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. Author manuscript; available in PMC: 2010 May 26.
Published in final edited form as: Curr Biol. 2009 May 14;19(10):807–815. doi: 10.1016/j.cub.2009.04.036

The Distribution of Polar Ejection Forces Determines the Amplitude of Chromosome Directional Instability

Kevin Ke 1, Jun Cheng 1, Alan J Hunt 1
PMCID: PMC2712573  NIHMSID: NIHMS120306  PMID: 19446456

Summary

Polar ejection forces (PEFs) have often been hypothesized to guide directional instability of mitotic chromosomes, but a direct link has never been established. This has lead, in part, to the resurgence of alternative theories. Taking advantage of extremely precise femtosecond pulsed laser microsurgery, we abruptly alter the magnitude of PEFs by severing vertebrate chromosome arms. Reduction of PEFs increases the amplitude of directional instability without altering other characteristics, thus establishing a direct link between PEFs and the direction of chromosome movements. We find that PEFs limit the range of chromosome oscillations by increasing the probability that motors at a leading kinetochore abruptly disengage or turn off, leading to a direction reversal. From the relation between the change in oscillation amplitude and the amount the chromosome arm is shortened, we are able to map the distribution of PEFs across the spindle, which is surprisingly different from previously assumed distributions. These results allow us to differentiate between the mechanisms proposed to underlie the directional instability of chromosomes.

Keywords: polar ejection force, directional instability, mitosis, laser microsurgery, metaphase

Introduction

Mitotic chromosome movements in vertebrates exhibit distinctive oscillatory movements called “directional instability” [1]. Directional instability has been observed across vertebrates [1-3], and in plots of position versus time appears as a triangular wave showing roughly constant-speed chromosome movements punctuated by abrupt direction reversals. The forces underlying these movements depend on interactions with microtubules (MTs) emanating from the spindle poles, including diffuse interactions between interpolar MTs and the chromosome arms, and kinetochore MTs attached to the nucleoprotein kinetochores located at a chromosome's primary constriction. Forces and movements directed from a kinetochore toward the pole it faces are termed “poleward”, and “antipoleward” refers to the direction away from the pole. Poleward motions are produced by force generators at the kinetochores, which follow the depolymerizing tips of the kinetochore MTs (reviewed in [4]), and by poleward flux of kinetochore MTs [5-8]. Movements toward a pole are opposed by “polar ejection forces” (PEFs) that push the arms of chromosomes away from the spindle poles [9, 10]. PEFs are thought to depend on interactions between spindle MTs and the chromosome arms, with antipoleward forces generated by chromosome-bound chromokinesin motors, or by polymerizing MT plus ends impinging against the chromosomes (for review see [11]). The known forces involved in chromosome movement are depicted in Figure 1.

Figure 1. Forces driving chromosome movement.

Figure 1

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The known forces acting on a chromosome are the poleward force on kinetochore microtubules (kMT), and PEFs. The PEFs that push the arms away from a nearby pole are developed by chromokinesin motors (green and black) that move toward the plus ends of microtubules, located distal to the spindle pole. Polymerizing microtubules impinging on the arms may also contribute to PEFs. PEFs from each pole are oppositely directed, with the PEF from the nearer (left) pole is expected to be greater due to the higher microtubule density. The depicted chromosome will move toward the left pole if the poleward left kinetochore force exceeds the net PEF. Drawing is not to scale, and for clarity the number of polar and kinetochore microtubules is greatly underrepresented. Upper right inset models PEFs analogous to a potential well and illustrates how this predicts a change in PEFs affects chromosome movements. Confined by PEFs pushing the chromosome toward the spindle equator, the oscillation amplitude depends on the force required to cause reversal of the leading kinetochores. Upon severing the chromosome arm, the PEF is decreased, leading to increased oscillation amplitude.

PEFs have been measured in vitro using optical tweezers at ∼0.5 pN per MT in lateral contact with isolated CHO chromosomes [12], and estimated at <1.1 pN per MT polymerizing against a chromosome by modeling the influence of MTs on what were assumed to be thermal fluctuations of chromosomes in Drosophila embryos [13]. As outlined by Rieder and Salmon [9], an appealing aspect of PEFs originating from chromosome-MT interactions, is that MT density decreases as MTs spread away from the spindle poles, so potentially PEFs could guide prometaphase/metaphase chromosomes toward the spindle equator, where forces from opposite poles balance. Such guidance could be achieved if increasing tension at the leading kinetochore increases the probability of a chromosome reversing direction [9, 14, 15]. This leads directly to the prediction that if PEFs are reduced, the frequency of reversals will decrease, and consequently the amplitude of oscillations will increase (Figure 1 upper right inset). Conversely, the amplitude will not be decreased if PEFs do not significantly guide chromosome movements or if, as suggested by Khodjakov et al. [16], PEFs guide chromosomes without influencing the force-generating state at the kinetochores, but determine the direction of chromosome movement when forces at the sister kinetochores are balanced.

The distribution of PEFs across the spindle has been modeled as an inverse square relation to the distance from the spindle poles [14, 15]. This is expected under the simplifying assumptions that all interpolar MTs are relatively straight, extend at least the length of the half spindle, and that the PEF is proportional to local MT density. The PEF is then also expected to depend on the size of a chromosome, roughly proportional to its cross-sectional area perpendicular to the spindle axis, which establishes the target area for encounters with MTs extending from the poles. Although these assumptions allow for a first approximation of the PEF distribution, not all the interpolar MTs are equal in length, and some do not even reach spindle equator [17], so the actual force distribution may differ significantly. In addition, given the dynamic nature of MTs, PEFs undoubtedly exhibit more complex spatial inhomogeneities and temporal variations.

Despite their postulated importance, it has never been established that PEFs directly influence directional instability, and recent work has argued that directional instability is instead guided by the behavior of kinetochore MTs [18], reminiscent to the “traction fiber” hypothesis first introduced by Ostregen [19]. Here we examine the role of PEFs by performing experiments to abruptly alter their magnitude in Newt lung cells. We lower the PEF by slicing off a chromosome's arms, thereby reducing the cross-sectional area available to interact with spindle MTs. To do this we take advantage of the precise nature of optical breakdown induced by femtosecond-pulsed (ultrafast) lasers [20-23]. For laser pulse duration lower than one picosecond, the highly reproducible and extremely nonlinear relation between optical breakdown and laser pulse energy allows damage to be limited to a region at the beam waist with dimensions smaller than the Gaussian diffraction-limited focus spot [24, 25]. Furthermore, since femtosecond lasers enable optical breakdown with only nanojoules of laser energy, we avoid collateral damage from shock waves and cavitation bubbles that may occur with longer pulses [26-28]. We find that severing chromosome arms increases the average amplitude of chromosome oscillations without altering the defining characteristics of directional instability, thereby broadly demonstrating PEFs importance in direction instability, and specifically establishing that PEFs influence the probability of kinetochores switching between force generating states, and thereby causing chromosome reversals. We discuss how this constrains existing theories of chromosome motility during mitosis, and calculate the distribution of PEFs based on the relationship between reduction in chromosome size and increased oscillation amplitude.

Results

Amputation of Chromosome Arms

We investigate the role of PEFs in directional instability by comparing oscillation characteristics before and after severing chromosomes arms using a femtosecond-pulsed laser. Figure 2 illustrates the laser-ablation setup. Restricting damage to sub-diffraction nanometer-scale regions [29, 30], and nanometer precision targeting allows chromosome arms to be severed with minimal collateral damage. For chromosome position measurements, we track the primary constriction since it is the most easily identified discrete region on a chromosome. Often kinetochore MTs are difficult to discern, so we used several criteria to identify bioriented chromosomes. We assume biorientation occurs when chromosomes initially drawn toward a spindle pole shift to the vicinity of the spindle equator. A further indications of biorientation is increased separation between sister chromatids as a chromosome undergoes directional instability, especially at direction reversals [31]. Although kinetochore fibers are difficult to identify near the kinetochores, they are often visible projecting from the centrosome toward a chromosome. For most clearly interpretable results, we select chromosomes that exhibit clearly discernable oscillations.

Figure 2. Laser microsurgery setup.

Figure 2

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An ultrafast pulsed laser is focused to a diffraction limited spot slightly exceeding the critical intensity for breakdown of biological material. Chromosomes are visualized by phase contrast, and targeted with a nanopositioning stage. A portion of an arm is severed by scanning the chromosome across the laser focus (e.g. within broken line). Circles show the locations of the spindle poles.

Laser microsurgery to sever a chromosome arm typically takes about 30 seconds. The process begins after locating a bioriented chromosome and following its movement for a few cycles of directional instability. Chromosomes typically oscillate within 10μm of the spindle equator, with peak-to-peak amplitudes ranging from 0.8 to 7.3μm before surgery. The ultrafast laser slightly exceeds the critical intensity for breakdown of biological material at the beam waist located on the chromosome (Figure 2). The focus is initially set at the edge of a chromosome arm, the beam is turned on, and the chromosome is moved across the focus with the nanopositioning stage. Since femtosecond-laser induced damage is restricted to a subdiffraction volume in all dimensions [24, 29], the procedure is repeated at successive z-axis positions to sever the entire thickness of the chromosome. The entire process is then repeated once to guarantee complete separation of the chromosome arm from the rest of the chromosome. The length of the severed chromosome arms ranged from 12% to 51% of the entire length of the chromosomes. Chromosome tracking continues until anaphase. Post surgery oscillation amplitude ranged from 1.7 to 9.5μm.

A typical chromosome trace is shown in Figure 3. In this case, the chromosome is tracked for about 450 seconds prior to ablation. The first image below the trace, at 0 sec, shows the intact chromosome marked green. The chromosome arm is about 2.1μm across and was severed in 28 seconds. The image at 464 seconds shows the chromosome immediately after surgery. The piece of the chromosome containing the kinetochore is marked green, while the severed arm is blue. Initially the severed arm follows closely with the movements of the rest of the chromosome, but after about 500 seconds, the arm begins to drift away, and its movements become independent. Such synchronization was often observed immediately following severing, and is probably due to steric constraints in closely packed, large Newt chromosomes; much like a person jostled in a crowd, a chromosome arm is swept along with nearby chromosomes. In support of this, we frequently observe similarly synchronized movements of adjacent chromosomes that are in close proximity (supplemental figure S1). After severing the arm, directional instability increases in average amplitude from 1.4 to 2.7μm. The amplitude does not increase for two nearby chromosomes serving as controls (Fig. 3, upper right inset). Note that when a chromosome reverses direction the trace is sometimes rounded rather than coming to a point expected for abrupt reversals often associated with directional instability. This typically occurs when reversals are close to the spindle equator where chromosomes are densely packed. This increases the probability that a tracked region gets pulled out of the plane of focus under/over another chromosome; such slight defocusing diminishes tracking precision, causing the trace to become rounded.

Figure 3. Chromosome movement before and after severing an arm.

Figure 3

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In the images and corresponding traces, blue indicates the severed arm, and green the kinetochore-containing region. Positions are relative to the spindle equator. In the images below the trace, the initially intact chromosome oscillates at average 1.4 μm peak-to-peak amplitude. The arm is severed immediately before the second frame. The region containing the kinetochores continues to exhibit directional instability but at higher amplitude (average 2.7 μm). The severed arm (blue) initially follows the rest of the chromosome, but loses synchronization by 1000 seconds. By 2063s, the chromosome and the severed arm have moved to opposite sides of the spindle equator. The oscillation amplitude of the control chromosomes does not increase.

The Speed of Severed Chromosomes Is Unchanged

16 chromosomes were tracked before and after their arms were severed. Before laser surgery, the average speed toward the spindle equator was the same as away (30.1 ± 16.5 nm/s (mean ± s.d., n=48 runs) and 32.3 ± 18.7 nm/s (n=53 runs), respectively) and consistent with published results [1, 2, 32]. The overall character of directional instability is not altered after chromosomes are severed, and the speeds are unchanged: 32.9 ± 13.3 nm/s (n = 75 runs) toward the spindle equator and 31.5 ± 12.9 nm/s away (n = 81 runs) (Figure 4). This extends the earlier observation that different sized chromosomes move at the same speed [33]: chromosomes have been observed to adopt preferred positions in the mitotic spindle (e.g., [34-36]), raising the possibility that local spindle structure compensates for the size of chromosomes; on the contrary, our findings suggest that constant speed is an intrinsic property of chromosomes.

Figure 4. Shortening a chromosome arm does not change speed.

Figure 4

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Antipoleward (toward spindle equator) and poleward are compared before and after severing chromosome arms. The average speed was about 31 nm/s, consistent with the work of Skibbens et al. [32], and was not changed by severing chromosome arms.

Severing Chromosome Arms Increases the Amplitude of Direction Instability

Although the defining characteristics of directional instability are not altered when chromosomes are shortened, the amplitude of oscillations changes, often abruptly. The average amplitude increases in nine of sixteen chromosomes after the arms are severed (Figure 5 A-I) while three show significantly decreased amplitude (Figure 5 J-L), and four are unchanged (Figure 5 M-P). On average, the amplitude across all chromosomes increases by 73%, in contrast to a decrease of 27% for control chromosomes (Figure 6A). For most chromosomes the larger the fraction of the chromosome severed, the bigger the increase in amplitude (Figure 6B). Since PEFs are diminished by severing the arms, this indicates the frequency of reversals depends on the magnitude of PEFs.

Figure 5. Chromosome oscillations before and after the arms are shortened.

Figure 5

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Each panel shows a different chromosome's movements before and after surgery (indicated by the vertical line on the traces). Positions are relative to the spindle equator. The arrow in the micrograph to the left of each trace indicates where each chromosome was severed, and the spindle poles are circled. The solid lines (Figure A & B) are linear regression fits used to determine oscillation speeds and amplitudes. The numbers in the ovals compare the oscillation amplitude before and after the ablation. A-I show significant increase in average amplitude (p<0.05, black oval). J-L show significant decrease in amplitude (p<0.05, dotted oval). M-P show no significant change (p>0.05, gray oval).

Figure 6. Estimation of the polar ejection force distribution.

Figure 6

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A) The relative change in the average amplitude of directional instability after severing a chromosome arm as a function of the average amplitude before severing the arm (squares). Black diamonds are control chromosomes located in the same cell as an experimental chromosome: in these cases the before and after amplitudes correspond to before and after severing the arm of the experimental chromosome. The average oscillation amplitude of the control chromosomes is 2.9 ± 1.6 μm (dashed line), and the dotted line is 2 standard deviations from the average. B) Estimation of the PEF distribution from the equation F=KAxn (see text). The two circled outlying data points were excluded from the line fit. The slope of the line, n, is 0.57 ± 0.11. The line fit does not pass through zero because of the decrease in oscillation amplitude as the mitosis progresses toward anaphase (see supplemental information), presumably due to increasing spindle microtubule density (e.g. [17]). C) From the line fit the PEF distribution is estimated to be proportional to x0.57 (black line), where x is the distance from the spindle equator. The straight dotted segments indicate regions outside the range of data where reversals occur. This differs substantially from the inverse square distribution (gray line), where the PEF is proportional to 1/(Λ-x)2, where Λ is half of the spindle length. D) Interpolar microtubule density at metaphase, and early anaphase of PtK1 cells, calculated from the data of Mastronarde et al. [17]. The polarity adjusted (net) density (squares) – the amount that the number of microtubules from one pole exceeds the other – is calculated by subtracting the right pole values (circles) from the left pole values (diamonds), and is similar to our estimation of PEF distribution (C, black line) for newt lung cells: steepest near the equator, and flattening toward the poles. The microtubule density then drops off very near the poles.

Not all chromosomes show an increase in oscillation amplitude after severing the arms, though all of them still exhibit directional instability. This can in part be attributed to normal variability and the tendency, indicated by the controls (Figure 6A diamonds), for the amplitude to decrease as mitosis progresses, but is also due to selection bias. Our studies necessarily focus on chromosomes whose directional instability can clearly be resolved and differentiated from the movements of other chromosomes, and these tend to be chromosomes undergoing large oscillations. This skews our analysis towards chromosomes that initially exhibit large oscillations, so there could be a tendency to decrease to more typical values (i.e. regression toward the mean), offsetting the increased amplitude due to severing the arms. Indeed analysis indicates that chromosomes having very high oscillation amplitude before surgery are less likely to show an increase in oscillation amplitude after arm shortening (Figure 6A). To compensate for this bias, we exclude data from three chromosomes exhibiting initial oscillation amplitudes more than two standard deviations from the mean (2.9 ± 1.6 μm), though this probably does not entirely compensate for the tendency to trend toward typical oscillation amplitudes (e.g. circled points in Figure 6A & B)

The Polar Ejection Force Distribution

Having established that direction reversals depend on the magnitude of PEFs, we can approximate the distribution of the PEFs from the relationship between the decrease in the length of the chromosome after severing an arm, and the resulting increase in amplitude. Assuming that the PEF increases monotonically as a chromosome moves away from the spindle equator, it can be approximated by the equation: F=KAxn, where F is the PEF, K is the average PEF per unit surface area of the chromosome, A is the surface area of the chromosome, x is the chromosome displacement relative to the spindle equator, and n is an exponent describing how the PEF increases as the chromosome moves away from the spindle equator. Note that the exact distribution of the PEFs may not follow this form, but it is a useful approximation since the exponent, n, captures the general curvature of the PEF distribution: positive curvature (n > 1) if the PEF rises increasingly steeply near the poles, as is the case for previously used approximations [14, 15]; negative curvature (n < 1) if the PEF increases less rapidly as the poles are approached; and n = 1 if the PEF increases linearly. To estimate the PEF distribution, we consider the force distribution before, Fb=KAbxbn, and after, Fa=KAaxan, severing a chromosome arm, denoted with subscripts b(efore) and a(fter). Then we consider the average values of x at the extremes of a chromosome's oscillations, denoted as Xb before, and Xa after severing the chromosome. We assume that at these locations, the PEF opposing movement of the leading kinetochore is equal to the maximum force that the kinetochore will bear before switching directions. Since we did not ablate the kinetochores or kinetochore MTs, we assume the kinetochore forces have not changed, so at Xb and Xa, Fb=Fa=constant. Based on this relationship, we balance and rearrange the force equations to obtain Ab/Aa=(Xa/Xb)n. Considering the high length to diameter ratio, and approximating a chromosome as a rod with constant diameter, Ab/Aa ≈ Lb/La where L is the length of the chromosome. Substituting L in place of A, we obtain Lb/La=(Xa/Xb)n, and taking the log of both sides of the equation, log(Lb/La)=n log(Xa/Xb). Fitting a line to log(Lb/La) plotted versus log(Xa/Xb) we solve for n (Figure 6B). We find n = 0.57 ± 0.11, less than unity and considerably different from the value of ∼ 2 for the inverse square relation used previously [14, 15].

Since the PEF has been hypothesized to depend on MT density [9, 12, 14, 15, 37, 38], we were intrigued by the low value of n, rather than the squared or higher relation that might be expected given 1) the spreading of relatively straight MTs as the distance increases from a common point of origin, the pole, and 2) the diminishing number of MTs originating from a given pole as the equator is approached from that pole, since not all MT extend the entire length of the half spindle [17]. To explain this, we examined serial section electron microscopy reconstructions of interpolar MTs in the mitotic spindle of PtK cells obtained by Mastronarde et al. [17]. Note that MTs on the outside of a kinetochore fiber bundle could conceivably contribute to PEFs, but these were not considered since using the reconstruction data [17] we estimate they make up only ∼5% of the spindle MTs. Two sets of MT data were provided by The Boulder Laboratory for 3-D Electron Microscopy of Cells: one for metaphase, and the other early anaphase. We calculate the density in each case by counting the number of MTs in each spindle cross-section and dividing by the spindle cross-section area (Figure 6D). The density of MTs is low near the spindle poles in early anaphase and metaphase, though substantially higher near one of the poles during metaphase (Figure 6D, metaphase left pole). The decreased density near the poles reflects the fact that many MTs do not extend all the way to the pole, as noted by Mastronarde et al. [17]. The MT density then rises to a peak before dropping off a few microns from the poles. The MTs emanating from each pole are opposite polarity, and so should result in opposing PEFs when interacting with the same chromosome. Thus by subtracting the MT density of one pole from the other, we obtain the expected PEF distribution (squares in Figure 6D), which turns out to exhibit negative curvature moving from the equator toward the pole, consistent with our estimation of the PEFs over the region near the spindle equator where directional instability of bioriented chromosomes generally takes place. This analysis supports the hypothesis that PEFs are proportional to MT density, and suggests that the previously used inverse square relation (Figure 6C light gray curve) fails to capture the PEF distribution because it does not account for the decreasing MT density near the poles, or the significant effect of MTs that extend past the spindle equator.

Discussion

To examine the role of PEFs in mitotic chromosome movements, we perturbed the balance of forces by severing chromosome arms with an ultrafast pulsed laser. We find that the resulting reduction of PEFs increases the amplitude of chromosome oscillations without affecting the hallmarks of directional instability – persistent speeds and abrupt reversals of direction. PEFs can be generated by the interactions of chromosome-bound motors with MTs [12], and directional instability is suppressed when these motors are inhibited [3]. Potentially PEFs may also arise from polymerization of MTs into chromosome arms (reviewed in [39]), though this is likely negligible in our experiments (see Supplemental Information). It has been suggested that chromosome reversals are induced by PEFs [e.g. 9], but as pointed out by Khodjakov et al. [16], this is not a prima facie requirement for directional instability. On the contrary, from changes in the amplitude of directional instability induced by severing chromosome arms, we now establish that PEFs do indeed induce chromosome reversals. At the maxima of a chromosome's oscillations, the PEF reaches the maximum force that the leading kinetochore can bear before failing, and since the speed of the chromosome remains constant, the less rapidly PEFs rise, the larger the excursions and amplitude of oscillations. Thus shortening a chromosome's arm increases the amplitude of directional instability by decreasing the area on which the PEFs act (Figure 6B). That this does not change the speed ([32] and figure 4) contrasts with the monotonic relation between force and velocity that is observed for conventional ATP-dependent motor proteins walking along MTs. We can therefore conclude that poleward forces developed at the kinetochore either are not generated by motors exhibiting this conventional behavior, or that the abrupt reversals reflect higher order behavior arising when groups of motors work together (see Supplemental Information). In either case, the constant speeds over varying loads represent a significant constraint that must be considered for modeling chromosome movements.

Since the leading kinetochore follows the tips of depolymerizing MTs, load independence implies that the rate of MT depolymerization at a kinetochore is not directly affected by the tension on a kinetochore; this significantly constrains the possible mechanisms by which kinetochores maintain attachments with kinetochore MTs (for review see [40]), and indicates that in vertebrates attachments are not maintained by slowing depolymerization in response to increased tension [41]. However, attachments could be maintained by switching MTs between polymerizing and depolymerizing states as seen in budding yeast [42], or the kinetochore fiber could be maintained by addition of MTs during the normal kinetochore MT turnover [8, 15].

Recently Stumpff et al. reported that the amplitude of directional instability is increased when kinesin-8 Kif18A is depleted in HeLa cells [18], and they suggest that directional instability may be guided by a gradient of Kif18A on kinetochore MTs. Our results show that PEFs must also be considered, and we propose an alternative interpretation of their data that directly integrates their results and ours (see Supplemental Information). Moreover our observation that closely packed chromosomes and even severed chromosome arms may transiently become synchronized (e.g., Figure 3, supplemental figure S1) suggests that directional instability is broadly influenced by mechanical constraints in the crowded spindle environment. This suggests an explanation for why directional instability occurs at all. PEFs and directional instability could prevent chromosomes from becoming entangled or damaged moving through other spindle components (e.g. other chromosomes and MTs). By pushing the arms toward the end of MTs, chromokinesins may prevent chromosomes from becoming ensnared in the spindle, and oscillations could allow a chromosome to switch directions when it encounters an obstruction, and try to pass again after the obstruction is removed (e.g. a dynamic MT could depolymerize). This is consistent with Levesque and Compton's [3] observations when the chromokinesin Kid is inhibited: despite the suppression of directional instability, chromosomes can still congress, but the chromosome arms appear tangled in the spindle, and the mitotic failure rate is intolerably high, with about 1/5 of cells failing to complete anaphase (For further discussion on this, and the relation between oscillations and position in the spindle, see Supplemental Information).

From the relationship between the severed length of the chromosomes and the change in oscillation amplitude, we calculate the PEF distribution, finding a sub-linear increase with the displacement from the spindle equator (exponent 0.57, Figure 6B): the PEF increases most rapidly near the equator and flattens toward the poles (Figure 6C). Although different than previously envisioned [14, 15], this result is similar to the PEF distribution that we estimate from the density of interpolar MTs in metaphase and early anaphase in PtK cells (Figure 6D) [17], providing strong support for the hypothesis that PEFs are proportional to the MT density and the size of chromosome arms [9]. Although high quality TEM data is only available for PtK cells, we estimate a similar MT density distribution from fluorescence microscopy data from newt lung cells (supplemental figure S2).

We have characterized the role of PEFs in direction instability, establishing that PEFs influence the force generating state at kinetochores, and constraining the potential mechanisms by which kinetochores generate forces and maintain attachments to spindle MTs. We estimate the distribution of PEFs, providing support for PEFs scaling with MT density. Our data reject exclusive “traction fiber” models, and other models in which direction switching is independent of PEFs (e.g. [16, 18, 19]), though it is possible that such mechanisms contribute to guidance in parallel with PEFs (e.g. see [18]). Our data supports mechanisms that predict the speed of kinetochore motors is load-independent up to the point where PEFs cause them to fail, and argues against mechanisms where MT attachments to kinetochores are maintained by changing the rate of MT depolymerization in response to tension.

Experimental Procedures

Tissue Culture

Newt lung cultures are prepared as previously described [43]. Briefly, red-spotted newts (Notophthalmus viridescens) obtained from Connecticut Valley Biological Supply Co. (Southampton, MA), are euthanized by immersion for 30 minutes in 1 mg/ml tricaine (Sigma #A5040, St. Louis, MO). The lungs are sterilely dissected, cut into 1 mm2 pieces, and soaked in L-15 medium supplemented with FBS and antibiotics for 24 hours. Explants are then lightly squashed onto the Petri dish glass, covered with a piece of dialysis filter, and held down by a Teflon ring, and incubated at room temperature (22-25°C). After about 7 days, when a few rows of epithelial cells surround the lung fragment, the dialysis filter is removed. Experiments are performed about 2 weeks after dissection. Cells are selected based on flatness during mitosis, the visibility of centrosomes, and the ability to identify individual chromosomes.

Femtosecond-laser Micro-surgery

For all experiments, we use a Zeiss 100×/1.30 NA Neofluar Phase 3 objective and matching condenser. High-precision ultrafast laser surgery is performed using a diode-pumped Nd:glass chirped pulse amplification (CPA) laser system (Intralase Corp., Irvine, CA) that generates 600 to 800 fs pulses at a repetition rate of up to 3 kHz. Dichroic and polarized mirrors couple the laser pulses into the illumination light path of an inverted microscope (Figure 2; Zeiss Axiovert 200, Thornwood, NY). To achieve high precision, the laser is focused to a diffraction-limited spot by completely filling the back focal aperture of the objective. A tri-axial, computer-controlled, piezoelectric stage (Mad City Labs, Inc., Madison, WI) is mounted on the manual stage to achieve nanometer precision while allowing scanning across a 35mm Petri dish with 14mm microwell (MatTek Corp., Ashland, MA). Custom software and design electronics allows control of laser pulse delivery, specimen targeting, and image capture.

Chromosome movements before and after ablation are tracked by phase-contrast video microscopy, time-lapse recorded at 2 to 3 second intervals. Phase-contrast is used instead of DIC because the greater depth of focus simplifies tracking, and assures that chromosomes are severed completely, as both sister chromatids are visible if either is in focus. This was verified by scanning the focus in the z-axis. Using a pulse energy of 2 to 3 nJ, the laser is scanned in a raster pattern to slice across a chromosome arm. Scans are repeated, once from top to bottom (estimated by the diameter of the chromosome), then again from bottom to top at 10nm steps, to ensure complete ablation. The total volume of ablated material is approximately 3 μm3, less than 0.1% of the cell volume.

Chromosome Tracking

We developed semi-automatic tracking software, using an algorithm and operating procedure similar to that described in Skibbens et al. [1], implementing National Instruments pattern matching routines. Additional processing to enhance tracking accuracy includes contrast equalization, image thresholding, and calculating the centroid of the cross-correlations. Reproducibility and accuracy were demonstrated by the tracking stationary objects, and by verifying consistent tracking data was obtained by independent operators. The accuracy depends on the variability of the chromosome image during the course of an experiment. Rolls, yaws, and pitches decrease the accuracy, especially if a chromosome moves out of the imaging plane. If significant changes in the region of interest occurred, tracking was terminated, or if the chromosome was still clearly identifiable, a new region of interest was selected.

Analysis

During mitosis the entire spindle often moves, and to accurately measure directional instability this must be taken into account, so the chromosome position is measured relative to one of the centrosomes. Traces are fit with multiple lines (e.g. lines overlaying data points in Figure 5A, B); each line fits the chromosome motion in a single direction within an oscillation cycle. The extent of a chromosome excursion is determined by iteratively changing the intersection of the line fits before and after a direction reversal, until both fits yield the minimum mean square error. The lines are categorized as either poleward or anti-poleward if the direction of movement persists for more than 10 seconds and the speed of movement is greater than 1/3 of the average speed of the particular chromosome. This lower bound is imposed to exclude periods where directed chromosome movement, and thus directional instability, are unclear. The speed is calculated from the slope of the line fits. Student's t-test is used to compare the speed of chromosome movements toward and away from the spindle equator, and before and after the laser ablation. The oscillation amplitude is calculated as the distance between direction reversals, and this distance is averaged across all reversals occurring before, and after surgery. For each chromosome, the average amplitude before and after surgery is compared using Student's t-test.

The movements of 32 chromosomes were tracked before and after severing their arms. Sixteen were rejected for one or more of the following reasons: tracking was poor due to the chromosome moving out of the focal plane, or becoming obscured by another chromosome in close proximity (5); following surgery the cell enters anaphase before a full cycle of oscillations is completed (5); chromosome severed very close to the centromere, possibly damaging the kinetochore (2); the centrosome was difficult to track (3); chromosome not bioriented (1). The 16 severed chromosomes that were tracked were in 8 cells with the distribution per cell: 1, 1, 1, 2, 6, 1, 2, 1.

Supplementary Material

01

Acknowledgments

We thank J.D. Hoff and J. Nees for laser support, E. Meyhöfer and A.P. Joglekar for valuable discussion, and D. Mastronarde, J. R. McIntosh, and the Boulder Laboratory for 3-D Fine Structure for PtK1 spindle structure data. This work was supported by NSF MCB-0334835, and NIH R01GM072006 to AJH. KK was supported by the Cellular Biotechnology Training Grant at University of Michigan.

Footnotes

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