Avalanche-like behavior in ciliary import

Abstract

Cilia and flagella are microtubule-based organelles that protrude from the cell body. Ciliary assembly requires intraflagellar transport (IFT), a motile system that delivers cargo from the cell body to the flagellar tip for assembly. The process controlling injections of IFT proteins into the flagellar compartment is, therefore, crucial to ciliogenesis. Extensive biochemical and genetic analyses have determined the molecular machinery of IFT, but these studies do not explain what regulates IFT injection rate. Here, we provide evidence that IFT injections result from avalanche-like releases of accumulated IFT material at the flagellar base and that the key regulated feature of length control is the recruitment of IFT material to the flagellar base. We used total internal reflection fluorescence microscopy of IFT proteins in live cells to quantify the size and frequency of injections over time. The injection dynamics reveal a power-law tailed distribution of injection event sizes and a negative correlation between injection size and frequency, as well as rich behaviors such as quasiperiodicity, bursting, and long-memory effects tied to the size of the localized load of IFT material awaiting injection at the flagellar base, collectively indicating that IFT injection dynamics result from avalanche-like behavior. Computational models based on avalanching recapitulate observed IFT dynamics, and we further show that the flagellar Ras-related nuclear protein (Ran) guanosine 5'-triphosphate (GTP) gradient can in theory act as a flagellar length sensor to regulate this localized accumulation of IFT. These results demonstrate that a self-organizing, physical mechanism can control a biochemically complex intracellular transport pathway.

Fig. 1.

The IFT train injector produces avalanche-like behavior. (A) TIRF microscopy produces movies of KAP-GFP (44) IFT train movement, which are then converted to kymographs of movement along the flagellar axis. (B) A median projection across the kymograph at angle θ (red on kymograph), the predominant angle of train movement (6), produces a smoothed time series of injections. Behaviors such as bursting (orange) and periodicity (blue) are evident. Details of the kymograph analysis are given in SI Materials and Methods. (C) The injector shows quasiperiodicity. We used the time series with a length >50 s (n = 37) to compute the averaged power spectrum. The average is representative of the individual power spectra. The white region highlights the portion of the spectrum that reflects the dwell times between successive injections. The gray regions correspond to nonadjacent injections (low frequency) and shape of individual peaks in the time series (high frequency). The broad peak in the power spectrum results from transient periodicity as indicated in Fig. S3. (D) The IFT injection size distribution (solid line) indicates a fat-tailed distribution (n = 2,537 injections). A lognormal distribution was fitted to the data (dashed line). We removed the smallest injections and fitted the remaining tail of the distribution (n = 1,435 injections) to a power law (). We found α = 2.85 with P = 0.018, using methods of Clauset et al. (49).

Fig. 2.

IFT injection dynamics match dynamics of avalanching systems. (A) In an experimental sandpile, a continuous incoming feed of sand grains produces a quasiperiodic, discontinuous series of avalanches. In a larger pile, the avalanches are larger and less frequent (13). (B) Mean IFT injection magnitude vs. the time since the previous injection shows that longer time intervals are associated with larger injections. (C) Mean IFT injection magnitude vs. the time until the next injection shows that longer times after an injection are associated with larger injections. Error bars are SEM.

Fig. 3.

Pharmacological and genetic perturbations modify the length-dependent injection rate but do not change injection dynamics. We used the lf4 mutation (50) (kinase) and lithium treatment (51) [GSK3 inhibitor (47)] to study the effects of long flagella on the IFT injector, and we used cycloheximide (52) (protein synthesis inhibitor) to study the effects of short flagella. (A) Examining the injection rate as a function of flagellar length showed a drastic effect on the normal length-dependent injection rate: Control trend (n = 168 flagella; blue circles, black solid line with extrapolation dashed) shows a decrease in the injection rate for longer flagella. Cycloheximide (n = 18 flagella; CHX, green circles) decreases the injection rate below the control trend. Lithium chloride (n = 38 flagella; LiCl, red circles) and the lf4 mutation (n = 29 flagella; lf4, yellow circles) increase the injection rate above the control trend. (B) A box and whisker plot of the residual for each dataset to the control (blue) trend line shows a significant decrease in CHX (green) and a significant increase in LiCl (red) as well as with the lf4 mutation (yellow) by multiple pairwise comparison using Bonferroni’s correction for α (***P < 0.0001). (C) Despite the significant change in the amount of injected material per second, we found no effect on the relationship between individual injection size and the time between events. We plotted the magnitude of each injection event, measured by GFP intensity, vs. the time since the previous injection event. The control trend line (solid black) for injection magnitude as a function of accumulation time represents all of the datasets well: control, n = 130 events, blue circles; CHX, n = 55 events, green circles; LiCl, n = 72 events, red circles; and lf4, n = 57 events, yellow circles. (D) Box and whisker plot of the residual in event magnitude from the control trend line shows no significant difference (NS) in injection dynamics due to the perturbations. Box and whicker plots: top and bottom of each colored box represent the 25th and 75th percentiles, respectively. The horizontal line within the box is the median. Whiskers extend to the last data point within 1.5× the interquartile range. Red crosses represent outlier values.

Fig. 4.

IFT dynamics are linked to IFT train localization intensity at the flagellar base. (A) An enlarged view of the flagellar base region shows that higher-intensity staining for kinesin-II occurs at the base of the regenerating flagella (R) in cells that have one steady-state-length flagellum (S) and one regenerating flagellum. Color bar indicates stain intensity ranging from lowest (blue) to highest (dark red). Inset (Upper Left) gives the cellular context for the magnified views. (B) The ratio of integrated kinesin-II staining between the flagellar bases of regenerating and steady-state-length flagella was quantified in 22 control cells with two equal-length flagella (ratio in control cells is the lower-intensity base to the higher-intensity base), in 23 single cells with unequal-length flagella (ratio in unequal-length flagella is the longer flagellum base to the shorter flagellum base), and in 15 view frames comparing one cell with two regenerating flagella to another cell with two steady-state-length flagella (ratio is the mean steady-state base to the mean regenerating base). Error bars are SEM. In every single case, the short regenerating flagella had higher-intensity staining at their bases compared with full-length flagella (38/38, P < 1 × 10⁻¹², binomial statistic). (C) Diagram illustrating how the RanGTP gradient can act as a length sensor. The model assumes RanGTP is produced at constant rate, degrades with first-order kinetics, and can diffuse out through the flagellar pore (for details and derivation of model see SI Appendix). (D) A graph of the model illustrates variation in RanGTP concentration at the flagellar base as a function of flagellar length. The model predicts that longer flagella should have a lower RanGTP concentration and therefore less IFT accumulation than shorter flagella, as seen experimentally in B. Parameters used for the plot: RanGTP production rate (53) of 10 molecules per second, RanGTP decay constant (54) of 10/s, RanGTP diffusion constant (54) of 3 µm²/s, flagellar cross-sectional area = 0.02 µm², and pore length = 0.2 µm. For effect of parameter variation see Fig. S12.