Tetsuya Komabayashi
email: tetsuya.komabayashi@ed.ac.uk

Giacomo Pesce

Guillaume Morard

Daniele Antonangeli

Ryosuke Sinmyo

Mohamed Mezouar

Phase transition boundary between fcc and hcp structures in Fe-Si alloy and its implications for terrestrial planetary cores

Keywords: pressure, diamond anvil cell, internal resistive heating, Fe-Si alloy

The phase transition between a face-centered cubic (fcc) and hexagonal close-packed (hcp) structures in Fe-4wt% Si alloy was examined in an internally resistive heated diamond anvil cell (DAC) under high-pressure (P) and -temperature (T) conditions to 71 GPa and 2000 K by in-situ synchrotron X-ray diffraction. Complementary laser-heated DAC experiments were performed in Fe-6.5wt% Si. The fcc-hcp phase transition boundaries in the Fe-Si alloys are located at higher temperatures than that in pure Fe, indicating that the addition of Si expands the hcp stability field. The dP/dT slope of the boundary of the entrant fcc phase in Fe-4wt% Si is similar to that of pure Fe, but the two-phases region is observed over a temperature range increasing with pressure, going from 50 K at 15 GPa to 150 K at 40 GPa. The triple point, where the fcc, hcp, and liquid phases coexist in Fe-4wt% Si, is placed at 90-105 GPa and 3300-3600 K with the melting curve same as in Fe is assumed. This supports the idea that the hcp phase is stable at Earth's inner core conditions. The stable structures of the inner cores of the other terrestrial planets are also discussed based on their P-T conditions relative to the triple point. In view of the reduced P-T conditions of the core of Mercury (well below the triple point), an Fe-Si alloy with a Si content up to 6.5 wt% would likely crystallize an inner core with an fcc structure. Both Venusian and Martian cores are believed to currently be totally molten. Upon secular cooling, Venus is expected to crystallize an inner core with an hcp structure, as the pressures are similar to those of the Earth's core (far beyond the triple point). Martian inner core will take an hcp or fcc structure depending on the actual Si content and temperature.

INTRODUCTION

Terrestrial core formation process has been discussed in relation to metal-silicate equilibration during accretion stage [START_REF] Li | Geochemistry of mantle-core differentiation at high pressure[END_REF][START_REF] Wade | Core formation and the oxidation state of the Earth[END_REF][START_REF] Siebert | Terrestrial Accretion Under Oxidizing Conditions[END_REF] although some recent models considered disequilibrium processes at a later stage [START_REF] Rubie | Heterogeneous accretion, composition and core-mantle differentiation of the Earth[END_REF]. The metal-silicate equilibration inevitably results in an impure iron rich metallic core [START_REF] Wade | Core formation and the oxidation state of the Earth[END_REF][START_REF] Siebert | Terrestrial Accretion Under Oxidizing Conditions[END_REF]). The impurity includes nickel and several less dense elements which are also called light elements (Poirier 1994;[START_REF] Allègre | The chemical composition of the Earth[END_REF]. [START_REF] Birch | Elasticity and constitution of the Earth's interior[END_REF] pointed out that the density of pure iron might be greater than the seismological determination for Earth's core. Such a density deficit has been associated with the presence of lighter element(s), and a recent internally consistent thermodynamic model of pure iron estimated the core density deficit to be 7% for the outer core and 4.5 % for the inner core [START_REF] Komabayashi | Thermodynamics of melting relations in the system Fe-FeO at high pressure: Implications for oxygen in the Earth's core[END_REF]. Other terrestrial planetary cores also likely contain light elements considering metal-silicate partitioning during their cores formation. In addition, the presence of a magnetic field found in some terrestrial planets may indicate the presence of a light element-bearing partially molten core (e.g., [START_REF] Sohl | Interior structure, composition, and mineralogy of the terrestrial planets[END_REF]. Light elements would be expelled at the bottom of the liquid outer core as it is less partitioned in the solid inner core and this would drive convection in the outer core [START_REF] Stevenson | Magnetism and Thermal Evolution of the Terrestrial Planets[END_REF][START_REF] Lister | The Strength and Efficiency of Thermal and Compositional Convection in the Geodynamo[END_REF].

Among the potential light elements, silicon is considered a plausible candidate for the terrestrial planetary cores for various reasons: i) silicon is the second most abundant element in the mantle and series of high-pressure (P) and -temperature (T) experiments demonstrated that silicon and oxygen could be dissolved from mantle silicates to core melt [START_REF] Takafuji | Solubilities of O and Si in liquid iron in equilibrium with (Mg,Fe)SiO 3 perovskite and the light elements in the core[END_REF][START_REF] Ozawa | Experimental study of reaction between perovskite and molten iron to 146 GPa and implications for chemically distinct buoyant layer at the top of the core[END_REF], and then silicon is partitioned between solid and liquid during core crystallization; ii) silicon isotopic composition of stony meteorites is different from bulk silicate Earth [START_REF] Georg | Silicon in the Earth's core[END_REF][START_REF] Fitoussi | Si isotope systematics of meteorites and terrestrial peridotites: implications for Mg/Si fractionation in the solar nebula and for Si in the Earth's core[END_REF], implying that silicon might have been partitioned into the core during core-mantle differentiation [START_REF] Shahar | High-temperature Si isotope fractionation between iron metal and silicate[END_REF][START_REF] Hin | Experimental determination of the Si isotope fractionation factor between liquid metal and liquid silicate[END_REF]; iii) all the core formation models based on silicate-metal equilibration inevitably have silicon as a light element in the core [START_REF] Wade | Core formation and the oxidation state of the Earth[END_REF][START_REF] Rubie | Heterogeneous accretion, composition and core-mantle differentiation of the Earth[END_REF][START_REF] Siebert | Terrestrial Accretion Under Oxidizing Conditions[END_REF].

Phase relations and equations of state (EoS) of solid phases in the system Fe-(Fe)Si have been extensively studied by both experiment and theory (Alfe et al. 2002;[START_REF] Dobson | A new high-pressure phase of FeSi[END_REF][START_REF] Lin | Iron-silicon alloy in Earth's core?[END_REF][START_REF] Kuwayama | Phase relations in the system Fe-FeSi at 21 GPa[END_REF][START_REF] Lin | Phase relations of Fe-Si alloy in Earth's core[END_REF][START_REF] Tateno | The structure of Fe-Si alloy in Earth's inner core[END_REF][START_REF] Ozawa | High-pressure melting experiments on Fe-Si alloys and implications for silicon as a light element in the core[END_REF]). An important phase relation is the transition between face-centered cubic (fcc) and hexagonal close-packed (hcp) structures, as this is central to address the solid inner core structure [START_REF] Uchida | Stability field and thermal equation of state of ε-iron determined by synchrotron X-ray diffraction in a multianvil apparatus[END_REF][START_REF] Asanuma | Phase relations of Fe-Si alloy up to core conditions: Implications for the Earth inner core[END_REF][START_REF] Komabayashi | In-situ X-ray diffraction measurements of the γ-ε transition boundary of iron in an internally-heated diamond anvil cell[END_REF], and the P-T location of the phase boundary can be used to deduce thermodynamic properties [START_REF] Wood | Carbon in the core[END_REF][START_REF] Komabayashi | Thermodynamics of melting relations in the system Fe-FeO at high pressure: Implications for oxygen in the Earth's core[END_REF]. Notably, the triple point P-T location where the hcp, fcc, and liquid phases coexist can be constrained from the fcc-hcp boundary and melting curve [START_REF] Zhang | Temperature of Earth's core constrained from melting of Fe and Fe0.9Ni0.1 at high pressures[END_REF]). An experimental study in a laser-heated diamond anvil cell (DAC) reported that the transition temperature was greatly reduced when 3.4 wt%Si was added to Fe [START_REF] Asanuma | Phase relations of Fe-Si alloy up to core conditions: Implications for the Earth inner core[END_REF]. In contrast, phase relations inferred by [START_REF] Fischer | Phase relations in the Fe-FeSi system at high pressures and temperatures[END_REF] suggested that addition of silicon should increase the transition temperature. [START_REF] Tateno | The structure of Fe-Si alloy in Earth's inner core[END_REF] experimentally demonstrated that the transition temperature was increased by the addition of 6.5 wt%Si to iron. As such the effect of Si on the transition temperature has been a controversy and the P-T conditions of the actual boundaries in the system Fe-Si are not unanimous.

In this study, we present the investigation of the P-T locations of the fcc-hcp transition boundaries in Fe-Si alloys in an internally resistive heated DAC. The internally heated DAC heats the sample by its resistance, with an improved accuracy in temperature with respect to conventional laser heated DAC [START_REF] Komabayashi | In-situ X-ray diffraction measurements of the γ-ε transition boundary of iron in an internally-heated diamond anvil cell[END_REF]2012). Based on these experimental results, we will discuss the effect of Si on the Fe properties under high P-T condition and address the stable structure of a solid Fe-Si alloy at the conditions of the inner cores of the terrestrial planets of the solar system.

EXPERIMENTAL PROCEDURE

We conducted high-P-T in-situ X-ray diffraction (XRD) experiments on Fe-Si samples at the beamline ID27, European Synchrotron Radiation Facility (ESRF). X-rays with a wavelength of 0.3738Å were focused to a 3x3 µm 2 spot at sample position and the diffracted X-rays were collected on a two dimensional detector (mar345 Image Plate Detector). The collection time was 10 seconds for each measurement. Using the fit-2D program [START_REF] Hammersley | FIT2D V12.012 Reference Manual[END_REF], the obtained data were converted to the conventional one-dimensional XRD pattern.

High pressure was generated in a DAC with a pair of diamond anvils with a culet size of 300 µm or 150-450 µm beveled depending on the pressure range. The starting material was a 5-7 µm thick Fe-Si alloy with 4 wt% Si (Rare Metallic. Co., hereafter Fe-4Si), placed in the sample chamber and connected to platinum leads. The junction between the Fe sample and Pt leads was outside the sample chamber (see [START_REF] Komabayashi | In-situ X-ray diffraction measurements of the γ-ε transition boundary of iron in an internally-heated diamond anvil cell[END_REF] for the sample geometry). SiO 2 glass layers served as a pressure transmitting medium and thermal insulator. High temperature was achieved with an internal resistive system [START_REF] Komabayashi | In-situ X-ray diffraction measurements of the γ-ε transition boundary of iron in an internally-heated diamond anvil cell[END_REF]2012;[START_REF] Antonangeli | Simultaneous sound velocity and density measurements of hcp iron up to 93 GPa and 1100 K: An experimental test of the Birch's law at high temperature[END_REF]. The sample was resistively heated by directly applying a DC voltage by an external power supply. The temperature was measured by a spectral radiometric system as conventional in laser heating experiments. Noteworthy, thanks to the improved time and spatial stability of the hotspot and the reduced thermal gradients, resulting uncertainties in temperature were about 50 K [START_REF] Komabayashi | In situ X-ray diffraction measurements of the fcc-hcp phase transition boundary of an Fe-Ni alloy in an internally heated diamond anvil cell[END_REF] Complementary laser heating experiments were conducted on an Fe-6.5Si sample (Rare Metallic. Co.) at ID27, ESRF (see [START_REF] Morard | Melting of Fe-Ni-Si and Fe-Ni-S alloys at megabar pressures: implications for the core-mantle boundary temperature[END_REF] for details of the laser heating experimental set up). The internal heating system was not applied because this alloy is so brittle that it was not possible to make it into thin foil. Irrespectively of the use of low numerical aperture and reflecting objectives which effectively minimize the chromatic aberration and improve reliability of temperature determination [START_REF] Mezouar | Methodology for in situ synchrotron X-ray studies in the laser-heated diamond anvil cell[END_REF], the laser heating experiments show larger temperature uncertainty due to large temperature gradient across the sample and laser fluctuations. The two microns diameter pinhole at the entrance of the spectrometer allows for a collection of signal only coming from the very central part of the hotspot and an optimal alignment of lasers and X-ray beam. [START_REF] Morard | Melting of Fe-Ni-Si and Fe-Ni-S alloys at megabar pressures: implications for the core-mantle boundary temperature[END_REF] discussed that the possible uncertainty in the temperature in this experimental setup might be 150 K at 3000 K. In the present study, we assumed a more conservative number, 10% of the generated temperature.

In all the runs, the pressure at any given temperature was calculated with a thermal EoS for Fe-4Si or Fe-6.5Si with the hcp structure that was assessed based on pure iron [START_REF] Dewaele | Quasihydrostatic equation of state of iron above2 Mbar[END_REF]) and Fe-9wt%Si [START_REF] Tateno | The structure of Fe-Si alloy in Earth's inner core[END_REF]. The room temperature parameters for the Vinet EoS were obtained by averaging on the basis of mole fraction between the two compositions: for Fe-4Si, V 0 = 22.56Å 3 , K 0 = 166 GPa, K' = 5.4, and for Fe-6.5Si, V 0 = 22.63 Å 3 , K 0 = 167 GPa, K' = 5.5, where V 0 , K 0 , K' are the unit-cell volume, bulk modulus, and its pressure derivative at 300 K and 1 bar, respectively. We assumed the same thermal parameters as for pure iron [START_REF] Dewaele | Quasihydrostatic equation of state of iron above2 Mbar[END_REF][START_REF] Tateno | The structure of Fe-Si alloy in Earth's inner core[END_REF].

The thermal pressure effect on the sample pressure was checked against the pressure for the SiO 2 pressure medium. The EoS for stishovite by [START_REF] Wang | P-V-T equation of state of stishovite up to mid-lower mantle conditions[END_REF] was used to calculate the pressure for SiO 2 . As the precise temperature for the pressure medium was unknown, we calculated the pressure for SiO 2 at the sample temperature and 300 K. At 42.8 GPa and 1940 K for the sample, the pressure for SiO 2 were 44.9 GPa and 34.1 GPa at 1940 K and 300 K respectively. Since the crystallized portion of the pressure medium should be at the same (or slightly lower) temperature of the sample, the above calculation independently supports our pressure determination for the iron alloy. Also, after quench, the pressure for SiO 2 is 37.6 ± 1.0 GPa, which is consistent with the sample pressure of 36.6 ± 0.4 GPa. Therefore, we can conclude that the pressure estimation at high temperatures is reasonable.

The use of the unit-cell volume of the hcp phase in the pressure calculation may introduce an uncertainty when the experimental condition is near the completion of the hcp-fcc reaction. Based on a binary temperature-composition (T-X) phase loop detailed below, the pressure could have been underestimated by less than 1.3 GPa at 40 GPa and 1870K. When the unit-cell volume for the hcp phase was not obtained, due to either grain growth or complete transition to the fcc phase, we assumed constant pressure upon further heating.

RESULTS

Fe-4Si

Six separate in-situ XRD experiments were carried out on the Fe-4Si sample in the internally heated DAC. The results are illustrated in Fig. 1a andsummarized in Table 1.

In the first run, the sample was compressed to 16.4 GPa and the XRD pattern shows coexistence of the bcc and hcp phases. Then the sample was heated to 1060 K and the fcc phase, with a minor amount of hcp phase, was observed. The hcp phase disappeared in the following XRD pattern at a similar temperature of 1050 K.

Temperature slightly increased with time to 1080 K at steady power from the DC power supply without further changes in the pattern. Then, we tried to reverse the reaction. As the spectroradiometric method could not reliably measure temperatures below 1000 K, the temperature was estimated based on the linear power-temperature relationship established at 1060 K. During the cooling path, the reversal reaction started at 860 K, 200 K lower than the reaction in the forward heating cycle. Further decreasing temperature to 770 K only slightly promoted the reaction, which suggests that nucleation of the hcp phase is very sluggish and implies that the width of the reaction in the backward cycle is much wider than the forward cycle. Accordingly, we constrained the P-T conditions of the reaction in the forward cycle only and the results of the backward cycle are not listed in Table 1 to avoid confusion.

In the following runs, we only employed heating cycles which started from the hcp phase towards the fcc stability field. In the runs 2, 3, and 4, we observed a transition sequence from hcp to hcp+fcc and to fcc with increasing temperature. Figure 2 shows a series of XRD patterns collected during the run 2 for increasing temperature at about 24 GPa. The temperature was first held at 1120 K for 4 minutes, observing only the hcp phase. Then we increased the temperature to 1230 K and fcc peaks appeared. No further changes in the XRD pattern were recognized during the following 40 minutes, during which the temperature was kept constant. We further increased the temperature to 1260 K, which instantaneously increased the intensity of the fcc peaks. During the following 30 minutes at constant temperature, the XRD patterns did not show significant changes.

The transition was completed at 1330 K. In summary, the drastic changes in XRD were observed only upon temperature increase. The transition from the hcp to fcc phase seems to be very fast, with minimal kinetic effects.

In the runs 5 and 6, we observed no structural change to the highest temperatures and confirmed stability of the hcp phase to 71.0 GPa and 2020 K.

Overall, thanks to the performances of the internal heating system, we have been able to place tight constraints on the P-T location of the transition boundaries. In particular, the width of the phase loop was accurately constrained. The dP/dT slope of the boundary of the entrant fcc phase in Fe-4wt% Si is similar to that of pure Fe, while the temperature interval of the two-phase region expands with increasing pressure from 50 K at 15 GPa to 150 K at 40 GPa (Fig. 1a).

Fe-6.5Si

Two separate laser-heating runs were conducted on the Fe-6.5Si sample (Fig. 1b). Same as for the internal-heating runs, we increased the temperature under high pressures. In the first run, we compressed the sample to 24.0 GPa at room temperature and then heated it by laser, reporting the appearance of fcc peaks at 1850 K in coexistence with hcp peaks. In the second run, we observed a complete transition to the fcc phase at 2340 K and 56.6 GPa. Considering the uncertainty in temperature in the laser heating experiment (i.e., ±10%), the present experimental data are consistent with results by [START_REF] Tateno | The structure of Fe-Si alloy in Earth's inner core[END_REF] (Fig. 1b).

DISCUSSION

Effect of Si on the fcc-hcp transition

The present experiments confirmed the enlarged high temperature stability of the hcp phase in Fe-4Si and Fe-6.5Si with respect to the case in pure Fe (Fig. 1), in agreement with [START_REF] Fischer | Phase relations in the Fe-FeSi system at high pressures and temperatures[END_REF] and [START_REF] Tateno | The structure of Fe-Si alloy in Earth's inner core[END_REF] but in contrast to [START_REF] Asanuma | Phase relations of Fe-Si alloy up to core conditions: Implications for the Earth inner core[END_REF]. Dissecting the XRD patterns in [START_REF] Asanuma | Phase relations of Fe-Si alloy up to core conditions: Implications for the Earth inner core[END_REF], we noted that they assigned tiny shallow rises as peaks from the fcc phase, while the appearance of the fcc phase is clearly marked by the presence of the ( 200) peak (Fig. 2) [START_REF] Komabayashi | In-situ X-ray diffraction measurements of the γ-ε transition boundary of iron in an internally-heated diamond anvil cell[END_REF]2012). We conclude that the transition temperature between the hcp and fcc phases increases with Si content.

Figure 3 shows a T-X diagram at 40 GPa based on the present data on Fe-4Si and Fe-6.5Si and existing experimental data on pure Fe and Fe-9Si [START_REF] Komabayashi | In-situ X-ray diffraction measurements of the γ-ε transition boundary of iron in an internally-heated diamond anvil cell[END_REF][START_REF] Tateno | The structure of Fe-Si alloy in Earth's inner core[END_REF]. The fcc-hcp transition temperature increases with Si content.

The P-T conditions for a reaction hcp = hcp + B2 phase [START_REF] Tateno | The structure of Fe-Si alloy in Earth's inner core[END_REF] placed additional constraint on the phase diagram (Fig. 3). The maximum solubility of Si into the fcc phase should be about 7 wt%. A thermodynamic model will be made to fit the data in the near future.

IMPLICATIONS

Figure 4 shows a phase diagram of iron alloys reporting the fcc-hcp boundaries in Fe, Fe-4Si, and Fe-6.5Si, together with the P-T ranges for the cores of Mars and Mercury. Addition of Si to Fe expands the stability of the hcp phase as confirmed by the P-T locations of the fcc-hcp transitions observed in this study, which are consistent with [START_REF] Tateno | The structure of Fe-Si alloy in Earth's inner core[END_REF] based on a laser-heated DAC experiments (Fig. 1b). The triple point where the fcc, hcp, and liquid phases coexist in Fe-4wt% Si is placed at 90-105 GPa and 3300-3600 K (the melting curve is assumed to be the same as in Fe as Si inclusion at 4wt% level should not significantly affect the melting temperature [START_REF] Morard | Melting of Fe-Ni-Si and Fe-Ni-S alloys at megabar pressures: implications for the core-mantle boundary temperature[END_REF])), supporting the idea that Earth's inner core at 330-364 GPa is made up with the hcp phase. [START_REF] Tateno | The structure of Fe-Si alloy in Earth's inner core[END_REF] similarly proposed that the inner core would be made of a sole hcp alloy if the Si content is up to 7 wt.%.

More complex can be the cases for the other terrestrial planets of the solar system, namely, Venus, Mercury, and Mars. Due to the lack of seismic data, information about their internal structures heavily depends on the average density. As such, the core density deficit cannot be pertinently discussed. Nevertheless geophysical modelling studies argued for the presence of light elements in the cores and kept this into consideration when simulating planetary core, and in particular when discussing their molten/solid state [START_REF] Stevenson | Magnetism and Thermal Evolution of the Terrestrial Planets[END_REF][START_REF] Williams | Thermal evolution of the Martian core: Implications for an early dynamo[END_REF][START_REF] Rivoldini | Geodesy constraints on the interior structure and composition of Mars[END_REF]Dumberry and Rivoldini 2015;[START_REF] Knibbe | The thermal evolution of Mercury's Fe-Si core[END_REF]. In the following, we will limit our discussion to the Fe-Si-S system. [START_REF] Tsujino | Equation of state of gamma-Fe: Reference density for planetary cores[END_REF] summarized existing thermal models for terrestrial core-mantle boundaries in the system Fe-S [START_REF] Stevenson | Magnetism and Thermal Evolution of the Terrestrial Planets[END_REF][START_REF] Sohl | The interior structure of Mars: Implications from SNC meteorites[END_REF][START_REF] Fei | Structure type and bulk modulus of Fe3S, a new iron-sulfur compound[END_REF][START_REF] Williams | Thermal evolution of the Martian core: Implications for an early dynamo[END_REF] and assessed the adiabats across the cores on the basis of the Grüneisen parameter for pure fcc iron (Fig. 4). The known reduction of the crystallizing temperature of iron by addition of silicon [START_REF] Kubaschewski | Phase diagram of binary iron alloys[END_REF][START_REF] Kuwayama | Phase relations in the system Fe-FeSi at 21 GPa[END_REF] implies that the thermal profiles in Fig. 4, which are based on the liquidus of the system Fe-S, can be considered as the maximum estimates for the system Fe-Si-S.

Venus' similar size to the Earth implies that its internal structure is differentiated into crust, mantle, and core [START_REF] Sohl | Interior structure, composition, and mineralogy of the terrestrial planets[END_REF]. However, contrarily to the Earth, Venus does not have a global magnetic field .The pressure at the center of the planet was estimated to be 295 GPa which is slightly lower than of the Earth and crystallization of the liquid core might have not yet started [START_REF] Stevenson | Magnetism and Thermal Evolution of the Terrestrial Planets[END_REF]. Since the core pressure is far greater than the triple point pressure in the system Fe-4Si (Fig. 4), when upon secular cooling the inner core will start crystallizing, likewise the Earth, it should take an hcp phase.

It is suggested that Mercury has a partially molten iron core as it shows a dipole magnetic field from a spacecraft observation [START_REF] Ness | Magnetic-Fields of Mercury, Mars, and Moon[END_REF]. Further support of the presence of a liquid portion of the core comes from and the amplitude of its librations (Margot et al. 2005). The suggested thermal structure of Mercurian core modeled on the basis of the system Fe-S argues for a temperature much higher than the fcc-hcp transition in Fe-6.5Si (Fig. 4). Recently proposed thermal models of Fe-Si cores showed a similar temperature range as in Fig. 4

(Knibbe and van Westrenen 2018). Hence

Mercurian inner core is expected to take an fcc structure if the Si content is less than 6.5 wt%. Only upon further cooling, the fcc-structured alloy in Mercurian inner core, will be transformed to the hcp phase.

Mars currently does not have an active global magnetic field, although it has a metallic core in view of its average density and moment of inertia [START_REF] Yoder | Fluid core size of mars from detection of the solar tide[END_REF].

However, the presence of magnetized rock records found in southern highland area indicates that the planet should have had a magnetic field in the past. [START_REF] Stevenson | Magnetism and Thermal Evolution of the Terrestrial Planets[END_REF] suggested that present Martian core should still be totally molten to account for the absence of the magnetic field and the rocks were magnetized by a field produced by a past, now extinct, thermal convection of the liquid core. The inferred thermal profiles of the core partially overlap with the fcc-hcp transition in Fe-4Si (Fig. 4). As such the first iron alloy crystal that will crystallize in the future will be either fcc or hcp phase depending on the actual Si content and exact temperature. In the case of the fcc phase, it will be transformed to the hcp phase as the core further cools down.

In summary, the inner core structure of the terrestrial planets can be discussed based on the phase relations in Fig. 4. The hcp core would show more anisotropic seismic properties [START_REF] Steinle-Neumann | Elasticity of iron at the tempeature of the Earth's inner core[END_REF] than the fcc core because of the anisotropic crystal structure. Also the hcp core would be denser than the fcc core as the fcc-hcp transition in Fe-4Si shows about 0.8% density jump. Those changes are important in future attempts to construct a precise density model for the planetary interior. in XRD patterns are plotted: inversed triangle, hcp+bcc; square, hcp; normal triangle, fcc+hcp; circle, fcc. In (a), the boundaries between the fcc and hcp phases in pure iron [START_REF] Komabayashi | In-situ X-ray diffraction measurements of the γ-ε transition boundary of iron in an internally-heated diamond anvil cell[END_REF]) and Fe-3.4Si [START_REF] Asanuma | Phase relations of Fe-Si alloy up to core conditions: Implications for the Earth inner core[END_REF]) are also plotted. The data with asterisk have larger temperature uncertainty. In (b), our data are shown together with experimental data by [START_REF] Tateno | The structure of Fe-Si alloy in Earth's inner core[END_REF]. The typical uncertainty (2.5 GPa and 200 K) is shown for a guide to the eye, see Table 1 for the uncertainty for each data point. The two datasets are fairly consistent considering the uncertainty in the laser heating experiments. [START_REF] Komabayashi | In-situ X-ray diffraction measurements of the γ-ε transition boundary of iron in an internally-heated diamond anvil cell[END_REF]; the star symbols are the fcc-hcp reactions constrained by the present experiments; the filled circle is the P-T condition for a reaction of hcp = hcp + B2 phase observed in [START_REF] Tateno | The structure of Fe-Si alloy in Earth's inner core[END_REF]. The stability fields of fcc+B2 and hcp+B2 were constrained by phase relations. In particular: (i) the boundary hcp = hcp+B2 should have a negative slope [START_REF] Tateno | The structure of Fe-Si alloy in Earth's inner core[END_REF] and (ii) the invariant boundary where the fcc, hcp, and B2 phases coexist should be placed at a temperature higher than the upper star at Fe-6.5Si.

Figure 4. The fcc-hcp boundaries in Fe-4Si and Fe-6.5Si (this study) with phase relations of pure iron (black lines) [START_REF] Komabayashi | In-situ X-ray diffraction measurements of the γ-ε transition boundary of iron in an internally-heated diamond anvil cell[END_REF][START_REF] Komabayashi | Thermodynamics of melting relations in the system Fe-FeO at high pressure: Implications for oxygen in the Earth's core[END_REF].

Thermal profiles of Mercurian and Martian cores in the system Fe-S are also shown [START_REF] Tsujino | Equation of state of gamma-Fe: Reference density for planetary cores[END_REF].

Figure captions Figure 1 .

 captions1 Figure captions

Figure 2 .

 2 Figure 2. Series of XRD patterns collected in the run 2 for increasing temperature. The

Figure 3 .

 3 Figure 3. Temperature-composition diagram for the fcc-hcp transition. The open circle

  figure1

Table 1 . Experimental conditions and results

 1 The uncertainty in temperature in the resistive and laser heating are typically 50 K and 10%, respectively. ** Temperature uncertainty is as large as ±100 K.

	Run P, GPa	T, K	*	Phase	V(hcp), Å 3 a (hcp), Å c (hcp), Å V(fcc), Å 3	Remarks
	Fe-4Si (internal resistive heating)
	16.4(6)	300		bcc+hcp 20.823(53) 2.4640(18) 3.9604(83)
	13.1(4)	1060 fcc+hcp(small) 21.660(0) 2.4855(0) 4.04853(0) 43.643(14)
	13.1(4)	1050	fcc				43.615(19)
	13.1(4)	1080	fcc				43.683(19)
	23.6(4)	300		hcp	20.265(27) 2.4394(14) 3.9323(24)
	22.6(4)	1120	hcp	20.816(3) 2.4554(2) 3.9866(3)
	21.9(5)	1230	hcp+fcc	20.955(3) 2.4596(2) 3.9998(3) 42.352(0)
	21.2(4)	1260	hcp+fcc	21.036(0) 2.4596(0) 4.0152(0) 42.343(38)
	21.2	1260	hcp+fcc	-	-	-	42.330(5) one peak for hcp
	21.2	1270	hcp+fcc	-	-	-	42.370(4) one peak for hcp
	21.2	1330	fcc				42.475(15)
	21.2	1360	fcc				42.520(12)
	21.2	1430	fcc				42.720(21)
	21.2	1450	fcc				42.854(69)
	33.3(2)	300		hcp	19.629(11) 2.4193(6) 3.8725(11)
	32.7(5)	1030	hcp	20.016(10) 2.4280(5) 3.9206(10)
	30.6(5)	1190	hcp	20.247(7) 2.4342(4) 3.9456(7)
	30.2(5)	1240	hcp	20.312(9) 2.4361(5) 3.9521(9)
	** 29.3(1.1) 1370 ** 29.3(1.0) 1300	hcp+fcc 20.411(13) 2.4399(7) 3.9592(13) 41.463(0) hcp+fcc 20.453(18) 2.4417(9) 3.9611(18) 41.392(0)
	29.0(6)	1440	hcp+fcc 20.524(14) 2.4434(7) 3.9696(14) 41.285(0)
	28.4(1)	1470	hcp+fcc	20.559(5) 2.4465(3) 3.9663(3) 41.344(51)
	28.6(8)	1500	hcp+fcc 20.595(25) 2.4472(14) 3.9710(16) 41.480(37)
	28.6	1580	fcc				41.652(23)
	28.6	1620	fcc				41.650(19)
	41.0(5)	300		hcp	19.198(26) 2.3956(14) 3.8626(24)
	43.7(6)	1130	hcp	19.392(13) 2.4019(7) 3.8813(12)
	43.6(6)	1190	hcp	19.426(13) 2.4028(7) 3.8852(12)
	43.3(6)	1250	hcp	19.473(10) 2.4043(5) 3.8899(9)
	42.8(6)	1310	hcp	19.527(9) 2.4060(5) 3.8949(8)
	42.3(5)	1380	hcp	19.592(7) 2.4081(4) 3.9011(6)
	41.9(5)	1460	hcp	19.659(7) 2.4103(4) 3.9074(7)
	41.8(7)	1410	hcp	19.637(14) 2.4106(8) 3.9021(13)
	41.4(7)	1450	hcp	19.686(13) 2.4125(7) 3.9056(12)
	41.5(7)	1560	hcp	19.736(13) 2.4139(7) 3.9111(12)
	41.2(7)	1600	hcp	19.777(17) 2.4157(9) 3.9133(15)
	41.5(8)	1680	hcp	19.799(25) 2.4158(13) 3.9173(23)
	41.6(6)	1740	hcp+fcc 19.833(11) 2.4160(6) 3.9234(10) 39.934(0)
	42.0(8)	1800	hcp+fcc 19.841(24) 2.4161(13) 3.9247(22) 40.055(0)
	42.1(9)	1870	hcp+fcc 19.868(28) 2.4175(15) 3.9253(26) 40.080(0)
	42.8(5)	1940	hcp+fcc	19.868(0) 2.4149(0) 3.9338(0) 40.133(10)
	42.8	2050	fcc				40.204(13)
	42.8	2090	fcc				40.216(36)
	42.8	2160	fcc				40.315(44)
	42.8	2230	fcc				40.344(43)
	42.8	2260	fcc				40.340(48)
	46.0(3)	300		hcp	18.938(15) 2.3856(9) 3.8426(15)
	50.0(6)	1050	hcp	19.020(12) 2.3882(7) 3.8507(11)
	50.3(6)	1120	hcp	19.036(10) 2.3885(5) 3.8530(9)
	50.6(5)	1230	hcp	19.068(7) 2.3890(4) 3.8579(6)

*

Acknowledgements

The synchrotron experiments were performed at ID27 ESRF. This research was supported by the European Research Council (ERC) Consolidator Grant to TK (Earth core #647723).


Sophie Massou

Filipe Nunes

Franziska Wetzel

Amine Mehidi

Dan Strehle

Cecile Leduc

Raphaël Voituriez

Olivier Rossier

Pierre , Nassoy

Grégory Giannone

Gregory Giannone
email: gregory.giannone@u-bordeaux.fr

Cell stretching is amplified by active actin remodelling to deform and recruit proteins in mechanosensitive structures

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION:

Growing evidence demonstrates that macromolecular assemblies driving critical cellular functions are regulated by mechanical forces. Mechanical tensions in cells are generated by their extracellular environment 1 , the plasma membrane [START_REF] Sinha | Cells respond to mechanical stress by rapid disassembly of caveolae[END_REF] and the cytoskeleton, including microtubules [START_REF] Dumont | Deformations within moving kinetochores reveal different sites of active and passive force generation[END_REF] , intermediate filaments [START_REF] Zhang | A tension-induced mechanotransduction pathway promotes epithelial morphogenesis[END_REF] and actin filaments [START_REF] Ladoux | Mechanobiology of collective cell behaviours[END_REF][START_REF] Iskratsch | Appreciating force and shape -the rise of mechanotransduction in cell biology[END_REF] . Among mechanosensitive structures including cadherin cell/cell adhesions [START_REF] Ladoux | Mechanobiology of collective cell behaviours[END_REF] , kinetochores [START_REF] Dumont | Deformations within moving kinetochores reveal different sites of active and passive force generation[END_REF] , caveolae [START_REF] Sinha | Cells respond to mechanical stress by rapid disassembly of caveolae[END_REF] or the nucleus [START_REF] Cho | Mechanosensing by the nucleus: From pathways to scaling relationships[END_REF] , integrin-based adhesions provide an intensively studied model [START_REF] Iskratsch | Appreciating force and shape -the rise of mechanotransduction in cell biology[END_REF][START_REF] Oria | Force loading explains spatial sensing of ligands by cells[END_REF] .

A variety of innovative techniques have been designed to measure and generate forces on proteins in vitro or within cells [START_REF] Iskratsch | Appreciating force and shape -the rise of mechanotransduction in cell biology[END_REF][START_REF] Goldyn | Forceinduced cell polarisation is linked to RhoA-driven microtubule-independent focaladhesion sliding[END_REF][START_REF] Grashoff | Measuring mechanical tension across vinculin reveals regulation of focal adhesion dynamics[END_REF][START_REF] Polacheck | Measuring cell-generated forces: A guide to the available tools[END_REF] , especially for adhesive and cytoskeletal proteins. For instance, forces applied by magnetic tweezers to purified talin, which connects integrins to the actin cytoskeleton, trigger unfolding that reveals hidden binding sites for vinculin [START_REF] Del Rio | Stretching Single Talin Rod Molecules Activates Vinculin Binding[END_REF][START_REF] Yao | The mechanical response of talin[END_REF] .

Techniques such as atomic force microscopy or optical tweezers demonstrated that forces exerted directly on proteins stabilize or destabilize interactions [START_REF] Huang | Vinculin forms a directionally asymmetric catch bond with F-actin[END_REF][START_REF] Kong | Demonstration of catch bonds between an integrin and its ligand[END_REF] . But whether those principles can be applied to proteins in the cellular context is still unclear. These techniques are also used to study biomechanical processes directly in living cells with molecular resolution [START_REF] Iskratsch | Appreciating force and shape -the rise of mechanotransduction in cell biology[END_REF][START_REF] Müller | Atomic force microscopy: A nanoscopic window on the cell surface[END_REF] .

However, they can only probe proteins on the dorsal surface of cells, and not in crowded macromolecular structures inside cells or confined at the cell interface with the extracellular environment.

Super-resolution microscopy (SRM) techniques and single protein tracking (SPT) revolutionized cell imaging. By delivering optical images with spatial resolutions below the diffraction limit of light, these techniques created possibilities to study the architecture and dynamics of biological structures at the protein level in cells [START_REF] Liu | Imaging Live-Cell Dynamics and Structure at the Single-Molecule Level[END_REF][START_REF] Sahl | Fluorescence nanoscopy in cell biology[END_REF][START_REF] Huang | Super-resolution fluorescence microscopy[END_REF][START_REF] Rossier | The journey of integrins and partners in a complex interactions landscape studied by super-resolution microscopy and single protein tracking[END_REF] . There are two major classes of SRM: stochastic approaches based on Single Molecule Localization Microscopy (SMLM: PALM, STORM, PAINT) that use time and space decorrelation of single molecules emission 17- 19 ; or targeted light-structuring techniques that control the emission states at precisely defined positions in the sample (STED, RESOLFT) [START_REF] Liu | Imaging Live-Cell Dynamics and Structure at the Single-Molecule Level[END_REF][START_REF] Sahl | Fluorescence nanoscopy in cell biology[END_REF][START_REF] Huang | Super-resolution fluorescence microscopy[END_REF] . Scrutinizing sub-cellular structures using SRM unraveled new protein organizations and showed that proteins are spatially segregated into distinct functional nano-domains. SPT techniques unveiled the correlation between protein dynamics and protein activation and/or binding states. The recent application of SRM and SPT lead to a drastic rethinking of macromolecular assemblies including cadherin-based adhesions [START_REF] Bertocchi | Nanoscale architecture of cadherin-based cell adhesions[END_REF] , axons [START_REF] Xu | Actin, spectrin, and associated proteins form a periodic cytoskeletal structure in axons[END_REF] , dendritic spines [START_REF] Nair | Super-resolution imaging reveals that AMPA receptors inside synapses are dynamically organized in nanodomains regulated by PSD95[END_REF][START_REF] Chazeau | Nanoscale segregation of actin nucleation and elongation factors determines dendritic spine protrusion[END_REF] , actin-based lamellipodium [START_REF] Mehidi | Transient Activations of Rac1 at the Lamellipodium Tip Trigger Membrane Protrusion[END_REF] and integrin-based focal adhesions (FAs) [START_REF] Kanchanawong | Nanoscale architecture of integrin-based cell adhesions[END_REF][START_REF] Rossier | Integrins β 1 and β 3 exhibit distinct dynamic nanoscale organizations inside focal adhesions[END_REF] .

Within FAs, SPT enabled to study the fast diffusive behaviors of proteins or their slow motions driven by intracellular force transmission [START_REF] Paszek | The cancer glycocalyx mechanically primes integrin-mediated growth and survival[END_REF][START_REF] Rossier | Integrins β 1 and β 3 exhibit distinct dynamic nanoscale organizations inside focal adhesions[END_REF] . SRM and SPT confirmed, together with fluorescent tension-sensors, that proteins are stretched under mechanical tension [START_REF] Grashoff | Measuring mechanical tension across vinculin reveals regulation of focal adhesion dynamics[END_REF][START_REF] Kanchanawong | Nanoscale architecture of integrin-based cell adhesions[END_REF][START_REF] Morimatsu | Molecular tension sensors report forces generated by single integrin molecules in living cells[END_REF][START_REF] Stabley | Visualizing mechanical tension across membrane receptors with a fluorescent sensor[END_REF] . For example, talin within mature FAs adopts an extended and polarized conformation (50-350 nm) with the integrin-binding site directed outward and the actin-binding sites oriented inwards [START_REF] Kanchanawong | Nanoscale architecture of integrin-based cell adhesions[END_REF] , possibly by the actin flow. Cellular force fluctuations within mature FAs were proposed to mediate substrate rigidity-sensing [START_REF] Plotnikov | Force Fluctuations within Focal Adhesions Mediate ECM-Rigidity Sensing to Guide Directed Cell Migration[END_REF] , which in turn could be correlated with talin stretchrelaxation cycles [START_REF] Margadant | Mechanotransduction in vivo by repeated talin stretch-relaxation events depends upon vinculin[END_REF] , and vinculin recruitment [START_REF] Del Rio | Stretching Single Talin Rod Molecules Activates Vinculin Binding[END_REF][START_REF] Yao | The mechanical response of talin[END_REF][START_REF] Ciobanasu | Actomyosin-dependent formation of the mechanosensitive talin-vinculin complex reinforces actin anchoring[END_REF] . However, the molecular rules underlying mechano-sensing in integrin-based adhesions or other mechano-sensitive structures are hidden by complex spatiotemporal force patterns generated by the cell. One way to decipher those rules is to actively apply external stretch to cells while monitoring with SRM and SPT the nanoscale reorganizations and deformations of protein assembly or individual proteins inside mechanosensitive structures.

RESULTS

Combining cell stretching with super resolution microscopy or single molecule tracking

Stretchable substrates of Polydimethylsiloxane (PDMS) have been coupled with optical imaging to investigate cell responses to external forces [START_REF] Sinha | Cells respond to mechanical stress by rapid disassembly of caveolae[END_REF][START_REF] Goldyn | Forceinduced cell polarisation is linked to RhoA-driven microtubule-independent focaladhesion sliding[END_REF][START_REF] Chen | Orientation-specific responses to sustained uniaxial stretching in focal adhesion growth and turnover[END_REF] . However, the simultaneous combination of SRM/SPT and cell stretching has never been achieved due to technical limitations (see Extended Discussion). Here, we designed a micromechanical device composed of an ultra-thin PDMS layer (10 µm) providing glass-like optical properties compatible with SRM/SPT (Fig. 1,2). To simultaneously perform substrate stretching and ensure flatness upon deformation, the PDMS sheet was gliding on a glycerol-lubricated glass cover-slip (Figure 1a,b). To generate uniaxial stretch, we designed a 3D-printed micromechanical device composed of a fixed holding arm and a mobile arm connected to a piezoelectric translator (Fig. 1a and Supplementary Video 1). Controlled and homogeneous strain was achieved over the entire observation chamber for deformations up to 90%, as demonstrated both numerically and experimentally (Extended Data Fig. 1 and Supplementary Video 2).

Then we demonstrated that our stretching device is compatible with the two major classes of SRM: coordinate stochastic (SMLM) and coordinate targeted (e.g. STED/RESOLFT). We used cytoskeleton structures that control cell shape and reorganize during external cell stretching, while serving as gold standards for SRM in cell biology. We acquired low resolution epifluorescence images, before live large stretching (30-50 %) followed by rapid cell fixation (Fig. 1c). Cells were labelled for SRM and imaged after stretching, first at low resolution and then with SRM. Our strategy allowed to acquire long lasting acquisitions required to obtain DNA-PAINT [START_REF] Schnitzbauer | Super-resolution microscopy with DNA-PAINT[END_REF] super-resolution images of vimentin intermediate filaments after live stretching of Mouse embryonic fibroblasts (MEFs) spread on fibronectin coated PDMS (Fig. 1d,e, Extended Data Fig. 2). We could also perform STED [START_REF] Sahl | Fluorescence nanoscopy in cell biology[END_REF] SRM of microtubules after live stretching, fixation and labelling (Fig. 1f,g, Extended Data Fig. 2). In addition, we demonstrated that our stretching device could be used to acquire STED images of live cells that experience stretching, using live labelling with SiR-tubulin and SiR-actin [START_REF] Lukinavičius | Fluorogenic probes for live-cell imaging of the cytoskeleton[END_REF] (Extended Data Fig. 2). These results prove that our stretching device is compatible with the two main modalities of SRM, enabling to obtain state of the art super-resolved images of protein reorganization after stretching.

Then, we tested whether our stretching device allowed to localize photo-activatable fluorescent proteins (e.g. mEos2, PA-GFP), which possess lower photon budgets reducing localization precision [START_REF] Dempsey | Evaluation of fluorophores for optimal performance in localization-based super-resolution imaging[END_REF] , compared to synthetic dyes used for PAINT and STORM (e.g. ATTOdyes, Cy-dyes, Alexa-dyes). This design enabled to localize individual purified mEos2 and to perform live Photo-activated localization microscopy (PALM) as well as single protein tracking PALM (sptPALM) acquisitions in cells with resolutions comparable to glass [START_REF] Rossier | Integrins β 1 and β 3 exhibit distinct dynamic nanoscale organizations inside focal adhesions[END_REF][START_REF] Betzig | Imaging intracellular fluorescent proteins at nanometer resolution[END_REF] (Extended Data Fig. 3). We generated live PALM (Fig. 2a,b) and SPT (Fig. 2a,c) before and after stretching of MEFs expressing β3-integrin-mEos2 and paxillin-GFP. Large stretching ( 30 %) induced FAs expansion, as reported by paxillin-GFP images (Fig. 2d). Importantly, the area of β3-integrin-mEos2 immobilizations grew accordingly to FAs expansion (Fig. 2b). Mechanical activation of integrins should lead to increased immobilization inside and outside FAs [START_REF] Paszek | The cancer glycocalyx mechanically primes integrin-mediated growth and survival[END_REF][START_REF] Kong | Demonstration of catch bonds between an integrin and its ligand[END_REF][START_REF] Rossier | Integrins β 1 and β 3 exhibit distinct dynamic nanoscale organizations inside focal adhesions[END_REF][START_REF] Friedland | Mechanically activated integrin switch controls alpha5beta1 function[END_REF] .

However, the fraction of immobile β3-integrin was similar before and after stretching (Fig. 2c,e,f), suggesting that force-induced integrin activation dissipates rapidly after stretching. In conclusion, the stretchable elastic substrate we designed is compatible with SRM and SPT and enables to investigate at the nanoscale the overall changes induced by mechanical forces.

The acute mechanical response of β3-integrins to external forces is elastic.

Assessing the acute mechanical response of proteins to force required maintaining the cell strictly in focus and in the field of observation during stretching. To compensate for the XYZ displacements, we used an autofocus system (Z) and manual or automated stage repositioning (XY). To test the strain homogeneity at nanometer scales, we tracked fluorescent beads adsorbed on the PDMS during trapeze-like patterns, composed of stretch-plateau-relax phases (Fig. 3a). All images were registered on an arbitrarily chosen origin bead, seen as immobile in super-resolved time-lapses [START_REF] Rossier | Integrins β 1 and β 3 exhibit distinct dynamic nanoscale organizations inside focal adhesions[END_REF] . Bead displacements, measured from kymographs, increased proportionally with the distance to the origin bead (Fig. 3b), attesting for the purely elastic and homogeneous response of our device. Accordingly, these displacements could be superimposed after normalization on the position of any given reference bead (Fig. 3c).

Likewise, we could extrapolate PDMS displacements at any given positions in the observation field (Figure 3c). Live XYZ repositioning was possible up to 6 % stretching. These performances allowed us to perform an in-depth investigation of the mechanical response of individual proteins during adhesion mechano-sensing, which has been reported to occur between 2 % and 10 % stretching [START_REF] Chen | Orientation-specific responses to sustained uniaxial stretching in focal adhesion growth and turnover[END_REF][START_REF] Cui | Cyclic stretching of soft substrates induces spreading and growth[END_REF] .

Using SPT, we previously measured integrins, actin and talin displacements driven by intracellular force transmission in mature FAs [START_REF] Rossier | Integrins β 1 and β 3 exhibit distinct dynamic nanoscale organizations inside focal adhesions[END_REF] . We demonstrated that β3-integrins are stationary within FAs, while most actin filaments are moving rearward (2-10 nm.s -1 ). Here we applied trapeze-like patterns to MEFs co-transfected with β3-integrin-mEos2 and paxillin-GFP (Fig. 3d-f, Supplementary Video 3). We then generated super-resolved time-lapses at 2 Hz to analyze the acute mechanical response of individual β3-integrins in and out FAs. The displacement pattern of integrins mirrored the shape of the trapeze-like substrate deformation (Fig. 3d, Supplementary Video 4,5). In addition, after normalization on a reference bead (Fig. 3e) the mean response was superimposed on the displacement of the stretchable substrate.

Reciprocally, because the PDMS substrate is purely elastic and the deformation is homogeneous (Fig. 3c and Extended Data Fig. 1), we could extrapolate the theoretical displacements of the substrate at the position of each integrin. In this reference frame the mean local displacement of β3-integrin-mEos2 was similar to the PDMS (Fig. 3f). Thus, integrin displacements closely followed the elastic displacements of the substrate (Fig. 3g). This indicates that most stationary integrins in and out FAs remained connected to fibronectin when challenged mechanically by stretching (2-5 %). Furthermore, this allowed us to test whether proteins mediating a dynamic mechanical coupling of integrins to F-actin [START_REF] Hu | Differential transmission of actin motion within focal adhesions[END_REF] follow or deviate from the elastic behavior of integrins.

The inelastic mechanical response of talin to external forces correspond to talin unfolding.

Among proteins that compose this mechanical coupling talin is critical since it activates integrins, directly connects them to F-actin and supports integrin force-sensing [START_REF] Del Rio | Stretching Single Talin Rod Molecules Activates Vinculin Binding[END_REF][START_REF] Yao | The mechanical response of talin[END_REF][START_REF] Jiang | Twopiconewton slip bond between fibronectin and the cytoskeleton depends on talin[END_REF][START_REF] Giannone | Talin1 is critical for force-dependent reinforcement of initial integrin-cytoskeleton bonds but not tyrosine kinase activation[END_REF][START_REF] Calderwood | Talins and kindlins: partners in integrin-mediated adhesion[END_REF] . Using SPT we previously showed that a large fraction of F-actin (74 %) is moving rearward compared to talin (25 %) and β3-integrins (8 %) [START_REF] Rossier | Integrins β 1 and β 3 exhibit distinct dynamic nanoscale organizations inside focal adhesions[END_REF] . These findings suggest that stationary talins are bound to stationary β-integrins in FAs, probably via their amino terminal FERM domain [START_REF] Calderwood | Talins and kindlins: partners in integrin-mediated adhesion[END_REF] . But whether these talins are also simultaneously connected to F-actin via carboxy terminal actinbinding sites, fully extended or prompt to be extended by external forces is unknown. To test the mechanical status of individual talins, we applied trapeze-like patterns to MEFs transfected with talin tagged with tdEOS at the carboxy (talin-C) or amino (talin-N) terminus (Fig. 4). A fraction of individual talin-C (35 %) mirrored the deformation of the substrate (Fig. 4a,b,d).

The average talin-C response was superimposed on substrate displacement after bead normalization (Fig. 4b) and the mean local displacement was close to PDMS displacement (Fig. 4e). Thus, like integrins, a subset of Talin-C displayed an elastic behavior. Importantly, a larger fraction of Talin-C (65 %) exhibited a complex displacement incompatible with an elastic response (Fig. 4a,c,d, Supplementary Video 6,7). Immediately after interruption of the stretching, during the plateau phase, Talin-C movements persisted towards the cell center, as shown by the measured arched-shaped kymographs. After reaching their maximal amplitude and before the relaxation, talin-C recoiled back towards the cell periphery (Fig. 4a,c). These inelastic, lagged and transient displacements were not due to atypical strains of the stretchable substrate, since elastic and inelastic responses could occur within very short distances (Fig. 4a, Supplementary Video 6). Bead normalization showed that the inelastic displacements overshot the expected elastic displacements (Fig. 4c). These deviations from the elastic regime caused additional local displacements (330 ± 30 nm), which we measured by subtracting the theoretical displacement of the elastic substrate at positions of detected Talin-C (Fig. 4e). Talin stretching should translate into distinct responses of Talin-C versus Talin-N, because they respectively bind F-actin and integrins (Fig. 4f). Like talin-C, talin-N displayed elastic and inelastic responses to trapeze-like patterns (Extended Data Fig. 4). However, in contrast to talin-C, the fraction of elastic responses (72 %) was higher compared to inelastic responses (28 %) (Fig. 4d), reflecting binding to integrins.

Like talin-C, the C-terminal domain of talin (mEos2-talin-THATCH) which binds and flows with actin in the same upper layer in FAs [START_REF] Kanchanawong | Nanoscale architecture of integrin-based cell adhesions[END_REF][START_REF] Rossier | Integrins β 1 and β 3 exhibit distinct dynamic nanoscale organizations inside focal adhesions[END_REF] , displayed a larger fraction of inelastic response (Fig. 4d). This suggests that inelastic responses of talin depend on displacements of the actin cytoskeleton. To test this hypothesis, we applied the same trapeze-like patterns to MEFs transfected with actin-mEos2 (Fig. 5). Actin-mEos2 mechanical responses were also partitioned between elastic and inelastic displacements (Fig. 5a-d, Supplementary Video 8).

Like Talin-C, inelastic displacements (62 %) were predominant over elastic ones (Fig. 5d). The average elastic response of actin-mEos2 was superimposed on substrate displacement after bead normalization (Fig. 5b,e). In addition, amplitudes of the local extra displacements measured for the inelastic responses were in the same range as talin displacements (260 ± 20 nm) (Fig. 5c,e).

The characteristic rise time of inelastic responses for actin-mEos2 (1.6 ± 0.1 s) and talin-C (1.7 ± 0.1 s) was similar, and corresponded to maximal instantaneous displacement rates ( 100 nm.s -1 ) faster than the flow of talin or actin in adhesive structures or the lamella ( 5-10 nm.s - 1 ) [START_REF] Rossier | Integrins β 1 and β 3 exhibit distinct dynamic nanoscale organizations inside focal adhesions[END_REF][START_REF] Hu | Differential transmission of actin motion within focal adhesions[END_REF] , suggesting that the actin flow is not driving inelastic responses. In order to compare the rise time from the recoil time, we applied single stretch-plateau patterns to examine the recoil phase independently from the relaxation (Extended Data Fig. 5, and Extended Discussion). The characteristic recoil time of actin-mEos2 was longer (4.6 ± 0.6 s) than the rise time, suggesting that they were triggered by distinct mechanisms. Overall, talin-N displayed mechanical responses similar to integrins, while talin-C behaves like the actin cytoskeleton. These results indicate that a significant fraction of inelastic displacements for talin-C correspond to talin stretching. Importantly, amplitudes of local extra displacements ( 200-300 nm) are in agreement with talin extension lengths measured in vitro [START_REF] Yao | The mechanical response of talin[END_REF] . Thus, our results suggest that molecular displacements induced by small (2-5 %) cell stretching are transiently ( 5 s) and locally amplified by the inelastic response of F-actin, hence triggering talin unfolding.

Transient and active remodeling of the acto-myosin network drives the inelastic response of actin.

Deviations from purely elastic responses, and in particular arched-shaped displacements during the plateau phase (Fig. 5g), could either reflect the passive viscoelastic properties of the cell, which can induce lagged responses in both rising and recoil phases, or an active cell response [START_REF] Trepat | Universal physical responses to stretch in the living cell[END_REF][START_REF] Mizuno | Nonequilibrium mechanics of active cytoskeletal networks[END_REF][START_REF] Gardel | Elastic behavior of cross-linked and bundled actin networks[END_REF][START_REF] Bausch | Local measurements of viscoelastic parameters of adherent cell surfaces by magnetic bead microrheometry[END_REF] . On general grounds a cell can be modeled as a mechanical transducer composed of several elements, which is locally pinned to the elastic PDMS via integrins. If the cell is homogenously elastic (Fig. 5g), 3 % stretch would result in minute local extra displacements (x) of talin, inconsistent with domain unfolding [START_REF] Del Rio | Stretching Single Talin Rod Molecules Activates Vinculin Binding[END_REF][START_REF] Yao | The mechanical response of talin[END_REF] (e.g. talin initial length 50 nm; x = 1.5 nm). Assuming that the cell is heterogeneously elastic (Fig. 5g) and composed of softer elements (e.g. talin) in series with stiffer elements (e.g. integrin and actin), it is found that under an imposed strain, the softer elements will undergo larger displacements than their corresponding reference point in the underlying homogeneous substrate. Deformation of talin from 50 nm to the measured  300 nm corresponds to an effective strain of  600 %, which implies a cell composed of 99.5 % rigid versus soft elements (see Extended Discussion). Thus, extra displacements of  200-300 nm (Fig. 4e,5e) could be attributed to a passive mechanism only if the cell is essentially unable to deform. However, micro-rheology studies demonstrate that cells could be rapidly deformed [START_REF] Trepat | Universal physical responses to stretch in the living cell[END_REF][START_REF] Desprat | Creep function of a single living cell[END_REF][START_REF] Wu | A comparison of methods to assess cell mechanical properties[END_REF] . This suggests that large effective strains cannot be attributed solely to passive effects, but involve an active contraction of actin structures in response to imposed strains (Fig. 5g).

To test whether an active process generated by the cell drives the inelastic displacements of actin, we performed the same experiments in fixed and permeabilized cells (Fig. 5 and Extended Data Fig. 6). This treatment transforms the actin cytoskeleton into a non-dynamic cross-linked network, preventing reorganization of actin cross-linkers, active actin polymerization or active contraction by myosin motors. Fixation/permeabilization decreased the fraction and mean amplitude of actin-mEos2 inelastic responses (Fig. 5d,e and Extended Data Fig. 6), supporting that they are driven by a dynamic or active response of the cell.

Inhibition of myosin II, using para-Nitroblebbistatin [START_REF] Várkuti | A highly soluble, non-phototoxic, non-fluorescent blebbistatin derivative[END_REF] , also decreased the fraction and mean amplitude of actin-mEos2 inelastic responses (Fig. 5d,e and Extended Data Fig. 6), suggesting that forces generated by myosin II on actin filaments actively drives these displacements (Fig. 5g).

Molecular vinculin recruitment is delayed and depends on the maturation state of integrin-based adhesions

Until here, we applied cell stretching combined with SRM/SPT to study forcedependent protein unfolding or deformations. Next we tested whether our approach could be used to study protein reorganizations within mechano-sensitive structures during external stress (Fig. 6; Fig. 7). We used as a paradigm the force-dependent recruitment of protein inside integrin-based adhesions. Within FAs, the association of proteins containing the zinc-fingertype LIM domain is particularly sensitive to mechanical tension [START_REF] Schiller | Mechanosensitivity and compositional dynamics of cellmatrix adhesions[END_REF][START_REF] Horton | Definition of a consensus integrin adhesome and its dynamics during adhesion complex assembly and disassembly[END_REF] . The recruitment of LIM proteins zyxin and paxillin to FAs is induced by cell stretching [START_REF] Chen | Orientation-specific responses to sustained uniaxial stretching in focal adhesion growth and turnover[END_REF][START_REF] Sawada | Force transduction by Triton cytoskeletons[END_REF][START_REF] Hirata | Mechanical forces facilitate actin polymerization at focal adhesions in a zyxin-dependent manner[END_REF] . We applied  4 % trapezelike patterns to MEFs co-transfected with zyxin-mEos3.2 and paxillin-GFP (Fig. 6a,b, Supplementary Video 9). To measure the acute zyxin-mEos3.2 molecular recruitment in mature FAs, we quantified the density of trajectories (trc/µm 2 ) before, during, and after the stretching plateau (Fig. 6c). Cell stretching triggered an increase in zyxin-mEos3.2 trajectories in mature FAs for 50 % (4/8) of the cells, while the remaining cells displayed no detectable variations. This recruitment was reversible since cell relaxation resulted in a decrease of trajectories to levels found before stretching (Fig. 6c). Zyxin molecular recruitment analyzed from kymographs or color-coding of super-resolved time-lapses (2 Hz) did not show obvious zyxin association in selective FAs regions (tip, center, rear) (Fig. 6d,e). Force-induced talin unfolding exposes vinculin binding sites, as demonstrated at the single molecule and ensemble level in in vitro system using purified proteins [START_REF] Del Rio | Stretching Single Talin Rod Molecules Activates Vinculin Binding[END_REF][START_REF] Yao | The mechanical response of talin[END_REF][START_REF] Ciobanasu | Actomyosin-dependent formation of the mechanosensitive talin-vinculin complex reinforces actin anchoring[END_REF] . Furthermore, vinculin turnover within integrin-based adhesions is tuned by mechanical forces [START_REF] Dumbauld | How vinculin regulates force transmission[END_REF][START_REF] Rothenberg | Vinculin Force-Sensitive Dynamics at Focal Adhesions Enable Effective Directed Cell Migration[END_REF] . Hence, we tested whether acute vinculin recruitment in mature FAs is triggered by external forces. We applied ~ 4% trapeze-like patterns to MEFs co-transfected with vinculin-mEos3.2 and paxillin-GFP (Fig. 6f,g). In contrast to zyxin, the density of vinculin trajectories during the stretching plateau did not increase significantly in mature FAs (0/7 cells) (Fig. 6h). The same result was found after larger stretches (~ 10 %) (0/5 cells) (Extended Data Fig. 7). One possible interpretation for this surprising result is that force-dependent recruitment occurs simultaneously with force-dependent dissociation, as demonstrated in vitro [START_REF] Yao | The mechanical response of talin[END_REF][START_REF] Yao | Mechanical activation of vinculin binding to talin locks talin in an unfolded conformation[END_REF] . Alternatively, force-induced vinculin recruitment could depend on the maturation state of integrin-based adhesions.

Consistent with the latter hypothesis, initiation and maturation of nascent adhesions (NAs) depend on forces generated on early integrin-talin-actin connections [START_REF] Giannone | Talin1 is critical for force-dependent reinforcement of initial integrin-cytoskeleton bonds but not tyrosine kinase activation[END_REF][START_REF] Zhang | Talin depletion reveals independence of initial cell spreading from integrin activation and traction[END_REF] triggering vinculin recruitment [START_REF] Giannone | Talin1 is critical for force-dependent reinforcement of initial integrin-cytoskeleton bonds but not tyrosine kinase activation[END_REF][START_REF] Galbraith | The relationship between force and focal complex development[END_REF] and connection to F-actin flows [START_REF] Grashoff | Measuring mechanical tension across vinculin reveals regulation of focal adhesion dynamics[END_REF][START_REF] Thievessen | Vinculin-actin interaction couples actin retrograde flow to focal adhesions, but is dispensable for focal adhesion growth[END_REF] . Thus, we performed experiments on NAs which form in protrusive structures of spreading and migrating cells [START_REF] Giannone | Lamellipodial actin mechanically links myosin activity with adhesion-site formation[END_REF][START_REF] Choi | Actin and alpha-actinin orchestrate the assembly and maturation of nascent adhesions in a myosin II motor-independent manner[END_REF] . We applied ~ 4% trapeze-like patterns to spreading MEFs co-transfected with vinculin-mEos2 and paxillin-GFP (Fig. 7a,b, Supplementary Video 11). By contrast with mature FAs, the density of vinculin-mEos2 trajectories in NAs increased in ~ 70 % (7/10) of the analyzed cells (Fig. 7c). Cell relaxation induced a reduction of trajectories but still above the levels measured before stretching (Fig. 7c). The density of talin-C trajectories in NAs did not exhibit large increase upon stretching (responding cells: 28 %; 2/7) (Fig. 7j), suggesting that vinculin recruitment occurs mainly on talin residing in NAs, and not by the recruitment of additional talin.

Furthermore, the fraction of talin-C displaying inelastic responses in NAs was similar to the one observed for mature FAs (Extended Data Fig. 8). Importantly, molecular vinculin-mEos2 recruitment did not reach its maximum immediately after stretching, but progressively or transiently increased during the plateau phase (Fig. 7f). This delayed vinculin recruitment in response to stretch is consistent with the lagged talin-C inelastic response occurring during the plateau (Fig. 4, Extended Data Fig. 8) and associated with talin unfolding (Fig. 4). Kymographs analysis and color-coding of super-resolved time-lapses revealed no region-selective recruitment of vinculin-mEos2 in NAs (Fig. 7d,e; Extended Data Fig. 9).

Discussion

A molecular understanding of mechano-sensing has emerged from in vitro mechanical manipulations of proteins [START_REF] Del Rio | Stretching Single Talin Rod Molecules Activates Vinculin Binding[END_REF][START_REF] Yao | The mechanical response of talin[END_REF][START_REF] Huang | Vinculin forms a directionally asymmetric catch bond with F-actin[END_REF] . These studies performed by applying force on purified proteins showed that mechano-sensing relies on protein unfolding and reorganization. The general consensus is that external stresses applied to cells are directly and instantaneously transmitted to proteins to trigger their deformation and reorganization in mechano-sensitive structures.

However, no experimental strategies were able to apply external forces to cells while simultaneously capturing the mechanical response of individual proteins. Here, by combining cell stretching with SRM and SPT, we could reveal at the nanoscale the mechanical response of mechano-sensitive structures. This provides the opportunity to study how polarized macromolecular complexes, composed of distinct functional nano-domains [START_REF] Xu | Actin, spectrin, and associated proteins form a periodic cytoskeletal structure in axons[END_REF][START_REF] Chazeau | Nanoscale segregation of actin nucleation and elongation factors determines dendritic spine protrusion[END_REF][START_REF] Kanchanawong | Nanoscale architecture of integrin-based cell adhesions[END_REF] , reorganize upon external stretch.

We found that protein deformations inside integrin-based adhesions are not triggered by direct transmission of the external stretch. Upon small (2-5%) stretching, actin filaments and talin displayed both elastic and inelastic responses. The inelastic responses lead to transient ( 5 s) and local displacements ( 250 nm) associated with talin deformations, as suggested by the larger fraction of inelastic responses for talin-C compared to talin-N. These distinct responses could also be interpreted as talin cleavage by calpain in integrin-based adhesions, a process triggering FAs disassembly [START_REF] Franco | Calpain-mediated proteolysis of talin regulates adhesion dynamics[END_REF] or NAs growth [START_REF] Saxena | Force-Induced Calpain Cleavage of Talin Is Critical for Growth, Adhesion Development, and Rigidity Sensing[END_REF] . Importantly, inelastic responses were decreased by cell fixation and myosin II inhibition, indicating a mechanism driven by active remodeling of the actin cytoskeleton. Thus, cells actively react to external forces, amplifying transiently and locally actin cytoskeleton displacements to trigger protein deformation in mechanosensitive structures.

The inelastic responses of the actin cytoskeleton and talin could also involve local ruptures of the actin cystoskeleton, in particular actin stress fibers (SFs). SFs are repaired by recruitment of actin binding proteins including zyxin, α-actinin, and VASP [START_REF] Smith | A zyxin-mediated mechanism for actin stress fiber maintenance and repair[END_REF][START_REF] Smith | LIM Domains Target Actin Regulators Paxillin and Zyxin to Sites of Stress Fiber Strain[END_REF] . Likewise, stimulation of myosin II contractility, using optogenetic activation of RhoA, leads to local recruitment of zyxin to SFs [START_REF] Oakes | Optogenetic control of RhoA reveals zyxin-mediated elasticity of stress fibres[END_REF] . Thus, zyxin-mediated SFs repair or mechanical homeostasis might be involved in inelastic responses. However, we showed that  4 % stretching did not cause major SFs ruptures or recruitment of zyxin and α-actinin to SFs (Extended Data Fig. 10, and Extended Discussion). Therefore, rupture/repair events are rare during ~ 4 % stretching and thus could not account for the inelastic responses of talin and actin. Nevertheless, micron-scale SFs homeostasis triggered by cell contractility [START_REF] Oakes | Optogenetic control of RhoA reveals zyxin-mediated elasticity of stress fibres[END_REF] and the inelastic responses of actin and talin could have common molecular players although at different spatiotemporal scales.

At the molecular level, mechanical force could reinforce [START_REF] Huang | Vinculin forms a directionally asymmetric catch bond with F-actin[END_REF][START_REF] Kong | Demonstration of catch bonds between an integrin and its ligand[END_REF][START_REF] Friedland | Mechanically activated integrin switch controls alpha5beta1 function[END_REF][START_REF] Giannone | Talin1 is critical for force-dependent reinforcement of initial integrin-cytoskeleton bonds but not tyrosine kinase activation[END_REF] or destabilize [START_REF] Sinha | Cells respond to mechanical stress by rapid disassembly of caveolae[END_REF][START_REF] Jiang | Twopiconewton slip bond between fibronectin and the cytoskeleton depends on talin[END_REF] interactions and expose hidden binding sites fostering protein recruitment, as demonstrated for integrin-based [START_REF] Del Rio | Stretching Single Talin Rod Molecules Activates Vinculin Binding[END_REF][START_REF] Yao | The mechanical response of talin[END_REF][START_REF] Ciobanasu | Actomyosin-dependent formation of the mechanosensitive talin-vinculin complex reinforces actin anchoring[END_REF] and cadherin-based [START_REF] Yonemura | alpha-Catenin as a tension transducer that induces adherens junction development[END_REF] adhesions. Combining cell stretching with SRM or SPT yields molecular resolution on protein reorganization which can be spatially and temporally heterogeneous within mechano-sensitive structures. For instance, molecular vinculin recruitment induced by stretching is delayed and depends on the maturation state of the integrin-talin-cytoskeleton connections. This supports the hypothesis that substrate stretching is not directly driving talin unfolding. Instead, our results would be consistent with a model where external stresses applied to cells trigger subsequent cellular active responses, e.g. active actin reorganization, leading to protein unfolding and recruitment. The ability of talin to recruit vinculin might depend on its force history and initial tensional state, which might differ in NAs versus FAs [START_REF] Ringer | Multiplexing molecular tension sensors reveals piconewton force gradient across talin-1[END_REF] . This is consistent with experiments performed in vitro using purified talin rod domains and vinculin. Vinculin-unloaded talin recruits vinculin upon an initial stretch, while vinculin-loaded talin will still be stretched by external forces without recruitment of additional vinculin [START_REF] Yao | The mechanical response of talin[END_REF][START_REF] Yao | Mechanical activation of vinculin binding to talin locks talin in an unfolded conformation[END_REF] . Larger stretching of already extended talin might further unfold vinculin binding domains leading to vinculin dissociation [START_REF] Yao | The mechanical response of talin[END_REF][START_REF] Yao | Mechanical activation of vinculin binding to talin locks talin in an unfolded conformation[END_REF] . Thus the undetectable molecular recruitment of vinculin in mature FAs might be explained by simultaneous recruitment and dissociation upon cell stretching. By contrast, newly recruited talin into NAs might be in lower tensional sates, free from any previous stretching, with all vinculin binding sites available for vinculin recruitment to trigger maturation to FAs. This idea is consistent with the axial redistribution of vinculin observed in NAs using tridimensional SRM iPALM in fixed cells [START_REF] Case | Molecular mechanism of vinculin activation and nanoscale spatial organization in focal adhesions[END_REF] .

Micro-rheology studies have demonstrated that mechanical stability of actin networks relies on their elastic properties which are prevalent at short time-scale. Conversely, remodeling occurs through inelastic or non-linear responses leading to stress stiffening or weakening over timescales of seconds to tens of seconds [START_REF] Trepat | Universal physical responses to stretch in the living cell[END_REF][START_REF] Mizuno | Nonequilibrium mechanics of active cytoskeletal networks[END_REF][START_REF] Gardel | Elastic behavior of cross-linked and bundled actin networks[END_REF] . However, conventional micro-rheology methods average over any heterogeneity, inelasticity and time fluctuations occurring at the molecular level. Combining cell stretching and SRM/SPT, our approach paves the way to nano-rheology of the cell. We have captured the excitable nature of the acto-myosin cytoskeleton at the nanoscale, which transiently amplifies displacements induced by extracellular forces, leading to local protein stretching and recruitment. Thus, our findings suggest that mechano-sensing must occur within a few seconds, during the local displacement amplification. Substrate mechano-sensing could be mediated by fluctuations of intracellular and extracellular forces [START_REF] Goldyn | Forceinduced cell polarisation is linked to RhoA-driven microtubule-independent focaladhesion sliding[END_REF][START_REF] Plotnikov | Force Fluctuations within Focal Adhesions Mediate ECM-Rigidity Sensing to Guide Directed Cell Migration[END_REF][START_REF] Cui | Cyclic stretching of soft substrates induces spreading and growth[END_REF] , hence the transient nature of this amplification might reset the capability of the cell to respond to successive mechanical stimuli. Spatiotemporal force fluctuation in FAs [START_REF] Plotnikov | Force Fluctuations within Focal Adhesions Mediate ECM-Rigidity Sensing to Guide Directed Cell Migration[END_REF] probably emerges from the heterogeneous tensional/connective states of proteins at the nanoscale [START_REF] Oria | Force loading explains spatial sensing of ligands by cells[END_REF] . Each stationary protein detected by conventional SRM/SPT conceals its tensional and connectional states, which we unveiled by challenging proteins through a uniform mechanical perturbation.

We expect that our approach will be applied to decipher at the molecular level the growing number of mechano-sensitive structures or organelles such as caveolae 2 , kinetochores [START_REF] Dumont | Deformations within moving kinetochores reveal different sites of active and passive force generation[END_REF] , hemidesmosomes [START_REF] Zhang | A tension-induced mechanotransduction pathway promotes epithelial morphogenesis[END_REF] or the nucleus [START_REF] Cho | Mechanosensing by the nucleus: From pathways to scaling relationships[END_REF] .

Supplementary Information:

Methods

Extended Data Figures

Extended Data Figure 1. Mechanical properties of the stretchable substrate compatible with SRM and SPT. Extended Data Figure 2. The stretchable elastic substrate enables to acquire SRM images of cellular structures deeper into the cells and live STED images on cells that experience stretching. Extended Data Figure 3 a, Schematic representation of the experimental workflow. Cells were co-transfected with proteins of FAs fused with photoactivatable/photoconvertible fluorescent proteins (e.g. mEos2, mEos3.2) and a reporter of FAs (e.g. paxillin-GFP). Low resolution epifluorescence images were acquired live before and after large stretching (30-50 %). Sequences of live SRM or SPT could be acquired before and after stretching. b, Super-resolution intensity images of β3integrin-mEos2 in MEFs before (left) and after (right) a 34% stretch (image acquisition rate 50 Hz, duration > 240 s). Outlines correspond to FAs, labelled by GFP-paxillin (greyscale), before (green) and after (magenta) stretching. Scale bar, 5 µm. Fluorescent beads adsorbed on the stretching chamber were used to measure PDMS deformation. c, Corresponding color-coded trajectories before (left) and after (right) the 34% stretch, overlaid on FAs labelled by GFPpaxillin (greyscale), showing the diffusion modes: free diffusion (magenta), confined diffusion (green) and immobilization (red) (right). Scale bars, 5 µm. d, Corresponding low resolution image of GFP-paxillin before (green) and after (magenta) the 34 % stretch. Scale bar, 5 µm. e, Distributions of the diffusion coefficient D computed from mEos2-β3-integrin trajectories inside (left) and outside (right) FAs, before (green) and after (magenta)  30 % stretches. D values inferior to 0.017 µm 2 .s -1 corresponds to immobilized proteins. Values represent the average of the distributions obtained from 5 different cells (see Supplementary Table 2). f, Fraction of proteins undergoing free diffusion, confined diffusion or immobilization inside (left) and outside (right) FAs before (green) and after (magenta)  30 % stretching. Values represent the average of the fractions obtained from 5 different cells (see Supplementary table 2; mean ± s.e.m. for cells). b-d, Data are representative of 5 independent experiments. e-f, All results for each condition correspond to pooled data from 5 independent experiments (cells/trajectories): before stretch (5/4643), after stretch (5/3071). Statistical significances were obtained using twotailed paired Student's t-tests. a, Schematic representation of PDMS mechanical response to trapeze-like patterns (right direction). The origin bead (white) is used for registration and the reference bead (magenta) is used for displacement and position normalizations. b, Mechanical response of a 10 µm PDMS assembly during a trapeze-like pattern measured using adsorbed fluorescent beads. Projection of all the images of a super-resolved time-lapse (stretching 3.7 %, 2 Hz, 40 s) (top). Positions on the PDMS of the origin bead (white), the reference bead (magenta), and two other beads (green, orange). Scale bar, 5 µm. Bead displacements were measured using kymographs (bottom) generated from the super-resolved time-lapse. Horizontal axis, space (500 nm); vertical axis, time (10 s). c, Displacement versus time plot for the beads corresponding to b (left). Displacement versus time plot for the orange and green beads after normalization to the initial position of magenta reference bead (middle). Displacement versus time plot for magenta bead after normalization to the initial positions of orange or green beads (right). Same procedure was applied to individual mEos2 labelled proteins (see e and f). d, Fluorescence image of paxillin-GFP in a MEF on the PDMS stretching device before stretching (up left). Projection of all β3-integrin-mEos2 super-resolution intensity images of a trapeze-like pattern time-lapse (stretching 2 %, 2 Hz, 40 s) (bottom left). Scale bar, 5 µm. Right, β3-integrin-mEos2 kymographs generated from the trapeze-like pattern time-lapse (as shown in the left panels, dashed lines). Horizontal axis, space (500 nm); vertical axis, time (5 s). The magenta kymograph corresponds to the reference bead, and the green kymographs correspond to β3integrin-mEos2. In between signal intermittencies result from on-off blinking characteristic of single mEos2 molecules. e, Displacement versus time plot for β3-integrin-mEos2 (green lines) after normalization to the initial position of the reference bead (magenta line) (up). Mean displacement ± SEM (bottom). f, Box plots displaying the median (line) and mean (square) ± percentile (25%-75%) of local displacements for β3-integrin-mEos2 after subtraction of the extrapolated PDMS displacements, using the magenta bead after normalization to the initial positions of each β3-integrin-mEos2. The same procedure was applied for beads adsorbed on PDMS, as displayed in c. e,f, Data pooled from 3 independent experiments (see Supplementary Table 3): β3-integrin-mEos2 (n = 3 independent experiments, 51 kymographs); beads (n = 3 independent experiments, 52 kymographs). g, Schematic representation of the acute mechanical response of β3-integrin. Statistical significances were obtained using two-tailed unpaired Student's t-tests. a, Fluorescence image of paxillin-GFP in a MEF on the PDMS stretching device before stretching (right direction) (up left). Projection of all talin-C-tdEos super-resolution intensity images of a trapeze-like pattern time-lapse (stretching 3.7 %, 2 Hz, 40 s) (bottom left). Scale bar, 5 µm. Right, talin-C-tdEos kymographs generated from the trapeze-like pattern time-lapse (as shown in the left panels, dashed lines). Horizontal axis, space (500 nm); vertical axis, time (5 s). The magenta kymograph corresponds to the reference bead, and the green kymographs correspond to talin-C-tdEos. b, Displacement versus time plot for elastic responses of talin-C-tdEos (green lines) after normalization to the initial position of the magenta reference bead (magenta line) (up). Corresponding mean displacement ± SEM (bottom). c, Same as b for inelastic responses of talin-C-tdEos. d, Fractions of elastic and inelastic responses inside and outside FAs for β3-integrin-mEos2, tdEos-talin-N, talin-C-tdEos, mEos2-talin-THATCH. Values represent the average of fractions obtained from at least three independent experiments (see Supplementary table 3; mean ± s.e.m. for cells). e, Box plots displaying the median (line) and mean (square) ± percentile (25%-75%) of local displacements for β3-integrin-mEos2, tdEos-talin-N, talin-C-tdEos, mEos2-talin-THATCH for elastic (E) and inelastic (IE) responses after subtraction of the extrapolated PDMS displacements. f, Schematic representation of the acute mechanical response of talin-N and talin-C compared to β3-integrin. b-e, Data pooled from several independent experiments (see Supplementary Table 3): beads (n = 3 independent experiments, 52 kymographs), β3-integrin-mEos2 (n = 3 independent experiments, 51 kymographs); tdEos-talin-N (n = 4 independent experiments, 98 kymographs); talin-C-tdEos (n = 3 independent experiments, 117 kymographs); mEos2-talin-THATCH (n = 3 independent experiments, 66 kymographs). Statistical significances were obtained using two-tailed unpaired Student's t-tests. a, Fluorescence image of paxillin-GFP in a MEF on the PDMS stretching device before stretching (right direction) (up left). Projection of all actin-mEos2 super-resolution intensity images of a trapeze-like pattern time-lapse (stretching 2.9 %, 2 Hz, 40 s) (bottom left). Scale bar, 5 µm. Right, actin-mEos2 kymographs generated from the trapeze-like pattern time-lapse (as shown in the left panels, dashed lines). Horizontal axis, space (500 nm); vertical axis, time (5 s). The magenta kymograph corresponds to the reference bead, and the green kymographs correspond to actin-mEos2. b, Displacement versus time plot for elastic responses of actin-mEos2 (green lines) after normalization to the initial position of the magenta reference bead (magenta line) (up). Corresponding mean displacement ± SEM (bottom). c, Same as b for inelastic responses of actin-mEos2. d, Fractions of elastic and inelastic responses inside and outside FAs for actin-mEos2 in control, fixed/permeabilized cells and cells treated with blebbistatin. Values represent the average of fractions obtained from at least three independent experiments (see Supplementary table 3; mean ± s.e.m. for cells). e, Box plots displaying the median (line) and mean (square) ± percentile (25%-75%) of local displacements for actin-mEos2 in control, fixed/permeabilized cells and cells treated with blebbistatin for elastic (E) and inelastic (IE) responses after subtraction of the extrapolated PDMS displacements. b-e, Data pooled from several independent experiments (see Supplementary table ). The density of trajectories was normalized to the value obtained before stretching. Individual cells (orange), mean trajectory ratio ± s.d. (bold orange), increase > 1.1 (plain), < 1.1 (dotted). Scale bar = 3 µm. d, Zyxin-mEos3.2 kymograph generated from the trapeze-like pattern time-lapse. Horizontal axis, space (2 µm); vertical axis, time (10s). The magenta kymograph corresponds to the reference bead; the green kymographs correspond to zyxin-mEos3.2. e, Color-coded projection of zyxin-mEos 3.2 intensity images during the plateau phase (red 0-3 s, green 4-7s, blue 8-11s, yellow 11-15s). f, Fluorescence image of paxillin-GFP in a MEF on the PDMS stretching device before stretching (right direction). g, Projection of vinculin-mEos2 super-resolution intensity images for the three phases of a trapeze-like pattern time-lapse (stretching 5 %, 2 Hz, 8s per phase): before (left), plateau (middle) and relax (right). The dotted region represents the area used to generate the kymograph in i. Scale bar = 3 µm. h, Variation of trajectory density (trc/µm 2 ) for vinculin-mEos2 (n = 7 cells, 3 independent experiments) throughout trapeze-like patterns (mean ± s.d.). The density of trajectories was normalized to the value obtained before stretching. Individual cells (green), mean trajectory ratio ± s.d. (bold green), increase > 1.1 (plain), < 1.1 (dotted). i, vinculin-mEos2 kymographs generated from trapeze-like pattern time-lapse. Horizontal axis, space (2 µm); vertical axis, time (10s). The magenta kymograph corresponds to the reference bead; green kymographs correspond to vinculin-mEos2. j, Schematic representation of zyxin recruitment in mature FAs. a,b,d,e, Data representative of 4 independent experiments; f,g,j, data representative of 3 independent experiments (see Supplementary Table 5). Statistical significance was calculated using two-tailed Wilcoxon matched-pairs signed rank tests. a, Fluorescence image of paxillin-GFP in a spreading MEF on the stretching device before stretching (right direction). b, Projection of vinculin-mEos2 super-resolution intensity images for the three phases of a trapeze-like pattern time-lapse (stretching 4.2 %, 2 Hz, 40s per phase): before (left), plateau (middle) and relax (right). The dotted region represents the area used to generate the kymograph in d. Scale bar = 3 µm. c, Variation of trajectory density (trc/µm 2 ) for vinculin-mEos2 (n = 10 cells, 4 independent experiments) throughout trapeze-like patterns (mean ± s.d.). The density of trajectories was normalized to the value obtained before stretching. Individual cells (green), mean trajectory ratio ± s.d. (bold green), increase > 1.1 (plain), < 1.1 (dotted). d, vinculin-mEos2 kymograph generated from trapeze-like pattern time-lapse. Horizontal axis, space (2 µm); vertical axis, time (10s). The magenta kymograph corresponds to the reference bead, and the green kymograph corresponds to vinculin-mEos2. e, Color-coded projection of all vinculin-mEos2 intensity images during the plateau phase (red 0-15 s, green 15-30s, blue 30-45s, yellow 45-60s). f, Temporal molecular recruitment of vinculin-mEos2 during the plateau phase. Each line represents an individual cell (green shades). The number of vinculin-mEos2 detections in NAs was normalized to the value obtained before stretching. g, Schematic representation of vinculin recruitment in early NAs. h, Fluorescence image of paxillin-GFP in a spreading MEF on the stretching device before stretching (right direction). i, Projection of talin-C-tdEos super-resolution intensity images for the three phases of a trapezelike pattern time-lapse (stretching 3.7 %, 2 Hz, 8 s per phase): before (left), plateau (middle) and relax (right). The dotted region in h and i represents the area used to generate the kymograph in k. Scale bar = 3 µm. j, Variation of trajectory density (trc/µm 2 ) for talin-C-tdEos (n = 7 cells, 3 independent experiments) throughout trapeze-like patterns (mean ± s.d.). The density of trajectories was normalized to the value obtained before stretching. Individual cells (green), mean trajectory ratio ± s.d. (bold green), increase > 1.1 (plain), < 1.1 (dotted). k, talin-C-tdEos kymographs generated from trapeze-like pattern time-lapse. Horizontal axis, space (2 µm); vertical axis, time (10s). The magenta kymograph corresponds to the reference bead, and the green kymograph corresponds to talin-C-tdEos. a,b,d,e Data representative of 4 independent experiments; h,i,k, data representative of 3 independent experiments (see Supplementary Table 5). Statistical significance was calculated using two-tailed Wilcoxon matched-pairs signed rank tests.

:

  The stretchable elastic substrate is compatible with single molecule localization microscopy. Extended Data Figure4. Elastic and inelastic mechanical response of talin-N to trapeze-like patterns. Extended Data Figure5. Elastic and inelastic mechanical responses of actin and talin-C to single stretch-plateau patterns. Extended Data Figure6. Elastic and inelastic mechanical response of actin to trapeze-like patterns after fixation and blebbistatin treatment. Extended Data Figure7. Vinculin is not recruited to mature integrin-based adhesions by larger scale (10 %) stretching. Extended Data Figure8. Elastic and inelastic mechanical response of talin-C to trapeze-like patterns in nascent integrin-based adhesions. Extended Data Figure9. Vinculin does not exhibit region-selective recruitment in nascent adhesions after small-scale (4 %) stretching. Extended Data Figure10. Trapeze-like patterns (4 %) are not triggering stress fiber ruptures and repair.

Figures:Figure 1 :

 1 Figures:

Figure 2 :

 2 Figure 2: Combining cell stretching with live super resolution microscopy or single molecule tracking.

Figure 3 :

 3 Figure 3: The acute mechanical response of β3-integrins to external forces is elastic.

Figure 4 :

 4 Figure 4: The inelastic mechanical response of talin to external forces correspond to talin unfolding.

Figure 5 :

 5 Figure 5: Transient and active remodeling of the acto-myosin network drives the inelastic response of actin.

3

 3

  ): beads (n = 3 independent experiments, 52 kymographs); actin-mEos2 (n = 3 independent experiments, 65 kymographs); actin-mEos2 fixed/permeabilized (n = 3 independent experiments, 85 kymographs); actin-mEos2 blebbistatin (n = 2 independent experiments, 4 stretches, 83 kymographs) . f, Schematic representation of the acute mechanical response of actin. g, Model of displacements amplification by transient active remodelling of the actin cytoskeleton. Statistical significances were obtained using two-tailed unpaired Student's t-tests.

Figure 6 .

 6 Figure6. Small-scale stretching triggers zyxin reorganization but has no effect on vinculin recruitment in mature FAs a, Fluorescence image of paxillin-GFP in a MEF on the PDMS stretching device before stretching (right direction). b, Projection of zyxin-mEos3.2 super-resolution intensity images for the three phases of a trapeze-like pattern time-lapse (stretching 4.3 %, 2 Hz, 8s per phase): before (left), plateau (middle) and relax (right). The dotted region represents the area used to generate the kymograph in d. Scale bar = 3 µm. c, Variation of trajectory density (trc/µm 2 ) for Zyxin-mEos3.2 (n = 8 cells, 4 independent experiments) throughout trapeze-like patterns (mean ± s.d.). The density of trajectories was normalized to the value obtained before stretching. Individual cells (orange), mean trajectory ratio ± s.d. (bold orange), increase > 1.1 (plain), < 1.1 (dotted). Scale bar = 3 µm. d, Zyxin-mEos3.2 kymograph generated from the trapeze-like pattern time-lapse. Horizontal axis, space (2 µm); vertical axis, time (10s). The magenta kymograph corresponds to the reference bead; the green kymographs correspond to zyxin-mEos3.2. e, Color-coded projection of zyxin-mEos 3.2 intensity images during the plateau phase (red 0-3 s, green 4-7s, blue 8-11s, yellow 11-15s). f, Fluorescence image of paxillin-GFP in a MEF on the PDMS stretching device before stretching (right direction). g, Projection of vinculin-mEos2 super-resolution intensity images for the three phases of a trapeze-like pattern time-lapse (stretching 5 %, 2 Hz, 8s per phase): before (left), plateau (middle) and relax (right). The dotted region represents the area used to generate the kymograph in i. Scale bar = 3 µm. h, Variation of trajectory density (trc/µm 2 ) for vinculin-mEos2 (n = 7 cells, 3 independent experiments) throughout trapeze-like patterns (mean ± s.d.). The density of trajectories was normalized to the value obtained before stretching. Individual cells (green), mean trajectory ratio ± s.d. (bold green), increase > 1.1 (plain), < 1.1 (dotted). i, vinculin-mEos2 kymographs generated from trapeze-like pattern time-lapse. Horizontal axis, space (2 µm); vertical axis, time (10s). The magenta kymograph corresponds to the reference bead; green kymographs correspond to vinculin-mEos2. j, Schematic representation of zyxin recruitment in mature FAs. a,b,d,e, Data representative of 4 independent experiments; f,g,j, data representative of 3 independent experiments (see Supplementary Table5). Statistical significance was calculated using two-tailed Wilcoxon matched-pairs signed rank tests.

Figure 7 .

 7 Figure 7. Small-scale stretching triggers vinculin recruitment in nascent adhesions without the recruitment of additional talin.

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Acknowledgments: We thank Z. Karatas, M. Fabre, R. Sterling, J. Carrere for technical assistance; T. Orré for helpful discussions. C. Poujol, S. Marais (Bordeaux Imaging Center, BIC) for technical help; F. Cordelières. (BIC) for support in kymograph analysis (Kymo Tool Box). We thank J. B. Sibarita (IINS, Bordeaux, France) for his support in sptPALM analysis; V. Studer (IINS, Bordeaux, France) and P.O. Strale (alvéole) for important discussions on microfabrication; M. Cabilic (IINS, Bordeaux, France) for the repositioning plugin developed in Metamorph; T. Schlichthärle, L. Fischer, R. Jungmann (MPI Biochemistry, Munich, Germany) and C. Grashoff (Institute for Molecular Cell Biology, Münster, Germany) for providing materials, support and important discussions on DNA-PAINT; P. Kanchanawong (MBI, NUS, Singapore) for providing the talin1-22-tdEOS (Talin-C), tdEOS-18-Talin1 (Talin-N), mEos2-7-TalinABS (THATCH) constructs. We acknowledge financial support from the French Ministry of Research and CNRS, ANR grant Integractome (GG), ANR grant FastNano (GG), ANR grant IntegrinNanoPlan (GG), ANR Decav-Recav (PN, ANR MecanoCav (PN), Fondation pour la Recherche Médicale (GG), and the Institut National du Cancer (PN). Authors declare no competing interests.

Methods

Full methods are available in the Supplementary Methods section.

Supplementary Tables

Supplementary Table 1 Pointing accuracies and densities of mEos2 detection. Supplementary Table 2. Results obtained using sptPALM acquisitions at 50 Hz. Supplementary Table 3

Conflict of interest statement:

The authors declare no conflict of interest.