Preparation of Proteins

Tubulin was purified from bovine brain according to [24] and assembled in BRB buffer (80 mM PIPES, pH 6.8, 1 mM EGTA, and 1 mM MgCl₂ plus 1 mM GTP). Bovine brains were obtained from a commercial slaughterhouse in Grenoble. Fluorescent tubulin (Alexa 488-labelled tubulin and Alexa 568-labelled tubulin) and biotinylated tubulin were prepared according to [25]. Recombinant Arabidopsis thaliana MAP65-1 and MAP65-4 were purified as tagged proteins with a His tag at the N and C termini, or GFP at the N terminus and His tag at the C terminus as described by [18]. They were purified on Ni Sepharose columns and stored at −80°C in 10% (v/v) glycerol, 50 mM NaPi, 0.1 M NaCl, and 0.5 mM DTT, pH 7.9.

Total Internal Reflection Fluorescence Microscopy Assays

Assays were done according to [17]. Briefly, assays were performed either in 5 µl final volume between a slide and a coverslip, or in a perfusion chamber (15 µl). Glass was cleaned with rounds of ethanol/water washes, and further silanized using dichloromethylsilan to limit interactions between MTs and the cover glass. GMPCPP-stabilized short MTs were assembled from 10 µM tubulin (3 µM Alexa 568-labelled tubulin, 7 µM biotinylated tubulin) with 0.5 mM GMPCPP in BRB buffer, for 2 hours at 37°C. These short MTs (0.3 µM) were incubated with MAP65-1 (0.1 µM MAP65-1/4) for 10 min at room temperature to generate MT seed bundles. They were then laid on neutravidin-coated slides for 10 min. After two washes with BRB-1%BSA, MT seed bundles were incubated with an elongation mix containing tubulin (17 µM of unlabeled tubulin, 5 µM of Alexa-labeled tubulin), MAP65-1/4 (from 0.1 µM to 1.5 µM), 1 mM GTP, an anti-fading cocktail (2 mg/mL glucose, 80 µg/mL catalase, and 0.67 mg/mL glucose oxydase), and 1.5% BSA (Figure 1A). MT assembly was visualized using an objective-based TIRF microscope (Nikon TE2000-E) and Quantem 512SC camera (Photometrics). Microscope stage was kept warm (32°C) using a warm stage controller (LINKAM MC60). Excitation was achieved using 491 nm and 561 nm lasers (Optical Insigths). Time-lapse microscopy (one frame every 2 s) was performed for 30 min using Metamorph software (Universal Imaging).

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Figure 1. Dynamics of MAP65-1 bundled MTs.

(A). Scheme of the experimental set-up. MT seed bundles consist of short stable fluorescent and biotinylated MTs cross-linked by MAP65. These MT seed bundles are attached to neutravidin-coated coverslips (step 1). Dynamic MTs elongate from the bundle seeds in the presence of fluorescent tubulin and GFP-MAP65 (step 2). (B). Time-lapse of bundles elongating from MT seed bundles in the presence of GFP-MAP65-1 (0.5 µM) observed by TIRF microscopy. Scale bar, 10 µm (C). Top panel: Time-lapse of an elongating bundle (arrowhead) simultaneously observed in the red Alexa 568-tubulin channel (top row) and green GFP-MAP65-1 channel (middle row). Lower row is the merged image. Bottom panel: Kymographs of the elongating bundle highlighted by the arrowhead. Tubulin (red) and GFP-MAP65-1 (green) traces are superimposable, indicating the binding of MAP65-1 is concomitant with MT elongation. (D). Examples of kymographs of MT bundles. Solid lines correspond to MT plus ends that elongate rapidly, and dotted lines correspond to MT minus ends. Schemes on top of the kymographs show the putative organization of MTs in the bundle. The kymograph shown on the left corresponds to a bundle with a large but unknown number of MTs. The right kymograph shows a bundle with two anti-parallel MTs. (E). Length history plots of 3 single MTs in the absence of MAP65-1 (left panel), and 3 MT bundles in the presence of increasing concentrations of MAP65-1 (three right panels). (F). Duration of elongation phases after a rescue event as a function of MAP65-1 concentration. Black dots indicate the mean values. (G). Depolymerization length of MTs in the presence of various concentrations of MAP65-1. (H–I). Estimation of rescue frequencies (F) and catastrophe frequencies (G) of MTs in bundles as a function of MAP65-1 concentration. The slope of the linear fit for catastrophe frequencies is not significantly different from 0.

https://doi.org/10.1371/journal.pone.0056808.g001

MT Nucleation from Axonemes

Sea urchin (Strongylocentrotus purpuratus) axonemes spotted on a coverslip were first mixed for 5 min with 10 µM tubulin at 35°C to initiate MT nucleation and elongation, and then perfused with various concentrations of MAP65-1. MT elongation was recorded on TIRFm as before.

Analysis of the MT Bundle Dynamics with Kymographs

Time-lapse movies were treated with filters (equalize light, low pass and flatten background of Metamorph software) to improve signal/noise ratio. Kymographs of the MTs were generated using Metamorph and analyzed with ImageJ (Rasband, W.S., ImageJ, U. S. National Institutes of Health, Bethesda, Maryland, USA, http://rsb.info.nih.gov/ij/, 1997-2008). In the present study, we considered as bundle all arrays that contain at least 2 distinguishable MTs, as judged by the presence of several MT traces on the kymographs. Kymographs where several MT traces could not be unambiguously distinguished have not been considered as bundles. Elongation/shortening rates correspond to the slope of elongating/shrinking MTs inside the bundles respectively. (+) and (−) MT ends were easily identified on kymographs of single MTs and of bundles containing a low number of MTs (2–3). (+/−) MT ends correspond to fast/slow growing ends (high/low slopes on the kymographs). In complex kymographs that correspond to bundles containing numerous MTs, the traces of individual MTs cannot be follow over long period. For such bundles, rates of MTs were calculated without assigning a specific polarity to the MTs. We considered that the bimodal distribution of rates correspond to (+) and (−) ends, in respect to the bimodal distribution of single MTs (Figure 2C–D, Figure S1A–B; Figure S2B–C; Figure S3C–D).

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Figure 2. Effect of MAP65-1 on the dynamics of individual MTs.

(A). Kymographs of single MTs that elongate in the absence of MAP65-1 (left kymograph), or in the presence of 0.1 µM of GFP-MAP65-1 (right kymograph). In the first kymograph, a single Alexa-488 MT (green) elongates from an Alexa-568 MT seed (red). In the right kymograph, Alexa-568 MT (red) elongates from an Alexa-568 MT seed (red) in the presence of GFP-MAP65-1 (green). The yellow color reveals the binding of GFP-MAP65-1 on the MT. Schemes on top of the kymographs show the orientation of MT ends. Bottom images show the MTs used to draw the kymographs. (B). Length history plots of 3 single MTs over time in the absence and in the presence of 0.1 µM MAP65-1. (C–D). Distribution of elongation rates (C) and shortening rates (D) of single MTs in the absence (top row) or in the presence of 0.1 µM MAP65-1 (bottom row). Data for MT (+) and (−) ends are shown in blue and green respectively. Average rates and population size are indicated. (E). Duration of elongation phases of single MTs after a rescue event in the absence and in the presence of 0.1 µM MAP65-1. Black dots indicate the mean duration of elongation phases. (F–G). Depolymerization length of MTs in the absence and in the presence of 0.1 µM MAP65-1, for MT minus end (F) and MT plus end (G).

https://doi.org/10.1371/journal.pone.0056808.g002

Measurements of the dynamics of MT bundles (duration of elongation, shrinking and elongation length) were extracted from the life history plots of the corresponding kymographs (see examples in Figure 1E and S2D). Traces correspond to the longest MT of the bundle, thus illustrating the dynamic of the whole bundle. Duration of elongation corresponds to the time between rescue and catastrophe events. Length of elongation corresponds to the distance on which MTs/bundles grow between rescue and catastrophe events. Length of depolymerization corresponds to the distance on which MTs/bundles shrink between catastrophe and rescue events. Catastrophe frequency corresponds to the number of catastrophe events divided by the time MTs/bundles elongate and pause. Rescue frequency corresponds to the number of rescue events divided by the time MTs/bundles depolymerize. The length of a bundle corresponds to the length of the longest MT of the bundle. The statistical significance was determined using Student’s t test and non-parametric Kruskal-Wallis test.

Modeling of MT Bundle Growth in the Presence of MAP65-1 and MAP65-4

We first simulated the kinetics of unbundled MTs, including polymerization/depolymerization rates and rescue/catastrophe frequencies to account for the dynamics of MT alone. Then we considered that MAP65 establish bonds between pairs of parallel and/or anti-parallel MTs, thereby modifying the MT bundle growth. Different models for the interactions between either MAP65-1 or MAP65-4 and MT orientation within bundles (parallel or anti-parallel) were studied to account for the average bundle growth observed in TIRF microscopy. See the supplementary material section, Figures S6 and S7 and Tables S1, S2 and S3 for a detailed description of the model.

Dynamics of MTs in MAP65-1/4 Induced Bundles

The main question we asked in this study is whether dynamics of MTs are modified by lateral MAP65 links between MTs as it occurs in bundles. To answer this question, we analyzed the dynamics of MAP65-1 induced bundles. We used an in vitro system to generate bundles of growing MTs (up to 7 MTs) (Figure 1A). First, short stable MTs were bundled by MAP65 in order to generate short stable bundles that were further attached to a coverslip via biotin/neutravidin interactions. In a second step, these short bundles served as seeds to elongate MTs in the presence of tubulin (22 µM) and various MAP65 concentrations. MT bundles formation was imaged in real time using a two-color Total Internal Reflection Fluorescence microscope (TIRFm). This in vitro reconstitution of MT bundles allows the study of their dynamics as units with their own characteristics. Note that in the present study, most of the bundles we observed contained more than 2 MTs. This may be an important difference with previous studies where only small bundles (2–3 MTs) were examined (see [19], [22] for example).

In the assays, knowing that apparent Kd of MAP65-1 for MTs is 0.57 µM ([26]; 1.03 µM as determined in [27]), we used MAP65-1 concentrations ranging from 0.1 µM to 1.5 µM. In the presence of MAP65-1, we observed that MT bundle length increased linearly with time and generated a dense array of MT bundles (Figure 1B, Movies S1 and S2). MAP65-1 accumulates on growing bundled MTs concomitantly with the elongation of MT bundles (Figure 1C). To identify what changes are responsible for this increased assembly, we generated kymographs of bundles (length/time plots; Figure 1D). In agreement with previous observations [18], kymographs revealed a mixed MT polarity in the bundles, confirming that MAP65-1 binds anti-parallel MTs. Length history plots of MT bundles (Figure 1E) show that MT assembly increases with MAP65-1 concentrations. Analysis of these plots revealed that the elongating bundles had two main characteristics. First, the elongation duration of bundled MTs, measured as the time interval between a rescue and a catastrophe event, increased as a function of MAP65-1 concentration (Figure 1F). This MT elongation, is 2.7 min on average in the absence of MAP65-1, but jumps to an average of 6.2 min in presence of 1 µM MAP65-1. Second, MAP65-1 bundling reduced the amplitude of MT depolymerization (Figure 1G). Indeed, in the absence of MAP65-1, half of the MTs depolymerized for at least 5 µm, whereas in the presence of 1.0 µM MAP65-1 half of the bundled MTs depolymerized over 2 µm. This is easily seen in the length history plots of MTs were single MTs depolymerized up to the seed (Figure 1E, left graph), whereas shrinking bundled MTs experienced a rescue before they reach the seed (Figure 1E, three right graphs). In consequence to the limited depolymerization of MTs, the growing front of bundles was composed of MT (+) ends that elongate in close vicinity to each other, in a process we further called coordinated growth. Both, the increase of the elongation duration of bundled MTs and the reduction of the distance over which they depolymerize correlate with the age of the MTs. Indeed MT elongation increases over the whole period (Figure S1C) and the mean depolymerization length decreases with time in the presence of MAP65-1 (Figure S1D). To understand the processes that underline this collective behavior of bundles, we used the kymographs to measure the parameters of the dynamics of individual MTs inside bundles. MT elongation and shortening rates were calculated from the slopes of MT traces (see the right kymograph in Figure 1D for example). We observed that growth and shortening rates of MTs cross-linked by MAP65-1 were similar to those determined for single MTs (Figure S1A and S1B). This suggests that the increased growth of bundled MTs is due to changes in their catastrophe and/or rescue frequencies in comparison with single MTs. We observed that the apparent rescue frequency of individual bundled MTs increases with MAP65-1 concentrations (Figure 1H). We did not experimentally detect a significant change in their apparent catastrophe frequency (Figure 1I). Note that these data have two limitations. First slowly growing MTs such as MT (−) ends were embedded in the center of bundles and were hardly detectable in kymographs (Figure 1D). Therefore it is probable that MT (−) ends are underrepresented in our analysis. Second, bundles in which individual MTs can unambiguously be traced over a long period are seldom, because of the complexity of bundles. This contributes to the large errors bars in Figures 1H and 1I. From all the experimental data we obtained, we conclude that MAP65-1 bundles are characterized by long elongation periods and short depolymerization phases. This collective behavior is correlated the increase of the apparent rescue frequencies of individual MTs inside bundles. This new dynamical regime of the whole bundle amplified with time, such that depolymerization length becomes shorter and shorter as the bundle ages.

We asked whether the new dynamical regime we observed also applies to bundles with a low number of MTs. Since our experimental set-up disfavor the formation of small bundles, we could not collect enough data for reliable statistical analysis. However our measurements indicate no significant correlation between the number of MTs and the bundle growth rate.

The sustained growth of MT bundles was not specific to MAP65-1 induced bundles, as we observed that MAP65-4 bundled MTs have similar dynamics as those bundled by MAP65-1 (Figure S2; movie S3; [17]). Mainly MT elongation/shortening rates are not affected (Figure S2 A-C) and elongation/shortening amplitudes increased/decreased respectively (Figure S2 D-H).

Dynamics of Single MTs in the Presence of MAP65-1

We then asked if the persistent growth of bundled MTs was either due to (i) the binding of MAP65 on the MT, or due to (ii) the MAP65 links between adjacent MTs. To answer this question, we compared the dynamics of single MTs in the absence of MAP65-1 (naked MTs) with the one of single MTs saturated with MAP65-1. Indeed we assumed that single MTs saturated with MAP65-1 are very similar to bundled MTs whose surface is covered with MAP65-1 that cross-link them. In our experimental set-up, maximal coverage of single MTs assembled from 22 µM tubulin was obtained with 0.1 µM MAP65-1. Indeed, when single MTs were polymerized with higher MAP65-1 concentrations, elongation of MTs was impaired and protein aggregation occurred. Therefore it is probable that 0.1 µM did not bind individual MTs with a 1∶1 stoichiometry, as it is observed in bundles [18], [19]. At the concentration of 0.1 µM MAP65-1, we observed that MAP65-1 binds along MTs (Figure 2A), and that length history plots of single MAP65-1 saturated MTs were similar to those of naked MTs (Figure 2B). Analysis of the dynamics of single naked MTs and single MAP65-1 saturated MTs reveals no difference (i) in MT shortening rates (Figure 2D), (ii) in the duration of MT elongation (Figure 2E), and (iii) in the MT depolymerization amplitude (Figure 2F and 2G). MT elongation rates were slightly reduced in the presence of 0.1 µM MAP65-1 (Figure 2C), also this was not observed in the presence of 50 nM MAP65-1 (Figure S3). In correlation with these results, there was no statistical difference between the frequencies of rescue and catastrophe events of naked MTs and MTs assembled in the presence of 0.1 µM MAP65-1 (Table 1). Thus we conclude that MAP65-1 does not affect significantly the dynamics of unbundled MTs.

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Table 1. Frequencies of catastrophe and rescue events of single MTs in the presence of MAP65-1.

https://doi.org/10.1371/journal.pone.0056808.t001

Modeling MT Bundle Dynamics

Our in vitro experimental setup gave only a macroscopic view of the growth of MT bundles. To fully understand the mechanisms that drive the sustained growth of bundled MTs, we should follow individual MTs dynamics inside bundles. In this attempt we set up a microscopic kinetic model in which we could quantify the dynamic parameters of bundled MTs, count the number of MTs in the bundles and correlate their dynamics with MAP65 properties.

In a first step, we simulated the dynamics of MTs that elongate from individual stable seeds using the dynamic parameters extracted from kymographs corresponding to individual MTs observed in vitro (Table 2; Figure 3A–C; Figure S4; movie S1). Results of the simulations are illustrated by kymographs of single MTs, as shown in Figure 3D–E and movie S4. Next, we simulated the assembly of MTs bundled by both MAP65-1 and MAP65-4. To account for the reduction of depolymerization length of bundled MTs observed in vitro (Figure 1G and Figure S2F; [17]), we hypothesized that the MAP65 bonds between MTs in a bundle act as a stop during MT shrinkage. When a MAP65-crosslinked MT undergoes depolymerisation, it shortens until the shrinking end reaches a MAP65. At this stage, either the MAP65 bond is removed, and MT depolymerization continues, or the MAP65 bond resists and MT depolymerization stops. The resistance of MAP65 bonds to depolymerization relies on multiple parameters such as the affinity of MAP65 for MT, the affinity between MAP65 dimers, the structural conformation of MAP65, or the density of MAP65 molecules on MTs. However, this study and available data from literature are not sufficient to test all these parameters independently. Thus we considered a lumped parameter to model the resistance of a MAP65 to MT depolymerization (Figure 4A). In the model, a MAP65 bond has a probability pR to be removed by a depolymerizing MT, and a probability (1-pR) to resist MT depolymerization and stop it. In addition, we consider that MAP65 connecting anti-parallel or parallel MTs inside a bundle are removed with probabilities pR_ap and pR_p, respectively (Figure 4B). Thus in our model the amplitude of MT depolymerisation depends on the MAP65 sensitivity to MT depolymerization (Figure 4C). On one hand, low pR_ap (or pR_p) (close to 0) limits the depolymerisation to short distances. On the other hand, with high pR_ap (or pR_p) (close to unity), MT-MT MAP65 bonds are easily removable and depolymerization extension is almost independent of the presence of MAP65. We simulated the MT dynamics in MT bundles for different values of pR_ap and pR_p, and for different numbers of MTs in the bundles. The accuracy of the model is evaluated by the difference between the expected maximal MT bundle length given by the model and the MT bundle length observed in vitro over a period of 20 minutes (Figure 5B, F and H). The distance between experiment and model is represented as a color map, and is explained in Figure S6. We estimated pR_ap (or pR_p) and the number of MTs in bundles as the parameter combination that minimizes this error for all tested MAP65 concentrations.

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Figure 3. Modelisation of the dynamics of individual MTs.

(A). Scheme of a dynamic MT (green) elongating from a stable MT seed (red). The different parameters of MT dynamics are (i) growth rates at (+/−) ends (V_G⁺/V_G⁻), (ii) shrinkage rates (V_s⁺/V_s⁻), (iii) catastrophe/rescue frequencies at MT (+) ends (f_res⁺/f_cat⁺) and (−) ends (f_cat^−/f_res⁻). (B). Experimental kymograph of an individual MT fluctuating away from the seed (dark band at the kymograph center). Scheme on right of the kymograph shows the orientation of MT ends. (C). History plots of two individual MTs observed by TIRFm. Blue and green traces correspond respectively to MT (+) and (−) ends. (D). Kymograph of two simulated independent MTs elongating from a seed (red). MT (+) ends are in blue; MT (−) ends are in green. (E). Corresponding fluctuation plots over time (same code color as in C).

https://doi.org/10.1371/journal.pone.0056808.g003

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Figure 4. A microscopic model for the growth of MTs in bundles.

(A). Rationale used to model the effect of a MAP65 bond on MT depolymerization. Stable MT seeds are in red, dynamic MTs are in green. For sake of simplicity, only one pair of MTs cross-linked by 3 MAP65 (bars) is shown. The upper MT end undergoes a catastrophe event (left panel) and MT depolymerizes until it reaches a MAP65 bond (shown in red) at the end of the cross-linked MT (middle panel). At this stage, the MAP65 either detaches from MT with probability pR (right, top panel), or stays bound to the MTs with a probability (1-pR) (right, bottom panel). In the first case, the MAP65 bond is removed and the MT continues to shrink. In the second case, the MAP65 bond resists MT depolymerisation, which stops. (B). During depolymerization, MAP65 (black bars) detaches from anti-parallel MTs with a probability pR_ap, or detach from parallel bundled MTs with a probability pR_p. The color code is the same as in (A). (C). Effect of the value of pR_ap and pR_p on the amplitude of MT depolymerization. The upper MT end undergoes a catastrophe event and MT depolymerizes (left panel) before it reaches the end of a cross-linked MT (right panel). At low pR_ap or pR_p (top panel), most of the MAP65 molecules stay bound to the MTs. Therefore MT depolymerization is stopped at the vicinity of the end of the adjacent MT (black broken line). If pR_ap or pR_p is high (labile MAP bonds; bottom panel), MT depolymerization may persist behind the end of a cross-linked MT, thus generating short bundles (red broken line).

https://doi.org/10.1371/journal.pone.0056808.g004

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Figure 5. Growth of MTs bundles is dependent on the lifetime of MAP65 links.

Results of MT growth simulation in the presence of MAP65-4 (A-E) and MAP65-1 (F-K). (A). Diagram showing the predicted maximal length of MT bundles that elongate for 20 min in the presence of 0.25 µM MAP65-4, as a function of the number of MTs in the bundle (horizontal axis) and removal probability pR (vertical axis). Predicted bundle length (µm) is coded by the color bar on the right. Black dot indicates the conditions at which predicted and experimental bundle have the closest lengths (explained in Figure S6). (B). Diagram of the error between calculated and measured maximal bundle length for different combinations of the number of MTs in the bundle (horizontal axis), removal probability pR (vertical axis), and for all available MAP65-4 concentrations. The error (µm) as coded by the color bar on the right, presents a marked minimum for a number of MTs above 10 MTs/bundle and a removal probability pR about 0.7. (C). Experimental kymograph of MTs (green) bundled by 0.25 µM MAP65-4. White plain lines indicate MT (+) ends; yellow dotted lines indicate MT (−) ends. (D–E). Kymographs of simulated bundles showing the dynamics of MTs (D) and the MAP65-4 binding (E) in the same conditions as in (D). The blue color represents the MAP65-4 binding wave as the MT elongation progresses. (F). Diagram of the error between calculated and measured maximal length of bundles, for different combinations of pR_ap and pR_p. Simulations were made with MAP65-1 concentrations ranging from 0.1 µM to 1.5 µM, and the number of MTs was kept fixed at 10. (G). Predicted maximal bundle length for different combinations of the MT number in the bundle and removal probabilities of MAP65-1 connecting parallel MTs (pR_p). The diagram was obtained using a MAP65-1 concentration of 0.5 µM and removal probabilities pR_ap in the range [0, 0.5]. (H). Diagram of the error between calculated and measured maximal bundle length for different combinations of the number of MTs in the bundle (horizontal axis) and removal probability from parallel MTs pR_p (vertical axis). We used MAP65-1 concentrations in the range from 0.1 µM to 0.5 µM and the removal probabilities of MAP65-1 connecting anti-parallel MTs pR_ap were taken in the interval [0, 0.5]. The error as coded by the color bar on the right, presents a marked minimum for a number of MTs above 10 MTs/bundle and a removal probability pR_p around 0.9. (I). Experimental kymograph of MTs (green) bundled by 1 µM MAP65-1. White plain lines indicate MT (+) ends. Note that (−) ends are buried in the kymograph. (J–K). Kymographs of simulated bundles showing the dynamic of MTs (F) and the MAP65-1 binding (G) in the same conditions as in (E). The blue color represents the MAP65-1 binding wave as the MT elongation progresses.

https://doi.org/10.1371/journal.pone.0056808.g005

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Table 2. Experimental values used to simulate the dynamics of individual MTs.

https://doi.org/10.1371/journal.pone.0056808.t002

MT Polarity Control Bundle Growth

We first consider a simple situation in which the polarity of bundled MTs is not a discriminant parameter to control bundle growth. This should be the case for bundles that elongate in the presence of MAP65-4, as MAP65-4 randomly cross-links parallel and anti-parallel MTs [17]. In this situation, we impose that pR_ap and pR_p have the same value, pR. Our model was sufficient to generate MT bundle whose lengths were comparable to those observed experimentally for different MAP65-4 concentrations (Table 3). We determined that the combination of at least 6 MTs with a pR of 0.7 gave the best match between the model and the experiments (Figure 5B). If pR <0.7, then the predicted MT length is larger than those measured in vitro (Figure 5A). Using these parameters (pR = 0.7; 10 MTs), predicted kymographs of MT bundles are very similar to their experimental counterparts (Figure 5C–E; movie S5). Note that kymograph similarity is measured by the difference between measured and simulated bundle length (Figure S6). They clearly show that bundles have a sustained growth, and that depolymerization phases are short. Kymograph of bound MAP65-4, given in Figure 5E, illustrates the residence time of MAP65-4 on bundled MTs. This kymograph shows that MAP65-4 accumulates in the bundles as MTs elongate, although MAP65-4 bonds are labile. Altogether these data are in agreement with recent experimental data that indicated the non-selectivity for MT polarity of MAP65-4 [17].

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Table 3. MT length in the presence of MAP65-4.

https://doi.org/10.1371/journal.pone.0056808.t003

We next ask how MT orientation inside bundles affects the growth of the bundles induced by MAP65-1. Since previous studies have shown that MAP65-1 strongly selects anti-parallel MTs [18], we impose that pR_ap is independent from pR_p. In a first step, we assumed that MAP65-1 connects anti-parallel MTs only (i.e. pR_p is set to 0). Using this hypothesis, we observed that the maximal MT length in the bundle is systematically underestimated by the model (Table 4), resulting into a large error. Because MTs coupling comes in pairs, the growth of MT ends by MAP65-1 is limited by the growth rate of the slowest growing MT end of the pair, i.e. the minus end in anti-parallel MT pairs. Thus we relaxed the assumption that MAP65-1 forms anti-parallel MT pairs only, and we introduced the possibility that MAP65-1 makes bonds between parallel MTs (i.e. pR_p ≠ 0, Figure 4A). To evaluate the respective effects of MAP65-1 links between parallel MTs versus anti-parallel MTs, we simulated the growth of bundles of 10 MTs for different combinations of pR_ap and pR_p. As before, we compared the maximal length of simulated bundles to the length of experimental MT bundles. Computed errors for all MAP65-1 concentrations revealed that the best fit was obtained for high pR_p (∼0.8) and low pR_ap (∼0.3) (Figure 5F). This result indicates that MAP65-1 bonds between parallel MTs are easily removed during MT depolymerization. It also suggests that although MAP65-1 bonds between parallel MTs are rather loose, they have a major effect on the length of the MT bundle. This makes sense as bonds between parallel MTs allow (+/+) MT ends connections that can readily elongate. If these bonds were absent or were too labile (pR_p close to 1), MT bundles would be shorter than those observed in vitro (Table 4; Figure 5F). If they were too stable (low pR_p), then MT bundles would be too long. In a second step, we varied the number of MTs and pR_p, and we calculated the length of MT bundles for a fixed pR_ap value chosen in the interval [0, 0.5]. Simulations were carried out for different MAP65-1 concentrations (0.1 µM; 0.15 µM; 0.5 µM) (Figure 5G; see also Figure S5A for a systematic evaluation of the bundle dynamics for different pR_ap). Best parameter fits were obtained for simulated bundles with more than 6 MTs and high pR_p (around 0.9) (Figure 5H), whatever the actual value of pR_ap or the concentration of MAP65-1. This confirms that MAP65-1 bonds between parallel MTs are labile (high pR_p); conversely, the error rapidly increases for low pR_p (Figure 5H) because the simulated MTs are too long compared to the experimental ones (Figure 5G). These data corroborate the hypothesis that bonds between parallel MTs have a strong effect on MT length. In bundles having more than 6 MTs, this property is independent of the sensitivity of MAP65-1 links between anti-parallel MTs (pR_p; Figure S5B), and of MAP65-1 concentration (Figure S5C). The predicted kymograph of MAP65-1 cross-linked MTs (Figure 5J, Movie S6) is similar to the experimental one (Figure 5I; Movie S2). This kymograph shows that leading MT (+) ends control the size of the bundle. Although MAP65-1 bonds can be easily removed, as indicated by the blue isolated segments (Figure 5K; movie S6), their effect is sufficient to protect parallel MTs from large depolymerization. Depolymerization of MT (+) ends is also blocked by MT (−) ends, as rescue events occurred in the vicinity of the MT (−) ends (Figure 5J).

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Table 4. MT length in the presence of MAP65-1.

https://doi.org/10.1371/journal.pone.0056808.t004

To validate that MAP65-1 has the ability to bundle parallel MTs as required by the model, we nucleated MTs from axonemes, thus creating an array of close parallel MTs. In the absence of MAP65-1, nucleated MTs radially organize from the axonemes, whereas in the presence of MAP65-1, they form a thick bundle (Figure S5D). Thus MAP65-1 also binds parallel MTs in vitro. Furthermore, we performed FRAP experiments on MAP65-1 mediated bundles, containing either parallel and anti-parallel MTs, or parallel MTs only (axoneme-nucleated MTs bundled with MAP65-1). Mean half-time recovery of MAP65-1 on parallel MTs was 25.4 sec (from 3.8 sec to 61 sec; N = 18), whereas it varies from 3.5 sec to 231 sec (N = 29) on bundles of mixed MT polarity. The range of half-time recovery, especially for bundles of mixed MT polarity, may result from the variability in the number of MTs present in each bundle, as this parameter influences the diffusion of MAP65-1 molecules between MTs. Nevertheless this observation suggest that MAP65-1 cross-links between parallel MTs are labile. These observations are in agreement with a recent study showing that the dwell-time of MAP65-1 on parallel MTs is larger than its dwell-time on anti-parallel MTs [27]. Altogether these data demonstrate that in bundles, MAP65-1 binds to both parallel and anti-parallel MTs. But the MAP65-1 links between parallel MTs are more sensitive to MT depolymerization than those between anti-parallel MTs. The stability of MAP65-1 bonds between parallel and anti-parallel MTs control the length of MT bundles.

MT Dynamics Inside Bundles

To get further insight in the dynamics of MTs in bundles, we computed the distribution of polymerization/depolymerization amplitude and the rescue/catastrophe frequencies in different conditions. We used the best-fit parameters obtained for MAP65-1 (pR_ap = 0.1 and pR_p = 0.8) and for MAP65-4 (pR_ap = pR_p = 0.7). In addition, we considered a hypothetical MAP, denoted MAP-X, with parameters pR_ap = 0.8 and pR_p = 0.1; note that MAP-X represents the “symmetric” of MAP65-1. Finally, we also simulated control conditions for which pR_ap = pR_p = 1, i.e. the MAP has no effect on MT depolymerisation. Bundle growth was simulated for a period of 20 min with 10 MTs in the bundle. We used 20 independent model runs, yielding an average of 10,000 events for each distribution curve. We found that in the presence of MAP65-1, MAP65-4 or MAP-X, the polymerization amplitude of bundled MTs was enhanced for both (+) and (−) MT ends (Figure 6A, left column). In marked contrast, the depolymerization amplitude was greatly reduced for both ends (Figure 6A, right column). These results show that the 3 MAP we tested affect the dynamics of MTs in bundles. This is in agreement with the growth of a whole bundle as observed at the microscopic level in vitro assay (Figure 1 and Figure S2).

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Figure 6. Model predictions for MT dynamics in bundles in the presence of MAP65.

Simulations were performed with MAP65 binding rates of k_on = 10 µM.s⁻¹, k_off = 0 s⁻¹, and MAP65 concentration of 0.1 µM; the number of MTs in the bundle is 10. The MAP65 removal probabilities are, for MAP65-1, pR_ap = 0.1 and pR_p = 0.8, for MAP65-4, pR_ap = pR_p = 0.7, and for MAP-X pR_ap = 0.8 and pR_p = 0.1. In marked contrast with MAP65-1, the hypothetical MAP-X favors pairs of parallel MT (low pR_p and high pR_ap). In control conditions, we have pR_ap = pR_p = 1. Each distribution curve corresponds to 20 independent model runs. (A). The distribution of polymerization length (left column) or depolymerization length (right column) is shown for all (+, top row) and (-, bottom row) MT ends in the bundle. The inset shows the depolymerization of the control bundle. Note the change in the scale of the abscissa axis. (B). Average distance between the longest (leader) MT and the shortest MT (last MT follower) (L_max−L_min) in the bundle. (C). Average distance between the leader MT and the next follower MT (L_max−L_follow). (D). Cartoon showing how (L_max−L_min) and (L_max−L_follow) are defined. Note that the identity of the leader and follower MTs can change in the course of time. The seed and the dynamic section of each MT are shown respectively in red and in green.

https://doi.org/10.1371/journal.pone.0056808.g006

To characterize the growth regime of bundles, we plotted the distance between the longest (L_max) and the shortest MT (L_min) in a bundle during its elongation (Figures 6B and 6D). In control conditions, this distance (L_max−L_min) increased slowly before reaching a plateau (∼8 µm), approximately 10 min after the initial rise (Figure 6B, black curve). The existence of a plateau indicates a steady-state regime characterized by the exact balance between depolymerisation and polymerization. This is related to the distribution of polymerization and depolymerization lengths of MT (+) ends, that both peak at about the same value (Figure 6A, black curves, top row). In contrast, the presence of MAP bonds (from MAP65-1, MAP65-4 or MAP-X) yields to a sustained linear increase of the (L_max−L_min) distance (Figure 6B, color curves). This indicates that polymerization and depolymerisation are no more balanced inside the bundle. This observation is coherent with the distribution of polymerization and depolymerisation lengths, since their maxima occur, respectively, at ∼5 µm (polymerization, Figure 6A, top, left, color curves) and at ∼0.08 µm (depolymerisation, Figure 6A, top, right, color curves). In consequence, the average MT polymerization is favored. To further understand the dynamics of the bundle extremity, we considered the distance between the MT leader (L_max) and the second MT follower (L_follow), (Figure 6C and 6D). In control conditions, this distance (L_max−L_follow) is very similar to (L_max−L_min), (compare black curves, Figure 6B and 6C) showing that all the MTs are at steady state, once the initial phase has ended. In presence of MAPs, this distance (L_max−L_follow) raises slowly before reaching a plateau, which is almost identical for all MAPs, and which is much smaller than the plateau observed in control conditions (about 0.8 µm vs. 3 µm for control). We conclude that, in presence of MAPs, the two closest MT ends forming the bundle tip are in a “bound” regime, characterized by a highly coordinated growth.

The reduction of the amplitude of MT depolymerization by MAP65 should induce an increase of their rescue frequencies. Indeed the model shows that in bundles, rescues are more frequent in the presence of MAP65, at both (+) and (−) ends (Figure 7A, compare black curve vs. color curves). These data are coherent with our experimental observations (Figure 1H). Interestingly, the model predicts a bimodal distribution for rescue frequencies at MT (+) ends (Figure 7A, top, color curves). The model gives a frequency of 2.5 rescue events.min⁻¹ for anti-parallel bundled MTs, and a frequency comprised between 4.3-4.8 rescue events.min⁻¹ for parallel bundled MTs. Moreover this bimodal distribution is observed for all MAP65, including MAP65-4, which has no selectivity for MT polarity. This implies that the differences in rescue frequencies may rely on the intrinsic dynamic properties of (+) and (−) MT ends, and not on the properties of MAP65 bonds. The model also predicts that catastrophe frequencies are decreased in the presence of MAP65 at both ends of the MTs (Figure 7B). Thus the combination of reduced catastrophe and increased rescue frequencies results into long polymerization periods and short depolymerization phases allowing MT bundles to grow steadily. Noticeably, the model predicts that MAP65-4 and MAP-X have a stronger effect than MAP65-1 (compare blue and green curves with red curves in Figures 6 and 7). Because MAP65-4 and MAP-X favor the existence of bonds between parallel MTs, these results reinforce the hypothesis that parallel bundled MTs control the growth of the bundles.

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Figure 7. Model prediction for catastrophe and rescue frequencies in the presence of MAP65.

Parameters for simulation are given in Figure 6. The distribution of rescues (A) and catastrophe (B) frequencies is shown for the plus (top row) and the minus (bottom row) MT ends in the bundle.

https://doi.org/10.1371/journal.pone.0056808.g007