SUPPLEMENTARY INFORMATION

Transcription

1 SUPPLEMENTARY INFORMATION Figure S1. Speckle intensities at different concentrations and additional tests of single-fluorophore imaging. (a) Speckle intensity scatter plots for movies shown in Fig. 1a. Each speckle was randomly assigned an identificationnumber (speckle index, horizontal axis). For concentrations 0 and I, scatter plots were first made over the full intensity range (left panel) and then for the range 0 to 500 for comparison with the plots at concentrations II

2 SUPPLEMENTARY INFORMATION to V (right panel). Green and blue lines represent 500 AU and 1000 AU intensity level, respectively. Number of measurements: V:193, IV: 349, III: 3733, II: 6055, I: 3195, 0:191. (b) To confirm that the speckles observed at the low tubulin concentrations (below 0.11 nm) were comprised of single fluorophores, we analyzed intensity changes of individual speckles over time. For speckles with initial intensity ~500AU we consistently observed a single step reduction in intensity of ~500AU, most likely due to single fluorophore photobleaching or blinking (top panel). For speckles with initial intensity of ~1000AU, predicted by our analysis to have two fluorophores, we observed two-step decreases in intensity over time; the magnitude of the decrease in intensity for the first step was ~500AU, followed by a second decrease to the background intensity level, as would be expected for the bleaching of each fluorophore at different times (bottom panel).red arrows indicate when the speckle was no longer detected. (c) As another test of the number of fluorophores in individual speckles at different fluorescent tubulin concentrations, we examined the average speckle intensities within each frame over time. Clustering analysis showed that speckles detected at the lower tubulin concentrations (0.11nM to 0.011nM) were predominantly at the single fluorophore level (average = 98%; n=9 spindles; Table S3). Consistent with this result, average speckle intensity remained ~500AU at these concentrations. In contrast, the average speckle intensities observed for the higher tubulin concentrations (3.3nM to 0.33nM) decayed over time with characteristics that would be expected for a population of multi-fluorophore speckles undergoing sequential bleaching of individual fluorophores in the speckle.

3 SUPPLEMENTARY INFORMATION Figure S. Single-fluorophore imaging revealed heterogeneity in the instantaneous velocity of the poleward movement of single microtubules. (a) Single-fluorophore 3

4 SUPPLEMENTARY INFORMATION FSM image of a spindle with ~0.033nM (concentration IV) of X-Rhodamine labeled tubulin. (b) Multi-fluorophore FSM image of a spindle with ~nm of X-Rhodamine labeled tubulin. (c, e) Speckle trajectories from (a) were color-coded according to their average instantaneous velocity (e) and overlaid on the original image. (d, f) Image in (b) overlaid with trajectories color-coded according to the average instantaneous velocity over the speckle lifetime (f). (e) When the changes in instantaneous velocities over a trajectory are large, the average instantaneous velocity, calculated by dividing the total travel distance by the lifetime of the trajectory, is different from the average velocity, calculated by dividing the head-to-tail distance (i.e. magnitude of the vector shown in red) by the lifetime of the trajectory, the case for (a). In contrast, when changes in instantaneous velocities are small, average instantaneous velocity and average velocity are similar, the case for (b). Bars = 10μm. 4

5 SUPPLEMENTARY INFORMATION Figure S3. Computation details in the generation of microtubule-tracing bands. (a) A D Gaussian filter kernel used for filtering of raw vectors and interpolation in computing the vector field of microtubule flux. The black arrow shows the estimated local average direction of flux at the point of calculation. X-Y: image coordinate system. (b) Construction of the central axes of microtubule-tracing bands. Left panel: Line PQ (in magenta) was drawn approximately at a position reflecting the metaphase plate. Starting points (in cyan) were generated at equal distances. Right panel: central axes (in red) for microtubule-tracing bands, computed by path integration of microtubule flux vector field from the starting points in two directions. (c) For each computed central axis, a spatial band (shown in green lines) of a uniform width was constructed by shifting the central axis (red line) perpendicularly to its left and right by half of the selected band-width. The same width was used to generate all bands. 5

6 SUPPLEMENTARY INFORMATION Figure S4. Detected speckle pairs on single microtubules in control and p150-cc1 spindles. (a) FSM image of a control spindle. (b) FSM image of a p150-cc1 (8uM) spindle. (c) Image (A) overlaid with synchronously moving speckle pairs (connected by randomly colored lines. Number of speckle pairs: 14. (d) Image (b) overlaid with synchronously moving speckle pairs. Number of speckle pairs: 16. Bars: 10μm. 6

7 SUPPLEMENTARY INFORMATION Figure S5. Sensitivity, uniqueness, and robustness of model fitting in determining microtubule length distribution. (a) Sensitivity and uniqueness of fitting using the 6 Rayleigh and exponential models at r = (magenta: exponential fit, blue: Rayleigh fit). Fitting errors against characteristic 1/ or mean ( s ) microtubule length defined for an exponential and Rayleigh distribution, respectively. Sensitivity and uniqueness of the fit are demonstrated by the existence of a global minimum with a sharp increase in fitting error away from the global minimum. (b) Sensitivity and uniqueness of 6 fitting using the left-truncated normal model fitting at r = X: mean of normal distribution. Y: standard deviation of normal distribution. Z: fitting error. A global minimum was detected. 7

8 SUPPLEMENTARY INFORMATION Figure S6. Speckle velocity distribution in a spindle treated with p150-cc1. (a) A representative spindle treated with 8uM of p150-cc1 and imaged with single-fluorophore speckles. (b, c) Trajectories are color-coded based on (c) and overlaid on the original image. Total speckle trajectory number = 147, average instantaneous velocity = 3.97±0.73 μm/min, average (head-to-tail) velocity =.41±0.67 μm/min. Bar: 10μm. Figure S7. Probability density distribution of the distance between a pair of speckles on a microtubule of length l. Inset: arclength parameterization of a microtubule. Only the straight line distance between B and C could be measured in single fluorophore speckle images. However, for the generally low curvature of microtubules, the distribution of the straight line distances is similar to the ones for the full arclength, as shown by an example (the red line), which was the p.d.f. of the straight line distance between two speckles on an arc of length l and curvature /l.. 8

9 SUPPLEMENTARY INFORMATION Supplemental movies Movie S1. FSM time-lapse movie of a control extract spindle imaged at a multiplefluorophore condition (concentration I: 1.1nM). Also shown in Fig. 1a. Movie S. FSM time-lapse movie of a control spindle imaged at a single-fluorophore condition (concentration IV: 0.033nM). Also shown in Fig. 1a. Movie S3. Dual-color FSM time-lapse movie of a control spindle. Movie S4. FSM time-lapse movie of a control spindle imaged at a single fluorophore condition (concentration III: 0.11nM). Notice the fast speckle in the red window that appears in the second half of the movie. It instantaneous velocity reaches ~14.4 μm/min. Movie S5. FSM time-lapse movie showing speckle pairs moving in synchronization. Movie S6. FSM time-lapse movie a spindle treated with 8uM p150-cc1 9

10 SUPPLEMENTARY INFORMATION X-Rhodamine tubulin Label Dilution ratio Concentration (nm) Fraction of labeled tubulin (r*) 0 1 : 10, E-4 I 1 : 30, E-5 II 1 : 100, E-5 III 1 : 300, E-6 IV 1 : 1,000, E-6 V 1 : 3,000, E-7 * Fraction of labeled tubulin in the tubulin pool 6 Supplemental Tables Table S1. Concentrations and fractions of X-Rhodamine labeled tubulin under different dilution ratios 10

11 SUPPLEMENTARY INFORMATION Table S. Initial speckle intensity cluster analysis results: (see Section S1.). The first movie under each concentration (highlighted) is the one shown for that concentration in Fig. 1A (first column). 11

12 SUPPLEMENTARY INFORMATION Table S3. Final speckle intensity clustering analysis results: Initial cluster analysis results in Table S were adjusted according to the strategies discussed in Section S1.. Clusters were sorted in ascending order based on their average intensity and were aligned for fluorophore number interpretation. The number in parenthesis represents percentage of speckles in each cluster. Numbers in bold italic were clusters that could not be merged. The first movie under each concentration (highlighted) is the one shown for that concentration in Fig. 1A (first column). 1

13 SUPPLEMENTARY INFORMATION Supplemental References 1. Yang, G., Matov, A. & Danuser, G. Reliable tracking of large-scale dense particle motion for fluorescent live cell imaging. Proc. IEEE Int. Conf. Computer Vision and Pattern Recognition 3, 138 (005).. Cameron, L. A. et al. Kinesin 5-independent poleward flux of kinetochore microtubules in PtK1 cells. J. Cell Biol. 173, (006). 3. Fraley, C. & Raftery, A. E. Model-based clustering, discriminant analysis and density estimation. J. American Statistical Association 97, (00). 4. Thalamuthu, A., Mukhopadhyay, I., Zheng, X. & Tseng, G. C. Evaluation and comparison of gene clustering methods in microarray analysis. Bioinformatics, (006). 5. Pierce, D. W. & Vale, R. D. in Green Fluorescent Protein (eds. Sullivan, K. F. & Kay, S. A.) 49-7 (Academic Press, 1999). 6. Waterman-Storer, C. M. & Salmon, E. D. How Microtubules Get Fluorescent Speckles. Biophys. J. 75, (1998). 7. Papoulis, A. & Pillai, S. U. Probability, Random Variables, and Stochastic Processes (McGraw- Hill New York, 00). 8. Ohi, R., Coughlin, M. L., Lane, W. S. & Mitchison, T. J. An inner centromere protein that stimulates the microtubule depolymerizing activity of a KinI kinesin. Dev. Cell 5, (003). 9. Do Carmo, M. P. Differential Geometry of Curves and Surfaces (Prentice-Hall, Englewood Cliffs, NJ, 1976). 10. Verde, F., Dogterom, M., Stelzer, E., Karsenti, E. & Leibler, S. Control of microtubule dynamics and length by Cyclin A-dependent and Cyclin B-dependent kinases in Xenopus egg extracts. J. Cell Biol. 118, (199). 11. Kinoshita, K., Arnal, I., Desai, A., Drechsel, D. N. & Hyman, A. A. Reconstitution of physiological microtubule dynamics using purified components. Science 94, (001). 13

14 Supplementary methods Construction of microtubule-tracing bands by path integration of microtubule flux (see main text Fig. ). To generate high-resolution maps of microtubule poleward flux, dense fields of multi-fluorophore speckles in the Alexa-488 channel were imaged and tracked by single particle methods as in 1,. Subsequently, microtubule-tracing bands were generated in three steps: (1) Extraction of raw vectors of speckle displacement from each trajectory: From the trajectory of multi-fluorophore speckle i, represented by a sequence of N points x,1, x,,..., x,, a raw vector was obtained from its displacement every 4 i i i i N i uuuuuur uuuuuur uuuuuur uuuuuuuuur frames, i.e. xi,1 xi,4, xi, xi,5, xi,3 xi,6,..., xi, N! 3 xi, N. The time interval of 4 frames was i i chosen to minimize the influence of limited spatial sampling due to the relatively large pixel size of 160nm. () Anisotropic filtering and interpolation of raw vectors using a D Gaussian kernel: ( x ( cos! + y ( sin! ) () x ( sin! + y ( cos! ) $ % 1 * 1 & '* G( x, y; " u, " v,! ) = exp -) +., #" u" v + " u ", * / v 1 0* (S1) whose major axis was aligned with the local average orientation of the raw vectors (Fig. S3.a). Parameters! u and! v represent the variances along the major and minor axes of the filter, and were chosen to be 0 and 15 pixels, respectively (The average minimum distance between speckles was approximately 5 pixels). Parameter θ denotes the orientation of the filtering kernel. Applying the filter kernel over the image generated a discrete representation of the global microtubule flux that defines 1

15 the orientation and instantaneous velocity of microtubule motion at each pixel within the spindle. (3) Generation of microtubule-tracing bands for the low-density single-fluorophore X- Rhodamine tubulin speckle channel: For each band a starting point S i was defined along a line approximately reflecting the position of the metaphase plate (denoted PQ; Fig. S3.b, left panel). The distance between starting points was adjusted according to the required band-width W. The number of starting points N was determined as N = PQ and rounded to the nearest W integer (Fig. S3.b, left panel). Hence, neighboring bands had approximately 50% overlap. Next, the central axis of the band containing S i was computed by numerical path integration of the flux vector field: Representing the central axis as a sequence of!!! points Pi, M, P,,, 1,...,0(,0),,1,... i i M P i i Pi Pi P!!! i, M, path integration was performed along the i, + microtubule flux vector field V (!) starting from S i in two opposite directions as ( ) ( ) P = P + V P " t, i, k i, k! 1 i, k! 1 P = P! V P " t,!!! i, k i, k! 1 i, k! 1 P = P = S, +! i,0 i,0 i (S) where t is the integration step size (typically chosen to be 0.1), and M i, + and M i,! denote the number of points along and opposite to the flux vector field starting from S i, respectively. The integration was stopped where the vector field was no

16 longer defined (outside the spindle area) or where the central axis reached the boundary of either the image or a user-defined region of interest (Fig. S3.b, right panel). The boundaries of the bands were computed by shifting the central axis half a bandwidth to the left and half a band-width to the right. Half band-width of 1.5,.5, and 3.5 pixels were used for bands of width 480nm, 800nm, and 110nm, respectively (Fig. S3.c). Supplementary Notes S.1 Speckle intensity cluster analysis (1) Model-based clustering of speckle intensities We analyzed the total speckle intensity distribution of each titration experiment movie (total movie number = 18; see examples in main text Fig. 1a) using the model-based clustering technique described in 3. The method classified speckle intensities into different clusters (groups), each of which contained similar intensities that should correspond to the same numbers of fluorophores. The clustering involved two steps: First, optimal approximations of the total intensity distribution were computed based on several different mixture models of normal distributions. Then, the best approximation among these models was selected based on their Bayesian information criterion (BIC) value 3. Hence, no a priori assumptions regarding the number of clusters were imposed on the 3

17 data fitting. Instead, the clustering method determined the number of clusters and the mean and variance of each cluster simultaneously and automatically 3. However, this approach has limitations when applied to speckle intensity analysis. First, the intensity distribution of speckles with the same number of fluorophores may not precisely follow a normal distribution. In this case, the clustering technique may use multiple normal distributions to approximate the intensity distribution of a single class of speckles. Furthermore, since this technique searches for the tightest fit possible to the measured speckle intensity distribution, it can be susceptible to noise and local minima in the optimization, resulting in small or irrelevant clusters. User input is sometimes required to address these issues 4. () Results Cluster analysis results of the 18 movies are summarized in Tables S and S3. For each movie, clusters are sorted by average intensities in ascending order. First, we examined the speckle intensity distribution of the concentration V (0.011 nm) movie in Fig. 1a. Although the distribution was apparently bell-shaped, several normality tests, including the Anderson-Darling test, the Lilliefors test, and the Shapiro-Francia test, rejected a normal distribution at p-value levels much smaller than Consistent with this result, clustering analysis returned a mixture of two clusters (µ±σ: 433±7 AU (8.3%), 616 ±146 AU (17.7%). (Speckle intensities are reported in arbitrary units (AU)). The value in parentheses denotes the percentage of speckle intensities in each cluster 4

18 (total number of measurements n= 193). Imposing a single normal distribution fit returned a cluster of 466±114 AU. Two possible interpretations could explain this clustering result. Although speckles of this movie consisted of the same number of fluorophores, their intensity distribution could not be represented with a normal distribution and therefore the clustering would apply a mixture of two normal distributions to fit the data. Alternatively, the fitted speckle intensity distributions originated from two groups with different number of fluorophores. Since speckles must consist of an integer number of fluorophores, the difference of ~180 AU between the classes would imply that the intensity of a singlefluorophore speckle should be 180 or an integer fraction of 180. No signal at this level was observed in any of the movies (Fig. S1.a). Cluster analysis of a second movie of concentration V returned two groups with (473±140 AU (95.4%), 107±140 AU (4.6%), n=139; Table S), corresponding to the single and double intensity levels of the merged clusters of movie 1. For the third movie, a single cluster was reported (39±96 AU, n =168; Table S). These results suggested that the two normal distributions reported for the first movie were likely from speckles with the same number of fluorophores. Clustering analysis of movies at concentration IV (0.033 nm) returned results similar to those of concentration V, namely a mixture of two normal distributions with mean values 5

19 around 500 AU (Table S). Normality tests also confirmed that none of their total intensity distributions was a single normal distribution. Increase in the concentration to III (0.11 nm) widened the speckle intensity distribution. Cluster analysis of the movie at this concentration in Fig. 1a returned three clusters (Table S). The first two were similar to those of V and IV, at 366±75 AU (4.5%) and 550±13 AU (47.4%). There was also a third cluster at 76±68 AU (10.1%). Cluster analysis of the second movie returned two clusters similar to those of V and IV. For the third movie, there was a small third cluster at 1106±483 AU (.9%) in addition to the two clusters similar to those of V and IV. Further increase in the concentration to II (0.33 nm) generated additional clusters that centered near 1000 AU and 1500 AU. This suggested that the first two clusters with centers near 500 found in movies of concentrations III V represented speckles of the same number of fluorophores, but with an intensity distribution not perfectly normal, hence requiring a mixture of two normal distributions. Further increase in concentration to I (1.1nM) and 0 (3.3nM) caused the disappearance of the two intensity clusters near 500 AU and the appearance of new clusters at higher intensity levels. Considering the ratio of between the average centers of the first two clusters in concentrations I to 0 and the centers of the first clusters in concentrations V to II, we concluded that the quantum intensity of a fluorophore would be 500 AU. Clusters with an intensity centering around 500 AU would consist of single-fluorophore speckles 6

20 and those around 1000 AU of two-fluorophore speckles. Consistent with this supposition, clusters with higher average intensities centered on multiples of 500 AU. Table S3 provides the final clustering results when the two lowest clusters around 500 AU are merged. The relatively wide spread of these clusters likely originated from both the amplified noise of EM CCD cameras and actual intensity fluctuations of speckles. We noticed that there were a small number of clusters whose mean intensities were not multiples of 500 and could not be directly adjusted based on the previous discussion (see Table S, bold italic numbers). However, their mean values were all approximately in the middle between two neighboring clusters whose centers were multiples of 500 AU. Hence, the overlap two neighboring clusters with relatively wide spread was sometime captured by the clustering technique as a third intermediate group. Also, we noticed that the ratio between the intensity levels of single-fluorophore and two-fluorophore speckles was not exactly. This phenomenon was also observed in single fluorophore imaging of, e.g. GFP 5. S. Modeling random incorporation of labeled tubulin and microtubule length distribution (1) Random incorporation of labeled tubulin follows a Poisson distribution. According to the random incorporation model of FSM 6, the probability of incorporation of k labeled tubulin subunits into a microtubule of N tubulin dimers follows a binomial distribution 7

21 " N # P n k $ % r r & k ' k { = } = ( 1! ) N! k, (S3) where r is the fraction of labeled subunits in the tubulin pool 6. There are 165 dimers in 1 µm of microtubule length. Since wavelength of X-Rhodamine fluorescence is at ~60nm while the NA of our microscope objective lens is 1.4, the corresponding Rayleigh diffraction limit is 70nm, which contains about N = 440 tubulin dimers 6. Since the measured speckle pair distances are greater than the diffraction limit (Fig. 3a), N is large for spindle microtubules. Therefore we approximate the binomial distribution by a Poisson distribution 7 : where v k! v v e P{ n = k} =, (S4) k! = N! r. This approximation is important for the subsequent numerical analysis since the probability calculation using Equation (S3) becomes numerically inaccurate under large N. () Multiple-fluorophore speckles are much more likely to be associated with multiple microtubules. Using Equation (S4), we verified this argument using simple calculation from two different perspectives. First, we computed the ratio between the probability of have one fluorophore versus M (M ) fluorophores within the diffraction limit on a single microtubule, { = } { = } P n 1 M! R1 = = M 1 P n M v!. (S5) 8

22 Taking concentration 0 as an example, the estimated fraction of labeled tubulin is 1.3E- 4 (see Table S1). For M =, the ratio R 1 = 34. As M becomes larger, the ratio R 1 becomes even higher. This indicates that on a single microtubule the probability of having multiple-fluorophore speckles is much smaller than that of having single-fluorophore speckles. Although this calculation provides simple verification of the argument, it is performed from the perspective of a single microtubule. A more accurate verification would be to compare the probabilities of multiple fluorophores of a speckle originating from a single microtubule versus from multiple microtubules. However, such comparison requires more detailed knowledge on microtubule organization. Here we show one example. Assuming that there are N microtubules within the diffraction limit and considering the case for a two-fluorophore speckle, the ratio between the probabilities of have microtubules each having a single fluorophore and having one microtubule with fluorophores can be calculated as R 1 CN! v! v ( ) ( ) N! CN ve e = = N! 1! v " v e #! v N! 1 $ %( e ) & '. When N = 5 or N = 10, this ratio is 4 or 9, respectively. This shows that the ratio computed previously for a single microtubule is somewhat an overestimation. Based on electron micrographs of extract spindle microtubules and the protocol adopted in 8, we deducted that the number of microtubules within the diffraction limit is high (likely >10). Therefore, the ratio R is also high. However, due to the different possible combinations, the calculation 9

23 for the multiple microtubule case becomes more complicated for speckles with higher numbers of fluorophores. In summary, based on the previous analysis, we conclude that multiple-fluorophore speckles are much more likely to be associated with multiple microtubules than single microtubules. (3) Distribution of single microtubule length We developed a model that links the steady state length distribution of individual spindle microtubules, denoted f(l), to the distribution of the distances between pairs of speckles on one microtubule (denoted d). This enabled us to test possible models for f(l) and determine their parameters by fitting the model to the experimentally measured distribution of d. The model was developed in four steps: 3.1 Conditional probability of two speckles observable on a microtubule of length l Given a microtubule of length l, the probability of incorporating k labeled tubulin subunits is (see Eq. S4) k k k! c" l" r c l r e P( n = k l) =, (S5) k! where the microtubule length l is measured in micron, and c = 165 dimers/micron. Besides the incorporation of two labeled subunits into a single microtubule, other factors also influence whether these fluorophores are observable as pairs of synchronously moving speckles in the microscope field of view. For example, speckles may disappear 10

24 due to photobleaching or movement away from the focal plane. We modeled these factors using a probability for the event of a pair of speckles to be observable, denoted r!, and made the assumption that r! is equal for all spindle microtubules. In the following, we use A to denote the event of having two speckles on a single microtubule that are observable in the field-of-view of the microscope. From Eq. S5 follows that the conditional probability of A given a microtubule length l is! c" l" r c l r e = r#. (S6) { } P A l 3. Conditional length distribution of microtubules labeled by two speckles Given the probability density function (p.d.f.) of the spindle microtubule length distribution f ( l ), the length distribution of microtubules labeled with two speckles p( l A) can be derived using the Bayes theorem 7 ( ) p l A Substituting S6 into S7, we obtain ( ) p l A 0 ( ) f ( l) ( ) ( ) P A l =, (S7) +! " P A u f u du +#! c" u" r u e 0 ( ) ( )! c" l" r l e f l =, (S8) $ f u du Notice that the unknown probability r! is canceled from this equation. 3.3 Cumulative distribution function of the distance between two speckles on a single microtubule of length l 11

25 To determine the distance distribution of speckle pairs on a microtubule of length l, we parameterized the microtubule by its arc length 9 and denoted distance between the two speckles B and C as d (Fig. S7. inset). The p.d.f. of d given the event A and a microtubule length l was determined as (Fig. S7) (, )! p d l A 1 d " = $ # % l & l '. (S9) The corresponding cumulative distribution function is! d d $ " if d # l P( D < d l, A) = % l l, (S10) $ & 1 if d > l 3.4 Cumulative distribution function of the distance between two speckles on a single microtubule with length distribution f(l) To establish the link between spindle microtubule length distribution and the distance distribution of speckle pairs on the same microtubule, we calculated the cumulative distribution function of speckle pair distances given a microtubule length distribution f ( l ) using the total probability theorem 7 : Based on Eq. S8 and S10, this results in +! ( < ) = ( <, ) ( ) P D d A " P D d l A p l A dl, (S11) 0 ( ) ( ) ( ) ( ) $ d +! " c# l# r " c# l# r + $ " 0 d < d A = +! " c# u# r $ u e f ( u) du P D l e f l dl dl d e f l dl 0. (S1) 1

26 S.3 Numerical computation of the single microtubule length distribution Using Eq. S1, our goal was to determine a distribution f ( l ) given the experimental measurement of P( D d A) < derived from the distances of synchronously moving speckle pairs (see main text). To constrain the search for possible function f ( l ) that fits the experimental data, we tested three existing models of f ( l )(see main text): l (1) Exponential distribution: f ( l) =! e "!#, ( ) 1 l " e s l! s () Rayleigh distribution: f ( l) =, ( ) F l = " e! F l = 1! e! (3) Truncated normal distribution (i.e. 0 1 ( l# µ ) l #! F ( l) = $ e dl 0! " " # l l s l > ): f ( l) 1 ( l# µ ) #! = e,! " To determine the model parameters, we performed an adaptive grid search of the parameter space. For each set of possible parameter values (for distributions (1) and () only one parameter had to be varied), we solved Equation (S1) numerically to obtain a prediction of P( D d A) experimental ˆP ( D d A) <. This prediction was then compared in 50 control points to the <. For the exponential distribution, we searched the range of 1µm to 50 µm (manually measured average spindle pole-pole distance) for the characteristic microtubule length 1, first at a step size 1 µm and then at a refined! 13

27 increment of 0.5 µm near the minimum (Fig. S5a). For the Rayleigh distribution, the same strategy and parameter range were used for searching of the average microtubule length s!. For the truncated normal distribution, a range of 1µm to 50 µm was searched for the mean value µ at an increment of 0.5 µm and for! = 0.1" k " µ where k = 1,..., 0 (Fig. S5b). Sensitivity analysis confirmed that the fitting was sensitive and gave a unique solution of parameters for all three models. After determining the best parameters for these models, we chose the overall best model that gave the smallest fitting error to be the microtubule length distribution. In contrast to previous analyses of microtubule length distributions 10, which required estimation of the parameters of microtubule dynamic instability, our method was dependent on a single parameter r, the fraction of labeled tubulin dimers in the tubulin pool, which we determined to be ! 6 " using an estimated total tubulin pool concentration of 5uM in 11 (see also Table S1). To examine the robustness of our analysis against errors in our estimation of r, we repeated our numerical solution while varying r by two orders of magnitude. The smallest fitting errors were plotted for each model over this range of r in Fig. 3f. Such results confirmed that our numerical solutions were insensitive to variation in r and thus provided robust estimation of the best fitting model parameters. 14