Centripetal nuclear shape fluctuations associate with chromatin condensation in early prophase

The nucleus plays a central role in several key cellular processes, including chromosome organisation, DNA replication and gene transcription. Recent work suggests an association between nuclear mechanics and cell-cycle progression, but many aspects of this connection remain unexplored. Here, by monitoring nuclear shape fluctuations at different cell cycle stages, we uncover increasing inward fluctuations in late G2 and in early prophase, which are initially transient, but develop into instabilities when approaching the nuclear-envelope breakdown. We demonstrate that such deformations correlate with chromatin condensation by perturbing both the chromatin and the cytoskeletal structures. We propose that the contrasting forces between an extensile stress and centripetal pulling from chromatin condensation could mechanically link chromosome condensation with nuclear-envelope breakdown, two main nuclear processes occurring during mitosis.

19.5 ± 2.7 3.9 ± 0.4 1.8 ± 0.5 Radius (µm) 4.18 ± 0.04 7.5 ± 0.1 8.5 ± 0.3 11.1 ± 0.5 9.6 ± 0.3 9.2 ± 0.4 Relaxation time mode 3 (s) 0.035 ± 0.008 2.1 ± 0.1 2.4 ± 0.1 2.0 ± 0.2 (14 cells) 2.4 ± 0.2 2.9 ± 0.2 Nuclear radius, effective tension, effective bending modulus and fluctuation timescale of mode 3, measured by flickering spectrometry, were compared at different times during the cell cycle. 6-34 modes were considered for the HeLa cell cycle, modes 8-20 for RBCs. Measurements were consolidated from 3 independent experiments for each phase. The nuclear radius is the mean calculated from the center of the nucleus. The average values and the respective standard errors of the mean (SEM) were calculated from the number of cells indicated in the table. Data shown in Fig. 1d-g.  Fig. 1,2, and 3. Pairwise statistical comparisons were performed using the two-sided Mann-Whitney U test and the two-sample t-test after checking whether the data followed a Gaussian distribution. Nuclear radius and tension measured by flickering spectrometry upon Calyculin A and Latrunculin A perturbations. Two biological replicates were measured for each condition, and the same nuclei were recorded before and after biochemical treatments.  Relative growth of nuclear cross section area across cell cycle. Observed a continuous increase in nuclear area throughout the cell cycle reaching maximum at late G2 and with a minor reduction at the onset of prophase and the nuclear envelope breakdown (n=8). This is in agreement with data on nuclear radii in Fig. 1d. Figure S2. The radius/tension dynamics of single cells agrees with the average behavior.
The plot shows nuclear shape properties of 7 cells followed along their cycle starting either from arrest in G1 or late G2, monitoring radius (black) and effective tension (red). Their behavior is generally in agreement with the average behavior shown in Fig. 1.  Experiments to rule out the role of myosin-2 mediated contractility as origin of nuclear invaginations due to calyculin A treatment. Blebbistatin and Y27632 (contrary to blebbistatin which is inactivated by blue light, Y27632 is not affected by illumination) confirm that the invagination phenotype is independent of actomyosin contractility. Nuclear radius (a), tension (b), amplitudes of nuclear envelope fluctuations (c) and skewness (d) of fluctuation distribution were measured for the same 8 unsynchronised cells before and after blebbistatin and blebbistatin+calyculin A (45 min incubation: 30 min with blebbistatin + 15 min incubation with both), and after Y27632 treatment (30 min incubation). No significant difference for all the properties measured between control and blebbistatin/Y27632 treatments, while the difference is significant with respect to the combination of blebbistatin + calyculin A as expected from Fig.3. P values highlighted in the figure: radius 0.0493 (control -blebbistatin + calyculin A) and 0.0295 (blebbistatin -blebbistatin + calyculin A); tension 0.0027 (control -blebbistatin + calyculin A) and 0.0016 (blebbistatin -blebbistatin + calyculin A); skewness 0.0174 (control -blebbistatin + calyculin A) and 0.0035 (blebbistatin -blebbistatin + calyculin A). Pairwise statistical comparisons were performed using the two-sided Mann-Whitney U test and the two-sample t-test after checking whether the data followed a Gaussian distribution.

Percentage of cells showing transient invaginations of NE for the same time interval halved after
Trichostatin A treatment (number of cells considered n=36 with respect to its control n=29 (31% in control, 17% TSA), on the contrary they increase after Calyculin A treatment (n=9) with respect to its control (n=9) (11% control, 55% Calyculin A). Chi-square test was used for statistical pairwise comparison.

Figure S7. The shape of invaginations in early prophase is compatible with prediction of a pinning force
The shape of invaginations at the early stage of nuclear prophase resemble the shape of an emerging tube when the membrane is pulled by a point force f. The data for one side of the invagination are fitted with the equation in the inset formulated by Derényi et al. 2002 [29], by knowing f0 and R0, which are related to the bending modulus and tension of the membrane (in our case effective bending modulus and tension).

Figure S8. Absence of separation between NE and chromatin globule surface (CGS) at the invagination sites
Instantaneous contours of NE and CGS of two representative nuclei from 11 cells in both early and late prophase stage do not exhibit any separation in the site of invaginations (highlighted in the black square). No separation between NE and CGS was reported throughout the invagination period for all cells analysed.

Figure S9. Correlation between histones and transient invaginations during mitosis
a) Examples of the negative correlation between the fluorescence signal of histones (green) in the proximity of the invagination (area highlighted in the green in the image of the nuclei) and the relative NE deformation (red) for nuclei in early and late prophase. The green plots show the mean fluorescence intensity of the area of interest normalized for the mean fluorescence intensity of the entire nuclei during transient invaginations, while the red plots show the nuclear contour for the angle at which the invagination is at its maximum and subtracting the initial frame. As shown in SI Video 8, the third nucleus has repetitive invaginations in the same section of the contour (white arrows). b) Pearson correlation coefficient between NE deformations and chromatin fluorescence, comparing locations with invaginations and locations with no invaginations for the same total time. The Pearson correlation is close to -1 for invaginations and close to 0 for control regions. 10 invaginations and 10 controls were analyzed in total.   Figure S11. Effect of ATR inhibition on NE Effective tension is reduced (P value = 0.0218) and effective bending modulus increases (p value = 0.0338) in cells treated with VE822, while radius and relaxation time for mode 3 do not change (a-d). Panel e shows the fluctuation spectra from the 2 sets of experiments. The increase of bending modulus could be due to changes in the lipid composition as suggested by Kidiyoor et al. 2020 [31]. Data from 2 sets of experiments: 29 cells for control, 38 cells for VE822 treatment. Pairwise statistical comparisons were performed using the two-sided Mann-Whitney U test and the twosample t-test after checking whether the data followed a Gaussian distribution. Figure S12. Summary of nuclear contour fluctuations throughout the cell cycle and after chemical perturbations Heat maps highlighting the contour fluctuations of representative nuclei (see Videos) at different times of the cell cycle and after treatments. For each nucleus, the x axis indicates the duration of the recorded video (500 frames = 125 s), the y axis the contour profile angle, and the color map is the deviation from the mean contour (negative inward, positive outward). Black arrows indicate transient and localised invaginations that characterise early prophase and they are similarly visible after Calyculin A early treatment.