Dynamics of the IFT machinery at the ciliary tip

Intraflagellar transport (IFT) is essential for the elongation and maintenance of eukaryotic cilia and flagella. Due to the traffic jam of multiple trains at the ciliary tip, how IFT trains are remodeled in these turnaround zones cannot be determined by conventional imaging. Using PhotoGate, we visualized the full range of movement of single IFT trains and motors in Chlamydomonas flagella. Anterograde trains split apart and IFT complexes mix with each other at the tip to assemble retrograde trains. Dynein-1b is carried to the tip by kinesin-II as inactive cargo on anterograde trains. Unlike dynein-1b, kinesin-II detaches from IFT trains at the tip and diffuses in flagella. As the flagellum grows longer, diffusion delays return of kinesin-II to the basal body, depleting kinesin-II available for anterograde transport. Our results suggest that dissociation of kinesin-II from IFT trains serves as a negative feedback mechanism that facilitates flagellar length control in Chlamydomonas.


Introduction
Cilia (or eukaryotic flagella, terms essentially referring to the same organelle) are hair-like organelles that extend from the plasma membrane of nearly all mammalian cells. The core structural component of a cilium is the axoneme, a ring of nine unipolar doublet microtubules surrounding a central pair of singlet microtubules. Cilia play essential roles in cell motility, generate the movement of fluids over multiciliated surfaces, and sense extracellular signals (Satir et al., 2010). To assemble and maintain functional cilia, the IFT machinery (Kozminski et al., 1993) transports axonemal precursors and sensory proteins bidirectionally between the cell body and the ciliary tip. Defects in IFT are linked to a wide range of human diseases including Bardet-Biedl syndrome, retinal degeneration, and polycystic kidney disease (Brown and Witman, 2014).
Intraflagellar cargoes interact with multiprotein complexes known as IFT particles that are organized into larger IFT trains as they enter the flagellum (Cole et al., 1998;Lechtreck et al., 2017;Pigino et al., 2009). In most species, the IFT trains are transported anterogradely from the base to the tip of a flagellum by heterotrimeric kinesin-II (Kozminski et al., 1995), but some species also use a second homodimeric kinesin to build more specialized sensory cilia (Snow et al., 2004). Once the trains reach the tip, they are reorganized and transported retrogradely to the ciliary base by dynein-1b (Pazour et al., 1999;Porter et al., 1999;Signor et al., 1999). Along the length of a cilium, the activities of kinesin and dynein motors are reciprocally coordinated, such that only one type of a motor is active at a time (Shih et al., 2013). As a result, trains move between the tip and base of the cilium without significant pauses or back-and-forth motion (Dentler, 2005;Engel et al., 2009) and switch directions at the turnaround zones (Ishikawa and Marshall, 2011;Laib et al., 2009;Shih et al., 2013). Dynein-1b requires kinesin-II activity to reach the ciliary tip, suggesting that it travels on anterograde trains (Iomini et al., 2001;Pedersen et al., 2006;Rompolas et al., 2007). Retrograde traces of kinesin-II have not been frequently observed in Chlamydomonas, and it remains unclear how kinesin-II returns to the basal body (Engel et al., 2009;Wingfield et al., 2017). Because anterograde and retrograde IFT trains have different sizes and depart at different frequencies (Dentler, 2005;Iomini et al., 2001), IFT trains must be remodeled at the distal tip and the flagellar base.
The mechanism underlying the remodeling of IFT complexes at the ciliary tip and base cannot be directly observed by conventional microscopy methods because multiple trains coexist in these turnaround zones (Buisson et al., 2013;Iomini et al., 2001;Wren et al., 2013). In this work, we adapted PhotoGate (Belyy et al., 2017) to control the number of fluorescent IFT trains entering the flagellum of the unicellular algae Chlamydomonas reinhardtii. Using this approach, we monitored the turnaround behavior and remodeling of single IFT trains at the flagellar tip. We also elucidated the mechanisms by which the kinesin and dynein motors are recycled in this process and IFT trains reverse their direction of motion. The dynamics of IFT motor turnover at the tip suggest a new mechanism for how Chlamydomonas controls the length of its flagella.

IFT trains split apart and mix with each other at the flagellar tip
To monitor IFT movement, we tracked the dynamic behavior of IFT27, a core component of the IFT complex B, in a pf18 IFT27-GFP strain (Engel et al., 2009;Qin et al., 2007). This strain has paralyzed flagella (pf) that readily adhere to the glass surface, enabling us to monitor IFT under total internal reflection (TIR) illumination (Engel et al., 2009). Consistent with previous studies (Dentler, 2005;Engel et al., 2009;Iomini et al., 2001;Kozminski et al., 1993;Qin et al., 2007;Shih et al., 2013), IFT trains moved processively along the length of flagella, reversing direction at eLife digest Cilia and flagella are hair-like structures that protrude from nearly every human cell and play a number of roles including transmitting signals and enabling cells to move. These structures lengthen when new material is deposited at their tip by a process called intraflagellar transport (IFT). In this process, protein complexes known as IFT trains carry cargo along tracks that run along the length of each flagellum. Different motor proteins power the IFT trains in different directions: kinesin moves IFT trains from the base to the tip, while dynein moves them back in the opposite direction.
When IFT trains arrive at the tip of the flagellum, they release their cargo and undergo a major reorganization process in which the trains switch motors in order to move back to the base. Because the many IFT trains at the tip form a kind of 'traffic jam', standard imaging techniques have been unable to distinguish exactly what happens during this reorganization.
A new imaging method called PhotoGate microscopy can track individual molecules inside crowded cells. Chien, Shih et al. have now used this method to visualize the full range of movements made by IFT trains and motors in the flagella of a species of single-celled algae. This revealed that at the tip of the flagellum, IFT trains split apart and mix with each other to assemble into new trains, which move back to the base. In addition, kinesin carries dynein to the tip as inactive cargo, detaches from IFT trains at the tip and diffuses back to the base of the flagellum. This delays kinesin's return and causes it to accumulate in the flagellum, which helps to explain why flagella assemble more slowly as they lengthen: as the flagellum grows longer, less kinesin is available at the base to transport material to the tip. Thus kinesin diffusion helps the algae to regulate the length of their flagella.
Further research is now needed to study whether similar mechanisms control the length of flagella in other organisms. Defects in the intraflagellar transport process have been linked to a range of human diseases known as ciliopathies, and so the results presented by Chien, Shih et al. could also help us to uncover the causes and potential treatments for these conditions. . Because a large number of GFP-labeled trains accumulated at the tip, the dwell and departure of individual trains at the tip could not be resolved by conventional TIR imaging ( Figure 1a).
To monitor the turnaround behavior of individual IFT trains at the flagellar tip, we developed the one-dimensional PhotoGate assay (Belyy et al., 2017) to track single fluorescent complexes at the flagellar tip. In this assay, fluorescent trains located at distal parts of a flagellum were initially photobleached by moving a focused laser beam from the tip of the flagellum to near its base. We next opened the 'gate' by turning off the focused beam until a single fluorescent train entered the flagellum. The gate beam was repeatedly turned on for 0.2 s at 1 Hz to photobleach any additional anterograde trains entering the flagellum (Figure 1b, Video 2). Under these conditions, less than 1% of anterograde IFT trains were able to pass the gate unbleached. This approach revealed the full range of movement of single fluorescent IFT trains within the flagellum. IFT movement can be divided into three stages: anterograde movement toward the tip, pausing at the tip, and returning to the base by retrograde transport.
We directly observed that a single anterograde train splits into multiple retrograde trains at the tip (Figure 1c-e, Figure 1-figure supplement 2a). On average, 2.4 retrograde trains were detected departing from the tip after the arrival of a single fluorescent anterograde train (Figure 1f, N = 97), consistent with higher frequencies of retrograde IFT trains than anterograde IFT trains (Dentler, 2005;Iomini et al., 2001;Qin et al., 2007). However, the number of retrograde trains per fluorescent anterograde   Figure 1c) was significantly higher (Welch's t-test, p=10 À20 ) than the ratio of retrograde to anterograde train frequencies (1.15, Figure 1a) (Dentler, 2005;Iomini et al., 2001;Reck et al., 2016). These observations suggested that IFT complexes from different anterograde trains recombine with each other to form retrograde trains at the tip. To test this possibility, we closed the gate after two or three fluorescent anterograde trains entered the flagellum ( Figure 1d,e, Videos 3 and 4) and measured the number and return frequency of retrograde trains departing from the tip. If individual trains split and return without mixing with each other, the number and frequency of fluorescent retrograde trains would be proportional to the number of fluorescent anterograde trains. In contrast, we observed 2.4, 3.6, and 4.2 returning trains on average for one, two, and three incoming trains, respectively (N = 97, 60, 42, Figure 1f). The return frequencies for one, two, and three incoming fluorescent trains were 0.57, 0.71, and 0.76 s À1 , respectively. Because the increase was sub-proportional with the number of anterograde trains, we concluded that the fluorescent complexes in the anterograde trains disassemble and mix with a pool of 'dark' complexes from the other photobleached trains at the tip before they reorganize into retrograde trains ( Figure 1f). Monte Carlo simulations revealed that our conclusions are not markedly affected by the limited number of IFT27-GFPs per anterograde train (~6) or GFP photobleaching under TIR illumination (0.07 s À1 , Figure 1g

IFT tip turnaround is regulated by dynein activity and extracellular Ca 2+
To understand how IFT trains are processed at the tip, we analyzed the time between the arrival of an anterograde train and the departure of fluorescent retrograde trains (referred to as tip resting time) at the tip ( Figure 2a). When only a single fluorescent anterograde IFT27-GFP train was left unbleached near the base of the flagellum, the tip resting time of the first retrograde train was 3.1 ± 0.3 s (mean ± s.e.m., N = 97, Figure 2b), comparable to that of IFT cargos (Craft et al., 2015;Reck et al., 2016;Wren et al., 2013). Tip resting time was independent of flagellar length (Figure 2-figure supplement 1). If IFT tip turnaround was rate-limited by a single process, we would expect a single exponential distribution of tip resting times. However, the tip resting time histogram of first retrograde trains fit well to a Gamma distribution with a shape parameter of 3 and a rate constant of~1 s À1 , indicating that tip turnaround of IFT trains occurs rapidly through a multistep process ( Figure 2b). We also observed that the tip resting time of first, second, third, and fourth fluorescent retrograde trains increases linearly (Figure 2c). Because the average time between successive retrograde trains (Dt = 1.7 s) is the same, we concluded that the tip departure is a purely stochastic process. The linear fit to the tip resting times has a y-intercept of 1.3 s (Figure 2c), revealing that the departure of the first train takes longer than Dt. Therefore, the complexes dwell at the tip through another rate limiting process before they can depart from the tip.
When two or three fluorescent anterograde trains were allowed to pass through the gate, Dt became shorter (1.4 and 1.3 s, Welch's t-test, p=0.03 and 0.02 for two and three trains, respectively; Figure 2c). This is because providing a higher number of fluorescent GFPs available at the tip increases the likelihood of retrograde trains to have at least one fluorescent GFP. Remarkably, the y-intercept remained constant when we allowed one to three more fluorescent anterograde trains to enter the flagellum (Figure 2c), suggesting that this duration corresponds to processing and breakdown of anterograde trains at the tip (referred to as tip remodeling time). The time between tip remodeling and departure of IFT trains is defined as the tip departure time (Figure 2a). We also tested whether extracellular calcium and the dynein inhibitor ciliobrevin D (Firestone et al., 2012) affect the duration of IFT tip turnaround. Calcium regulates pausing of IFT trains along the flagellum (Collingridge et al., 2013;Shih et al., 2013), and disrupting calciumdependent kinesin-II phosphorylation causes abnormal accumulations of IFT proteins at the ciliary tip (Liang et al., 2014). When extracellular calcium in media (0.34 mM) was chelated using 0.5 mM EGTA, the tip departure time increased to 2.8 s (Welch's t-test, p=0.01), whereas tip remodeling time (1.4 s) remained unaltered (Figure 2d,e). Therefore, calcium has minimal effect on the breakdown of anterograde trains, but may have a regulatory role in the assembly or departure of retrograde trains. Addition of 0.1 mM ciliobrevin D to media results in 50% reduction in the frequency of retrograde and anterograde trains, and 50% and 28% reduction in retrograde and anterograde train velocities, respectively (Shih et al., 2013). In this case, the tip resting time of IFT27 increased over two-fold ( Figure 2e, p<10 À4 ), suggesting that rapid turnover of IFT trains depends on dynein activity.

Kinesin-II dissociates from IFT trains at the tip
We next turned our attention to the movement of the IFT motors and their exchange at the flagellar tip. Dynein-1b was tagged with GFP at its light intermediate chain (D1bLIC), which assembles into the dynein-1b complex and rescues d1blic mutant phenotypes (Reck et al., 2016). In the d1blic:: D1bLIC-GFP strain, D1bLIC moved continuously in the anterograde and retrograde directions at velocities similar to that of the IFT trains (Reck et al., 2016) (Figure 3a, Figure 1-figure supplement 1). Kinesin-II was tagged with GFP at its non-motor subunit KAP that localizes kinesin-II to the flagellar base (Mueller et al., 2005). In the fla3::KAP-GFP strain, KAP moved primarily in the anterograde direction to the flagellar tip at a similar speed to anterograde IFT27 ( Figure 3b, Figure 1figure supplement 1). Unlike D1bLIC, retrograde traces of KAP were not frequently observed (Engel et al., 2009;Wingfield et al., 2017), suggesting that kinesin-II dissociates from IFT trains at the tip (Engel et al., 2009;Engel et al., 2012).
PhotoGate assays revealed that D1bLIC-GFP has similar tip turnaround dynamics to IFT27-GFP ( Figure 3c, Figure 1-figure supplement 2b, Video 5). After arrival of a single anterograde D1bLIC-GFP train at the tip, we detected on average 2.5 retrograde D1bLIC trains. The average tip resting time until the departure of the first retrograde train was 1.8 ± 0.2 s (mean ± s.e.m., N = 60, Figure 3d), with additional~1.1 ± 0.1 s between subsequent departure events ( Figure 3e). Photo-Gate imaging of KAP-GFP cells showed that single KAP-GFP trains moved anterogradely to the tip and rested at the tip for 2.2 ± 0.2 s (N = 95). Unlike D1bLIC, individual KAP-GFP particles moved away from the tip by rapid saltatory motion (Figure 3f,g, Figure 1-figure supplement 2c, Video 6). Mean square displacement (MSD) analysis showed that KAP undergoes one-dimensional diffusion at 1.68 ± 0.04 mm 2 s À1 (mean ± s.e.m., N = 27 traces) within the flagellum after it departs from the tip (Figure 3h), consistent with the values measured for tubulin and EB1 that undergo diffusion within the ciliary space (Craft et al., 2015;Harris et al., 2016).  Unlike IFT trains, the majority (89%, N = 95) of KAP-GFPs simultaneously departed from the tip in a single step ( Figure 3-figure supplement 1). Because each anterograde train contains multiple (6) KAP-GFPs on average (Engel et al., 2009), this observation indicates that kinesin-II departs from the tip in the same oligomeric state as it arrives. 34% of kymographs clearly showed a single diffusing fluorescent spot after departure (Figure 3f), suggesting that KAPs are held together in a single complex. In 30% of kymographs, the KAP signal spread quickly along the length of a flagellum after departure, suggesting that kinesin-IIs can also diffuse alone ( We next investigated whether KAP slides linearly along the microtubule track, similar to the nonprocessive, microtubule-depolymerizing kinesin MCAK (Helenius et al., 2006). In this case, KAP clusters are expected to move along the microtubule long axis, so the fluctuation in KAP position in the perpendicular axis would be similar to the error of single particle tracking. The KAP-GFP particles had lateral fluctuations of 19 ± 2 nm (mean ± s.d.) when moving in the anterograde direction. After departing from the tip, lateral fluctuations of diffusing spots increased to 65 ± 7 nm (Figure 3i,j), comparable to the radius of the axoneme. The intensity of fluorescent spots stayed relatively constant during anterograde transport and diffusion, suggesting that the measured lateral fluctuations are due to diffusive motion rather than decreased tracking precision. We concluded that after KAP detaches from the flagellar tip, it freely explores the space between the flagellar membrane and the axonemal surface rather than sliding along microtubules.

Kinesin-II carries dynein-1b as an inactive passenger during anterograde IFT
To investigate how kinesin-II and dynein-1b motors interact with anterograde and retrograde trains and how they are recycled back to the basal body, we transformed a d1blic mutant with both D1bLIC-crCherry and KAP-GFP constructs and simultaneously tracked the movement of KAP and D1bLIC subunits in the rescued cells (Figure 4-figure supplement 1, Video 8). The D1bLIC-crCherry transgene rescued the flagellar assembly defects in the d1blic mutant, increasing the flagellar length to 12.2 ± 1.6 mm (mean ± s.d., N = 100 flagella). Both tagged motors were expressed at near wild-type levels ( Figure 4-figure supplement 1). The velocities of anterograde and retrograde D1bLIC-crCherry trains were similar to those observed with IFT27-GFP ( Figure 4a, Figure 1-figure supplement 1). We observed strong co-localization of D1bLIC-crCherry and KAP-GFP on anterograde trajectories (Figure 4a), demonstrating that dynein-1b is carried to the flagellar tip by kinesin-II. Only D1bLIC-crCherry trains showed robust retrograde transport, while retrograde traces of KAP-GFP were rarely observed, consistent with dissociation of kinesin-II from IFT trains at the tip.
To determine which motor first departs from the tip after the arrival of an anterograde train, we performed two-color Photogate experiments to simultaneously track KAP-GFP and D1bLIC-crCherry from individual anterograde trains ( Figure 4b). Out of 21 cells, KAP began diffusive motion before the retrograde movement of D1bLIC in 10 cells (Figure 4b), D1bLIC left the tip before KAP in 8 cells ( Figure 4-figure supplement 2), and both appeared to exit the tip simultaneously (within 0.24 s) in 3 cells. These results suggest that kinesin-II and dynein-1b exit the flagellar tip independently from each other.

Kinesin-II returns from the ciliary tip to the cell body by diffusion
Dissociation of KAP from IFT trains at the tip is consistent with the recycling of kinesin-II to the cell body in the absence of active retrograde IFT (Engel et al., 2012;Pedersen et al., 2006;Reck et al., 2016). However, it remained unclear how kinesin-II achieves this long-range movement without active transport. To test whether diffusion from the tip effectively recycles KAP to the cell body, we performed fluorescence recovery after photobleaching (FRAP) assays in the middle sections of full-length flagella of fla3::KAP-GFP cells (~12 mm, Figure 5a, Video 9). Directional movements of KAP-GFP labeled trains into the photobleached area were seen from the anterograde direction, whereas recovery of GFP fluorescence from the retrograde direction was primarily due to diffusion of KAP-GFP from the tip. These results suggest that the high levels of background observed in KAP-GFP flagella were caused by kinesin-II motors dissociated from IFT trains at the tip. The diffusion constant calculated from the fluorescence recovery (1.8 ± 0.1 mm 2 s À1 , Figure 5b)  We ran Monte Carlo simulations to estimate the accumulation of KAP in a flagellum at a steadystate using the measured values of IFT train loading (Engel et al., 2009), diffusion coefficient, flagellar length, and IFT train frequency. The model assumes that KAP is released from anterograde IFT trains at the tip, diffuses within a flagellum, and is taken up by the basal body. Under these conditions, simulations confirmed the build-up of a linear concentration gradient of KAP in the flagellum ( Figure 5-figure supplement 1b). In fully-grown flagella, the return of KAP to the flagellar base takes 42 s on average, an order of magnitude longer than the travel of retrograde trains (4 s) to the base. This delay leads to a~4 fold higher amount of KAP inside the flagellum compared to a case in which KAP returns to the base with retrograde trains (Figure 5-figure supplement 1c). Unlike KAP, IFT27-GFP cells have a low fluorescence background without an obvious concentration gradient along the length of the flagellum (Figure 5d) due to active transport of the IFT trains in both directions.
Kinesin-II is depleted from the basal body during flagellar regrowth KAP-GFP loading on IFT particles has been shown to decrease with increasing flagellar length (Engel et al., 2009), but the underlying mechanism remained unclear. Because a larger amount of KAP builds up in the flagellum as the flagella elongate ( Figure 5-figure supplement 1), loading of KAP onto the subsequent IFT trains may be reduced by depletion of KAP at the flagellar base. To test this model, we deflagellated fla3::KAP-GFP cells and measured the GFP fluorescence at the basal body and in the flagellum during flagellar regrowth using confocal microscopy ( Figure 6a). The total amount of KAP localized to the base and flagellum increased by two-fold with flagellar length, indicating the upregulation of IFT components during flagellar growth. The fluorescence intensity at the flagellar base was highest for short flagella (1-4 mm) and decreased~4 fold as cells grew full-length flagella (~10 mm, Figure 6b), significantly larger than~1.6 fold reduction reported previously (Ludington et al., 2015). We also observed that the KAP fluorescence in the flagellum was low in short flagella and increased~10 fold as the flagellar length reached the steady-state (Figure 6b).
Changes in the amount of IFT complexes were markedly different from that of KAP during flagellar regrowth (Figure 6a). Unlike KAP-GFP, basal body fluorescence of IFT20-GFP remained nearly constant across all flagellar lengths in IFT20::IFT20-GFP cells (Figure 6c), presumably because they   are rapidly returned to the base through active transport. We also observed an increase of the GFP signal in the flagellum with elongation (Figure 6c), in contrast to the previous observation that the total amount of IFT components remains constant during flagellar regeneration (Marshall and Rosenbaum, 2001). This discrepancy may be related to differences in methods for quantifying IFT components in flagella. We next determined the localization of KAP-GFP to the basal body and flagellum in cells that grow abnormally long and short flagella. Chlamydomonas grows~1.5X longer flagella in the presence of Li + (Nakamura et al., 1987) by recruiting flagellar proteins from the cell body pool into the flagella (Nakamura et al., 1987) rather than requiring new protein synthesis (Wilson and Lefebvre, 2004). Consistent with previous observations, the KAP-GFP strain grew longer flagella in 50 mM Li + . After reaching the steady state length, we calculated the total KAP fluorescence at the basal body and the flagellum (Figure 6d, Figure 6-figure supplement 1). In agreement with our model, we observed that KAP gets depleted at the basal body at equilibrium. The KAP fluorescence localized to a flagellum correlated strongly with flagellar length (Pearson's R = 0.86), similar to untreated cells. The total KAP fluorescence in the flagellum was 50% higher than untreated cells.
In the absence of new protein synthesis, Chlamydomonas can grow half-length flagella after deflagellation, suggesting that the cytoplasmic pool of flagellar proteins is at least one half of that localized to the flagellar compartment (Rosenbaum et al., 1969). We deflagellated KAP-GFP cells with pH shock and regrew their flagella in the presence of the protein synthesis inhibitor cycloheximide. In agreement with untreated and Li + treated cells, we observed that the KAP fluorescence at the flagellum correlates strongly with the flagellar length (Pearson's R = 0.86), whereas the KAP intensity was depleted at the basal body (Figure 6d, Figure 6-figure supplement 1). Total KAP fluorescence was one half of untreated cells, consistent with the fact that a large amount of KAP is lost during deflagellation. Therefore, over a wide range of flagellar lengths (2-22 mm), KAP gets depleted at the basal body when the flagella reach their equilibrium length.

Remodeling of IFT complexes and motors at the flagellar tip in Chlamydomonas
Using PhotoGate, we have visualized the turnaround behavior of individual components of the IFT machinery at the flagellar tip. We present evidence that when IFT trains arrive at the tip, the complexes split apart and mix with complexes from other trains at the flagellar tip before initiating retrograde transport (Figure 4c). This dynamic disassembly and reassembly process may lead to differences in size, shape, and structure of anterograde and retrograde trains, as previously suggested by transmission electron microscopy (Dentler, 2005; Stepanek and Pigino, 2016). Remarkably, remodeling of IFT trains is completed within 1.3 s, with a 1.7 s average waiting time between the departures of successive trains, consistent with  previously measured values for IFT complex subunits, dynein-1b, and other axonemal cargoes (Craft et al., 2015;Qin et al., 2007;Reck et al., 2016;Wren et al., 2013). Kinetic analysis of the tip resting time revealed that disassembly of anterograde trains and reassembly of the retrograde trains is a multistep process regulated by extracellular calcium and the concentration of active dynein motors.
Simultaneous tracking of the anterograde motor kinesin-II (with KAP-GFP) and the retrograde motor dynein-1b (with D1bLIC-Cherry) has further revealed significant differences in how these motors are recycled back and forth within a flagellum. Kinesin-II drives anterograde trains in a highly processive fashion and then dissociates from the IFT trains when they reach at the flagellar tip. KAP-GFP then returns to the flagellar base by diffusing within the flagellum, similar to the diffusion of kinesin-1 in mammalian neurons (Blasius et al., 2013) and in contrast to the retrograde transport of kinesin-II observed in other cilia (Signor et al., 1999;Broekhuis et al., 2014;Williams et al., 2014;Prevo et al., 2015), see below). We propose that the diffusion of KAP-GFP represents the movement of the entire heterotrimeric kinesin-II complex because KAP and the kinesin-II motor subunits co-sediment in sucrose density gradients of purified flagella extracts (Cole et al., 1998;Mueller et al., 2005) and neither KAP nor FLA10 accumulate in flagella during inactivation of retrograde transport (Engel et al., 2012;Pedersen et al., 2006;Reck et al., 2016). In certain cases, KAP-GFP appears to diffuse in an oligomeric form. It remains to be studied what holds KAPs together and whether other components of the IFT trains diffuse with KAP clusters after splitting and mixing at the tip.
The retrograde motor dynein-1b is transported to the flagellar tip on anterograde trains (Reck et al., 2016). Because kinesin and dynein motors do not compete against each other in a tugof-war on anterograde trains (Shih et al., 2013), we concluded that dynein-1b is carried as an inactive motor complex (Toropova et al., 2017;Zhang et al., 2017), and it actively engages with microtubules only when it reaches the flagellar tip ( Figure 4c). The average tip resting time of dynein-1b is similar to kinesin-II (Welch's t test, p=0.05), but the initiation of retrograde transport by dynein-1b does not require departure of kinesin-II motors from the tip, suggesting that these processes are independent from each other.

The dynamic behavior of the IFT motors in Chlamydomonas flagella differs from that in other cilia
Several studies have revealed differences in IFT in the cilia and flagella of different organisms . First, the microtubule tracks can vary considerably. In Chlamydomonas, the axoneme contains nine doublet microtubules, each composed of a complete A-tubule (with 13 protofilaments) and an incomplete B-tubule (with 10 protofilaments). The B-tubule terminates before the A-tubule less than 1 mm from the flagellar tip (Ringo, 1967;Satish Tammana et al., 2013). Recent electron microscopy studies have revealed that anterograde IFT trains are transported primarily on the B-tubule, whereas retrograde IFT trains are transported on the A-tubule (Stepanek and Pigino, 2016). The pausing of IFT particles observed at the flagellar tip in Chlamydomonas may therefore reflect not only the time involved in the re-organization of the IFT particles, but also the time required for switching between microtubule tracks.
In other cilia, such as C. elegans sensory and mammalian olfactory cilia, the proximal doublet microtubule segment is shorter, and the distal singlet MTs can vary significantly in length (~2.5 mm in C. elegans to >100 mm in mouse olfactory cilia). These cilia also employ two different kinesin-II motors for anterograde IFT (Prevo et al., 2015;Snow et al., 2004;Williams et al., 2014). In C. elegans, heterotrimeric kinesin-II is concentrated near the basal body region and transports anterograde IFT particles into the proximal doublet segment, where they are gradually handed over to a homodimeric kinesin-II, OSM-3, for transport into the distal singlet segment (Prevo et al., 2015;Snow et al., 2004). Unlike Chlamydomonas, both the heterotrimeric and homodimeric kinesin-II motors are recycled to the ciliary base by retrograde IFT, not by diffusion, in these and other metazoan cilia studied to date (Broekhuis et al., 2014;Mijalkovic et al., 2017;Prevo et al., 2015;Signor et al., 1999;Williams et al., 2014).
Another important difference between IFT in Chlamydomonas and metazoan cilia is the dynamic behavior of the motors themselves. IFT particles and motors move processively in the Chlamydomonas flagellum (Dentler, 2005), with little or no evidence for the frequent pausing and reversal along the axoneme previously described in C. elegans or mouse olfactory sensory cilia (Mijalkovic et al., 2017;Prevo et al., 2015). We also did not observe acceleration and deceleration of IFT motors near turnaround zones, nor the instantaneous (<600 ms) reversal of dynein-1b at the ciliary tip described in C. elegans (Mijalkovic et al., 2017;Prevo et al., 2015). The reasons for these  Figure 6 continued on next page differences in IFT dynamics and turnover remain unknown, but they may be related to the variations in ciliary structure and organization described above, differential phosphorylation of kinesin-II motors (Liang et al., 2014), posttranslational modification of the microtubule tracks (Stepanek and Pigino, 2016), and other unidentified factors. In addition, both the frequency and speed of IFT is higher in Chlamydomonas (Dentler, 2005;Engel et al., 2009;Engel et al., 2012;Iomini et al., 2001;Reck et al., 2016;Snow et al., 2004;Williams et al., 2014;Wingfield et al., 2017) than that measured thus far in metazoan cilia (Li et al., 2015;Yi et al., 2017). This may allow Chlamydomonas to rapidly adjust the length of its flagella in response to internal or external stimuli, whereas most cilia in C. elegans sensory neurons or mammalian cells do not undergo extensive structural rearrangements once formed.

A model for flagellar length control in Chlamydomonas
Cilia and flagella serve as a model system to study how cells precisely control organelle size because they elongate only in one direction. According to the balance point model, flagellar length is set when flagellar assembly and disassembly rates reach equilibrium . While the disassembly rate is independent of flagellar length (Kozminski et al., 1995), the assembly rate is determined by the injection of IFT trains . The amount of material being transported by these trains to the tip is correlated strongly with the amount of material localized to the flagellar base (Ludington et al., 2013;Ludington et al., 2015;Wren et al., 2013), which serves as a loading dock. Previous studies showed that IFT train size and the number of ciliary cargos per train scales inversely with flagellar length (Craft et al., 2015;Engel et al., 2009), consistent with the reduction of the assembly rate as flagella elongate . However, it remained unclear which essential component of the IFT machinery limits the assembly of IFT trains at the basal body during elongation. We propose that dissociation of kinesin-II from IFT trains serves as a negative feedback mechanism to control the assembly rate in Chlamydomonas. Our results show that the majority of kinesin-II dissociates from IFT trains at the flagellar tip and diffuses within the flagellum. Diffusion leads to a large accumulation of kinesin-II in the flagellum as the flagellum grows longer, while the amount of kinesin-II at the base decreases several-fold. As a result, lower amounts of kinesin-II are available to bring new anterograde IFT trains to the flagellar tip. This may lead to a reduction in the IFT train size and the rate of flagellar assembly as the flagella elongate (Figure 6e,f). Indeed, a recent theoretical study demonstrated that increased diffusion time of kinesin-II in longer flagella can explain the inverse relationship between length and IFT motor recruitment rate (Hendel et al., 2017). Consistent with this model, previous studies showed that KAP intensity at the basal body correlates with KAP loading on IFT trains and the assembly rate during flagellar regeneration (Ludington et al., 2013). In the temperature-sensitive mutant strain fla10 ts , inactivation of kinesin-II motility ceases IFT and leads to resorption of the flagellum at a constant rate (Kozminski et al., 1995;Marshall et al., 2005). At intermediate temperatures, flagellar length correlates strongly with the estimated fraction of active kinesin-II motors in fla10 ts cells (Marshall and Rosenbaum, 2001), indicating that the amount of active kinesin-II limits flagellar growth. The experiments performed under Li + and cycloheximide treatments (Figure 6d) also support the idea that altering the amount When the flagellum is short, IFT trains contain more kinesin-II from the large basal body pool. As flagella elongate, the number of kinesin-II per IFT train decreases because a significant fraction of the kinesin-II unloads at the tip and undergoes diffusion in the flagellar lumen, depleting the kinesin-II pool at the flagellar base. (f) An analogy for kinesin-II loading on IFT trains. Passengers (dynein-1b) travel from the left shore (basal body) to the right shore (flagellar tip) on a boat (IFT trains) with oars (kinesin-II). At the right shore, the passengers get out and walk the boats back to the dock. Oars are left on the water and can only be collected when they randomly float back to the left shore. If the distance between the shores is large, oars build up on the water and are not readily available for new boats at the left shore. DOI: https://doi.org/10.7554/eLife.28606.027 The following figure supplement is available for figure 6: of KAP available for the flagellar compartment positively correlates with the flagellar length and that the equilibrium length is set when KAP gets depleted below a certain threshold at the basal body. We note that the KAP intensity at the flagellar base was lower (34-40%) in Li + and cycloheximide treated cells than in control cells at equilibrium (p<0.0001, Figure 6d, left). Although the reason for this difference remains unclear, it could be due to a reduction of KAP concentration in the cytoplasm or changes in the flagellar disassembly rate under treatment (Wilson and Lefebvre, 2004).
Unlike kinesin-II, IFT components are rapidly recycled to the cell body by dynein-1b and the amount of these components at the flagellar base remains nearly constant as the flagella elongate. Therefore, the abundance of IFT components and dynein-1b at the flagellar base is not limiting to maintain the length, consistent with previous observations that a small amount of IFT complexes and dynein-1b is sufficient to maintain fully grown flagella (Reck et al., 2016;Wang et al., 2009).
Diffusion is also proposed to play a role in setting the length of bacterial flagella (Renault et al., 2017), long polymers made from a single protein flagellin. Similar to the flagellar length control model originally proposed for Chlamydomonas (Levy, 1974), flagellins are injected into the channel of the filament and they diffuse to reach the assembly site at the filament tip, generating a concentration gradient decreasing towards the tip. As the filament elongates, it grows more slowly because it takes longer for the components to reach the tip. In contrast to bacterial flagellin, structural components are carried to the tip by IFT in eukaryotic flagella. In Chlamydomonas, we showed that diffusion of kinesin-II from the tip sets a concentration gradient decreasing towards the basal body, and its return to the flagellar base is delayed as the flagella elongate. This delay limits the amount of kinesin-II available for building longer flagella.
Our model is challenged by studies showing that the kinesin-II mutant strains fla10 ts and fla3 maintain nearly full-length flagella at permissive temperatures although they accumulate significantly lower amounts of kinesin-II in the flagellar compartment (Kozminski et al., 1995;Mueller et al., 2005;Pedersen et al., 2006). Remarkably, fla3 cells exhibit slower flagellar regeneration (Mueller et al., 2005), consistent with our prediction that the lower amount of kinesin-II negatively affects the assembly rate. However, a more recent study showed that fla10 ts flagella contain wildtype levels of kinesin-II at permissive temperatures (Wang et al., 2009). Given these apparent discrepancies, more quantitative approaches will be required to address whether the amount of kinesin-II correlates with flagellar length.
According to the balance-point model, flagella that contain lower amounts of kinesin-II can still maintain nearly full-length if they also have a lower disassembly rate. The studies that reported a reduction in kinesin-II expression in fla10 ts and fla3 cells also noted significantly reduced anterograde IFT frequency and IFT particle subunits in flagella (Mueller et al., 2005;Pedersen et al., 2006). This could negatively affect the disassembly rate because IFT is required for efficiently removing certain axonemal precursors (Qin et al., 2004) and resorbing the flagellum prior to mitosis. Indeed, flagellar resorption before mitosis occurs at a faster rate than flagellar disassembly after inactivation of IFT Pan and Snell, 2005).
The mechanisms that control the expression of IFT components after deflagellation, regulate the exchange of material between the basal body and cytoplasm, and load material onto IFT trains must also play a major role in determining the length of flagella. Several studies have shown that IFT components are upregulated and accumulate in large numbers at the flagellar base after deflagellation (Albee et al., 2013;Lefebvre and Rosenbaum, 1986;Stolc et al., 2005). Additionally, a large pool of IFT components in the cytoplasm partially exchanges with the flagellar pool (Buisson et al., 2013;Engel et al., 2009;Wingfield et al., 2017) because cells can grow half-length flagella after deflagellation under complete inhibition of protein synthesis (Rosenbaum et al., 1969). However, molecular cues that govern these processes remain poorly understood and further studies in mutant cell lines that have abnormally long (Nguyen et al., 2005;Tam et al., 2007) or short flagella may provide new insight for the mechanism of flagellar length control.

Strains and cell culture
The pf18 IFT27-GFP strain was obtained from the Marshall laboratory (University of California San Francisco) after crossing the IFT27-GFP transgene into the pf18 background as previously described (Engel et al., 2009;Qin et al., 2007). The ift20::IFT20-GFP strain (Lechtreck et al., 2009) was obtained from the Lechtreck laboratory (University of Georgia). The fla3::KAP-GFP (Mueller et al., 2005) and d1blic::D1bLIC-GFP (Reck et al., 2016) strains are available from Chlamydomonas Resource Center at the University of Minnesota (RRID: SCR_014960, Minneapolis, MN). The d1blic:: D1bLIC-crCherry KAP-GFP strain was generated as described below. These strains were not authenticated or tested for mycoplasma contamination. Strains were maintained on plates of TAP media containing 1% agar. For light microscopy, vegetative cells were resuspended in liquid TAP media at 22˚C for 24-48 hr and passaged to fresh liquid TAP before introduction into a flow chamber.
Isolation and characterization of the d1blic::D1bLIC-crCherry KAP-GFP strain The D1bLIC-crCherry construct was generated by subcloning a Chlamydomonas codon-optimized version of the Cherry tag into a genomic copy of the D1bLIC gene (Reck et al., 2016). The Cherry tag was amplified by PCR from the plasmid pBR9 mCherryCr (Rasala et al., 2013) and inserted into a unique AscI site located in the last exon of D1bLIC. The D1bLIC-crCherry construct was linearized with BamHI and co-transformed into d1blic (CC-4487) with the selectable marker pSI103 and plated on TAP medium plus 10 mg/ml paromomycin. 960 transformants were picked into TAP media and screened for changes in colony morphology. 84 colonies were further examined by both phase contrast and fluorescence microscopy for rescue of flagellar assembly and expression of Cherry. Isolated flagella from four colonies were analyzed by Western blot for the presence of full-length D1bLIC-Cherry. A single colony was selected for a second round of transformation using the KAP-GFP construct (Mueller et al., 2005) and the plasmid pHyg3 (Berthold et al., 2002) and selection on 10 mg/ ml of hygromycin B. Two out of 96 transformants were identified as positive for both GFP and Cherry by fluorescence microscopy, and western blots of isolated flagella confirmed the presence of both D1bLIC-Cherry and KAP-GFP in the rescued strains. Antibodies used included a rat antibody against Chlamydomonas KAP (Mueller et al., 2005), a mouse antibody against GFP (Covance, Inc., Princeton, NJ), a rabbit antibody against Chlamydomonas D1bLIC (Perrone et al., 2003), and a rabbit antibody against mCherry (Rockland Immunochemicals, Limerick, PA).

Drug treatment
0.34 mM Ca 2+ in TAP media was depleted by adding 0.5 mM EGTA, which resulted in a free Ca 2+ concentration of 1.5 mM. The concentration of free Ca 2+ in the assay buffer as a function of added EGTA was calculated from the Chelator program (http://maxchelator.stanford.edu). For dynein-1b inhibition assays, a final concentration of 100 mM ciliobrevin D was added to the TAP media, and the data was collected within 5-10 minof the treatment.
For cycloheximide treatment, cells were deflagellated by pH shock and cycloheximide was added to a final concentration of 1.5 mg/ml immediately afterwards. Cells were allowed to regrow flagella for 2 hr before fixation and imaging. For Li + treatment, 50 mM LiCl was added to liquid cell suspensions, and cells were incubated for 2 hr before fixation and imaging.

Deflagellation and flagellar regrowth
For imaging the diffusion gradient in live fla3::KAP-GFP cells, we deflagellated cells in TAP media using shear force by rapidly pushing them through a 20G1 ½ syringe. Cells regenerating flagella were imaged in the following hour. For imaging the accumulation of GFP signal at the basal body region and in regenerating flagella, fla3::KAP-GFP and IFT20::IFT20-GFP cells were deflagellated with pH shock by adding 60 ml 0.5 N acetic acid to 1 ml of cells in TAP media, waiting 45 s, and adding 60 ml 0.5 N KOH. Cells were fixed 15, 30, 45, 60, and 75 min after pH shock. Fixation was done by pipetting 200 ml of liquid TAP cell culture onto a poly-lysine treated coverslip for 1 min, then gently treating the coverslip with 4% paraformaldehyde in water for 10 min. Afterwards, the coverslip was treated twice with 100% methanol chilled to À20˚C for 5 min. Coverslips were dipped in water to remove methanol, mounted in a flow chamber with TAP media, and then imaged immediately.

TIR microscopy
A custom-built objective-type TIR fluorescence microscope was set up using a Nikon TiE inverted microscope equipped with a perfect focusing unit, bright-field illumination, and a 100-X 1.49 NA Pla-nApo oil immersion objective (Nikon, Melville, NY). 488 nm and 561 nm solid state lasers (Coherent, Santa Clara, CA) were used for GFP and crCherry excitation, respectively. The angle of incident light was adjusted lower than the critical angle to illuminate a deeper field (~300 nm) near the coverslip surface. The fluorescent signal was recorded by an iXon 512 Â 512 electron-multiplied charge-coupled device (EM-CCD) camera (Andor, Belfast, United Kingdom). 1.5x extra magnification was used to obtain an effective pixel size of 106 nm. Data were collected at 10 Hz. Excitation laser beams were controlled by shutters (Uniblitz, Rochester, NY). Because the CCD image saturates under intense laser illumination of the focused gate beam, shutter timing was synchronized with the camera acquisition by a data acquisition card (NI, USB-6221) to minimize the number of saturated frames in recorded movies. For two-color imaging, GFP and crCherry fluorescence were separated into two channels on a CCD camera using Optosplit II (Cairn, Kent, United Kingdom). To avoid bleed-through between channels, movies were acquired using time-sharing between the 488 nm and 561 nm laser beams, synchronized with camera acquisition at 60 ms frame time. The effective pixel size was 160 nm.

PhotoGate assays
The PhotoGate system was assembled as previously described (Belyy et al., 2017). Briefly, a 488 nm laser beam was split into two paths using a half-wave plate and a polarizer beamsplitter cube. The first path was used for objective-type TIR imaging. The second path was focused (2 MW cm À2 ) to the image plane and steered with a fast piezo-driven mirror (S-330.8SL, Physik Instrumente, Karlsruhe, Germany). The piezo-driven mirror was mounted at a position conjugate to the back-focal plane of the objective to ensure that the tilting of the mirror resulted in pure translation of the focused beam in the image plane. The mirror provided a usable travel range of 30 mm x 30 mm area at the image plane. The mirror's angle was updated via analog output channels of a data acquisition card (National Instruments, Austin, TX, USB-6221) and controlled by software customwritten in LabVIEW.
Flagellar orientation of surface adhered cells was visualized by TIR imaging. Initially, the gate beam was placed at the tip of flagellum and moved along the flagellar orientation to prebleach the distal half of the flagellum. The gate beam was turned off when it was positioned near the base of the flagellum to allow a single fluorescent anterograde train to enter the flagellum. Occasionally (<5%), two anterograde trains overlapped and entered the flagellum simultaneously. The gate beam was then turned on for 0.2 s of every 1 s to bleach other anterograde trains. Based on the size of the gate beam in the image plane, gating frequency was adjusted such that less than 1% of anterograde IFT trains moved faster than the cutoff speed (3.0 mm s À1 ). The trajectories of these trains can be distinguished from each other as they move at different speeds along the flagellum. The locations of flagellar tips were determined by brightfield imaging (data not shown). In two-color photogate experiments, the focused 488 nm laser beam was used to bleach both GFP and crCherry, and 488 and 561 beams were used in a time-sharing mode for TIR excitation.

FRAP assays
FRAP assays on the fla3::KAP-GFP strain were performed by photobleaching the center part of the flagellum (5 mm in length) for 200 ms at 25 kW cm À2 in the epifluorescence mode. The recovery of fluorescence signal in the bleached area was simultaneously monitored by imaging with a 100 W cm À2 TIR excitation. The analysis was performed by measuring the total fluorescence intensity within the bleached area. Fluorescent signal of anterograde transport was manually excluded from the analysis. Thirteen different recovery traces were used in the MSD analysis. The intensity of each trace was normalized according to the initial and final intensity.

Confocal microscopy
fla3::KAP-GFP and IFT20::IFT20-GFP cells were fixed with paraformaldehyde and imaged on a confocal microscope using 488 nm laser excitation (Zeiss, Oberkochen, Germany). Images were recorded with 560 nm z step, 63 nm pixel size, and 1.58 ms photon collection per pixel. Fluorescence in basal body and flagellum was quantified using ImageJ. The ratio of flagellar to basal-body KAP-GFP fluorescence in confocal images was similar to that of live cell imaging under TIR excitation, indicating that the fixation protocol did not result in the loss of diffusing KAP-GFP signal from the flagella.

Data analysis
Anterograde and retrograde trajectories were manually assigned from kymographs. After the arrival of a single anterograde particle at the tip, the departure of fluorescent retrograde trains was determined at single pixel and frame resolution. The tip resting time for each retrograde train was defined as the duration between the arrival of the fluorescent anterograde train and the departure of the retrograde train from the tip. Tip resting time histograms were constructed and fitted to a Gamma function using MATLAB. The Gamma function was defined as G(t) = t a-1 e -lt , where a and l are shape and rate parameters, respectively.
For single particle tracking analysis, the positions of fluorescent spots were determined by a 2D Gaussian fitting algorithm. The positions were fitted throughout the movie except at the frames when the gate beam was on or the frames in which the tracked particle overlapped with other fluorophores. The intensity of the fluorescent spots was estimated by the volume of the 2D Gaussian peak. In a typical assay, we adjusted excitation power to achieve 20 nm localization accuracy at 10 Hz image acquisition rate. Individual GFP particles were tracked for 5 s on average before photobleaching and the diffusion constant was obtained by MSD analysis of individual spots. In certain kymographs, diffusion of individual KAPs within a flagellum could not be resolved due to the diffraction limit.
To determine the distribution of the KAP-GFP background in flagella, anterograde trajectories in kymographs of fla3::KAP-GFP cells were manually removed using custom ImageJ plugins. The remaining pixels were averaged over the kymograph's time axis, giving a time-averaged plot of the KAP-GFP background over the flagellum length. The cells were grouped by flagellar length. The background intensity and flagellum length of each cell were normalized. The average background intensity along the length of the flagellum was calculated for each group of cells.
KAP-GFP efflux from the flagellum was calculated using Fick's law. The slope of the KAP-GFP background over the length of a flagellum was multiplied by the diffusion constant (1.7 mm 2 s À1 ). To calculate KAP-GFP influx, the KAP-GFP background was subtracted from the kymographs. Then, the average intensity of anterograde trains was multiplied by the train frequency (1.3 trains s À1 ) to calculate the influx.
GFP photobleaching rate under TIR illumination was estimated by heavily decorating the coverslip surface with eGFP and calculating the rate of decrease in GFP fluorescence. To estimate the live-cell GFP photobleaching rate in pf18 IFT27-GFP cells, the fluorescent intensities of 94 anterograde trains from 9 cells were quantified at each time point en route to the flagellar tip. Each train's intensity profile was normalized by the mean intensity. The normalized intensity values were plotted against time and fit to a single exponential decay. The decay constant was used as the photobleaching rate.

Monte Carlo simulations
Monte Carlo simulations were performed to test the effect of limited number of GFPs per train and GFP photobleaching in PhotoGate experiments using the pf18 IFT27-GFP strain. Experimentally measured values were used for the velocity and frequency of anterograde and retrograde trains. Simulations assumed that anterograde trains arrive and retrograde trains depart from the tip through a purely stochastic process, adding and subtracting particles to a mixed flagellar tip pool.
We estimated that each anterograde train contains six fluorescent GFPs by comparing the fluorescent intensities of anterograde trains in the pf18 IFT27-GFP strain to those of KAP-GFP spots in the fla3::KAP-GFP strain under the same imaging conditions and calibrating the number of molecules based on previous photobleaching analysis of the fla3::KAP-GFP strain (Engel et al., 2009). Each retrograde train was constructed by a random selection of IFT particles available at the tip. Tip intensity measurements revealed that the signal of the IFT complexes located at the tip is approximately three times brighter than an average anterograde train. The photobleaching of GFPs (0.07 s À1 ) under TIR illumination was accounted for in simulations and trains with at least one fluorescent GFP upon leaving the tip were marked detectable.
Simulations were also run to estimate the distribution of diffusing KAP molecules in the flagellum at a steady-state. In these simulations, previously reported values for the anterograde train injection rate (1.3 trains s À1 ) (Mueller et al., 2005) and the average number of KAP bound to a single anterograde train for each flagellar length (Engel et al., 2009) were used to estimate the number of KAP that arrives at the flagellar tip per second. KAP dissociated from the trains at the tip and immediately started one dimensional diffusion in the flagellum. The resting time of KAP at the tip was insignificant, and was not accounted for. The flagellum was modeled as a 5-12 mm long linear grid with spacing defined as the MSD of KAP diffusing at 1.7 mm 2 s À1 (Figure 3h) during the time-step of the simulation (5 ms). At every time point, each active molecule had its grid position changed by +1 or À1. The molecules at the extreme terminus of the tip only moved towards the base. The diffusing KAP molecules were perfectly absorbed to the cell body as they arrived at the flagellar base (i.e. perfect sink) and exited the simulation. The simulations were run for 100,000 time points to allow molecules to reach a steady-state. The number of molecules at each grid position was calculated to plot the distribution of KAP molecules diffusing along the length of the flagellum. The total number of KAP was calculated by integrating the number of KAP diffusing along the entire flagellum and KAP on the anterograde trains. This number was compared to a hypothetical scenario that KAP returns to the cell body with active transport. The simulations were run 10 times to calculate the error.