domain: spi chim phys

text:
P Luo

M Li

H Jiang

R Zhao

F Zontone

Q S Zeng

H Y Bai

Beatrice Ruta
email: beatrice.ruta@univ-lyon1.fr

W H Wang

‡ M X Li

‡ H Y Jiang

Nonmonotonous atomic motions in metallic glasses

Keywords: metallic glass, physical aging, relaxation, intermittent dynamics, XPCS

HAL is

I. INTRODUCTION

Glasses are usually formed by rapid cooling high-temperature liquids. This process brings the materials in a non-equilibrium state, from where they spontaneously relax toward the corresponding equilibrium liquid. Knowledge of the relaxation dynamics in glasses and its evolution due to physical aging is crucial for understanding their mechanical response and controlling the long-time evolution of their properties during applications [1][2][3]. Two main microscopic relaxation processes have been identified in glasses, the locally initiated βrelaxation and the large-scale α process [4][5][6][START_REF] Ngai | Relaxation and Diffusion in Complex Systems[END_REF]. The first process can be associated with microscopic islands of mobility in the material, while the second one corresponds to collective motions of the whole system. Both processes contribute to the glass formation and physical aging, but their role and interplay are not yet fully understood [START_REF] Ngai | Relaxation and Diffusion in Complex Systems[END_REF].

Recent enthalpy recovery and stress relaxation studies in hard and soft glasses have shown the existence of a surprising multi-steps relaxation process for long annealing, which contrasts with the usual steady evolution of the dynamics during physical aging [START_REF] Cangialosi | [END_REF][9][10]. Distinct aging regimes have been reported also during the evolution of the microscopic structural relaxation process in metallic glasses (MGs) at the atomic scale [11] and in complex soft materials [12][13][14], and are likely related to internal stresses [15,16]. In the case of MGs, abrupt intermittent fluctuations of the microscopic structural relaxation time have also been reported [17],

suggesting an avalanche-like particle motion [18,19]. This anomalous intermittent dynamics of MGs at atomic scale has been observed under annealing protocols [20] and in-situ application of external stresses at ambient temperature [21]. In this latter case, the effect has been attributed to microplastic events occurring in the material. Despite these two excellent studies, the origin of this anomalous intermittent dynamics is still elusive. In particular, it is not clear yet what are the physical parameters triggering these abrupt dynamical events, and why the intermittent dynamics has been reported only in very few cases.

In order to shed some light on the nature of the microscopic intermittent dynamics of MGs, we use the x-ray photon correlation spectroscopy (XPCS) technique to explore the atomic motions in a Zr44Ti11Cu10Ni10Be25 (vit1b) MG with distinct fictive temperatures (Tf) obtained by pre-annealing the samples below the glass transition temperature (Tg), and as a function of external stresses induced in the material. In the XPCS measurements, incoming coherent hard x-rays are scattered when going through the material, leading to an interference pattern whose intensity is related to the exact spatial arrangements of the scatters in the material. Information on the dynamics can be obtained by the temporal correlation of the fluctuations of the scattered intensity [START_REF] Madsen | Synchrotron Light Sources and Free-Electron Lasers[END_REF]. Additional differential scanning calorimetry (DSC), high-resolution transmission electron microscopy (HRTEM), high-energy synchrotron x-ray diffraction (XRD), and mechanical stress relaxation measurements were performed to determine the fictive temperature, the microstructure and the macroscopic relaxation behavior of the samples. Our results show that the intermittent atomic motion is related to the activation of a fast secondary relaxation and can be tuned at wish by changing the applied thermal and mechanical protocols to the sample. Although the microscopic intermittent dynamics seems contrasting with the macroscopic steady relaxation of glass properties, our results indicate that an underlying correlation between the two exists.

II. EXPERIMENTAL TECHNIQUES

A. Materials

Zr44Ti11Cu10Ni10Be25 (at.%) master alloys were prepared by arc-melting elements with purities above 99.99% in a Ti-getter high-purity (99.9995%) argon atmosphere. MG ribbons 20 μm in thickness were produced by melt-spinning technic. Bulk MG plates were prepared by copper-mold-casting. The pre-annealing was conducted at 559 K in a muffle furnace with temperature stability of ±1 K, with the samples sealed in quartz tubes with high-purity argon gas to prevent oxidation.

The DSC measurements were performed on a Perkin-Elmer DSC 8000 to examine the thermodynamic properties of the samples at a heating rate of 20 K min -1 with 20 mL min -1 flowing high-purity argon gas to prevent possible surface oxidation. The instrument was calibrated according to the melting transitions of indium and zinc. The mass of DSC samples was ~20 mg to achieve good data accuracy. The stress relaxation experiments were conducted on a dynamic mechanical analyzer (DMA, TA Q800). As the temperature was stabilized at the planned temperature, a 0.3% tensile strain was applied on the MG ribbon and the stress evolution was simultaneously detected.

The microstructure of the samples was characterized by HRTEM and high-energy synchrotron XRD. The TEM samples were carefully prepared by ion milling with 2 keV argon ions at the liquid nitrogen temperature. HRTEM observations were conducted using a JEOL-2100 plus TEM. The high-energy XRD was performed at beamline 11-IDC at Advanced Photon Source, Argonne National Laboratory, U.S.A. The x-ray energy is 105.1 keV and the beam size is ~0.5 mm × 0.5 mm. The experiment was carried out at room temperature in transmission geometry for bulk MGs ~0.4 mm in thickness with exposure time of 20 s.

Assuming independent atomic contributions to the scattering, the static structure factor, S(q) is calculated as:

𝑆(𝑞) = 𝛼𝐼 s (𝑞) -𝐼 C (𝑞) 𝑍 tot 2 (𝑞)𝑓 eff 2 (𝑞) ,
where Ztot is the sum, weighted by the atomic concentrations, of the atomic numbers Z of the atoms, IC is the Compton scattering calculated as the sum of the individual atomic components and feff the effective electronic form factor, calculated as the weighted sum of the atomic scattering factors, divided by Ztot. Is is the sample scattering after subtraction of the background signal and α a density dependent normalization factor, which is found following the iterative procedure reported in Ref. [START_REF] Eggert | [END_REF].

B. X-ray photon correlation spectroscopy measurements and data processing

XPCS measurements were performed at beamline ID10 at the ESRF in Grenoble, France.

Coherent x-rays were used with an energy of 8.1 keV (λ = 1.53 Å) and a coherent flux of ~10 11 photons per second per 200 mA, and a size of 10 µm × 10 µm. Series of speckles patterns were collected in transmission geometry by a charge-coupled-device from Andor technology (13 µm × 13 µm pixel size) placed ~70 cm downstream the sample at an angle ~38° corresponding to the maximum of the first sharp diffraction peak of our samples. The detector was mounted on a diffractometer which could rotate around the sample in order to measure the corresponding static structure factor S(q) as well. More details about the experimental set-up can be found in Refs [24,25]. The samples were mounted in a furnace providing a temperature stability of 0.1 K and heated at 12 K min -1 from 300 K to the isothermal temperature of 539 K. The measurements were conducted in a way that after collecting every 3000 or 4000 frames (i.e. about 3 or 4 h each) the S(q) was measured to ascertain that the sample remains amorphous, which leads to gaps of about 10 min in the data. The raw data were treated as in Ref. [26].

The time evolution of the microscopic dynamics is directly captured in XPCS by the intensity two-time correlation function (TTCF) C(t1, t2), which is defined as 𝐶(𝑞, 𝑡 1 , 𝑡 2 ) = < 𝐼(𝑞, 𝑡 1 )𝐼(𝑞, 𝑡 2 ) > 𝑝 < 𝐼(𝑞, 𝑡 1 ) > 𝑝 < 𝐼(𝑞, 𝑡 2 ) > 𝑝 ,

where <…>p denotes an ensemble averaging performed on all pixels of the detector corresponding to the same wave vector q [START_REF] Madsen | Synchrotron Light Sources and Free-Electron Lasers[END_REF]. The time-averaged dynamics are extracted from the TTCF as a function of the waiting time, 𝑡 𝑤 = 𝑡 0 + (𝑡 𝑓 -𝑡 𝑖 )/2 where t0 is the delay time between sample temperature equilibration and the first measurement point, and tf and ti are the final and starting times, respectively. This is accomplished through a temporal averaging of the TTCF within a fixed time interval δt = tfti over all possible starting times ti and expressed as a one-time intensity correlation function 𝑔 2 (𝑞, 𝑡) =< 𝐶(𝑞, 𝑡 𝑖 , δ𝑡) > . The g2(q, t) was calculated from the TTCF within a time range defined by a certain number of frames. In order to calculate the dependence of g2(q, t) on tw, a certain frame step was chosen and g2(q, t) was calculated as a function of successive frame steps over the given frame range. Depending on the observed behavior of the TTCF, frame range of about 1000 images were chosen to give sufficient measurement statistics and evaluate correctly the different parameters, while taking care not to average out any interesting dynamical features of the TTCF. The values of τ(tw), c•fq 2 (tw) and β(tw) shown in Fig. 4, Fig. 5 and Fig. 7 were taken from the Kohlrausch-Williams-Watts (KWW) fits of the g2(q0, t) functions. τ(tw) was obtained using a continuous binning of 200 images as in Ref. [20] and around the intermittent events, where the dynamics is too slow to see substantial decay in the correlation functions, it was calculated from binning of larger groups of images, while for c•fq 2 (tw) and β(tw) we used around 1000 frames like those plotted in Fig. 2. This different approach is due to the fact that while τ(tw) is a more robust parameter unaffected by the usage of 200 or 1000 images, c•fq 2 (tw) and β(tw) are better evaluated with more statistics.

III. RESULTS

A. Fictive temperature

Figure 1a shows the DSC profiles of the as-cast MG and samples pre-annealed at 559 K for 3 h and 192 h. Compared to the annealed samples, the as-cast glass is highly unstable and exhibits a broad sub-Tg exothermic peak, indicative of the abundant excess enthalpy trapped in the glass with a structure far away from equilibrium. Upon annealing, the excess enthalpy is sequentially released, followed by an increase in the endothermic peak above Tg associated to enthalpy recovery. The inset shows the enthalpy of the samples obtained by integrating the heat flow profiles. The Tf is determined from the intersection between the extrapolated enthalpies of glass and supercooled liquid [27]. Annealing induces a remarkable reduction in enthalpy and Tf, implying an increased stability of the glass [6]. The as-cast MG has a Tg = 621 K and exhibits the highest enthalpy with Tf = 752 K, ≈1.2Tg, consistent with previous reports [28].

When the sample is annealed for 3 h, Tf decreases to 603 K, while the 192 h annealed glass shows much lower enthalpy with Tf = 565 K, almost 200 K lower than that of the as-cast glass.

B. Microscopic structure

As is visible in Fig. 1b andc, both the as-cast and the 192 h pre-annealed samples show a homogeneous maze-like pattern in the HRTEM images, indicative of a fully amorphous structure. The diffuse halos in the electron diffraction patterns (see the insets in Fig. 1b andc)

further corroborate the amorphous nature of the samples. Figure 1d shows the static structure factor S(q) obtained at room temperature for the as-cast and the 192 h pre-annealed samples obtained from high-energy synchrotron XRD measurements. The inset in Fig. 1d is a close-up view of the first peaks of S(q), which show smooth curves without any indication of crystallization even for the longest 192 h annealed sample. Moreover, a slight shift of the peak position towards larger q values can be observed for the 192 h pre-annealed sample, indicating an increment of the density typical of physical aging [29].

C. Atomic-scale dynamics by XPCS

The microscopic structural relaxation process and its temporal evolution was studied with XPCS by performing long isotherms at 539 K, thus below the Tf of all samples, and for a unique wave vector q0 = 2.67 Å -1 corresponding to the first maximum of S(q) (Fig. 1d). In this configuration, we are directly probing the atomic motions on a characteristic inter-particle length scale 2π/q0 = 2.35 Å. We performed a systematic study of the atomic motions in three representative samples, the as-cast, the 3 h pre-annealed, and the 192 h pre-annealed, with and without in-situ mechanical stresses. The free samples were directly mounted in the furnace, thus without external stress during the XPCS measurements. To induce external stress in the samples, we designed an ad-hoc clamp as illustrated in Fig. 1e to restrict the MG ribbon around a mandrel with a diameter 𝛷 = 4.0 mm. For a bent ribbon, the strain on the outer surface is tensile and that on the inner surface is compressive, the neutral surface has no strain. The MG ribbons have smooth surfaces and a uniform thickness of d = 20 μm. The largest strain on the surfaces is ε = d/(𝛷+d) = 0.5%. The Young's modulus E and the yield strength 𝜎y of the studied MG is 96±1 GPa and 1900±100 MPa, respectively [30]. Therefore, the stress induced on the surfaces is 480 MPa ≈ 0.25𝜎y. The increase of E for the longest annealed MG would be ≈10% [31,32], which means a variation of just 0.025𝜎y for the applied stress. As such, well-defined in-situ elastic strain/stress was induced during the XPCS measurements.

Figure 2a shows the typical intensity-intensity correlation functions, g2(q0, t), measured for the stressed as-cast sample. The decay of the curves provides information on the atomic motions, being g2(q, t) related to the density fluctuations, thus to the intermediate scattering function, f(q, t), through the Siegert relation 𝑔 2 (𝑞, 𝑡) = 1 + 𝑐|𝑓(𝑞, 𝑡)| 2 , where c is a set-up dependent contrast related to the coherent degree of the x-rays, the scattering angle, and the thickness of the samples [START_REF] Grübel | Soft-Matter Characterization[END_REF]. The data can be modeled with the KWW function 𝑔 2 (𝑞 0 , 𝑡) =

1 + 𝑐 • 𝑓 𝑞 2 (𝑡 w ) exp[-2(𝑡/𝜏(𝑡 w )) 𝛽(𝑡 w )
] where all parameters depend on the waiting time, tw, elapsed since the beginning of the isotherm at 539 K: τ(tw) is the decay time of the relaxation process, β(tw) the shape parameter, and fq(tw) is the nonergodic plateau associated to the trapping of the particles in the nearest neighbors cage before their escape during the structural relaxation [START_REF] Cavagna | [END_REF]. With increasing tw, g2(q0, t) experiences firstly a continuous shift towards longer decays, signaling that the dynamics becomes spontaneously slower, and then a backward shift to faster decays. Such a behavior strongly contrasts with the steady slowing-down of relaxation dynamics reported in macroscopic studies, revealing a spontaneous intermittent aging process. Intriguingly, we found that this nonmonotonous evolution of the dynamics is accompanied by a surprising abrupt drop of the initial plateau value of g2(q0, t). This effect is better appreciated in Fig. 2b where the same data are scaled along the x-axis and reported as a function of the reduced time t/τ(tw).

In the macroscopic limit of q→0, the short-time plateau of g2(q0, t)-1, c•fq 2 (tw), is related to the elastic properties of the material through the nonergodicity parameter, and it usually increases steadily with time due to the growth in elasticity as reported in gels and colloidal suspensions [13,[35][36][37]. Although the elasticity of MG also increases during isotherms [31,32,38,39], here c•fq 2 (tw) decreases by almost 20% with tw (Fig. 2b). Furthermore, our measurements are performed at the maximum of the S(q), where the nonergodicity factor is expected to be close to unity [40]. Hence, we cannot attribute the observed phenomenology to changes in the elastic response of the material. From the technical point of view, beamline instabilities may affect XPCS measurements leading to a drop in contrast in different ways: 1)

Beam jumps. Sudden changes in beam position (e.g. induce by the electron beam instabilities in the synchrotron radiation storage ring) will decorrelate the data breaking the continuity of the TTCFs. We never observed such events and it is clearly not the case as the contrast drop is observed at the slowest dynamics (i.e. any fast sudden instability will kill immediately the data).

2) Contrast decreasing because of the degradation of the beamline optical alignment. For XPCS, the stability of the optical alignment of the beamline is critical for the optimum contrast, since any (transient) misalignment will produce a degradation of the contrast. This is usually the result either of a drift of the optics (monochromator, focusing optics) or by the progressive degradation of a beamline component due to heat load. We point out that these effects cannot be solved spontaneously, i.e. they need the human intervention either to restore the optimum alignment or to adjust the damaged component. Furthermore, the induced degradation is usually progressive, i.e. beamline contrast is degrading progressively with time. We never observed such slow contrast degradation trends in our measurements and we didn't need to realign systematically beamline optics beyond standard fast daily beam checks, in particular not during the intermittent events or between the gap of XPCS data sets due to the necessity to check the S(q). During our experiment, the data jump from high to low contrast, depending on the sample and waiting time. The measured initial contrast of about 2.2% is thus restored several times during the whole beamtime, guaranteeing the reproducibility of the value.

Following these observations, we think that the only possible explanation for the contrast variation observed along a smooth and slow dynamics is to activate an additional internal fast process prior to the primary structural rearrangements. This process results in an additional step decay in the correlation functions at times too short to be directly captured in the temporal window of the current XPCS, and with a strength corresponding to the missing value of c•fq 2 (tw).

A drop in c•fq 2 (tw) has been reported also in Pd77Si16.5Cu6.5 MG [41]. Differently from our case, this phenomenon was therein triggered by temperature changes and it has been ascribed to a thermally activated secondary relaxation process associated to the onset of crystallization, but without any fluctuation in the relaxation time τ [41]. In our experiments, it has been corroborated by both high energy synchrotron XRD and HRTEM that our samples, including the longest 192 h pre-annealed one, keep fully amorphous without any indication of nanocrystallization (Fig. 1b-d). Furthermore, the structure has been checked in-situ after collecting every 4000 frames during the XPCS measurements. Figure 3 shows the XRD pattern for the 192 h pre-annealed sample after the collection of all XPCS data at 539 K, the sample keeps fully amorphous. These observations exclude the possibility that our results were related to crystallization. Previous studies reported that Be-containing ZrCu-based MGs are prone to chemical phase separation subjected to annealing near or above the glass transition [42,43],

while it has been demonstrated in Zr41.2Ti13.8Cu12.5Ni10Be22.5 MG that no phase separation occurs prior to crystallization [44]. We have also carefully verified with both dark field and bright field HRTEM at different length scales that no phase separation occurs in all our samples.

Therefore, we conclude that the intermittent microscopic dynamics observed also in other MGs [11,20] is an intrinsic property of glass relaxation, rather than a result of nanocrystallization or chemical decomposition.

The connection between the intermittent dynamics and the secondary relaxation process can be more appreciated by looking at the temporal evolution of the relaxation time τ(tw) and c•fq 2 (tw) as shown in Fig. 4a. The as-cast MGs show highly heterogeneous dynamics. In the stressed sample, for tw < 1.7×10 4 s, τ(tw) increases rapidly to 1.2×10 4 s. It subsequently decreases dramatically, and finally becomes stationary with τ(tw) ≈ 3×10 3 s. This intermittent event leading to the peak in τ(tw) spans approximately 1.3×10 4 s with a fluctuation of △τ(tw) ≈ 8.8×10 3 s. As marked by the red hatched area in Fig. 4a, this dynamical fluctuation is accompanied by an abrupt drop of c•fq 2 (tw) (bottom panel), indicating the strong connection between these two features. In the free as-cast glass, we observe also a sharp intermittent event at much earlier stage of the isotherm and a simultaneous rapid drop of c•fq 2 (tw) (see the olive hatched area in Fig. 4a). Although the fluctuation of τ(tw) is not as large as in the stressed MG, it is equally sharp, with an increase of △τ(tw) ≈ 800 s spanning 1.6×10 3 s, and the drop in c•fq 2 (tw) is of equal amount to that of the stressed sample. Despite the missing data for the free as-cast MG at larger times due to beam lost in the synchrotron, the present data clearly show that both samples exhibit intermittent dynamics accompanied by a secondary relaxation process.

The temporal evolution of the intermittent microscopic dynamics can be better visualized by looking at the TTCF C(t1, t2), which represents the instantaneous correlation between averaged configurations measured at times t1 and t2. Figure 4b andc show the TTCFs corresponding to the data for the as-cast sample with stress. The diagonal from the bottom left to the top right corner indicates the evolution with tw, while the width of the yellow-red ridge along the diagonal is proportional to τ(tw). Thus, Fig. 4b andc illustrate visibly the fast slowingdown and the subsequent abrupt speeding-up of the structural relaxation process.

Interestingly, we found that the intermittent dynamics is strongly suppressed by the concomitant use of stress and pre-annealing. Figure 5a plots τ(tw) and c•fq 2 (tw) for the 3 h preannealed glass. The free sample shows distinct regimes of atomic motions: i) An abrupt increase in τ(tw) up to tw ≈ 1.1×10 4 s, ii) a stationary regime where τ(tw) remains basically constant at 4×10 3 s, and iii) a rapid acceleration to another stationary regime with τ(tw) ≈ 1×10 3 s. As marked by the olive hatched area, also in this case the intermittent event is accompanied by a substantial reduction in c•fq 2 (tw), but in a slower way than in as-cast sample. In stark contrast, the sample under stress shows a monotonous slowing-down of the dynamics with only tiny fluctuations in τ(tw) and a slight decrease in c•fq 2 (tw). Notwithstanding, the relaxation times of both samples (i.e. with and without stresses) do overlap at long waiting times, indicating that the presence of external stress affects only the appearance of the intermittent event.

Figure 5b provides a comprehensive comparison between the dynamics in all as-cast and pre-annealed samples. The decreased Tf induced by thermal pre-annealing leads to: i) a delay in the intermittency, from tw ≈ 3.3×10 3 s for the as-cast sample to tw ≈ 2.1×10 4 s in the 192 h pre-annealed one, ii) a change in the shape of the intermittent event, from a sharp peak in τ(tw)

in the as-cast glass, to a blunt one with a stationary regime between the rapid increase and the decrease in τ(tw) in the 3h pre-annealed glass. A similar event occurs also for the 192 h preannealed MG, while due to its much longer delay we do not have the full event depicted. When stress is applied, the intermittent event is observed but only in the as-cast sample and it occurs at later times than in the free glass, whereas both pre-annealed MGs display only a monotonous temporal slowing-down of the dynamics. Surprisingly, the τ(tw) of the 3 h and 192 h preannealed MGs under stress coincides, contrasting with their macroscopic relaxation behaviors which show a difference in timescale by over one order of magnitude (Fig. 6). By looking at the τ(tw) of the 3 h and the 192 h pre-annealed MGs in Fig. 5, it is clear that when the intermittent events terminate or become well suppressed by the simultaneous use of stress and pre-annealing, the microscopic relaxations exhibit consistent dynamics with the same τ(tw), independently on the Tf of the glass. These observations suggest two mechanisms responsible for the aging process at the microscopic scale: i) the intermittent dynamical event that is sensitive to the variation of the sample's Tf and external loading, and ii) the steady slowingdown of the dynamics which is independent of the material state.

IV. DISCUSSION

Nonmonotonous relaxations have been reported also in an excellent work of Mauro and colleagues following the evolution of fluctuations in density and enthalpy in distinct glasses [45]. Studying glasses equilibrated at distinct Tf and then quenched at a given temperature, they

show that both enthalpy and density fluctuations initially overshoot the equilibrium value and then relax from the other side. Furthermore, the magnitude of the overshoot increases with the increasing distance between the measured temperature and the initial Tf of the glass. In this picture, the intermittent events in the density fluctuations observed by XPCS here and in other MGs [20], can be viewed as similar nonmonotonous relaxations of the characteristic time of collective atomic motions due to density fluctuations during isotherms at temperatures lower than Tf. It is important to stress that our case the final state is metastable although persistent for long times. The system is still in the glassy state and the relaxation time is far from the corresponding equilibrium liquid value.

Our data show that the abrupt intermittent relaxations are accompanied by the spontaneous activation of a fast secondary relaxation process as signaled by c•fq 2 (tw). The sharper the event in τ(tw), the larger is the strength of the process and thus the drop in c•fq 2 (tw). The presence of a secondary relaxation process suggests that the abrupt fluctuations in the structural relaxation time come from the activation of the motion of fast components in the amorphous matrix, that persist even after the event as confirmed by the persistent low value of c•fq 2 (tw). In other words, the applied stress (and/or temperature) activates a secondary relaxation process which -at the first stage -perturbs the main structural relaxation process leading to strong fluctuations in the relaxation time. Pre-annealing leads to a much smaller and slower drop in c•fq 2 (tw), partially suppressing the secondary process. This decrease of the process with annealing is typical for secondary relaxation processes and has been reported also for the β-relaxation in mechanical studies [46][47][48]. Unfortunately, due to technical constraints, we are not able to quantify the timescale associated to the secondary relaxation process related to the intermittent dynamics and compare it with other known processes. The current advent of 4 th generation synchrotrons [49], will help elucidating the nature of this microscopic secondary process.

Interestingly, we find a constant compressed (i.e. β(tw) >1) value of the shape of the g2(q0, t) for all samples (see Fig. 7), in agreement with previous works [11,17,20,25,41,50]. No discernable dependence of β(tw) on the sample age or the stress state is observed, while we do observe a minimum in correspondence of the peak maximum of the sharp intermittent dynamical events (denoted by the arrows in Fig. 7), consistent with the previous observation in Ref. [20]. The fact that the shape parameter does not display any particular trend, means that its nature is basically not affected by external stress and thermal history, at least in the studied composition, being more a property of the glassy state. The initial increase of β(tw) is likely to be an artefact induced by the limited points at short times and requires further studies. The anomalous compressed shape of the relaxation process is often considered a signature of out of equilibrium dynamics in many complex systems [25,[51][52][53]. Recent numerical simulations in MGs associate this behavior to an increasing number of icosahedral clusters during the vitrification which generate additional frustration in the material [16]. In this regard, the compressed decay appears more as an intrinsic property of the out-of-equilibrium frozen structure as suggested also by studies in ultrastable MGs [50].

XPCS measurements have been previously performed in different MGs [17], while intermittent dynamics has only been observed during isothermal studies in Pd43Cu27Ni10P20

MG [20] and in a smoother way in Au49Ag5.5Pd2.3Cu26.9Si16.3 MG [11]. Here, we report the presence of much stronger intermittent effects in Zr44Ti11Cu10Ni10Be25 MG. This is likely due to the applied protocol that is, a combination of rapid heating, relatively low measuring temperature and long observation time. Strong intermittent dynamics has also been reported in a Zr-based MG under mechanical stresses at room temperature and attributed to microplastic events occurring in the material [21]. In contrast to our work and Ref. [20], the intermittency is there driven only by the stress, and no events have been observed in its absence. This apparent discrepancy is likely a consequence of the fact that those measurements were performed at room temperature (0.44Tg), while in our work and in Ref. [20], the dynamics is mainly triggered by temperature changes (the rapid heating to 0.87Tg in our case). This observation is in agreement also with numerical simulations which have shown the occurrence of similar thermally-activated or stress-activated avalanche-like atomic motion in MGs [18,54].

Finally, it is important to highlight that the increased uniformity of the dynamics under the small applied stress in our work is in agreement with previous studies in glassy systems [55,56].

Molecular dynamics (MD) simulations [56][57][58] have shown that depending on the strength of the applied strain (or stress) it is possible to drive the glass through deeper or higher minima in the potential energy landscape, corresponding thus to new states overaged or rejuvenated with respect to the initial one. In particular, small strain (or stress) is found to drive the glass in metastable state with lower energy minima and thus more stable, in agreement with the results reported in our work, being the strain induced in our sample less than 0.5%, i.e., well below the yielding strain of metallic glasses at our experimental temperature [59]. Following the results of MD simulations, thus the fact that small strain leads to overaging [57], it is then normal to expect a delayed intermittent event in the as-cast sample under stress (Fig. 4a). Such a delay is a signature of the increased stability as indeed it occurs also with the pre-annealing (and without stresses, Fig. 5b). In this scenario, the almost stationary dynamics in pre-annealed samples measured under stress, indicates that the combination of temperature and stress suppress the occurrence of intermittent event in agreement with MD results showing the occurrence of localized, non-diffusive dynamics for small stress [58,60].

V. CONCLUSION

We have performed a systematic study of the relaxation dynamics of a series of Zr44Ti11Cu10Ni10Be25 MGs with distinct stability and in-situ stress, with the aim at shedding some light on the recently discovered intermittent microscopic dynamics [20,21]. We show that the nonmonotoneous temporal evolution of τ(tw) results from the thermal activation of the motion of fast components in the amorphous matrix as signaled by the simultaneous appearance of a secondary relaxation process. The events in τ(tw) and the secondary process are strongly affected by the stability of the glass. Large intermittent dynamical events are indeed more frequently observed in the most unstable (i.e., the as-cast) MG. As Tf decreases upon preannealing, the dynamic intermittency gets delayed. The simultaneous use of stress and preannealing, allows tuning the glass in a stationary metastable state which appears independent on the details of the system. )

T (K) 20 J g -1 T f =603 K T f =565 K T f =752 K 192 h as-cast 3 h as-cast 3 h 192 h T (K) Heat Flow Endo. Up 0.2 J g -1 K -1 T g = 621 K

Figure 1 .

 1 Figure 1. (a) Thermodynamic characterization of the MGs with different thermal histories: as-

Figure 2 .

 2 Figure 2. (a) Waiting time dependent g2(q0, t) functions measured with XPCS for the as-cast

10

 10

Figure 3 .

 3 Figure 3. X-ray diffraction in the vicinity of the first diffraction maximum measured in-situ

Figure 4 .

 4 Figure 4. (a) τ(tw) (upper panel) and c•fq 2 (tw) (lower panel) for the as-cast sample during

Figure 5 .

 5 Figure 5. (a) τ(tw) (upper panel) and c•fq 2 (tw) (lower panel) for the 3 h pre-annealed MG

Figure 6 .

 6 Figure 6. Stress relaxation at 539 K for as-cast and pre-annealed MGs. The stress σ(t) is

Figure 7 .

 7 Figure 7. Waiting time dependent shape parameters of different samples. The arrows

ACKNOWLEDGMENTS

We thank Y. Chushkin for providing the program for the XPCS data analysis. K. L'Hoste is thanked for his technical assistance during the experiments. This research was supported by the NSF of China (51571209 and 51461165101); the MOST 973 Program (2015CB856800), National Key Research and Development Plan (Grant No. 2016YFB0300501 & 2017YFB0903902); and the Key Research Program of Frontier Sciences (QYZDY-SSW-JSC017) and the Strategic Priority Research of the Chinese Academy of Sciences (XDPB0601).

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.


Coline Arnould

Gaëlle Legube
email: gaelle.legube@univ-tlse3.fr

The Secret Life of Chromosome Loops upon DNA Double Strand Break

DNA Double Strand Breaks (DSB) are harmful lesions that severely challenge genomic integrity and recent evidence suggests that DSBs occur more frequently on the genome than previously thought. These lesions activate a complex and multilayered response called the DNA Damage Response, which allows to coordinate their repair with the cell cycle progression. While the mechanistic details of repair processes have been narrowed thanks to several decades of intense studies, our knowledge of the impact of DSB on chromatin composition and chromosome architecture is still very sparse. However, the recent development of various tools to induce DSB at annotated loci, compatible with nextgeneration sequencing-based approaches, is opening a new framework to tackle these questions. Here we discuss the influence of initial and DSB-induced chromatin conformation and on the strong potential of 3C-based technologies to decipher the contribution of chromosome architecture during DSB repair.

The DNA Double Strand Break response and repair DNA Double Strand Breaks (DSBs) represent challenging lesions for cells, as they can lead to major genome rearrangement such as translocations, aneuploidy, and deletions/amplifications.

While previously considered to be almost exclusively induced by environmental agents (radiation, chemicals) with the exception of programmed induction by endogenous nucleases (during meiosis and Immunoglobulin loci rearrangement), it is now well admitted that DSBs are also regularly triggered during normal cell metabolism. More specifically, the development of DSB mapping technologies, such as BLESS, BLISS, DSBCapture, END-seq or BrlTL ( [START_REF] Yan | BLISS is a versatile and quantitative method for genome-wide profiling of DNA doublestrand breaks[END_REF][START_REF] Biernacka | i-BLESS is an ultra-sensitive method for detection of DNA double-strand breaks[END_REF][START_REF] Crosetto | Nucleotideresolution DNA double-strand break mapping by next-generation sequencing[END_REF][START_REF] Canela | DNA Breaks and End Resection Measured Genome-wide by End Sequencing[END_REF][START_REF] Shastri | Genome-wide Identification of Structure-Forming Repeats as Principal Sites of Fork Collapse upon ATR Inhibition[END_REF][START_REF] Lensing | DSBCapture: in situ capture and sequencing of DNA breaks[END_REF], reviewed in [START_REF] Puget | Non-canonical DNA/RNA structures during Transcription-Coupled Double-Strand Break Repair: Roadblocks or Bona fide repair intermediates?[END_REF]) have recently revealed insights on the distribution of endogenous DSBs across the genome. These genome-wide analyzes identified transcriptionally active loci and Transcription Start Sites (TSS) as particularly prone to breakage (for instance [START_REF] Crosetto | Nucleotideresolution DNA double-strand break mapping by next-generation sequencing[END_REF][START_REF] Lensing | DSBCapture: in situ capture and sequencing of DNA breaks[END_REF], reviewed in [START_REF] Puget | Non-canonical DNA/RNA structures during Transcription-Coupled Double-Strand Break Repair: Roadblocks or Bona fide repair intermediates?[END_REF][START_REF] Marnef | Transcription-Coupled DNA Double-Strand Break Repair: Active Genes Need Special Care[END_REF]). These studies also further revealed a compelling connection between DSB production and chromosome architecture, identifying binding sites for CTCF and cohesin (main genome organizers) as preferential damage sites due to Topoisomerase activity and/or fork collapse [START_REF] Shastri | Genome-wide Identification of Structure-Forming Repeats as Principal Sites of Fork Collapse upon ATR Inhibition[END_REF][START_REF] Canela | Topoisomerase II-Induced Chromosome Breakage and Translocation Is Determined by Chromosome Architecture and Transcriptional Activity[END_REF][START_REF] Canela | Genome organization drives chromosome fragility[END_REF][START_REF] Gothe | Spatial chromosome folding and active transcription drive DNA fragility and formation of oncogenic MLL translocations[END_REF][START_REF] Madabhushi | Activity-Induced DNA Breaks Govern the Expression of Neuronal Early-Response Genes[END_REF]. At loop anchors, Topoisomerase II recruitment could further trigger production of DSB, upon transcriptional activation of closeby genes [START_REF] Canela | Topoisomerase II-Induced Chromosome Breakage and Translocation Is Determined by Chromosome Architecture and Transcriptional Activity[END_REF][START_REF] Canela | Genome organization drives chromosome fragility[END_REF][START_REF] Gothe | Spatial chromosome folding and active transcription drive DNA fragility and formation of oncogenic MLL translocations[END_REF].

Beyond the influence of chromosome loops in DSB formation, supported by a growing body of evidence, an emerging concept is also that DSB formation further modifies chromosome architecture and organization in the nuclear space. Given the potential for unscheduled rejoining of two DSBs to trigger translocations, and the previously reported bias for translocation to occur in active loci in cancer cells, it is urgent to understand how DSBs modify chromosome organization and architecture and how this impacts genome (in)stability.

Various pathways contribute to repair DSB in eukaryotes, including Homologous Recombination (HR) and Non Homologous End Joining (NHEJ) (reviewed in [START_REF] Mladenov | DNA double-strand-break repair in higher eukaryotes and its role in genomic instability and cancer: Cell cycle and proliferation-dependent regulation[END_REF][START_REF] Scully | DNA double-strand break repair-pathway choice in somatic mammalian cells[END_REF]). HR entails processing of DNA ends in order to generate single strand DNA (resection) which will invade a homologous copy of the broken locus, further used as template for DNA synthesis.

NHEJ rather directly rejoins the two DNA ends. Mechanistically these two pathways are profoundly different and likely necessitate different chromatin composition and properties for proper execution. At a molecular level, ChIP-seq and imaging studies have started to determine the histone modifications landscape assembled at DSB, as well as their function in DSB repair (reviewed in [START_REF] Clouaire | A Snapshot on the Cis Chromatin Response to DNA Double-Strand Breaks[END_REF]). Yet the conformation of chromatin around DSBs and the chromosome organization in damaged nuclei have only recently started to be investigated.

One of the striking feature of the DNA Damage Response (DDR) is the assembly of microscopically visible foci in the nucleus, which display massive phosphorylation of the H2AX histone variant (H2AX) [START_REF] Rogakou | DNA double-stranded breaks induce histone H2AX phosphorylation on serine 139[END_REF], as well as accumulation of repair factors. Although efforts have been made to understand the protein content of these foci, their exact composition and conformation at the DNA level is still unknown. One of the main reasons for this scarcity of data stands in the long-lasted inability to control the position of induced DSB on the genome. Indeed, except in yeast where the ability of the HO endonuclease to cleave the MAT locus for mating type switching was utilized as a tool to investigate site-specific DSB repair, DSBs have routinely been induced by exposure to genotoxic (drugs and radiation) generating damage in a heterogeneous manner in the cell population and at unknown (but not necessarily random) positions, which precluded the use of Chromosome Conformation Capture (3C)-based methods to investigate chromatin conformation around DSBs. This has been solved recently thanks to the development of several tools to induce breaks at annotated positions, using restriction enzymes and homing endonucleases (e.g. AsiSI, I-PpoI), Zinc Fingers and TALE Nucleases, or the CRISPR/Cas9 system [START_REF] Mladenova | Novel biological approaches for testing the contributions of single dsbs and DSB clusters to the biological effects high LET radiation[END_REF]. With these novel experimental systems, the molecular characterization of DNA conformation around DSB and more generally the folding of damaged chromosomes within the nucleus is now within reach.

Two main questions should primarily focus our attention. First we need to understand how the initial chromosome conformation and organization in the nucleus may contribute to ensure proper DSB signaling and repair. Second, we shall wonder how this initial chromatin conformation is modified upon damage to participate in repair events safeguarding genome integrity.

How does initial chromatin architecture contribute to DSB signaling and repair?

The genomic localization of DSBs strongly impacts their signalization and repair. For instance, clear evidence suggests that DSB occurring in heterochromatin [START_REF] Fortuny | The response to DNA damage in heterochromatin domains[END_REF][START_REF] Lemaître | Double strand break (DSB) repair in heterochromatin and heterochromatin proteins in DSB repair[END_REF], rDNA [START_REF] Van Sluis | Nucleolar reorganization in response to rDNA damage[END_REF] or transcribed loci [START_REF] Marnef | Transcription-Coupled DNA Double-Strand Break Repair: Active Genes Need Special Care[END_REF] display specialized repair pathways. The chromatin composition of the broken locus (involving for example histone marks like H3K36me3 for Transcription-Coupled DSB repair [START_REF] Aymard | Transcriptionally active chromatin recruits homologous recombination at DNA double-strand breaks[END_REF][START_REF] Pfister | SETD2dependent histone H3K36 trimethylation is required for homologous recombination repair and genome stability[END_REF][START_REF] Daugaard | LEDGF (p75) promotes DNA-end resection and homologous recombination[END_REF]; or bona fide chromatin constituents such as KAP1 for heterochromatic repair [START_REF] Ziv | Chromatin relaxation in response to DNA double-strand breaks is modulated by a novel ATMand KAP-1 dependent pathway[END_REF][START_REF] Goodarzi | KAP-1 phosphorylation regulates CHD3 nucleosome remodeling during the DNA double-strand break response[END_REF]) as well as its spatial position within the nucleus (for instance, at the nuclear periphery [START_REF] Lemaître | Nuclear position dictates DNA repair pathway choice[END_REF]) have been clearly established as main contributors in determining which pathway should be used at each genomic location (a decision known as "DSB repair pathway choice") [START_REF] Clouaire | DNA double strand break repair pathway choice: a chromatin based decision?[END_REF]. However, at this stage it is not known whether, beyond the sub-nuclear localization of a locus and its chromatin composition, the chromosome conformation also plays a role in DSBs signaling and repair. Nevertheless, some hints suggest this is likely the case.

Initial chromatin conformation regulates HR.

The fact that chromosome conformation within the nucleus regulates HR is particularly evident from studies in yeast, showing that efficiency of sub-telomeric recombination is strongly affected by telomeres clustering and anchorage [START_REF] Batté | Recombination at subtelomeres is regulated by physical distance, double-strand break resection and chromatin status[END_REF][START_REF] Agmon | Effect of nuclear architecture on the efficiency of double-strand break repair[END_REF]. Beyond telomeres, moving an HO site at different positions along yeast chromosomes revealed a compelling correlation between the frequency of homologous recombination and the proximity with the homologous locus, observed by 3C before damage induction [START_REF] Lee | Chromosome position determines the success of double-strand break repair[END_REF]. Thus initial spatial proximity between the broken locus and a donor sequence is a key feature that determines the efficiency of homologous recombination.

Initial chromatin conformation could regulate H2AX spreading.

Evidence also suggests that chromosome architecture might control H2AX spreading (reviewed in [START_REF] Marnef | Organizing DNA repair in the nucleus: DSBs hit the road[END_REF][START_REF] Aymard | A TAD closer to ATM[END_REF]) (Figure 1). Indeed, H2AX mapping by ChIP-chip around multiple DSBs induced by the restriction enzyme AsiSI in human cells (the so called DIvA cell line for DSB Induced via AsiSI) revealed that H2AX spreads on 1-2 megabases surrounding DSBs, in a manner that is i) reproducible and constrained within boundaries, ii) not necessary symmetrical around the break and iii) uneven with peaks and valleys, suggesting that the surrounding epigenomic landscape and/or chromatin architecture may regulate H2AX spreading [START_REF] Iacovoni | Highresolution profiling of gammaH2AX around DNA double strand breaks in the mammalian genome[END_REF]. A follow up study uncovered a potential function for cohesins in regulating H2AX distribution and in insulating transcribed genes encompassed in H2AX domains from transcription extinction [START_REF] Caron | Cohesin protects genes against γH2AX Induced by DNA double-strand breaks[END_REF]. Moreover, by then, comparison of published Hi-C data generated in undamaged cells [START_REF] Lieberman-Aiden | Comprehensive mapping of long-range interactions reveals folding principles of the human genome[END_REF] with H2AX domains boundaries revealed a striking tendency of H2AX spreading to stop at Topologically Associating Domains (TADs) boundaries [START_REF] Caron | Cohesin protects genes against γH2AX Induced by DNA double-strand breaks[END_REF]. In agreement, the occupancy of the chromatin looping factor CTCF was found juxtaposed to γH2AX foci using super-resolution light microscopy [START_REF] Natale | Identification of the elementary structural units of the DNA damage response[END_REF]. Altogether, these results raise the exciting hypothesis that once bound to the DSB, the kinase(s) involved in H2AX phosphorylation allows H2AX spreading by modifying nucleosomes brought into spatial proximity thanks to the initial chromatin architecture surrounding the DSB (the "Intra-TAD model" [START_REF] Marnef | Organizing DNA repair in the nucleus: DSBs hit the road[END_REF][START_REF] Aymard | A TAD closer to ATM[END_REF]) rather than by linearly walking along the chromosome. This hypothesis is further supported in yeast, where H2A spreading was also found to occur in trans (on other chromosomes) when a DSB was induced close to a centromere, as a consequence of centromeres clustering within nuclei [START_REF] Lee | Dynamics of yeast histone H2A and H2B phosphorylation in response to a double-strand break[END_REF].

Initial chromatin conformation regulates production and repair of programmed DSB.

Beyond these evidences that pre-existing chromosome architecture contributes to DSB signaling and repair, chromosome organization is also likely a key feature in the repair of programmed DSBs induced during meiosis and immunoglobulin loci rearrangements (Figure 1). During the prophase of meiosis, chromosomes undergo profound reorganization which entails progressive condensation, loss of long-range inter-chromosomal contacts, TADs dissolution and the formation of arrays of chromatin loops anchored to a chromosomal axis [START_REF] Muller | Characterizing meiotic chromosomes' structure and pairing using a designer sequence optimized for Hi-C[END_REF][START_REF] Dekker | Capturing chromosome conformation[END_REF][START_REF] Patel | Dynamic reorganization of the genome shapes the recombination landscape in meiotic prophase[END_REF][START_REF] Schalbetter | Principles of meiotic chromosome assembly[END_REF][START_REF] Wang | Reprogramming of Meiotic Chromatin Architecture during Spermatogenesis[END_REF][START_REF] Alavattam | Attenuated chromatin compartmentalization in meiosis and its maturation in sperm development[END_REF]. Within this context, the topoisomerase-like Spo11 endonuclease induces DSBs in a tightly regulated manner, which are further processed and -for some of them-converted into mature crossovers, necessary to ensure chromosome segregation and completion of meiosis.

Importantly, crossover formation depends on the "homologous bias" that consists in choosing the homologous chromosome as a template over the sister chromatid (reviewed in [START_REF] Lao | Trying to avoid your sister[END_REF][START_REF] Borde | Meiosis: early DNA double-strand breaks pave the way for inter-homolog repair[END_REF]).

Notably, germ cells-specific chromosome architecture plays a critical role in both determining the distribution of DSBs along the chromosome and in the homologous bias. Indeed, in S.cerevisae, Spo11-dependent DSBs are being formed within DNA loops in a manner that depends on multiple axial factors such as the meiosis specific cohesin subunit Rec8 [START_REF] Blat | Physical and functional interactions among basic chromosome organizational features govern early steps of meiotic chiasma formation[END_REF][START_REF] Kim | Sister cohesion and structural axis components mediate homolog bias of meiotic recombination[END_REF], the Spp1 protein [START_REF] Sommermeyer | Spp1, a member of the Set1 Complex, promotes meiotic DSB formation in promoters by tethering histone H3K4 methylation sites to chromosome axes[END_REF], Red1 [START_REF] Blat | Physical and functional interactions among basic chromosome organizational features govern early steps of meiotic chiasma formation[END_REF], or the Spo11 accessory complex, RRM (Rec114-Mei4-Mer2) [START_REF] Panizza | Spo11-accessory proteins link double-strand break sites to the chromosome axis in early meiotic recombination[END_REF]. Additionally, components of the structural axis (such as Rec8 or Red1) are also strongly involved in regulating the homologous bias [START_REF] Kim | Sister cohesion and structural axis components mediate homolog bias of meiotic recombination[END_REF] and the axis further acts as a platform for recombination. This peculiar chromosome architecture that is assembled in meiotic cells hence displays a prominent role into DSB production and repair.

Programmed DSBs also occur at the Immunoglobulin (Ig) loci to ensure V(D)J recombination for antibody diversification and Class Switch Recombination (CSR) to generate different antibody isotypes. On the Ig heavy chain locus (Igh) productive CSR results in a deletion event after recombination between two Switch (SH) sequences, located up to 100kb apart. Here as well, the initial 3D chromatin conformation exerts a regulatory role on both break formation and repair ( [START_REF] Vian | The energetics and physiological impact of cohesin extrusion[END_REF][START_REF] Rocha | A Damage-Independent Role for 53BP1 that Impacts Break Order and Igh Architecture during Class Switch Recombination[END_REF] reviewed in [START_REF] Aiden | Somatic rearrangement in B cells: it's (mostly) nuclear physics[END_REF]). For instance, deletion of the CTCF-binding sites encompassed in the Igh Superanchor (SA), correlates with a decrease in cohesin-mediated loop extrusion (detected by "stripes" on Hi-C maps) and reduces CSR [START_REF] Vian | The energetics and physiological impact of cohesin extrusion[END_REF]. Similarly, V(D)J recombination, both on Ig and Igh loci, strongly relies on long-range chromatin interactions.

For instance, deletion of CTCF-binding sites in the Intergenic Control Region-1 (IGCR1) upstream the D segments on Igh locus, impairs normal V to DJ recombination and B cells development in a manner that coincides with modification of chromosomal loops [START_REF] Guo | CTCF-binding elements mediate control of V(D)J recombination[END_REF][START_REF] Jain | CTCF-Binding Elements Mediate Accessibility of RAG Substrates During Chromatin Scanning[END_REF].

Similarly, deletion of a specific enhancer-CTCF bound-element on the Ig locus perturbs the antibody repertoire in a manner that also correlates with the loss of long-range interaction [START_REF] Barajas-Mora | A B-Cell-Specific Enhancer Orchestrates Nuclear Architecture to Generate a Diverse Antigen Receptor Repertoire[END_REF].

It is hence clear from all these studies that the initial chromosome architecture contributes to DSB signaling, processing and repair. Yet, while our knowledge regarding the role of longrange chromatin interactions and TADs during repair of programmed DSBs quickly expands, our understanding of their function into repair of endogenous DSBs in somatic cells still lags behind and will necessitate future 3C-based studies using sequence-specific DSB induction systems.

How does Chromatin Architecture change post-damage in cis to DSB, within H2AX

domains?

Another important question that needs to be addressed is the nature of the changes in chromosome architecture following damage (Figure 2). Indeed, DSB-induced modifications in the size of DNA loops or the position of TADs boundaries could regulate chromatin flexibility (stiffness) thereby regulating the DSB mobility in the nucleus [START_REF] Herbert | Chromatin stiffening underlies enhanced locus mobility after DNA damage in budding yeast[END_REF]. This could also help to "burry" (ie. protect) the DSB from its environment which therefore may have profound impacts on translocation biogenesis, partner choice for homologous recombination and more generally on genome integrity. Plenty of evidence supports that chromatin in cis to DSB displays a different behavior in terms of mobility, rigidity and compaction (reviewed in [START_REF] Marnef | Organizing DNA repair in the nucleus: DSBs hit the road[END_REF][START_REF] Zimmer | Chromatin mobility upon DNA damage: state of the art and remaining questions[END_REF]). In particular, laser-mediated, localized damage triggers a rapid chromatin decompaction at the sites of breaks [START_REF] Luijsterburg | PARP1 Links CHD2-Mediated Chromatin Expansion and H3.3 Deposition to DNA Repair by Non-homologous End-Joining[END_REF][START_REF] Sellou | The poly(ADP-ribose)-dependent chromatin remodeler Alc1 induces local chromatin relaxation upon DNA damage[END_REF][START_REF] Burgess | Activation of DNA damage response signaling by condensed chromatin[END_REF], in agreement with observations that H2AX foci displays decondensedlike appearance [START_REF] Kruhlak | Changes in chromatin structure and mobility in living cells at sites of DNA double-strand breaks[END_REF][START_REF] Dellaire | High resolution imaging of changes in the structure and spatial organization of chromatin, gamma-H2A.X and the MRN complex within etoposide-induced DNA repair foci[END_REF], suggesting that indeed, a DSB induces dramatic changes in chromatin conformation in cis. However, nearly all studies were performed using imaging, and our current knowledge of DSB-promoted 3D changes at the level of DNA sequence remains incredibly sparse. The first experiment using 3C methodology to assess cis modification of long-range interactions was performed in yeast following induction of a single DSB within the MAT locus by the HO endonuclease [START_REF] Oza | Mechanisms that regulate localization of a DNA double-strand break to the nuclear periphery[END_REF]. Strikingly long-range contacts were dramatically reduced following DSB in asynchronous cells, while such a decrease was not observed in G1-arrested cells [START_REF] Oza | Mechanisms that regulate localization of a DNA double-strand break to the nuclear periphery[END_REF], suggesting that end-processing (which occurs specifically in S/G2) rather than H2A spreading and checkpoint activation (occurring all throughout the cell cycle) was responsible for decreased chromosomal contacts. Reduced chromosome interaction frequency was further shown to depends on Rad51 loading and attributed to the sequestration of the DSB at the nuclear periphery [START_REF] Oza | Mechanisms that regulate localization of a DNA double-strand break to the nuclear periphery[END_REF][START_REF] Nagai | Functional targeting of DNA damage to a nuclear pore-associated SUMOdependent ubiquitin ligase[END_REF] (see next section). However, this decrease in long-range interaction following DSB was not reported in human cells [START_REF] Aymard | Genome-wide mapping of long-range contacts unveils clustering of DNA doublestrand breaks at damaged active genes[END_REF]. Instead, by using Capture Hi-C in the DIvA system (in which ~100 DSBs can be induced at annotated loci ( [START_REF] Aymard | Transcriptionally active chromatin recruits homologous recombination at DNA double-strand breaks[END_REF][START_REF] Iacovoni | Highresolution profiling of gammaH2AX around DNA double strand breaks in the mammalian genome[END_REF])) it was shown that, in average, the DSB itself engages more long-range contacts with neighboring sequences encompassed in H2AX domains, than before break induction ( [START_REF] Aymard | Genome-wide mapping of long-range contacts unveils clustering of DNA doublestrand breaks at damaged active genes[END_REF], reviewed in [START_REF] Clouaire | Taming Tricky DSBs: ATM on duty[END_REF]). Contrary to yeast, DSBs have not been found to relocate to the nuclear envelope in mammalian cells, which may account for the discrepancy between both studies. Notably, enhanced interactions between the DSB and DNA loci embedded in H2AX domains, would be in agreement with the increased mobility of DNA ends reported in multiple studies (reviewed in [START_REF] Marnef | Organizing DNA repair in the nucleus: DSBs hit the road[END_REF][START_REF] Zimmer | Chromatin mobility upon DNA damage: state of the art and remaining questions[END_REF][START_REF] Smith | Poetry in motion: Increased chromosomal mobility after DNA damage[END_REF]).

Of note, the resolution achieved by Capture-HiC in the above-mentioned study [START_REF] Aymard | Genome-wide mapping of long-range contacts unveils clustering of DNA doublestrand breaks at damaged active genes[END_REF] was insufficient to draw conclusions regarding the DNA loops reorganization around DSBs. Interestingly, although this was not directly assessed using Hi-C or 4C experiment, strong evidence suggests that chromosome loops are reorganized in cis to DSB induced by Spo11 in yeast meiotic cells. Indeed, in a WT strain, DSB production by Spo11 is negatively counteracted in a ~100kb window around an initial Spo11-created break. Notably, this phenomenon, called negative interference, depends on the yeast ATM ortholog Tel1, one of the main kinase activated during DDR [START_REF] Garcia | Tel1(ATM)-mediated interference suppresses clustered meiotic double-strand-break formation[END_REF]. This led to the proposal that, in cis to an initial break, ATM/Tel1 activation could drive chromatin loops reorganization, themselves being required and targeted for DSB formation (see previous section), hence contributing to negative interference and ensuring a proper distribution of DSBs along meiotic chromosomes [START_REF] Garcia | Tel1(ATM)-mediated interference suppresses clustered meiotic double-strand-break formation[END_REF][START_REF] Cooper | Meiotic DSB patterning: A multifaceted process[END_REF].

It is likely that the usual suspects shaping chromosome architecture, i.e. the cohesin complex and CTCF, are involved in such DSB-induced DNA loops reorganization. Studies in both yeast and mammals have demonstrated that cohesins and their loaders/regulators are recruited at DSBs [START_REF] Caron | Cohesin protects genes against γH2AX Induced by DNA double-strand breaks[END_REF][START_REF] Potts | Human SMC5/6 complex promotes sister chromatid homologous recombination by recruiting the SMC1/3 cohesin complex to doublestrand breaks[END_REF][START_REF] Unal | DNA damage response pathway uses histone modification to assemble a double-strand break-specific cohesin domain[END_REF][START_REF] Ström | Postreplicative recruitment of cohesin to double-strand breaks is required for DNA repair[END_REF][START_REF] Bot | Independent mechanisms recruit the cohesin loader protein NIPBL to sites of DNA damage[END_REF][START_REF] Meisenberg | Repression of Transcription at DNA Breaks Requires Cohesin throughout Interphase and Prevents Genome Instability[END_REF][START_REF] Ström | Postreplicative formation of cohesion is required for repair and induced by a single DNA break[END_REF][START_REF] Kim | Involvement of the cohesin protein, Smc1, in Atmdependent and independent responses to DNA damage[END_REF][START_REF] Wu | Scc1 sumoylation by Mms21 promotes sister chromatid recombination through counteracting Wapl[END_REF][START_REF] Hellmuth | Local activation of mammalian separase in interphase promotes double-strand break repair and prevents oncogenic transformation[END_REF][START_REF] Oka | Recruitment of the cohesin loading factor NIPBL to DNA double-strand breaks depends on MDC1, RNF168 and HP1γ in human cells[END_REF][START_REF] Lightfoot | Loading of meiotic cohesin by SCC-2 is required for early processing of DSBs and for the DNA damage checkpoint[END_REF][START_REF] Kong | Distinct functions of human cohesin-SA1 and cohesin-SA2 in double-strand break repair[END_REF], and post-translationally modified following damage (for instance, [START_REF] Kim | Involvement of the cohesin protein, Smc1, in Atmdependent and independent responses to DNA damage[END_REF][START_REF] Wu | Scc1 sumoylation by Mms21 promotes sister chromatid recombination through counteracting Wapl[END_REF][START_REF] Yazdi | SMC1 is a downstream effector in the ATM/NBS1 branch of the human S-phase checkpoint[END_REF][START_REF] Unal | DNA double-strand breaks trigger genomewide sister-chromatid cohesion through Eco1 (Ctf7)[END_REF][START_REF] Mcaleenan | SUMOylation of the α-kleisin subunit of cohesin is required for DNA damageinduced cohesion[END_REF][START_REF] Heidinger-Pauli | Distinct targets of the Eco1 acetyltransferase modulate cohesion in S phase and in response to DNA damage[END_REF]). Strikingly, in yeast, DSB-induced cohesin binding takes place on a large chromosomal domain surrounding the break [START_REF] Unal | DNA damage response pathway uses histone modification to assemble a double-strand break-specific cohesin domain[END_REF][START_REF] Ström | Postreplicative recruitment of cohesin to double-strand breaks is required for DNA repair[END_REF], in contrast to mammalian cells, where it only occurs on few kilobases [START_REF] Caron | Cohesin protects genes against γH2AX Induced by DNA double-strand breaks[END_REF]. While cohesin loading has long been involved in sister chromatid cohesion during HR [START_REF] Ström | Postreplicative formation of cohesion is required for repair and induced by a single DNA break[END_REF][START_REF] Unal | DNA double-strand breaks trigger genomewide sister-chromatid cohesion through Eco1 (Ctf7)[END_REF][START_REF] Mcaleenan | SUMOylation of the α-kleisin subunit of cohesin is required for DNA damageinduced cohesion[END_REF][START_REF] Takahashi | The MCM-binding protein ETG1 aids sister chromatid cohesion required for postreplicative homologous recombination repair[END_REF][START_REF] Bauerschmidt | Cohesin promotes the repair of ionizing radiation-induced DNA double-strand breaks in replicated chromatin[END_REF][START_REF] Covo | Cohesin Is limiting for the suppression of DNA damage-induced recombination between homologous chromosomes[END_REF][START_REF] Sjögren | Sister chromatid cohesion is required for postreplicative double-strand break repair in Saccharomyces cerevisiae[END_REF][START_REF] Dodson | Increased sister chromatid cohesion and DNA damage response factor localization at an enzyme-induced DNA double-strand break in vertebrate cells[END_REF], in mammalian cells, it is also recruited at DSBs during G1 phase [START_REF] Caron | Cohesin protects genes against γH2AX Induced by DNA double-strand breaks[END_REF][START_REF] Meisenberg | Repression of Transcription at DNA Breaks Requires Cohesin throughout Interphase and Prevents Genome Instability[END_REF], suggesting that this complex exerts a function beyond sister chromatid cohesion at DSB. In agreement, cohesin regulates transcriptional repression of genes immediately in cis to DSBs [START_REF] Meisenberg | Repression of Transcription at DNA Breaks Requires Cohesin throughout Interphase and Prevents Genome Instability[END_REF], insulate the active genes located farther within the H2AX domain to maintain their transcription [START_REF] Caron | Cohesin protects genes against γH2AX Induced by DNA double-strand breaks[END_REF] and controls the NHEJ repair pathway [START_REF] Gelot | The cohesin complex prevents the end-joining of distant DNA double-strand ends in S phase: Consequences on genome stability maintenance[END_REF].

Similarly, CTCF has also been shown to be recruited at DSBs [START_REF] Lang | CTCF prevents genomic instability by promoting homologous recombination-directed DNA double-strand break repair[END_REF][START_REF] Hilmi | CTCF facilitates DNA double-strand break repair by enhancing homologous recombination repair[END_REF][START_REF] Han | CTCF participates in DNA damage response via poly(ADP-ribosyl)ation[END_REF] and to contribute to HR [START_REF] Lang | CTCF prevents genomic instability by promoting homologous recombination-directed DNA double-strand break repair[END_REF][START_REF] Hilmi | CTCF facilitates DNA double-strand break repair by enhancing homologous recombination repair[END_REF].

Beyond these well-known architectural proteins involved in chromatin looping, DSB repair factors may also contribute to shape chromatin 3D structure in cis to DSB. Among these, 53BP1 is an interesting candidate since it was shown to spread on entire H2AX domains [START_REF] Clouaire | Comprehensive Mapping of Histone Modifications at DNA Double-Strand Breaks Deciphers Repair Pathway Chromatin Signatures[END_REF] and to be a critical determinant of the architecture of the Igh locus, even before damage formation [START_REF] Rocha | A Damage-Independent Role for 53BP1 that Impacts Break Order and Igh Architecture during Class Switch Recombination[END_REF][START_REF] Feldman | 53BP1 Contributes to Igh Locus Chromatin Topology during Class Switch Recombination[END_REF]. Additionally, the 53BP1 effector Rif1, which is recruited at DSB to regulate resection [START_REF] Chapman | RIF1 is essential for 53BP1-dependent nonhomologous end joining and suppression of DNA double-strand break resection[END_REF][START_REF] Virgilio | Rif1 prevents resection of DNA breaks and promotes immunoglobulin class switching[END_REF][START_REF] Zimmermann | 53BP1 regulates DSB repair using Rif1 to control 5' end resection[END_REF] is also of interest, as it was recently shown by 4C-seq to be a main organizer of chromatin architecture in unchallenged cells [START_REF] Foti | Nuclear Architecture Organized by Rif1 Underpins the Replication-Timing Program[END_REF]. Importantly both factors are essential for productive CSR [START_REF] Chapman | RIF1 is essential for 53BP1-dependent nonhomologous end joining and suppression of DNA double-strand break resection[END_REF][START_REF] Virgilio | Rif1 prevents resection of DNA breaks and promotes immunoglobulin class switching[END_REF][START_REF] Manis | 53BP1 links DNA damage-response pathways to immunoglobulin heavy chain class-switch recombination[END_REF][START_REF] Bothmer | Regulation of DNA end joining, resection, and immunoglobulin class switch recombination by 53BP1[END_REF], which further highlight their potential role in organizing the 3D structure of DSB-surrounding chromatin.

Yet, despite all these studies, a clear picture of the DNA conformation within H2AX foci is still awaited. Mapping of architectural proteins using ChIP-seq as well as determining chromatin conformation by 3C-based approaches around annotated DSBs, will certainly help to better understand the nature and function of DSB-induced chromosome loops changes.

How does Chromatin Architecture change post-damage in trans to DSB, within the nucleus?

In addition to the changes in cis described in the previous section, damaged chromosomes also experience more global reorganization within the nucleus. This is particularly apparent in yeast and Drosophila, where persistent, heterochromatic and/or rDNA breaks are relocalized at the nuclear periphery ( [START_REF] Oza | Mechanisms that regulate localization of a DNA double-strand break to the nuclear periphery[END_REF][START_REF] Nagai | Functional targeting of DNA damage to a nuclear pore-associated SUMOdependent ubiquitin ligase[END_REF][START_REF] Ryu | Heterochromatic breaks move to the nuclear periphery to continue recombinational repair[END_REF][START_REF] Horigome | Ribosomal RNA gene repeats associate with the nuclear pore complex for maintenance after DNA damage[END_REF] reviewed in [START_REF] Marnef | Organizing DNA repair in the nucleus: DSBs hit the road[END_REF]). Similarly in mammals, DSBs induced in rDNA and  satellites are extruded at the periphery of the nuclear sub-compartment (nucleolus and heterochromatic focus respectively) [START_REF] Tsouroula | Temporal and Spatial Uncoupling of DNA Double Strand Break Repair Pathways within Mammalian Heterochromatin[END_REF][START_REF] Van Sluis | A localized nucleolar DNA damage response facilitates recruitment of the homology-directed repair machinery independent of cell cycle stage[END_REF][START_REF] Harding | ATM dependent silencing links nucleolar chromatin reorganization to DNA damage recognition[END_REF]. Beyond these large scale reorganizations, DSBs are also capable of clustering together (i.e.: regrouping in one visible focus) ( [START_REF] Aymard | Genome-wide mapping of long-range contacts unveils clustering of DNA doublestrand breaks at damaged active genes[END_REF][START_REF] Aten | Dynamics of DNA double-strand breaks revealed by clustering of damaged chromosome domains[END_REF][START_REF] Krawczyk | Clustering of double strand break-containing chromosome domains is not inhibited by inactivation of major repair proteins[END_REF][START_REF] Neumaier | Evidence for formation of DNA repair centers and dose-response nonlinearity in human cells[END_REF][START_REF] Cho | Interchromosomal homology searches drive directional ALT telomere movement and synapsis[END_REF][START_REF] Caron | Non-redundant Functions of ATM and DNA-PKcs in Response to DNA Double-Strand Breaks[END_REF][START_REF] Krawczyk | Chromatin mobility is increased at sites of DNA double-strand breaks[END_REF][START_REF] Schrank | Nuclear ARP2/3 drives DNA break clustering for homology-directed repair[END_REF][START_REF] Waterman | Live cell monitoring of double strand breaks in S. cerevisiae[END_REF] reviewed in [START_REF] Marnef | Organizing DNA repair in the nucleus: DSBs hit the road[END_REF][START_REF] Guénolé | A meeting at risk: Unrepaired DSBs go for broke[END_REF]). Using Capture Hi-C to map long-range interactions following induction of multiple annotated DSBs on the human genome, it was recently demonstrated that DSBs can cluster together if they occur in transcriptionally active, RNA Pol II-bound, loci [START_REF] Aymard | Genome-wide mapping of long-range contacts unveils clustering of DNA doublestrand breaks at damaged active genes[END_REF] (reviewed in [START_REF] Marnef | Transcription-Coupled DNA Double-Strand Break Repair: Active Genes Need Special Care[END_REF][START_REF] Clouaire | A Snapshot on the Cis Chromatin Response to DNA Double-Strand Breaks[END_REF][START_REF] Guénolé | A meeting at risk: Unrepaired DSBs go for broke[END_REF]). Of interest, clustering was mostly observed in G1 cells [START_REF] Aymard | Genome-wide mapping of long-range contacts unveils clustering of DNA doublestrand breaks at damaged active genes[END_REF][START_REF] Aten | Dynamics of DNA double-strand breaks revealed by clustering of damaged chromosome domains[END_REF] and coincided with delayed repair [START_REF] Aymard | Genome-wide mapping of long-range contacts unveils clustering of DNA doublestrand breaks at damaged active genes[END_REF], suggesting that it may contribute in "poising" DSB repair in order to ensure faithful genetic information recovery [START_REF] Aymard | Genome-wide mapping of long-range contacts unveils clustering of DNA doublestrand breaks at damaged active genes[END_REF][START_REF] Guénolé | A meeting at risk: Unrepaired DSBs go for broke[END_REF]. The mechanism(s) at work to ensure DSB clustering and other DSB mobility events are still under investigation but may rely on both active/directional and passive/diffusive movement (Figure 3).

Cyto and nucleo-skeleton networks.

Evidence suggests that DSB ends mobility and DSB clustering are mediated at least in part thanks to the cyto-and nucleo-skeleton network (reviewed in [START_REF] Guénolé | A meeting at risk: Unrepaired DSBs go for broke[END_REF][START_REF] Hurst | Nuclear Actin and Actin-Binding Proteins in DNA Repair[END_REF]). Indeed, formin 2, an actin organizer, as well as the Arp2/3 actin branching factor and the Arp2/3 activator WASP, are required for clustering in human cells [START_REF] Aymard | Genome-wide mapping of long-range contacts unveils clustering of DNA doublestrand breaks at damaged active genes[END_REF][START_REF] Schrank | Nuclear ARP2/3 drives DNA break clustering for homology-directed repair[END_REF] (Figure 3, left panel). Moreover, nuclear myosin 1 and actin were recently reported as mediating damaged-induced homologous chromosome pairing in G0/G1 cells, in a manner that depends on the ability of actin to polymerize (by the use of actin mutants) [START_REF] Evdokimova | Nuclear myosin/actin-motored contact between homologous chromosomes is initiated by ATM kinase and homology-directed repair proteins at double-strand DNA breaks to suppress chromosome rearrangements[END_REF]. Of importance, although nuclear actin filaments (F-actin) have been reported and involved in relocating heterochromatic DSBs in Drosophila nuclei [START_REF] Caridi | Nuclear Factin and myosins drive relocalization of heterochromatic breaks[END_REF], such actin filaments still remain to be observed in mammalian nuclei. Indeed, DNA damaging agents do induce nuclear F-actin [START_REF] Belin | DNA damage induces nuclear actin filament assembly by Formin -2 and Spire-½ that promotes efficient DNA repair[END_REF], but no clear link with damage sites were reported. More recently, actin was described to form foci colocalizing with H2AX rather than filaments following damage [START_REF] Schrank | Nuclear ARP2/3 drives DNA break clustering for homology-directed repair[END_REF]. Hence the contribution of nuclear F-actin during clustering still needs further clarification. On another hand, the microtubule (MTs) network may also contribute to DSB mobility and clustering. Perturbation of MTs using drugs impairs DNA ends mobility [START_REF] Lottersberger | 53BP1 and the LINC Complex Promote Microtubule-Dependent DSB Mobility and DNA Repair[END_REF][START_REF] Lawrimore | Microtubule dynamics drive enhanced chromatin motion and mobilize telomeres in response to DNA damage[END_REF], although this was not observed in other settings [START_REF] Waterman | Live cell monitoring of double strand breaks in S. cerevisiae[END_REF][START_REF] Amitai | Visualization of Chromatin Decompaction and Break Site Extrusion as Predicted by Statistical Polymer Modeling of Single-Locus Trajectories[END_REF]. Moreover, nuclear MTs were observed in yeast damaged nuclei and proposed to mediate directional movement [START_REF] Oshidari | Nuclear microtubule filaments mediate non-linear directional motion of chromatin and promote DNA repair[END_REF]. While DSB-induced nuclear MTs still need to be identified in other conditions and organisms, it is nevertheless clear from many studies that the LINC complex, embedded in the nuclear envelope and connecting the cytoskeleton (including cytoplasmic MTs) to nuclear lamina and chromatin, also controls DSB mobility and clustering ( [START_REF] Aymard | Genome-wide mapping of long-range contacts unveils clustering of DNA doublestrand breaks at damaged active genes[END_REF][START_REF] Lottersberger | 53BP1 and the LINC Complex Promote Microtubule-Dependent DSB Mobility and DNA Repair[END_REF], reviewed in [START_REF] Marnef | Organizing DNA repair in the nucleus: DSBs hit the road[END_REF][START_REF] Guénolé | A meeting at risk: Unrepaired DSBs go for broke[END_REF]). It was therefore proposed that the cytoskeleton may also contribute to DSB mobility and clustering by transmitting forces from the cytoplasm to chromatin through the nuclear envelope and the LINC complex ( [START_REF] Lottersberger | 53BP1 and the LINC Complex Promote Microtubule-Dependent DSB Mobility and DNA Repair[END_REF], reviewed in in [START_REF] Guénolé | A meeting at risk: Unrepaired DSBs go for broke[END_REF]) (Figure 3 middle panel).

Contribution of phase separation in compartmentalization.

It is also tempting to speculate that phase separation could contribute into DSB clustering, as reported for heterochromatin foci formation (Figure 3 right panel). Indeed, H3K9me3 covered chromatin tends to phase separate thanks to the contribution of Heterochromatin Protein 1 (HP1) [START_REF] Larson | Liquid droplet formation by HP1α suggests a role for phase separation in heterochromatin[END_REF][START_REF] Strom | Phase separation drives heterochromatin domain formation[END_REF]. In this respect it is of interest that HP1 is involved in DSB repair and recruited at DSB [START_REF] Oka | Recruitment of the cohesin loading factor NIPBL to DNA double-strand breaks depends on MDC1, RNF168 and HP1γ in human cells[END_REF][START_REF] Baldeyron | HP1alpha recruitment to DNA damage by p150CAF-1 promotes homologous recombination repair[END_REF][START_REF] Lee | HP1 promotes tumor suppressor BRCA1 functions during the DNA damage response[END_REF][START_REF] Wu | Interaction of BARD1 and HP1 is required for BRCA1 retention at sites of DNA damage[END_REF][START_REF] Alagoz | SETDB1, HP1 and SUV39 promote repositioning of 53BP1 to extend resection during homologous recombination in G2 cells[END_REF][START_REF] Luijsterburg | Heterochromatin protein 1 is recruited to various types of DNA damage[END_REF][START_REF] Ayrapetov | DNA double-strand breaks promote methylation of histone H3 on lysine 9 and transient formation of repressive chromatin[END_REF]. Moreover damage foci were found to form liquid-like compartments in a manner that is seeded by Poly-ADP-Ribose Polymerase (PARP) activity and by the formation of Poly-ADP-Ribose (PAR) chains [START_REF] Altmeyer | Liquid demixing of intrinsically disordered proteins is seeded by poly(ADP-ribose)[END_REF], as well as by the contribution of the low-complexity domains (LCDs) RNA binding proteins, such as FUS [START_REF] Singatulina | PARP-1 Activation Directs FUS to DNA Damage Sites to Form PARG-Reversible Compartments Enriched in Damaged DNA[END_REF]. Notably, a recent study reported that 53BP1 foci display droplet like behavior, and that their assembly, fusion and dissociation are phase separation dependent [START_REF] Kilic | Phase separation of 53BP1 determines liquid-like behavior of DNA repair compartments[END_REF]. Hence, the chromatin landscape established in cis to DSB (including histone modifications but also LCD-proteins, or other repair proteins recruitment at sites of damage), may contribute to compartmentalize DSBs repair sites through a phaseseparation driven mechanism.

Concluding remarks

While our knowledge of the nature and function of chromatin during DSB repair recently greatly expanded, more studies are now necessary to understand the nature and function of chromatin conformation in these processes. Importantly, modifications of chromosome looping likely display essential function in safeguarding genome integrity and driving genome evolution. For instance, chromosome architecture is strongly linked to the generation of translocation involving the Igh locus [START_REF] Zhang | Spatial organization of the mouse genome and its role in recurrent chromosomal translocations[END_REF] and DSB clustering is a key player in translocation biogenesis [START_REF] Gothe | Dynamics of Double-Strand Breaks: Implications for the Formation of Chromosome Translocations[END_REF]. In conclusion, time has now come to make use of the ever growing, sequencing-based, methodologies designed to investigate chromosome architecture at the highest achievable resolution, to tackle the function of chromatin conformation and looping in genome stability. Following DSB production and H2AX spreading, the 3D conformation of damaged TAD could also be modified, due to the binding of cohesin, CTCF or repair proteins with potential function in chromatin architecture such as 53BP1 and RIF1. The DSB-induced histones modifications (including H2AX spreading), nucleosome loss or/and generation of single strand DNA (resection) may also collectively change the dynamics of chromatin within TADs.

Altogether, these changes could translate in enhanced mobility and efficient DSB repair.

Figure 1 :

 1 Figure 1: Contribution of the initial chromatin conformation into H2AX establishment

Figure 3 :

 3 Figure 3: Changes in chromosome conformation upon damage in trans such as during

Acknowledgements

We apologize to our colleagues whose works could not be included in this review owing to space limitations. The G.L. laboratory is funded by grants from the European Research Council (ERC-2014-CoG 647344), Agence Nationale pour la Recherche (ANR-14-CE10-0002-01 and ANR-13-BSV8-0013), the Institut National contre le Cancer (INCA), and the Ligue Nationale contre le Cancer (LNCC).

Competing interests

The authors have no competing interest to declare.

A. The initial chromosome conformation may dictate H2AX spreading following DSB induction. In this model, ATM, the main H2AX kinase is locally recruited at the DSB. Once bound, it is able to phosphorylate H2AX containing nucleosomes brought to its physical proximity, thanks to chromatin dynamics that takes place within the TAD. Sustained signaling and ATM activation eventually triggers the phosphorylation of H2AX on the entire TAD. In this model, H2AX distribution, as observed by ChIP-seq, should mimic the 3D chromatin conformation.

B. Chromosome conformation is critical during meiotic breaks formation by Spo11. During prophase, meiotic chromosomes are strongly reorganized with the formation of DNA loops anchored to a proteinaceous axis. Spo11 generates DSBs within DNA loops, which can further pair with the homologous chromosome in order to produce crossover and to complete meiosis.

The 3D chromatin structure and the chromosomal axis are required for both DSB production by Spo11 and to ensure the "homologous bias" (i.e. the choice of the homologous chromosome rather than the sister chromatid, as a template for HR) C. Chromosome conformation is also critical for the rearrangements that occur on immunoglobulin loci, in order to generate immunoglobulin isotypes (class switch recombination (CSR)) and the antibody repertoire (VDJ recombination). For example, during CSR (shown here), the long-range physical interactions between switch (S) sequences on the heavy chain locus (Igh) allows two DSBs to be rejoined.