The mitotic spindle is chiral due to torques generated by motor proteins

Mitosis relies on forces generated in the spindle, a micro-machine composed of microtubules and associated proteins1,2. Forces are required for the congression of chromosomes to the metaphase plate and separation of chromatids in anaphase3-6. However, torques may also exist in the spindle, yet they have not been investigated. Here we show that the spindle is chiral. Chirality is evident from the finding that microtubule bundles follow a left-handed helical path, which cannot be explained by forces but rather by torques acting in the bundles. STED super-resolution microscopy, as well as confocal microscopy, of human spindles shows that the bundles have complex curved shapes. The average helicity of the bundles with respect to the spindle axis is 1.2°/μm. Inactivation of kinesin-5 (Eg5/Kif11) abolished the chirality of the spindle, suggesting that this motor generates the helical shape of microtubule bundles. To explain the observed shapes, we introduce a theoretical model for the balance of forces and torques acting in the spindle, and show that torque is required to generate the helical shapes. We conclude that torques generated by motor proteins, in addition to forces, exist in the spindle and determine its architecture.

imaged them by confocal microscopy (Fig. 1b). In these spindles, optical sections are roughly perpendicular to the microtubule bundles, allowing for precise determination of the bundle location in each section and thus of the whole three-dimensional contour (Methods). We used fixed HeLa cells expressing GFP-tagged protein regulator of cytokinesis 1 (PRC1) 9,10 , which binds overlap zones of antiparallel microtubules 11,12 . Almost all overlap bundles in the spindle are associated with a pair of sister kinetochores, acting as a bridge between the respective kinetochore fibers [13][14][15] . Thus, PRC1-GFP shows the position of overlap bundles together with their kinetochore fibres, without interference from other microtubules such as polar and astral ones. PRC1-labeled bundles, which appear as spots in a single image plane, were tracked through the z-stacks ( Fig. 1b and Methods). We found that individual bundles follow a lefthanded helical path along the spindle axis ( Fig. 1b and Supplementary Video 1). The arrows connecting starting and ending points of PRC1-GFP bundles traced in the upwards direction rotate clockwise, revealing left-handed chirality of the spindle ( Fig. 1b and Extended Data Fig  1b). A 3D plot of all traced points shows the helical shape and spatial arrangement of the bundles (Supplementary Video 2). The helicity of bundles, defined as the average change in angle with height where positive numbers denote left-handed helicity, was 2.1±0.3 °/µm (results are mean±s.e.m. averaged over bundles, unless stated otherwise; n=415 bundles from 10 cells; Fig.  1d). Similar results were obtained when averaging the helicity over cells (Extended Data Fig.  1d). We conclude that the mitotic spindle is a chiral object with left-handed helicity of the microtubule bundles.
To test whether chirality is a specific property of vertically oriented spindles, we measured the average helicity of bundles in fixed horizontally oriented spindles (Fig. 1c). To trace the bundles in these spindles, we rearranged the z-stacks to obtain the slices perpendicular to the spindle axis, similar to the z-stacks of vertical spindles (Fig. 1c, Extended Data Fig 1c and Methods). The bundles in horizontally oriented spindles showed left-handed helicity as in vertical spindles, but with a larger value of 3.3±0.4 °/µm (n=391 bundles from 10 cells; Fig. 1d, Extended Data Fig. 1d shows results averaged over cells). Thus, spindles have left-handed chirality independent of its orientation within the cell.
To test if the fixation process causes spindle chirality, we imaged both vertical and horizontal spindles in live HeLa cells expressing PRC1-GFP. In both cases we observed the lefthanded chiral nature of the spindle with helicities for vertical and horizontal spindles of 1.0±0.3 °/µm (n=806 bundles from 23 cells) and 2.7±0.4 °/µm (115 bundles from 5 cells), respectively (Fig. 1d, Extended Data Fig. 1d shows results averaged over cells). These results indicate that chirality is a property of spindles in live cells as well as in fixed cells. Finally, to test if the chirality is limited to a specific cell line, we examined the spindles in U2OS cells expressing mCherry-tubulin and GFP-CENP-A. The helicity of the bundles in these spindles was 1.0±0.3 °/µm (n=477 bundles from 20 cells; Fig. 1d, Extended Data Fig. 1d shows results averaged over cells) indicating that in human cells, microtubule bundles follow a left-handed helical path in different cell lines. Taken together, our results suggest that even though the average helicity value differs among various conditions and cell lines, the bundles consistently twist in a lefthanded direction with average value for all cells of 1.2±0.3 °/µm. We conclude that left-handed chirality is a robust feature of the spindle.
Next, we set out to investigate the molecular mechanisms that contribute to the generation of twist in the spindle. We first hypothesized that twist is generated within the bundles, by motor proteins that rotate the microtubule while walking. In vitro gliding motility studies showed that kinesin-5 (Kif11/Eg5) switches protofilaments with biased steps towards the left 16 . To inactivate Eg5, we treated HeLa cells with vertically oriented spindles in metaphase with S-trityl-L-cysteine (STLC), a reversible tight-binding inhibitor 17,18 . The arrows connecting starting and ending points of the bundles traced in the upwards direction show a change from a clockwise rotation before treatment to a more random distribution after STLC treatment (Fig.  2a). Inactivation of Eg5 caused the reduction of bundle helicity in the same cells from 0.6±0.3 °/µm (n=347 bundles from 10 cells) before STLC treatment to 0.2±0.3 °/µm (n=341 bundles from 10 cells) and 0.2±0.3 °/µm (n=153 bundles from 6 cells) at 5 and 10 minutes after STLC addition, respectively (Fig. 2b, 2c, Extended Data Fig. 2a shows results averaged over cells). Whereas the helicities before STLC treatment were significantly different from 0 (p=4x10 -7 ), no significant difference from 0 was found after STLC addition (p=0.11 and 0.28 for 5 and 10 minutes after STLC addition, respectively). Thus, the average bundle twist was left-handed before the treatment, whereas there was no preferred handedness after Eg5 inactivation. On the contrary, the bundle helicity in control cells did not change significantly within 10 minutes, suggesting that the helicity does not fluctuate significantly during metaphase in individual cells (Fig. 2d). Similarly, Eg5 inactivation in U2OS abolished spindle chirality (Fig.2c). Based on these results, we conclude that kinesin-5 contributes to the generation of spindle chirality.
Twist in the spindle may be also regulated by astral microtubules. To test the contribution of astral pulling forces at the cell cortex to the twist in the spindle, we treated the cells with latrunculin A, which depolymerizes cortical actin 19 . Consequently, it disrupts the cortical localization of LGN protein, which is a part of NuMA/LGN/Ga complex that anchors dynein on the cell cortex 20,21 . Cortical dynein positions the spindle with respect to the cell cortex by pulling on astral microtubules 22 . We found that microtubule bundles in latrunculin-treated Hela cells had a helicity of 2.4±0.4 °/µm (n=245 bundles from 10 cells, Fig. 2e), which is similar to the bundle helicity in untreated HeLa cells (2.7±0.4 °/µm, 115 bundles from 5 cells). In these experiments, we used horizontally oriented spindles to confirm the effect of latrunculin A on spindle position (Extended Data Fig. 2b and Methods). Our results indicate that pulling forces generated by astral microtubules at the cell cortex have a minor effect on spindle chirality.
To explain the observed shapes, we introduce a theoretical model for the balance of forces and torques acting on the microtubule bundles in the spindle, taking into account microtubule elastic properties. In our model, two spindle poles are represented as spheres of radius with centers separated by vector of length = , whereas microtubule bundles are represented as curved lines connecting these spheres (Fig. 3a). Microtubule bundles, denoted by index = 1, … , , extend between points located at the surface of the left and right sphere, where positions with respect to center of each sphere are given by vectors + and + ′, respectively. Here, denotes number of microtubule bundles. Based on the observation that spindle shape is rather constant during metaphase, we introduce balance of forces and torques on the spindle pole. For the left pole, force balance reads and the balance of torques reads Here, + and + denote forces and torques exerted by the left pole at the -th microtubule bundle, respectively. Balances of forces and torques at the right pole are obtained by equations analogues to equations (1) and (2), where + , + , and + are replaced with + ′, + ′ and + ′, respectively.
Here and throughout the text the prime sign corresponds to the right pole. We also introduce balance of forces and torques for the microtubule bundle (4) Forces and torques acting at the microtubule bundle change its shape, because microtubule bundles are elastic objects 13,23,24 . We describe a microtubule bundle as a single elastic rod of bending elasticity and torsional rigidity . The contour of elastic rod is described by its length, , and radial vector, ( ). The normalized tangent vector is calculated by = / . The torsion angle, ( ), describes orientation of the cross-section along the length of the rod (Fig. 3b). The curvature and the torsion of an elastic rod are described by the static Kirchoff equation 25 Our model provides a description for the force and torque balance of the entire spindle and makes a link between shape of microtubule bundles and forces and torques at the spindle poles. The model describes a system consisting of microtubule bundles, where torques and forces can vary between bundles, resulting in a system with a large number of degrees of freedom. To reduce the number of degrees of freedom, we consider a case with two microtubule bundles, = 1, 2. Further, we use rotational symmetry of the spindle with respect to the major axis by imposing the symmetry for forces @∥ = B∥ , @C = − BC and for torques @∥ = B∥ , @C = − BC . Here, index ∥ and ⊥ denotes components of vectors that are parallel and perpendicular to the vector , respectively, obeying + = +∥ + +C and + = +∥ + +C . In addition, we impose that the magnitude of torque is equal at both poles, + = + ′ , that the components of torque parallel to are balanced, +∥ = − +∥ ′, and • +C = 4 • +C 4 = 0. For simplicity, we also choose that vectors and ′ are perpendicular to . To solve the model, we choose a Cartesian coordinate system with the origin at the center of left spindle pole and -axis parallel to . In this coordinate system, radial vector has components = ( , , ) and torques have components + = ( +J , +K , +L ). The orientation of the coordinate system is chosen such that +K = +K ′ and +L = − +L ′. Thus, our model has only two free parameters (see Methods).
In the small angle approximation, equation (5) has simple analytical solutions and the twisting moment corresponds to the component of torque parallel to -axis. If torque has a bending moment only, @J = 0, there are two solutions which are both planar, the symmetric Cshape and the anti-symmetric S-shape (Fig. 3c). However, by adding a twisting moment, shapes become three-dimensional with a non-vanishing helicity in either case (Fig. 3d). Thus, our theory predicts that a twisting moment is required for a microtubule bundle to have a helical shape.
To compare the results of our model with the experimentally observed shapes of microtubule bundles, we fit our analytical solutions to the traces of microtubule bundles from live HeLa cells expressing PRC1-GFP (Fig. 3e). Our theory reproduces three-dimensional helical shapes, as well as symmetric C-shapes ( Fig. 3e; Extended Data Fig. 3 shows additional examples). In the case of the helical shape shown in Fig. 3e the twisting moment was @J = −2.6 µ , whereas in the case of the C-shapes it was 10 times smaller. The bending moment was similar in both cases. For 48 bundles the twisting moment was @J = −0.5 ± 0.2 µ and the bending moment was @C = 69 ± 4 µ (see Methods). Our results show that a twisting moment is required to reproduce the experimentally observed helical shapes, whereas a bending moment is required for all curved shapes.
In summary, we found that the mitotic spindle is a chiral object. Chirality is an intriguing property of the biological world, present at all scales ranging from molecules to whole organisms. We find that spindle chirality cannot be explained by forces but rather by torques. Based on our experiments and theory, we conclude that torques generated by motor proteins, in addition to forces, exist in the spindle and determine the spatial organization of the microtubule bundles. To visualize kinetochores and identify the metaphase, HeLa celles expressing PRC1-GFP cells were transfected by electroporation using Nucleofector Kit R (Lonza, Basel, Switzerland) with the Nucleofector 2b Device (Lonza, Basel, Switzerland), using the high-viability O-005 program. Transfection protocol provided by the manufacturer was followed. 25-35 h before imaging, 1x10 6 cells were transfected with 2.5 µg of mRFP-CENP-B plasmid DNA (pMX234) provided by Linda Wordeman (University of Washington). To visualize chromosomes and determine the metaphase state, 1 hour prior to imaging SIR-DNA (Spirochrome AG, Stein am Rhein, Switzerland) was added to the dish with live HeLa cells at 100nM final concentration.

Methods
To prepare samples for microscopy, HeLa and U2OS cells were seeded and cultured in 1.5 mL DMEM medium with supplements at 37°C and 5% CO 2 on uncoated 35-mm glass coverslip dishes, No 1.5 coverglass (MatTek Corporation, Ashland, MA, USA). Before live-cell imaging, the medium was replaced with Leibovitz's L-15 CO 2 -independent medium supplemented with fetal bovine serum (FBS, Life Technologies, Carlsbad, CA, USA). For experiments with the fixed samples, cells were fixed in ice-cold methanol for 3 min and washed three times with phosphate buffered saline (PBS, Merck, Darmstadt, Germany).

Drug treatments.
The stock solution of S-trityl-L-cysteine (STLC) and latrunculin A were prepared in DMSO to a final concentration of 1mM. Both drugs and solvent were obtained from Sigma-Aldrich. The working solution was prepared in DMEM medium at 2x final concentration. At the time of treatment, the working solution was added to cells at 1:1 volume ratio. STLC treated samples were acquired as follows: images of a cell with vertical spindle were acquired, then the drug was added at a final concentration of 50 µM and the same spindle was imaged after 5 and 10 minutes. Appearance of monopolar spindles confirmed the effect of STLC. For latrunculin A treatment experiment, the PRC1-GFP HeLa cells were treated with 2 µM latrunculin A for one hour prior to imaging, which was done between one and two hours post treatment. The effect of latrunculin A was confirmed by significant cell blebbing immediately after drug addition, decrease of cell diameter and spindle mis-positioning (Extended Data Fig.  2b). Here 21 out of 30 latrunculin-treated cells had spindles close to the cell cortex, which is rare in untreated cells). For mock-treated experiments, cells were treated with the concentration of DMSO that was used for preparation of drug treatments. STED microscopy. STED images of HeLa and U2OS cells were recorded at the Core Facility Bioimaging at the Biomedical Center, LMU Munich. STED resolution images were taken of Sir-Tubulin signal, whereas GFP signal of kinetochores and centrin1 was taken in confocal resolution. Gated STED images were acquired with a Leica TCS SP8 STED 3X microscope with pulsed White Light Laser excitation at 652 nm and pulsed depletion with a 775 nm laser (Leica, Wetzlar, Germany). Objective used was HC PL APO CS2 93x/1.30 GLYC with motorized correction collar. Scanning was done bidirectionally at 30-50 Hz, a pinhole setting of 0.93 AU (at 580 nm) and the pixel size was set to 20 x 20 nm. The signals were detected with Hybrid detectors with the following spectral settings: Sir-Tubulin (excitation 652; emission: 662 -715 nm; counting mode, gating: 0.35 -6 ns), GFP (excitation 488; emission 498-550; counting mode, no gating).
Confocal microscopy image acquisition. Fixed HeLa cells expressing PRC1-GFP were imaged by using a Leica TCS SP8 X laser scanning confocal microscope with a HC PL APO 63x/1.4 oil immersion objective (Leica, Wetzlar, Germany) heated with an objective integrated heater system (Okolab, Burlingame, CA, USA). Excitation and emission lights were separated with Acousto-Optical Beam Splitter (AOBS, Leica, Wetzlar, Germany). For excitation, a 488-nm line of a visible gas Argon laser and a gated STED supercontinuum visible white light laser at 575 nm were used for GFP and mRFP, respectively. GFP and mRFP emissions were detected with HyD (hybrid) detectors in ranges of 498-558 and 585-665 nm, respectively. Pinhole diameter was set to 0.8 µm. Images were acquired at 25-35 focal planes with 0.5 µm spacing and 400 Hz unidirectional xyz scan mode. The system was controlled with the Leica Application Suite X software (LASX, 1.8.1.13759, Leica, Wetzlar, Germany).
Live HeLa and U2OS cells were imaged using Bruker Opterra Multipoint Scanning Confocal Microscope (Bruker Nano Surfaces, Middleton, WI, USA). The system was mounted on a Nikon Ti-E inverted microscope equipped with a Nikon CFI Plan Apo VC 100x/1.4 numerical aperture oil objective (Nikon, Tokyo, Japan). During imaging, cells were maintained at 37°C in Okolab Cage Incubator (Okolab, Pozzuoli, NA, Italy). 60 µm pinhole aperture was used and the xy-pixel size was set to 0.83 µm by placing a 2x relay lens in front of the camera. For excitation of GFP and mCherry fluorescence, a 488 and a 561 nm diode laser line were used, respectively. The excitation light was separated from the emitted fluorescence by using Opterra Dichroic and Barrier Filter Set 405/488/561/640. Images were captured with an Evolve 512 Delta EMCCD Camera (Photometrics, Tucson, AZ, USA) with no binning performed. To cover the whole metaphase vertical spindle, Z-stacks were acquired at 30-60 focal planes separated by 0.5 µm spacing with unidirectional xyz scan mode and without frame averaging. In latrunculin A treated cells horizontal spindles were imaged, with Z-stacks acquired at 48 focal planes separated by 0.5 µm spacing with unidirectional xyz scan mode and with four frame averages. The system was controlled with the Prairie View Imaging Software (Bruker Nano Surfaces, Middleton, WI, USA).

Image analysis.
Microscopy images were analysed in Fiji software 26 . Tracking of bundles was done using the available Multi-point tool. Obtained data was further analysed and plotted in R programming language.
Transformation of vertical spindles from horizontal spindle images was also done using code written in R. Since images obtained by using confocal microscopy have a gap between them, during transformation we had to fill this gap by copying the same pixel a required number of times depending on the initial pixel size. Also, the gap size doesn't have to be a multiple of the pixel size. To take this into consideration, pixel width was changed accordingly. For instance, if we had a 500 nm gap between horizontal spindle images and 80 nm pixels, the best we could do is copy 6 pixels in the gap. This would leave us with unaccounted 20 nm so we introduced a correction by saying the width of each pixel is 500/6 = 83.3 nm. To ensure that spindles are maximally vertical after the transformation, horizontal spindles were chosen for transformation if both poles could be seen simultaneously in one image. For the same reason, before transformation, the images were rotated so that the spindle long axis was approximately parallel to the x axis. Analogously, vertical spindle images were transformed into a horizontal spindle.
Forces and torques for the system of 2 bundles and with the imposed symmetries. From equation (1) and the symmetry @∥ = B∥ , we obtain that @J = BJ = 0. From @C = − BC , the other two components obey @K = − BK , @L = − BL . For coordinate system with orientation in which +K = +K ′ and +L = − +L ′ the -component of equation (4) reads @K = 0 andcomponent of the force vanishes, @K = 0. By using the -component of equation (2), @J + K @L = 0, together with the -component of equation (4), 2 @K − @L = 0, we obtain K = − @J /2 @K . By using the -component of equation (2) for the right centrosome, we obtain K = K ′. Because we imposed the symmetry • @C = ′ • @C ′ = 0, and is perpendicular to , components of vectors and ′obey L = − K @K / @L and L = − L 4 . By using K B + L B = B , we obtain the relation between the parameters @J , @K and @L : (S1)

Analytical solutions of equation (5).
To solve equation (5) we use a Cartesian coordinate system in which this equation is given by system of three nonlinear differential equations. In the small angle approximation, where ≈ , these equations simplify and become linear: where +@,+B = ∓ +J + +J B + 4 +J 2 .
Note that in the case of two bundles, with imposed symmetries, these solutions simplify because @J = @K = 0. Integration constants @ , @ , @ , @ are obtained from the boundary conditions 0 = = K , 0 = − ( ) = L Comparison of the model to experimentally observed shapes. We have compared the theoretically obtained shapes, given by equations (S5) and (S6), to the tracking data of live HeLa cells expressing PRC1. The parameters of the fit are J and K , and the orientation of the coordinate system of the tracked shape. Used parameters are = 0.5 µ , and = 900 µ B . Parameter is obtained from the experimentally measured distance between the poles. Torque L and forces K and L are calculated after all other parameters are known. We fitted 60 traced bundles and for 80 % of all the shapes discrepancy between fitted curves and experimental data was smaller than: Here, f , f , f are measured coordinates of the imaging plane , and denotes number of data points used for fitting a single bundle. We used shapes with maximal distance from the major axis larger than 1 µ .