Nonlinear mechanics of human mitotic chromosomes – Nature

Cell lines and cell culture

All cell lines were cultured in DMEM supplemented with 10% fetal bovine serum (FBS) and penicillin–streptomycin in a humidified incubator at 37 °C and 5% CO₂. Unless indicated otherwise, all cell lines were obtained from and authenticated by the ATCC by karyotyping and STR profiling. The U2OS TRF1-BirA cell line²² was a gift from R. J. O’ Sullivan and was authenticated by karyotyping. Endogenous H2B in the U2Os TRF1-BirA cell line was tagged with eGFP, as described previously⁵. To rapidly deplete TOP2A, we used a HCT116 TOP2A-mAID cell line that also expressed H2B–eGFP, facilitating chromosome identification. The HCT116 TOP2A-mAID H2B-eGFP cell line was a gift from D. F. Hudson and authentic by karyotyping, and was described in a previous report⁵. All cell lines were routinely tested for mycoplasma and shown to be negative. To achieve tight temporal control over cell synchrony, the HCT116 TOP2A-mAID H2B-eGFP cell line was modified for CDK1as chemical genetics by knock-in of CDK1as and knockout of endogenous CDK1, as described previously⁴² and based on another previous report⁴³. The constructs for CDK1as were gifts from W. Earnshaw (Addgene 118596 and 118597) and from Z. Izsvak (Addgene 34879). We determined that treatment with 0.25 µM 1NM-PP1 (529581, Sigma-Aldrich) for 16 h efficiently arrests HCT116 TOP2A-mAID H2B-eGFP CDK1as cells at the G2–M boundary (Extended Data Fig. 6a, b). The incubation time and concentration of 1NM-PP1 were optimized by propidium iodide flow cytometry (Extended Data Fig. 5a), performed as described before⁵. Efficient release from the arrest was achieved with two wash cycles by centrifugation with preheated medium. A Neon transfection system (Thermo Fisher Scientific) was used for transfections of HCT116 and U2OS cell lines according to the manufacturer’s recommendations. 1NM-PP1 and nocodazole were purchased from Sigma-Aldrich. The synthetic auxin indole-3-acetic acid (IAA) sodium salt (sc-215171, Santa Cruz) was used. Six days before chromosome isolation, HCT116 TOP2A-mAID CDK1as cells were transduced with lentiviruses introducing TRF1-BirA into the genome. These cells were treated for 16 h with 0.25 µM 1NM-PP1, before release into 100 ng ml⁻¹ nocodazole (Sigma-Aldrich) with or without 500 µM auxin for 4 h, to arrest cells in prometaphase and deplete TOP2A, respectively. Mitotic cells were detached by shaking and chromosomes were isolated from this population (Extended Data Fig. 6c). Chromosome spreads were performed as described previously⁵ and showed an altered chromosome morphology following exposure to auxin in accordance with what was reported⁵. Approximately 75% of TOP2A depleted chromosomes appeared hypocondensed compared to 5% of control chromosomes (Extended Data Fig. 6d). Immunostaining of TOP2A on chromosome spreads was not detectable in auxin-treated samples, confirming efficient depletion of TOP2A (Extended Data Fig. 5e).

Lentiviral production and transduction

Third-generation lentiviral particles were generated for integration of BirA-TRF1. HEK293T cells were grown with 25 µM chloroquine diphosphate (Sigma-Aldrich) for 5 h before being transfected with plasmids pMD2.G, pMDLg/pRRE and pRSV-Rev (Addgene 12259, 12251 and 12253, deposited by D. Trono⁴⁴) and a transfer plasmid for BirA-TRF1 integration. A Calphos mammalian transfection kit (Clontech) was used for transfections according to the manufacturer’s protocol. Eighteen hours after transfection, the medium was replaced with fresh medium. Forty-eight hours after transfection, the growth medium was collected and centrifuged at 500g for 5 min, and the supernatant containing viral particles was filtered through a 0.45-µm membrane before being concentrated 10× using an Amicon Ultra-15 100 kDa centrifugal unit (Merck-Millipore). The viral concentrate was snap-frozen and stored at −80 °C. For lentiviral transduction, a T-75 flask of 75% confluent HCT116 TOP2A-mAID CDK1as cells was incubated with 7.5 µg ml⁻¹ polybrene in 3 ml 10× lentiviral concentrate and 7 ml growth medium for 1 h with mixing every 15 min. Cells were then seeded in a T-175 flask and the culture was expanded before chromosome isolation.

Chromosome isolation

A previously reported method, with modifications, was used to isolate mitotic chromosomes in large quantities with minimal contamination with cell debris²³. In brief, cells were grown with 12.2 mg l⁻¹ biotin (Sigma-Aldrich) for 24 h before isolation. On the day of isolation, 8–10 T175 flasks of cells were treated for 4 h with 200 ng ml⁻¹ nocodazole (Sigma-Aldrich) and then mitotic shake-off was used to enrich for mitotic cells, resulting in 1 × 10⁷–2 × 10⁷ mitotic cells. The mitotic cells were centrifuged at 300g for 5 min, resuspended in 10 ml 75 mM KCl and 5 mM Tris-HCl (pH 8.0) and then incubated for 10 min at room temperature. All subsequent steps were carried out at 4 °C. Cells were centrifuged at 300g for 5 min and then resuspended in 8 ml polyamine (PA) buffer (15 mM Tris-HCl (pH 8.0), 2 mM EDTA, 0.5 mM EGTA, 80 mM KCl, 20 mM NaCl, 0.5 mM spermidine, 0.2 mM spermine and 0.2% Tween-20) for U2OS cells and a PA* buffer (15mM Tris-HCl (pH 7.4), 0.5 mM EDTA-K, 80 mM KCl, 1 mM spermidine, 0.4 mM spermine and 0.1% Tween-20) for HCT116 cells, both supplemented with Complete mini protease and PhosSTOP phosphatase inhibitor cocktails (Roche). This suspension was then lysed in a Dounce homogenizer using 25 strokes with a tight pestle. The suspension was cleared twice of cell debris by centrifugation at 300g for 5 min. Chromosomes were purified using a glycerol step gradient containing two layers (60% and 30% glycerol in PA). After centrifugation at 1,750g for 30 min, the chromosomes were collected from the 60% glycerol fraction and stored at −20 °C in around 60% glycerol in PA buffer at a concentration of 10⁶–10⁷ chromosomes per ml. Chromosomes could be stored for up to two months without undergoing any noticeable change in mechanical properties.

Dual trap optical tweezers with wide-field fluorescence

The dual trap optical set-up was described previously²⁴. In brief, two optical traps were created using a 20 W, 1064 nm CW fibre laser (YLR-20-LP-IPG, IPG Photonics). Two traps were created by splitting the laser beam into two paths using a polarizing beam splitter cube and could be steered independently using one accurate piezo mirror (Nano-MTA2X10, Mad City Labs) and one coarse positioning piezo step mirror (AG-M100N). After the two paths were recombined, they were coupled into a Nikon microscope body using two 300 mm lenses, and focused in the flow cell with a 1.2 NA water immersion objective (Nikon, Plan apo VC NA1.2). Back-focal plane interferometry was used to measure forces, and bead tracking was performed by LED illuminated bright-field imaging on a CMOS camera (DCC1545M, Thorlabs). Wide-field epifluorescence was achieved by illumination with 488, 532, 561 and 639 nm lasers (Cobolt 06-01 Series) and detection by separation of the emission light using an OptoSplit III (Cairn Research) and imaging on an EMCCD camera (iXon 897 Life, Andor Oxford Instruments Technology).

Microfluidics and flow cell preparation

A microfluidic flow-system (u-Flux, LUMICKS B.V.) was used to insert solutions into a five-channel flow cell (LUMICKS B.V.; Fig. 1b). Before each experiment, bleach cleaning was performed to remove residual debris from flow cell, followed by sodium thiosulfate neutralization. Passivation was performed to reduce chromosome attachment to tubing and flow cell walls by incubation for 1 h with 0.05% casein solution, followed by excessive rinsing with PA buffer. Chromosomes diluted in PA buffer (10–20 µl in 500 µl) were inserted into a side channel of the flow cell (Fig. 1b). Streptavidin-coated polystyrene microspheres (diameter: 4.6 µm, Spherotech) in PA buffer (4 µl in 300 µl) were inserted in one of the main channels. Other channels were filled with PA buffer unless stated otherwise.

Chromosome attachment and force-extension

To facilitate attachment of the biotinylated chromosome between two streptavidin-coated microspheres (diameter: 4.6 µm), one trapped microsphere was brought into the proximity of a chromosome in solution, resulting in attachment of the telomeric end of the chromosome to the microsphere (Fig. 1b, Extended Data Fig. 1b). Next, the microspheres were moved to another microfluidic channel and fluid flow was activated (Fig. 1b). The chromosome attached to one of the microspheres was flow-stretched to confirm correct attachment (Extended Data Fig. 1b, c) and then brought into the proximity of the other microsphere to induce attachment of the other chromosome end (Fig. 1c). Note that owing to the relatively small cross-section of chromosomes compared to the microspheres, both telomeric ends from one sister chromatid would attach to the microsphere occasionally. Non-biotinylated chromosomes showed only very limited attachment to the microspheres (Extended Data Fig. 1d).

Immunofluorescence

Chromosomes were incubated overnight at 4 °C with primary antibody in a concentration of 5 µg ml⁻¹ and were subsequently diluted fivefold in PA buffer and stored for 1 h at 4 °C. Next, chromosomes were incubated with secondary antibody in a concentration of 5 µg ml⁻¹ for 1 h at room temperature. After addition of PA buffer to dilute the sample again by fivefold, chromosomes were stored for 30 min at 4 °C. To remove excess antibody, chromosomes were centrifuged at 750g for 5 min on a 20 µl glycerol cushion. The supernatant was then removed, leaving around 100 µl chromosome solution that could be used for imaging. Primary antibodies were anti-NCAPH (1:100, HPA002647, Sigma Aldrich), CREST anti-sera (1:200 HCT-0100, Immunovision), anti-TRF2 (1:100, sc-9143, Santa Cruz), anti-H3S10 (1:400, 06-570, Sigma-Aldrich) and anti-H3-Alexa Fluor 647 (1:200, 15930862, Thermo Fisher Scientific). Secondary antibodies were anti-rabbit IgG-Alexa Fluor 647 (1:500, A-21244, Thermo Fisher Scientific), anti-rabbit IgG-Alexa Fluor 568 (1:500, A-11011, Thermo Fisher Scientific) and anti-human IgG-Alexa Fluor 488 (1:500, A-11013, Thermo Fisher Scientific). Biotinylated TRF1 was detected using streptavidin–Alexa Fluor 568 (1:200, S11226, Invitrogen).

Immunoblotting

SDS–PAGE and immunoblotting was performed as described previously⁵. In brief, cell pellets were lysed in RIPA buffer containing cOmplete Mini EDTA free (Roche) on ice for 20 min. Samples were then sonicated in a water-cooled Bioruptor Pico (Diagenode) and centrifuged at 21,000g for 15 min at 4 °C. Protein concentration was determined using a Pierce BCA protein assay kit (Thermo Fisher Scientific). Forty micrograms of protein was loaded per well. The primary antibodies were anti-CDK1 (1:1,000, ab133327, Abcam), anti-Myc (1:1,000, sc-40, Santa Cruz) and anti-histone H3.3 (1:5,000, ab176840, Abcam). The secondary antibodies were anti-mouse IgG peroxidase conjugate (1:10,000, A4416, Sigma-Aldrich) and anti-rabbit IgG peroxidase conjugate (1:10,000, A6154, Sigma-Aldrich).

Determination of differential stiffness, stiffening length and compliance

To calculate the differential stiffness from force-distance curves, the force distance curve was first smoothed using a moving average with a window size of 1/15 of the total data points in the force curve, followed by numerical differentiation of force with respect to distance. To determine the onset of stiffening, the plateau stiffness was determined as the most likely stiffness at forces below 50 pN, as estimated from the maximum of a kernel density estimate of the stiffness values. The onset of stiffening was then determined as the point at which the stiffness exceeds the plateau stiffness by one standard deviation of all stiffnesses below 50 pN. To determine the compliance at 200 pN, the inverse of the stiffness of the chromosome at a force of 200 pN was used.

Collapse of stiffness-force curves

To achieve a collapse of the stiffness-force curves they were normalized on a log-log-scale. Therefore, curves were interpolated to a logarithmic force scale to get evenly spaced data after taking the logarithm. In addition, negative values for force and stiffness were discarded. Then the logarithms of force ln(F) and stiffness ln(K) were calculated and fitted with a piecewise function y = ln(K₀) for x ≤ ln(F_c) and y = c − ln(F_c) + ln(K₀) for x > ln(F_c) to determine the initial stiffness K₀ and the critical force F_c. If the determined parameters for K₀ and F_c were in the range of the stiffness-force curve, the curves normalized by K₀ and F_c were plotted in a double-logarithmic plot to achieve the collapse. The criteria that K₀ and F_c had to be positive and within the range of the stiffness-force curve were met by 29 out of 44 curves.

Microrheology

Oscillations of the optical trap were generated by applying a sinusoidal voltage to the analogue input of the piezo mirror controller (Nano-Drive, MCL) to apply the oscillation on top of the digitally controlled mirror position. The signal was first generated digitally using Labview (National Instruments). The analogue voltage was then produced with a digital analogue converter (DAQ, National Instruments). Oscillations were produced with an amplitude of 25 mV corresponding to a trap displacement of roughly 200 nm. The frequency of the oscillation was varied between 2 mHz and 100 Hz. When the frequency was varied in the experiment, the pre-tension was kept constant at 50 pN (Fig. 2f). Experiments for different pre-tension were performed with a frequency of 0.1 Hz (Fig. 2g). To avoid limitations by the frame rate of the bead tracking camera at higher frequencies (>1 Hz), the bead position at high frequencies was calculated from the force and the trap position (Fig. 2f, green line). Data analysis of the oscillations was performed in MATLAB (Mathworks). First, the bead–bead distance and the force were synchronized on the basis of the position of the stationary bead where the force was measured, based on the cross-correlation between the bead position from bead tracking and the measured force. Then the oscillatory data were analysed following a previously described procedure⁴⁵. In brief, both the force and the bead–bead separation were detrended and fitted with a sine function with a fixed frequency set to the experimental frequency and an additional offset. Then the complex stiffness was calculated as (k=frac{{A}_{{rm{F}}}}{{A}_{{rm{d}}}}{{rm{e}}}^{ileft({phi }_{{rm{F}}}-{phi }_{{rm{d}}}right)}) with the amplitude and the phase of the force oscillation A_F and φ_F, and the amplitude and the phase of the distance oscillation A_d and φ_d, respectively.

Calculating HWLC force responses

Model curves in Fig. 3d, e were constructed by first defining a distribution for each system parameter. For simplicity, the number of sub-chains, N, and the length of each sub-chain, L/N, were kept constant. A power-law or exponential distribution with cut-offs was chosen for the sub-chain critical force, f_c. Given these distributions, we analysed the responses of 500 HWLC configurations, each constructed by sampling N values of f_c. The force-response of each configuration was computed by summing the extensions of each sub-chain at a given force, found by numerically solving the flexible WLC equation (Supplementary Note 1). The force-response curve was then numerically differentiated, and the mean and standard deviation of the stiffness-force curve were compared to experimental data.

Distribution of F
_c

The distribution of the critical force of a HWLC assembly, F_c,corresponds to the force at which its softest element starts stiffening. Hence, for a given distribution, P(f_c), F_c is distributed as the minimum of N independent samples. Its cumulative distribution function (CDF) satisfies (Pleft({F}_{{rm{c}}}le xright)=1-{left(1-Pleft({f}_{{rm{c}}}le xright)right)}^{N}.) This expression can be differentiated to yield the probability density function (PDF),({P}left({F}_{{rm{c}}}=xright)={N; P}left({f}_{{rm{c}}}=xright),{left(1-Pleft({f}_{{rm{c}}}le xright)right)}^{N-1}). Figure 3f shows P(F_c = x) for the power-law distribution with cut-offs and for an exponential distribution with cut-offs. The experimental critical forces were determined as described above.

Statistics and reproducibility

Average values and errors were represented as mean ± s.e.m. unless indicated otherwise. Differences in populations are tested using a two-sided Wilcoxon rank-sum test, where P < 0.05 is regarded as significant (*) and P  < 0.01 as highly significant (**). The sample sizes for representative microscopy images are as follows: Fig. 1cn = 91, Fig. 1d–fn = 3, Fig. 2bn = 91, Fig. 4bn = 5, Fig. 4dn = 20, Extended Data Fig. 1an = 24, Extended Data Fig. 1b, cn = 3, Extended Data Fig. 1en = 10, Extended Data Fig. 1f–hn = 3, Extended Data Fig. 6an = 2, Extended Data Fig. 6e (amount of cells) n = 117 (15 min), n = 120 (20 min), n = 98 (25 min), n = 121 (30 min), n = 110 (40 min), n = 115 (50 min), Extended Data Fig. 6gn = 16 (control), n = 19 (+auxin), Extended Data Fig. 7dn = 5.

Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this paper.