Accurate chromosome segregation depends on proper kinetochore–microtubule attachment. Upon microtubule interaction, kinetochores are subjected to forces generated by the microtubules. In this work, we used laser ablation to sever microtubules attached to a merotelic kinetochore, which is laterally stretched by opposing pulling forces exerted by microtubules, and inferred the mechanical response of the kinetochore from its length change. In both mammalian PtK1 cells and in the fission yeast Schizosaccharomyces pombe, kinetochores shortened after microtubule severing. Interestingly, the inner kinetochore–centromere relaxed faster than the outer kinetochore. Whereas in fission yeast all kinetochores relaxed to a similar length, in PtK1 cells the more stretched kinetochores remained more stretched. Simple models suggest that these differences arise because the mechanical structure of the mammalian kinetochore is more complex. Our study establishes merotelic kinetochores as an experimental model for studying the mechanical response of the kinetochore in live cells and reveals a viscoelastic behavior of the kinetochore that is conserved in yeast and mammalian cells.

The function of many biological systems is known to depend on the mechanical properties of the system components. For instance, it is widely acknowledged that the mechanical properties of muscle cells dictate muscle function and that certain molecular components of connective tissues confer the elasticity necessary to react to mechanical stress without rupturing. Whereas physiology approaches have been used for many years to study the mechanics of living tissues, studying the mechanical properties of subcellular structures has been a more challenging endeavor. Nevertheless, it is believed that the mechanical properties of certain subcellular structures are important for proper cellular function, and in recent years, several investigators have used cell biology and biophysics approaches to study such properties. For instance, biophysical approaches have been used to study the mechanical properties of mitotic apparatus components, including chromosomes (Poirier et al., 2000; Sun et al., 2011) and spindles (Gatlin et al., 2010; Shimamoto et al., 2011). Moreover, recent studies suggested that the mechanical properties of kinetochores (KTs) and the underlying centromeric chromatin may be important for several KT functions, including establishment of correct attachment of KTs to microtubules (MTs), correction of erroneous KT attachments, chromosome congression, and chromosome segregation (Loncarek et al., 2007; Maresca and Salmon, 2009; Uchida et al., 2009; Akiyoshi et al., 2010; Stephens et al., 2011, 2013; Dumont et al., 2012; Umbreit et al., 2014). It is particularly important to analyze such KT properties in the context of live cells, where KT behavior is determined not only by its intrinsic mechanical properties but also by multiple KT-independent factors. Here, we used anaphase merotelic KTs as an experimental model to investigate the mechanical response of eukaryotic KTs upon release of the pulling forces exerted by MTs. Merotelic KTs are attached to MTs emanating from both spindle poles and, during anaphase, become laterally stretched by opposing pulling forces exerted by the bound MTs (Khodjakov et al., 1997; Cimini et al., 2001; Gregan et al., 2007). In our assay, we released the pulling forces acting on the merotelic KT by laser severing of attached MTs (Fig. 1 A) and examined the dynamics by which KT length changed. The mechanical properties of the KT were then interpreted by using two simple theoretical models that took into account the kinetics of KT length changes.

### Stretched KTs progressively shorten after MT severing in both PtK1 cells and fission yeast

We first analyzed mammalian PtK1 cells stably expressing outer KT component Hec1 fused to GFP (Hec1-GFP), released from nocodazole to increase the frequency of merotelic attachments (Cimini et al., 2001) and microinjected during prometaphase with X-rhodamine–labeled tubulin to visualize the spindle. Once cells reached anaphase, we selected those displaying merotelically attached KTs and used a focused laser beam to sever one of the two MT bundles attached to the stretched merotelic KT (Fig. 1 A, single ablation). Depolymerization of MT plus ends at the site of ablation indicated successful MT severing (Fig. S1 A). Cells were imaged every 2–5 s for 5–10 min, and the changes in KT length upon release of the pulling forces were analyzed. We found that upon successful ablation, stretched KTs typically shortened gradually after severing of the K-fiber (Fig. 1, B–D; Video 1; and see Fig. S2 A for mean trace data and Fig. S1, C and D, for less frequent types of response). Recent studies found more rapid relaxation times of the distance between sister KTs after laser severing of K-fibers in metaphase cells (Elting et al., 2014; Sikirzhytski et al., 2014). However, it is difficult to compare our data with the data from those studies because of the substantially different experimental setups (i.e., anaphase merotelic KTs vs. metaphase chromosomes). This difference in relaxation times could be due to various causes, including considerably lower stretch of individual KTs in metaphase than that observed for anaphase merotelic KTs and the presence of centromeric sister-chromatid cohesion in metaphase cells.

In experiments in which MT severing was not successful and only photobleaching occurred, KT length did not change, suggesting that the irradiation caused by the laser does not affect KT morphology (Fig. S2 A). Overall, the observation that the KT shortens after the forces are released is a signature of its elastic properties, whereas the slowdown in shortening reflects its viscous properties (Figs. 1 D and S2 A; Meyers and Chawla, 2009). Thus, we conclude that the outer KT domain of PtK1 cells exhibits a viscoelastic behavior upon release of the pulling forces exerted by one of the two attached MT bundles.

To determine whether mechanical response of the KT is evolutionary conserved, we performed similar experiments in the fission yeast Schizosaccharomyces pombe. We performed our experiments in pcs1Δ mutant cells, which exhibit high frequencies of lagging chromosomes because of merotelic attachment (Gregan et al., 2007; Rumpf et al., 2010) and used Ndc80-GFP and mCherry-Atb2 to visualize the outer KT and MTs, respectively. To distinguish whether the lagging KT signal in S. pombe anaphase cells was a single KT or two/few adjacent KTs, we quantified the relative KT signal intensity (Materials and methods; Courtheoux et al., 2009). As described for PtK1 cells (see previous two paragraphs), we used a laser to sever K-fibers. However, unlike in PtK1 cells, it was not possible to distinguish individual MT bundles attached to a merotelic KT. To ensure that we cut all MTs attached to the KT from one side, we severed all spindle MTs, which resulted in spindle breakage and inward movement of the spindle poles (Fig. S1 B), as previously described (Tolić-Nørrelykke et al., 2004; Raabe et al., 2009; Maghelli and Tolić-Nørrelykke, 2010, 2011). The merotelic KT moved poleward after MT severing, which was not the case in PtK1 cells. However, similarly to what we found in PtK1 cells, we observed a gradual decrease in KT length after MT severing (Fig. 1, E–G; Video 2; and see Fig. S2 B for mean trace data). Unsuccessful MT severing had only a minor effect on KT length (Fig. S2 B). Collectively, our results suggest that the viscoelastic behavior of the KT is evolutionarily conserved in both fission yeast and mammalian PtK1 cells.

### The inner KT/centromere relaxes faster than the outer KT

The KT is a sophisticated molecular assembly composed of more than 80 proteins organized into two major domains, the outer and the inner KT, which interact with MTs and centromeric DNA, respectively (Santaguida and Musacchio, 2009). The viscoelastic response observed in our MT-severing experiments is likely to depend on the combined response of KT proteins and the underlying centromeric heterochromatin. Our previous analyses of merotelic KTs in fixed fission yeast showed that the outer KT domain is stretched more than the inner domain (Gregan et al., 2007). Similarly, we found that in fixed PtK1 cells, the KT domain defined by Hec1 was more stretched compared with the CenpA KT domain within the same anaphase merotelic KT (unpublished data). These observations suggest that the mechanical response of the outer KT and the inner KT/centromere upon release of the pulling forces exerted by MTs may also be different. Therefore, we decided to use the same MT-severing approach to characterize the mechanical behavior of the inner KT/centromere visualized by GFP-tagged CenpA/Cnp1 (PtK1/S. pombe). CenpA/Cnp1 is a histone-like protein found in nucleosomes within the centromeric DNA region. Thus, behavior of the GFP-tagged CenpA/Cnp1 reflects the combined properties of the inner KT domain and the underlying centromeric heterochromatin. Our analyses in live cells confirmed that in both fission yeast and PtK1 cells, the outer KT is stretched more than the inner KT/centromere (Fig. S2, D and E). Moreover, we found that the inner KT/centromere shortened gradually (Fig. 2, A–F; Videos 3 and 4; and Fig. 3). Thus, also in the case of the inner KT/centromere, the observed kinetics suggested a viscoelastic behavior. However, we found that the relaxation of the inner KT/centromere was faster than the relaxation observed for the outer KT (compare graphs in Fig. 2, C and F, with Fig. 1, D and G; see also Fig. 3), suggesting that the elastic component plays a more important role in the relaxation response of the inner KT/centromere compared with the outer KT. This indicates that the chromatin, which has been shown to behave as an elastic material (Poirier et al., 2000; Bouck and Bloom, 2007; Sun et al., 2011), may have a strong influence on the mechanical response of the inner KT. Alternatively, factors external to the KT, such as residual pulling forces exerted by the residual MT stub that remains bound to the KT after laser ablation (Elting et al., 2014; Sikirzhytski et al., 2014), may differentially affect the behavior of the inner and outer KT. In cases in which MT severing was not successful, we observed only a minor effect on inner KT morphology immediately after laser ablation (Fig. S2 C).

We also observed that in fission yeast, stretched merotelic KTs occasionally relaxed independent of MT severing (Fig. S1, E and F). These events likely reflect correction of merotelic KT–MT attachment during anaphase. Importantly, the relaxation kinetics of these KTs was indistinguishable from those where we induced relaxation by MT severing (Fig. S2 F), suggesting that similar mechanisms drive KT shortening in both cases. In conclusion, our experiments indicate that inner KT/centromere and outer KT display similar viscoelastic response but different relaxation kinetics.

### Insights into the different mechanical response of inner and outer KT

Because the outer KT domain (and particularly Hec1) is responsible for establishing MT attachment, we considered the possibility that the slower relaxation of the outer KT may depend on the pulling forces exerted by the unsevered MT bundle. To test this possibility, we performed ablations on both sides of the KT (double ablation experiments) in cells expressing GFP-tagged Hec1/Ndc80 (Fig. 1 A, double ablation; Fig. 3, A, B, D, and E; and Videos 5 and 6). We found that KT relaxation in both PtK1 and fission yeast cells was faster after double ablation compared with single ablation and that double ablation resulted in kinetics of Hec1/Ndc80 that were more similar to the kinetics of CenpA/Cnp1 after single ablation (Fig. 3, C and F). This suggests that the forces exerted by the unsevered MT bundle contribute to the slower shortening of the outer KT versus the inner KT/centromere.

Previous studies using EM tomography have shown that MTs are attached end-on to merotelic KTs (Khodjakov et al., 1997; Cimini et al., 2001). However, the orientation of the MTs with respect to the KT outer plate is different than that observed in metaphase. Indeed, MTs are positioned perpendicularly with respect to metaphase KTs. Instead, for most anaphase merotelic KTs, the MTs are oriented nearly parallel, although a few with nearly perpendicular orientation can be observed (Fig. S3, A and B). To determine whether these differences in MT orientation produced any difference in behavior, we compared two sets of KTs in which the bound MTs were oriented either perpendicularly or parallel. We found that there were only minor differences when we compared relaxation response of KTs with perpendicular or parallel orientation (Fig. S3, C–G).

In previous experiments where K-fibers were cut at different distances from metaphase KTs, the centromeric chromatin relaxed less when the severing was performed further from the KT because of forces exerted by the MT stub that remained attached to the KT after MT severing (Kajtez et al., 2016). Similarly, Maiato et al. observed that K-fiber ablation did not reduce centromere stretch of metaphase chromosomes (Maiato et al., 2004a), yet when the ablation site was closer to the KT, the centromere relaxed (Elting et al., 2014; Sikirzhytski et al., 2014). To identify a possible correlation between KT relaxation kinetics and MT stub length in our assay, we plotted the relaxation times (half-life), the final length of the KT after ablation (relaxed length) and the difference between the initial and the final KT length (absolute and relative relaxation length) versus MT stub length. We found no significant correlation between KT relaxation characteristics and MT stub length (Fig. S2 G), but we cannot exclude the possibility that the absence of correlation may be caused by a small range of stub lengths. Interestingly, treatment of PtK1 cells with 9 µM nocodazole (NOC), which causes nearly complete MT depolymerization (a notable exception was the presence of MT stubs that remained attached to KTs after NOC treatment; Fig. 3 G), resulted in a small but significant decrease of the relaxed length of the outer KT domain in PtK1 cells as compared with relaxation by laser severing (Fig. 3, G–I; Fig. 4, A and E; and Video 7).

### After MT severing, KTs exhibit residual stretching

As described in previous sections, we found that in both yeast and PtK1 cells the KT quickly relaxed upon release of the pulling forces exerted by MTs. Importantly, we observed that the fission yeast inner KT shortened close to the typical unstretched length within ∼100–150 s after the pulling force was released via MT severing. In contrast, the yeast outer KT and especially PtK1 KTs (both inner and outer domains) shortened but did not regain the length typical of unstretched KTs (Fig. 4, A–D). We exclude the possibility that this is caused by the pulling forces exerted by the unsevered MT bundle, because the PtK1 and the yeast outer KTs failed to regain the initial unstretched length even after double ablation or 9 µM NOC treatment (Fig. 4, A and C). One possible explanation is that the persisting KT stretch is caused by forces exerted by the MT stubs that remain attached to the KT after MT severing or NOC treatment. In addition, nonkinetochore MTs that interact laterally with the KT and that cannot be detected in our experimental setup may also contribute to the persisting KT stretch. However, another possibility is that this residual stretch may be caused by intrinsic plastic properties of the KT or permanent unraveling of the underlying centromeric chromatin.

We also explored the correlation between the stretched length and the relaxed length. In PtK1 cells, the relaxed length was larger for KTs that were stretched more (Fig. 4 E). Conversely, in fission yeast, the relaxed length was independent of the stretched length (Fig. 4 F). Both inner and outer KT domains showed the same qualitative behavior in each of the two cell types (Fig. 4, E and F).

### Simple viscoelastic models suggest differences in KT mechanical structure in PtK1 and S. pombe cells

Our experimental data suggest that the KT behaves as a viscoelastic material both in PtK1 and fission yeast cells. However, in PtK1 cells, but not in fission yeast, the more stretched KTs remain more stretched after severing. We set out to explain our observations by considering simple models of viscoelastic materials. A minimal representation of a viscoelastic material includes a Hookean spring characterized by a spring constant and a linear dashpot characterized by a drag coefficient. The spring and the dashpot can be connected either in series, which is known as the Maxwell model (Fig. 5 A), or in parallel, which is known as the Voigt model (Fig. 5 B).

The two models can be distinguished by their characteristic response to force. We consider a simple case of constant force acting for a certain period of time (Fig. 5, C and D; and see Materials and methods), although forces acting on the KT may change during anaphase (Rago and Cheeseman, 2013). In the Maxwell model, when the force is removed, the object relaxes immediately to a new relaxed length, which is larger for objects that were stretched more before the force was removed (Fig. 5, C and E). On the contrary, in the Voigt model, when the force is removed, the object relaxes gradually to its original relaxed length (Fig. 5, D and F). Thus, a qualitative difference between these models can be used to identify the model relevant for KTs in PtK1 and fission yeast cells.

Our experiments showed that in PtK1 cells, the relaxed length was larger for KTs that were stretched more (Fig. 4 E). Conversely, fission yeast KTs relaxed to a length close to the length of control KTs, irrespective of how much they were initially stretched (Fig. 4 F). These findings suggest that the behavior of the KT in PtK1 cells is closer to the Maxwell model (compare Figs. 4 E and 5 E), whereas the fission yeast KT is closer to the Voigt model (compare Figs. 4 F and 5 F).

Our experiments also showed that KT relaxation was gradual both in PtK1 and fission yeast cells, being slower in yeast (Fig. 3, C and F). Thus, the Voigt model explains not only the extent of relaxation but also the relaxation kinetics of fission yeast KTs (compare Fig. 3 F and Fig. 5 D). However, the Maxwell model does not explain the relaxation kinetics of PtK1 KTs (compare Fig. 3 C and Fig. 5 C), even though it does explain the extent of their relaxation, as discussed in previous paragraphs. A combination of the Maxwell and the Voigt model could explain the complete response of PtK1 KTs, suggesting that the mechanical structure of the mammalian KT is more complex than that of the yeast KT.

Our simple models provide additional testable predictions. The Maxwell model predicts that the KT length increases at a constant rate upon exertion of MT pulling forces (Fig. 5 C). Conversely, the Voigt model predicts that the extended KT length cannot exceed a certain maximum value and that the time required for achieving this maximum stretch is similar to the time required for relaxation (Fig. 5 D). Although it would be interesting to test these predictions by measuring the kinetics of stretching of merotelic KTs in the two model systems, this may be technically difficult because of the challenge of identifying merotelic KTs before anaphase onset.

In summary, our study establishes merotelic KTs as an experimental system for studying the mechanical response of the KT in live cells and describes a viscoelastic response of the KT upon release of the pulling forces exerted by MTs that is conserved in both yeast and mammalian cells. Our experimental assay is unique in that we were able to exploit a force being applied by the cell itself and release such force nearly instantaneously by laser ablating MT bundles attached to an anaphase merotelic KT. Using anaphase KTs allowed us to analyze properties of a single KT independent of the sister KT/chromatid, which may affect KT behavior in metaphase. This also enabled us to analyze the mechanical response of the KT in its native environment, where both mechanical properties of the KT as well as KT-independent factors determine KT behavior. Several studies suggested that the mechanical properties of KTs may be important for KT functions including establishment of correct attachment of KTs to MTs and faithful chromosome segregation (Loncarek et al., 2007; Maresca and Salmon, 2009; Uchida et al., 2009; Akiyoshi et al., 2010; Stephens et al., 2011, 2013; Dumont et al., 2012; Umbreit et al., 2014). We therefore believe that the viscoelastic response of the merotelic KT characterized in this study is relevant to processes that involve properly attached KTs. Future studies should be aimed at identifying KT components that provide these viscoelastic properties and determine the physiological relevance of the KT viscoelastic behavior. Our work thus opens new lines of research including studies of how cells can use the KT mechanical properties to prevent and repair merotelic KT attachments, how kinetochore mechanical properties may contribute to metaphase and anaphase KT function, and how meiosis-specific KT alterations affect KT properties.

### Generation of Hec1-GFP and GFP-CenpA PtK1 cell lines

PtK1 cells stably expressing fluorescently tagged human Hec1 or PtK1 CenpA were produced through the transduction of retroviral particles according to the instructions for high-titer retrovirus production provided by Takara Bio Inc. The EGFP-N1 plasmid carrying the HEC1 gene was a gift from J. DeLuca (Colorado State University, Fort Collins, CO). In brief, the HEC1-EGFP gene was initially subcloned into the XhoI and NotI sites of the pLNCX2 retroviral vector (Takara Bio Inc.) that harbors the Ψ packaging sequence. The PtK2 CENP-A gene was cloned and initially inserted into mCherry vector for N-terminal tagging (pJag456). We used BglII and SalI restriction sites to subclone the PtK2 CENP-A gene into the pRetroQ-AcGFP1-C1 retroviral vector (Takara Bio Inc.), also harboring the Ψ packaging sequence. To produce high-efficiency retroviral particles, we transfected the packaging GP2-293 cells (Takara Bio Inc.), carrying the viral gag and pol genes, with the pLNCX2-HEC1-EGFP plasmid or the pRetroQ-AcGFP1-CENP-A together with the VSV-G vector (Takara Bio Inc.) that provided the viral envelope gene (env). The resulting retroviral particles were used to infect PtK1 cells that were subsequently placed under selection in Geneticin- or Puromycin-containing media to respectively obtain the Hec1-GFP PtK1 and the GFP-CenpA PtK1 cell lines used in this study.

### Cell culture

Hec1-GFP PtK1 and GFP-CenpA PtK1 cells were grown in Ham’s F12 medium (Invitrogen) supplemented with 1% sodium pyruvate (Invitrogen), 1% antibiotic/antimycotic (Invitrogen), and 10% fetal bovine serum (Invitrogen) and maintained at 37°C in a humidified CO2 incubator. For experiments, cells were grown in 35-mm glass-bottom MatTek dishes for 24 or 48 h before observation. During time-lapse imaging, Ham’s F12 medium was replaced with phenol red–free L-15 medium supplemented with 4.5 g/l glucose (Sigma-Aldrich), 1% antibiotic/antimycotic (Invitrogen), and 10% fetal bovine serum (Invitrogen).

### Generation of S. pombe strains

JM2595 (h kanMX6-Pcnp1-mEGFP-cnp1 ade6-M210 leu1-32 ura4-D18) strain (provided by J.Q. Wu, The Ohio State University, Columbus, OH) was crossed with JG16070 (h+ mCherry-atb2-hph leu1-32, ura4-D18) to generate JG16573 (h+ kanMX6-Pcnp1-mEGFP-cnp1 mCherry-atb2-hph leu1-32, ura4-D18). To delete the pcs1+ gene, JG16573 was transformed with the plasmid p17, resulting in JG16633 (h+ kanMX6-Pcnp1-mEGFP-cnp1 mCherry-atb2-hph pcs1::natMX4 leu1-32, ura4-D18).

FY14794 (h90 ade6-216 leu1-32 lys1-131 ura4-D18 ndc80::ndc80-GFP-HA-kan) was crossed with JG16070 (h+ mCherry-atb2-hph leu1-32, ura4-D18) to generate JG16559 (h+ ndc80::ndc80-GFP-HA-kan mCherry-atb2-hph leu1-32, ura4-D18). To delete the pcs1+ gene, JG16559 was transformed with the plasmid p17, resulting in JG16621 (h+ ndc80::ndc80-GFP-HA-kan mCherry-atb2-hph pcs1::natMX4 leu1-32, ura4-D18).

### Sample preparation: PtK1

Merotelic attachments were induced using a NOC washout protocol. A 6.6 mM stock solution of nocodazole (Sigma-Aldrich) in DMSO (Sigma-Aldrich) was diluted into Ham’s F12 medium to a final concentration of 3 µM, which was used to treat the cells for ∼60–90 min. For MT visualization, a 0.5-µg/µl final concentration of X-rhodamine–labeled tubulin in injection buffer (20 mM Hepes, 100 mM KCl, and 1 mM DTT in H2O) was used. Microinjection was performed during the NOC treatment, using the semiautomatic mode of a microinjector (InjectMan NI 2; Eppendorf). To prevent tubulin polymerization inside of the needle, microinjection was performed at room temperature. Once injected, the NOC was washed out and the cells were incubated at 37°C for ∼15 min before starting the observation.

Cells in which the MT bundles attached to the merotelic KT were not severed but depolymerized were treated with 9 µM NOC for 15–25 min once they reached anaphase and the merotelic KT was clearly visible.

### Sample preparation: yeast

S. pombe strains were grown overnight (14–16 h) on yeast extract media (YE5S) agar plates with supplements (adenine, leucine, uracil, histidine, and arginine) at 25°C. For manipulation and imaging, fresh cells were resuspended in liquid Edinburgh minimal medium with adenine, leucine, uracil, histidine, and arginine (EMM5S) and transferred to the base of a 35-mm Petri dish (MatTek Corporation) coated with 2 µl of 2-mg/ml lectin (Sigma-Aldrich). Free cells were removed by washing with EMM5S, and the Petri dish was filled with 300 µl EMM5S and covered with a coverslip sealed with silicone (GE Bayer Silicones). Cell manipulation and imaging was performed at 25°C in a Bachhoffer chamber (Tempcontrol 37–2 digital; ZEISS).

### Microscopy and image acquisition: PtK1

Two inverted confocal microscopes were used for imaging and MT severing in PtK1 cells. First, we used NLO microscope (LSM 710; ZEISS) and a Plan Apochromat 63×/1.40 oil differential interference contrast objective (ZEISS), the inverted version of the (LSM 780; ZEISS) used for experiments in yeast. Both ZEISS microscopes were operated with Zen Black software 2011. GFP fluorescence was excited with a 488-nm line of a multiline argon-ion laser (LASOS) and a primary dichroic mirror (DM 488/561). For X-rhodamine excitation, we used a diode-pumped 561-nm solid-state laser. GFP and X-rhodamine emission were detected in the range of 490–570 and 570–735 nm, respectively. No images were taken during the laser ablation. Time-lapse Z-stacks of ∼15 optical sections, with a 500-nm z-distance, were taken at 3.5- to 6.5-s intervals using unidirectional scanning. The images have an xy pixel size of 150–215 nm.

MT bundle severing was performed using a single Ti:Sa femtosecond pulsed laser (Chameleon Vision II; Coherent), tuned to a wavelength of 800 nm and a theoretical pulse duration of 140 fs at 80 MHz. The beam was coupled to the bleaching port of the NLO laser-scanning microscope (LSM 710). The light path of the pulsed laser was different from the path of the imaging one. The pulsed laser light was reflected onto the objective by a long pass dichroic mirror LP690. For a maximum output power of 3030 mW corresponding to 100% of the laser, the measured power before the objective was 1,053 mW (using a Coherent power meter). The estimated power at the sample, corresponding to a 35–50% range of the maximum output power, was ∼37–53 mW. The objective transmission at 800 nm is ∼10%. MT bundle severing was achieved by scanning the laser, over a user-defined region of interest, for ∼50–80 ms total exposure time. This corresponds to a total energy ∼1.9–4.3 mJ. The ablation was performed as close as possible to the KT to avoid the effect previously reported by Maiato et al. (2004b) that ablations of K-fiber at sites distant from the KT did not reduce the centromere stretch.

Cells were also imaged and manipulated using an inverted microscope (IX71; Olympus) with a back illuminated EMCCD camera (iXon 897; Andor Technology) with 16-µm pixel size, a spinning-disc scan head (CSU10; Yokogawa Electric Corporation) equipped with a fast piezo objective z-positioner (PIFOC; Physik Instrumente GmbH & K.G.), and a UPlanSApo 100×/1.4 NA oil objective (Olympus). iQ software 3.0 (Andor Technology) was used to operate the acquisition, camera, and piezo stage. GFP and X-Rhodamine fluorescence were excited at 488 and 561 nm, respectively. Images were acquired at 1.9- to 2.6-s time intervals. The laser intensity was controlled using the acousto-optic tunable filter inside the Revolution Laser Combiner (ALC; Andor Technology). The emission wavelength was selected using respective emission filters BL 525/30 (Semrock) and ET 605/70 (Chroma) mounted in a fast, motorized filter wheel (Lambda-10B; Sutter Instrument). The images have an xy pixel size of 168 nm.

MT bundle severing was performed using a MicroPoint (ALC; Andor Technology) with 408-nm dye resonator cell.

### Microscopy and image acquisition: yeast

Time-lapse images of live cells were taken with an infinity-corrected optics NLO upright microscope (LSM 780) with infinity-corrected optics and a Plan-Apochromat 63–/1.40 oil differential interference contrast objective (ZEISS). GFP was excited with a 488 nm line of a multiline argon-ion laser (LASOS) and a primary dichroic mirror DM 488/561. For mCherry excitation, we used a diode-pumped 561-nm solid-state laser. GFP and mCherry emissions were detected using an internal GaAsP detector (Hamamatsu Photonics) in the range of 490–570 nm and 580–680 nm, respectively. No images were acquired during laser ablation. Time-lapse Z-stacks of 8–11 optical sections, with a 500-nm z-distance, were taken at 2.5- to 5-s intervals using unidirectional scanning. Images have an xy pixel size of 90–135 nm.

MT/spindle severing was performed using a single Ti:Sa femtosecond pulsed laser (Chameleon Vision II; Coherent), tuned to a wavelength of 745 nm and a theoretical pulse duration of 140 fs at 80 MHz. The beam was coupled to the bleaching port of the NLO laser-scanning microscope (LSM 780). The light path of the pulsed laser was different from the path of the imaging one. The pulsed laser light was reflected onto the objective by a long pass dichroic mirror LP690. For a maximum output power of 2,480 mW corresponding to 100% of the laser, the measured power before the objective was 857 mW (using a Coherent power meter). The estimated power at the sample, corresponding to a 20–30% range of the maximum output power, was ∼20–30 mW. The objective transmission at 745 nm is 12%. MT severing was achieved by scanning the laser, over a user-defined region of interest, for ∼40–60-ms total exposure time. This corresponds to a total energy ∼0.8–1.8 mJ.

### KT tracking

Stretched KT ends were tracked using an ImageJ plugin, Low Light Tracking Tool (Fig. S3 H; http://fiji.sc/Low_Light_Tracking_Tool; Krull et al., 2014). KT lengths were obtained by calculating the distance between the two KT ends using MatLAB (The MathWorks).

Size of control KTs was determined by using a custom automated ImageJ routine to detect and count pixels with KT-specific signal (Fig. S3 I). Channel of GFP-tagged KTs was separated, Z-projected, and loaded (Fig. S3 I, second image) into Fiji plugin. By creating a profile plot of the KTs and their surrounding region, the initial background threshold and neighborhood threshold of what is considered to be the control KT was set. The working image was scanned and, at each pixel, the mean neighborhood value was computed, and then its intensity value and the mean neighborhood value were compared with both thresholds conditions. If one of them was not met, the pixel state would be set to 0; otherwise, 1. According to this, the working image would display the marked pixels (Fig. S3 I, third image) while running the algorithm. At this point, lines that indicate the KTs to be measured and the orientation of the measurement (Fig. S3 I, fourth image) could be drawn.

To distinguish a single KT from two/several adjacent KTs in S. pombe, the following method was used. The total KT signal along the spindle was measured using the ImageJ tool, Plot profile. The background was subtracted. The datasets were exported to MatLAB (The Mathworks), where a ratio of the lagging KT signal between SPBs and the total signal along the spindle was calculated. Assuming that each cell has six KTs, the ratio of 1:6 was considered a single KT.

### Models of KT relaxation

#### Maxwell model: spring and dashpot connected in series

The total length of the system consisting of a spring with extension xs and a dashpot with extension xd, which are connected in series, reads x = xs + xd (Fig. 5 A). In this system, both mechanical elements are under tension F. For the spring characterized by a spring constant κ and the dashpot characterized by a drag coefficient γ, the respective force-balance equations read:

$F=κx s ,$
(1)

and

$F=γdx d dt .$
(2)

We solve Eqs. 1 and 2 by considering three time intervals: (a) for time t < 0, the tensile force is zero (F = 0); (b) for time 0 < t <T1, the tensile force F is constant; and (c) for time t < T1, the tensile force vanishes again (Fig. 5 C, bottom). In (a), the extensions of the spring and the dashpot are 0, giving the total extension for the system x = 0 (Fig. 5 C). In (b), the extension of the spring has a constant value:

$x s =F κ ,$

whereas the extension of the dashpot increases linearly with time:

$x d =F γ t,$

giving the total length

$x=F κ +F γ t.$

In (c), the extension of the spring relaxes to xs = 0, and the extension of the dashpot has a constant value

$x d =F γ T 1 .$

Thus, the total length is

$x=F γ T 1 .$

If the system has an initial length xc, the total length is given as x + xc (Fig. 5 C).

#### Voigt model: spring and dashpot connected in parallel

When connected in parallel, the spring and the dashpot have the same extension, $x≡x s =x d$ (Fig. 5 B), and the force balance reads

$F=κx+γdx dt .$
(3)

As in the case for the serial connection, we solve Eq. 3 for the same three time intervals (Fig. 5 D, bottom). In the time interval (a), the total extension of the system is x = 0 (Fig. 5 D). In the time interval (b), the total extension of the system obeys

In the time interval (c), the total extension of the system relaxes, obeying

$x=F κ (1−e −κT 1 /γ )e −κt/γ .$

If the system has an initial length xc, the total length is given as x + xc (Fig. 5 D).

### Estimation of parameters

For PtK1 cells, we assume that the force acting on the KT is in the range of 400–1,000 pN, based on the previously measured value of 700 pN for nonmerotelic KTs in anaphase (Nicklas, 1983). We assume that this force was acting on the KT for 7–12 min, which corresponds to the time between the initial stretching of the merotelic KT and our MT severing late in anaphase. By using these values for force and time, together with the spring constant κ = 1,000 pN/µm and the drag coefficient γ = 5 × 105 pNs/µm, the Maxwell model reproduces the relationship between the relaxed and the stretched length measured for the PtK1 outer KT (Fig. 4 E). In particular, the parameters κ and γ were chosen in such a way that the theoretical data matched the experimental data (compare Fig. 4 E and Fig. 5 E).

For fission yeast KTs, we use the assumption that the force at the KT depends on the number of attached MTs, which is on average 25 in PtK1 cells (McDonald et al., 1992) and 2–4 in fission yeast (Ding et al., 1993). Thus, we assume that the force acting on the merotelic KT in fission yeast is roughly eight times lower than in PtK1 cells, i.e., in the range of 50–200 pN. By using these values in the Voigt model, we find that for a spring constant value κ = 100 pN/µm, the model reproduces the measured relationship between the relaxed and the stretched length of the outer KT (compare Fig. 4 F and Fig. 5 F). By using the experimentally measured relaxation time value for the outer KT, half-life = 25 s (Fig. 3 F), we obtain the drag coefficient γ = 3,600 pNs/µm.

### Online supplemental material

Fig. S1 shows indications of successful MT severing in PtK1 and fission yeast cells and KT behavior observed after successful or unsuccessful MT severing. Fig. S2 shows normalized KT length observed after successful or unsuccessful MT severing, comparison of outer KT and inner KT/centromere stretch, kinetics of relaxation for KTs that were repaired spontaneously, and effect of MT stub length on KT relaxation. Fig. S3 shows comparison of relaxation response of KTs with perpendicular or parallel MT attachments and a scheme of KT tracking. Video 1 shows single ablation in PtK1 cells expressing Hec1-GFP. Video 2 shows single ablation in S. pombe cells expressing Ndc80-GFP. Video 3 shows single ablation in PtK1 cells expressing GFP-CenpA. Video 4 shows single ablation in S. pombe cells expressing Cnp1-GFP. Video 5 shows double ablation in PtK1 cells expressing Hec1-GFP. Video 6 shows double ablation in S. pombe cells expressing Ndc80-GFP. Video 7 shows PtK1 cells expressing Hec1-GFP treated with NOC. Additional data are available in the JCB DataViewer at http://dx.doi.org/10.1083/jcb.201506011.dv.

We thank the Max Planck Institute of Molecular Cell Biology and Genetics Light Microscopy Facility, N. Maghelli, and the Research Institute of Molecular Pathology for help with experimental setups; A. Krull for the tracking software; G. Civelekoglu-Scholey, T. Franzmann, and members of the Tolić and Cimini groups for helpful discussions; W.J. Qiu and J. DeLuca for sharing material; and I. Šarić for help with figures.

This work was supported by Human Frontier Science Program grant RGY0069/2010 to J. Gregan, D. Cimini, and I.M. Tolić. Additional support was provided by National Science Foundation grants MCB-0842551 and MCB-1517506 to D. Cimini. J.V. Shah was supported by a Beckman Laser Institute Faculty Fellowship. J. Gregan was supported by the following grants from the Austrian Science Fund: P21437 and P23609, EC (PCIG11-GA-2012-322300), APVV (APVV-0334-12), and VEGA (1/0196/14).

The authors declare no competing financial interests.

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Abbreviations used in this paper:

• KT

kinetochore

•
• MT

microtubule

•
• NOC

nocodazole

## Author notes

*

G. Cojoc and E. Roscioli contributed equally to this paper.

G. Cojoc’s present address is Biotechnology Center, Technische Universität Dresden, 01307 Dresden, Germany.

E. Roscioli’s present address is Division of Biomedical Sciences, Warwick Medical School, University of Warwick, CV4 7AL Coventry, England, UK.

L. Zhang’s present address is Advanced Microscopy, Vienna Biocenter Core Facilities GmbH, 1030 Vienna, Austria.

J. Gregan’s present address is Dept. of Genetics, Faculty of Natural Sciences, Comenius University, 84215 Bratislava, Slovak Republic.