $6\%$ over the parameter range explored.

Figure 5

(a) MFPT as a function of filament length and number with lines of constant mass in white. (b) MFPT as a function of filament length for different filament masses. Network-averaged MFPT standard deviation (c) and normalized average standard deviation (d) as a function of filament length and number. Averaging is over 400 cargo and 100 different networks.