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BIOPHYSICS
Microtubule movements on the arms of mitotic chromosomes: Polar ejection forces quantified in vitro
Department of Biomedical Engineering, University of Michigan, 2131 Gerstacker, 2200 Bonisteel Boulevard, Ann Arbor, MI 48109
Communicated by J. Richard McIntosh, University of Colorado, Boulder, CO, July 18, 2005 (received for review April 12, 2004)
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mitosis | optical tweezers | chromokinesin | Kid
PEFs could be caused by plus-end-directed chromokinesin MT motor proteins on chromosome arms (11–17) and the polymerization of spindle MTs into a chromosome (4). Although "chromokinesin" first referred to the protein isolated from chicken (11), the name has since grown to connote the family of kinesin-like motor proteins with a DNA-binding cargo domain that immunolocalize to chromosome arms and the spindle MTs during mitosis (11–17). Presumably, these motors produce force against spindle MTs in lateral contact with chromosome arms. Likewise, MT polymerization has been demonstrated to produce force against barriers (18, 19), suggesting a plausible mechanism for PEF generation by end-on contact of a MT tip (4). Again difficulties resolving chromosome–MT interactions in vivo make it hard to determine whether these postulated mechanisms produce forces that could significantly affect chromosome movements.
To address the lack of data on the individual interactions between spindle MTs and chromosome arms, we present in vitro experiments that directly observe and quantify PEFs exerted by chromosome arms against single MTs. By using optical tweezers, individual MTs are placed across the arms of isolated prometaphase Chinese hamster ovary (CHO) chromosomes adhered to the upper surface of a flow chamber (see Fig. 1 and Materials and Methods). The MT movements resulting from these interactions are observed by using a silica bead attached to the MT and held in the optical trap. Bead movements are monitored by high-resolution back focal plane interferometry that records the location of the bead relative to the center of the optical trap with nanometer precision (20, 21). We observe unidirectional forces and movements that explain how PEFs can direct chromosome movements without producing large local distortions of the easily deformed chromosome, and why discrete force-generating interactions between chromosome arms and single MTs are not observed in vivo. Antibody inhibition experiments implicate the chromokinesin Kid as the motor producing these forces. Combined with in vitro research on chromosome structure and Kid activity, these results build a compelling description of the biomechanics of polar ejection forces, wherein the chromokinesins act gently on their cargo to bias the chromosomes toward the spindle equator.
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Attaching MTs to Silica Beads by Biotin-Streptavidin. The paclitaxel-stabilized MTs are biotinylated by the addition of 1.7 mM biotin-XX-SE (Molecular Probes) in DMSO and incubation for 15 min at 37°C. The biotinylation reaction is quenched by the addition of 3 vol of 100 mM glycine/10 µM paclitaxel solution. After biotinylation, the MTs are pelleted in an Airfuge (Beckman), and the pellet is washed twice with BRB-80 buffer/10 µM paclitaxel and then resuspended. This washing procedure is repeated once.
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The biotinylated MTs and streptavidin-coated silica beads are mixed together for each experiment, with concentrations selected to produce about one 1 MT bound to each bead (3).
Optical Tweezers. The optical tweezers instrument used in these experiments has been described in ref. 20. The device features: (i) acousto-optic deflectors (AODs) for trap-steering, (ii) back-focal-plane interferometry with quadrant photodiode detectors (QPDs), and (iii) both differential interference contrast (DIC) and fluorescence microscopy concurrent with optical trapping. The optical tweezers are calibrated for two parameters: 
, the QPD sensitivity in V/nm, and 
, the trap stiffness in pN/nm. The calibration is verified by three methods: viscous drag, power spectral analysis, and application of the equipartition theorem.
In Vitro Motility Assay. An aliquot of chromosomes is mixed with a1/100 dilution of 0.3 mg/ml DAPI solution. The chromosomes are centrifuged and resuspended in "motility assay buffer": BRB-80 supplemented with 10 µM paclitaxel, 4 mM MgCl2, 1 mM DTT, a fluorescence antifade mixture (30 mM glucose/0.6 mg/ml glucose oxidase/0.12 mg/ml catalase), and ATP (0 or 4 mM). The chromosome solution is introduced into an 
40-µm-deep "flow chamber" that is created between a microscope slide and cover glass separated by two thin strips of aluminum foil. A thin film of vacuum grease holds the aluminum foil and glass in place. The chamber is inverted and placed for 15 min on an iced aluminum block. After the chromosomes have settled onto the upper surface, the chamber is reverted and then rinsed with 3 vol of motility assay buffer. After introduction of streptavidin-coated silica beads and freshly biotinylated MTs, the chamber is sealed with nail polish for use.
By using the optical tweezers, one silica bead is trapped and lifted to a distance 2 µm below the upper surface. An Argus II image processor (Hamamatsu Photonics, Bridgewater, NJ) is used to perform background subtractions and contrast enhancements that allow for the visualization of the MT(s) attached to the bead. Individual MTs are clearly distinguishable under this video-enhancement technique (Fig. 1). Next, lone chromosomes are identified by DIC and fluorescence microscopy; each chromosome is inspected for shape, wholeness, and contamination with other cellular debris. The AOD is used to steer the bead and MT underneath the chromosome, the laser power is set to a precalibrated level, and the MT is brought into contact with the chromosome by using the z-axis focus knob of the microscope. The MT is positioned across the chromosome arm such that the end of the MT does not encounter the chromosome arm (Fig. 1). Contact between the MT and the chromosome is detected from damping of thermal vibrations of the MT and/or when a low-power optical trap is unable to move the MT away from the chromosome. After contact is established, the optical trap is left stationary, and the displacement of the silica bead bound to the MT indicates movements resulting from interactions with the chromosome. The position of the bead in the optical trap is monitored with the QPD at 4 kHz, and video is recorded throughout. The 4-kHz QPD voltage signals are analyzed by (i) low-pass filtering with a cut-off frequency of 25 Hz, (ii) subtraction of a QPD baseline signal to zero the position signal, (iii) application of QPD sensitivity , (iv) application of the Pythagorean theorem to merge x-axis and y-axis QPD signals into a single radial displacement signal, and (v) application of trap stiffness to convert the displacement signal into a force signal. The data streams were recorded at a common trap stiffness of = 0.074 pN/nm.
Antibody Experiments. These experiments were performed by using primary polyclonal rabbit antibodies raised against the human Kid protein (24) and the human KIF4 protein (25) (see Supporting Text, which is published as supporting information on the PNAS web site). A Western blot was performed to demonstrate the cross-reactivity of the antibodies to monkey, mouse, and hamster cell lysates (COS, CAD, CHO, respectively). Two sets of experiments were performed: (i) antibody blocking of MT binding to chromosomes, and (ii) quantitative fluorescence measurements of motor density.
In the antibody blocking experiments, chromosomes are washed and adhered to the upper surface of a flow chamber as described above, using identical buffers. In the absence of ATP, a solution of paclitaxel-stabilized, rhodamine-labeled MTs is introduced into the flow chamber. Chromosomes are located and inspected as described above, and then fluorescence and/or DIC microscopy is used to capture an image of the number of MTs that bind to lone chromosomes. Counts are performed on DAPI-labeled chromosomes (n = 25), anti-Kid-labeled chromosomes (n = 21), and anti-KIF4-labeled chromosomes (n = 15). A control was also performed by using antibodies to topoisomerase II
, a chromatin cross-linking protein (n = 15).
For quantitative fluorescence microscopy, the primary antibody is used along with a FITC-conjugated monoclonal anti-rabbit IgG secondary antibody. A Zeiss Axioplan 2 microscope is fitted with a CoolSnap CF cooled charge-coupled device (CCD) camera (Photometrics, Tucson, AZ), and the camera's signal is recorded by using V++ software (Digital Optics, Auckland). The calibration of the quantitative fluorescence apparatus is carried out by using standard solutions of secondary antibody, as well as commercially available fluorescence standards (26). The calibration factor kF (pixel intensity/antibody) relates CCD pixel intensity to the number of secondary antibody molecules contributing to the image. This factor is computed from an integral based on z-axis slices of the chamber volume; the integral evaluates the contribution of each fluorophore in the z-axis slice.
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where IT is the measured pixel intensity, cF is the fluorophore concentration, z is the depth of the flow chamber, x0 and y0 are the dimensions of the rectangular region of interest, and r0 is the spot size of the illumination light at the focal plane (see Supporting Text and Fig. 4, which is published as supporting information on the PNAS web site). Calibrations were performed on five dilutions of the secondary antibody solution (1:50, 1:100, 1:200, 1:500, and 1:1,000) from a stock of 1.1 mg/ml (see Fig. 5, which is published as supporting information on the PNAS web site). Camera-noise background was subtracted from all images. The calibration experiments were performed before and after each experiment series with chromosomes, as well as in separate control experiments to characterize bleaching. The calibration experiments were found to vary less than 10% from slide to slide and from day to day.
The measurements on chromosomes use a 1:1,000 dilution of the primary antibody (anti-Kid or anti-KIF4), a 1:100 dilution of secondary antibody solution, and a 1:100 dilution of 0.3 mg/ml DAPI solution. After 10–15 min, the chromosomes are pelleted and resuspended in BRB-80 buffer/4 mM MgCl2/antifade mixture. The labeled chromosomes are adhered to the upper surface of a flow chamber, located, and inspected as described above. Then, a 10-s exposure FITC image is captured. In the absence of anti-Kid (see Fig. 6, which is published as supporting information on the PNAS web site) or anti-KIF4 antibody, the secondary antibody fails to localize to the chromosomes (see Table 1, which is published as supporting information on the PNAS web site).
Quick Stretch Experiments. In a quick stretch experiment, a chromosome–MT interaction is established in the presence of ATP as described above. After contact is established, the AOD is used to displace the trap center rapidly to a new location. The AOD rise-time is 4.2 µs, which is the effective switching rate between trap positions. The silica bead immediately moves to a new equilibrium position in response to the trap displacement.
The bead displacement associated with each quick stretch is a fraction of the total trap displacement; the remainder is attributed to the stretching of compliant elements in the system (
x in Fig. 3B). The change in force divided by the stretching of the compliant elements yields the stiffness. Multiple quick stretches are performed, and a stiffness value is calculated for each.
The average stiffness of the series compliant elements is used to estimate the velocity of motor activity in the in vitro motility assay. The velocity of bead movements measured from the QPD data trace is multiplied by the ratio of (chromo + trap)/chromo to yield the estimated motor velocity. In other words, the movements in the QPD data are a fraction of the total MT movement relative to the motor, where this fraction is determined by the ratio of the total stiffness and the stiffness of the series compliant elements (see Supporting Text).
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Additionally, the motor forces are unidirectional: for a given MT, force is generated in only one direction. The displacement signals are never observed to move both above and below the zero-force baseline position; thus, although a given MT may reverse direction as it relaxes into the center of the trap, the direction of forces generated by chromosome-bound motors is always the same. This unidirectionality implies that the motor proteins producing the movements are also unidirectional, and that plus-end-directed motors and minus-end-directed motors do not coexist on the chromosome arms.
To estimate the average PEF per MT, we calculated the time-averaged force across each chromosome–MT interaction, where force is defined as displacement away from the baseline. The time-averaged force across all chromosome–MT interactions was 0.5 pN per MT. By taking the average force for all interactions, we hope to approximate how the force is distributed across all chromosome–MT encounters in vivo, and in turn estimate the average force experienced by an entire chromosome. In conjunction with spindle microtubule density, the time-averaged force allows for the best estimate of the average PEF per chromosome.
Although the precise molecular basis of PEFs is of great interest, force and displacement measurements are paramount and the most relevant to mechanical models of chromosome movement. They represent an in vitro observation of the in vivo circumstance of a spindle MT in lateral contact with the chromosome.
Antibody Inhibition of CHO Kid Blocks MT Movements. Because these ATP-dependent movements indicate the presence of motors on the chromosome arms, we examined our chromosomes for chromokinesins (29, 30). Chromosomes were stained with polyclonal primary antibodies raised against the known human chromokinesins Kid and KIF4 (24, 25). Both antibodies bound to the chromosomes.
We tested whether these antibodies inhibit the efficiency of MT binding to chromosomes in vitro. In the absence of ATP and antibodies, MTs introduced into a flow chamber will bind to chromosomes in a rigor condition. At moderate MT concentration (1:100 dilution of 5 mg/ml polymerized tubulin), the efficiency of binding (eB) was 1.6 ± 0.8 MTs bound per chromosome. In contrast, in the presence of the anti-Kid antibody, MTs do not bind to chromosomes at this concentration. In the presence of the anti-KIF4 antibody, however, the MT binding was only modestly reduced relative to controls; eB = 0.8 ± 0.4 MTs per chromosome. Further control experiments were performed with an antibody to topoisomerase II, a chromatin cross-linking protein, which did not inhibit MT binding relative to controls (eB = 1.8 ± 0.4 MTs per chromosome). These results argue that Kid mediates the binding of MTs to chromosomes in vitro and that the motors form rigor-bonds in the absence of ATP, as is typical for motor proteins. The binding efficiencies for the four experimental conditions retained similar ratios as the concentration of MTs was varied (see Table 2, which is published as supporting information on the PNAS web site).
The in vitro motility assay was then repeated with chromosomes preincubated with the antibodies to Kid or KIF4. For Kid-blocked chromosomes, no motor activity was observed for five chromosome–MT interactions, over a total of 50 min. For KIF4-blocked chromosomes, the observed activity was indistinguishable from the data presented in Fig. 2, although it should be noted that the KIF4 antibody has not been conclusively demonstrated to inhibit KIF4 function (see Supporting Text).
Immunostaining was also used to determine the density of Kid and KIF4 on chromosomes by quantitative fluorescence, using a FITC-conjugated secondary antibody. The fluorescence measurement was calibrated with standard solutions of secondary antibody, and the calibration was verified with commercially available fluorescence standards (26). The fluorescence intensity measured from both antibodies varied less than 10% between experiments (see Fig. 5). We record an average level of 400 ± 100 Kid molecules per µm2 of chromosome surface and 300 ± 50 KIF4 molecules per µm2 at a saturating concentration of the primary antibodies. At these densities, a MT laterally encountering a chromosome arm (modeled as interaction with a planar surface of 1 µm x 100 nm) would be within range of 10 Kid motor proteins and 7 KIF4 proteins. These values could be lessened if some motors recorded in the fluorescence signal were not physically accessible to MTs. This density is logical for producing PEFs, as it is sufficient to ensure parsimoniously that most MTs encounter motors.
Velocities of MT Movements. An estimate of the motor velocities in our experiments requires knowledge of the series compliances present in the mechanical system: (i) the bead-to-MT compliance and (ii) the chromosome compliance (Fig. 3A). As the chromokinesins perform work on the MT, a portion of this work will be stored as strain energy within these compliances. To estimate the magnitude of the series compliances, we performed quick-stretch experiments on a MT attached to a chromosome, in which the optical trap is quickly moved to a new location (Fig. 3A 
3B and see Materials and Methods). The bead moves to a new equilibrium location, which is a fraction of the total trap displacement; because the time course of this movement is much faster than the chromosome-bound motors, the series compliant elements in the system are stretched (x in Fig. 3B). The change in tension divided by the stretching gives the stiffness of the bead–MT–chromosome complex.
Fig. 3C shows a data trace taken during a quick-stretch experiment and Fig. 3D shows the calculated stiffness values from two such experiments. Because the series compliance undoubtedly varies with the position on the chromosome and with time as different motors engage and disengage from the microtubule, the value is expected to be intrinsically variable. Such variability is observed experimentally; even at a single location on a chromosome the displacements of the bead may vary 2-fold in response to a given trap displacement (Fig. 3). The average series stiffness = 0.027 pN/nm gives an estimate of the peak motor velocities of 63 ± 41 nm/s (e.g., arrows in Fig. 2); a more cautious estimate puts the peak motor velocity on the order of 60 nm/s. These velocities are in reasonable agreement with those reported for recombinant Kid (31) and are similar to chromosome velocities during mitosis (17 nm/s or 1 µm/min).
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, and more) (3, 32). Thus, we believe that these in vitro mechanical characteristics apply to the lateral interaction between spindle MTs and chromosomes in the cell. Nevertheless, as for any reduced system, it is possible that some physiologic context has been lost.
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0.5 µm from the spindle equator and surpasses 100 pN at 1.6 µm from the equator during metaphase. This magnitude makes sense for guiding prometaphase chromosomes to the spindle equator, because the force required to affect kinetochore-driven chromosome movements in anaphase, as measured in meiotic insect cells, is on the order of 100 pN (35).
The antibody binding experiments and the quantitative fluorescence measurements strongly suggest that the CHO homologue to Kid is the force-producing agent in these experiments. Antibody inhibition of Kid in HeLa cells causes a phenotype indicative of a loss of PEFs (24). The movements we observe are also qualitatively similar to those produced by bacterially expressed Kid, albeit at much higher motor densities. Yajima et al. (31) coated microbeads with a 5,000-fold excess of a biotinylated construct of Kid and used optical tweezers to place these beads on immobilized MTs. These experiments demonstrated that Kid is a plus-end-directed motor protein. On these well coated beads, the unknown number of active motors showed frequent backwards slippage and stalls at 2 pN and moved at an average velocity of 160 nm/s, in movements visually similar to the movements observed in our experiments.
In our in vitro motility assay, the regions of chromosome–MT overlap were in excess of 1 µm. The quantitative fluorescence measurement suggests that the movements we observe are likely generated by at least one Kid motor, and the stalls observed at various levels of force suggest that multiple motors are involved (e.g., Fig. 2B). Conversely, if the motors were in much higher numbers we might expect sustained movements, such as when many myosin motors continuously propel actin filaments in vitro, although a single motor cannot (36). It remains theoretically possible that more than one type of motor is responsible for the observed forces, because the other chromokinesin KIF4 is also present on the CHO chromosome arms. However, antibody inhibition of KIF4 in HeLa cells causes no apparent change in prometaphase chromosome movements (Duane Compton, personal communication). In addition, the Drosophila homologue to KIF4, KLP3A (16), and the Xenopus homologue, Xklp1 (37), affect spindle pole formation and MT dynamics, respectively. We believe that (i) the similarity of the in vitro Kid data to our experimental findings, (ii) the inhibition of MT binding by anti-Kid antibodies in vitro, and (iii) the in vivo anti-Kid antibody-knockout experiments (24) discussed below suggest that Kid is the principal motor protein that produces lateral PEFs.
The chromosome-bound Kid activity we observe is quite different from other motors in the kinesin family. Compared with conventional kinesin, Kid is slower and weaker; indeed, it is slow and weak compared with dynein and myosin as well. Its peak velocities are 25–30% of the velocity of kinesin, and whereas individual kinesin motors produce 5 pN of force (27, 28), our results indicate a maximum force of only 2–3 pN from what is probably the combined effort of multiple chromokinesins. Likewise, although one kinesin motor can propel a MT for many micrometers, even multiple chromokinesins appear unable to produce movements sustained for more than tens of nanometers (31).
The question arises: Why would nature evolve a specifically weak motor protein that cannot sustain movement? These characteristics of Kid make sense given the flexibility of the motor's substrate, the mitotic chromosome. The chromosome is made up of chromatin fiber that is cross-linked together in a complex manner involving numerous proteins. Mechanically, the chromosome is an elastic isotropic structure capable of 5x increases in length followed by a return to its native state (38, 39). The Young's modulus for mitotic chromosomes is a mere 102 to 103 Pa (40), which is several orders of magnitude less than the modulus for rubber (1.7 MPa) and for nylon (2.4 GPa). The material properties are perhaps akin to cotton candy, fibrous and easily deformable (data not shown), except the chromosome exhibits greater elastic ability to return to its native state. If the cell targeted a strong, processive motor onto this highly elastic and fibrous material, the action of the motor protein would stretch and distort the condensed chromosome structure. Stretching of the chromosome would risk separation of chromatin strands from the chromosome arm, entanglement of these strands, and loss of individuation of the sister chromatids. It is a quandary to carry such delicate cargo.
Yet the cell needs the weak PEFs produced by Kid for the fidelity of the mitotic process. When Kid is inhibited by antibody injection (24), a significant fraction of HeLa cells (17.5%) never initiate anaphase, demonstrating that lack of Kid causes an unsustainable mitotic failure rate for an organism. In addition, the video data from Levesque and Compton (24) suggest the arms of some chromosomes become entangled near the spindle pole. Moreover, the chromosomes in treated cells move abnormally; all of the observed chromosome motions lacked the characteristic oscillations known as "directional instability." (41) These oscillations occur before and after congression to the spindle equator and are characterized by periods of approximately constant velocity movement punctuated by abrupt changes in direction. This behavior argues that Kid-mediated PEFs enable directional instability. Indeed, a mechanistic model for directional instability predicts the magnitude of PEFs, the only entirely free parameter in the model, to be 0.3 pN per MT, very near our measurement of 0.5 pN per MT (34). Our measurements are also in good agreement with the 1.1-pN PEF estimated assuming that PEFs are generated by MTs polymerizing into chromosomes, although the mechanism modeled is fundamentally different (8).
The behavior of Kid on chromosome arms is well suited for producing the requisite PEFs. This motor protein exerts force against MTs through slow, weak, and discontinuous action to bias chromosome movements toward the spindle equator. Because movements along a single MT are not sustained, chromosomes are not unduly stretched or damaged; indeed, this lack of sustained force explains why no clear evidence of forces generated against single MTs on the arms has been observed in vivo. However, the combined action of many chromokinesins against the spindle MTs will generate a significant "polar wind" to push the chromosome arms away from the regions of higher MT density at the spindle poles (42). These lateral PEFs provide a crucial force that enables directional instability and prevents the chromosome arms from becoming entangled in the dense cytoskeletal matrix within the spindle.
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Abbreviations: PEF, polar ejection force; MT, microtubule; QPD, quadrant photodiode detector; AOD, acousto-optic deflector; DIC, differential interference contrast.
* To whom correspondence and requests for materials should be addressed. E-mail: ajhunt{at}umich.edu.
© 2005 by The National Academy of Sciences of the USA
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