Spatiotemporal organization of branched microtubule networks

To understand how chromosomes are segregated, it is necessary to explain the precise spatiotemporal organization of microtubules (MTs) in the mitotic spindle. We use Xenopus egg extracts to study the nucleation and dynamics of MTs in branched networks, a process that is critical for spindle assembly. Surprisingly, new branched MTs preferentially originate near the minus-ends of pre-existing MTs. A sequential reaction model, consisting of deposition of nucleation sites on an existing MT, followed by rate-limiting nucleation of branches, reproduces the measured spatial profile of nucleation, the distribution of MT plus-ends and tubulin intensity. By regulating the availability of the branching effectors TPX2, augmin and γ-TuRC, combined with single-molecule observations, we show that first TPX2 is deposited on pre-existing MTs, followed by binding of augmin/γ-TuRC to result in the nucleation of branched MTs. In sum, regulating the localization and kinetics of nucleation effectors governs the architecture of branched MT networks.

5 experimentally ( Fig. 1-supplement 3A). The sequential reaction model also results in branched 151 networks that resemble those observed in experiments (Fig. 1D). Three realizations out of 152 thousands of simulations are displayed in Fig. 1-supplement 3B and Movie S4. 153 154 Measuring the first branching events in branched microtubule networks 155 To characterize the spatial organization of MTs in branched networks and distinguish between 156 the single-step versus the sequential models, we measured the position of the first branching 157 nucleation event on each mother MT (Fig. 2-supplement 1A). We find that the first branching 158 nucleation event is more likely to occur from older lattice regions near the minus-end of the 159 mother MT (blue curve in Fig. 2A-B and Fig. 2-supplement 1B), supporting our previous visual 160 observation (Fig. 1A). Surprisingly, not a single nucleation event was observed in the region 2.1 161 µm from the plus-end of the mother MT (n=381 measurements), resulting in a dead-zone for 162 branching near the plus-end. Most branching events occurred 5-15 µm away from the mother's 163 plus-end ( Fig. 2A, blue curve). We used a non-dimensional measure of this bias in branch 164 location by dividing the distance between the branching site and the mother's minus-end by the 165 total length of the mother MT at the time of branching. The probability of branching as a 166 function of this rescaled distance decreases sharply from its highest value near the mother's 167 minus-end to zero at the mother's plus-end (Fig. 2B, blue curve). 168 We next compare these probability distributions using the two different computational 169 models ( Fig. 2A-B). The single-step model does not display an exclusion zone near the plus-end 170 ( Fig. 2A, red curve) or a non-dimensional bias (Fig. 2B). In a single reaction step that includes 171 nucleator binding and instantaneous branch formation, branches are equally likely to occur 172 anywhere on the mother MT. In contrast, the sequential model recapitulates the bias in branch 173 location from older lattice near the minus-end and resulting exclusion of the plus-ends ( Fig. 2A-174 B, green curves), as more nucleation sites deposit on older lattice while the mother's plus-end 175 continues to grow in the time it takes on average for to nucleate a branch from the deposited site. 176 Is branched network architecture sensitive to the parameters in the sequential model? By  177 changing the dimensionless ratio of the branching rate constant to the effective binding rate 178 constant " # $%&'() *#$+', -./ 0 derived in Appendix 1, we find that the bias is present when the branching 179 rate is slower than the binding of nucleators . Further decreasing the ratio 180 of rates does not result in a more pronounced bias because the relative profile of deposited 181 nucleation sites remains unchanged. However, when the second reaction step is fast and no 182 longer rate-limiting (Fig architectures and is not sensitive to chosen parameters. 185 Our simulations further show that the minus-end bias persists for every subsequent 186 branching event in a dense network, similar to the first nucleation event, and broadly 187 characterizes branched MT networks (compare Fig. 2-supplement 2D-E with Fig. 2A-B). In 188 conclusion, the sequential reaction model recapitulates the spatial nucleation profile that we 189 measured experimentally, whereas the single-step model does not.

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Architecture of branched networks at high microtubule density 192 To study how branched networks evolve over time, we next characterized the network 193 architecture for large branched networks. By measuring the position of nucleation sites using our 194 simulations, we observed that minus-ends are typically located closer to the origin of the network 195 (defined as the minus-end of the first MT) in the sequential model than in the single-step model 196 (Fig. 2C). Measuring the position of plus-ends as well as the tubulin intensity shows that the total 197 MT mass and plus-ends are also closer to the origin in the sequential model ( Fig. 2D-E). 198 Is either organization reflected in our experimental networks? The MT plus-ends and 199 tubulin intensity profile in our experimental networks (Fig. 2-supplement 2) are distributed 200 closer to the origin (Fig. 2D-E, blue), in striking agreement with the sequential model ( Fig. 2D-201 E, green). We conclude that the sequential model recapitulates the spatial architecture of 202 branched networks, and branching results in origin-biased MT organization due to higher age of 203 those MT lattice regions (Fig. 2F). 204 Interestingly, networks simulated by the two models do not change their overall 205 architecture over time such that the normalized minus-end, plus-end or tubulin intensity 206 distributions remain unchanged with time as the MT networks grow (Fig. 2-supplement 3A-C). 207 This suggests that branched networks are self-similar in time and maintain their architecture, 208 which is a key characteristic of fractal structures (Meakin, 1990). Can this feature be observed in 209 our experimental networks too? Measuring these distributions experimentally at early and late 210 time-points also shows evidence of self-similarity (Fig. 2-supplement 3D-E). Taken together, our 211 data suggests that branched MT networks are self-similar in time, where branching events occur 212 via a sequential, autocatalytic reaction scheme.

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Concentration of TPX2 and augmin determine the branching nucleation profile 215 We next asked if the known branching effectors, TPX2 and augmin, participate in the rate-216 limiting steps of our sequential model (Fig. 3). We reasoned that if the unimolecular binding rate 217 of augmin or TPX2 to branched networks underlie the two steps in our sequential model, the net 218 branching nucleation rate can be altered by proportionately varying the bulk concentration of 219 these two effectors in Xenopus egg extracts. We first modified the concentration of TPX2 by 220 immunodepleting to 20% of the endogenous concentration or adding recombinant TPX2 protein 221 at 9.6-fold excess (Fig. 3A, supplement 1A-B and Movie S5). In parallel, we partially 222 immunodepleted the augmin complex to 20% of the endogenous concentration in Xenopus egg 223 extracts (Fig. 3A, supplement 1C and Movie S5). We observed that branching was delayed with 224 a decrease in concentration of augmin or TPX2 and accelerated with TPX2 addition (Movie S5). 225 Strikingly, TPX2 concentration determines the rate of nucleation in our networks  supplement 1D). 227 To quantitatively compare these experimental perturbations with the equivalent variation 228 in rate constants, we measured the position of the first branching event on a mother MT (Fig. 229 3B). The distance of the first branching site from the mother MT's minus-or plus-end increased 230 with decreasing TPX2 or augmin to 20% endogenous concentration (red and yellow curves, Fig.  231 3B, top and middle panels). This variation in the nucleation profile quantitatively agrees with the 232 predictions from our model when the binding or branching rate constants, kbind and kbranch, were 233 decreased to 20%, because the mother MTs grow longer before a branching event occurs (orange 234 curve, Fig. 3B, top and middle panels). Similarly, increasing the concentration of TPX2 to 9.6-235 fold decreases the distance between nucleation site and mother MT's minus-or plus-end, which 236 quantitatively compares with equivalent increase in kbind or kbranch (green curve, Fig. 3B, top and 237 middle panels). Finally, our model predicts that the non-dimensional spatial bias remains 238 unaltered upon varying the rate constants by 5-10 fold, which was reproduced in experimental 239 profiles upon equivalent change in concentration of TPX2 or augmin (Fig. 3B,  followed by the binding of augmin/γ-TuRC prior to nucleation of branch MT from the mother 277 MT.

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Measuring the TPX2 binding rate to microtubules in Xenopus egg extracts 280 To further assess TPX2's role in depositing the branch nucleation sites, we measured the binding 281 rate of TPX2 to individual MTs in Xenopus egg extracts during formation of branched networks. 282 We hypothesized that TPX2 binds to the MT lattice significantly below lattice saturation 283 resulting in preference towards the older regions of the MT lattice near the minus-ends, 284 analogous to the spatial profile of branching effector 1 in our sequential model ( Fig. 4-285 supplement 2A). To directly measure the binding rate of TPX2, we adapted our assay to form 286 branches on passivated coverslips to reduce fluorescent background, and replaced the 287 endogenous TPX2 with an equivalent concentration of GFP-labelled TPX2 (Fig. 4D, Fig. 3-288 supplement 1A and Movie S8). First, we observed that TPX2-GFP associated with individual 289 MTs, including the first de novo MT prior to the formation of the first branched MT ( Fig. 4D and 290 Movie S8), supporting the molecular sequence during branch formation. The binding of TPX2 to 291 MTs was slow, such that the plus-ends were mostly devoid of TPX2 signal, and a decreasing 292 profile of TPX2 from minus-to plus-ends was observed (Fig. 4D). To quantify the binding rate 293 of TPX2, we measured the rate of increase in TPX2 intensity at individual pixels on the MT 294 lattice (Fig. 4E). The fluorescence intensity of single TPX2-GFP molecules was obtained from 295 fluorescence photobleaching traces and used for normalization (Fig.  Third, we show that the nucleator γ-TuRC cannot be recruited by TPX2 independently, but 342 requires augmin (Fig. 4C), which could not be ruled out based on previous work. Finally, we 343 note that our work does not rule out the participation of other, yet unknown effectors in 344 branching MT nucleation. The minor differences between our experimental nucleation profiles 345 and sequential model (Fig. 2) may indicate the involvement of more than two steps 346 corresponding to binding of undiscovered effectors, or time-dependent regulation of known 347 effectors. In the future, it will be important to identify new branching effectors and elucidate the 348 detailed mechanism of branching with bottom-up in vitro reconstitution.

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The experiments, we show that the MT networks are organized by rate-limited deposition of 372 nucleation sites and followed by branch emergence. We posit that the localization of nucleators, 373 not their activation, regulates nucleation in the mitotic spindle. Third, and most importantly, the 374 preferential nucleation from older MT lattice regions could allow for precise control over where 375 branching occurs in the spindle. We propose that TPX2, which is released in the vicinity of 376 chromosomes (  RanQ69L, and time-lapse is displayed for one representative branched network. MTs were 586 labeled with Cy5-tubulin (red) and their plus-ends with EB1-mCherry (pseudo-colored as green). 587 0 seconds represents estimated nucleation of the first mother MT. Scale bar, 10 µm. The 588 highlighted region shows that new nucleation events (marked by EB1 spots) occur near the 589 minus-ends and exclude the lattice near the growing plus-ends. The experiment was repeated 590 with more than ten independent egg extract preparations.

591
(B) Angle of branching for all branching nucleation events was calculated as described in 592 Methods. Polar histogram of n = 339 measurements from 19 branched networks is plotted. The 593 median branch angle is 0° with a standard deviation of 9°. See Figure supplements and Movies 594 S1-2.   Spatial location of first branching event on a naked mother MT was recorded during the 614 formation of individual branched MT networks, and the following distributions were measured. 615 See Fig. 2-supplement 1A for representative examples.

616
(A) Distance of the nucleation site from the mother's plus-end was measured at the time point 617 when first branching event occurred. Rightmost (0 µm) point on the horizontal axis denotes 618 nucleation near the mother's plus-end. Inverted x-axis is plotted for consistency with (B).

619
(B) Fractional distance was obtained by dividing the branching nucleation site from the mother's 620 minus-end by the total length of the mother MT when first branching event occurred. Leftmost 621 (0) point on x-axis denotes nucleation near the mother's minus-end, while rightmost (1) 622 represents nucleation near the mother's plus-end.   four conditions: buffer addition or control depletion, addition of 260 nM TPX2, partial depletion 661 of TPX2 (20% of control), or partial depletion of augmin (20% of control). For each condition, at 662 least 5-10 identical reactions were performed with each preparation of Xenopus extracts, and 663 repeated with at least 3 independent extract preparations, except TPX2 addition was repeated 664 with 2 independent extract preparations. Scale bars, 10 µm. See Fig. 3-supplement 1.  665 (B) Spatial location of first branching event on a naked mother MT was recorded for each 666 condition in (A) and compared with prediction from sequential model. Distance of the branching 667 nucleation site from the mother MT's minus-end (top), plus-end (middle) and fractional distance 668 of nucleation from the minus-end (bottom) were measured, resulting probability distribution was 669 plotted. Shaded area represents 95% confidence interval. Leftmost and rightmost points on x-axis 670 denote nucleation site near the mother's minus-end or the plus-end respectively. The insets show 671 the rate constants in sequential model corresponding to changes in protein concentrations: blue 672 (1x rate constants, control reactions), green (9.6x kbind or kbranch, 9.6x TPX2 concentration), 673 mustard and red (0.2x TPX2 and augmin concentration, respectively) compared to orange (0.2x 674 kbind or kbranch). Number of experimental measurements: buffer or control depletion (blue, n=283), 675 TPX2 addition (green, n=45), TPX2 partial depletion (yellow, n=157), augmin partial depletion 676 (red, n=65). Number of simulations: n=4000 for each condition. See   Sequential mechanism of branching MT nucleation (A-C).

(A) De novo MTs (blue) were generated by performing branching reaction in augmin-depleted 684
Xenopus egg extracts where TPX2 is present. Non MT-bound, soluble proteins were removed 685 with buffer wash, and Xenopus egg extracts containing augmin but no TPX2 was introduced. 686 Branched MTs (red), with their plus-ends labelled with EB1-mCherry (pseudo-colored as green), 687 nucleated immediately from de novo MTs (blue), highlighted in the zoomed-in region. Late time 688 point (7 minutes) shows formation of dense branched networks around the initial de novo MTs 689 (blue). 0 seconds marks the time of extract exchange in the reaction chamber. Scale bar, 10 µm. 690 The experiment was repeated six times with independent egg extract preparations.

691
(B) De novo MTs (blue) were generated by performing branching reaction in Xenopus egg 692 extracts containing augmin but no TPX2. Non MT-bound, soluble proteins were removed with 693 buffer wash, and Xenopus egg extracts containing TPX2 but no augmin was introduced. No 694 branching was seen, and only MT plus-ends elongated (Cy5-MTs in red and EB1-mCherry 695 pseudo-colored as green) was observed. Late time point (7 minutes) depicted for comparison 696 with (A). 0 seconds marks the time extract exchange in the reaction chamber. Scale bar, 10 µm. 697 The experiment was repeated four times with independent egg extract preparations.

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(C) De novo MTs (blue) were generated by performing branching reaction in Xenopus egg 699 extracts containing TPX2 and γ-TuRC but no augmin. Non MT-bound, soluble proteins were 700 removed with buffer wash, and γ-TuRC-depleted Xenopus egg extracts containing TPX2 and 701 augmin was introduced. At initial time points, only elongation of MT plus-ends (red with EB1-702 mCherry pseudo-colored as green) was observed. Rare branching events were seen at late time 703 point (7 minutes), highlighted with white arrow. 0 seconds marks the time extract exchange in 704 the reaction chamber. Scale bar, 10 µm. The experiment was repeated thrice with independent 705 extract preparations. See also Fig. 4-supplement 1.

706
(D-E) Endogenous TPX2 was replaced with 20-30nM recombinant GFP-TPX2 in Xenopus egg 707 extracts. Branched MT networks were generated with 10 µM RanQ69L, and time-lapse of TPX2 708 on the networks was recorded. MTs were labeled with Cy5-tubulin (red), their plus-ends with 709 EB1 (green), and TPX2 is displayed in cyan. 0 seconds marks the start of the reaction. Scale bar, 710 10 µm. Arrows denote the plus-ends, while asterisks show TPX2's deposition on older lattice 711 regions near the minus-ends and no binding to newly formed plus-ends. The experiment was 712 repeated thrice with independent egg extract preparations. TPX2's intensity was measured over 713 time on individual pixels (highlighted with yellow line) corresponding to de novo MT before the 714 first branching event occurred, normalized by single TPX2's fluorescence and converted into 715 number TPX2 molecules. A representative trace is shown in (E), which was fit to straight line 716 (red). Slope was calculated to obtain the binding rate of TPX2 as 0.4±0.2 (mean±s.d.) molecules 717 µm -1 s -1 (n=32 traces). A constant background noise level of 7 molecules was observed, which 718 does not affect the calculated binding rate. The experiment was repeated thrice with independent 719 extract preparations. See also Fig. 4-supplement 2. 720 were made when the EB1 comet first emerged (216 s and 256 s respectively). Distance from the 772 mother's minus-end is denoted by a solid line segment, and from mother's plus-end by a dashed 773 line segment. The fractional distance was measured dividing the solid segment length by the sum 774 of solid and dashed segment lengths. These measurements were made for n=381 branched 775 networks and are plotted in (B) and Figure 2A-B. Scale bars, 10 µm.

776
(B) Spatial location of first branching event on a naked mother MT was recorded during the 777 formation of individual branched MT networks. The distance of the branching nucleation site 778 from the mother's minus-end was measured, and compared with single-step and sequential 779 models as in Fig. 2A-B. Leftmost (0 µm) point on x-axis denotes nucleation near the mother's 780 minus-end. Normalized probability was plotted for n = 381 experimental measurements (blue), 781 and n = 4000 each using the single-step model (red) or the sequential model (green). Shaded 782 regions depict the 95% bootstrap confidence intervals. The experiments and analyses were 783 performed with three independent extract preparations and all data was pooled.

784
(C) Robustness of sequential model was tested by varying the dimensionless ratio of the 785 branching rate, kbranch (units: sec -1 ), and effective binding rate constant, √(kbind vpe) (units: sec -1 ). 786 The fractional position of the first nucleation event along the mother was compared. Bias was 787 observed for events in a dense branched network was measured in stochastic simulations. Analogous to Figure  793 2A-B, the distance of branching site was measured from (D) its mother's plus-end, Fractional 794 distance of each branching site along its corresponding mother was measured in (E). Leftmost 795 point on x-axis denotes nucleation near the mother's minus-end, while the rightmost point 796 represents nucleation near the mother's plus-end. Normalized probability of branching was 797 plotted for roughly 250 branched networks containing 200 MT on average. n = 49750 798 measurements for single-step model (red) and n = 55030 measurements for sequential model 799 (green) were obtained. Shaded regions depict the 95% confidence intervals. Probability 800 distributions demonstrate that the spatial bias similar to the first nucleation event ( Fig. 2A-B) 801 persists over subsequent nucleation events. Methods. The cartesian distances of all EB1 comets from the origin (yellow, right panel) were 807 measured. Three example measurements are illustrated with cyan line segments. All distances 808 were normalized by the longest distance (marked 3*) for each branched network. Measurements 809 were pooled from multiple branched networks and the probability distribution was reported in 810 Fig. 2D. Scale bar, 10 µm.

811
(B) Tubulin intensity was measured in dense branched networks as follows. Background 812 illumination was corrected for the tubulin intensity as described in Methods. The convex hull 813 around the branched network was generated (dashed white boundary, right panel) and average 814 intensity outside the image was subtracted. For all pixels within the convex hull, the subtracted 815 intensity was recorded and their distances from the origin was measured. All distances were 816 normalized by the longest distance of any vertex of the convex hull from origin for each 817 branched network. For any specified distance, all measured intensities were pooled from multiple 818 branched networks and reported in Fig. 2D. Scale bar, 10 µm.  networks, data was pooled for 10-60 MTs in 250 branched networks each simulated using the 839 single-step model (red, n=633517) and sequential model (green, n=495794). Shaded regions 840 depict the 95% confidence intervals. The experiments and analyses were repeated with two 841 independent extract preparations and representative experiment was reported. See Fig. 2-842 supplement 2 and Methods for measurement procedure.

843
(E) Tubulin intensity in branched networks was plotted against distance from the origin, 844 normalized by the longest distance (set to 1). Snapshots of branched networks were imaged at 845 early time-point (10 minutes, cyan), and the same networks were imaged again later (14 minutes, 846 blue). All measurements were pooled for 59 branched networks generated with one Xenopus 847 extract preparation, and the experiments and analyses were repeated for two independent extract 848 preparations. For simulations, data was pooled for 50-250 MTs in roughly 250 branched 849 networks each simulated using the single-step model (red) and sequential model (green). Shaded 850 regions depict the standard deviation in intensity measurements. See Fig. 2-supplement 2 and 851 Methods for measurement procedure. 852 853  (B) Partial depletion of TPX2 from Xenopus egg extracts was assessed using quantitative, 862 fluorescence western blot. Untreated extract (input), IgG-depleted (control) and TPX2 depleted 863 extracts were compared and probed via anti-TPX2 antibody. α-tubulin was used as loading 864 control. The experiment was repeated more than thrice with independent extract preparations.

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(E) Position of first branching event on a naked mother MT was recorded during the formation of 880 individual branched MT networks. Example measurement for buffer or control depletion, 881 addition of 260 nM TPX2, partial depletion of TPX2 (20% of control), or partial depletion of 882 augmin (20% of control) are displayed. For all networks, second displayed frame shows 883 emergence of an EB1 comet on the naked mother. Distance from the mother's minus-end is 884 denoted by solid line segment, and from mother's plus-end by dashed line segment. The 885 fractional distance from mother's minus-end was measured as solid segment length divided by 886 sum of solid and dashed segment lengths. These measurements were made for multiple branched 887 networks and plotted in Fig. 3B. Scale bars, 10 µm.