Duclair Tchana Kamgne

Bridinette Thiodjio Sendja

Danilo Oliveira De Souza
email: danilo.oliveiradesouza@elettra.eu

Dominik Schaniel

Giuliana Aquilanti

An experimental XAS and ab initio approach to describe the electronic and local structure of sodium nitroprussiate single crystals

Keywords: Photoswitchable compound, Electronic properties, X-ray Absorption Spectroscopy, Pre-edge features, NO ligand

The electronic and local structural properties of single crystals in the ground state (GS) of the photo-switchable compound Na2[Fe(CN)5NO]•2H2O (sodium nitroprussiate, SNP) have been investigated by X-ray Absorption Fine Structure Spectroscopy (XAFS) and FEFF simulations. In SNP, the XANES (X-ray Absorption Near Edge Structure) pre-edge region presents three distinct peaks with different intensities depending on the crystal axis orientation with respect to the polarization direction of the X-ray beam. The peaks correspond to a combination of 1s to 4p and 1s to 3d transitions with possibly mixed dipole and quadrupole character. The EXAFS fitting reveals, as expected, a biased structure according to the relative position of the crystal with respect to the beam polarization and the fittings are in accordance to theoretical values. The best fitted model has a large contribution from multi-scattering paths, which clarifies the interpretation of the actual peak contributions on the Fourier Transformed signal.

Introduction

Na2[Fe(CN)5NO]•2H2O or sodium nitroprussiate (SNP) is an intriguing compound with interesting properties. On the one hand, it is well known and used in clinical applications, namely as a vasodilator [START_REF] Carlson | Review of Vasodilators in acute decompensated heart failure: the old and the new[END_REF] but has also been investigated for cancer therapeutics due to its potential as a nitric oxide donor [START_REF] Huerta | Nitric Oxide Donors : Novel Cancer Therapeutics[END_REF]. On the other hand, SNP has been investigated due to its photosensitivity, especially since the discovery of so-called metastable states (see e.g. [START_REF] Gütlich | Photoswitchable coordination compounds[END_REF] for a review of these properties). As a matter of fact, these metastable states correspond to linkage isomers of the nitrosyl ligand, which are stable at low temperatures (at 100 K the lifetime is several years). As shown by X-ray and neutron diffraction as well as DFT calculations, the NO ligand can adopt three different structural configurations with respect to the central iron atom of the [Fe(CN)5NO] 2-octahedron: the nitrogen bound linear Fe-N-O ground state (GS), the oxygen bound linear Fe-O-N metastable state 1 (MS1) and the side-on bound bent η 2 (FeNO) metastable state 2 (MS2) [4], [START_REF] Carducci | Diffraction studies of photoexcited crystals: Metastable nitrosyl-linkage isomers of sodium nitroprusside[END_REF], [START_REF] Delley | Giant lifetimes of optically excited states and the elusive structure of sodiumnitroprusside[END_REF], [START_REF] Schaniel | Structure of the light-induced metastable state SII in Na2[Fe(CN)5NO]•2H2O[END_REF], [START_REF] Schaniel | Neutron diffraction shows a photoinduced isonitrosyl linkage isomer in the metastable state SI of Na2[Fe(CN)5NO]•2D2O[END_REF]. The generation of these photoinduced linkage isomers is ultrafast (a few hundred femtoseconds) and has been studied by time-resolved optical and infrared spectroscopy on single crystals [9,10] and is accompanied by large photochromic and photorefractive effects [START_REF] Schaniel | Light-induced absorption changes by excitation of metastable states in Na2[Fe(CN)5NO]•2H2O single crystals[END_REF][START_REF] Schaniel | Photoinduced Nitrosyl Linkage Isomers Uncover a Variety of Unconventional Photorefractive Media[END_REF]. These different structural configurations can be reversibly transferred between GS, MS1, and MS2 depending on the chosen irradiation wavelength as well as the polarization direction of the light with respect to the crystal axes [START_REF] Woike | Population dynamics of the two light-induced metastable states in Na2[Fe(CN)5NO]•2H2O single crystals[END_REF]. The peculiar polarization dependent properties of SNP have been investigated by polarized optical absorption spectroscopy on single crystals which revealed the light-induced absorption changes in SNP caused by the excitation of MS1 and MS2 and allowed for the assignment of the electronic transitions and comparison with theoretical results [START_REF] Schaniel | Light-induced absorption changes by excitation of metastable states in Na2[Fe(CN)5NO]•2H2O single crystals[END_REF]. Overall, to understand the properties of the metastable and ground states in SNP, many different techniques have been employed, but only a few studies using X-ray Absorption Spectroscopy (XAS), namely polarization dependent XAS on SNP single crystals on the Fe K-edge [START_REF] Gadeke | Electronic structure and local geometry of Na2[Fe(CN)5NO]•2H2O single crystals investigated by polarizationdependent x-ray absorption spectroscopy[END_REF] and XAS on the Fe L2,3 edge on SNP powder [START_REF] Nanba | Anisotropic charge-transfer effects in the asymmetric Fe(CN)5NO octahedron of sodium nitroprusside: a soft X-ray absorption spectroscopy study[END_REF]. [START_REF] Gadeke | Electronic structure and local geometry of Na2[Fe(CN)5NO]•2H2O single crystals investigated by polarizationdependent x-ray absorption spectroscopy[END_REF] [14] reported a strong dependence of the XANES and EXAFS spectra on the angle between polarization direction of the X-ray beam and the crystal axis.

XAS is element-specific and is suited to study in detail the local environment (geometry and electronic configuration) of a given atom to gain accurate insight into small changes that would occur upon photoexcitation of linkage isomers such as MS1 or MS2 in SNP. In this work we report a XAS experimental and ab initio study on the GS of SNP single crystals in different crystal axis orientation with a full modelling of the EXAFS and XANES spectra, which allow us to get newer insight on the fine structure of the molecule and pave the path to tailored in situ experiments in order to fully understand the physics behind metastable states on this compound. XAS is able to determine around the photo-absorber the interatomic distance, the number and type of species of the neighboring atoms, and the thermal or structural disorder of the positions of the neighboring atoms. It is a powerful tool which can provide chemical shortrange structural and electronic information of the neighbourhood of the photo absorber in various materials. It has been extensively used for such complex materials [[16], [START_REF] Deguchi | EXAFS study of doped ceria using multiple data set fit[END_REF], [START_REF] Cabaret | First-principles calculations of X-ray absorption spectra at the K edge of 3d transition metals: an electronic structure analysis of the pre-edge[END_REF], [START_REF] Lobacheva | The local structure and ferromagnetism in Fe-implanted SrTiO3 single crystals[END_REF], [START_REF] Giannici | Structure and Oxide Ion Conductivity: Local Order, Defect Interactions and Grain Boundary Effects in Acceptor-DopedCeria[END_REF]].

Materials and Methods

2.1.

Sample preparation

Large single crystals of SNP were recrystallized by slow evaporation from aqueous solutions using reagent grade Sodium nitroprusside dehydrate Na2[Fe(CN)5NO]•2H2O. Thin plates of the orthorhombic crystals (space group Pnnm [21,22]) were cut perpendicular to the crystal axes a, b, or c and ground to thicknesses of about 100 μm before being polished to optical quality. Powder of SNP was produced by grinding single crystals.

XAS experimental details

The SNP samples used for measurements were a powder and crystals cut along the, a-, band c-crystal axis. The ideal thickness of SNP for XAS measurements in transmission mode, is ~ 100 μm yielding an absorption jump of 1.2 and a total absorption of 1.55. These values are calculated considering the Fe K edge. Three different SNP crystals were used for the XAS measurements, corresponding to cuts perpendicular to the, a-, b-, and c-axis. The three platelike crystals had a thickness of about 84 μm along aand c-axis, and 165 μm along b-axis. The lateral dimensions of the crystals were 10 mm x 3 mm. The SNP powder was mixed with polyvinylpyrrolidone (PVP) in a proper dilution to have an absorption jump of ~1 and then compacted in a pellet of 13 mm of diameter. XAS measurements were carried out in transmission mode for powder and crystal samples at room temperature, at the Fe K edge (7112 eV) at the XAFS beamline [START_REF] Di | Novel XAFS capabilities at ELETTRA synchrotron light source[END_REF] of Elettra Synchrotron (Trieste, Italy). The storage ring was operated at 2 GeV yielding a minimum current of 309 mA. A double crystal silicon Si (111) monochromator was used with a detuning of 0.3 for harmonic rejection and the energy resolution ΔE/E was about 10 -4 . The value of 7112 eV was assigned to the first inflexion point of the XANES spectrum of Fe metal foil for the calibration of the monochromator. The ions chambers were filled with a mixture of Ar, N2 and He to have an absorption of 10%, 80% and 95% in the I0, I1, and I2 respectively at the energy of 7000 eV. The data were collected in the energy range of [6817-8350] eV with an energy step variable depending on the energy region. At least two scans were collected for the powder sample and four for crystals. The crystals were placed such as a-, b-or c-axis was perpendicular to the electric field 𝐸 ⃗ of the X-ray incident beam characterized by a wavevector 𝑘 ⃗ parallel to the crystal face considered.

EXAFS data analysis

EXAFS data analysis was performed for all measurements using the least-square fitting based on the multiple scattering approximation. The normalization and background extraction steps were done in Athena program according to Ravel and Newville [START_REF] Ravel | Athena, Artemis, Hephaestus: data analysis for x-ray absorption spectroscopy using Ifeffit[END_REF]. Spectra of the same sample were averaged in order to improve the statistical noise. Data were then normalized to one absorption event and aligned within 0.01 eV. The EXAFS signal was obtained as shown in the following equation:

(𝐄) = (𝝁-𝝁 𝟎 ) 𝝁 𝟎 . ( 1
)
Where µ and µ0 are the experimental absorption coefficient and a smooth spline representing the embedded-atom absorption background respectively. This step was followed by the Fourier Transform (FT) of the k-weighted EXAFS functions k²χ(E) using a Hanning window in the k range of [3-14] Å -1 . In order to evaluate the backscattering amplitudes and the phase shifts parameters, the FEFF6 code based on the ab initio multiple scattering calculations

𝑅 𝑓𝑎𝑐𝑡𝑜𝑟 = ∑ |𝑘 𝑠 2 (𝑘 𝑠 ) 𝑒𝑥𝑝 -𝑘 𝑠 2 (𝑘 𝑠 ) 𝑐𝑎𝑙𝑐 | |𝑘 𝑠 2 (𝑘 𝑠 ) 𝑒𝑥𝑝 | 𝑠 . ( 2
)

2.4.

XAS simulation

Ab initio XANES simulations were obtained by performing full multiple scattering calculations using FEFF9.0 at the Fe K edge of SNP based on the crystallographic structure obtained by Carducci et al. [START_REF] Carducci | Diffraction studies of photoexcited crystals: Metastable nitrosyl-linkage isomers of sodium nitroprusside[END_REF]. The XANES simulation in FEFF9 considers the treatment of the core-hole within the random phase approximation (RPA), the many-pole self-energy and the many-body spectral function convolution [START_REF] Rehr | Parameter-free calculations of X-ray spectra with FEFF9[END_REF]. We have used a self-consistent energy dependent exchange correlation Hedin-Lunqvist potential [28]. Self-consistency was obtained by successively calculating the electron density of states, electron density and Fermi level at each stage of simulation within a cluster centered on Fe atom of 3.3 Å, and then iterating. Full multiple scattering (FMS) calculations were carried out for a larger cluster of 4.6 Å. To simulate different orientations of the crystal as supposed to be irradiated by the linearly polarized x-ray beam, the polarization and ellipticity were used and adjusted accordingly. Further details on XANES simulations are available as Supplementary Material (SI).

The EXAFS simulation was done in linear polarization. It was performed through the calculations of potentials and phase shifts for a distance up to 5 Å. The paths with a represented weight percentage characterizing the scattering from the nearest neighbors were considered and the number was limited to improve the EXAFS results. The simulation was satisfactorily done in the Debye correlated model with the Debye-Waller factor adjusted to 0.02 Å 2 and Debye-temperature range of [190-315] K.

Results and discussion

Crystal orientation

Synchrotron radiation is linearly polarized in the orbit plane. Given that the wavevector 𝑘 ⃗ is perpendicular to the electric field of the x-ray beam, the orientation of the crystal is given with respect to the polarized x-ray beam that is characterized by the wavevector 𝑘 ⃗ and therefore the electric field 𝐸 ⃗ . Fig. 1 presents the main aspects of the crystal structure of SNP and the orientation of the [Fe(CN)5NO] 2-anion with respect to the crystal axes. In particular we note that the quasi-fourfold axis C-N-Fe-N-O lies within the ab-plane (Fe-N-O angle of 176.2°, C-Fe-N angle of 176.8°, and Fe-C-N angle of 179.8°). In the case of 𝑘 ⃗ //𝑎 , the electric field 𝐸 ⃗ can be parallel either to b-or to c-crystal axis [29]. In the same way, for 𝑘 ⃗ // 𝑏 ⃗ , 𝐸 ⃗ can be parallel to a-or c-crystal axis while it can be parallel to a-or b-crystal axis in the case of 𝑘 ⃗ // 𝑐 . By reasoning so, six orientations can be obtained. Fig. 1 illustrates the situation for a bcut crystal, for which the propagation vector 𝑘 ⃗ // 𝑏 ⃗ offers two possibilities to orient the electric field vector 𝐸 ⃗ along the a-or c-axis of the crystal. If 𝐸 ⃗ is along the c-axis, the electric field oscillates thus perpendicular to the C-N-Fe-N-O axis, whereas in the case of 𝐸 ⃗ is along the aaxis, the electric field vector oscillates along a and has thus a component parallel to C-N-Fe-N-O axis.

XANES results and discussions

Fig. 2 presents the simulated (panel a) and experimental (panel b) XANES spectra at Fe K-edge. The experimental spectrum collected of the powder sample could be simulated without considering the polarization in FEFF9, while the polarization has been taken into account as discussed in section 2.4 to simulate the data collected on the single crystals. The experimental data show similar features although some differences can be observed. The main resonance of the spectrum with polarization parallel to the c-axis is more intense and shifted to lower energy with respect to the other polarizations, while the spectrum of the powder sample clearly presents average features. The three vertical lines highlight the pre-edge features, indicated as A, B and C. These are all well-defined for the spectrum with 𝐸 ⃗ // 𝑐 . The features B and C broaden significantly for the other polarization configurations, resulting in an almost complete vanishing of peak C. In general, the pre-peak features observed in the pre-edge region of the Fe K-edge XANES absorption and the features above the edge are characteristic of the transition to bound states 1𝑠 → 3𝑑 and/or 1𝑠 → 4𝑝 [30, 31]. The region above the edge generally indicates the multiple scattering diffusion and the edge-crest describes the transitions to continuum or delocalized states as reported [START_REF] Berry | XANES calibrations for the oxidation state of iron in a silicate glass[END_REF]. The occupations of the 3d-orbitals depend on the properties of the ligands in the metal-ligand complexes. In such compounds, the molecular orbitals are formed as a linear combination between the metal valence orbitals which can be 3d, 4s and 4p on the one hand, and the ligand orbitals which are σ, π, σ * and π * , on the other hand. Also, the interactions between them (valence-ligand) depend on the symmetry of the complexes. Thus, it can be understood that, the SNP samples corresponding to 𝐸 ⃗ // 𝑎 , 𝐸 ⃗ // 𝑏 ⃗ and 𝐸 ⃗ //c contain in the pre-edge region transition to hybridized orbitals with likely both, dipolar and quadrupolar characters, as manifest by the three peaks at energy values of 7114.40 eV, 7119.12 eV and 7123.76 eV.

The octahedral systems are expected to have a K pre-edge structure dominated by quadrupolar transitions and can be deconvoluted in distinct contributions representing, essentially, the transitions to splitted-3d components t2g and eg. However, in lower symmetries and particularly on SNP single crystals, further orbital splitting may rise, including dipolar transitions, as observed in Fe II mineral samples [32] and α-Fe2O3 [START_REF] Dräger | On the Multipole Character of the X-Ray Transitions in the Pre-Edge Structure of Fe K Absorption Spectra. An Experimental Study[END_REF]. For that reason, we performed the modeling and fitting of the pre-edge region (the peak A in Fig. 2) using 2-4 pseudo-Voigt peaks. Fraction and sigma parameters of the pseudo-Voigt functions were constrained to be the same for all the peaks in the fit.

In the [Fe(CN)5NO] 2-anion of SNP the C4v symmetry is not perfect, the Fe-N-O angle is slightly smaller than 180 degrees. However, the quasi-fourfold axis N-C-Fe-N-O lies in the ab plane of the orthorhombic crystal structure, giving rise to a pronounced polarization dependence of the absorption spectra. Therefore 𝐸 ⃗ // 𝑐 indicates a polarization perpendicular to this rotation axis, while for 𝐸 ⃗ // 𝑎, 𝑏 ⃗⃗⃗⃗⃗⃗ , the polarization has contributions parallel to this fourfold rotation axis (see Fig. 1).

Considering that XANES from spectra 𝐸 ⃗ // 𝑎 are equal to 𝐸 ⃗ // 𝑏 ⃗ , we discuss them as one single representative direction. In this sense, both different crystal orientations (i.e., 𝐸 ⃗ // 𝑎 and 𝐸 ⃗ // 𝑐 ) were best fitted by using a 3-component model (Fig. 3), featuring a prominent one at higher energy, and intermediate intensity peak in the middle and a tiny shoulder at lower energy. Qualitatively, we observe that the individual components hold their position no matter the crystal orientation. Further, the centroid shift observed when comparing 𝐸 ⃗ // 𝑎 and 𝐸 ⃗ //c is due exclusively to the increasing in amplitude of the component centered around 7113 eV, while the main component (~ 7114.5 eV) remains with the same height. This isotropic behavior of the latter may suggest a dipolar transition, but a dedicated experiment is required to deal with this issue. Thus, a deep analysis on the angular dependence of the pre-peak intensities will be presented in a dedicated paper. Table 1 summarizes the results of the fits. The energy difference between the higher-energy peak component and the lower one is 3.7 eV and 4.8 eV, respectively, for 𝐸 ⃗ // 𝑎 and 𝐸 ⃗ //c , which suggests a ferric low-spin electronic configuration with an increased 10Dq due to stronger field induced by CN -ligands, as already observed on Fe III complexes [34]. This difference is a direct probe of the 10Dq parameter of the crystalline field and can help us to understand the electronic structure of the crystal. In order to do that, we consider the optical absorption study on the same material performed by one of the authors to correlate to the information obtained from pre-peaks and try to get newer insights on the electronic structure of the SNP molecule.

3.7702

As stated before, in XANES the difference in energy between the peaks of pre-edge corresponds to a direct measurement of the 10Dq parameter of the crystalline splitting of the material. However, it is well known that this value is quite different from that obtained by optical spectroscopy, instead it corresponds to about 80% of the ground state value [START_REF] Dräger | On the Multipole Character of the X-Ray Transitions in the Pre-Edge Structure of Fe K Absorption Spectra. An Experimental Study[END_REF]. In short words, this is mainly because in the final state in a XAS process, the excitation promoted by the x-ray photons let a core hole on the inner shell, as consequence there is a strong influence on the valence band due to the lower screening effect by the nucleus. Regarding 𝐸 ⃗ //𝑎 , one observes that the 10Dq value obtained from deconvolution of the pre-peak (ΔE = 3.7 eV) likely corresponds to the optical transition 6e→5a1 (ΔE = 4.66 eV, Fig. 4). Since regular XANES spectroscopy do not provide enough energy resolution (note that the full width at half maximum (FWHM) value is slight below 2 eV, Table 1), we do not attempt to attribute the component energy values from pre-edge region to a particular transition in the electronic structure obtained by optical spectroscopy. In an overall scenario, we can point out that, the low-energy pre-edge peak possibly includes 6e and 2b2 (or the t2g group) levels while the highenergy one includes 5a1 and 3b1 levels (eg group). The higher transitions (7119 and 7121 eV) are probably due, respectively, to metal to ligand charge transfer (MLCT) involving 8e (π*(CN)) [35, 36] and a long-range order effect [START_REF] Penfold | X-ray Spectroscopic Study of Solvent Effects on the Ferrous and Ferric Hexacyanide Anions[END_REF]. We have performed a 5-peak fitting model in a wider range in energy to include these two higher energy features (B and C in Fig. 2) in the pre-peak region (see Table 1). It is worth to note that this long-range fitting does not change the values of intensity and peak position from those obtained from 3-peak model.

Regarding 𝐸 ⃗ //c , the overall picture is quite similar. We observe, however, a wider distance between t2g and eg levels (ΔE = 4.8 eV). Also, the two "edge" peaks (features B and C, on the inset of Fig. 2b) are now resolved in two well separated peaks. It seems quite suggestive that -NO bond, responsible also for low down the crystal symmetry, is in charge for this effect. However, a quantitative analysis of this particular situation requires more experimental details (like a single crystal angular-dependence analysis, for instance) and maybe further theoretical calculations (preferentially using DFT).

SNP ([Fe(CN)5NO] 2-anion) exhibits a particular electronic structure, since the lowest unoccupied molecular orbital (LUMO) is the π*(NO), which energetically is placed in between the t2g and eg 3d iron orbitals (right) Scheme for the analysis of XANES measurements, assuming an initial transition 1s→3dx2-y2 followed by the emission of an Auger electron to 4pz and the corresponding relaxation of a t2g electron back to the 1s. Fig. 5 shows the EXAFS functions 𝑘 2 (𝑘) and the moduli of the Fourier transform (FT) of the experimental data collected for powder, 𝐸 ⃗ // 𝑎 , 𝐸 ⃗ // 𝑏 ⃗ and 𝐸 ⃗ // 𝑐 , and of the simulated data without polarization factors. Overall, the EXAFS spectra for all polarization directions and the powder spectrum exhibit the same main frequency and are in good agreement with the simulated spectrum. However, in the spectra with polarization parallel to the a-and baxis one can clearly observe an additional shoulder at about 3 Å -1 as well as some broadening in the range 5.5-6 Å -1 . These at first sight rather small differences result in significant differences in real space, as can be seen in Fig. 5b. The peaks are labelled P1, P2, P3 and P4 considering the 0-distance axis as the reference. In an earlier interpretation made by Gädeke et al. [START_REF] Gadeke | Electronic structure and local geometry of Na2[Fe(CN)5NO]•2H2O single crystals investigated by polarizationdependent x-ray absorption spectroscopy[END_REF], the two strong peaks P2 and P4 observed in all spectra would correspond to the Fe neighboring C and N atoms from the CN ligand. Then, when the polarization vector is parallel to the crystal a-or b-axis, the FT spectra clearly exhibit two more peaks P1 and P3 as a result of the additional scattering contribution from the -NO ligand. Thus, the resulting four peaks would be assigned respectively (according to the authors) to the N, C atoms of the CN ligand and O, N of the NO ligand. In the following, we report our finds in EXAFS analysis including multiple scattering. Fig. 7 shows the magnitude of the experimental functions at Fe K edge of SNP in both, R (the modulus as well as the real part) and k space, superimposed with the curves obtained by a least-square fitting procedure for samples corresponding to the powder, 𝐸 ⃗ // 𝑎 and 𝐸 ⃗ // 𝑐 , respectively. An accurate reproduction of the experimental spectra allowed us to determine the structural parameters characterizing the SNP system . Quantitative results related to the E0 value, interatomic distances (R), coordination numbers (CNu) and Debye-Waller factor ( 2 ) are presented in Table 2. The amplitude reduction factor S0 2 was fixed to 1 for all paths. The structural parameters for the sample 𝐸 ⃗ // 𝑏 ⃗ (not reported) are very close to those for sample 𝐸 ⃗ // 𝑎 . The goodness of the fit (Rfactor) is given for each case. The theoretical values of the interatomic distance are also shown for comparison. Differences on FT profile of Fig. 7 and8 are due to distinct window type used on the transformation, respectively, sine and Hanning.

EXAFS results and discussions

The powder sample (Fig. 7a, right and left panel) presents two distinct peaks, but it is expected to have contributions from all atoms on each ligand in any axis direction. The blue line on the picture stands for our best fit (green line on the right panel, which corresponds to the real part of the FT function), and the results are given in Table 2. For this fit, due to the fact that we use high-quality single crystals that are well characterized by x-ray diffraction (not shown here), all the coordination numbers were fixed to their nominal value. By doing so, we were able to test the theoretical expected bond distances and compare with the experimental results. Besides the excellent match between theory and experiment, we highlight that the sensitivity of the technique for this system is on the order of one hundredth of an Ångströms, which is an important parameter to be considered when dealing with our future experiments dedicated to depict the metastable states. Further, our results also show the slight distortion on the straight angle of the -NO branch with respect to the ab-plane, note that direct measurement of Fe-O is slightly lower than the multi-scattering path Fe-N1-O-N1-Fe, respectively, 2.8093(3) and 2.83(1) Å.

When fitting 𝐸 ⃗ // 𝑎 (and analogously for 𝐸 ⃗ // 𝑏 ⃗ , Figure 7b, left and right) the direction of the beam polarization with respect to the crystal allows us to see contributions from all the scatters of the system. We expect to see the short Nitrogen bond tied by an oxygen (corresponding to the -NO ligand, lying in the ab-plane) as well as the four-fold degenerated Carbon tied to a longer Nitrogen contribution from the -CN ligand (out of plane). FEFF calculations have shown the high weight of multiple scattering paths for the total signal, thus the addition of them considerably improved the quality of the fit (Table 2), as previously observed elsewhere [START_REF] Tolkiehn | 'experimental investigation of the systematic k-and zdependence of exafs back-scattering amplitudes and comparison with theory[END_REF]. To perform this fit we have considered three different N bonds on the system, since they are not equivalent: a short one from the -NO ligand (N1), one longer (N2) from -CN, both lying on the mirror plane, and a third from the -CN ligands that are out of plane (N3, which is four-fold degenerated). It is worth to note that in alternative N2 and N3 could be considered as one single contribution, as they are very close in value. However, actually they are not the same, and this is particularly important for our system description since multiscattering paths play an important role for the overall shape of the spectra, as we discussed above. Further, we did try a fit by doing N2 = N3 and we got the same Rfactor value (0.01), nonetheless the reduced-χ 2 favors the model where N2 is independent from N3 (actually, constrained to be twice N2 value). Following this argument, we have also proposed two distinct carbon contributions for our model, one tied to the -CN ligand in the ab-plane (C1) and the other related to carbon from out-of-plane scatterings (C2), which must be four-fold degenerated. On the latter, also the coordination number was constrained to be twice that from c-axis, i.e., C2 = 4*C1. As a matter of fact, a model where carbon atoms were fixed to the nominal value gave a far worst fit. On the Table 2, we added a corresponding subscript to make clearer the correspondence among parameter and axis origin. Concerning the bond distances, they are inside the expected range, for instance, N1 matches the value from powder fit as well as the average value from C1 and C2 matches the one from powder sample. The coordination numbers of the carbon or nitrogen atoms from -CN ligands are acceptable considering the error bars and the relatively higher values may come from some correlation with other parameters, for instance C1 has its higher correlation value equals to 0.6737 with ΔE0. Indeed, ΔE0 parameter on the a-axis fit is the one that presents the higher error bar comparing to the other fits (even if it is inside the typical range). For sake of clarity, -N1 and O contributions come from exclusively from -NO ligand and must be always equals to 1. For that reason, we kept fixed coordination numbers of these two components. The FT of EXAFS signal in 𝐸 ⃗ // 𝑐 (Figure 7c, left and right panels) presents a completely different shape when compared to 𝐸 ⃗ // 𝑎 and this can be understood, as already discussed, considering the polarization direction of the beam with respect to the crystal orientation, which acts as a sort of filter for a selected direction. In this particular case, it filters the ab-plane, in which lies the N-C-Fe-N-O branch of the structure. We thus expected to observe only the contributions from the four -CN ligands out of the ab-plane. Another point to be highlighted is that the apparent similarity of powder and 𝐸 ⃗ // 𝑐 FT spectra and any possibility of qualitative misinterpretation based on peak position of intensity is promptly broke when one looks at real part of the spectra (green lines on Fig. 7a and7c, right panels). The distinction between them means that the origin of the peaks is different, as we actually see on the results of the fits (Table 3), and their close final shape is just a coincidence. We have seen so far with the EXAFS fitting of the different faces of the crystal that multi-scattering paths have a huge contribution for the final aspect of the curve and they cannot be neglected during the modeling. To make clearer this issue, Fig. 8 highlight the individual contributions of the scattering paths of the model to the fit of the powder sample, as an example of the importance of such scatterings for the overall spectrum. In the left panel is drawn the FT of EXAFS in R-space (open circles), its fit (blue line) and the individual contribution of each scattering to the fit (actually, the real part). It is shown clearly that even if we have 4 different atomic contributions (short N and C atoms from -CN ligand as well as O, N from -NO ligand) in the structure, they cannot be individualized as a single peak in the FT (nor even a convolution), which is a current misconception in EXAFS analysis. On a hypothetical radial distribution function scenario, carbon should count as the position and intensity of the first high FT peak (~ 1.6 Å, without phase correction), but definitely both nitrogen scatterings contribute for this first peak as well as multiple-scatterings, which spans from 0.5 up to 3.5 Å. In fact, their presence dominates the high term (R > 2 Å) on FT of both data. Actually, for longer distances, the focusing effect promoted by the alignment of the scatters highlights the longer contributions, as viewed in the intensities of the back transformed waves on right panels of Fig. 8. It is worth to note that the presence of simulated multi-scattering paths contributes to reinforce the stability of the proposed model and to support the veracity of the fit results. Summarily, our EXAFS results show great accordance with the expected structure and we were able to describe fine aspects from the crystal, such as the distinction of 3 different N contributions on 𝐸 ⃗ // 𝑎 fit. On the other hand, this full description with a particular importance of the inclusion of multi-scattering peaks and their influence for the final aspect of the Fourier

~C ~N2 ~C

Transform of the EXAFS is fundamental to update the interpretation given by Gadeke et al.

[14], which attributed single peaks to single atomic contributions. As our analysis clearly shows this oversimplified interpretation is inadequate and might even lead to false conclusions if taken as such.

Conclusion

To conclude, we have shown that the properties of a complex system such as SNP (Na2[Fe(CN)5NO]2H2O, prototype) can be investigated through polarized x-ray absorption spectroscopy. Fine and full modelling of XANES and EXAFS allowed to see details from the lower symmetry of the crystal (e.g., difference in pre-peak XANES and coordination numbers after EXAFS fitting). FEFF.9 code fails to nicely describe minor, nonetheless important, XANES features, however it is suitable to simulate polarization dependence in the EXAFS regime. In the XANES region, SNP exhibits pre-edge features which correspond to the combination of 1𝑠 → 4𝑝 and 1𝑠 → 3𝑑 transitions with a dominant character assimilated to a dipole character, as revealed by the difference between the two axes. A deconvolution of Fe pre-peaks allows to see that according to the energy range, they can possibly include 6e and 2b2 levels of t2g group and 5a1 and 3b1 of eg group. Another possibility is the presence of 8e (π*(CN) at high pre-peak energy. Even if a perfect correspondence with optical transition was not possible, our results pave a direction in how to perform further investigations coupling well-designed XAS study (using angle dependence detection and low temperature), FEFF simulation and optical experiments to solve the electronic structure of the crystal and to study its metastable state. EXAFS showed good agreement with theoretical values and we were able to also observe the influence of the distortion of the structure on coordination number and bond distances. Nevertheless, the most important achievement was to update the old (mis)interpretation in literature in which associated single peaks on Fourier transform to single atomic contributions of the crystal. We have seen the fundamental role played by multiscattering paths to the overall shape of the spectra and we expect that this work contributes to overcome such aged, guileless but still present understanding of the EXAFS as a radial distribution function.

[ 24 ]

 24 was used to generate the theoretical EXAFS signals using a cif file with the crystallographic parameters taken from Carducci et al. [5]. The fitting of the theoretical signals on the EXAFS experimental data was performed using Artemis program [24]. The data were fitted considering the k range of [3-14] Å -1 and R range of [1.1-3.0], [1.3-3.0] Å (respectively, for c-axis and aaxis). The fit for the powder were performed in the k range of [3-15.5] Å -1 and R of [1.1-3.0] Å. The reliability of the fits is reported through the Rfactor parameter minimizing the difference between the experimental (𝒌 𝒔 𝟐 (𝒌 𝒔 ) 𝒆𝒙𝒑 ) and calculated (𝒌 𝒔 𝟐 (𝒌 𝒔 ) 𝒄𝒂𝒍𝒄 ) spectra according to the following equation [25,26]

Figure 1 :

 1 Figure 1: (Left and top panel) Representation of the crystal structure of SNP (view along aaxis, sodium counter ions and water molecules have been omitted for clarity). The quasifourfold axis C-N-Fe-N-O lies within the ab-plane. (Lower right panel) If the b-axis of the crystal is parallel to the propagation vector of the X-ray beam (𝑘 ⃗ // 𝑏 ⃗ ), the electric field vector can be oriented 𝐸 ⃗ // 𝑎 ) or 𝐸 ⃗ // 𝑐 ) and thus parallel or perpendicular to the C-N-Fe-N-O molecular axis.

Figure 2 :

 2 Figure 2: Normalized Fe K-edge XANES spectra of SNP samples; a) simulated data, and Sim_Normal stands for simulated data without considering a polarization factor. b) Experimental data corresponding to 𝐸 ⃗ // 𝑎 , 𝐸 ⃗ // 𝑏 ⃗ and 𝐸 ⃗ // 𝑐 . Powder stands for the data collected on the powder sample. The insert is shown to highlight the pre-edge features in the experimental spectra.

Figure 3 :

 3 Figure 3: Fit of the pre-peak of Fe K-edge showing a deconvolution of three components related to dipolar and quadrupolar transitions. Fit corresponding to a-axis (upper panel), c-axis (middle) and experimental curves for a-and c-axis showing a clear shift in the centroid position (bottom). The blue line on the bottom panel is the difference between both experimental lines.

  [START_REF] Manoharan | Electronic Structure of Nitroprusside Ion[END_REF]. Adopting the nomenclature used elsewhere [6, 11, 36], the highest occupied molecular orbital (HOMO) is the dxy labelled 2b2 (see Fig.4, left panel), which together with the HOMO-1, the energetically degenerate dxz and dyz (6e) form the t2g. The eg composed of dz2 (5a1) and dx2-y2 (3b1) constitute the LUMO+1 and LUMO+2 (the energetic order of these two orbitals being inversed between Manoharan and Gray [36], and Delley et al. [6], The 7e π*(NO) LUMO has significant admixture of 3d orbitals, a characteristic of NO backbonding, which is reflected also in a significant admixture of π*(NO) to the 6e dxz and dyz orbitals (see e.g. Manoharan and Gray [36], or Braga et al. [37]). Polarized (optical) absorption spectroscopy has allowed for assignment of transitions within the 3d manifold and the π*(NO), as illustrated in Fig.4, the lowest lying transition 2b2→7e is found at 2.5 eV, followed by another transition 6e→7e into the LUMO and further intra-d transitions in the energy range of 3.95-4.65 eV. Transitions into higher states have been observed in solution [36], namely the 6e→8e (π*(CN)) at approximately 6.2 eV. Ref.[START_REF] Manoharan | Electronic Structure of Nitroprusside Ion[END_REF] provides calculated one-electron MO energies up to much higher levels, including the iron 4p states and further ligand-based orbitals such as π*(CN), σ(CN), and σ(NO). Several of these higher states have significant admixture of 3d, and potential transitions resulting from these calculations would yield energies (with respect to 2b2) around 6.4-8 eV, 9.4-10.1 eV and 14.1 eV.

Figure 4 :

 4 Figure 4: (left) Electronic structure of SNP with optical transitions as observed by polarized absorption spectroscopy [11]; (right) Scheme for the analysis of XANES measurements, assuming an initial transition 1s→3dx2-y2 followed by the emission of an Auger electron to 4pz and the corresponding relaxation of a t2g electron back to the 1s.

Figure 5 :

 5 Figure 5: a) Superimposed EXAFS oscillations and b) Fourier Transform functions (using a sine window function as filter) of the SNP experimental data collected for powder, 𝐸 ⃗ // 𝑎 (along a-crystal axis), 𝐸 ⃗ // 𝑏 ⃗ (along b-crystal axis), 𝐸 ⃗ // 𝑐 (along c-crystal axis) and simulated data without polarization factors. The plots have been done with stack for clarity.

Figure 6 :

 6 Figure 6: GS configuration according to X-ray diffraction results (at room temperature), highlighting the direction N-C-Fe-N-O in the ab plane, with their corresponding bond lengths and angles. The C-N-Fe-N-O direction has an angle of approximately 35° with the a-axis of the crystal.

Figure 7 .

 7 Figure 7. EXAFS signal of Fe K-edge experimental data and the best fit in k-space (left) as well as the Fourier Transform, i.e., in R-space (right) for powder sample (top), 𝐸 ⃗ // 𝑎 (middle) and 𝐸 ⃗ // 𝑐 (bottom). For the R-plot is shown the magnitude and the real part of the function.

Figure 8 .

 8 Figure 8. Individual contribution of the scattering paths for the real part of the FT EXAFS signal ( left) as well as the back Fourier Transform ( right) from Fe K-edge of SNP powder sample.

Table 1 -

 1 Main parameters fitted on deconvolution of Fe K-edge pre-peak of SNP. Two different ranges in energy were proposed, respectively, i) a 3-peak model ranged at 7108-7118 eV and ii) a 5-peak model ranged at 7108-7125 eV.

	Crystal Orientation	Peak Energy (eV)	Intensity (u. a.) (x 100)	FWHM	Red-χ 2 (x 10 -07 )
		7110.80 (0.20)	0.21 (0.03)
	i) E//a	7113.36 (0.04)	2.00 (0.10)	1.98 (0.02)	3.3052
		7114.50 (0.03)	3.60 (0.10)
		7109.90 (0.20)	0.11 (0.03)
	i) E//c	7113.26 (0.08)	0.67 (0.60)	1.80 (0.02)	3.4325
		7114.74 (0.01)	3.44 (0.50)
		7111.60 (0.70)	0.70 (0.60)	1.91 (0.04)
		7113.48 (0.05)	2.10 (0.10)	1.91 (0.04)
	ii) E//a	7114.57 (0.04)	3.30 (0.20)	1.91 (0.04)	3.6397
		7119.07 (0.07)	3.00 (0.10)	2.60 (0.40)
		7121.90 (0.10)	11.00 (1.00)	5.20 (0.80)
		7109.50 (0.50)	0.70 (0.50)	1.94 (0.04)
		7113.20 (0.20)	0.40 (0.10)	1.94 (0.04)
	ii) E//c	7114.76 (0.02)	3.40 (0.20)	1.94 (0.04)
		7119.24 (0.01)	9.20 (0.30)	2.57 (0.02)
		7123.80 (0.10)	16.00 (1.00)	6.10 (0.30)

Table 2 .

 2 Fitted structural parameters for the Fe bonding atoms of SNP complex. Rreff stands for theoretical interatomic distance. Number in parenthesis are the uncertainties, f superscript stands for fixed parameter during the fit and the * symbol corresponds to degeneracies of the multi-scattering paths instead of coordination number itself.

	Scattering	Ligands	CN u	R reff (Å)	R (Å)	² (Ų)
		Powder: Rfactor = 0.01, E0 = 1.6 (5) eV
	N1	-NO	1 f	1.663	1.66(1)	0.0041 (2)
	C	-CN	5 f	1.922	1.93(1)	0.0041 (2)
	O	-NO	1 f	2.809	2.8093(3)	0.0041 (2)
	N2	-CN	5 f	3.097	3.08(1)	0.0041 (2)
	~N1 ~O	-NO	2 *	2.809	2.83(1)	0.0041 (2)
	~N1 ~O ~N1	-NO	1 *	2.810	2.83(1)	0.0041 (2)
	~C ~N2	-CN	10 *	3.097	3.09(2)	0.0041 (2)
	~C ~N2 ~C	-CN	5 *	3.097	3.09(2)	0.0041 (2)
		𝐸 ⃗ // 𝑎 : Rfactor = 0.01, E0 = -2 (1) eV
	N1	-NO	1 f	1.663	1.64 (1)	0.0032 (6)
	C1	-CNc	1.2 (2)	1.913	1.880 (9)	0.0032 (6)
	C2	-CNab	4.8 (8)	1.922	1.96 (2)	0.0032 (6)
	O	-NO	1 f	2.809	2.82 (1)	0.0032 (6)
	N2	-CNc	1.2 (2)	3.085	3.089 (9)	0.0032 (6)
	N3	-CNab	4.8 (8)	3.096	3.11 (2)	0.0032 (6)
	~N1 ~O	-NO	2 *	2.809	2.81 (2)	0.0032 (6)
	~N1 ~O ~N1	-NO	1 *	2.810	2.81 (2)	0.0032 (6)
	~C1 ~N2	-CNc	4.8 (8)*	3.085	3.05 (1)	0.0032 (6)
	~C1 ~N2 ~C1	-CNc	1.2 (2)*	3.085	3.05 (1)	0.0032 (6)
	~C2 ~N3	-CNab	4.8 (8)*	3.096	3.15 (4)	0.0032 (6)
		𝐸 ⃗ // 𝑐 : Rfactor = 0.02, E0 = 0.1(8) eV
	C	-CNab	4.6 (4)	1.922	1.930 (7)	0.0015 (5)
	N	-CNab	4.6 (4)	3.097	3.092 (8)	0.0015 (5)
	~C ~N	-CNab	9.2 (8) f *	3.097	3.10 (1)	0.003 (1)
	~C ~N ~C	-CNab	4.6 (4) f *	3.097	3.10 (2)	0.003 (1)

Acknowledgments

The authors are grateful to IUPAP-IUCr-LAAMP within the ICSU Grants Programme 2016-2019 (Ref: 41100IUP12) who provided the support to Duclair Tchana Kamgne and Bridinette Thiodjio Sendja for the training in ELETTRA Synchrotron. They are also grateful to the XAFS beamline staff (Dr Simone Pollastri, Mr Luca Olivi and Mr Ricardo Grisonich) of Elettra Sincrotrone (Trieste, Italy). They also extend their acknowledgement to Andrea Lausi responsible of the LAAAMP in ELETTRA and Vivian Zaccaria of ICTP external of office activities. We thank Theo Woike for preparation of oriented SNP single crystals.


Alexandre Berquand

PhD Marie Meunier

MS Jessica Thevenard Devy

PhD Corinne Ivaldi

PhD Océane Campion

MS Stéphane Dedieu

PhD Michael Molinari
email: michael.molinari@u-bordeaux.fr

PhD Jérôme Devy
email: jerome.devy@univ-reims.fr

A gentle approach to investigate the influence of LRP-1 silencing on the migratory behavior of breast cancer cells by Atomic Force Microscopy and dynamic cell studies

Keywords:

To get more insight into the role of LRP-1 in the mechanism of tumor progression in triple negative breast cancer. Atomic force microscopy, videomicroscopy, confocal microscopy and Rho-GTPAse activity assay were used on MDA-MB-231 and LRP-1-silenced cells. Silencing of LRP-1 in MDA-MB-231 cells was shown to led to a dramatic increase in the Young's modulus in parallel to a spectacular drop in membrane extension dynamics as well as a decrease in the cells migration abilities on both collagen I and fibronectin substrates. These results were perfectly correlated to a corresponding change in cell morphology and spreading capacity as well as in Rho-GTPases activity. By a multi-technique approach, it was demonstrated that LRP-1 played a crucial role in the migration of MDA-MB-231 cells by modulating the membrane extension dynamic. The originality of this AFM investigation lies in the noninvasive aspect of the measurements.

Background

The low-density lipoprotein receptor-related protein-1 (LRP-1) is a large multifunctional endocytic receptor involved in the clearance of various molecules from the extracellular matrix. LRP-1 is synthesized as a 600 kDa precursor and maturated in a 515 kDa α-chain noncovalently linked to a 85 kDa transmembrane and intracellular β-chain. The extracellular α-chain protruding in the extracellular space is composed of four interaction domains of ligand-binding type cystein-rich repeats able to bind more than forty ligands as lipoproteins, extracellular matrix (ECM) macromolecules, proteinases, proteinase/inhibitor complexes [START_REF] Lillis | Murine low-density lipoprotein receptor-related protein 1 (LRP) is required for phagocytosis of targets bearing LRP ligands but is not required for C1q-triggered enhancement of phagocytosis[END_REF][START_REF] Gonias | LDL receptor-related protein-1: a regulator of inflammation in atherosclerosis, cancer, and injury to the nervous system[END_REF]. The LRP-1 β chain includes YxxL, a dileucine and two NPxY motifs involved in endocytosis and as binding sites for signaling adapter proteins. LRP-1 is involved in many physiological and pathological processes including the regulation of vascular integrity [START_REF] Strickland | Low-density lipoprotein receptorrelated protein-1: role in the regulation of vascular integrity[END_REF], blood brain barrier permeability [START_REF] Zhao | The role of the low-density lipoprotein receptorrelated protein 1 (LRP-1) in regulating blood-brain barrier integrity[END_REF], peripheral nerve regeneration [START_REF] Landowski | Lowdensity Lipoprotein Receptor-related Proteins in a Novel Mechanism of Axon Guidance and Peripheral Nerve Regeneration[END_REF], or in the cell migration and proliferation [START_REF] Llorente-Cortes | Low density lipoprotein receptor-related protein 1 modulates the proliferation and migration of human hepatic stellate cells[END_REF].

Over the last decade, many studies have also highlighted the role of LRP-1 in the regulation of proteolytic cascades involved in tumor progression, although this was subject to controversy. Indeed, LRP-1 was reported to exhibit anti-tumor properties in cell lines derived from prostate [START_REF] Kancha | Decreased expression of the low density lipoprotein receptor-related protein/alpha 2-macroglobulin receptor in invasive cell clones derived from human prostate and breast tumor cells[END_REF], kidney [START_REF] Desrosiers | Decrease in LDL receptor-related protein expression and function correlates with advanced stages of Wilms tumors[END_REF], colon [START_REF] Obermeyer | The expression of low density lipoprotein receptor-related protein in colorectal carcinoma[END_REF][START_REF] Boulagnon-Rombi | LRP1 expression in colon cancer predicts clinical outcome[END_REF] or endometrium [START_REF] Foca | Differential expression of the alpha(2)macroglobulin receptor and the receptor associated protein in normal human endometrium and endometrial carcinoma[END_REF] cancers, and pro-tumor properties in cell lines derived from brain cancer [12]. Interestingly, LRP-1 was also found to drive both anti-and pro-tumor functions in the same cell line, like shown for those derived from thyroid [START_REF] Sid | Human thyroid carcinoma cell invasion is controlled by the low density lipoprotein receptor-related proteinmediated clearance of urokinase plasminogen activator[END_REF][START_REF] Dedieu | LRP-1 silencing prevents malignant cell invasion despite increased pericellular proteolytic activities[END_REF] and breast [START_REF] Kancha | Decreased expression of the low density lipoprotein receptor-related protein/alpha 2-macroglobulin receptor in invasive cell clones derived from human prostate and breast tumor cells[END_REF][START_REF] Li | In vitro invasiveness of human breast cancer cells is promoted by low density lipoprotein receptor-related protein[END_REF][START_REF] Fayard | The serine protease inhibitor protease nexin-1 controls mammary cancer metastasis through LRP-1-mediated MMP-9 expression[END_REF] cancers. As shown in previous studies conducted from thyroid carcinomas, the pro-tumor role of LRP-1 mainly lies in its capacity to control the cytoskeleton organization. Particularly, LRP-1 balances the traction and adherence forces and rules the internalization of adherence complexes [START_REF] Dedieu | LRP-1 silencing prevents malignant cell invasion despite increased pericellular proteolytic activities[END_REF][START_REF] Theret | Identification of LRP-1 as an endocytosis and recycling receptor for β1integrin in thyroid cancer cells[END_REF]. Therefore, there is a critical need to identify the precise role of this endocytic receptor during tumor progression and to decipher the underlying mechanisms.

Various studies have prompted the importance of heterogeneity in cell mechanical properties on adhesion, division and migration capabilities. The easiest way to appraise such properties is to assess the cell stiffness. Among the most commonly used techniques, one can cite micropipette aspiration [START_REF] Berk | Detachment of agglutinin-bonded red blood cells. III. Mechanical analysis for large contact areas[END_REF], microfluidics [START_REF] Tsukada | Direct measurement of erythrocyte deformability in diabetes mellitus with a transparent microchannel capillary model and high-speed video camera system[END_REF], optical trapping [20], magnetic tweezers [START_REF] Bausch | Local measurements of viscoelastic parameters of adherent cell surfaces by magnetic bead microrheometry[END_REF], traction force microscopy [START_REF] Wang | Micropatterning tractional forces in living cells[END_REF], and atomic force microscopy [START_REF] Wojcikiewicz | Force and Compliance Measurements on Living Cells Using Atomic Force Microscopy (AFM)[END_REF][START_REF] Radmacher | Studying the mechanics of cellular processes by atomic force microscopy[END_REF][START_REF] Dokukin | Quantitative study of the elastic modulus of loosely attached cells in AFM indentation experiments[END_REF][START_REF] Guz | If cell mechanics can be described by elastic modulus: study of different models and probes used in indentation experiments[END_REF]. This last technique developed in the 80's [START_REF] Binnig | Atomic force microscope[END_REF] turned out to be one of the most proper technique to assess the topography and the mechanical properties of live cells in near-physiological conditions [START_REF] Sokolov | Recovery of elasticity of aged human epithelial cells in vitro[END_REF][START_REF] Callies | Membrane potential depolarization decreases the stiffness of vascular endothelial cells[END_REF].

Over the last 15 years, numerous studies reported that cancer cells and their normal counterparts exhibited different mechanical properties. Generally speaking, in response to an indenter-mediated stimulation, cancer cells are softer than their homologues. This has been proved in the case of bladder [START_REF] Lekka | Elasticity of normal and cancerous human bladder cells studied by scanning force microscopy[END_REF], blood [START_REF] Rosenbluth | Force microscopy of nonadherent cells: a comparison of leukemia cell deformability[END_REF], breast [START_REF] Cross | Nanomechanical analysis of cells from cancer patients[END_REF] and others tissues. The pioneering experiment of AFM imaging on live cells was performed in 1992 [33] where the dynamic behavior of the cytoskeleton of glial cells was investigated in contact mode. In 90's, tapping mode [START_REF] Zhong | Fractured polymer/silica fiber surface studied by tapping mode atomic force microscopy[END_REF] was released to avoid this drawback; in that case, the tip only intermittently interacts with the surface, resulting in negligible friction and shear forces.

Nevertheless, with both techniques, extracting the sample's mechanical properties is not possible. On the contrary, force spectroscopy, and more in particular, force volume can be used to map the stiffness and the adhesion of live cells in a quantitative manner [START_REF] Hoh | Surface morphology and mechanical properties of MDCK monolayers by atomic force microscopy[END_REF][START_REF] Rotsch | Drug-induced changes of cytoskeletal structure and mechanics in fibroblasts: an atomic force microscopy study[END_REF], although the technique suffers from a very slow acquisition speed. To overcome this limitation, the PeakForce QNM technique, an oscillating mode where loading forces can be minimized and from which quantitative mechanical information can be obtained in a reasonable amount of time, has been developed. This technique has been already successfully used to image and investigate the mechanical properties of live U-251 cancer cells [37].

In a previous work [START_REF] Le Cigne | Analysis of the effect of LRP-1 silencing on the invasive potential of cancer cells by nanomechanical probing and adhesion force measurements using atomic force microscopy[END_REF], standard force spectroscopy was used to extract the average Young's modulus of FTC-133 cells using colloidal probes but due to the slow acquisition speed, it was not possible to follow the dynamics of the cell properties in real-time and to correlate the results with the migration properties of the studied cells while it seems important to clearly understand the role of LRP-1. In the present study, the PeakForce QNM mode was used to probe the differences between control cells (shCtrl) and LRP-1 silenced breast cancer live cells (shLRP-1) in terms of topography, mechanical properties and migration abilities on collagen I and fibronectin substrates, in parallel to videomicroscopy, confocal and RHoGTPases activity experiments.

Methods

Cell Culture

All the experiments were performed using a human breast cancer adenocarcinoma cell line (MDA-MB-231) provided by the American Type Culture Collection (ATCC, catalogue No.

ATCC-HTB-26™

). The cells were grown in Dulbecco's Modified Eagle Medium (DMEM) supplemented with GlutaMAX™-I (PAN-Biotech) and 10% fetal bovine serum (FBS; PAN-Biotech) at 37°C in a 5% CO2 atmosphere. LRP-1 silencing in MDA-MB-231 cells was achieved using a LacSwitch II mammalian expression system (Agilent Technologies, Stratagene Products Division, La Jolla, USA) and shRNA sequences described by Dedieu et al [START_REF] Dedieu | LRP-1 silencing prevents malignant cell invasion despite increased pericellular proteolytic activities[END_REF].

Fibronectin and type I collagen coating

The fibronectin used for all experiments came from bovine plasma (Sigma-Aldrich, Saint-Louis, USA). The fibronectin [1mg/ml] was diluted with sterile PBS solution to a final concentration of 7μg/ml. The type I collagen was purchased from Stago (Stago BNL, Netherlands), diluted according to the specifications of the supplier, and used at a concentration of 35µg/ml. A saturation step with 1% denatured BSA has been done before seeding the cells.

RT-qPCR and western blot analysis

Briefly, a mass of up to 250 ng of the isolated RNAs was used for cDNA synthesis. The mixtures were incubated in a thermocycler at 42 °C for 30 min and 95 °C for 2 min. Realtime PCR conditions were 15 min at 95 °C followed by 40 cycles of 15 s at 95 °C (denaturation) and 1 min at 60 °C (annealing/extension). MDA-MB-231 shCTRL was chosen to represent a 1× expression of the genes of interest, and the levels in the treated samples were expressed relatively to those in the corresponding control sample. For western blotting, the cells lysates were harvested and centrifuged. The proteins were separated by electrophoresis and transferred onto a nitrocellulose membrane. The membranes were incubated in blocking buffer for 1 h at room temperature and incubated overnight at 4 °C with an anti-LRP-1 primary antibody (EPR3724, abcam, Paris, France) in blocking buffer. After washes, the membranes were incubated in the presence of a secondary antibody, and after revelation the bands from the immunoblots were quantified.

Immunofluorescence

Cells (25×10 4 ) were plated on glass-slides, coated with fibronectin or type I collagen and incubated for 24h `at 37°C. The fixation of the samples was made using 4% (v/v) paraformaldehyde. The slides were washed with PBS, incubated with BSA 3% (w/v) for 30 min and overnight with an anti-talin antibody (Merck millipore, Fontenay sous bois, France).

Then cells were washed with PBS and incubated for 45 min with an Alexafluor-488conjugated phalloidin and with an anti-rabbit Alexfluor-568 (Thermofisher, Villebon sur Yvette, France). . Slides were incubated with mounting medium containing DAPI.

Immunofluorescence-labeled cell preparations were analyzed using a Zeiss LSM 710 confocal laser scanning microscope with the 63X oil-immersion objective Zeiss operating system (Carl Zeiss MicroImaging GmbH, Deutschland). Projection and surfacic representations were realized using AMIRA (v6.2) software (Thermofisher, Villebon sur Yvette, France). To compare cell labeling, a same threshold was applied for each channel of shCtrl versus shLRP-1 cells. For colocalization studies, a multichannel field module was used, followed by a correlation plot treatment (sub-ranges values 15-255, gamma 0.5).

AFM imaging

A Bioscope Catalyst TM (Bruker, Billerica, USA) coupled to a Nikon Eclipse Ti inverted microscope (Nikon, Tokyo, Japan) were used for the AFM experiments. PFQNM mode was systematically used to obtain mapping of the Young's modulus as it allows a higher resolution at faster acquisition speed than the classical Force-Volume measurements [START_REF] Alsteens | High-resolution imaging of chemical and biological sites on living cells using peak force tapping atomic force microscopy[END_REF].

Preliminary experiments in force-volume (see supplementary information) mode were also performed for each cell type and have shown that the two modes give similar results for the Young's modulus values as already shown by other comparative studies using nanomechanical modes [START_REF] Pittenger | Quantitative mechanical property mapping at the nanoscale with PeakForce QNM[END_REF].

PFQNM-LC-A-CAL probes, having a nominal spring constant of 0.1 N/m and a resonance frequency of ~45 kHz were used to image the cells, the tips being calibrated as previously described [START_REF] Heu | Glyphosate-induced stiffening of HaCaT keratinocytes, a Peak Force Tapping study on living cells[END_REF]. The tip geometry ("ace of spades" pyramidal shape, with a tip height of 17 µm and an apex diameter of 130 nm) was designed on purpose to minimize the background effect. For PFQNM experiments, we used a PeakForce frequency of 0.25 kHz so to be as low as possible in order to maximize the contact time between the tip and the sample, a PeakForce amplitude of 1 µm so to be as high as possible since the cells are quite high.

Images were captured in culture medium at a resolution of 256 or 128 pixels per line, at 37°C using a Perfusing Stage Incubator (Bruker, Billerica, USA). The petri dish was put on the baseplate when the temperature setpoint was reached and stable over time. The Young's modulus, step height, surface and volume measurements were calculated using Nanoscope Analysis (Bruker, Billerica, USA). Regarding the Young's modulus calculation, for each type of cells, 3 different cell dishes coming from the same culture were analyzed one after the other to avoid to work more than 3 hours with each dish and the experiments were triplicated to draw a reliable conclusion. At the end, between 45 and 60 cells for each condition. Referring to both the information displayed by the deformation channel and the cross section on the height channel, the measurements were made only at locations were the cell height was at least 4 times superior to the indentation depth, i.e. in cell area with a minimum height of 1µm, in order to exclude any influence of the substrate on the measured values. Thus, perinuclar areas were avoided. The Sneddon approximation [START_REF] Sneddon | The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile[END_REF] was used to estimate the interaction between the tip and the substrate. In order to avoid generating mechanical stress to the cells, the loading force was adjusted between a few tens up to a few hundreds of piconewtons. The force curves were extracted from chosen area from the PFQNM images using the Peak Force Capture option from the Nanoscope software. Because of the geometry of the tip which could be considered as spherical at the apex, the force curves were then fitted using the Hertz model to get the Young's modulus values for each point of the area and the Young's Modulus values for each type of cells were represented using boxplots.

For the topographical AFM measurements (height sections and counting of lamellipodia and protrusions), a minimum of 50 images were processed for each condition while regarding the AFM migration measurements, about 50 images per condition were captured but only approximately half of them were taken into account for our migration measurements as such measurements are highly challenging since after capturing the first image, the cell is often out of the field of view on the second image.

Videomicroscopy imaging

To measure velocity of MDA-MB-231 cells, the cells were seeded on type I collagen or fibronectin-coated, glass-bottomed chamber slide and allowed to attach to the substrate. Cells were then observed with a x20 magnification objective, for 24 h using a Zeiss Axio Observer Carl Zeiss MicroImaging GmbH, Deutschland). The cells were maintained at 37°C and 5% CO2 in a temperature-controlled chamber (PECON). The data were acquired using the MetaMorph software (Roper Scientific). Cell speed and directional persistence analysis were performed using ImageJ software (National Institutes of Health, Bethesda, MD, USA).

For each conditions, 48 cells have been tracked.

Rho-GTPase assay

MDA-MB-231 cells (1 × 10 6 per well) were grown over 48h in culture plate coated with, fibronectin or type I collagen-until 90% of confluency. Then cells were lysed and Rho-GTPase activity was determined using an Active Rho Pull-Down and Detection Kit (Thermofisher, Pierce Biotechnology, USA, ref 16116) following the provider instructions.

Statistics

All the results are means ± SEM raised from two or three independent experiments.

Statistical significance of differences was calculated using Two sample t-test or Mann

Results

In order to evaluate the effect of the LRP-1 on breast cancer cells behavior, type I collagen and fibronectin coatings were used. These two ECM glycoproteins are present in breast cancer tumor microenvironment and regulate expression and activation of specific cell receptors and downstream signaling.

LRP-1 silencing in breast cancer cells

In order to study the effect of LRP-1 in breast cancer cells, MDA-MB-231 cells weretransfected to stably express a shRNA directed against LRP-1 mRNA (shLRP-1) or an shRNA with no target (shCTRL). As shown in figure 1, RT-qPCR (Fig1A) and western blot (Fig 1B)

experiments revealed a decrease of the expression of LRP-1 by 60% (mRNA) and by 67% (protein). Thus, this model was used for the different experiments.

Young's moduli calculation

Our measurements were performed on type I collagen and fibronectin. As shown on Figure 2A, the Young's modulus was found to be remarkably stable on control cells with values of 2.05 +/-0.8 kPa, and 2.06 +/-1.03 kPa on collagen and fibronectin, respectively. In LRP-1 silenced cells, the Young's modulus dramatically increased: 5.95 +/-2.08, and 5.03 +/-1.84 kPa on type I collagen and fibronectin, respectively (Figure 2A). Figure 2B

Topographical measurements

LRP-1 silencing consequences in MDA-MB-231 cells were further evaluated by topographical measurements (surface and height section). As shown in Figure 3, in the case of type I collagen, LRP-1 invalidation led to a flattening effect of the cells (8.7 +/-2.3 µm for shCtrl cells and 6.6 +/-1.9 µm for shLRP-1 cells). This came with an increase of the average surface (584.6 +/-62.1 µm 2 for control cells and 778.4 +/-83.1 µm 2 for shLRP-1 cells). Interestingly, this effect was not significant on fibronectin-coated plates.

Cell speed and directional measurements

As the correlation between the Young's modulus and cell migration is well documented [START_REF] Nagayama | Drastic change of local stiffness distribution correlating to cell migration in living fibroblasts[END_REF][START_REF] Kuznetsova | Atomic force microscopy probing of cell elasticity[END_REF], time-lapse microscopy experiments were performed during 24 hrs to estimate velocity and direction of shCtrl and shLRP-1 cells seeded onto either type I collagen or fibronectin. As shown in Figure 4A, shCtrl cells seeded onto collagen exhibit a high directional persistence, the highest velocity (0.729 µm/min) and the highest traveled distance (1051 µm/24 hrs). Indeed, onto fibronectin, shCtrl cells exhibits a lower speed (0.414 µm/min), a lower traveled distance (596 µm/24 hrs) as well as a lower directional persistence compared to shLRP-1 cells. LRP-1 silencing impaired cell migration on both substrates with a more pronounced effect on collagen (speed: 0.412 µm/min, traveled distance: 593 µm/24 hrs) compared to fibronectin (speed: 0.290 µm/min, traveled distance 418 µm/24 hrs) (Figure 4B). It can be noticed that approximately 20% of shLRP-1 cells seeded onto fibronectin, kept a behavior close to shCtrl cells.

Migration speed measurements and topographical information obtained by AFM

Traditionally, cell migration speed is measured by video-microscopy experiments as proceeded above. Nevertheless, in these experiments, only the cell core is taken as a reference spot and over a large period of time (usually 24 hours). To provide complementary information to video-microscopy, AFM was performed as it allows to follow the cell dynamics with high resolution. AFM experiments were then carried out by focusing on membrane extension dynamics at migration front and retraction tails (which is not possible in video-microscopy, since the cells move too fast). Figure 5A panels 1&2 and Figure 5B focused on the retraction tail dynamics. On control conditions, cell tails were found to retract quite quickly on type I collagen (1.18 +/-0.29 µm/min) and slightly slower on fibronectin (0.83 +/-0.12 µm/min). LRP-1 silencing led to a spectacular drop in the migration speed, on collagen (0.35 +/-0.34 µm/min), and to a minor extent on fibronectin (0.39 +/-0.25 µm/min). The measurements taken on the migration fronts (Figure 5A panels 3&4, Figure 5B) led to similar observations: control cells were able to move quite fast on the two substrates (1.08 +/-0.15 µm/min on collagen, and 0.79 +/-0.18 µm/min on fibronectin). This time, LRP-1 invalidation led to a spectacular decrease in the migration capabilities on the fibronectin (0.24 +/-0.01 µm/min) and with a less extent on collagen (0.51 +/-0.09 µm/min).

The clear morphological differences obtained between shCtrl and shLRP-1 cells on collagen prompted us to investigate more in details the height images obtained on this substrate, particularly the number of filopodiae and protrusions at the migration front. Figure 6-panel 1 shows a typical migration front where the filopodia can be numbered, and Figure 6-panel 2, a typical cross-section achieved on a protrusion. The number of filopodiae on type I collagen (Table 1) was quite similar between the control (12) and the LRP-1-silenced (13.5) cells as well as the number of membrane protrusions (27.7 for the shCtrl cells and 21.1 for the shLRP-1 cells). On the other hand, the average height of the protrusions was systematically found to be more important on shCtrl (381.9 nm on collagen) than on shLRP-1 (269 nm on collagen) cells. Taken together, those results tend to prove that the membrane remodeling at the leading edge of shCtrl and shLRP-1 cells seeded onto type I collagen is quite similar.

Considering the obtained data, additional experiments were carried out by assaying Rho-GTPase protein activities, molecular actors involved in the regulation of actin cytoskeleton dynamics.

Rho-GTPases assay

Rho GTPases include Rho, Rac and CDC42 proteins known to be mainly involved in cell migration and morphology especially by controlling the dynamic of actin cytoskeleton. Rho GTPase activity is regulated by GDP (inactive state) and GTP (active state). Activated Rho GTPases are able to interact with specific signaling molecules and induce downstream signaling [START_REF] Ridley | Rho GTPase signalling in cell migration[END_REF].

In order to establish a potential correlation between AFM and time-lapse microscopy analyses, immunoprecipitation of Rho GTPases in shCtrl and shLRP-1 cells was also performed. As shown in Figure 7, we observed a decrease of 50% of the Rho GTPase activity when LRP-1 was silenced, only when cells were seeded onto fibronectin. These results corroborate the decrease of cell migration observed in time-lapse microscopy (Figure 4) as well as the decrease of membrane dynamics observed using AFM at the leading edge of the cells (Figure 5).

Immunofluorescence experiments

To go deeper in the understanding of these observations, immunofluorescence experiments were also performed and actin microfilaments and talin were labelled to visualize actin cytoskeleton extensions and focal adhesion contacts, respectively.

As shown in Figure 8

Discussion

Triple negative breast cancer (TNBC) counts among the more aggressive breast cancer [START_REF] Khosravi-Shahi | Metastatic triple negative breast cancer: Optimizing treatment options, new and emerging targeted therapies[END_REF].It constitutes an essential challenge to identify molecular regulators involved in cancer cell migration and/or invasion as these processes represent key steps in the process of tumor cell dissemination to establish metastasis [START_REF] Redig | Breast cancer as a systemic disease: a view of metastasis[END_REF]. Among these molecular actors, LRP-1, an endocytic scavenger receptor already described for its role in cancer progression [START_REF] Montel | The low-density lipoprotein receptor-related protein regulates cancer cell survival and metastasis development[END_REF], seems to support pro-tumor functionalities in breast cancers [START_REF] Montel | The low-density lipoprotein receptor-related protein regulates cancer cell survival and metastasis development[END_REF].

The aim of our study was to evaluate the role of LRP-1 on elasticity, migration and spreading of MDA-MB-231 breast cancer cells seeded on both type-I collagen and fibronectin. These two glycoproteins represent the major components of breast cancer tumor microenvironment [START_REF] Robertson | The extracellular matrix in breast cancer predicts prognosis through composition, splicing, and crosslinking[END_REF]. Indeed, type I collagen constitutes the scaffold of tumor microenvironment and can promote tumor infiltration, angiogenesis, invasion and migration [START_REF] Fang | Collagen as a double-edged sword in tumor progression[END_REF]. Fibronectin in turn is a primary component of the mammary mesenchymal compartment [START_REF] Li | Fibronectin induces epithelial-mesenchymal transition in human breast cancer MCF-7 cells via activation of calpain[END_REF]. Its expression represents a robust indicator of lymph node involvement and is also correlated to mortality risk [START_REF] Mohamed | Inflammatory breast cancer: New factors contribute to disease etiology: A review[END_REF]. In this context, AFM approaches in PeakForce QNM mode were used to study live cells [START_REF] Heu | Glyphosate-induced stiffening of HaCaT keratinocytes, a Peak Force Tapping study on living cells[END_REF]. The Young's modulus from shCtrl cells reaches 2.0 kPa on both fibronectin and type I collagen. Interestingly, Teng et al. have previously reported a Young's modulus of 1.1 kPa and 2.2 kPa for MDA-MB-231 seeded on collagen and fibronectin, respectively [START_REF] Teng | Effects of type I collagen and fibronectin on regulation of breast cancer cell biological and biomechanical characteristics[END_REF]. These authors have performed a recording in the vicinity of the nucleus and have shown that fibronectin induced an increase of the mean young modulus compared to type I collagen. In our study, QNM acquisitions were achieved everywhere on the cell with due respect of a recorded zone at least 4 times superior to the indentation depth. Regarding the results obtained in LRP-1-silenced cells, a significant increase of the Young's modulus was measured, that reached 5.95 and 5.03 kPa onto collagen and fibronectin, respectively. Numerous studies have reported that the increase of cellular stiffness is related to a less invasive phenotype [START_REF] Lekka | Discrimination Between Normal and Cancerous Cells Using AFM[END_REF].

These data suggest, in accordance with our previous studies performed on FTC-133 thyroid carcinoma cells [START_REF] Dedieu | LRP-1 silencing prevents malignant cell invasion despite increased pericellular proteolytic activities[END_REF][START_REF] Le Cigne | Analysis of the effect of LRP-1 silencing on the invasive potential of cancer cells by nanomechanical probing and adhesion force measurements using atomic force microscopy[END_REF], that LRP-1 silencing appears correlated to an impaired ability for the cells to deform and migrate. When type I collagen was used as a coating, LRP-1 invalidation led to a flattening effect and an increase of the average cell surface. Interestingly, no significant difference was observed on fibronectin-coated plates, in terms of height section and surface. These observations could be linked to the high spread of shCtrl cells on fibronectin. Our results indicated that LRP-1-expressing breast tumor cells seeded onto collagen exhibited a higher directional persistence as well as a higher velocity compared to cells seeded onto fibronectin. Considering these results, collagen which is found in breast cancer tumor microenvironment, represents a privileged guide for cell dissemination, that participates in the increase of cell aggressiveness [55]. LRP-1 silencing reduced cell velocity by 45% (24.7 µm/h) and 30% (17.4 µm/h) on collagen and fibronectin respectively which is in line with the Young modulus variations determined by AFM (Fig. 2). Nevertheless, an important observation in our study concerns the fact that the Young modulus value of MDA-MB-231 is quite identical on type I collagen and fibronectin whereas tumor cells have a different behavior on these two matrix associated substrates. Lekka have already pointed out the fact that Young modulus is not sufficient by itself to explain/characterize cell behavior [START_REF] Lekka | Discrimination Between Normal and Cancerous Cells Using AFM[END_REF]. To complement our measurements, AFM was used to focus on different cell parts, like the migration front or the retraction. It was demonstrated that the tails of the control cells retract quite quickly on type I collagen (1.18 µm/min) and slightly slower on fibronectin (0.83 µm/min). As for the LRP-1 silencing cells, we measured a spectacular drop in the migration speed at the tail extension, by 2.7 fold on collagen (0.35 µm/min), and a minor extent on fibronectin (by 2.1 fold to 0.39 µm/min). At the migration front, LRP-1 invalidation led to a substantial decrease of the migration abilities of the cells on fibronectin (by 3.6 fold to 0.24 µm/min) and to a slightly lesser extent on collagen (by 2.1 fold to 0.51 µm/min). Actin microfilament and talin labelling, pointed out the fact that the morphologies of breast cancer cells are quite similar on both collagen and fibronectin with a welldeveloped actin cytoskeleton associated with focal contacts at the leading edge. However, the morphology of tumor cells on type I collagen seems to be more polarized and that could explain the highest migration speed on this substrate. When LRP-1 is silenced, striking differences are observed for cell morphology onto collagen with a stretch phenotype and a loss of the polarized extensions. These effects are less pronounced in shLRP-1 cells seeded on fibronectin than shCtrl cells and corroborate with the cell velocity data (Fig. 7 and Fig. 8).

To investigate more precisely the dynamic of cytoskeleton, Rho GTPase activities were investigated. This family is represented by Rho, Rac and CDC42 proteins, and is involved in cell migration and morphology by controlling the dynamic of actin cytoskeleton [START_REF] Tapon | Rho, Rac and Cdc42 GTPases regulate the organization of the actin cytoskeleton[END_REF].

Previous results obtained on Schwann cells have demonstrated the ability of LRP-1 to regulate these proteins [START_REF] Mantuano | Low density lipoprotein receptorrelated protein (LRP1) regulates Rac1 and RhoA reciprocally to control Schwann cell adhesion and migration[END_REF] Interestingly, a decrease by 50% of Rho GTPase activity was observed in LRP-1-deficient cells cultured onto fibronectin which can be correlated to the results obtained using AFM and videomicroscopy (Fig. 2 and Fig. 4). When cells are cultured on type I collagen, no significant modification were observed when LRP-1 was silenced. It is worth to mention that our study measured the global activity of RhoGTPases and not only Rho. It could be of interest to focus only on Rho proteins and their associated kinases.

Moreover, RhoA was usually maximally activated to nearby to the leading edge [START_REF] Machacek | Coordination of Rho GTPase activities during cell protrusion[END_REF].

By looking at the results of immunofluorescence more closely, it seems that shLRP-1 cells seeded on collagen lost their polarity and turned out to be characterized by two leading edges inducing a migration way in opposite direction without efficient movement. These observations have been corroborated by time lapse study (see supplementary video files).

In conclusion, our study demonstrates thanks to a multi-technique approach focusing on AFM measurements that LRP-1 acts as a pro-migratory actor in MDA-MB-231 cells and that extracellular proteins found in breast microenvironment such as fibronectin or type I collagen are able to modulate this effect.

Figures legends

Table 1. Quantification of the number of membrane protrusion on collagen and fibronectin

On both substrates, the data tend to prove than the membrane remodeling is more present on control than on ShLRP-1 cells, which is a marker of higher migration capabilities.

  Withney-U test assays (Prism software; GraphPad). P values referring to corresponding controls are indicated in Figure legends. *P < 0.05; **P < 0.01; ***P < 0.001; NS = nonsignificant.

  shows Young´s modulus mapping on shCtrl MDA-MB-231 cells (Fig 2B panel 1) and on LRP-1 silenced MDA-MB-231 cells (Fig 2B panel 2). The darker part of image which corresponds to the softer material, is mainly localized in the center of the cell. Lamellipodia and filopodia of shCtrl cells exhibit a higher stiffness compared to the cell body. LRP-1-deficient cells exhibit a stretch phenotype associated with stiff cytoplasmic extensions.

  , the morphology of shCtrl cells was quite similar on both type-I collagen and fibronectin with a developed actin cytoskeleton associated to focal contacts at the leading edge (Figs. 8A, 8B). Nevertheless, cells seeded onto collagen exhibited a polarized phenotype associated with numerous focal adhesion contacts at the leading edge (Fig 8A, panels 1&3) as shown by co-localized voxels between actin and talin (Fig 8A, panels 5, arrows). Concerning the shLRP-1 cells, striking differences were observed on collagen associated with a thin stretch phenotype ((Fig. 8A, panels 2,4) containing focal contact at each side of the cell (Fig. 8A, panel 6, arrows). LRP-1 silencing also affects cell morphology when cells are seeded on fibronectin (Fig 8B). Indeed, LRP-1-silenced cells adopted a more stretched phenotype (Fig. 8B, panels 2, 4), however the cell polarity seemed to be preserved. The intensity and size of focal contact decrease as observed in Fig 8B (panel 6 vs panel 5, arrows).

Figure 1 :

 1 Figure 1: Short hairpin LRP-1 strategy induced LRP-1 silencing in triple negative breast

Figure 2 .Figure 3 :

 23 Figure 2. LRP-1 silencing in MDA-MB-231 leads to an increase of the Young's modulus by

Figure 4 LRP- 1

 41 Figure 4 LRP-1 silencing in MDA-MB-231 decreases the cell speed and impairs directional

Figure 5 .

 5 Figure 5. LRP-1 silencing MDA-MB-231 impairs the migration speed, measured over the

Figure 6 .

 6 Figure 6. LRP-1 silencing decreases the number of membrane protrusions on type collagen

Figure 7 .

 7 Figure 7. LRP-1 silencing impairs RhoGTPases activities on fibronectin

Table 1

 1

	Sample	filopodes	protrusions	Protrusion height
	Ctrl Coll	12	27,7	381,9 nm
	SHLRP1 Coll	13,5	21,1	269 nm
	Ctrl Fibro	33,3	22,4	319,3
	SHLRP1 Fibro	(ND)	14	167

Acknowledgments

The authors thank the Region Champagne Ardenne, URCA, DRRT Grand Est and FEDER program. The video microscopy and confocal microscopy experiments were performed at the PICT platform, URCA, with assistance from Christine Terryn and Arnaud Bonnomet. The AFM experiments were performed in the NanoMat' facility. The authors would like to thank Cathy Hachet for her technical assistance. Graphical abstract was realized with the help of Adrien Dos Santos.


Didier Raoult
email: didier.raoult@gmail.com

Prof. Didier Raoult

Resistance to antibiotics of bacteria in tropical countries

Keywords: Antibiotic resistance, tropical countries, natural antibiotic compounds

2

The identification of the source of resistance of bacteria to antibiotics is, in my opinion, too naïve and too much based on the guilt of human-related activity. This perception of the world yields analyses that claim to establish an exclusive link between the use of man-made antibiotics and the resistance of microorganisms to antibiotics. This illusion neglects the importance of the source of natural antibiotics. Most antibiotics are secreted naturally by microorganisms, bacteria, of the actinomycetes phylum, or fungi [START_REF] Angelakis | Related actions of probiotics and antibiotics on gut microbiota and weight modification[END_REF]. These antibiotics are naturally present in the environment and the antibiotic resistance of microorganisms existed long before their medical use. Beta-lactamases are found in genetic sequences of microorganisms from the Middle Ages, and the resistance of Staphylococcus aureus in the 19th century has recently been demonstrated [START_REF] Raoult | The Living Croquet Theory: The Staphylococcus aureus Paradigm[END_REF]. Antibiotics are assembled in microorganisms by non-ribosomal protein synthases and polyketides synthases, which are the only known translation devices outside the ribosome. Their existence may have preceded that of ribosomes and may be archaic translation machineries. Since biodiversity in general is much higher in the humid intertropical zone, it is also likely to be the place where the most diverse microorganisms are found, as evidenced by the richness of the human microbiota in rural intertropical areas compared to urban or temperate areas(3). This biodiversity can be accompanied by a biodiversity of molecules with antibiotic activity. Finally, the molecules secreted by non-ribosomal protein synthase and polyketide synthase have multiple activities, not only antimicrobial but also antifungal. Against eukaryotes, some molecules are used as anti-cancer treatments. Some human beta lactamases have anticancer drug inhibitory activity as with mitomycin(4). The spectrum of activity of beta lactamases far exceeds the anti-beta lactamine activity, playing a role in the digestion of nucleic acid (4).

Antibiotic resistance is a global concern and, interestingly, the source of resistance is often found in the world's intertropical or hottest regions [START_REF] Collignon | Anthropological and socioeconomic factors contributing to global antimicrobial resistance: a univariate and multivariable analysis[END_REF]. This specificity has not been satisfactorily explained and has just been confirmed by a very extensive study carried out in this journal [START_REF] Hassell | Epidemiology of Clinically Relevant Antimicrobial Resistance at the Wildlife-Livestock-Human Interface in Nairobi[END_REF] which shows that a country's overall antibiotic consumption is not correlated with the level of bacterial resistance. On the contrary, there is an inverse relationship, the lower the prescription rate, the higher the resistance level. We have confirmation of this in France, where antibiotic consumption is one of the highest in the world, and where the level of resistance is one of the lowest in the world, particularly in Marseille [START_REF] Page | No global increase in resistance to antibiotics: a snapshot of resistance from 2001 to 2016 in Marseille, France[END_REF].The same is true in the United States, where difficult-to-treat Gram-negative bacteria represent a very small proportion of the bacteria isolated from the blood cultures of hospitalized patients [START_REF] Raoult | The paradigm of the Shadoks and antibiotic resistance[END_REF]. The reason for these differences remains poorly explained. One of the explanations proposed was the poor management of antibiotics prescribing in humans, which could explain this discrepancy [START_REF] Collignon | Anthropological and socioeconomic factors contributing to global antimicrobial resistance: a univariate and multivariable analysis[END_REF]. This seems to overlook the idea that man-made antibiotics are the only source of antibiotics, neglecting those produced in the environment. Antibiotics can eventually be used as food by other microorganisms, which in turn develop enzymes to digest them for consumption [START_REF] Hibbing | Bacterial competition: surviving and thriving in the microbial jungle[END_REF]. It has been evaluated that most families of antibiotics can be used as growth factors for soil microorganisms, and the digestion of penicillin and its use as a sole source of carbon has been demonstrated in Escherichia coli transformed in vitro. This shows that antibiotics do not only kill microorganisms, but can also serve as a nutrient, especially in areas particularly rich in environmental microorganisms. In addition, it has recently been shown that some arthropods are capable of secreting penicillins and cephalosporins, leading to a less simplistic view of antibiotics, of selection pressure exclusively from human-made drugs, and resistance [START_REF] Pontarotti | Why do arthropods secrete beta-lactams?[END_REF]. Thus, beta-lactam resistance genes are detected in all vertebrates, including humans, but also in archaea, which are not sensitive to beta-lactams [START_REF] Keshri | Phylogenomic Analysis of beta-Lactamase in Archaea and Bacteria Enables the Identification of Putative New Members[END_REF].The work conducted in this journal on Kenya shows that in a city where antibiotic prescribing is extremely low, the level of resistance of Escherichia coli is particularly high, not only in humans but also in wildlife. This study must put into perspective a much less anthropocentric approach but integrate the fact that antibiotics are probably more than 3 billion years old, as are antibiotic resistance enzymes, and that we can only understand, and therefore combat antibiotic resistance, if we have a more scientific vision of this world.

In conclusion, public health considerations lead to a significant simplification, in particular for sending simple messages that can be understandable to all, but partially false. This needs to be acknowledged. Control measures should not prevent the integration of recent scientific data for fear of misuse of antibiotics. Such a line of thought might end up being dangerous for humans and more emphasis should be put on the complexity of the relationships between antibiotics and the enzymes that, among others, digest them.

Funding

No funding was received for this work.

Competing interests

There are no conflicts of interest.