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W4292615460 abstract "Article Figures and data Abstract Editor's evaluation Introduction Results Discussion Materials and methods Appendix 1 Data availability References Decision letter Author response Article and author information Metrics Abstract During eukaryotic cell division, chromosomes are linked to microtubules (MTs) in the spindle by a macromolecular complex called the kinetochore. The bound kinetochore microtubules (KMTs) are crucial to ensuring accurate chromosome segregation. Recent reconstructions by electron tomography (Kiewisz et al., 2022) captured the positions and configurations of every MT in human mitotic spindles, revealing that roughly half the KMTs in these spindles do not reach the pole. Here, we investigate the processes that give rise to this distribution of KMTs using a combination of analysis of large-scale electron tomography, photoconversion experiments, quantitative polarized light microscopy, and biophysical modeling. Our results indicate that in metaphase, KMTs grow away from the kinetochores along well-defined trajectories, with the speed of the KMT minus ends continually decreasing as the minus ends approach the pole, implying that longer KMTs grow more slowly than shorter KMTs. The locations of KMT minus ends, and the turnover and movements of tubulin in KMTs, are consistent with models in which KMTs predominately nucleate de novo at kinetochores in metaphase and are inconsistent with substantial numbers of non-KMTs being recruited to the kinetochore in metaphase. Taken together, this work leads to a mathematical model of the self-organization of kinetochore-fibers in human mitotic spindles. Editor's evaluation Conway and colleagues use a combination of experiments and theory to test models for the dynamics of kinetochore-fibers during metaphase in mammalian mitotic spindles. Their work is consistent with a model where kinetochore-fiber turnover is due primarily to the nucleation of microtubules at kinetochores, rather than from a search-and-capture of microtubules initiated elsewhere. This work should be of interest to experimentalists and theorists broadly interested in the control of form and in cell division. https://doi.org/10.7554/eLife.75458.sa0 Decision letter Reviews on Sciety eLife's review process Introduction When eukaryotic cells divide, a spindle composed of microtubules (MTs) and associated proteins assembles and segregates the chromosomes to the daughter cells (Strasburger, 1880; McIntosh et al., 2012; Heald and Khodjakov, 2015; Petry, 2016; Prosser and Pelletier, 2017, Oriola et al., 2018, O’Toole et al., 2020, Anjur-Dietrich et al., 2021). A macromolecular protein complex called the kinetochore binds each sister chromatid to MTs in the spindle thereby bi-orienting the two sisters to ensure they segregate to opposite daughter cells (McDonald et al., 1992; McEwen et al., 1997; Maiato et al., 2004a; Yoo et al., 2018, Monda and Cheeseman, 2018; Rieder, 1982; Maiato et al., 2004b, Musacchio and Desai, 2017, Pesenti, 2018; Monda and Cheeseman, 2018; DeLuca et al., 2011; Redemann et al., 2017; Long et al., 2019). Any MT whose plus end is embedded in the kinetochore is referred to as a kinetochore microtubule (KMT) and the collection of all KMTs associated with an individual kinetochore is called a kinetochore-fiber (K-Fiber). The kinetochore-microtubule interaction stabilizes KMTs and generates tension across the sister chromatid pair (Brinkley and Cartwright, 1975; Gorbsky and Borisy, 1989; Nicklas and Ward, 1994; Bakhoum et al., 2009; DeLuca et al., 2006; Cheeseman et al., 2006; Tanaka and Desai, 2008; Akiyoshi et al., 2010; Kabeche and Compton, 2013; Cheerambathur et al., 2017; Monda and Cheeseman, 2018; Steblyanko et al., 2020; Warren et al., 2020). Modulation of the kinetochore-MT interaction is thought to be important in correcting mitotic errors (DeLuca et al., 2011; Godek et al., 2015; Funabiki, 2019; Long et al., 2019). Kinetochore-MT binding is thus central to normal mitotic progression and correctly segregating sister chromatids to opposite daughter cells (Cimini et al., 2001; Chiang et al., 2010; Auckland and McAinsh, 2015; Lampson and Grishchuk, 2017; Dudka et al., 2018). Chromosome segregation errors are implicated in a host of diseases ranging from cancer to development disorders such as Downs’ and Turners’ Syndromes (Touati and Wassmann, 2016; Compton, 2017, Jo et al., 2021). The lifecycle of a metaphase KMT consists of its recruitment to the kinetochore, its subsequent motion, polymerization and depolymerization, and its eventual detachment from the kinetochore. In metaphase, KMTs turnover with a half-life of ~2.5min, so the KMTs that originally attached during initial spindle assembly in early prometaphase have long since detached from the kinetochore and been replaced by freshly recruited KMTs over the ~25min from nuclear envelope breakdown to anaphase. The number of KMTs remains relatively constant over the course of mitosis (McEwen et al., 1997; McEwen et al., 1998), so new KMTs must be continually recruited to kinetochores throughout metaphase to replace the detaching KMTs. Prior experiments have established that kinetochores are capable of both nucleating KMTs de novo and capturing exiting non-KMTs (Telzer et al., 1975; ; Mitchison and Kirschner, 1985a; Mitchison and Kirschner, 1985b, Mitchison and Kirschner, 1986, Huitorel and Kirschner, 1988; Heald and Khodjakov, 2015; LaFountain and Oldenbourg, 2014; Petry, 2016; Sikirzhytski et al., 2018; David et al., 2019; Renda and Khodjakov, 2021). Either of these mechanisms could potentially be responsible for the KMT recruitment to kinetochores during metaphase. The de novo kinetochore nucleated MTs may in fact be nucleated in the vicinity of the kinetochore and then attach while they are still near zero length, though this process would be distinct from indiscriminate capture of non-KMTs of varied lengths from the spindle (Sikirzhytski et al., 2018). Once attached, the plus-ends of KMTs can polymerize and depolymerize while remaining attached to the kinetochore, leading to a net flux of tubulin through the K-Fiber from the kinetochore toward the spindle pole (Mitchison and Kirschner, 1985a, Mitchison, 1989; Rieder and Alexander, 1990; Mitchison and Salmon, 1992; Zhai et al., 1995; Waters et al., 1996; Khodjakov et al., 2003; Gadde and Heald, 2004; McIntosh et al., 2012; Steblyanko et al., 2020; DeLuca et al., 2011; Elting et al., 2014; Elting et al., 2017, Neahring et al., 2021; Risteski et al., 2021). For human cells in metaphase, it is unclear to what extent these motions are due to movement of entire K-Fibers, movement of individual KMTs within a K-Fiber, or movement of tubulin through individual KMTs. Finally, when KMTs detach from the kinetochore, they become non-KMTs by definition. The regulation of KMT detachments is thought to be important for correcting improper attachments and ensuring accurate chromosome segregation (Tanaka et al., 2002; Bakhoum et al., 2009, DeLuca et al., 2011; Godek et al., 2015; Krenn and Musacchio, 2015; Lampson and Grishchuk, 2017; Funabiki, 2019; Long et al., 2019). KMT detachments typically occur with a time scale of ~2.5min in metaphase in human mitotic cells (Kabeche and Compton, 2013). How these processes – KMT recruitment, motion, polymerization and depolymerization, and detachment – lead to the self-organization of metaphase K-Fibers remains incompletely understood. In a companion paper, we used serial-section electron tomography to reconstruct the locations, lengths, and configurations of MTs in metaphase spindles in HeLa cells (Kiewisz et al., 2022). These whole spindle reconstructions can unambiguously identify which MTs are bound to the kinetochore and measure their lengths, providing a remarkable new tool for the study of KMTs. Here, we sought to combine the electron tomography spindle reconstructions with live-cell experiments and biophysical modeling to characterize the lifecycle of KMTs in metaphase spindles in HeLa cells. The electron tomography reconstructions revealed that only ~50% of KMTs have their minus ends at spindle poles. We used photoconversion experiments to measure the dynamics of KMTs, which revealed that while their stability does not spatially vary, their speed is greatest in the middle of the spindle and continually decreases closer to poles. We next show that the orientations of MTs throughout the spindle, measured by electron tomography and polarized light microscopy, can be quantitively explained by an active liquid crystal theory in which the mutual interactions between MTs cause them to locally align with each other. This argues that KMTs tend to move along well-defined trajectories in the spindle. We show that the distribution of KMT minus ends along these trajectories (measured by electron tomography) is only consistent with the motion and turnover of KMTs (measured by photoconversion) if KMTs predominately nucleate at kinetochores. Taken together, these results lead us to construct a model in which metaphase KMTs nucleate at the kinetochore and grow towards the spindle pole along defined trajectories. The KMT minus ends slow down as they approach the pole. Since the flux of tubulin is constant throughout a single KMT at any given moment in time, the minus end slowdown is coupled to a decrease in the polymerization rate at the KMT plus end. KMTs detach from the kinetochore at a constant rate, independent of the minus end position. Such a model of K-Fiber self-organization can quantitively explain the lengths, locations, configurations, motions, and turnover of KMTs throughout metaphase spindles in HeLa cells. Results Many KMT minus ends are not at the pole We first analyzed a recent cellular tomography electron microscopy (EM) reconstruction data set which captured the trajectories of every MT in the mitotic spindle of three HeLa cells (Kiewisz et al., 2022). We defined KMTs as MTs with one end near a kinetochore in the reconstructions and assigned the plus end to the end at the kinetochore and the minus end to the opposite end of the MT (Figure 1A). KMT minus ends are located throughout the spindle, with approximately 51% of them more than 1.7μm away from the pole, as found in Kiewisz et al., 2022 (Figure 1B). We defined the location of the pole as the center of the mother centriole. KMT minus ends are distributed throughout individual K-Fibers (Figure 1C), indicating that the processes that lead to a broad distribution of KMT minus end locations can occur at the level of individual kinetochores. We wanted to know how the observed distribution of KMT minus end locations results from the behaviors of KMTs. This requires understanding the life cycle of a metaphase KMT, namely (Figure 1D): How are KMTs recruited to kinetochores in metaphase? To what extent are they nucleated de novo at the kinetochore vs. resulting from non-KMTs being captured from the bulk of the spindle? How do KMTs move and grow? What are their growth trajectories and the minus end speeds? How do KMTs detach from kinetochores? Figure 1 Download asset Open asset Many KMT minus ends are not in the vicinity of the pole. (A) A sample half spindle showing the KMTs from the EM ultrastructure. KMTs are shown in red while minus ends are marked in black. The spindle pole lies at 0µm on the spindle axis while the metaphase plate is between 4 and 6µm on the spindle axis. (B) The frequency of 3D minus end distance from the pole. Inset: the fraction of minus ends within 1.7µm of the pole (as shown in Kiewisz et al., 2022). (C) A sample k-Fiber. Again, KMTs are shown in red, minus ends are shown in black. The large red circle is the kinetochore. Inset: probability of k-Fiber with fraction of KMTs with their minus ends within 1.7µm of the pole. The mark shows the fraction of KMTs near the pole in the sample k-Fiber. (D) Schematic representation of models of KMT gain, motion, and loss. MTs could be recruited to the k-Fiber by de-novo nucleation at the kinetochore or by the capture and conversion of an pre-existing non-KMT to a KMT. The motion of KMTs is described by the trajectory and speed of the KMT minus ends. At some rate, KMTs detach from the kinetochore and become non-KMTs, by definition. We sought to answer these questions with a series of live-cell experiments, further analysis of the spindle reconstructions obtained from electron tomography, and mathematical modeling. The fraction of slow-turnover tubulin measured by photoactivation matches the fraction of tubulin in KMTs measured by electron tomography To understand how the motion and turnover of KMTs results in the observed ultrastructure, we first sought to characterize the motion and stability of KMTs throughout the spindle. To that end, we constructed a HeLa line stably expressing SNAP:centrin to mark the spindle poles and PA-GFP:alpha-tubulin to mark tubulin. PA-GFP is a photoactivatable fluorophore that converts from a dark state to green fluorescence upon exposure to 750nm light using a two-photon photoactivation system. This photoactivation allows subsequent tracking of the tubulin that was in a photoactivated region at time t=0. After photoactivating a line of tubulin in the spindle, the converted tubulin moves poleward and fades over time (Figure 2A; Mitchison, 1989; DeLuca, 2010; Kabeche and Compton, 2013; Fürthauer et al., 2019; Steblyanko et al., 2020). Figure 2 with 2 supplements see all Download asset Open asset Photoactivation of spindle tubulin in live HeLa cells. (A) Photoactivation experiment showing PA-GFP:alpha-tubulin and SNAP-SIR:centrin immediately preceding photoactivation, 0 s, 30 s, and 60 s after photoactivation with a 750nm femtosecond pulsed laser; 500ms 488nm excitation, 514/30 bandpass emission filter; 300ms 647nm excitation, 647 longpass emission filter; 5s frame rate. (B) Line profile generated by averaging the intensity in 15 pixels on either side of the spindle axis in the dotted box shown in A. The intensity is corrected for background from the opposite side of the spindle (see methods). (C) Line profiles (shades of green) fit to Gaussian profiles (shades of grey) at 0s, 5s and 25s. Lighter shades are earlier times. The solid line on the fit represents the fit pixels. (D) Blue dots: fit position of the line profile peak from the sample cell shown in A, B, and C over time. Black line: linear fit to the central position of the fit peak over time. (E) Red dots: fit height of the line profile peak from the sample cell shown in A, B, and C over time. Black line: dual-exponential fit to the fit height of the peak over time. (F) Sample ultrastructure from a 3D spindle reconstructed by electron tomography (Kiewisz et al., 2022). KMTs are shown in red, non-KMTs yellow. (G) Comparison between the mean slow fraction from the photoconversion data (26% ± 2%, n=52 cells, error bars are standard error of the mean) and the fraction of KMTs (25% ± 2%, n=3 cells, error bars are standard error of the mean) from the EM data. The two means are statistically indistinguishable with P=0.86 on a Student’s t-test. To measure the speed and turnover of MTs, we first projected the intensity of the photoconverted tubulin onto the spindle axis (Figure 2B; Kabeche and Compton, 2013). This projection will group together more bent KMTs near the spindle edge with less bent KMTs near the spindle center; however, the line of photoconverted tubulin remains coherent over the typical times that we tracked the photoconverted tubulin suggesting that such a projection is appropriate. The two-photon photoactivation produced a narrow line in the z-direction perpendicular to the imaging plane (σ=1.0 ± 0.1µm), so the contribution of out of focus photoactivated tubulin entering the imaging plane is minimal (Figure 2—figure supplement 1). We then fit the resulting peak to a Gaussian to track the motion of its center position and decay of its height over time (Figure 2C). We fit the position of the peak center over time to a line to determine the speed of tubulin movement in the spindle (Figure 2D). We then corrected the peak heights for bleaching by dividing by a bleaching reference (Figure 2—figure supplement 2) and fit the resulting time course to a dual-exponential decay to measure the tubulin turnover dynamics (Figure 2E; DeLuca, 2010). Since the tubulin turnover is well-fit by a dual-exponential decay, it suggests that there are two subpopulations of MTs with different stabilities in the spindle, as previously argued for many model systems (Brinkley and Cartwright, 1975; Salmon et al., 1976; Lambert and Bajer, 1977, Rieder and Bajer, 1977; Rieder, 1981; Cassimeris et al., 1990; DeLuca, 2010). In prior studies, the slow-turnover subpopulation has typically been ascribed to the KMTs, while the fast-turnover subpopulation has typically been ascribed to the non-KMTs (Zhai et al., 1995; DeLuca, 2010; Kabeche and Compton, 2013). However, it is hypothetically possible that a portion of non-KMTs is also stabilized, due to bundling or some other mechanism (Tipton and Gorbsky, 2022). To gain insight into this issue, we generated a cell line with SNAP:centrin to mark the poles and mEOS3.2:alpha tubulin to mark MTs and performed photoconversion experiments on a total of 70 spindles. We compared the fraction of tubulin in KMTs, 25% ± 2% (n=3), measured by electron tomography (in which a KMT is defined morphologically as a MT with one end associated with a kinetochore; Figure 2F; Kiewisz et al., 2022) to the fraction of the slow-turnover subpopulation measured from photoconversion experiments, 26% ± 2% (n=52). Since these two fractions are statistically indistinguishable (Figure 2G, p=0.86 on a Students’ t-test), we conclude that the slow-turnover subpopulation are indeed KMTs, and that there is not a significant number of stabilized non-KMTs. KMT speed is spatially varying while both KMT and non-KMT stability are uniform in the spindle bulk We next explored the extent to which the speed and stability of MTs changed throughout the spindle (Burbank et al., 2007; Yang et al., 2008). To do this, we compared photoconversion results from lines drawn at different position along the spindle axis. After photoconverting close to the center of the spindle (~4.5 µm from the pole), the resulting line of marked tubulin migrated towards the pole (Figure 3A). This poleward motion was less evident when we photoconverted a line halfway between the kinetochores and the pole (Figure 3B), and barely visible when we photoconverted a line near the pole itself (Figure 3C). Tracking the subsequent motions of these photoconverted lines in different regions revealed clear differences in their speeds (Figure 3D), while their turnover appeared to be similar (Figure 3E). To quantitively study this phenomenon, we photoconverted lines in 52 different spindles, at various distances from the pole and measured the speed and turnover times at each location. Combining data from these different spindles revealed that average speed of the photoconverted lines increased with increasing distance from the pole (Figure 3F; Slope = 0.25 ± 0.04(µm/min)/µm, p=4 × 10–8), while both the KMT (Figure 3G; Slope = −0.10 ± 0.15 (1/min)/µm, p=0.50) and non-KMT (Figure 3H; Slope = 0.01 ± 0.01 (1/min)/µm, p=0.13) turnover were independent of distance from the pole. Since the non-KMTs turnover roughly every 15–20s, the non-KMT contribution to the motion of the photoconverted line should be negligible roughly 1 minute after photoconversion. We typically track the photoconverted line for ~2.5min, so the line speed we measure is primarily the result of motion of tubulin in KMTs. The faster line speed further from the pole implies that tubulin in short KMTs, whose minus ends are near the kinetochore, move more quickly than tubulin in long KMTs that reach all the way from the kinetochore to the pole. The speeds we observed with the two-photon photoactivation were very similar to the speeds we observed with a traditional one-photon photoactivation system (Figure 3—figure supplement 1). The measured KMT and non-KMT lifetimes were indistinguishable between the one- and two-photon activation systems (KMT Lifetime: One-Photon: 2.7±0.2min, Two-Photon: 2.8±0.2min, p=0.71; Non-KMT Lifetime: One-Photon: 0.29±0.02min, Two-Photon: 0.26±0.01min, p=0.10). To test if the observed tubulin slowdown near the poles was a consequence of the increased curvature of MTs near the pole, we analyzed the motion of a thinner 2 μm section of the photoactivation line near the spindle axis where the MTs are relatively straight (Figure 3—figure supplement 2). We found that the motion of this central portion of the line moved at very similar speeds to the entire line binned together, suggesting that the observed slowdown was a not a consequence of increased curvature near the poles. These results therefore suggest that the speed of the KMTs is faster the further they are from the pole, and that the stability of KMTs and non-KMTs are constant throughout the spindle. Figure 3 with 2 supplements see all Download asset Open asset Spatial dependence of photoconversion parameters. (A) Sample photoactivated frames (488 nm, 500ms exposure, 5s frame rate) and line profiles from a line drawn near the kinetochore. (B) Sample photoconverted frames and line profiles from a line drawn halfway between the kinetochores and the pole. (C) Sample photoconverted frames and line profile from a line drawn near the pole. (D) Linear fits to the central position of the peaks from A, B and C to measure the line speeds (E) Dual-exponential fits to the intensity of the line in A, B, and C to measure the KMT and non-KMT lifetimes. (F) Line speed vs. initial position of the line drawn on the spindle axis. The area near the pole and in the spindle bulk are marked, divided by a dashed line at 1µm. Error bars are standard error of the mean. (0–1µm: n=5; 1–2µm: n=11; 2–3µm: n=15; 3–4µm: n=10; 4–5µm: n=10) (G) KMT lifetime vs. initial position of the line drawn on the spindle axis. (H) Non-KMT lifetime vs. initial position of the line drawn on the spindle axis. KMTs and non-KMTs are well aligned in the spindle To connect the static ultrastructure of KMTs (visualized by electron tomography) to the spatially varying KMT speeds (measured by photoconversion), we next sought to better characterize the orientation and alignment of MTs in the spindle. We started by separately analyzing the non-KMTs and KMTs (Figure 4A) in all three electron tomography reconstructions (Figure 4—figure supplements 1 and 2). We projected the MTs into a 2D XY plane and calculated the average orientation, ⟨θ⟩ where tan⁡θ=nynx , in the spindle for both non-KMTs (Figure 4B) and KMTs (Figure 4C). For each spindle, we averaged the spindle every π10 radians to produce a uniform projection. The orientations of non-KMTs and KMTs were very similar to each other throughout the spindle, as can be seen by comparing the mean orientation of both sets of MTs along the spindle axis (Figure 4D). Thus, the non-KMTs and KMTs align along the same orientation field in the spindle. Figure 4 with 2 supplements see all Download asset Open asset Measuring nematic alignment of non-KMTs and KMTs (3D reconstructed cell #1). (A) Sample from a 3D reconstruction of non-KMTs (yellow) and KMTS (red) from electron tomography (Kiewisz et al., 2022). (B) Mean local orientation of non-KMTs projected into a 2D XY plane averaged over the spindle rotated every π10 radians along the spindle axis. Sample calculations of the local orientation in three representative pixels are shown above (yellow θ=π/4, blue θ=0 red θ=-π/4). (C) Mean local orientation of KMTs projected into a 2D XY plane averaged over the spindle rotated every π10 radians along the spindle axis (D) Averaged orientation angle of KMTs (red) and non-KMTs (black) along the spindle axis. (E) Local alignment of the non-KMTs projected into a 2D XY plane and averaged over the spindle rotated every π10 radians along the spindle axis. Sample calculation of the local alignment in three representative pixels are shown above (red S=0.9; orange S=0.7; yellow S=0.5). (F) Local alignment of the KMTs projected into a 2D XY plane and averaged over the spindle rotated every π10 radians along the spindle axis. (G) Average alignment of the non-KMTs (black) and KMTs (red). The above analysis addresses how the average orientation of MTs varies throughout the spindle. We next sought to quantify the degree to which MTs are well aligned along these average orientations. This is conveniently achieved by calculating the scalar nematic order parameter, S=⟨32cos2⁡(θ−⟨θ⟩)−1⟩, which would be 1 for perfectly aligned MTs and 0 for randomly ordered MTs (De Gennes and Post, 1993). We calculated S for both non-KMTs (Figure 4E) and KMTs (Figure 4F) throughout the spindle. Both sets of MTs are well aligned throughout the spindle (Figure 4G) with S=0.90±0.01 for KMTs and S=0.78±0.01 for non-KMTs. The strong alignment of MTs in the spindle along the (spatially varying) average orientation field suggests that MTs in the spindle tend to move and grow along this orientation field. We next calculated the orientation field of MTs in HeLa spindles by averaging together data from both non-KMTs and KMTs from all three EM reconstructions by rescaling each spindle to have the same pole-pole distance and radial width (Figure 5A). We sought to test if the resulting orientation field was representative by obtaining data on additional HeLa spindles. Performing significantly more large-scale EM reconstructions is prohibitively time consuming, so we turned to an alternative technique: the LC-Polscope, a form of polarized light microscopy that can quantitively measure the optical slow axis (i.e. the average MT orientation) and the optical retardance (which is related to the integrated MT density over the image depth) with optical resolution (Oldenbourg, 1998). Due to our use of a low numerical aperture condenser (NA = 0.85), it is reasonable to approximate the Polscope measurements as projections over the z-depth of the spindle. Consistent with this expectation, the measured retardance from the PolScope agrees with the predicted retardance from projecting the entire z-depth of the EM reconstructions onto one plane (Figure 5—figure supplement 1). We next averaged together live-cell LC-Polscope data from eleven HeLa spindles and obtained an orientational field (Figure 5B) that looked remarkably similar to the projected orientations measured by EM (compare Figure 5A and B). Figure 5 with 4 supplements see all Download asset Open asset Experiment and theory of the orientation field of MTs in HeLa spindles. (A) Orientation field of MTs from averaging three spindle reconstructions from electron tomography. (B) Orientation field of MTs from averaging polarized light microscopy (LC-PolScope) data from 11 spindles. (C) A theoretical active liquid crystal model of the spindle geometry with tangential anchoring at the elliptical spindle boundary and point defects at the poles. Lower inset: graphic depicting the boundary conditions used in the model (tangential anchoring along the spindle boundary and radial anchoring at two point defects) (D) Average angle along narrow cuts parallel to the spindle and radial axis (red-lower spindle cut, blue-upper spindle cut purple-radial cut near pole, green-radial cut halfway between pole and kinetochore, teal-radial cut near kinetochore) shows close agreement between orientations from EM, polscope, and theory (black lines). Previous work has shown that an active liquid crystal theory can quantitatively describe the morphology of Xenopus egg extract spindles, as well as the statistics of spontaneous fluctuations of MT density, orientations, and stresses in those spindles (Brugués and Needleman, 2014; Oriola et al., 2020). Active liquid crystal theories are continuum theories of the collective behaviors of locally interacting, energy consuming molecules that spontaneously align (Marchetti et al., 2013; Needleman and Dogic, 2017). The central underlying assumptions in applying these theories to the spindle are that MTs align relative to each other due to their local, mutual interactions, that MTs in the spindle tend to move and grow along the direction defined by their axis, and that the phenomena of interest occur at sufficiently large length-scale such that the continuum approximation is appropriate. In this picture, the spindle is a finite size active liquid crystal ‘droplet’ made of interacting MTs and associated proteins. The shape of the spindle is then determined by a balance of forces in the droplet including the bending elasticity of MTs, a ‘surface tension’ at the spindle boundary arising from MT crosslinkers, and ‘active ‘stresses” caused by molecular motors and MT polymerization/depolymerization, along with a potential role of spatially regulated MT nucleation, polymerization, and depolymerization. Such active liquid crystal theories can be derived by explicitly coarse-graining equations describing the motions and interactions of MTs, molecular motors, and associated proteins (Fürthauer et al., 2019; Fürthauer et al., 2021). The resulting active liquid crystal theories can be complex and generally contain multiple coupled fields, as is the case for the previously validated active liquid crystal theory of Xenopus egg extract spindles. The theory, however, dramatically simplifies when there are no hydrodynamic flows, as previously observed in the spindle (Brugués and Needleman, 2014). We also use a single nematic elastic constant approximation, which often produces accurate results even when splay, bend, and twist deformation are associated with different moduli (as is presumably the case in the spindle" @default.
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W4292615460 title "Editor's evaluation: Self-organization of kinetochore-fibers in human mitotic spindles" @default.
W4292615460 doi "https://doi.org/10.7554/elife.75458.sa0" @default.
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