Length Control of the Metaphase Spindle

Length Control of the Metaphase Spindle Gohta Goshima1,2,4, Roy Wollman1,3,4, Nico Stuurman1,2, Jonathan M Scholey3, and Ronald D Vale1,2# Physiology Course 2004, Marine Biological Laboratory, Woods Hole, MA, USA The Howard Hughes Medical Institute and the Department of Cellular and Molecular Pharmacology, University of California, San Francisco, CA, USA Department of Molecular and Cellular Biology, University of California, Davis, CA, USA These authors contributed equally to this work #Corresponding author E-mail: vale@cmp.ucsf.edu Phone: 415 476-6380 Fax: 415 476-5233 Running title: Length control of the metaphase spindle Key words: RNAi, mitosis, microtubule, Drosophila S2 cell 1/29 Summary Background: The pole-to-pole distance of the metaphase spindle is reasonably constant in a given cell type; in the case of vertebrate female oocytes, this steady state length can be maintained for substantial lengths of time, during which time microtubules remain highly dynamic While a number of molecular perturbations have been shown to influence spindle length, a global understanding of the factors that determine metaphase spindle length has not been achieved Results: Using the Drosophila S2 cell line, we depleted or overexpressed proteins that either generate sliding forces between spindle microtubules (Kinesin-5, Kinesin-14, dynein), promote microtubule polymerization (EB1, Mast/Orbit [CLASP], Minispindles [Dis1/XMAP215/TOG]) or depolymerization (Kinesin-8, Kinesin-13), or mediate sister chromatid cohesion (Rad21) in order to explore how these forces influence spindle length Using high-throughput automated microscopy and semi-automated image analyses of >4000 spindles, we found a reduction in spindle size after RNAi of microtubule polymerizing factors or overexpression of Kinesin-8, whereas longer spindles resulted from the knockdown of Rad21, Kinesin-8 or Kinesin-13 In contrast, and differing from previous reports, bipolar spindle length is relatively insensitive to increase in motorgenerated sliding forces However, an ultrasensitive monopolar-to-bipolar transition in spindle architecture was observed at a critical concentration of the Kinesin-5 sliding motor These observations could be explained by a quantitative model that proposes a coupling between microtubule depolymerization rates and microtubule sliding forces Conclusions: By integrating extensive RNAi with high-throughput image processing methodology and mathematical modeling, we reach to a conclusion that metaphase spindle length is sensitive to alterations in microtubule dynamics and sister chromatid cohesion, but robust against alterations of microtubule sliding force 2/29 Introduction Microtubules (MTs) are highly dynamic polymers that continually change their length by growth or shrinkage [1] Remarkably, while individual MTs fluctuate in length, the ensemble of microtubules in the mitotic spindle maintains a constant spindle length throughout metaphase [2] Several studies using various experimental systems from yeast to humans have shown that spindle length can be influenced by changes in MT polymer dynamics, mitotic motor activity or sister chromatid cohesion [3-11] However, a systematic and quantitative analysis of the factors that establish and maintain the steady state spindle length at metaphase has not been performed Moreover, studies on the consequences of perturbations of individual proteins on metaphase spindle length are often not consistent among different experimental systems For example, alterations in MT length by inhibition of MT dynamics regulators directly affect spindle length in some systems (e.g [3, 11]) but not in others [9] A quantitative assessment of the contributions of different force generators to spindle length in a single cell type would greatly aid efforts to understand and potentially computationally model the balance of forces acting to maintain the length of the metaphase spindle [12-14] The Drosophila S2 cell line is a good animal cell for investigating spindle length control, since it has a diamond-shaped spindle that has similar morphological features to somatic vertebrate cells and since a number of conserved proteins that affect spindle morphology have been identified by RNAi-based functional analyses [3, 4, 15-17] In this study, we determined metaphase spindle length after RNAi knockdown and/or overexpression of factors that mediate MT sliding, MT dynamics, or sister chromatid cohesion We examined the following proteins whose mitotic phenotypes after RNAi depletion and, in most cases, in vitro molecular activities have been characterized To modulate MT sliding, we focused on Klp61F [Kinesin-5], a conserved, bipolar, plus-end-directed kinesin that is thought to generate outward sliding forces between antiparallel MTs and would be expected to elongate the spindle Indeed, previous studies in yeast have shown that overproduction or reduction of Kinesin-5 causes metaphase spindle lengthening or shortening, respectively [5, 7] We also examined two minus-end-directed motors, Kinesin-14 (Ncd in Drosophila) and cytoplasmic DHC (Dhc64C), since these motors could influence metaphase spindle length by generating an inward sliding force that opposes the actions of Kinesin-5 [5, 6, 8, 9, 18] (in some cells, dynein could also augment Kinesin-5 by pulling astral MTs towards the cell cortex [19]) To explore factors that influence MT dynamics, we examined three proteins that promote MT assembly at the MT plus end: the plus-end-tracking protein EB1 [16], Msps 3/29 [Dis1/XMAP215/TOG] [20], and Mast/Orbit [CLASP] [17, 21], as well as the MT depolymerizing factor, Klp10A [Kinesin-13] [3, 4], and the putative depolymerizer Klp67A [Kinesin-8] [3, 22-24] The actions of Mast/Orbit and Klp67A are thought to be exerted primarily at kinetochores [17, 21-24] Klp10A and EB1, on the other hand, are concentrated at the centrosome, although both are likely to modulate MT assembly throughout the mitotic cytoplasm as well [3, 4, 16] To interfere with sister chromosome tension, we depleted the critical sister chromatid cohesion protein, Rad21 [cohesin] [15] Our results show that modulators of MT dynamics and chromatid cohesion are the major governors of spindle length In contrast, bipolar spindle length is robust to changes in MT sliding forces produced by the Kinesin-5 We produce a mathematical model that provides a framework for understanding these observations Results and Discussions Mitotic cells are relatively rare in the S2 cell population (1-3%) Therefore, we required a method to obtain images of sufficient numbers of mitotic spindles for quantitation and statistical comparison between different RNAi treatments In most cases, we employed a high throughput procedure of image collection and analysis, as summarized below and in Figure (and Suppl Figure 1) for control GFP-tubulin expressing cells [3] Cells were plated onto concanavalin-A-coated, 96-well glass-bottom dishes, and then fixed and stained for -tubulin (as a marker of centrosome locations) and chromosomes (Figure 1A) For the majority of our experiments, images were collected using a high-throughput automated microscope, and a semi-automated image analysis procedure was used to identify the rare mitotic cells in the images This algorithm, which took advantage of the fact that most interphase S2 cells not exhibit punctuate signals of -tubulin [3], recognizes -tubulin spots and identifies a cell as mitotic if it contains a pair of -tubulin spots with a DAPIstaining chromosomal mass in-between (Figure 1B) During this process, -tubulin spotspot distances were measured automatically Potential metaphase cells were then displayed into visual galleries, and a manual selection was performed to eliminate prophase, anaphase, aberrant interphase cells as well as metaphase cells with multipolar spindles, which had been also selected by the automated selection process (see Suppl Figure for an example of manual selection) The average distribution of the spindle length (herein we define as centrosome-to-centrosome distance) in 703 control cells from several experiments was 11.5 ± 2.0 µm (Figure 1D) This length distribution was broader than those observed in yeast or fly embryos [6, 10] However, using a sufficient sample, we obtained consistent 4/29 average metaphase spindle length between experiments (10.95 – 11.84 µm; Suppl Table 1) By plotting spindle length versus GFP intensity for individual cells, we also established that the spindle length was independent of GFP-tubulin expression levels (Figure 1E) Next, we applied the same procedure to examine metaphase spindle length in cells depleted of various proteins by RNAi (Figure 2, see also Suppl Table for statistical summary) One general caveat of RNAi approach is that the targeted proteins are not completely depleted and that the observed phenotypes (especially “no phenotype”) could be still “hypomorphic” due to the residual proteins While this is also the case of our study, we confirmed significant protein level reduction for most of the genes (Suppl Figure 2A) and could observe specific spindle/chromosome phenotypes (Figure 2B) First, we found that reduction of Rad21, a protein essential for sister chromatid cohesion, led to longer spindles, as documented in yeast [10] After Rad21 RNAi, anti-Cid staining (an inner kinetochore marker) revealed no paired sister kinetochore dots and thin chromosomal masses were scattered, strongly suggesting the precocious separation of sister chromatids (Suppl Figure 4A)[15] Statistically significant effects also were observed for regulators of MT dynamics In agreement with previous qualitative descriptions [3, 4, 16, 17, 25], RNAi of the MT stabilizers EB1, Msps, and Mast caused shortening of metaphase spindle (61% 83%; all p-values < 0.0007), whereas knockdowns of MT depolymerases (Klp10A and Klp67A) caused expansion (125% - 147%, all p-values < 0.004) Notably, the outer kinetochore-enriched regulators of MT plus ends (Klp67A, Mast) affected the length more severely than the global or centrosome-localized MT regulators- EB1, Msps, and Klp10A Klp67A [3] and EB1 [16] RNAi sometimes causes centrosome detachment from the kinetochore microtubules (kMTs), which could skew our measured centrosome-tocentrosome distance from the actual spindle length However, the degree of centrosome separation from the kMT for EB1 RNAi is small, only accounting for a 0.2 µm increase to the measurement of spindle length [26] In the case of Klp67A, the centrosome is detached, but is not always localized along the axis Indeed, by comparing measurements of centrosome-centrosome distance to the distances of the minus ends of the kMT in 32 bipolar spindles, we find that the centrosome-centrosome distance in Klp67A RNAi cells underestimates spindle length by 0.3 µm compared with control cells Nevertheless, these effects are small and not affect our conclusions that EB1 and Klp67A RNAi treatments shorten and lengthen spindle length respectively If spindle length is controlled by a balance of MT polymerization and depolymerization, we reasoned that a phenotype generated by depletion of the MT depolymerizing protein Klp67A might be rescued by depletion of MT polymerizing proteins (e.g Msps or Mast) 5/29 In accordance with this idea, the simultaneous knockdown of Klp67A and Msps or Mast produced an average length that was intermediate between single Klp67A and single Msps or Mast knockdowns (Figure 2A) The important role played by MT polymerization dynamics in determining spindle length was also discovered recently in Xenopus egg extracts by Mitchison and colleagues who also argued that an unidentified non-MT tensile element, possibly a “spindle matrix” [27], may constrain spindle length [28] Although we cannot exclude the existence of such an element, our results have not uncovered evidence for its existence For example, shortening of MT length by EB1 or Msps RNAi produced short metaphase spindles without significantly perturbing its shape (Figure 2B) Previous studies have shown that the inhibition of a minus-end-directed kinesin (Kinesin14) causes spindle elongation in yeast [5, 8] Dynein inhibition causes drastic spindle elongation or shortening depending upon the cell type [6, 9] However, RNAi of Ncd [Kinesin 14] or Dhc64C [cytoplasmic DHC] only slightly changed the spindle size in S2 cells (3% - 17% increase; Figure 2A and Suppl Table 1) The slight increase after dynein knockdown can be explained by the effect of detachment of centrosomes from spindle poles [29, 30], as we recently found in another study that detachment of the centrosomes from the minus end of kMT alone accounts for average 14% increase in the centrosome-tocentrosome distance [26] The spindle length increase after dynein RNAi is less than observed by Morales-Mulia and Scholey [31] for reasons that are not clear However, these authors also noted a partial mis-recruitment of the Klp10A depolymerase to the poles which may have contributed to this effect The lack of dramatic effect upon Ncd RNAi is unlikely to due of residual proteins, since we noted splaying of kinetochore fibers (a characteristic of Ncd RNAi knockdown [3, 26]) in the majority of the mitotic spindles examined (80%), found significant depletion (>90%) of Ncd at the population level by immunoblot analysis, and found that 33 of 36 mitotic spindles scored had no detectable immunofluorescence signal for Ncd after Ncd RNAi However, the slight increase of the spindle length might be explained by the reduced spindle elasticity upon unfocusing of kinetochore fibers (discussed below in Box 1) Depletion of Klp61F [Kinesin-5] by RNAi produced monopolar spindles [3], so the length of bipolar spindles was not a measurable parameter Collectively these quantitative comparisons of spindle length following RNAimediated protein depletion indicate that MT polymer dynamics and sister chromatid cohesion more dramatically affect metaphase spindle length than depletion of minus-enddirected motor proteins 6/29 We next examined whether increasing the levels of MT-sliding motors (Klp61F, Ncd) or of MT depolymerases (Klp10A, Klp67A) influences spindle length (Figure 3) To correlate expression level and spindle length on a cell-to-cell basis, GFP-tagged kinesins were expressed from an inducible promoter (Figure 3B) and GFP levels and spindle lengths were measured for individual cells In support of our assumption that the exogenous fusion proteins are physiologically functional, we observed that moderate expression of these kinesin-GFP fusions rescued the loss-of-function spindle phenotypes produced by depletion of the corresponding endogenous kinesin by RNAi, which suggests that GFP-tagging did not destroy the kinesin’s function [22] Moreover, overexpressed Klp67A-GFP localized primarily to kinetochores and kinetochore MTs (kMTs) and overexpressed Ncd-GFP and Klp61F-GFP localized primarily to the main body of the mitotic spindle, as is true of the endogenous motors (Figure 3B) Klp10A-GFP localized primarily to centrosomes/centromeres when expressed at low-level although cytoplamic accumulation was also detected after overexpression (Figure 3B) Therefore, overexpression of Klp10AGFP might not result in increased motor concentrations at spindle poles Figure 3A reveals that expression of the MT depolymerase, Klp67A, caused a dose-dependent shortening of the metaphase spindle (more data sets are available in Suppl Figure and Suppl Table 2) In contrast, overexpression of Klp10A-GFP did not result in a statistically significant change in metaphase spindle length in our overexpression range (Figure 3A) Surprisingly, overexpression of Ncd caused a statistically significant dose-dependent elongation of the metaphase spindle in two out of four experiments (Figure 3A) This result is opposite to that expected from prior results and models implicating Ncd as a motor that generates an inward force on antiparallel MTs [5, 6, 8] However, an in vitro study shows that the MT binding domain within the non-motor region of Ncd can induce MT nucleation, stabilization and bundling [32], so the length increase may be attributed to MT stabilizing effects of motor overxpression (Figure 3B) Perhaps the biggest surprise was the lack of correlation between Klp61F-GFP expression level and spindle length in six independent experiments (Figure 3A, Suppl Figure and Suppl Table 2) Thus, in contrast to previous results obtained in yeast [5], we conclude that the overexpression of the sliding motor Klp61F has no effect on spindle length in S2 cells To better understand how balances of forces might govern spindle length, we developed a preliminary quantitative model (described in detail in Box 1) This quantitative analysis is based on several plausible but unproven assumptions First, we assumed that MT sliding forces are proportional to forces applied by Kinesin-5 based on linear force-velocity curve Second, we assumed that the spindle elastic properties can be approximated by a Hookean spring Third, sister chromatids are under tension at the kinetochores in which pulling 7/29 force generated by antiparallel MT sliding and/or MT depolymerization at the poles is opposed by sister chromatid cohesion To test if the third assumption is relevant in S2 cells, we measured sister kinetochore distance as a maker of sister chromatid tension, where longer distance (“stretched” centromeres) represents stronger pulling force at the kinetochore by kMTs [33] By immunofluorescence of Cid (Drosophila CENP-A, histone H3 variant that localizes to inner kinetochores), we found, consistent with previous reports [30, 34], that sister kinetochore distance during metaphase is 25% longer (1.0 ± 0.13 µm [n=23], p70%) in the stable cell line express GFP Note, however, that the expression level of GFP is variable among cells, but this variable enhanced our study since we could correlate expression with spindle length on a cell-by-cell basis Immunofluorescence microscopy Cells were fixed by 3-6% paraformaldehyde for 15 min, permeablized by 0.5% SDS treatment for 15 and stained by anti--tubulin antibody (GTU-88 [SIGMA]; 1:500) and DAPI or Hoechst 33342 (0.5 µg/ml) in PBS containing 0.5% Triton and 10% goat serum Specimens were imaged either automatically by ImageXpress (Axon Instruments) or manually by a cooled CCD camera Sensicam mounted on a Zeiss Axiovert microscope 40x objective lens was used for ImageXpress microscopy Anti-Cid (a gift from S Henikoff) was used at 1:1000 dilution Image data analysis Images were separated into channels based on DNA, -tubulin and GFP staining DNA images were convolved with a Gaussian matrix 10 pixels in size with a  of pixels tubulin spots were identified by segmentation of the image resulting from a Top-Hat 22/29 morphological filter using a disk structural element of pixels A list of all -tubulin spots was generated by sorting the -tubulin average intensities When the computational detection process identified more than 500 -tubulin spots during the analysis of one image (because of very high background noise or artifactual aggregation of -tubulin signals), further image analysis was halted When 50-500 possible -tubulin spots were identified for one image, only the spots with average intensity larger than a threshold were used for length measurement This threshold was determined based on the size of the list and the mean spot intensity When two -tubulin spots were less than 25 µm apart and had DNA staining in between, the object was selected as a potential spindle Montages of all potential spindles were generated and metaphase spindles were selected manually as shown in Suppl Figure Bipolar spindle is visible by either GFP-tubulin signals or, in the case where the cell does not express GFP-tubulin, whole-spindle staining by anti--tubulin staining All image analysis code was written in Matlab using functions from the Image analysis toolbox A total of 10 images containing approximately 106 cells were obtained using an automated high-throughput microscope; 103 images were taken manually Statistical analysis All comparisons were tested using a t-test assuming equal variance Significance was determined after a Bonferroni correction for multiplicity All correlation was tested using linear regression analysis, testing that the slope is significantly different from zero Regression analysis was corrected for multiplicity as well FSM (fluorescent speckle microscopy) Images of low-expressing GFP-tubulin cells were collected at 2-3 sec intervals with 0.5-1 sec exposure times at room temperature (23˚C) using a cooled CCD camera OrcaER2 (Hamamatsu) attached to a Yokogawa spinning-disk confocal scanhead (Perkin Elmer) that was mounted on a Zeiss Axiovert inverted microscope Camera and AOTF were controlled by Metamorph software on a PC computer (Universal Imaging, Molecular Devices) 23/29 Supplemental Figures and Movies Suppl Figure 1: Manual selection of metaphase cells from automatically-generated image gallery An example of a gallery of control GFP-tubulin cells selected by our automated analysis algorithm (see Supplementary Experimental Procedures) Two -tubulin punctate signals were automatically detected (yellow lines) This algorithm selects metaphase cells (yellow frame) as well as other non-metaphase cells which were eliminated by manual inspection Although many non-metaphase cells were in the cell galleries derived from this automated detection, the automation nevertheless greatly facilitated our procedure, since metaphase cells with two -tubulin signals are rare (80% reduction was detected after RNAi for most of the proteins However, considerable residual Msps was detected after our 3-day RNAi treatment (the antibody is a gift from J Raff) We found that this was the best condition to accumulate metaphase cells with the bipolar spindle >4 day treatment caused severe centrosomal defects and bipolar spindles were rarely observed (N Mahoney, G.G., A Douglass, R.D.V., submitted) Arrows in (B) indicate GFP-tagged kinesins, whereas asterisks indicate endogenous kinesins All the antibodies were previously used [3, 4, 16, 22, 31] Suppl Figure 3: Correlation of protein over expression with spindle length After overexpression of GFP-tagged protein, both spindle length and GFP intensity were measured Scatter plot show the correlation between the overexpression of the motor and spindle length in independent experiments Linear regression lines are plotted only in cases where the slope was significantly different from zero More statistical details are shown in Suppl Table Suppl Figure 4: Sister kinetochores are under tension at metaphase in the presence of sister chromatid cohesion (A) Immunofluorescence of Cid (Drosophila CENP-A), an inner kinetochore protein Sister inner kinetochore distance of control metaphase cells was ~25% longer than in cells treated with colchicine, indicating that sister chromatids are under tension in the bipolar 24/29 spindle In contrast, paired Cid dots were not detected in Rad21 RNAi spindles, in which thinner, unalinged sister chromatids are frequently detected, strongly suggesting the generation of weaker tension due to precious separation of sister chromatids Bar, µm (B) Distance of sister Klp67A-GFP signals (Klp67A is an outer kinetochore marker [22]), rapidly decreased upon MT depolymerization by colchicines in metaphase Time-lapse imaging was performed using spinning-disk confocal microscope See also Movie Suppl Figure 5: Decreased poleward flux rate after Klp61F RNAi Poleward flux observation by fluorescent speckle microscopy (FSM), a technique in which low level of GFP-tubulin results in the random incorporation of GFP speckles into the MT lattice [4] (A) The poleward flux of GFP-tubulin speckles was detected by kymograph analyses after RNAi of Klp61F and for control cells Bar, µm See also Movies and (B) Distribution of rates of speckle movement based upon kymograph analyses for control bipolar spindles (speckle number=109) and monopolar spindles after Klp61F RNAi (n=89) The graph likely represents a mixed population of kMTs and non-kinetochore MTs The majority of the speckles move poleward at 1.5 µm/min velocity For control cells, we could also detect 19 speckles that move across the chromosome region and therefore are undoubtedly not derived from kMTs The average rate of those movement of interpolar (ip) MTs was 2.2 ± 0.6 µm/min, which is much faster than the rate of kMT flux in S2 cells (0.7 ± 0.15 µm/min [21]) This fast rate was scarcely seen in the Klp61F RNAi spindles, suggesting that Klp61F-dependent sliding contributes to generate poleward flux of ipMTs in the bipolar spindles However, the fact that some, albeit slow flux remains after Klp61F RNAi suggests that there is a Kinesin-5 independent component of flux in these cells Movie 1: Klp67A-GFP dynamics upon colchicine treatment Images were acquired every 30 sec by spinning-disk confocal microscope Sister Klp67AGFP distance (marked by red line) rapidly decreased upon MT depolymerization Movie and 3: Fluorescent speckle microscopy (FSM) of GFP-tubulin in spindles without RNAi treatment (2) and after Klp61F RNAi (3) Images were acquired every sec (each 600 ms exposure time) by spinning-disk confocal microscope 25/29 Supplemental Table 1: Quantification of the metaphase spindle length after RNAi Gene Avg Length (µm) Klp10A Klp10A Klp67A Klp67A Klp67A Klp67A Klp67A 67A/Mast 67A/Mast 67A/Msps 67A/Msps Dhc Dhc EB1 EB1 EB1 Mast Mast Msps Msps Ncd Ncd Rad21 14.41 13.29 18.51 16.22 17.06 15.01 18.69 9.69 10.22 11.53 9.94 12.44 11.45 10.07 9.19 8.92 7.03 7.44 8.10 8.39 13.02 11.64 13.89 Control Length (µm) 11.06 11.08 11.52 11.06 11.76 11.08 12.32 11.52 12.32 11.73 11.76 11.08 11.06 11.84 11.06 11.08 11.52 12.32 11.76 12.32 11.08 11.06 10.95 Normalized Length 1.30 1.20 1.61 1.47 1.45 1.35 1.52 0.84 0.83 0.98 0.85 1.12 1.03 0.85 0.83 0.81 0.61 0.60 0.69 0.68 1.17 1.05 1.27 Std (µm) SEM (µm) 3.46 3.43 4.41 4.83 4.86 4.02 4.75 3.96 4.10 2.8 2.32 3.51 2.79 1.84 1.96 2.02 2.64 2.82 1.67 1.32 2.14 2.45 3.08 0.79 0.92 0.61 0.51 0.72 0.70 0.88 0.45 0.72 0.47 0.23 0.28 0.14 0.29 0.19 0.41 0.34 0.47 0.21 0.21 0.59 0.45 0.39 N P -Value 19 14 52 91 46 33 29 77 32 36 99 159 393 41 108 24 60 36 62 39 13 30 61 1.76E-07 3.12E-03 5.67E-15 0.00E+00 5.75E-09 1.55E-10 1.51E-08 6.73E-03 1.68E-02 7.50E-01 1.33E-04 4.75E-04 9.52E-02 6.68E-04 5.32E-11 9.73E-05 9.38E-15 2.49E-10 9.59E-12 1.98E-12 7.50E-03 2.38E-01 1.80E-07 Quantitation of spindle length in separate RNAi experiments P-values are derived from comparison with the control cell sample (no RNA addition) stained at the same day N represents the number of spindles analyzed in each treatment 26/29 Supplemental Table 2: Quantification of the metaphase spindle length after over production (OP) Gene N P -Value Klp10A Klp10A Klp10A Klp10A Klp61F Klp61F Klp61F Klp61F Klp61F Klp61F Klp67A Klp67A Ncd Ncd Ncd Ncd 52 97 56 35 19 20 29 79 136 41 80 82 18 148 56 16 0.015 0.2066 0.0875 0.0732 0.0943 0.8314 0.2686 0.6693 0.1727 0.8756 0.0023 3) CATATTGATCAATTGAAAC GACATCGATCTCCTTGCG CATTTTCGATAGAATGCTCC 5UTR* Klp67A TGAAGTAACAACTATTCCGC TGCTTGGATGAGGGCAAGG 254 3-5 GCTCTAAGCACAGAAGTGGTGC CAGTGATAAAAACGCAGACTGG ATCCAAGGTGAATCATAATGCC CCATTCGAATCTCCATGTCC GGGCAGCTATGTCTAATGTTCC AGACAATGAGGACGATGATGG 631 613 671 3 GTACAAAATACCGTTGGTTCGG AAACTCAACAGAATTAACGCCC ATACCAAAGAGAACGAGAACGC ATTTGAAACGTGAACGAAAACC TTGGTACTTGTCACACCACTCC CTGGGAATTTCATAGTTGTCCC 653 660 565 5 3UTR* Ncd Mast/Orbit Minispindles (Msps) EB1 Dhc64C Rad21 Length (bp) 268 644 156 Day 3-5 T7 promoter sequences (TAATACGACTCACTATAGGG) were added to 5 end of primer * For Klp67A, dsRNA of both 5 and 3UTRs were mixed and added to cells for RNAi [22] 28/29 Supplemental Table 4: Parameters used in sensitivity analyses in Box 1-C Symbol Meaning Values Units  pN m K bT Boltzmann constant 4.2 10 -3 N Number of interpolar MTs 100 # S0 Whole spindle tension rest length 10  m Vsliding ,max Free load velocity of Kinesin-5 0.1  m / s  Vd , Minimal depolymerization velocity 0.01  m / s  Vdep ,max Maximal depolymerization 0.06 velocity due to sliding force Plus end polymerization 0.06  velocity  V poly  m / s m / s  pN / m Total force per unit length of sliding motors 100  Spindle tension spring constant 80  pN / m Fkt ,0 Depolymerization force on the kinetochore 100  pN   Minimal distance for polymerization  nm 29/29  ... computationally model the balance of forces acting to maintain the length of the metaphase spindle [12-14] The Drosophila S2 cell line is a good animal cell for investigating spindle length control, since... level and spindle length, indicating that GFP-tubulin expression itself did not perturb the spindle Bars, 10 µm Figure 2: Metaphase spindle length after RNAi (A) Average length of metaphase spindle. .. that although the exact length can change due to changes in the parameter values used, the existence of a solution, and therefore the existence of a stable metaphase steady state length is guaranteed