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.
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).
Table 1.
Frequencies of catastrophe and rescue events of single MTs in the presence of MAP65-1.
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 (VG+/VG−), (ii) shrinkage rates (Vs+/Vs−), (iii) catastrophe/rescue frequencies at MT (+) ends (fres+/fcat+) and (−) ends (fcat−/fres−). (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).
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 pRap, or detach from parallel bundled MTs with a probability pRp. The color code is the same as in (A). (C). Effect of the value of pRap and pRp 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 pRap or pRp (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 pRap or pRp 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).
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 pRap and pRp. 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 (pRp). The diagram was obtained using a MAP65-1 concentration of 0.5 µM and removal probabilities pRap 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 pRp (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 pRap 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 pRp 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.
Table 2.
Experimental values used to simulate the dynamics of individual MTs.
Table 3.
MT length in the presence of MAP65-4.
Table 4.
MT length in the presence of MAP65-1.
Figure 6.
Model predictions for MT dynamics in bundles in the presence of MAP65.
Simulations were performed with MAP65 binding rates of kon = 10 µM.s−1, koff = 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, pRap = 0.1 and pRp = 0.8, for MAP65-4, pRap = pRp = 0.7, and for MAP-X pRap = 0.8 and pRp = 0.1. In marked contrast with MAP65-1, the hypothetical MAP-X favors pairs of parallel MT (low pRp and high pRap). In control conditions, we have pRap = pRp = 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) (Lmax−Lmin) in the bundle. (C). Average distance between the leader MT and the next follower MT (Lmax−Lfollow). (D). Cartoon showing how (Lmax−Lmin) and (Lmax−Lfollow) 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.
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.