Centripetal nuclear shape fluctuations associate with chromatin condensation towards mitosis

The cell nucleus plays a central role in several key cellular processes, including chromosome organisation, replication and transcription. Recent work intriguingly 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 early mitosis, which are initially transient, but develop into instabilities that culminate into nuclear-envelope breakdown in mitosis. Perturbation experiments and correlation analysis reveal an association of these processes with chromatin condensation. We propose that the contrasting forces between an extensile stress and centripetal pulling from chromatin condensation could link mechanically chromosome condensation and nuclear- envelope breakdown, the two main nuclear processes during mitosis. Significance Statement The nucleus was recently shown to exhibit shape fluctuations that vary with cell-cycle stage, but we know very little about the possible links between nuclear mechanics and cell cycle- progression. Through flickering analysis, this study monitors radius and nuclear envelope fluctuations across the cell cycle. The authors discover that as the cell cycle progresses towards mitosis, localised inward invaginations of the nuclear shape form initially transiently and gradually increasing their amplitude, in association with chromatin condensation. This phenomenon develops into nuclear envelope breakdown, suggesting a novel link between cell cycle, chromatin mechanics and nuclear shape fluctuations.


Significance Statement
The nucleus was recently shown to exhibit shape fluctuations that vary with cell-cycle stage, but we know very little about the possible links between nuclear mechanics and cell cycleprogression. Through flickering analysis, this study monitors radius and nuclear envelope fluctuations across the cell cycle. The authors discover that as the cell cycle progresses towards mitosis, localised inward invaginations of the nuclear shape form initially transiently and gradually increasing their amplitude, in association with chromatin condensation. This phenomenon develops into nuclear envelope breakdown, suggesting a novel link between cell cycle, chromatin mechanics and nuclear shape fluctuations.    Fig. S1b). Cells 106 were arrested at the G1/S transition (by a double thymidine 107 block) or at the G2/M transition (by CDK1 inhibition) and 108 then released to follow them through cell cycle progression.

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Cell cycle stage was univocally assigned by monitoring the 110 cells every 3 hours from release (Fig. 1a).

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Although the system is out of equilibrium, if we assume 126 that the active forces play the role of an increased 'effective 127 temperature' then it is possible to use the standard model for 128 fluctuations (15), and extract effective biophysical parameters.

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As anticipated above, it is important to stress that these mea-130 sured effective parameters are not the same as the biophysical 131 ones but a byproduct of constitutive parameters and the action 132 of active forces. We will refer to these as effective tension and 133 bending modulus in the following, and explicitly discuss their 134 interpretation whenever necessary.

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Compared to previous work, we adopted two important  range of modes considered in our analysis, the nuclear fluc-166 tuations are mainly affected by effective tension, as the 167 mean-square amplitude spectrum is dominated by the 1/qx 168 trend (4,22).

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It is instructive to plot nuclear radius versus effective ten-170 sion in the different cell-cycle stages (Fig. 1c). Effective 171 tension initially increases with radius, as would be expected 172 for an "inflated" passive membrane. However, this trend is 173 inverted starting from the G2 phase, so that radius keeps 174 increasing while effective tension is reduced. The physical 175 properties of the lamina may change significantly in this part 176 of the cell cycle due to lamin phosphorilation (25, 26), but an 177 increase in the active forces could also concomitantly drive 178 nuclear shape fluctuations. Hence the decrease in effective 179 tension in late G2 and mitosis could be due to a drop in 180 physical tension, and/or an effect of active forces. Overall, 181 Fig. 1c shows how during the cell cycle the nucleus follows 182 a counterclockwise trajectory in the effective tension-radius 183 plane, which starts at nucleus birth and culminates in NE 184 breakdown at late mitosis. The changes in radius and effective 185 tension across phases of cell cycle are statistically significant 186 ( Fig. 1d-f ), while effective bending rigidity, remains fairly 187 constant. Looking at cells that were imaged over several stages 188 of the cell cycle, we verified which of the average trends of the 189 parameters were robust in single cell trajectories (SI Fig. S2). 190 From our measurements, it is possible to monitor the re-191 laxation time scales of the dominant deformation modes. For 192 a passive membrane, the modes decay exponentially and the 193 relaxation time scale is the ration of the modulus driving the 194 relaxation, and the viscosity. When the modulus is determined 195 from a passive spectrum, e.g. the tension, then this allows to 196 determine the viscosity. However, for an active surface such 197 as this one, the time scales reflect active dynamics, and the 198 decay of the modes can become very complex. We considered 199 the relaxation time τ of mode 3, where we found that no com-200 plex behavior appears and the decay is a simple exponential, 201 (see SI Fig. S3). Fig. 1g displays longer relaxation time for 202 late mitosis. This can be interpreted as a signature of active 203 fluctuations/deformations from active nuclear or cytoplasmic 204 pulling or pushing elements, visible in the movies during mi-205 tosis, which could trigger different characteristic times (due 206 to the dynamics of the active elements) than those of passive 207 relaxation.

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Red blood cell (RBC) fluctuations have been extensively 209 studied, representing a simpler well-understood system, yet 210 with some common biophysical properties in common with 211 cell nuclei (e.g., being supported by cytoskeletal elements). 212 Hence, we decided that it could be instructive to use them as 213 a reference, and we compared the behavior of HeLa cell nuclei 214 with those of RBC (grey bands in Fig. 1). HeLa nuclei have 215 in general larger dimensions, a longer relaxation time, and 216 smaller effective bending modulus, but their effective tension 217 is similar to RBC if we exclude the dramatic changes occurring 218 for nuclei at mitosis (3,4). The mean and SEM of nuclear 219 biophysical properties from HeLa cells at different stages of 220 the cell cycle are reported in SI Table S1, and p values in 221  Table S2.  mechanically driven by condensing chromatin and cytoskeletal 288 remodelling, therefore mechanical or biochemical signalling 289 triggered at chromatin condensation might be sufficient to 290 generate the nuclear shape remodeling observed before NE 291 breakdown. To address the possible concern that calyculin 292 may affect lamin phosphorilation -which is a signaling part 293 of nuclear envelope breakdown, we performed a Western blot 294 analysis of phospho-Lamin staining in calyculin A treated cells 295 (SI Fig. S4), finding no visible change.

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Since calyculin A activates myosin-2 mediated contractil-297 ity (29), we checked whether the increased centripetal invagi-298 nations observed upon treatment with this drug could be a 299 byproduct of increased actomyosin contractility. As a control, 300 we performed a double chemical perturbation with calyculin 301 A and blebbistatin (a myosin inhibitor). Nuclear fluctua-302 tions, as well as their radius and effective tension, replicate 303 the nuclear features after treatment with calyculin A. Treat-304 ment with blebbistatin alone did not affect the dominance of 305  (Fig. 2c) (Fig. 3c). Invagination width at the between the profile and a reference profile calculated as the 361 average shape of ten frames before the invagination developed 362 (Fig. 3d,e). Inward invaginations (< -0.5µ, orange band in are wider for cell mitosis (grey histogram in Fig. 3d) and 367 post-calyculin A treatment (cyan), with respect to interphase 368 (G1 and pre-treatment respectively black and red histograms). 369 Polar plots represent the total number of frames of inward 370 and outward fluctuations at every angle.

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To quantify the behavior of inwards vs outwards defor-372 mations, Fig. 2e uses the skewness of their distribution as 373 summary statistics. A negative skewness corresponds to an 374 enrichment in inward deformations. The results confirm that 375 inward deformations increase in early and late mitosis, as well 376 as upon calyculin A treatment, while it is unaffected by la-377 trunculin A. Incidentally, we noticed that the typical shape of 378 inward deformations fits well the theoretical shape of a mem-379  (SI Fig. S7). 396 Subsequently, we quantified the cross-correlation between  Fig. S10 and SI Video 9 report kymographs that sum-444 marize all our main results visually. Our results confirm the 445 scenario proposed by Chu and coworkers (15), whereby nuclear 446 shape fluctuations are driven by a combination of thermal mo-447 tion and forces from chromatin and cytoskeleton. Fully in line 448 with this study, we find that latrunculin A (actin depolymeriza-449 tion) increases shape fluctuations (decreasing effective tension), 450 and decreases nuclear radius, while blebbistatin (Myosin-II 451 inhibition) increases nuclear radius and effective tension. This 452 data suggests that the dynamic flickering of nuclear envelope 453 might be countered by the presence of actin stress fibers (which 454 are lost with latrunculin A), possibly via LINC connections, 455 while the dynamic rearrangement of stress fibers caused by 456 loss of myosin contractility has a more complex "stiffening" 457 effect, which also (surprisingly) leads to radius increase. In 458 addition to this, Chu et al. reported that nuclear processes, 459 including transcription and nuclear transport, also influence 460 nuclear shape fluctuations ( Table 1). Combining the two 461 observations, we confirm the picture of a NE that is a dynamic 462 component rather than a static organelle, which responds 463 to cellular and nuclear events. However, when considering 464 cell-cycle changes, Chu et al. only reported a decrease in 465 amplitude of symmetric fluctuations, with the progress of in-466 terphase (G1-S-G2). They interpreted this as a change of 467 material properties and/or a reduction of the forces driving 468 the shape fluctuations. While our observations are compatible 469 with this study, we focused on deformations occurring during 470 G2 phase and onset of mitosis, using different perturbations, 471 which lead us to surprising results.

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Specifically, after the genome has completed replication, we 473 find evidence supporting active pinning centripetal forces that 474 drive increasingly strong shape fluctuations (also resulting in 475 a drop in effective tension) from G2 to mitosis, up until NE 476 breakdown. Hence, (i) shape fluctuations can dramatically 477 increase from G2 to mitosis, and (ii) they can become highly 478 non-symmetric at this stage. Fluctuation asymmetry favoring 479 in-wards displacements appears already in G2, together with 480 reversible "pinning" centripetal deformations. These defor-481 mations become increasingly long lasting and irreversible as 482 the cell cycle progresses towards NE breakdown. Interestingly, 483 neither latrunculin A nor blebbistatin / Y27632 treatments 484 affect the asymmetry of the shape fluctuations, while calyculin 485 A treatment makes them centripetal. These observations sug-486 gest that chromatin dynamics can be related to NE centripetal 487 shape fluctuations.

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Our data also allow us to formulate some hypotheses on 489 the force balance between the physical processes that regulate 490 nuclear mechanics. Physically, nuclear shape is set by three 491 mechanical components: chromatin, lamins, and the cytoskele-492 ton. Chromatin and lamin A are typically seen as resistive 493 elements that together maintain nuclear shape. Lamins alone, 494 on the contrary, cannot maintain nuclear shape, and the lam-495 ina buckles under mechanical stress when it is unsupported 496 by chromatin, suggesting a physical model of the nucleus as a 497 polymeric shell enclosing a stiffer chromatin gel (14). The role 498 of the cytoskeleton is less clear, and sometimes it is pictured 499 Legend: T = thermally driven and A = active. Data from Fig. 1 and 2 localised stress from inner chromatin, affecting its shape fluc-541 tuations. Isotropic contributions to these stresses also likely 542 come from forces of osmotic origin (39, 40).

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The phenomena observed here could play a role in the 544 coordination of chromatin condensation and NE breakdown 545 during mitosis. It seems natural to think that the timing of 546 these two events should be coordinated -just like NE reassem-547 bly should be coordinated with chromosome segregation (10). 548 Since the NE is squeezed between the cell cytoskeleton on the 549 cytoplasmic side and chromatin on the nucleoplasmic side, and 550 both of these active systems undergo major rearrangements 551 over the cell cycle, it is possible that the cell-cycle dependent 552 flickering may be not only a byproduct but also a driver of 553 cell-cycle progression. Since chromatin pulling events deform-554 ing the nucleus develop into widespread invaginations that 555 eventually culminate into NE breakdown, we speculate that 556 the intensity of the opposed forces on the NE increases dur-557 ing G2 and mitosis, and may be a driver of NE breakdown. 558 This could happen in several ways. The centripetal pulling 559 by chromatin could mechanically rupture the membrane and 560 lamin nuclear surfaces through the exerted forces, or it could 561 trigger mechanosensitive signaling cascades, as in the case of 562 the cPLA protein (19), leading to downstream events related 563 to different aspects of mitosis progression. Chemically, NE 564 breakdown is known to be triggered by maturation-promoting 565 factor (MPF), which moves into the nucleus and phospho-566 rylates several targets (41, 42), prominently causing lamin 567 depolymerization (25, 26, 43). The opening of the nuclear 568 membrane is less well understood. Work in starfish indicates 569 that it is initiated by loss of the exclusion barrier of nuclear 570 pore complexes, followed by NE fenestration (11, 44). Re-571 cently, a mechanical action from the actin cytoskeleton has 572 been implicated in these processes (45). Studies applying ex-573 ternal transient tensile stress on the nuclear membrane suggest 574 that the force range causing the typical NE deformations are 575 sufficient to trigger nuclear membrane rupture (46).

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Chromatin, through its structure and mechanics, is a key 577 factor of nuclear function. Our results highlight that combined 578 mechanical and/or mechano-chemical cues from condensing 579 chromatin and cytoskeleton could also contribute to the timing 580 and the synchronization of NE disruption with chromosome 581 D R A F T condensation during mitosis.