Schmidt Frédéric

Costard François

Bouley Sylvain

Séjourné Antoine

Aleinov Igor

Circumpolar Ocean stability on Mars 3 Gy ago

This manuscript was compiled on [START_REF] Bk Lucchitta | Antarctic ice streams and outflow channels on mars[END_REF] What was the nature of the Late Hesperian climate? Warm and wet or cold and dry? Formulated this way the question leads to an apparent paradox since both options seem implausible. A warm and wet climate would have produced extensive fluvial erosion but few valley networks have been observed at the age of late Hesperian. A cold and dry climate would have kept any northern ocean frozen most of the time. But this would prevent tsunami formation, for which there is some evidence. Here, we provide new insights from numerical climate simulations in agreement with surface geological features to demonstrate that the Martian climate could have been both cold and wet. Using an advanced General Circulation Model (GCM), we demonstrate that an ocean can be stable, even if the Martian mean surface temperature is lower than 0 • C. Rainfall is moderate near the shorelines and in the ocean. The southern plateau is mostly covered by ice with a mean temperature below 0 • C. This climate is achieved with a 1 bar CO 2 dominated atmosphere with 10% H 2 . Under this scenario 3 Ga, the geologic evidence of a shoreline and tsunami deposits along the ocean/land dichotomy are compatible with ice sheets and glacial valleys in the southern highlands. T he possibility of a late Martian ocean is a topic of debate with strong implications on the habitability of the Red Planet [START_REF] Vr | Ancient oceans, ice sheets and the hydrological cycle on mars[END_REF]. A review of this controversy has been proposed recently [START_REF] Zi Dickeson | Martian oceans[END_REF]. There is evidence of Martian paleo-shorelines [START_REF] Parker | Coastal geomorphology 359 of the martian northern plains[END_REF] in Deuteronilus Mensae (sometimes noted contact [START_REF] Zi Dickeson | Martian oceans[END_REF] in a geometry close to the current equipotential height [START_REF] Head | Possible ancient oceans on mars: Evidence from mars orbiter laser altimeter 361 data[END_REF].

The Deuteronilus shoreline seems to be formed during the last stage of the true polar wander induced by Tharsis [START_REF] Ri Citron | Timing of oceans on mars from shoreline deformation[END_REF]. A northern ocean is also supported by specific radar properties [START_REF] Mouginot | Dielectric map of the martian northern hemisphere and the nature of plain filling materials[END_REF], smooth surface roughness [START_REF] Ma Kreslavsky | Kilometer-scale roughness of Mars: Results from MOLA data analysis[END_REF] and by a fractal analysis of the topography [START_REF] Saberi | Evidence for an ancient sea level on mars[END_REF]. Crater counting datation of the Vastitas Borealis Formation near Deuteronilus Mensae is 3.5 Ga (9) but the ocean can be more recent. Detailed studies in Kasei Valles imply that such an ocean rose in elevation (∼ 1000 m) between ca. 3.6 Ga and 3.2 Ga [START_REF] Duran | The kasei valles, mars: a unified record of episodic channel flows and ancient ocean levels[END_REF]. Along this shoreline, tsunami deposits have been identified at an age of 3 Ga [START_REF] Rodriguez | Tsunami waves extensively resurfaced the shorelines of an early martian ocean[END_REF][START_REF] Costard | Modeling tsunami propagation and the emplacement of thumbprint terrain in an early mars ocean[END_REF] with at least two impact events. The Lomonosov crater morphology is coherent with an impact in shallow water, at the very same age of the tsunami deposits [START_REF] Costard | The lomonosov crater impact event: A possible mega-tsunami source on mars[END_REF] and is thus the most probable source.

The stability of an ocean in a warm and wet scenario, even transient, at 3 Ga has been questioned since intense and widespread rainfall in such a scenario is not consistent with few observed dendritic valley networks from this time [START_REF] Rd Wordsworth | The climate of early mars[END_REF][START_REF] Turbet | The paradoxes of the late hesperian mars ocean[END_REF].

In previous work, a cold and wet Mars seemed impossible since the long term stability of an ocean (open or ice covered) in such a scenario has never been achieved by a 3D-GCM [START_REF] Rd Wordsworth | The climate of early mars[END_REF][START_REF] Turbet | The paradoxes of the late hesperian mars ocean[END_REF][START_REF] Forget | 3d modelling of the early martian climate under a denser CO 2 atmosphere: Temperatures and CO 2 ice clouds[END_REF][START_REF] Wordsworth | Global modelling of the early martian climate under a denser CO 2 atmosphere: Water cycle and ice evolution[END_REF][START_REF] Turbet | 3D modelling of the climatic impact of outflow channel formation events on early mars[END_REF][START_REF] Es Kite | Warm early mars surface enabled by highaltitude water ice clouds[END_REF]. Nevertheless, liquid brines are possible in this case but only with significant anti-freezing properties [START_REF] Ag Fairén | A cold and wet mars[END_REF].

Cool and wet scenarios in the case of a faint young sun (in 30 the Noachian-Hesperian boundary at 3.6 Ga) demonstrated 31 that the ocean freezes for pressure below 1 bar and still predict 32 intense rainfall when average temperature is higher than 0 [START_REF] Schmidt | Configuration and assessment of the giss modele2 contributions to the cmip5 archive[END_REF]. R3D allows us to estimate the inter-41 action between atmosphere/ocean circulation but also encom-42 passes a surface hydrological scheme. We assume the solar 43 luminosity to be ∼ 79% (25) of its current value (1360.67 ancient Mars, but R3D is capable of a range of salinities [START_REF] Del Genio | Habitable climate scenarios for proxima centauri b with as dynamic ocean[END_REF]. [START_REF] Sm Clifford | The evolution of the martian hydrosphere: Implications for the fate of a primordial ocean and the current state of the northern plains[END_REF] In addition, the glacier mass must be added but the thickness 57 of glacier cannot be constraint by our model. In any case, the 58 water budget must be compatible with D/H measurements 59 that implies 100-300 m GEL in the Hesperian [START_REF] Pr Mahaffy | The imprint of atmospheric evolution in the d/h of hesperian clay minerals on mars[END_REF][START_REF] El Scheller | Long-term drying of mars by sequestration of ocean-scale volumes of water in the crust[END_REF]. [START_REF] Turbet | The paradoxes of the late hesperian mars ocean[END_REF][START_REF] Es Kite | Geologic constraints on early mars climate[END_REF]. For 20% H2 in a CO2 dominated atmosphere the 63

Significance Statement

The current Martian climate is not habitable and far from Earth's climate. At the same time that Life spread on Earth (3 Gy ago), the Red Planet was possibly more similar to our Blue Planet. Our model includes a coupled model with dynamic ocean and atmosphere including a hydrological cycle. We show that an ocean is stable in agreement with some geological records.

Please provide details of author contributions here.

Please declare any competing interests here.

D R A F T

greenhouse effect is efficient enough to warm the entire planet, as expected [START_REF] Kamada | A coupled atmosphere-hydrosphere global climate model of early mars: A 'cool and wet' scenario for the formation of water channels[END_REF]. The average surface temperature is always greater than 10 • C with a stable ocean (Northern ocean and Hellas basin sea) and intense rainfall, corresponding to the warm and wet scenario [START_REF] Rd Wordsworth | Comparison of "warm and wet" and "cold and icy" scenarios for early mars in a 3-d climate model[END_REF]. For 10% H2 the globally averaged surface temperature is below 0 • C but the Northern ocean surface temperature remains surprisingly around 6 • C and is thus stable from freezing. The source of H2 may be volcanic or serpentinization, but such large concentration is not expected for more than My [START_REF] Ramirez | Warming early mars with CO 2 and H 2[END_REF][START_REF] Batalha | Testing the early mars H 2 -CO 2 greenhouse hypothesis with a 1-d photochemical model[END_REF][START_REF] Wordsworth | Transient reducing greenhouse warming on early mars[END_REF]. The lower limit of H2 necessary to stabilize the ocean will be matter of a future investigation. Mat.). The major effect of water, ice and snow dependence on incidence angles are included (See Materials and Methods).

The relatively modest effect of obliquity is due to the 1 bar atmospheric engine that redistribute more efficiently the heat than at present-day 6 mbar.

Despite an average temperature below 0 • C, the ocean remains above freezing due to its circulation, low altitude and low albedo. The effect of circulation is a regional warming in the Northern region of 2.5 • C (see Sup Mat. Figure 10). The altitude of the boundary varies from -700 to -3000 meters for obliquity from 0 • to 60 • .

In the high altitude domain, commonly referred to as the "icy highlands", the surface is mostly frozen and snow precipitation is dominant. The extensive accumulation of snow in the highlands can lead to the formation of significant ice sheets that may flow down to the Northern ocean and Hellas basin ocean. Our current model is not able to simulate details regarding the glacier flow, but only a global mass flux from land to the ocean. Glacial processes such as accumulation (snow compaction), flow (path, erosion), and ablation (direct melting, fluvio-glacial river) are thus not included. Nevertheless, the global mass flux (see Materials and Methods) is estimated around 3 × 10 15 kg.y -1 and seems to be very robust to obliquity changes and H2 content. For comparison, this flux is currently 1 to 5 × 10 14 kg.y -1 on the Earth [START_REF] Radić | Glaciers in the earth's hydrological cycle: Assessments of glacier mass and runoff changes on global and regional scales[END_REF]. Given the relative sizes of the planetary bodies, our value is relatively high.

In the lowest altitude domain, called the "wet lowlands", rain, evaporation and surface runoff are in a cycle with the ocean. Wet lowlands represent a minor surface fraction (22% at 40 • obliquity) of the planet for H2=10% (see Fig. 3).

The rain occurs mainly over the ocean (65% of the total rain), and the ocean evaporation is 60% compensated by rain.

The snow precipitation over icy highlands is intense but 80% compensated by high sublimation rates. Our climate model differs from the "icy highlands model" [START_REF] Wordsworth | Global modelling of the early martian climate under a denser CO 2 atmosphere: Water cycle and ice evolution[END_REF] since the ocean is stable.

125

From these results, one can describe a cold and wet climatic 126 regime (see Fig. 3 bottom) with significant glacier return flow 127 from cold highlands back to the ocean and moderate surface 128 runoff near the shoreline.

129

Comparison to geological evidence 130

The proposed scenario is in agreement with a long term sta-131 bility of the ocean, with the paleo-shoreline and tsunami 132 deposits. In addition, this climatic regime is in agreement 133 with independent geological evidence concerning fluvial and 134 glacial processes. Figure 3 plots the major geological features 135 of similar late Hesperian/early Amazonian age.

136

Contrary to the Noachian epoch, the modest appearance 137 and development of dendritic valleys (rainfall related) during 138 the late Hesperian/early Amazonian has been tied to major 139 changes in climate. Several valleys at 2.9 Ga have been identi-140 fied in the North of Alba Patera with a substantial temporal 141 peak in the drainage density [START_REF] Bm Hynek | Updated global map of martian valley networks and implications for climate and hydrologic processes[END_REF], located in the dichotomy 142 boundary, in agreement with large rainfall predicted by our 143 model (see Fig. 1). In addition a relatively high density net-144 work has been located in the South of Hellas basin [START_REF] Bernhardt | Photogeologic mapping and the geologic history of the hellas basin floor[END_REF]. Along 145 the highland/lowland boundary (northwestern Arabia Terra 146 and in Deuteronilus Mensae regions) some aligned channels 147 are observed displaying streamlined islands of Hesperian age 148 of possible marine [START_REF] Rodriguez | Tsunami waves extensively resurfaced the shorelines of an early martian ocean[END_REF] or fluvial origin [START_REF] Kl Tanaka | Geologic map of Mars[END_REF]. The wet lowlands 149 have been significantly covered by more recent Amazonian 150 processes (including volcanic resurfacing) [START_REF] Kl Tanaka | Geologic map of Mars[END_REF], erasing most 151 of the geological features of this age available at the surface.

152

Global extensive ice sheets have been proposed in the South-153 ern hemisphere. Some deposits in the region of Malea Planum 154 (Pityusa Patera) are possible remnants of an extensive polar 155 ice sheet emplaced during the Hesperian period [START_REF] Head | Extensive hesperian-aged south polar ice sheet on mars: Evidence for massive melting and retreat, and lateral flow and ponding of meltwater[END_REF][START_REF] Gj Leonard | Geologic Map of the Hellas Region of Mars[END_REF]. In 156 addition, a 3 Ga old polythermal ice sheet should had covered 157 the entire basin of Isidis Planitia with a maximum thickness 158 of 4.9 km [START_REF] Souček | A 3 ga old polythermal ice sheet in isidis planitia, mars: Dynamics and thermal regime inferred from numerical modeling[END_REF][START_REF] Guidat | Landform assemblage in isidis planitia, mars: Evidence for a 3 ga old polythermal ice sheet[END_REF]. Since this basin is right nearby the 0 • C 159 isotherm, a glacier could have flowed from the accumulation 160 zone in the highlands down to the ablation zone in Isidis, as 161 mapped by Jöns [START_REF] Hp Jöns | Large Fossil Mud Lakes or Giant Mud Sheet Floods in Syrtis Major (Isidis Planitia) and Mare Australe[END_REF].

162

Reull Vallis is a 1500 km long U-shaped valley post-dating 163 the Hesperian ridged plains with a long and complex history 164 [START_REF] Sc Mest | Geology of the reull vallis region[END_REF]. It has been carved by glacial flow along the channel 165 during a younger resurfacing episode of late Hesperian-early 166 Amazonian age [START_REF] Vp Kostama | Topographic and morphologic characteristics of reull vallis, mars: Implications for the history of the reull vallis fluvial system[END_REF]. With a length of ∼ 3000 km, ∼ 500 167 km width, and a depth of ∼ 3 km, Kasei Valles is the largest 168 outflow channel on Mars. Flooding activity occurred mostly 169 at the Hesperian between 3.6 and 3.8 Ga, with continuing 170 activity possible to 2.5 ± 1 Ga. [START_REF] Andrews-Hanna | Hydrological modeling of outflow channels and chaos regions on mars[END_REF]. The morphology of 171 Kasei Valles region is consistent with an origin by ice with 172 a striking analogy to Alaskan glaciers [START_REF] Bk Lucchitta | Ice sculpture in the martian outflow channels[END_REF] and Antarctic ice 173 streams [START_REF] Bk Lucchitta | Antarctic ice streams and outflow channels on mars[END_REF]. A glacial interpretation of the Kasei Valles 174 outflow was also proposed to explain the presence of scour 175 features, tunnel valleys and esker forms [START_REF] Arfstrom | Equatorial ice sheets of mars[END_REF]. Ares Vallis is a 176 1500 km long Hesperian outflow channel displaying multiple 177 catastrophic flooding events. Its floor shows geomorphological 178 evidence of ice-covered flooding [START_REF] Wallace | Evaporation of ice in planetary atmospheres: Ice-covered rivers on mars[END_REF] and glacial erosion [START_REF] Pacifici | Geological evolution of ares vallis on mars: Formation by multiple events of catastrophic flooding, glacial and periglacial processes[END_REF] 179 with subsequent thermokarst degradation [START_REF] Costard | Thermokarst landforms and processes in ares vallis[END_REF]. The presence 180 of thermokarst lakes formed after flooding [START_REF] Costard | Thermokarst landforms and processes in ares vallis[END_REF][START_REF] Warner | Hesperian equatorial thermokarst lakes in ares vallis as evidence for transient warm conditions on mars[END_REF] supports a 181 hypothesis of the thawing of ground ice during the Hesperian 182 (i.e., 3.6-3.0 Ga). In addition, evidence of past glaciations (be-183 tween 1.4 Ga to 3.5 Ga) was reported within Valles Marineris. 184 Morphological evidence shows that extensive subglacial erosion of the lower parts of Valles Marineris wallslopes, together with sackung deformations by deglaciation of the upper wallslopes occurred [START_REF] Mège | Equatorial glaciations on mars revealed by gravitational collapse of valles marineris wallslopes[END_REF][START_REF] Gourronc | One million cubic kilometers of fossil ice in valles marineris: Relicts of a 3.5gy old glacial landsystem along the martian equator[END_REF]. Finally, one has to note that the extensive outflow channels are contemporaneous to the ocean. An ocean at the Hesperian is also compatible with the timing of peak outflow channel activities [START_REF] Sm Clifford | The evolution of the martian hydrosphere: Implications for the fate of a primordial ocean and the current state of the northern plains[END_REF][START_REF] Warner | A refined chronology of catastrophic outflow events in ares vallis, mars[END_REF]. Outflows probably formed by aquifer disruption [START_REF] Carr | Formation of martian flood features by release of water from confined aquifers[END_REF] or glacial erosion [START_REF] Bk Lucchitta | Ice sculpture in the martian outflow channels[END_REF][START_REF] Pacifici | Geological evolution of ares vallis on mars: Formation by multiple events of catastrophic flooding, glacial and periglacial processes[END_REF]. More abundant signs of glaciation in the icy highlands may have been prevented by less erosive cold-based glaciers ( 59) and by post-dating Amazonian processes, such as volcanic events [START_REF] Kl Tanaka | Geologic map of Mars[END_REF].

D R A F T

One also has to remind the arguments that must face the stable ocean scenario. First, the interpretation and location of the paleoshoreline itself is matter of controversy [START_REF] Mh Carr | Oceans on Mars: An assessment of the observational evidence and possible fate[END_REF][START_REF] Sf Sholes | Quantitative high-resolution reexamination of a hypothesized ocean shoreline in cydonia mensae on mars[END_REF]. Some studies claimed that the putative shorelines are mutually inconsistent (62) but it mainly concerns Contact 1 (Arabia potential shoreline), not Contact 2 (younger Deuteronilus shoreline) that we actually using in our study. Second, mineralogical data seems inconsistent with an Late Hesparian ocean [START_REF] Jp Bibring | Global mineralogical and aqueous mars history derived from omega/mars express data[END_REF][START_REF] Carter | Hydrous minerals on mars as seen by the crism and omega imaging spectrometers: Updated global view[END_REF]. In particular, mineralogy from impact crater excavated terrains [START_REF] Pan | The stratigraphy and history of mars' northern lowlands through mineralogy of impact craters: A comprehensive survey[END_REF] and clays occurence in central peaks [START_REF] Vz Sun | Ancient and recent clay formation on mars as revealed from a global survey of hydrous minerals in crater central peaks[END_REF] are more consistent with a volcanic origin. But a widespread sedimentary rock has been identified in the Northern plains of Mars [START_REF] Mr Salvatore | Evidence for widespread aqueous sedimentation in the northern plains of mars[END_REF]. Last, there is a lack of observed carbonates at the surface, that imply that the ocean was acidic. But acidic ocean seems unfavorable in presence of mafic rocks [START_REF] Pb Niles | Geochemistry of carbonates on mars: Implications for climate history and nature of aqueous environments[END_REF]. Scenarios alternative to ocean have been proposed implying lava flows [START_REF] Head | Northern lowlands of mars: Evidence for widespread volcanic flooding and tectonic deformation in the hesperian period[END_REF] or ice-related processes [START_REF] Sm Clifford | The evolution of the martian hydrosphere: Implications for the fate of a primordial ocean and the current state of the northern plains[END_REF][START_REF] Bk Lucchitta | Mars and earth: Comparison of cold-climate features[END_REF]. In addition, crater's ejecta has been proposed as an alternative to tsunami deposits for form the thumbprint terrains [START_REF] Es Kite | Geologic constraints on early mars climate[END_REF].

Our results demonstrate that a cold and wet climate could have been stable and coherent with geomorphologic evidence. Using fully coupled atmosphere / dynamic ocean modeling, we show that the ocean's circulation warm regionally the surface by 2.5 • C. In these conditions, ocean is stable even for a global mean planetary temperature below 0 • C. This Martian climate is similar to the one on the Earth with an active water cycle at the same age of the early stage of Life's appearance. Future work should encompass careful analysis of this stability domain H 2 provides a powerful greenhouse component in combination with CO 2 as a background gas, but other gas combinations involving CH 4 or H 2 S may have an equivalent radiative effect even if the motivation for their use is lacking. Recent measurements of collision induced absorption of CO 1 and CH 4 shows that this possibility is not favored [START_REF] Turbet | Measurements and semi-empirical calculations of CO 2 + CH 4 and CO 2 +H 2 collision-induced absorption across a wide range of wavelengths and temperatures. application for the prediction of early mars surface temperature[END_REF]. We run simulations with 10% and 20% H 2 in a CO 2 dominated atmosphere at 1 bar surface pressure to simulate the climate at 3 Ga, as in [START_REF] Turbet | The paradoxes of the late hesperian mars ocean[END_REF]. We run simulations with 0 • , 20 Short description about cloud modeling (radiatively active/passive, H2O, CO2 ?, precipitation, snow/ice fraction)

The surface radiative properties are described in [START_REF] Schmidt | Present-day atmospheric simulations using GISS ModelE: Comparison to in situ, satellite, and reanalysis data[END_REF]. The spectral and solar zenith angle dependence of ocean albedo is based on calculations of Fresnel reflection from wave surface distributions as a function of wind velocity [START_REF] Cox | Slopes of the sea surface deduced from photographs of sun glitter[END_REF]. The effects of foam on ocean albedo are also included [START_REF] Hr Gordon | Albedo of the ocean-atmosphere system: influence of sea foam[END_REF]. In addition, ROCKE-3D also includes the dependance of the cosine of the zenith angle for snow both on the ocean ice and on the land [START_REF] Wj Wiscombe | A model for the spectral albedo of snow. i: Pure snow[END_REF].

OGCM. The ocean model assumes Earth's values of salinity (35 PSU) and included XXX processes (sea ice, salinity change due to fresh water incorporation by surface runoff, precipitation and sea ice). The spatial resolution is XXX vertical and XXX vertical. The time step is XXX. Initialization as liquid.

Topography is assumed to be identical to present time (except the cap that are removed). According to topography analysis, the Late Hesperian stage of the paleoshoreline is coherent with current altitude, i.e.: without correction of the True Polar Wander due to Tharsis [START_REF] Head | Possible ancient oceans on mars: Evidence from mars orbiter laser altimeter 361 data[END_REF][START_REF] Ri Citron | Timing of oceans on mars from shoreline deformation[END_REF][START_REF] Jt Perron | Evidence for an ancient martian ocean in the topography of deformed shorelines[END_REF][START_REF] Bouley | Late tharsis formation and implications for early mars[END_REF]. The ocean shoreline is set to -3900 meters in all runs. This gives an ocean surface fraction of ∼16% which is small in comparison to Earth at ∼ 71%. The ocean is also shallower

Mars|

  Paleoclimate | Dynamic ocean | Ice sheet

44 W 45 W.m - 2 .

 44452 .m -2 ), hence at 3 Ga, the flux at Mars was set to 452.[START_REF] Saberi | Evidence for an ancient sea level on mars[END_REF] The total water budget is 150 m GEL to fill the ocean 46 basin in the north and Hellas. The ocean model has 13 layers 47 to a hypothetical depth of 4647m. The ocean bathymetry 48 is determined by the topography. In Hellas basin the ocean 49 depth reaches 3194m (level 12 of 13) while in the northern 50 ocean it is 1294m (level 10 of 13). A detailed description of 51 the ocean is documented in (23). The sea ice is interactive and 52 is determined by the salinity and corresponding freezing point 53 of water and is again documented in (23). The salinity was set 54 to modern Earth ocean values given the lack of constraints for 55

60 Four sets of numerical simulations were performed for 61 0 • , 20

 606120

Figure 1

 1 Figure 1 shows the simulated surface fields averaged over 10 Martian years for H2=10% and obliquity 40 • . Interestingly this climate changes only slightly with obliquity (See Sup.

Figure 2

 2 Figure 2 top shows the horizontal heat flux contributing to the ocean stabilization. Streamlines show the effect of ocean gyres transporting heat poleward, as expected for fast-rotating planet (34).Figure 2 bottom presents the surface tempera-

Figure 2

 2 bottom presents the surface temperature increase due to the active circulation of the ocean, as a function of latitude. At 0 • obliquity, the increase is 0.5 • C in average on the full planet but up to 2.5 • C in the Northern polar ocean region. At 40 • obliquity, the increase is 2.0 • C in average but up to 2.5 • C in the Northern region. On land, there is a clear boundary at the 0 • C isotherm which corresponds approximately to the Martian dichotomy.

Fig. 1 .ig. 2 .

 12 Fig. 1.3D GCM output at 40 • obliquity and H2=10% for the rain precipitation, snow and ice fraction at the surface, snowfall, sea/ground surface temperature.Black contour lines represent surface elevation level (-2000, 0, 2000 and 8000 meters) and the red contour line is the paleo-shoreline (-3900 meters).

Fig. 3 .

 3 Fig. 3. Proposed scenario of cold and wet climate at the Hesperian age (3 Ga). (top) Map of the climatic zones at 40 • obliquity: ocean, wet lowlands and icy highlands, separated respectively by -3900 m and the 0 • C isotherm (-1990 m). The topography is modern topography without the North Polar Layered Deposits. Geological evidence of past glaciers with possible paths indicating return flow to the oceans are highlighted. Geological evidence of high drainage density valley networks 3 Ga is rare but noted above. (bottom) Simplified scheme of the hydrological cycle using box modeling. Fluxes in parenthesis have units of 10 15 kg.y -1 .

  than the mean depth for Earth. For this reason the time to bring Hydrological cycle. In addition to ocean and atmospheric modeling, 304 the model encompasses a surface scheme to simulate the hydro-305 logical cycle, including a surface runoff scheme. It is challenging 306 to couple glaciers in GCM simulations due to their much longer 307 time-scales (∼10 4-5 years) versus the typical timescales modeled 308 in 3-D GCM simulations (∼10 3 ). In CMIP studies ice sheets are 309 normally calculated off-line and incorporated into GCM simulations 310 at different epochs (85). Here we propose a first order simulation 311 : when snow accumulation reaches 1.9 m H 2 O equivalent (∼ 6.5m snow), the extra-water ice content is instantaneously moved back 313 to the ocean. This strategy has been used to model Earth climate, 314 for instance the last glacial maximum on Earth, 21,000 years ago 315 (86). The threshold at 1.9 meter is artificial but various test have 316 demonstrated that the final results do not depend on this parame-317 ter. This scheme allows one to simulate a static representation of 318 this cold and wet climate. Due to this glacier simulation scheme, 319 the surface ice height is not meaningful. Instead, we focus on the 320 snow/ice fraction inside the grid cell and the mass balance. At the 321 surface temperatures found in our results (> 250K), the ice can 322 easily flow on Mars (87-89) 323 Box modeling. The complex 3D climate system is summarized by 324 box modeling. We divided the surface into 3 zones : icy highlands, 325 wet lowlands and ocean, delimited respectively by the mean altitude 326 of the 0 • C isotherm and -3900 m. For each surface box, but also for 327 the atmosphere and the ocean, we compute the sum of all incoming D R A F T

  • , 40• , 60 • obliquity, with 1 bar atmospheric pressure

	62

F.S. contributed equally to this work with M.J.W.

To whom correspondence should be addressed. E-mail: frederic.schmidt@@universite-parissaclay.fr www.pnas.org/cgi/doi/10.1073/pnas.XXXXXXXXXX PNAS | September 24, 2021 | vol. XXX | no. XX | 1-6

| www.pnas.org/cgi/doi/10.1073/pnas.XXXXXXXXXX Schmidt et al.

Schmidt et al. PNAS | September 24, 2021 | vol. XXX | no. XX | 3

| www.pnas.org/cgi/doi/10.1073/pnas.XXXXXXXXXX Schmidt et al.

| www.pnas.org/cgi/doi/10.1073/pnas.XXXXXXXXXX Schmidt et al.

our ancient Mars model ocean and atmosphere into equilibrium 294 is much shorter (∼ 100s of years) than would be the case for an 295 Earth like ocean (∼ 1000s of years). We assume this equilibrium 296 has been reached when the net radiative balance (the difference 297 between incoming and outgoing fluxes) is less than 0.2 W m -2 .

298

Model runs typically require 300 martian years to reach equilibrium.

299

All outputs are averaged over 10 Martian years, after radiative 300 equilibrium. All quantities are expressed in Earth year, noted "y".

301

When referring about time before present, we used the Earth year


Jing Xie

Javad Najafi

Rémi Le Borgne

Jean-Marc Verbavatz

Catherine Durieu

Jeremy Sallé

Nicolas Minc
email: nicolas.minc@ijm.fr

Contribution of cytoplasm viscoelastic properties to mitotic spindle positioning

Keywords: Cell division, Mitotic spindles, Forces, Cytoplasm, Flows, Rheology

Cells are filled with macromolecules and polymer networks that set scale-dependent viscous and elastic properties to the cytoplasm. Although the role of these parameters in molecular diffusion, reaction kinetics and cellular biochemistry is being increasingly recognized, their contributions to the motion and positioning of larger organelles, such as mitotic spindles for cell division remain unknown. Here, using magnetic tweezers to displace and rotate mitotic spindles in living embryos, we uncovered that the cytoplasm can impart viscoelastic reactive forces that move spindles, or passive objects with similar size, back to their original position. These forces are independent of cytoskeletal force generators, yet reach hundreds of piconewtons and scale with cytoplasm crowding. Spindle motion shears and fluidizes the cytoplasm, dissipating elastic energy and limiting spindle recoils with functional implications for asymmetric and oriented divisions. These findings suggest that bulk cytoplasm material properties may constitute important control elements for the regulation of division positioning and cellular organization.

Significance Statement

The regulation of mitotic spindle positioning is a key process for tissue architecture, embryo development and stem cells. To date, most models have assumed that spindles are positioned by forces exerted by polar cytoskeleton networks, like microtubule asters or acto-myosin bundles. Here, using in situ magnetic tweezers to apply calibrated forces and torques to mitotic spindles in live dividing sea urchin cells, we found that the viscoelastic properties of the cytoplasm medium in which spindles are embedded can hold spindles in place, and move them back if their original position is perturbed. These viscoelastic forces are large and may significantly participate in the force balance that position and orient mitotic spindles in many cell types.

Main Text

Introduction

The cytoplasm is a heterogeneous composite material crowded with large macromolecular complexes, endomembranes, and entangled cytoskeletal networks [START_REF] Luby-Phelps | Probing the structure of cytoplasm[END_REF][START_REF] Mogilner | Intracellular Fluid Mechanics: Coupling Cytoplasmic Flow with Active Cytoskeletal Gel[END_REF]. These set a hierarchy of pore and mesh sizes which define rheological properties, such as viscosity and elasticity, that impact fundamental processes ranging from the kinetics of biochemical reactions to vesicular transport and cell shape control [START_REF] Moeendarbary | The cytoplasm of living cells behaves as a poroelastic material[END_REF][START_REF] Palenzuela | In vitro reconstitution of dynein force exertion in a bulk viscous medium[END_REF][START_REF] Luby-Phelps | Cytoarchitecture and physical properties of cytoplasm: volume, viscosity, diffusion, intracellular surface area[END_REF]. The importance of cytoplasm material properties for cellular physiology has been recognized and studied for decades, starting from early micro-rheology experiments by Crick or Hiramoto [START_REF] Crick | The physical properties of cytoplasm: A study by means of the magnetic particle method Part I[END_REF][START_REF] Hiramoto | Mechanical properties of the protoplasm of the sea urchin egg. II. Fertilized egg[END_REF][START_REF] Hiramoto | Mechanical properties of the protoplasm of the sea urchin egg. I. Unfertilized egg[END_REF]. These showed that injected micrometric beads displaced in the cytoplasm exhibit typical viscoelastic responses, with partial positional feedback that move them back towards their initial position. Thus, the cytoplasm features both solid-like and fluid-like behavior, with bulk elastic moduli on the order of ~1-10 Pa, typical of soft gels and viscosities 100-1000 times that of water. More recent studies have now established that these rheological characteristics exhibit size, force or frequency dependence, and provided more refined descriptions of the cytoplasm using frameworks of non-linear viscoelasticity or poroelasticity [START_REF] Mogilner | Intracellular Fluid Mechanics: Coupling Cytoplasmic Flow with Active Cytoskeletal Gel[END_REF][START_REF] Moeendarbary | The cytoplasm of living cells behaves as a poroelastic material[END_REF][START_REF] Tseng | Micromechanical Mapping of Live Cells by Multiple-Particle-Tracking Microrheology[END_REF][START_REF] Guo | Probing the stochastic, motor-driven properties of the cytoplasm using force spectrum microscopy[END_REF][START_REF] Hu | Size-and speed-dependent mechanical behavior in living mammalian cytoplasm[END_REF]. Object size is of particular relevance, given that components floating in the cytoplasm may range over 4-5 orders of magnitudes. Indeed, cytoplasm rheology has been proposed to transit from that of a Newtonian fluid for small particles to that of a more glassy or elastic solid for larger elements [START_REF] Hu | Size-and speed-dependent mechanical behavior in living mammalian cytoplasm[END_REF][START_REF] Parry | The bacterial cytoplasm has glass-like properties and is fluidized by metabolic activity[END_REF]. To date, however, many studies of bulk cytoplasm properties and their functions have focused on relatively small objects, leaving the fundamental problem of how they impact the motion of large organelles, like nuclei or cytoskeletal assemblies poorly explored.

The mitotic spindle is one such large assembly that resides at a precise location in the cytoplasm to specify cytokinesis, and thus the size and position of daughter cells in tissues [START_REF] Minc | Predicting division plane position and orientation[END_REF][START_REF] Di Pietro | Regulation of mitotic spindle orientation: an integrated view[END_REF]. Spindles are built from dynamic microtubules (MTs) and motors and can take up significant portions of cellular space. They are commonly associated with networks of nuclear intermediate filaments and endomembranes that form a socalled spindle matrix [START_REF] Zheng | A membranous spindle matrix orchestrates cell division[END_REF][START_REF] Schweizer | An organelle-exclusion envelope assists mitosis and underlies distinct molecular crowding in the spindle region[END_REF]. These considerations suggest that their motion in the dense cytoplasm could be associated with large viscous and elastic drags, with potential implications for division positioning and chromosome segregation. Until now however, the literature covering the mechanics of spindle positioning has been dominated by the role of active directed forces from polar cytoskeletal networks [START_REF] Minc | Predicting division plane position and orientation[END_REF][START_REF] Di Pietro | Regulation of mitotic spindle orientation: an integrated view[END_REF][START_REF] Xie | Cytoskeleton Force Exertion in Bulk Cytoplasm[END_REF].

Spindles may for instance decenter or rotate, during asymmetric or oriented divisions, a process typically associated with forces generated by contractile acto-myosin networks [START_REF] Schuh | A new model for asymmetric spindle positioning in mouse oocytes[END_REF][START_REF] Azoury | Spindle positioning in mouse oocytes relies on a dynamic meshwork of actin filaments[END_REF] or astral microtubules (MTs) and associated motors like dynein [START_REF] Grill | The distribution of active force generators controls mitotic spindle position[END_REF]. For symmetric divisions, mitotic spindles reside stably in the cell center. This is thought to be regulated by MTs that grow to contact cell boundaries and exert lengthdependent pushing and/or pulling forces on the spindle: when spindles become off-centered, asymmetries in MT lengths and forces act as an effective spring related to cell shape to re-center spindles [START_REF] Haupt | How cells sense their own shape -mechanisms to probe cell geometry and their implications in cellular organization and function[END_REF][START_REF] Dogterom | Force generation by dynamic microtubules[END_REF][START_REF] Howard | Elastic and damping forces generated by confined arrays of dynamic microtubules[END_REF][START_REF] Tolic-Norrelykke | Push-me-pull-you: how microtubules organize the cell interior[END_REF][START_REF] Howard | Physical Limits on the Precision of Mitotic Spindle Positioning by Microtubule Pushing forces: Mechanics of mitotic spindle positioning[END_REF]. Net forces applied by MT asters or acto-myosin networks may range from few tens to hundreds of piconewtons (pN) [START_REF] Garzon-Coral | A force-generating machinery maintains the spindle at the cell center during mitosis[END_REF][START_REF] Ierushalmi | Centering and symmetry breaking in confined contracting actomyosin networks[END_REF][START_REF] Salle | Asymmetric division through a reduction of microtubule centering forces[END_REF]. A displacement of an impermeable objects with the radius of a spindle of R= 5 µm by a distance d=5 µm, typical of many asymmetric divisions, in a medium with an elastic modulus of G=1 Pa, like the cytoplasm, would generate a reactive force F=6πR*G*d ~500 pN. Thus, viscoelastic properties of the cytoplasm could in principle be highly relevant to the mechanics of spindle positioning. To date, however, the lack of proper assays to probe cytoplasm rheology at the scale of a moving spindle has impaired testing this fundamental problem for cell organization.

Here, by exploiting large sea urchin cells, where mitotic asters are too short to reach the cell surface, we establish and quantify the direct contribution of bulk cytoplasm viscoelasticity to the mechanics of spindle positioning. We use spindles or large passive oil droplets moved and rotated by calibrated magnetic tweezers in intact cells to probe cytoplasm viscosity and elasticity, at time and length scales representative of spindle movements commonly observed in asymmetric or oriented divisions. We find that the stress exerted by the spindle on the cytoplasm causes it to flow and deform, and exert large reactive spring-like forces that move back this large organelle towards its initial position. Cellular-scale flows also shear and rearrange the cytoplasm, dissipating elastic energy and rendering spindle repositioning time-dependent which facilitates rotational over translational spindle motions. Our results place cytoplasm rheology as a hitherto unappreciated element in the force balance that controls the positioning of mitotic spindle and potentially other large organelles.

Results

Viscoelastic forces maintain metaphase spindle position even in the absence of astral MTs contacting the cortex

In many small cells, mitotic spindles are connected to the cell cortex by dynamic MTs which act as dominant force generators to maintain or modulate spindle position [START_REF] Kiyomitsu | Cortical dynein and asymmetric membrane elongation coordinately position the spindle in anaphase[END_REF]. In larger cells, limits in spindle size may prevent bounded metaphase mitotic asters from reaching the cell surface [START_REF] Minc | Influence of cell geometry on division-plane positioning[END_REF][START_REF] Mitchison | Growth, interaction, and positioning of microtubule asters in extremely large vertebrate embryo cells[END_REF][START_REF] Wühr | Evidence for an Upper Limit to Mitotic Spindle Length[END_REF][START_REF] Foe | Stable and dynamic microtubules coordinately shape the myosin activation zone during cytokinetic furrow formation[END_REF][START_REF] Rieckhoff | Spindle Scaling Is Governed by Cell Boundary Regulation of Microtubule Nucleation[END_REF]. Using immunofluorescence and Airy-scan confocal microscopy to detect individual astral MTs around metaphase spindles of 95 µm-sized sea urchin zygotes, we computed a mean distance from astral MTs +tips to the actin-rich cortex of 14.5 +/-9.8 µm (+/-SD), which corresponds to ~15 % of egg size. Out of ~4000 MTs tracked we found a mean of only 3.35 +/-3.4 MTs/cell that came within 5 µm of the egg surface, a distance typically larger than the actin cortex in these eggs (Fig 1A -1B) [START_REF] Spudich | Unfertilized sea urchin eggs contain a discrete cortical shell of actin that is subdivided into two organizational states[END_REF]. These results were confirmed by visualizing MTs in live cells with different probes, as well as with transmission electron microscopy of eggs fixed with optimized methods to reveal MTs (Fig S1A -S1D) [START_REF] Asnes | Cell cleavage. Ultrastructural evidence against equatorial stimulation by aster microtubules[END_REF]. In sharp contrast, and as previously reported, interphase and anaphase/telophase asters spanned the whole cell with a mean of 373 +/-12 and 408 +/-33 MTs/cell reaching a distance less than 5 µm to the surface, respectively (Fig 1C andFig S1E) [START_REF] Minc | Influence of cell geometry on division-plane positioning[END_REF][START_REF] Foe | Stable and dynamic microtubules coordinately shape the myosin activation zone during cytokinetic furrow formation[END_REF]. In spite of lacking MT contact with the cell surface, the spindle appeared largely static at the cell center in both position and orientation, over the typical ~10 min duration of metaphase, or over longer timescales up to 35-40 min when metaphase was prolonged with the proteasome inhibitor MG132 (Movie S1).

Thus, metaphase spindles can robustly maintain their position and orientation for long periods of times, even in the absence of astral MTs contacting the cell cortex.

To directly modulate spindle position and orientation, we implemented in vivo magnetic tweezers to apply forces and torques to spindles in live cells [START_REF] Garzon-Coral | A force-generating machinery maintains the spindle at the cell center during mitosis[END_REF]. We injected a specific type of magnetic beads in unfertilized eggs, and added sperm to trigger fertilization [START_REF] Salle | Asymmetric division through a reduction of microtubule centering forces[END_REF][START_REF] Tanimoto | Physical Forces Determining the Persistency and Centering Precision of Microtubule Asters[END_REF]. These beads exhibit spontaneous centripetal motion along MT asters and form compact aggregates that stay attached to centrosomes through the cell cycle in these cells, allowing to apply magnetic forces on centrosomes by approaching a magnet tip. These beads also form aggregates in vitro, which allows for the calibration of the magnetic force as function of aggregate size and distance to the magnet tip, by tracking beads velocities in test viscous fluids [START_REF] Tanimoto | Physical Forces Determining the Persistency and Centering Precision of Microtubule Asters[END_REF]. The presence of beads at spindle poles did not affect spindle dimensions, and had no notable effect on cell cycle progression (Fig S1F -S1G). In some embryos, beads often split into two aggregates, following centrosome duplication in interphase or early prophase. In others, the beads only tracked one centrosome, allowing a point force application at a single spindle pole (Fig S1H -S1I). Using those, we applied external forces ranging from ~70 to 700 pN along different axis, and monitored resultant spindle motion. Pulling the spindle parallel to its long axis, caused the spindle to translate towards the magnet tip, while a force applied orthogonal to the spindle axis caused both translational and rotational motions that tended to align the spindle along the magnetic force axis (Fig 1D -1E and 1H-1I, Movie S2 and S3). Therefore, these experiments allowed to recapitulate spindle movements typically observed in asymmetric or oriented divisions with calibrated forces and torques in intact cells.

Astral MTs that grow to the cortex, to push or pull on spindles, may act effectively as an active elastic system related to cell shape that brings back a spindle to the cell center if its position is perturbed [START_REF] Haupt | How cells sense their own shape -mechanisms to probe cell geometry and their implications in cellular organization and function[END_REF][START_REF] Howard | Elastic and damping forces generated by confined arrays of dynamic microtubules[END_REF]. In our system, where spindles lack MTs reaching cell boundaries, we anticipated a viscous response to applied forces with no elastic positional feedback. To test this, we collapsed displacement-time curves from individual spindle pulls under different force magnitudes, by rescaling spindle displacement by force [START_REF] Garzon-Coral | A force-generating machinery maintains the spindle at the cell center during mitosis[END_REF]. This rescaling also allowed to compensate for small variations (~10-20%) in external forces during each pull. Strikingly, these rescaled displacement-time curves of spindles moved parallel or orthogonal to their long axis, exhibited a typical viscoelastic response: spindle motion was first linear at short time-scales below 10-30s, following a viscous regime, with an initial speed proportional to the applied force, but then slowed down, yielding an inflection in the displacement-time curve indicative of internal elastic forces that push or pull back the spindle to oppose external forces (Fig 1F , 1J andS1J). Accordingly, larger forces yielded larger displacements at a fixed time point in the inflecting regime, and when the force was released, the spindle recoiled back (Fig 1G,1K and Fig S1K). We also noted that at longer time scales above ~100-200 s the curve tended to converge onto another linear regime. In addition, recoils were only partial, with spindles recovering ~ 40-60 % of their initial displacements, often yielding a small asymmetry in division plane positioning (Fig 1G and1K). These behaviors reflect significant dissipations in the stored elastic energy.

Rotational dynamics of spindles submitted to magnetic torques also exhibited a viscoelastic response, but elastic recoils appeared less pronounced than in translation, causing spindles to tilt and mostly maintain their final orientation at the time of force release (Fig 1L and1M). Importantly, similar responses were obtained in cells arrested in metaphase with MG132, ruling out putative contributions of aster regrowth and initial cortex contact in late metaphase. Spindle pulling assays were also limited to a small enough displacement that ensured that mitotic asters did not contact the cortex, and spindle re-centering did not exhibit any correlation with the final distance to the cortex (Fig 1F -1G, 1J-1M and Fig S1L). Thus, although these data cannot firmly reject a minor role of MTs contacting the cortex, they suggest that most of this viscoelastic response may be attributed to elements in the cytoplasm. Together these results suggest the existence of viscoelastic restoring forces that maintain spindle positon and orientation, even in the absence of MTs reaching the cell cortex.

Spindle repositioning is caused by viscoelastic restoring forces from bulk cytoplasm material.

To understand the origin of these viscoelastic restoring forces, we tested the role of MTs as prominent forcegenerators for spindle positioning. We displaced spindles with magnetic tweezers, and rapidly rinsed cells To more directly establish that viscoelastic repositioning forces are independent of spindle associated cytoskeletal elements, we sought to recapitulate early micro-rheology assays performed by Crick or Hiramoto [START_REF] Crick | The physical properties of cytoplasm: A study by means of the magnetic particle method Part I[END_REF][START_REF] Hiramoto | Mechanical properties of the protoplasm of the sea urchin egg. II. Fertilized egg[END_REF][START_REF] Hiramoto | Mechanical properties of the protoplasm of the sea urchin egg. I. Unfertilized egg[END_REF], but using objects that have similar sizes as mitotic spindles. Inspired by recent experiments performed in mouse oocytes and in Xenopus extracts [START_REF] Ierushalmi | Centering and symmetry breaking in confined contracting actomyosin networks[END_REF][START_REF] Colin | Active diffusion in oocytes nonspecifically centers large objects during prophase I and meiosis I[END_REF], we embedded hydrophobic magnetic beads in soybean oil, and injected large 30-35 µm oil droplets to move them in the cytoplasm with magnetic tweezers. We purposely used unfertilized eggs, to circumvent the presence of large asters or spindles that could affect droplet motion in the cytoplasm from steric hindrance or by generating active flows and stresses (39) (Fig 2E -2F). In the absence of external forces, oil droplets were immobile in the cytoplasm for long durations of up to 1h, much like female nuclei in these unfertilized eggs (Fig S2F -S2K). Remarkably, droplets exhibited a viscoelastic response to external forces similar to spindles, with a rapid initial constant velocity followed by a saturating elastic regime. Upon force cessation, droplets moved back towards their initial position with similar offsets as spindles, but shorter time-scales. Droplets viscoelastic recoils occurred along the same straight path as during force application, indicating that this elastic recoiling behavior is not restricted to objects initially positioned at the cell center (Fig 2G-2K and Movie S4). These data suggest that elements in bulk cytoplasm may generate viscoelastic reactive forces that move spindles or similar-sized passive objects back to their initial positions.

While mitotic spindles are often pictured as polar networks made of MT filaments, the accumulation of membranous organelles or other nuclear intermediate filaments on their MT network has suggested the existence of a spindle matrix, which could render them more physically akin to an impermeable droplet [START_REF] Zheng | A membranous spindle matrix orchestrates cell division[END_REF][START_REF] Wang | Symmetry breaking in hydrodynamic forces drives meiotic spindle rotation in mammalian oocytes[END_REF]. Accordingly, by performing Serial Block Face electron microscopy, we found that spindles were covered by packed endomembranes, with an "onion peel arrangement" typical of mitotic endoplasmic reticulum (ER) networks [START_REF] Carlton | Membrane and organelle dynamics during cell division[END_REF] (Fig 2L and Movie S5). This endomembrane accumulation is readily evident in DIC images as a smooth area around spindles (Movie S1-S3). Immunofluorescence further validated this accumulation, and segmentation of ER membranes provided an estimate of an upper-bound pore size of 0.2-0.5µm between membranes (Fig 2L -2M). Thus, metaphase spindles may be impermeable to relatively large objects and networks, a property which like oil droplets, allows them to be dragged by viscoelastic flows and forces from bulk cytoplasm.

The cytoplasm applies large elastic and viscous drags to the mitotic spindle.

To quantify restoring stiffness and viscous drags, we fitted experimental data with a three-element Jeffreys' model, which provided the simplest 1D linear model for the observed rising and relaxation curves [START_REF] Barnes | An introduction to rheology[END_REF]. This model has been employed to describe, among others, the rheology of suspensions of elastic spheres, polymeric liquids, and was previously used to understand viscoelastic properties of the cytoplasm [START_REF] Hiramoto | Mechanical properties of the protoplasm of the sea urchin egg. II. Fertilized egg[END_REF][START_REF] Frohlich | Theory of the rheological properties of dispersions[END_REF]44). This model features an elastic spring of stiffness κ, in parallel with a dashpot of viscosity γ1, in series with a second dashpot of viscosity γ2, defining two characteristic time-scales. The first one, 𝜏 1 = 𝛾 1 /𝜅 is the time-scale needed for spindle associated flows to charge the elastic elements in the material. The second, 𝜏 2 = 𝛾 2 /𝜅 sets the rate of plastic yield of these elements or fluidization of the material, which limit elastic restoration and generates an offset in the relaxation (42) (Fig 3A -3B).

Using this model, we computed a restoring stiffness for spindles pulled along their long axis of κ = 55 +/-24 pN/µm (n=19 cells) and 54 +/-25 pN/µm for orthogonal pulls (n= 21 cells). This shows that a displacement away from the cell center of 5% of the cell diameter (~4 µm), generates a restoring force of ~250 pN. These are forces equivalent to that generated by hundreds of molecular motors [START_REF] Howard | Mechanics of Motor Proteins and the Cytoskeleton[END_REF]. The stiffness measured for oil droplets was twice higher than for spindles, accounting for their shorter relaxation time-scales (Fig 3C and Fig 2J). One possible interpretation is that oil droplets are actuated in an unfertilized cytoplasm previously reported to be twice stiffer than the mitotic cytoplasm [START_REF] Hiramoto | Mechanical properties of the protoplasm of the sea urchin egg. II. Fertilized egg[END_REF][START_REF] Hiramoto | Mechanical properties of the protoplasm of the sea urchin egg. I. Unfertilized egg[END_REF]. An alternative, is that the spindle may be porous to smaller elastic elements in the cytoplasm. These numbers amount to a lower-bound value of the effective bulk modulus, G=κ/6πR, with R the size of spindles, to be on the order of 0.2-0.3 Pa. This is smaller, but in the same range as previous rheological measurements of cytoplasm stiffness in different cell types and extracts [START_REF] Hiramoto | Mechanical properties of the protoplasm of the sea urchin egg. I. Unfertilized egg[END_REF][START_REF] Guo | Probing the stochastic, motor-driven properties of the cytoplasm using force spectrum microscopy[END_REF][START_REF] Valentine | Mechanical properties of Xenopus egg cytoplasmic extracts[END_REF]. Spindle viscous drags were unexpectedly high with a parallel drag of 4493 +/-3592 pN.s/µm and an orthogonal drag of 4498 +/-3359 pN.s/µm (Fig 3D). Considering reported values of cytoplasm viscosity in these cells [START_REF] Hiramoto | Mechanical properties of the protoplasm of the sea urchin egg. II. Fertilized egg[END_REF], they amount to the drag of an object typically ten times larger than the spindle. This enhanced drag could be explained by the hydrodynamic coupling of the spindle with the cell surface which reduces spindle mobility [START_REF] Nazockdast | Cytoplasmic flows as signatures for the mechanics of mitotic positioning[END_REF][START_REF] Simone | Uncovering the balance of forces driving microtubule aster migration in C. elegans zygotes[END_REF]. Accordingly, theoretical predictions for a solid object moving in a viscous fluid contained in a sphere, with a radius twice that of the object, yield to a 10-20 fold increase of the object's drag coefficients [START_REF] Happel | Low Reynolds number hydrodynamics: with special applications to particulate media[END_REF]. This suggests that spindle large drags could primarily result from its interaction with the cytoplasm fluid confined by cell boundaries. Overall, these analyses support that the response of spindles to external forces are primarily associated to the viscoelastic properties of the cytoplasm (Fig S3A -S3D).

To compare the efficiency of bulk cytoplasm viscoelastic properties to that of active MT asters and motors, we next measured centering stiffness in anaphase, which follows metaphase by only few minutes. In anaphase, asters regrow to fill the whole cell volume, with an estimate of several hundreds of MTs contacting the cortex (Fig 1C and Fig S1E). Anaphase is thought to imply the largest MT based forces along the cell cycle, as MTs engage with dynein motors at the surface or in the cytoplasm, to separate chromosomes and move asters apart [START_REF] Garzon-Coral | A force-generating machinery maintains the spindle at the cell center during mitosis[END_REF][START_REF] Pelletier | Co-movement of astral microtubules, organelles and F-actin by dynein and actomyosin forces in frog egg cytoplasm[END_REF][START_REF] Nicklas | Measurements of the force produced by the mitotic spindle in anaphase[END_REF]. Here, magnetic forces were only applied orthogonal to the spindle axis, as parallel pulls interfered with chromosome force-separation systems (Fig S3E -S3G). While the drags of anaphase spindles were similar to that found for metaphase spindles, a net difference was obtained in term of elastic behavior, with a restoring stiffness for anaphase spindles of 150 +/-57 pN/µm, nearly three times higher than during metaphase (Fig 3E -3G). These results suggest that bulk cytoplasm restoring forces can amount to ~30% of the maximum MT/dynein based force-generating system in these cells.

Cytoplasm forces depend on crowding and bulk F-actin meshworks.

Crowding agents in bulk cytoplasm, that contribute to set elastic and viscous properties may include among others, cytoskeletal networks, endomembranes like Yolk granules and mitochondria, or ribosomes which are highly abundant in the cytoplasm (Fig 2L). As a general assay to affect cytoplasm crowding, we immersed cells ~5 min prior to mitosis in diluted or concentrated artificial sea water (ASW) and pulled spindles at metaphase onset. We limited the amplitude of these shocks to a range in which spindles length, anaphase and cytokinesis were unaffected, but we noted delays in metaphase in hypertonic treatments (Fig S4A -S4D). A hypotonic treatment in 80% ASW caused water to flow into the cells with a minor cell size increase, and reduced spindle restoring stiffness and drags in this diluted cytoplasm to 50.2% and 49.6% of control values respectively. Conversely, a hypertonic treatment in 110% ASW, shrank cells by ~6% and concentrated the cytoplasm, increasing spindle restoring stiffness and drags to 151.4% and 114.4% of control values, respectively (Fig 4A -4D and Fig S4E -S4H). These results demonstrate that viscoelastic reactive forces applied on spindles are directly related to cytoplasm crowding. Furthermore, as one element which has been shown to contribute to bulk cytoplasm material properties we tested the role of F-actin [START_REF] Guo | Probing the stochastic, motor-driven properties of the cytoplasm using force spectrum microscopy[END_REF][START_REF] Valentine | Mechanical properties of Xenopus egg cytoplasmic extracts[END_REF]. Imaging injected labelled utrophin, that binds F-actin, we detected a significant amount of disordered bulk F-actin meshes that surrounded the spindle, though unsurprisingly, the cortex was the most abundant part of the cell. Similar results were obtained with phalloidin staining (Fig ). These data suggest that bulk F-actin meshworks may act as important crowders that contribute to ~40-50% of cytoplasm elastic and viscous drags on pulled spindle.

Functional implications of cytoplasm mechanics for asymmetric and oriented divisions.

We next investigated an important feature of spindle response, which is the linear rising phase at long timescale and the offset in the relaxation, which reflect progressive plastic rearrangements or fluidization of elastic elements in the cytoplasm. A prediction of this effect is that a longer force application should dissipate more elastic energy, allowing spindles to stay further from their initial position when the force is released.

Accordingly, in the Jeffrey's model, the relaxation offset, a, depends mostly on the ratio of 𝜏 2 to the duration of force application, T, with 𝑎 = ). Thus, rotating spindles appear to dissipate faster rotationally stored elastic energy, causing spindle reorientation to be less-well restored by the cytoplasm than translation. This effect will tend to favor spindle rotation over translation, allowing for instance active force generators to easily tilt spindles, without translating it. We conclude that the dissipation of spindle elastic restoration by plastic rearrangements or fluidization of the cytoplasm and their time-dependence may be highly relevant to understand spindle positioning phenotypes.

Large-scale flows of cytoplasm material associated with spindle motions

To understand how the cytoplasm reorganizes in response to spindle motion and forces, we mapped

Discussion

Function of bulk cytoplasm rheology in the mechanics of spindle positioning.

How spindles are positioned and oriented in embryos and tissues is a fundamental problem for cell and developmental biology highly relevant to the emergence of developmental disorders and cancer [START_REF] Di Pietro | Regulation of mitotic spindle orientation: an integrated view[END_REF][START_REF] Bergstralh | Spindle orientation: what if it goes wrong?[END_REF].

One current dogma in many animal cells, is that spindles are placed with respect to cell boundaries by active forces from astral MTs that grow to the cell cortex. Here, by exploring a regime where mitotic MT asters do not reach out to the cortex, we demonstrate that the cytoplasm acts as a viscoelastic medium that holds spindles or other large objects in place, and moves them back if their position is perturbed. Restoring forces are large and shall participate in the force balance positioning spindles and asters, by for instance opposing asymmetric cytoskeleton forces during nuclear or spindle decentration for asymmetric divisions, or those needed to center asters at fertilization [START_REF] Grill | The distribution of active force generators controls mitotic spindle position[END_REF][START_REF] Tanimoto | Physical Forces Determining the Persistency and Centering Precision of Microtubule Asters[END_REF][START_REF] Simone | Uncovering the balance of forces driving microtubule aster migration in C. elegans zygotes[END_REF]. Accordingly, the cytoplasm restoring stiffness on spindles measured here, is of similar magnitude as that measured during sperm aster centration in the same model system (37), and ~3X higher than that associated to metaphase spindle maintenance at the cell center in C. elegans [START_REF] Garzon-Coral | A force-generating machinery maintains the spindle at the cell center during mitosis[END_REF]. Our findings also suggest that restoring forces vanish faster in rotation than in translation, which we attribute in part to the geometry of rotational shear flows, and anisotropies in plastic yields of the cytoplasm material. Therefore a tilt acquired during force exertion is better maintained than a positional offset. This could allow an asymmetric cortical domain enriched in motors to reorient spindles without creating an asymmetric division, a phenotype commonly observed in many tissues [START_REF] Di Pietro | Regulation of mitotic spindle orientation: an integrated view[END_REF][START_REF] Larson | Automated mitotic spindle tracking suggests a link between spindle dynamics, spindle orientation, and anaphase onset in epithelial cells[END_REF][START_REF] Tang | Mechanical Forces Program the Orientation of Cell Division during Airway Tube Morphogenesis[END_REF].

It is important, however, to outline that at rest, the cytoplasm does not apply any net force, and cannot a priori center or decenter spindles, asters or nuclei. In large cells, this is achieved earlier in the cell cycle by interphase MT asters that reach to the cell boundaries, and pre-position centrosomes before metaphase [START_REF] Minc | Influence of cell geometry on division-plane positioning[END_REF][START_REF] Mitchison | Growth, interaction, and positioning of microtubule asters in extremely large vertebrate embryo cells[END_REF]. We propose that the cytoplasm holds these prepositioned centrosomes in place. As spindles scale with cell size, cytoplasm rheology could very well be also relevant to spindle positioning in smaller cells lacking proper mitotic asters, or in which astral MTs do not reach the cell surface [START_REF] Stevens | From stem cell to embryo without centrioles[END_REF][START_REF] Khodjakov | Centrosome-independent mitotic spindle formation in vertebrates[END_REF]. However, an important open question, is how much these properties contribute in cells where numerous MTs clearly contact the cortex to exert forces that stabilize asters or spindles [START_REF] Garzon-Coral | A force-generating machinery maintains the spindle at the cell center during mitosis[END_REF][START_REF] Tanimoto | Physical Forces Determining the Persistency and Centering Precision of Microtubule Asters[END_REF]. One possibility is that the impact of cytoplasm elasticity is reduced as astral MTs and motors push back organelles and networks away from spindles, effectively confining elastic elements to a zone much closer to the cortex. Another one, which we favor, is that transport by motors along MTs could fluidize the cytoplasm space occupied by mitotic asters, effectively decreasing the elastic response of the cytoplasm. Further work will be required to understand how active polar cytoskeleton forces and material properties of bulk cytoplasm are integrated to regulate cell division and organization.

Probing cytoplasm material properties at the scale of mitotic spindles.

The cytoplasm is a complex material, whose rheological properties and their impact on cellular functions are emerging as important concepts in cell biology. Here, we probed cytoplasm rheology at scales and speeds, typical of physiological mitotic spindle repositioning and reorientation. In line with previous rheological descriptions of the cytoplasm for small objects [START_REF] Hiramoto | Mechanical properties of the protoplasm of the sea urchin egg. II. Fertilized egg[END_REF][START_REF] Hiramoto | Mechanical properties of the protoplasm of the sea urchin egg. I. Unfertilized egg[END_REF], we find that a simple linear 1D viscoelastic Jeffreys' model can predict key rheological behavior including rising and relaxation curves, and timedependent elastic dissipation. Although this suggests that we can treat the effect of the cytoplasm as that of an "inert" Jeffreys' material, these physical properties, are likely dictated and regulated by energy-driven active metabolic processes and random motor motion [START_REF] Guo | Probing the stochastic, motor-driven properties of the cytoplasm using force spectrum microscopy[END_REF][START_REF] Parry | The bacterial cytoplasm has glass-like properties and is fluidized by metabolic activity[END_REF]. We also envision that more advanced linear viscoelastic or poroelastic description of the cytoplasm could capture many of the features we report in here. Elasticity could for instance be graded, being stiffer close to the cortex and softer in the cell interior, due to the progressive stacking of organelles and networks. Inspections of electron micrographs do not immediately support this view, at least in this system. Poroelasticity would picture the cytoplasm as a porous elastic solid, with a small pore size bathed in cytosolic liquid [START_REF] Moeendarbary | The cytoplasm of living cells behaves as a poroelastic material[END_REF][START_REF] Mitchison | Implications of a poroelastic cytoplasm for the dynamics of animal cell shape[END_REF]. As spindles would compress this poroelastic medium, slowly dissipating pressure gradients would form and push back spindles in place.

Beyond physical frameworks to describe cytoplasm rheology, another important question is which elements define relevant material properties of the cytoplasm at the spindle scale. Meshworks of bulk F-actin filaments contributed to a fraction of ~40-50% of viscous and elastic behavior, acting as one important crowding agent and organelle stabilizer at this scale [START_REF] Chaigne | F-actin mechanics control spindle centring in the mouse zygote[END_REF][START_REF] Colin | Actin-Network Architecture Regulates Microtubule Dynamics[END_REF]. Intermediate filaments, like keratin or vimentin could not be tested here, but have been proposed to influence elastic properties of egg cytoplasm extracts [START_REF] Valentine | Mechanical properties of Xenopus egg cytoplasmic extracts[END_REF]. In addition, we propose that small organelles like mitochondria, yolk granules or lysosomes could behave as dense suspensions of small elastic colloids, which generate mesoscopic elasticity as is known for classical suspension such as paints or bitumen [START_REF] Frohlich | Theory of the rheological properties of dispersions[END_REF]. Further experiments of cytoplasm reconstitution will be required to determine which of these elements are dominant or dispensable at the spindle scale, or assay the role of their potential interactions.

Finally, our experiments comparing spindles and oil droplets, raise interesting questions on the physical nature of the mitotic spindle itself. In the context of our assays, we propose that spindles behave as objects impermeable to components larger than a fraction of a micron. Recent reports suggest that small particles of ~10nm in size can diffuse in and out of spindles [START_REF] Carlini | Microtubules Enhance Mesoscale Effective Diffusivity in the Crowded Metaphase Cytoplasm[END_REF]. Spindles may thus be largely porous to proteins and molecular complexes such as ribosomes, so that elastic and viscous forces they experience may only result from the response of larger organelles and networks in the cytoplasm. Mitotic spindles also feature important elastic properties, with axial stiffness measured in vitro to range around 80-900 pN/µm [START_REF] Shimamoto | Insights into the micromechanical properties of the metaphase spindle[END_REF]. In our experiments, we detected minor lengthening of mitotic spindles under force, which amounted to similar values. Recent experiments on MT asters also support models of more porous or elastic structures with important implications for mechanisms of centrosome movement [START_REF] Pelletier | Co-movement of astral microtubules, organelles and F-actin by dynein and actomyosin forces in frog egg cytoplasm[END_REF]. By bringing numbers which have been largely missing in the literature, force measurements within live cells will strongly impact our understanding of the very basic mechanisms of cell organization and morphogenesis. In parallel pulls, the cytoplasm made of relatively large objects including cytoskeletal elements and endomembranes (Yolk, mitochondria or ER), is compressed at the spindle front and stretched at the rear, which causes it to push or pull back the spindle with elastic restoring forces. At the same time, the cytoplasm material is sheared along the spindle. In orthogonal pulls, compression of the cytoplasm may be prominent at the spindle front, like in parallel pulls, but in rotation, the broken symmetry causes shear to dominate over compression. Shear stresses fluidize or plastically rearrange the cytoplasm faster than in compression potentially accounting for reduced elastic restoring of spindle angles as compared to positions upon force applications. Results were compared by using a two-tailed Mann-Whitney test. **, P < 0.01. Scale bars, 20 µm.

  with Nocodazole, to affect MTs, and monitored the ability of spindles to recoil back (Fig2A). In controls, the positional recovery followed a single exponential with a decay time-scale of 103 +/-92 s and a positional offset of 43 +/-24%. Nocodazole treated spindles shrank in size to eventually disassemble, over a period of ~5-10 min, but recovered their positions with similar dynamics and offsets as controls (Fig 2B-2Dand FigS2A-S2E). Therefore, in agreement with the lack of MTs reaching cell boundaries, astral MT polymerization pushing or pulling forces at the cortex or in the cytoplasm appear to be dispensable for repositioning spindles to the cell center.

  Fig S4I, S4L-S4O). These data suggest that bulk F-actin meshworks may act as important crowders that

  for sufficiently large T (Fig5A). To test this, we arrested cells in metaphase with MG132, pulled spindles and held them for increasing periods of time (Fig5B).Practically, this implied decreasing the pulling force gradually by progressively distancing the magnet, to avoid spindles moving onto the cortex. Remarkably, spindles held longer progressively lost their recoiling behavior with a well-matched alignment of experimental data on the predicted theoretical curve (Fig 5C-5Dand Fig S5A-S5D). Therefore, elastic restoration by the cytoplasm may be very effective at short-time scales to stabilize spindles against random thermal or active forces, but vanishes over longer time-scales to facilitate spindle decentration during asymmetric divisions.As another important read out of this effect, we found that 𝜏 2 was significantly smaller in rotation than in translation (Fig 5E-5F and Fig S5E-S5H). This was reflected both in the more linear shape of the rising curve under force and in the higher values in the angular relaxation offset as compared to translation for the same spindles (Fig 1L and Fig 5G-5H

  cytoplasmic flows. We tracked cytoplasmic granules of ~1 µm in size with Particle Image Velocimetry (PIV) (movie S6). These elements are larger than measured spindle pore size and are dominated by advection with estimated Peclet numbers exceeding 10 2 -10 3 , therefore best representing potential rearrangement of entangled elastic meshworks in the cytoplasm. When spindles were pulled along their long axis, the cytoplasm flowed along with the spindle and recirculated, forming large symmetric vortices mirrored along the spindle axis. As spindles relaxed, similar vortices formed but with an opposite rotational direction (Fig 6A-6B and Fig S6A). By computing the local divergence of the flow pattern, which provides a qualitative indicator of how a viscoelastic material may contract or expand, we found that the portion of the cytoplasm at the front of a pulled spindle appeared compressed, while the portion at the back was more stretched (Fig S6D-S6E). Vorticities in the flow field allowed to visualize shear, and to extract a time-scale from the inverse of the shear rate, on the order of 570 +/-260 s, close to the time scales for plastic dissipation 𝜏 2 of spindle viscoelastic response (Fig S6B, S6G and S6K). These data indicate that spindle displacement causes the viscoelastic cytoplasm to locally compress and/or stretch and apply reactive elastic forces, and shear away from the spindle front. In orthogonal pulls, the flow patterns were markedly different, with one dominant large vortex centered around a point located bottom-right in the cell with respect to the pulled spindle pole (Fig 6C and Fig S6F). This vortex was significantly larger than in translation (Fig 6E and Fig S6C, S6H). Furthermore, the divergence map appeared asymmetric orthogonal to the spindle axis, but did not reveal notable left-right asymmetric patterns, plausibly reflecting the reduced ability of the cytoplasm to rotate back spindles (Fig S6I-S6J). In relaxation, the flows were mostly vertical, in agreement with the dominance of a translational over rotational spindle recoil (Fig 6D). Therefore, a spindle rotating in the confined boundaries of a cell, appears to shear rather than compress the cytoplasm (Fig 6F). In light of the differential viscoelastic response of translating vs rotating spindles, these flow analyses suggest that shear fluid stress could cause cytoplasm elements to plastically yield faster than in compression, a process typical of many viscoelastic materials (42). We conclude that the organization of viscoelastic flows in response to spindles moving in a cytoplasm confined by cell boundaries, may have a key impact on mitotic spindle positioning phenotypes (Fig 6F).

Figure 1 .

 1 Figure 1. Viscoelastic forces hold spindles in the center of large cells even in the absence of astral Microtubules contacting the cell cortex. (A) (Left) Airy-scan confocal image of a sea urchin zygote in metaphase fixed and stained for Microtubules (MTs), DNA and F-actin. (Right) Close up view on + Ends of microtubules, marked with white arrowheads, and the actin-rich cortex. (B) Quantification of the distance from MT+ TIPS to the actin cortex (n= 168 MTs from 4 eggs). (C) Number of MTs reaching a distance less than 5 µm from the cortex in different phase of the first cell cycle (n= 3, 20, 5 and 2 cells respectively). Error bars correspond to +/-SEM. (D-E) Time-lapse of metaphase spindles with magnetic beads bound to one spindle pole, displaced by magnetic forces applied parallel to the spindle axis by the presence of a magnet tip, and recoiling upon force cessation. (F) Time evolution of the displacement measured from the initial centered position of the spindle normalized by the applied force for metaphase spindles in normal cells (n=11) and in cells treated with MG132 to arrest cells in metaphase (n=9). (G) Time evolution of the displacement back to the cell center when the external force is released, normalized to that at the moment of force cessation, for the same cells and conditions as in F. (H-I) Time-lapse of metaphase spindles displaced and rotated by magnetic forces applied orthogonal to the spindle axis, and spindle recoiling upon force cessation. (J) Time evolution of the displacement measured from the initial centered position of the spindle and normalized by the applied force in normal cells (n=14) and in cells treated with MG132 (n=7). (K) Time evolution of the normalized displacement back to the cell center when the external force is released for the same cells and conditions as in J. (L) Time evolution of the spindle axis angle normalized by the external torque applied in normal cells (n=14) and in cells treated with MG132 (n=7). (M) Time evolution of the normalized angle when the external torque is released for the same cells and conditions as in L. In F-G, and J-M, the bold lines correspond to fits of the data using general creep or relaxation equations of the Jeffreys' viscoelastic model (see main text and methods). Error bars are represented as shades in these curves and correspond to +/-S.D/2. Scale bars, 20 µm.

Figure 2 .

 2 Figure 2. Visco-elastic restoring forces on spindles are associated to the material properties of bulk cytoplasm. (A-B) Metaphase spindles are displaced with magnetic tweezers and treated with either DMSO as controls (n=5) or Nocodazole to affect microtubules (n=5 cells), and their recoiling behavior to the cell center is assayed. (C-D) Quantification of the positional offsets to the cell center, a, and decay time-scales τ1 of relaxation curves plotted in B, using a single exponential model as indicated in the inset in B. (E) Scheme representing injected oil droplets containing hydrophobic magnetic beads used to actuate large objects with magnetic tweezers in the cytoplasm. (F) Time-lapse of a magnetic oil droplet displaced with an external magnetic force and recoiling upon force cessation. (G) Time evolution of the displacement measured from the initial position of the droplet and normalized by the applied force (n=5 cells). (H) Time evolution of the normalized displacement of the droplet back to its initial position upon force cessation. (I-J) Relaxation offset and decay time-scales for metaphase spindles (n=15) and oil droplets (n=8). (K) Final vertical offset plotted as a function of the initial vertical offset for droplets displaced horizontally with magnetic

Figure 3 .

 3 Figure 3. Cytoplasm material generates large elastic and viscous drags on mitotic spindles of similar magnitude as those applied by active microtubule arrays. (A) Scheme of metaphase spindles held in the cell center by viscoelastic elements in the cytoplasm. (B) Scheme of Jeffreys 3-element model made of a spring and a dashpot in parallel and another dashpot in series, and typical creep and relaxation behavior of this element. (C-D) Cytoplasm restoring stiffness and viscous drags on mitotic spindles moved parallel or orthogonal to the spindle axis (n= 18 and 19 respectively) and for oil droplets (n=7), computed using fits to the Jeffreys' models represented in B. Open and closed dots correspond respectively to data obtained in control or MG132 treated cells. (E) Time evolution of the displacement measured from the initial centered position of the spindle and normalized by the applied force in metaphase and anaphase. (F-G) Restoring stiffness and viscous drags of metaphase and anaphase spindles moved orthogonal to the spindle axis (n=19 and 17 respectively). Error bars and shades correspond to +/-S.E.M and +/-S.D/2 respectively. Results were compared by using a two-tailed Mann-Whitney test. n.s, P > 0.05, **, P < 0.01, ****, P < 0.0001.

Figure 4 . 20 Figure 5 .

 4205 Figure 4. Influence of cytoplasm crowding and F-actin meshwork on spindle restoring stiffness and drags. (A) Scheme representing experiments to change cytoplasmic density by placing eggs in hypotonic or hypertonic artificial sea water (ASW). (B) Displacement normalized by applied force of metaphase spindles in control (n=10), hypotonic (n=6) and hypertonic (n=7) sea water. (C-D) Cytoplasm resorting stiffness and viscous drags on mitotic spindles moved parallel to the spindle axis, in controls, hypotonic or hypertonic sea water. (E) Confocal images of eggs injected with Utrophin-488 to visualize F-actin at metaphase in bulk cytoplasm (top) and ~5 min after treating the same cell with Latrunculin B (bottom). The two images are treated with the same contrast to compare F-actin signals. (F) Displacement normalized by applied force of metaphase spindles in control (n=10), cells treated with Latrunculin B (n=13) and cells treated with Blebbistatin (n=6). (G-H) Cytoplasm restoring stiffness and viscous drags in controls, cells treated with Latrunculin B and cells treated with Blebbistatin. Error bars and shades correspond to +/-S.E.M and +/-S.D/2 respectively. Results were compared by using a two-tailed Mann-Whitney test. n.s, P > 0.05, *, P < 0.05. Scale bars, 20 µm.

Figure 6 .

 6 Figure 6. Large-scale flows of cytoplasm elements associated with spindle motions. (A-D) Cytoplasm streamlines averaged on a duration of 60 s and size of 50 µm during parallel force application on spindles (A) and during spindle recoils (B), or during orthogonal force applications averaged on a duration of 100 s and size of 90 µm (C) and relaxation (D). Streamlines are superimposed onto a color map of local flow vorticities, ω. (E) Quantification of flow vortices size during parallel or orthogonal pulls (n=8 and 13 cells respectively). (F) Proposed models based on flow map analysis and force response of metaphase spindles.

Acknowledgment

We thank P. Lenart, B. Lacroix and J. Dumont for sharing reagents, as well as our colleagues C. Leduc, S. Dmitrieff, G. Romet-Lemonne, Y. Bellaïche and J-L. Maître for carefully reading this MS. We gratefully thank all members of the Minc team for discussion and technical help. J.X. acknowledges the "École Doctorale FIRE -Program Bettencourt", a fellowship from the Chinese Scholarship Council (201708070046) and from the LabEx "Who am I?" (ANR-11-LABX-0071). J.N. is supported by a fellowship from the ARC foundation (PDF20191209818) and is an EMBO Non-Stipendiary Fellow (ALTF 881-2019). We acknowledge the ImagoSeine core facility of the Institut Jacques Monod, member of Infrastructure en Biologie Santé et Agronomie and France-BioImaging (ANR-10-INBS-04) infrastructures. This work was supported by the Centre National de la Recherche Scientifique (CNRS), the Université de Paris, and grants from La Ligue Contre le Cancer (EL2021.LNCC/ NiM), Agence Nationale pour la Recherche (ANR, "TiMecaDev"), the Fondation Bettencourt Schueller ("Coup d'élan"), and the European Research Council (ERC CoG "Forcaster" no. 647073) to N.M.

Material and methods

Detailed methods are provided in the SI appendix. They include protocols to obtain and handle sea urchin animals and gametes, and procedures used for chemical inhibitions of cytoskeletal components and modulations of sea water osmolarity. All methods for live and fixed imaging of zygotes are also provided, including those used for transmission electron microscopy, serial block face electron microscopy and endomembrane registration in three dimensions. Finally, we also provide all detailed procedures for injecting magnetic beads, calibrating magnetic forces in vitro, and computing magnetic forces in vivo, as well as extract viscoelastic parameters and map and analyze viscoelastic flows in live cells.