Edithe Selwa

Eddy Elisée

Agustin Zavala

Bogdan I Iorga
email: bogdan.iorga@cnrs.fr

‡ Eddy Elisee

Blinded evaluation of farnesoid X receptor

Keywords: docking, scoring function, Gold, Vina, Autodock, Farnesoid X receptor, FXR, D3R, Drug

come

INTRODUCTION

Drug Design Data Resource (D3R, https://drugdesigndata.org/) organizes, on a regular basis, blinded prediction challenges with the aim to evaluate the performance of tools and protocols that are used in real-life computer-aided drug discovery projects. To achieve this, datasets presenting different levels of difficulty are presented to the community, which is asked to predict, in "blind" conditions, the binding modes and the relative affinities of compounds.

The D3R Grand Challenge 2, which was held in 2016, was focused on a single protein, farnesoid X receptor (FXR, Figure 1), a target with multiple potential applications that has received much attention during the recent years . In Phase 1 the participants were asked to provide affinity predictions for 102 FXR ligands and pose predictions for 36 of them. In Phase 2 the participants were required to provide the same affinity predictions as in Phase 1, taking into account the additional structural data (36 new protein-ligand complexes) released at the end of Phase 1.

Figure 2 shows the chemical structures of compounds from FXR dataset for which the pose predictions were required. Most of the compounds included in this dataset can be organized in four homogeneous classes based on their chemical structures (benzimidazoles, isoxazoles, sulfonamides, spiro compounds), and the remaining ones presented inhomogeneous structures and were included in a group called miscellaneous. Biological activities data were available for some compounds from this dataset [31][32][33]. The exact composition of each group can be found in the Electronic Supplementary Material, as well as the structures of the entire FXR dataset, containing 102 ligands used for ranking prediction (Figure S1). Additionally, the participants were asked to predict the relative affinities for two homogeneous subsets of compounds that are suited for free energy calculations. The structures of compounds (count of 15 and 18, respectively) included in the two free energy subsets are presented in Figures 3 and4.

METHODS

Protein structures. We found 27 crystal structures available in the Protein Data Bank (PDB) [34] for FXR (see the Electronic Supplementary Material for the complete list). These structures constituted our evaluation dataset. All ligands, ions and solvent molecules that were present were manually removed, then the structures were superimposed on the reference structure apo FXR provided by the D3R Grand Challenge organizers, in order to conserve the same coordinate system through the whole process. Missing residues in the structures were added using Modeller 9v12 [35]. Hydrogen atoms were added using Hermes, the graphical interface of Gold v5.2.2

[36] software, or with AutoDock Tools [START_REF] Morris | AutoDock4 and AutoDockTools4: Automated docking with selective receptor flexibility[END_REF] prior to docking.

Ligands. Ligand structures from the evaluation dataset were retrieved from PDB in the SMILES format and they were converted into three-dimensional MOL2 files using CORINA v3.60 (http://www.molecular-networks.com/). This protocol was used instead of retrieving directly the three-dimensional coordinates from the PDB in order to avoid any bias in the docking process that might be related to the initial coordinates of the ligands. Ligand structures used in Phase 1 were obtained from the SMILES strings provided by organizers upon conversion into three-dimensional MOL2 files using CORINA. Three-dimensional coordinates of the ligands used in Phase 2 were built using UCSF Chimera [START_REF] Pettersen | UCSF Chimera --a visualization system for exploratory research and analysis[END_REF], by superimposing their common backbone on the released FXR_17, FXR_10 and FXR_12 crystal structures and by manual addition of the appropriate substituents. In all cases, the protonation state for all compounds was adjusted at physiological pH using LigPrep (Schrödinger, http://www.schrodinger.com/). Docking. In the preliminary analysis step, several docking software and scoring functions have been tested (re-docking and cross-docking) for their ability to reproduce the protein-ligand complexes from the evaluation dataset: Gold [36] with the GoldScore, ChemScore, ChemPLP and ASP scoring functions, Vina [START_REF] Trott | AutoDock Vina: Improving the speed and accuracy of docking with a new scoring function, efficient optimization, and multithreading[END_REF] and AutoDock [START_REF] Morris | AutoDock4 and AutoDockTools4: Automated docking with selective receptor flexibility[END_REF]. Default parameters were used in all cases for docking, except with Gold, where a search efficiency of 200% was used in order to better explore the conformational space. The binding sites were considered with Gold as spheres with a 20 Å radius around the Cα atom of Ala288 (numbering from the 1OSV structure). With Vina and AutoDock, the binding sites were defined as a 40 x 40 x 40 Å 3 cube centered on the same atom. The protein was considered to be either rigid, or with a few key residues (Leu291/Asn297/Met332/Arg335/Ser336/His451/Trp458 or Arg335 only) from the binding site as flexible. As a result of preliminary analysis, Gold with the ASP scoring function and the rigid protein was used in the Phase 1 predictions. In Phase 2, the rescoring of the FXR complexes was carried out using Gold with the ASP scoring function. For submission, the protein structures were converted into PDB format using UCSF Chimera [START_REF] Pettersen | UCSF Chimera --a visualization system for exploratory research and analysis[END_REF], and the docking poses were converted into MOL format using CORINA (the MOL format corresponds to the SDF output format in CORINA). Unfortunately, the ligand conversion with CORINA was carried out initially without the option "-d no3d", which led to the generation of new coordinates and therefore invalid conformations in our "rjyhz" submission. The results reported here (named "rjyhz_revised") represent the correct poses, obtained with the option "-d no3d".

Free energy calculations. The protein used for free energy calculation was taken from PDB database with PDB entry corresponding to 3FLI. Three-dimensional coordinates of ligands were built using UCSF Chimera [START_REF] Pettersen | UCSF Chimera --a visualization system for exploratory research and analysis[END_REF], by superimposing common backbone on released FXR_17, FXR_10 and FXR_12 structures. In the set2, the structure solved by X-ray crystallography for FXR_12 had two alternative positions for the aromatic ring substituent (AA and AB). Both of them were considered in our calculations, and the one leading to the most favorable energy chosen for the submission. Alchemical free energies were calculated using Gromacs [START_REF] Pronk | GROMACS 4.5: a high-throughput and highly parallel open source molecular simulation toolkit[END_REF] and OPLS-AA force field [START_REF] Kaminski | Evaluation and Reparametrization of the OPLS-AA Force Field for Proteins via Comparison with Accurate Quantum Chemical Calculations on Peptides[END_REF][START_REF] Robertson | Improved Peptide and Protein Torsional Energetics with the OPLSAA Force Field[END_REF], some scripts from the PMX software [START_REF] Gapsys | pmx: Automated protein structure and topology generation for alchemical perturbations[END_REF][START_REF] Gapsys | Calculation of binding free energies[END_REF][START_REF] Gapsys | Accurate and Rigorous Prediction of the Changes in Protein Free Energies in a Large-Scale Mutation Scan[END_REF] and some in house developed scripts. The main steps of this protocol are presented in Figure 5. Hybrid structures and topologies were built using a modified version of the MOL2FF package developed in our team. Hybrid topologies represent simultaneously both ligands, the contribution of each structure being controlled by a parameter λ. For example, a λ value of 0 represents exclusively the ligand A, a λ value of 1 represents exclusively the ligand B, and a λ value of 0.3 represents a contribution of 70% of the ligand A and a contribution of 30% of the ligand B. FXR_91 was used as reference structure for set1, and FXR_10 or FXR_12 for set2. Equilibrium 10 ns MD simulations were performed for the two states (corresponding to lambda 0 and 1), using Gromacs [START_REF] Pronk | GROMACS 4.5: a high-throughput and highly parallel open source molecular simulation toolkit[END_REF] and OPLS-AA force field [START_REF] Kaminski | Evaluation and Reparametrization of the OPLS-AA Force Field for Proteins via Comparison with Accurate Quantum Chemical Calculations on Peptides[END_REF][START_REF] Robertson | Improved Peptide and Protein Torsional Energetics with the OPLSAA Force Field[END_REF]. Snapshots from the equilibrium runs were extracted to spawn 100 simulations of 50 ps each to alchemically morph between the two states of the system. The work values over every non-equilibrium transition were extracted and further used to estimate the free energy differences relying on the Crooks Fluctuation Theorem and utilizing Crooks-Gaussian Intersection as estimator. When the charge was the same in the two ligands considered for the alchemical transformation, separate calculations were carried out for the transformation A into B of the protein-ligand complex and of the ligand alone, the relative free energy of binding being the difference between the corresponding work for these two transformations (see Figures S2 andS3 in the Electronic Supplementary Material file). When the charge was different between the two ligands, a single box containing the protein-ligand complex and the ligand alone, separated by 30 Å, was considered. The ligand from the complex was converted from state A into B, whereas the ligand alone was converted simultaneously from state B into A. In these conditions, the overall charge of the system was conserved during the whole simulation, and the relative free energy of binding between ligands corresponds to the global work for this system (see Figure S4 in the Electronic Supplementary Material file). Graphics. Chemical structures were depicted using CACTVS Chemoinformatics Toolkit v3.409 (Xemistry, http://www.xemistry.com/), images for protein structures were generated using PyMol 1.8.1 (Schrödinger, http://www.pymol.org/) and histograms were obtained using the R package (http://www.r-project.org).

Statistics. Statistics were computed using the online tools available at http://www.sthda.com/english/rsthda/correlation.php.

Chemoinformatics. Tanimoto similarities were computed using CACTVS Chemoinformatics Toolkit v3.409 (Xemistry, http://www.xemistry.com/).

RESULTS AND DISCUSSION

In our previous participations to the SAMPL3 (2011) [START_REF] Surpateanu | Evaluation of docking performance in a blinded virtual screening of fragment-like trypsin inhibitors[END_REF], SAMPL4 (2013) [START_REF] Colas | Virtual screening of the SAMPL4 blinded HIV integrase inhibitors dataset[END_REF], CSAR (2014) [START_REF] Martiny | Blind pose prediction, scoring, and affinity ranking of the CSAR 2014 dataset[END_REF] and D3R Grand Challenge (2015) [START_REF] Selwa | Molecular docking performance evaluated on the D3R Grand Challenge 2015 drug-like ligand datasets[END_REF] docking and virtual screening challenges we followed an approach involving two steps. The first step consists in a preliminary analysis of information available in literature (structural, and in some cases enzymatic data), which allows the identification of the best combination of docking software and scoring function that are suited for studying the system of interest. In the second step, the combination of docking software and scoring function is used to predict the binding modes (pose prediction) and the relative affinities of ligands (scoring). As our previous studies [START_REF] Surpateanu | Evaluation of docking performance in a blinded virtual screening of fragment-like trypsin inhibitors[END_REF][START_REF] Colas | Virtual screening of the SAMPL4 blinded HIV integrase inhibitors dataset[END_REF][START_REF] Martiny | Blind pose prediction, scoring, and affinity ranking of the CSAR 2014 dataset[END_REF][START_REF] Selwa | Molecular docking performance evaluated on the D3R Grand Challenge 2015 drug-like ligand datasets[END_REF] highlighted the importance of using enhanced genetic algorithm parameters for docking (a search efficiency of 200%), in this work we used the same parameters in order to ensure an adequate conformational sampling of docking conformations.

Preliminary analysis

We found 27 crystal structures of FXR that were available in the Protein Data Bank (PDB) [34]. These structures were organized in five distinct groups, according to their conformation and the ligand present in the binding site (see the Electronic Supplementary Material for a complete list of these structures and the exact composition of each group). A representative structure was selected from each group, based on the crystal structure resolution and the lack of missing residues. The three-dimensional structure of protein in these structures is well conserved, with the exception of two fragments (residues 258-285 and 335-358) that are very flexible (Figure 6). These five structures, together with the apo FXR structure provided by the organizers, constitute our evaluation dataset, which was used in re-docking and cross-docking calculations using the FXR ligands from all the 27 structures available and several combinations of docking software and scoring functions: Gold with the GoldScore, ChemScore, ChemPLP and ASP scoring functions, Vina and Autodock. RMSD values compared with the native ligands from the crystallographic structures were calculated for all docking poses. In order to evaluate the accuracy of docking and scoring, we have considered the lowest RMSD value and the RMSD value of the best ranking pose for each combination protein-ligand-(docking software)-(scoring function). AutoDock provided very poor results, with most of the docking conformations positioned outside the binding site, whereas Gold/ASP, followed by Gold/GoldScore and Vina, could reproduce rather well the native protein-ligand complexes, especially in the cross-docking calculations. As expected, the redocking results outperformed the cross-docking results. It was also observed that the combination of a protein and a ligand belonging to the same group was more favorable than a combination of a protein and a ligand from different groups.

Pose prediction and scoring

The 102 FXR ligands from the D3R Grand Challenge 2 dataset containing 180 ligands were docked on the 6 representative FXR structures shown in Figure 6 using Gold with the ASP scoring function. For each ligand, the best-ranked docking conformation was selected and the overall ranking was submitted, as well as the coordinates for the ligands FXR_1 to FXR_36. For the ligands belonging to a group for which crystal structures were available (e.g. benzimidazoles, isoxazoles), the RMSD was calculated using the largest common fragment, and the conformations with the best RMSD were selected for a second submission. The RMSD calculation was realized using an in house developed script based on CACTVS Chemoinformatics Toolkit. The poses from the spiro and sulfonamides groups were visually inspected using UCSF Chimera. Only the 3FLI and the APO structures provided docking poses with a carboxylate group (that is present in most spiro structures and in FXR_101 from the sulfonamides group) interacting with Arg335. This was considered as the correct orientation, since most of the crystalized ligands show the same kind of interaction. Overall, poses obtained with the structure 3OLF were selected for benzimidazoles, with 1OSV for steroids, with 3HC5 for isoxazoles and with 3FLI for all others.

The performance of submissions for pose prediction (best RMSD and RMSD of pose 1) is presented in Figure 7, showing a relatively good result that we obtained in this category compared with the other participants. Our scoring results for the two submissions in Phase 1 were very modest, with Kendall Tau values of 0.13 and 0.072. Table S1 from the Supplementary Information file shows the rank of the best RMSD pose for compounds with existing reference structural data (53 compounds out of 102 compounds from the dataset). A mean value of 4.68 (out of 10 poses in each case) was obtained for this rank, which is quite low. If we also consider that for the remaining 49 compounds with no reference structure available we have no information about the docking reliability, these data altogether might explain the incorrect scoring prediction.

The crystallographic structures of the 36 FXR complexes proposed for pose prediction were released at the end of Phase 1. A comparison of several representative docking poses and the corresponding crystallographic conformations is provided in Figure 8. We predicted well the conformation of most benzimidazoles, but the other three groups (isoxazoles, spiro compounds and sulfonamides) were more challenging, and we could predict correctly only the overall orientation of the ligand, but not the details of the interaction with the binding site. The compounds from the miscellaneous group were even more difficult, and in some cases our prediction was completely opposite compared to the crystal structure. In Phase 2, the three-dimensional coordinates of the ligands FXR_37 to FXR_102 were built using UCSF Chimera [START_REF] Pettersen | UCSF Chimera --a visualization system for exploratory research and analysis[END_REF], by superimposing their common backbone on the released FXR_17, FXR_10 and FXR_12 crystal structures. The protein-ligand complexes of these ligands, together with the 36 ligands from the crystal structures, were rescored using Gold with the ASP scoring function and the results were slightly improved compared with Phase 1, with a Kendall Tau value of 0.17.

Free energy calculations

The free energy calculations were carried out using a protocol adapted from the methodology implemented within the PMX software [START_REF] Gapsys | pmx: Automated protein structure and topology generation for alchemical perturbations[END_REF][START_REF] Gapsys | Calculation of binding free energies[END_REF][START_REF] Gapsys | Accurate and Rigorous Prediction of the Changes in Protein Free Energies in a Large-Scale Mutation Scan[END_REF]. An important advantage of our procedure is the possibility to simulate transformations involving charge modification, which is relatively difficult or even impossible using other protocols (see the Methods section and Figures S2,S3 and S4 in the Electronic Supplementary Material for more details).

We obtained very good results for the free energy prediction of the set1 (sulfonamides), our submission nszkx being ranked #2. However, the corresponding submission 2ytv8 for set2 (spiro compounds) was not at all competitive, being ranked #20 (Figure 9). After the end of the D3R Grand Challenge 2 we have recomputed all data after fixing a bug in the hybrid topologies, and also using docking poses instead of crystal structures (equivalent of Phase 1 calculations carried out retrospectively) and using AMBER/GAFF force field instead of OPLS-AA (Figure 9). For set1, similar results were obtained with OPLS-AA before and after correction, as well as with AMBER/GAFF force field. However, when docking poses were used as initial coordinates (which represents Phase 1 calculations carried out retrospectively), no correlation was obtained.

This corroborates with the pose prediction results, showing that no good quality predictions can be obtained from inaccurate docking poses. For set2, the results were quite disappointing, with negative correlations with OPLS-AA before and after the correction. Apparent better correlations were obtained with OPLS-AA using the docking poses and with AMBER/GAFF, but they are not representative since they were computed only for 12 and 6 values, all of them belonging to the FXR_12 subset (see Table 2 for the compounds belonging to the FXR_10 and FXR_12 subsets), so we decided not to represent them in Figure 9.

Table 2. Free energies computed for set2. The FXR_10 subset contains the five compounds marked with a star, and the FXR_12 subset contains the remaining compounds. FXR_10 and FXR_12 were used as reference compounds for each subset, then all free energies from subset FXR_10 were translated relative to FXR_12. We tried to find a rational explanation for the discrepancy of the results obtained for set1 and set2, using the same protocol. Among the possible hypotheses, we can mention: i) the intrinsic greater structural diversity in set2 compared with set1; ii) incorrect force field parameters and iii) insufficient conformation sampling of ligands.

To validate the first hypothesis, we computed the Tanimoto similarity matrix for set1 and set2

(see Tables S2 andS3 in Electronic Supplementary Material). The global mean values of Tanimoto similarity for the two datasets are very close, 0.88 and 0.86, respectively, suggesting a similar degree of diversity. However, a visual inspection of the two datasets shows that set1 is quite homogeneous, with variations on the substitution pattern of a single phenyl ring. On the other hand, compounds from set2 contain variations on two fragments: one can be a diversely substituted phenyl ring, and the other can be either a thienyl ring or a diversely substituted phenyl ring. According to the presence or not of the thienyl ring, set2 can be divided into two subsets, which have FXR_10 and FXR_12 as representative compounds. We computed the statistics separately on these two subsets and the results are presented in Table 3. Compared with the whole set2, only a small improvement in the correlation with experimental data is observed for the FXR_12 subset. However, for the FXR_10 subset we observe almost a perfect anticorrelation with the experimental data. Overall, this analysis shows that the differences between the structural diversity of set1 and set2 are too small to be discriminated by descriptors such as Tanimoto similarity, but the set2 is more diverse and can be divided in two subsets. One of these subsets, containing a thienyl substituent, has a major negative impact in the prediction of free energies for set2. To evaluate the pertinence of the second hypothesis, we analyzed the conformational distribution of the ligands FXR_17, FXR_10 and FXR_12, as representative structures for set1 and the two subsets of set2, in two force fields, OPLS-AA and AMBER/GAFF. In each case, we extracted and superimposed all the 501 conformations from the 10 ns molecular dynamics simulation of the ligand alone in water. The result is presented in Figure S5 (Electronic Supplementary Material).

For compound FXR_17, we observe 4 main differences between the distributions OPLS-AA (a) and AMBER/GAFF (b): i) the phenyl ring is mostly parallel with the bicyclic system in a, and perpendicular in b; ii) the amide group is mostly perpendicular with the bicyclic system in a, and parallel in b; iii) the distribution of the thienyl ring around the dihedral C-N-S-C is restricted to a very narrow window in a, whereas in b there are two larger windows in opposite positions, showing in the latter case an unrestricted exchange between these two positions; iv) in a the thienyl ring shows equivalent populations of both faces, whereas in b the rotation around the dihedral N-S-C-S is very much restricted. However, as the predictions of set1 using either OPLS-AA or AMBER/GAFF are very similar (see Figure 9a and Table 1), these differences should not have a major contribution or, more probably, should cancel mutually.

For compound FXR_10, we observe in a a restricted rotation around the C-N-S-C dihedral and, in opposition with FXR_17, an impossible rotation around the N-S-C-S dihedral, probably because of the close proximity of the amide oxygen. In the case of b, we observe a free rotation around the C-N-S-C dihedral and a restricted rotation around the N-S-C-S dihedral, similar with FXR_17.

Finally, we observe for FXR_12 a restricted rotation around the C-N-S-CA dihedral in a and a free rotation around the N-S-CA-CA dihedral (the chlorine substituent is positioned equally on both sides), whereas in b the rotation around the C-N-S-CA dihedral is relatively free in the conditions of simulations, but the rotation around the N-S-CA-CA dihedral is almost completely restricted.

These results suggest the possible existence of two non-optimal dihedrals associated with the sulfonamide group, similarly with a recent report regarding the incorrect conformational sampling of linezolid [START_REF] Grunenberg | Effective in silico prediction of new oxazolidinone antibiotics: Force field simulations of the antibiotic-ribosome complex supervised by experiment and electronic structure methods[END_REF]. For set1, their influence might be compensated by two other dihedrals, which is not the case for set2. Additionally, in the FXR_12 subset there are two atropoisomers that can contribute to the overall binding energy, whereas in our calculations we have considered only one, the most favorable.

The third hypothesis, insufficient conformation sampling of ligands, is not very probable given the length of our molecular dynamics simulations and the relative rigidity of the ligands. If the conformation space is not sampled correctly, this should be more due to inadequate force field parameters than to insufficient length of simulations. Along the same lines, in a few specific cases, the standard deviation of our predictions is unusually high (see the "ΔΔG error" columns in Tables 1 and2), especially for set2. 27 structures were available in the PDB for FXR at the moment when the D3R Grand Challenge 2 took place. They were organized in 5 distinct groups, according to the type of ligand and the binding site conformation. The representative structure for each group (based on the crystal structure resolution and lack of missing residues) is colored in red.

Claudel T, Sturm

Group 1 (isoxazoles): 3dct, 3dcu, 3gd2, 3hc5, 3hc6, 3p88, 3p89, 3rut, 3ruu, 3rvf

Group 2 (benzimidazoles): 3okh, 3oki, 3olf, 3omk, 3omm, 3oof, 3ook

Group 3 (FXR_5-like): 3l1b, 3fli

Group 4 (steroid, FXR_34-like): 3bej, 1osv, 1ot7, 4qe6

Group 5 (miscellaneous): 1osh, 4oiv, 4qe8, 4wvd FXR ligands regroupment according to their chemical structure Isoxazoles: FXR_4, FXR_23, FXR_33, FXR_65

Benzimidazoles: FXR_6, FXR_7, FXR_8, FXR_9, FXR_13, FXR_14, FXR_19, FXR_20, FXR_21, FXR_22, FXR_24, FXR_25, FXR_26, FXR_27, FXR_28, FXR_29, FXR_30, FXR_31, FXR_32, FXR_35, FXR_36, FXR_37, FXR_39, FXR_40, FXR_42, FXR_50, FXR_51, FXR_52, FXR_53, FXR_54, FXR_55, FXR_56, FXR_57, FXR_58, FXR_59, FXR_60, FXR_61, FXR_62, FXR_63, FXR_64, FXR_66, FXR_67, FXR_68, FXR_69, FXR_70, FXR_71, FXR_72

Spiro compounds: FXR_10, FXR_11, FXR_12, FXR_38, FXR_41, FXR_73, FXR_74, FXR_75, FXR_76, FXR_77, FXR_78, FXR_79, FXR_80, FXR_81, FXR_82, FXR_83, FXR_84, FXR_85, FXR_86, FXR_87,

FXR_88, FXR_89

Sulfonamides: FXR_15, FXR_16, FXR_17, FXR_43, FXR_44, FXR_45, FXR_46, FXR_47, FXR_48, FXR_49, FXR_90, FXR_91, FXR_92, FXR_93, FXR_94, FXR_95, FXR_96, FXR_97, FXR_98, FXR_99, FXR_100, FXR_101, FXR_102

Miscellaneous: FXR_1, FXR_2, FXR_3, FXR_5, FXR_18, FXR_34

Figure 1 .

 1 Figure 1. Mesh surface representation of a representative crystal structure (PDB code 3OLF) of

Figure 2 .

 2 Figure 2. Chemical structures of the 36 FXR ligands included in Phase 1 for pose prediction

Figure 3 .

 3 Figure 3. Chemical structures of the 15 FXR ligands included in free energy set1

Figure 4 .

 4 Figure 4. Chemical structures of the 18 FXR ligands included in free energy set2 (spiro

Figure 5 .

 5 Figure 5. The main steps of the protocol used for the calculation of alchemical free energies.

Figure 6 .

 6 Figure 6. Representative 6 FXR PDB structures superimposed: a) general view, showing a very

Figure 7 .

 7 Figure 7. Performance of Phase 1 pose prediction submissions (Kendall Tau) for the FXR D3R

Figure 8 .

 8 Figure 8. Comparison of our docking poses (cyan) with crystal structure conformations

Figure 9 .

 9 Figure 9. Performance of Phase 2 free energy submissions for set1 (a) and set2 (b). The

Figure S1 .FXR_102Figure S5 .

 S1S5 Figure S1. Chemical structures of the entire FXR dataset, containing 102 ligands used for ranking prediction.

Table 1 .

 1 Free energies computed for set1. FXR_91 was used as reference compound.

		Experimental IC50 (μM)	OPLS-AA before correction (nszkx) ΔΔG (kJ/mol) ΔΔG error (kJ/mol)	OPLS-AA after correction (nszkx_af) ΔΔG (kJ/mol) ΔΔG error (kJ/mol)
	FXR_17	0.79	-9.32	1.16	-18.35	1.12
	FXR_45	28.85	-3.14	2.33	-21.21	2.15
	FXR_46	62.37	-3.81	21.82	-12.98	1.26
	FXR_47	20.96	NA	NA	-18.61	2.41
	FXR_48	100.00	NA	NA	5.36	1.75
	FXR_49	100.00	-3.73	1.48	-9.47	1.02
	FXR_91	29.63	0.00	0.00	0.00	0.00
	FXR_93	46.66	-8.98	1.26	-4.04	0.39
	FXR_95	32.17	-8.39	1.45	-6.63	1.21
	FXR_96	58.86	-19.12	1.62	-21.36	2.15
	FXR_98	13.14	-21.07	1.42	-12.95	0.97
	FXR_99	100.00	-6.34	1.59	-11.07	0.56
	FXR_100	19.14	-15.86	2.49	-25.81	3.05
	FXR_101	27.64	-36.24	3.38	-27.94	3.69
	FXR_102	29.23	-0.15	2.85	13.45	2.17
			Correlation coefficient	p-value	Correlation coefficient	p-value

Table 3 .

 3 Statistics computed for the subsets FXR_10 and FXR_12 of set2. See Table2and text for the list of compounds included in each subset.

		OPLS-AA before correction	OPLS-AA after correction
	FXR_10 subset	Correlation	p-value	Correlation	p-value
	Kendall's rank correlation tau Spearman's rank correlation	coefficient -0.5270 -0.6669	0.2065 0.2189	coefficient -0.9487 -0.9747	0.0230 0.0048
	rho Pearson's product-moment	-0.8377	0.0766	-0.7737	0.1247
	correlation r
	FXR_12 subset	Correlation	p-value	Correlation	p-value
	Kendall's rank correlation tau Spearman's rank correlation	coefficient -0.2564 -0.2692	0.2519 0.3733	coefficient -0.0513 -0.0330	0.8577 0.9206
	rho Pearson's product-moment	-0.3261	0.2769	-0.0902	0.7696
	correlation r

Table S1 .

 S1 Rank of the best RMSD poses. When no reference structure was available, the score of the first ranked pose was reported for the two submissions, therefore no rank of best RMSD pose is considered.

	FXR_54	46.19	48.11	4
	FXR_55	45.06	45.37	4
	Ligand FXR_56 FXR_57 FXR_1 FXR_58 FXR_2 FXR_59 FXR_3 FXR_60 FXR_4 FXR_61 FXR_5 FXR_62 FXR_6 FXR_63 FXR_7 FXR_64 FXR_8 FXR_65 FXR_9 FXR_66 FXR_10 FXR_67 FXR_11 FXR_68 FXR_12 FXR_69 FXR_13 FXR_70 FXR_14 FXR_71 FXR_15 FXR_72 FXR_16 FXR_73 FXR_17 FXR_74 FXR_18 FXR_75 FXR_19 FXR_76 FXR_20 FXR_77 FXR_21 FXR_78 FXR_22 FXR_79 FXR_23 FXR_80 FXR_24 FXR_81 FXR_25 FXR_82 FXR_26 FXR_83 FXR_27 FXR_84 FXR_28 FXR_85 FXR_29 FXR_86 FXR_30 FXR_87 FXR_31 FXR_88 FXR_32 FXR_89 FXR_33 FXR_90 FXR_34 FXR_91 FXR_35 FXR_92 FXR_36 FXR_93 FXR_37 FXR_94 FXR_38 FXR_95 FXR_39 FXR_96 FXR_40 FXR_97 FXR_41 FXR_98 FXR_42 FXR_99 FXR_43 FXR_100 FXR_44 FXR_101 FXR_45 FXR_102 FXR_46 Mean rank of best RMSD pose (from 53 values) Score of first ranked pose Score of best RMSD pose 43.69 43.69 47.05 48.29 57.25 57.25 38.19 38.19 57.27 57.27 39.35 41.05 59.03 59.03 41.27 43.93 63.35 64.13 40.38 43.31 58.53 62.45 38.54 38.63 49.10 52.44 40.07 40.55 48.07 49.36 39.42 41.64 53.28 54.13 38.25 40.65 43.55 43.55 41.96 43.83 51.19 51.19 36.46 37.87 44.97 44.97 41.87 44.72 47.66 47.66 33.62 33.66 41.27 41.27 39.28 45.34 45.85 46.23 36.91 38.68 49.65 49.65 38.51 38.77 56.47 56.47 49.38 49.38 42.05 42.05 48.03 48.03 54.34 54.34 50.52 50.52 49.24 52.23 48.20 48.20 48.05 49.73 44.43 44.43 46.07 46.26 46.49 46.49 51.95 51.95 48.64 48.64 53.66 57.20 37.81 37.81 44.42 45.46 44.02 44.02 46.74 47.83 45.46 45.46 39.43 39.43 45.72 45.72 39.50 41.40 47.15 47.15 40.42 42.27 46.19 46.19 41.16 43.78 44.59 44.59 41.54 44.58 41.90 41.90 44.30 45.09 41.68 41.68 52.50 53.19 47.94 47.94 40.94 42.95 41.55 41.55 52.87 59.51 48.44 48.44 40.64 40.64 55.18 55.18 32.84 35.97 49.39 49.39 55.97 58.21 53.68 53.68 50.16 50.16 41.40 41.40 51.58 51.66 42.61 42.61 48.89 51.89 55.88 55.88 45.89 45.89 42.50 42.50 45.92 50.25 45.73 45.73 46.24 46.24 40.67 40.67 48.13 48.13 45.12 45.12 39.38 39.38 40.80 40.80 42.54 42.54	1 Rank of best RMSD 8 pose (out of 10 poses) 1 -4 -2 -5 6 7 7 9 4 4 4 7 3 5 1 2 -3 -2 -6 1 7 2 2 --------9 -2 -2 -1 -10 -7 -7 -1 -5 -7 -6 -7 -4 -2 -5 -10 -1 -7 -10 ---4 -5 ---7 -------4.68
	FXR_47	51.05	51.05	-
	FXR_48	43.75	43.75	-
	FXR_49	43.65	43.65	-
	FXR_50	52.93	54.39	6
	FXR_51	48.25	48.74	2
	FXR_52	45.76	54.79	3
	FXR_53	39.81	41.12	7

Table S2 .

 S2 Tanimoto similarity matrix for the compounds belonging to set1.

	Tanimoto	FXR _17	FXR _45	FXR _46	FXR _47	FXR _48	FXR _49	FXR _91	FXR _93	FXR _95	FXR _96	FXR _98	FXR _99	FXR _100	FXR _101	FXR _102	Mean value per compound
	FXR_17	1.00	0.91	0.88	0.95	0.93	0.87	0.84	0.68	0.85	0.88	0.88	0.86	0.84	0.94	0.87	0.88
		0.84	0.77	0.95	0.86	0.89	0.93	0.98	0.77	0.97	0.93	0.93	0.85	1.00	0.86	0.89	0.89
	FXR_101	0.94	0.86	0.90	0.90	0.90	0.88	0.86	0.69	0.85	0.89	0.89	0.83	0.86	1.00	0.85	0.87
	FXR_102	0.87	0.80	0.94	0.85	0.89	0.92	0.90	0.73	0.89	0.94	0.93	0.80	0.89	0.85	1.00	0.88
	Global mean value															0.88

Table S3 .

 S3 Tanimoto similarity matrix for the compounds belonging to set2.

	Tanimoto	FXR _10	FXR _12	FXR _38	FXR _41	FXR _73	FXR _74	FXR _75	FXR _76	FXR _77	FXR _78	FXR _79	FXR _81	FXR _82	FXR _83	FXR _84	FXR _85	FXR _88	FXR _89	Mean value per compound
	FXR_10	1.00 0.85 0.94 0.81 0.87 0.89 0.75 0.90 0.82 0.83 0.95 0.83 0.84 0.83 0.89 0.89 0.87 0.85	0.87
	FXR_12	0.85 1.00 0.81 0.94 0.75 0.92 0.64 0.94 0.96 0.97 0.82 0.95 0.96 0.97 0.92 0.92 0.91 0.97	0.90
	FXR_38	0.94 0.81 1.00 0.85 0.83 0.84 0.74 0.85 0.78 0.79 0.91 0.80 0.80 0.79 0.84 0.85 0.83 0.81	0.84
	FXR_41	0.81 0.94 0.85 1.00 0.71 0.87 0.63 0.89 0.91 0.92 0.78 0.91 0.91 0.92 0.87 0.88 0.86 0.92	0.87
	FXR_73	0.87 0.75 0.83 0.71 1.00 0.77 0.75 0.79 0.72 0.73 0.88 0.73 0.73 0.73 0.77 0.77 0.76 0.75	0.78
	FXR_74	0.89 0.92 0.84 0.87 0.77 1.00 0.66 0.98 0.89 0.90 0.85 0.90 0.91 0.90 0.96 0.96 0.95 0.92	0.89
	FXR_75	0.75 0.64 0.74 0.63 0.75 0.66 1.00 0.67 0.62 0.62 0.74 0.62 0.63 0.62 0.66 0.66 0.65 0.64	0.68
	FXR_76	0.90 0.94 0.85 0.89 0.79 0.98 0.67 1.00 0.90 0.92 0.86 0.91 0.92 0.91 0.98 0.98 0.96 0.94	0.91
	FXR_77	0.82 0.96 0.78 0.91 0.72 0.89 0.62 0.90 1.00 0.95 0.79 0.93 0.94 0.96 0.89 0.89 0.88 0.94	0.88
	FXR_78	0.83 0.97 0.79 0.92 0.73 0.90 0.62 0.92 0.95 1.00 0.80 0.93 0.94 0.96 0.90 0.90 0.89 0.95	0.88
	FXR_79	0.95 0.82 0.91 0.78 0.88 0.85 0.74 0.86 0.79 0.80 1.00 0.80 0.81 0.80 0.85 0.85 0.84 0.82	0.84
	FXR_81	0.83 0.95 0.80 0.91 0.73 0.90 0.62 0.91 0.93 0.93 0.80 1.00 0.95 0.94 0.90 0.93 0.90 0.95	0.88
	FXR_82	0.84 0.96 0.80 0.91 0.73 0.91 0.63 0.92 0.94 0.94 0.81 0.95 1.00 0.95 0.94 0.91 0.91 0.96	0.89
	FXR_83	0.83 0.97 0.79 0.92 0.73 0.90 0.62 0.91 0.96 0.96 0.80 0.94 0.95 1.00 0.90 0.90 0.88 0.95	0.88
	FXR_84	0.89 0.92 0.84 0.87 0.77 0.96 0.66 0.98 0.89 0.90 0.85 0.90 0.94 0.90 1.00 0.96 0.97 0.92	0.90
	FXR_85	0.89 0.92 0.85 0.88 0.77 0.96 0.66 0.98 0.89 0.90 0.85 0.93 0.91 0.90 0.96 1.00 0.97 0.92	0.90
	FXR_88	0.87 0.91 0.83 0.86 0.76 0.95 0.65 0.96 0.88 0.89 0.84 0.90 0.91 0.88 0.97 0.97 1.00 0.91	0.89
	FXR_89	0.85 0.97 0.81 0.92 0.75 0.92 0.64 0.94 0.94 0.95 0.82 0.95 0.96 0.95 0.92 0.92 0.91 1.00	0.90
	Global mean value																	0.86

Acknowledgments. We thank Prof. Bert de Groot for helpful discussions. The comments and suggestions of the reviewers are also acknowledged, as they greatly contributed to improve the manuscript. This work was supported by the Laboratory of Excellence in Research on Medication and Innovative Therapeutics (LERMIT) [grant number ANR-10-LABX-33], by the JPIAMR transnational project DesInMBL [grant number ANR-14-JAMR-0002] and by the Région Ile-de-France (DIM Malinf).

CONCLUSIONS

We used in this work a protocol in two steps, involving an initial analysis of the available structural data from the PDB, which allows the selection of the most appropriate combination of docking software and scoring function. Subsequent docking calculations showed that the pose prediction can be carried out with a certain precision, but this is dependent on the specific nature of the ligands. The correct ranking of docking poses is still a problem and cannot be successful in the absence of good pose predictions. Our free energy calculations on two different subsets provided contrasted results, which might have the origin in non-optimal force field parameters associated with the sulfonamide chemical moiety. Electronic Supplementary Material. The Electronic Supplementary Material contains the chemical structures of the entire FXR dataset, the rank of best RMSD poses, conformational distribution of representative ligands, Tanimoto similarity matrices and a schematic description of the systems and thermodynamic cycles used for free energy calculations.

Electronic Supplementary Material

Blinded evaluation of farnesoid X receptor (FXR) ligands binding using molecular docking and free energy calculations Edithe Selwa, 1, ‡ Eddy Elisee, 1, ‡ Agustin Zavala, 1, ‡ Bogdan I. Iorga 1,* 1 Institut de Chimie des Substances Naturelles, CNRS UPR 2301, LabEx LERMIT, 91198 Gif-sur-Yvette,

France

Corresponding Author

* Phone: +33 1 6982 3094; Fax: +33 1 6907 7247; Email: bogdan.iorga@cnrs.fr (B.I.I.).

Author Contributions ‡ These authors contributed equally.

Table of contents

Protein Data Bank (PDB) structures used for the preliminary analysis S2

FXR ligands regroupment according to their chemical structure S2


Marine Scius-Bertrand
email: marine.sciusbertrand@cea.fr

Laurent Videau

Alexandre Rondepierre

Emilien Lescoute

Yann Rouchausse

Jan Kaufman

Danijela Rostohar

Jan Brajer

Laurent Berthe
email: laurent.berthe@ensam.eu

Laser induced plasma characterization in direct and water confined regimes: new advances in experimental studies and numerical modelling

Keywords: laser shock, LSP, LASAT, laser-matter interaction, WCR, VISAR, plasma

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

Introduction

Laser shock is used in several processes such as the laser shock peening (LSP) and the LASer Adhesion Test (LASAT). The propagation of shock and release waves through materials induces compression and traction zones [START_REF] Antoun | Spall Fracture[END_REF][START_REF] Meyers | Dynamic Behavior of Materials[END_REF]. While the residual stresses arising from the compression of matter are relevant for the LSP treatment [START_REF] Clauer | Laser shock peening, the path to production[END_REF], the LASAT process exploits the traction peak stress that arises at the meeting point of two release waves [START_REF] Yuan | Measurement of interface strength by the modified laser spallation technique. i. experiment and simulation of the spallation process[END_REF][START_REF] Bolis | Physical approach to adhesion testing using laser-driven shock waves[END_REF]. The LSP treatment, when applied to a metallic target, has already proven its capability to improve mechanical properties and fatigue performance [START_REF] Ballard | Residual stresses induced by laser-shocks[END_REF][START_REF] Fairand | Laser shock-induced microstructural and mechanical property changes in 7075 aluminum[END_REF][START_REF] Peyre | Laser shock processing of materials, physical processes involved and examples of applications[END_REF][START_REF] Peyre | Laser shock processing of aluminium alloys. Application to high cycle fatigue behaviour[END_REF][START_REF] Clauer | Laser shock peening for fatigue resistance[END_REF]: crack initiation is inhibited and crack growth is delayed. The LASAT capability was first demonstrated by Vossen [START_REF] Vossen | Measurements of film-substrate bond strength by laser spallation Adhesion Measurement of Thin Films[END_REF]; its state of the art was published in 2011 [START_REF] Berthe | State-of-the-art laser adhesion test (LASAT) Nondestruct[END_REF]. Several studies since have shown that it can be used as an extended non-destructive test for aeronautical bonding [START_REF] Bardy | Numerical study of laser ablation on aluminum for shock-wave applications: development of a suitable model by comparison with recent experiments[END_REF][START_REF] Sagnard | Development of the symmetrical laser shock test for weak bond inspection[END_REF][START_REF] Ecault | Laser Shock Adhesion test for composite bonding assessment[END_REF].

The application of a high-powered laser to a metallic surface causes vaporization of a layer a few micrometers thick, leading to the formation of an expanding plasma [START_REF] Mora | Theoretical model of absorption of laser light by a plasma[END_REF][START_REF] Ambartsumyan | Heating of matter by focused laser radiation[END_REF]. In reaction to the plasma expansion, a mechanical loading, equivalent to an ablation pressure (P abl ), is applied to the target, resulting in a shock wave that propagates through the material (figure 1). The illumination of the surface can be direct (figure 1(b)) or in a confined regime (figure 1(a)). The confinement can be any medium transparent to the laser wavelength that will slow the expansion of the plasma. The use of confinement therefore increases the equivalent pressure by up to one order of magnitude and makes the shock wave last two to three times longer than the pulse duration [START_REF] Anderholm | Laser-generated stress waves[END_REF][START_REF] O'keefe | Laser-induced stress-wave and impulse augmentation[END_REF][START_REF] Peyre | Laser shock processing: a review of the physics and applications[END_REF][START_REF] Fabbro | Physical study of laser-produced plasma in confined geometry[END_REF]. However, in a dielectric medium such as water or air, a breakdown phenomenon can occur at certain laser intensities, leading to a pressure saturation and a shorter shock wave duration [START_REF] Berthe | Shock waves from a water-confined laser-generated plasma[END_REF][START_REF] Berthe | Experimental study of the transmission of breakdown plasma generated during laser shock processing[END_REF][START_REF] Sollier | Numerical modeling of the transmission of breakdown plasma generated in water during laser shock processing[END_REF][START_REF] Bras | Laser shock peening: toward the use of pliable solid polymers for confinement[END_REF]. The determination of the intensity threshold above which breakdown appears is essential to identify the usable range of pressures as a function of incident power density.

LSP and LASAT technologies use similar lasers, neodymium-doped yttrium aluminum garnet (Nd:YAG) or neodymium-doped glass (Nd:glass), with wavelengths ranging from 532 to 1064 nm and energies from a few joules to several tens of joules focused on millimeter-sized focal spots. It is essential to master the laser-induced plasma in order to control the process. In addition, this investigation offers the opportunity to examine material properties under shock. Currently, some models already exist that can characterize the physical processes of a confined laser shock [START_REF] Fabbro | Physical study of laser-produced plasma in confined geometry[END_REF] or calculate the maximal induced pressure from the experimental velocities [START_REF] Tollier | Study of the laser-driven spallation process by the velocity interferometer system for any reflector interferometry technique[END_REF]. However, their validation has been done using one set of laser parameters, with different means of pressure characterization but with a lack of laser metrology and no reliable beam-quality [START_REF] Fabbro | Physical study of laser-produced plasma in confined geometry[END_REF][START_REF] Berthe | Shock waves from a water-confined laser-generated plasma[END_REF][START_REF] Berthe | Experimental study of the transmission of breakdown plasma generated during laser shock processing[END_REF][START_REF] Sano | Residual stress improvement in metal surface by underwater laser irradiation[END_REF]. In addition, there is no self-consistent model for the prediction of plasma temporal pressure profiles. The improvement of experimental and numerical tools over the past few years has enabled new advances in plasma characterization aiming at verifying recent experimental reliability as well as extracting a self-consistent numerical model. Therefore, for the first time, this work consists of a collection of an extensive range of experiments to validate a model able to predict the loading profile necessary to simulate the laser shock process. Based on the ESTHER numerical code, it permits a characterization of the plasma (temperature, duration and thickness). This paper presents an experimental and numerical study of laser-matter interaction in the water-confined regime and direct illumination at three laser facilities allowing different focal spots (round and square) and variable pulse shapes and durations. For every experiment, an effort has been made to characterize the laser in terms of its beam profile, energy and temporal pulse shape. First, we present velocity interferometer system for any reflector (VISAR) measurements of free surface velocity (FSV) versus time for pure aluminum. These are then compared to the numerical simulation obtained from the ESTHER code. Thanks to its laser-matter interaction prediction module, the plasma temperature is obtained from the code as well as the equivalent ablation pressure and the amount of ablated materials. Finally, practical scaling laws are extracted from these results. The latter provide a plasma temporal pressure profile for any of the above configurations, which can be used to simulate the behaviour of aluminum under laser shock using mechanical simulation software.

Experimental study

Three laser facilities with several setups were used: Héphaïstos in the Process and Engineering in Mechanics and Materials laboratory (PIMM lab) (Paris), the HiLASE research center (Prague) and the Transportable Laser Shock Generator (GCLT) of the French Alternative Energies and Atomic Energy Commission (CEA/DAM/DIF) (Paris). Each source is described more precisely thereafter. A 2-3 mm waterconfined regime was used consistently at all experimental facilities (figure 1(a)), achieved by depositing water on the sample's surface. In addition, the vacuum chamber of the GCLT (figure 1(b)) was used for direct irradiation regime. A particular effort was made to ensure precise knowledge of the experimental parameters. The target laser energies are measured and saved for each shot using calibrated calorimeters. Diffractive optical elements (DOE) were added to every beam path at Héphaïstos and GCLT to homogenize their spatial distributions [START_REF] Sagnard | Development of the symmetrical laser shock test for weak bond inspection[END_REF]. Before starting the experiments, the on-target focal spot diameters (ϕ) are measured using a charge-coupled device (CCD) camera and the temporal profiles are measured using photodiodes. The GCLT can change these profiles on demand, therefore they are measured and saved for each shot. The rear FSVs were measured using VISAR [START_REF] Tollier | Study of the laser-driven spallation process by the velocity interferometer system for any reflector interferometry technique[END_REF][START_REF] Barker | Laser interferometer for measuring high velocities of any reflecting surface[END_REF][START_REF] Barker | Correction to the velocity-per-fringe relationship for the VISAR interferometer[END_REF][START_REF] Tollier | Study of the laser-driven spallation process by the VISAR interferometry technique. II. Experiment and simulation of the spallation process[END_REF]. A 100 µm-diameter laser probe is focused on the back face of the sample and aligned to scan the middle of the working laser's focal spot. The photomultiplier's response time offers timeresolved velocity measurements with a precision on the nanosecond scale. The global uncertainty of the velocity measurement and the corresponding laser intensity is estimated to be ±15% rms.

Laser facilities

The Héphaïstos platform uses a Thales Gaïa High Power laser composed of two Nd:YAG lasers at 532 nm. Together, they can deliver up to 14 J with a pulse duration of 7 ns full width at half maximum (FWHM) of a Gaussian pulse (figure 2(a)). The focal spot diameters are 3 and 4 mm, leading to intensities ranging from 0.7 to 13 GW cm -2 . The spatial shape of a 4 mm focal spot taken by a CCD camera is displayed in figure 2(b).

The main laser system of the HiLASE research center is called BIVOJ. It is a diode-pumped solid-state laser working at 1029 nm and delivering 10 ns pulses with energy levels of up to 105 J [START_REF] Divoky | Performance comparison of yb:yag ceramics and crystal gain material in a large-area, high-energy, high average-power diode-pumped laser[END_REF]. Both the spatial and temporal shapes of the pulses are square (figure 3). The use of a 3.5 mm focal spot led to intensities ranging from 0.6 to 11.8 GW cm -2 .

The GCLT is based on an Nd:glass laser (Lumibird) with a wavelength of 1053 nm that delivers pulses from 4 to 100 ns with energies of up to 40 J. The laser pulse temporal profile can be chosen to be, for example, Gaussian-like, triangular or top hat. Figure 4(a) displays the top-hat pulse duration obtained for a requested pulse of 10-40 ns. A vacuum chamber enables the study of the direct-illumination regime. For the water-confined regime, a 5.1 mm focal spot was used (figure 4(b)), leading to intensities ranging from 0.2 to 11.5 GW cm -2 . In order to reach the same induced pressure in the direct-irradiation regime, the intensities have to be much higher (from 8 to 200 GW cm -2 ). With the same laser energies available, the laser focal spots were 2.5 and 1 mm.

Materials

The thicknesses of the samples were chosen in accordance with the focal spots to avoid edge effects by making the ratio of sample thickness to focal spot diameter smaller than 0.25 [START_REF]Etude du comportement dynamique de matériaux sous choc laser sub-picoseconde[END_REF][START_REF] Boustie | Study of damage phenomena induced by edge effects into materials under laser driven shocks[END_REF]. This study was thus conducted using two thicknesses (100 µm and 500 µm, respectively, for direct illumination and the water-confined regime) of pure aluminum. The Steinberg-Cochran-Guinan (SCG) model was used to obtain their elastoplatic behaviors (cf section 3) [START_REF] Steinberg | A constitutive model for metals applicable at high-strain rate[END_REF]. The mechanical properties used in this study are displayed in table 1 [START_REF] Bardy | Development of a numerical code for laser-induced shock waves applications[END_REF]. The initial and maximal yield strengths are Y 0 and Y max , respectively (in the von Mises sense), β and n are work-hardening parameters, ε i is the initial equivalent plastic strain, G 0 is the shear modulus at the reference state (temperature T = 300 K, pressure P = 0 and ε = 0), and G ′ p and G ′ T are the shear modulus derivatives with respect to the pressure and temperature, respectively.

Experimental Results

This section presents VISAR measurements performed under two illumination regimes at three laser facilities (Hephaïstos, HiLASE and GCLT). For each configuration, the dependences of the rear FSV measurements on the laser pulse duration ∆T (ns) and/or the intensity I (GW cm -2 ) are presented (figures 5 and 7) together with the simulations, which will be discussed in section 3. Plotting the maximal FSV versus the laser intensity (figures 6 and 8) enables us to observe the global behavior of the target under direct and water-confined irradiation, to identify the breakdown phenomenon threshold, and to compare the results from one installation to another.

Direct illumination regime.

This study is based on a large set of data gathered from numerous experiments carried out with several focal spots, laser intensities, and pulse durations, ensuring a wide range of results. Some representative signals of the FSV as a function of time are displayed in figure 5 for ∆T = 10, 20 and 40 ns at different power densities. A comparison with the simulation (colored dashed lines) and the ±15% uncertainty of the incident power density (grey area) will be discussed in section 3. The first peak is of particular interest, since it corresponds to the first emergence of the shock wave and has a direct relationship to the plasma pressure [START_REF] Berthe | Experimental study of the transmission of breakdown plasma generated during laser shock processing[END_REF][START_REF] Tollier | Study of the laser-driven spallation process by the velocity interferometer system for any reflector interferometry technique[END_REF]. The other peaks correspond to wave reflections within the target. By comparing the first maxima for two pulse durations (10 and 20 ns, figure 5(a) 1 and 5(b) 1) it is possible to conclude that pulse duration does not affect the respective velocity maxima (115 m s -1 for I = 16.7 GW cm -2 and 60 m s -1 for I = 8.1 GW cm -2 ): the maximum velocity is only influenced by applied peak intensities. The peak width is related to the pulse duration: a longer pulse duration (from 10 to 20 ns) induces broader peaks (from 16 to 28 ns at half maximum). In the case of a 40 ns pulse striking a 100 µm sample, the shock duration is longer than the time needed by the wave to go back and forth in the target (37 ns), hence the release wave arriving at the end of the laser pulse reloads the reflected release wave and the peak increases again before decreasing to its minimum (figure 5(c)).

The first peak maximum of the rear FSV was determined for three pulse durations (10, 20 and 40 ns) and two focal spot sizes (1.1 and 2.5 mm). In the case of a clear peak (figures 5(a) and (c)), its highest value was extracted, otherwise the maximum was set to the mean value of the plateau (figure 5(b)). Figure 6 collates the maximum velocities of the first peaks extracted from the measurements for all pulse durations and spot diameters included in the direct illumination regime. From this graph, it is clear that neither the focal spot nor the laser pulse duration has an influence on the maximal FSV in the direct irradiation regime when applied to a 100 µm pure-aluminum target. The maximal FSV increases with the intensity in the entire range studied (from 8 to 195 GW cm -2 corresponding, respectively, to velocities of 50 and 630 m s -1 ).

Water confined regime (WCR).

Water confined regime experiments were carried out at three wavelengths (532, 1029 and 1053 nm) with four pulse durations (7, 10, 20 and 40 ns) and four focal spots (3, 3.5, 4 and 5 mm). Typical velocity profiles are displayed in figure 7. First of all, the effect of confinement on the pressure should be noted; less intensity is needed to reach the same velocities in the water-confined regime (WCR) than with the direct-irradiation regime. For example, in the direct illumination regime, a top-hat pulse of 10 ns from the GCLT platform with 112 GW cm -2 induces a rear FSV of almost 400 m s -1 , whereas only 5 GW cm -2 at the same pulse duration is required in the WCR for almost the same FSV. This is in good agreement with a previous study showing that the use of confinement increases the ablation pressure [START_REF] Fabbro | Physical study of laser-produced plasma in confined geometry[END_REF]. Figure 7 displays the FSV versus time for (a) 7 ns Gaussian pulses at 532 nm and (b) 10 ns top-hat pulses at 1053 nm. In this case, the shape of the FSV peaks is not influenced by the laser-pulse shape nor the wavelength: the peaks widths durations at half maximum are 32 and 20 ns, respectively. When using longer top-hat pulse durations, the widths of the peaks increase : pulses of 20 and 40 ns (figures 7(c) and (d)) result in FSV first peak widths at half maximum of 41 and 79 ns, respectively.

The maximal rear FSV was set the same as for the direct illumination regime, and is plotted versus the laser intensity in figure 8. From these graphs, the influence of the wavelength and the pulse duration on the FSV maxima is established. However, small variations of the wavelength (from 1029 to 1053 nm) and focal spots (round and square) do not affect the maximum peak velocity. The results of the experiments carried out at the two laser facilities (GCLT and HiLASE) are consistent with each other (figure 8(b)), demonstrating the reliability of the method. For all sets of data obtained, two different behaviors can be observed: firstly, the velocities increase as a function of power density; secondly, the maximal velocities saturate from a threshold corresponding to the intensity (I th ), above which the plasma breakdown has a detrimental effect on the maximal FSV. For the 7 ns laser pulse at 532 nm, the I th is equal to 8-10 GW cm -2 with a maximal FSV of 720 m s -1 (figure 8(a)). For laser pulses at 1029 and 1053 nm with pulse durations of 10, 20 and 40 ns, the I th values are equal to 5 to 6, 3 to 4 and 2 to 3 GW cm -2 , respectively, with maximal velocities of 530, 440 and 300 m s -1 (figures 8(b)-(d)). These thresholds are collated in table 2.

Numerical study

The numerical study was performed using one-dimensional Lagrangian code called ESTHER. It is widely described in the literature [START_REF] Bardy | Numerical study of laser ablation on aluminum for shock-wave applications: development of a suitable model by comparison with recent experiments[END_REF][START_REF] Bardy | Development of a numerical code for laser-induced shock waves applications[END_REF][START_REF] Colombier | Hydrodynamic simulations of metal ablation by femtosecond laser irradiation[END_REF][START_REF] Boustie | Spallation generated by femtosecond laser driven shocks in thin metallic targets[END_REF]. In the studied range of power densities, the plasma is dominated by inverse bremsstrahlung laser absorption and hydrodynamic phenomena including ionization, phase transformation, temperature and pressure determination. In the code, the material stack is divided into several cells. The laser-matter interaction is reproduced by solving the Helmholtz equations within each cell using the complex refractive indexes given by Palik's tables [START_REF] Palik | Handbook of Optical Constants of Solids[END_REF] for the solid state, and calculated from the Lorenz plasma model [START_REF] Spitzer | Physics of Fully Ionized Gases[END_REF] in the plasma state. The hydrodynamics of each cell are modelled by solving equations for the cell position's evolution together with the equations for the conservation of mass, momentum and energy in finite volumes in the planar mono-dimensional hypothesis. The global hydrodynamic in the entire stack of cells is described using, in our case, a SESAME-tabulated state equation provided by the Los Alamos National Laboratory. The mechanical behavior of the stack is simulated using the SCG model [START_REF] Steinberg | A constitutive model for metals applicable at high-strain rate[END_REF]. The code reliability in the direct-irradiation regime at 1053 nm and the WCR at 532 nm was proven by Bardy [START_REF] Bardy | Development of a numerical code for laser-induced shock waves applications[END_REF]. The aim of this study is to extend its range of application under WCR at 1053 nm to extract ablation pressure temporal profiles and find numerical equations to reproduce them without a laser-matter interaction code. In addition, plasma temperature profiles and the ablated layer thickness are obtained from the simulation to evaluate the impact of the plasma laser on the surface of the material. The SESAME equation for state number 3720 and the aluminum elastoplastic model properties are taken directly from previous studies (cf table 1) [START_REF] Bardy | Development of a numerical code for laser-induced shock waves applications[END_REF]. For the WCR, all the parameters from the previous study were adopted, except for the optical constant of water, which had been adapted for the 1053 nm wavelength (n 1 = 1.33, n 2 = 1.3 × 10 -6 ) [START_REF] Kedenburg | Linear refractive index and absorption measurements of nonlinear optical liquids in the visible and near-infrared spectral region[END_REF] where n 1 + n 2 is the complex refractive index.

Free surface velocity

The simulations of the FSV under direct illumination and the WCR are displayed in figures 5 and 7 (colored dashed lines) and compared with the experimental results (black lines). The simulation uncertainty is directly linked to the intensity input deduced from the focal spot and energy experimental measurements (cf section 2). Therefore it is also taken at ±15%. It is represented by grey areas. The SCG mechanical model is correct for every configuration and its good agreement with the experiments is shown in figures 5 and 7. In both illumination regimes, the first peak amplitude is accurately determined when ε is taken in account. In the directillumination regime, small discrepancies in the peak shape and duration can be seen (figures 5(a) 2 and (b) 2), highlighting a potential area for improvement in the elastoplastic model. However, this study is focusing on the plasma pressure, which is directly related to the first peak and thus will not be affected by those discrepancies. In the direct-illumination regime as well as the WCR, the experimental curves for each wavelength and pulse duration are accurately described by the code when only the laser power density changes. This supports the validity of the code at 532 nm in the WCR with ∆T = 7 ns and intensities ranging from 2.4 to 6 GW cm -2 and at 1053 nm, as follows:

• ∆T = 10 ns, laser intensities ranging from 15 to 110 and 1.3 to 5 GW cm -2 for direct illumination and WCR, respectively • ∆T = 20 ns, laser intensities ranging from 10 to 130 and 1.5 to 2.3 GW cm -2 for direct illumination and WCR, respectively • ∆T = 40 ns, laser intensities ranging from 25 to 80 and 0.8 to 2 GW cm -2 for direct illumination and WCR, respectively.

Consequently, the interesting physical data, such as the pressure as a function of time, can be extracted from the code for each corresponding validity domain.

Ablation pressure

The ablation pressure, P abl , versus time was obtained from the code at the ablation front location. Figure 9 presents the results for the ablation pressures at 10, 20 and 40 ns at 1053 nm in the direct-illumination regime. These correspond to the conditions presented in figure 5. The pulse duration has a strong influence on the shape of the pressure temporal profile. First, the pressure rises drastically when the plasma is heated by the laser, then a plateau can be observed until the end of the laser pulse. Finally, when the laser pulse ends, the pressure drops dramatically until the ambient pressure is reached, following adiabatic matter expansion.

In the WCR, the same method was applied to obtain the pressure from the simulation of the FSV presented in figure 7.

In the case of a 7 ns Gaussian pulse at 532 nm (figure 10(a)) the pressure profile increases slowly during the few ns needed to warm up the matter and create the plasma. Then it increases almost as a Gaussian up to the the maximal ablation pressure (P abl,max ); finally it reduces as the matter expands. For pressure profiles extracted at 1053 nm, the three steps identified in the direct-illumination regime are also visible in the WCR. However for the 20 and 40 ns pulses (figures 10(c) and (d)), the profiles are very similar with an almost perfectly flat plateau corresponding to the pulse duration. The pulse duration does not affect the maximal value; a 2.3 GW cm -2 pulse with tophat pulses of either 10 or 20 ns will induce maximal ablation pressures of 2.5 or 2.7 GPa, respectively (figures 10(b) 1 and (c) 2).

To simulate the behavior of the target under laser shock, the temporal pressure profiles extracted from ESTHER (figures 9 and 10) were used instead of the laser-matter interaction module. The resulting FSV profiles are similar to the ones presented in figures 5 and 7, confirming the reliability of the temporal pressure profiles. Thanks to the model developed within the code, it is now possible to obtain the pressure as a function of time to calculate the FSVs of all the experiments realized within the area of validity defined in section 3.1.

Plasma parameters

The plasma temperature at the end of the laser pulse has been extracted from the entire simulated stack for each laser configuration (figures 5 and 7). Figure 11 displays the plasma temperatures for different incident laser intensities (I) with (a) 10, (b) 20 (c) and 40 (d) ns laser pulse durations in the direct illumination regime. The surface of the target is defined as x = 0. The laser is, by convention, coming from the right of the stack. The warmest region is the plasma corona with temperatures from 10 to 15 eV for any pulse duration. The shock front is propagating through the target with temperatures from 2 eV to room temperature (0.03 eV). The amount of ablated aluminum is proportional to the pulse duration and the incident laser intensity. At ∆T = 20 ns, with intensities of 8.1 and 133.6 GW cm -2 , 5 and 13 µm of aluminum are ablated, respectively.

In the WCR, the plasma temperature was extracted at the time when the pressure and the temperature were maximal, which corresponds to 12.5 ns for 7ns Gaussian pulses. In the case of 10, 20 and 40 ns top-hat pulses, the maximum temperature is at the end of the pulse duration (11.5, 22.5 and 42.5 ns precisely). The plasma temperature is displayed for laser pulses at 532 and 1053 nm in figure 12. In ESTHER, the modelling of the plasma under the WCR is composed of Al (black) and H 2 O (blue) media. The temperature range is similar for all laser configurations (8-14 eV). With the wavelength and incident laser intensity kept constant, the plasma thickness, L, and temperature, T, are proportional to the pulse duration. In figure 12, the temperatures are 9 and 13 eV and the plasma lengths 9 and 20 µm, respectively, for 10 ns ((b) 1) and 20 ns ((c) 2) top-hat pulses. These results are in agreement with Fabbro's model [START_REF] Fabbro | Physical study of laser-produced plasma in confined geometry[END_REF] (L = 7 µm for I = 10 GW cm -2 and ∆T = 10 ns on a 10 mm copper target confined with glass). At the end of the laser pulse, the ablated zone can be evaluated using the temperature profile; table 2 presents these values together with the plasma thickness for every configuration. For the laser shock process, it is interesting to know the depth of the vaporized material, to quantify the required thermal protection [START_REF] Clauer | Laser shock hardening of weld zones in aluminum alloys[END_REF][START_REF] Montross | Laser shock processing and its effects on microstructure and properties of metal alloys: a review[END_REF].

Scaling laws

The reliability of the numerical code and the extracted pressure profile was established in section 3. The pressure versus time relation is of particular interest, since it enables any code to calculate the behavior of materials under shock, without the need for a laser-matter interaction module. However, each

= 0.4 GW cm -2 , (2) I = 1.1 GW cm -2 .
ablation pressure curve that is obtained requires the ESTHER code and a few minutes of calculation. The aim of this section is to present an analytic formula for the pressure dependence on the laser wavelength, pulse duration and incident intensity for the direct and water confined regimes. To support this aim, tens of simulations were run within the validity area defined by the experiments, i.e. at 532 nm in the WCR with T pul between 7 and 20 ns and intensities ranging from 1 to 10 GW cm -2 and at 1053 nm for the WCR, T pul between 10 and 40 ns and intensities I from 1 to 6 GW cm -2 and for direct illumination regime, T pul between 5 and 40 ns andintensities I from 10 to 500 GW cm -2 . Numerical fits that can reproduce the temporal pressure profiles were then found. Finally, two methods yielding the maximum pressure are compared: the first is extracted from a numerical fit of the pressure temporal profile, and the second is calculated from the experimental FSVs presented in figures 5 and 7, using formula (1) [START_REF] Tollier | Study of the laser-driven spallation process by the velocity interferometer system for any reflector interferometry technique[END_REF].

P max = ρ 0 ( C 0 + S FSV max 2 ) FSV max 2 + ∆P + 2 3 σ Y0 [GPa]
(1) where ρ 0 is the density of the material [gm -3 ], C 0 is the sound velocity in this material [m s -1 ], S is the parameter regulating the growth of the shock speed with the material speed, σ Y0 the elastic limit [GPa], and ∆P the attenuation (hydrodynamic and elastic-plastic) [GPa]. ∆P is calculated numerically accordingly to [START_REF] Bras | Laser shock peening: toward the use of pliable solid polymers for confinement[END_REF]. It has to be noticed that the fit is only valid before the water breakdown power density.

Direct illumination regime

To describe the pressure temporal profile, the temporal area was divided into four zones represented in figure 13; each zone is reproduced by one fit. T 0 and T i are set at 0.5 ns and 3 2 T pul , respectively, for the following calculations.

• Linear rising t ≤ T 0 : P(t) = P max • Linear connection T pul ≤ t ≤ T i connection between the points [T pul ; P(T pul )] and [T i ; P i = P(T i )]

• Final release zone t ≥ T i :

P(t) = P i ( Ti-Tiδ t-Tiδ
) n .

The parameters P max , P i (pressure at time equals T i ), p, n and δ were adjusted for the entire intensity and pulse duration range. On the contrary, the parameters P max and p do not depend on the pulse duration, therefore they were adjusted for the longest pulse duration, i.e 40 ns. P m corresponds to the minimal pressure obtained at the end of this pulse duration. The three other parameters related to the relaxation, P i , n, and δ depend on the pulse duration T pul . They are all given by the equations in A.1.

The pressure profiles obtained with the above equations are in good agreement with the one obtained via the laser-matter interaction module in ESTHER. Consequently, the FSVs calculated by the code using the pressure profile and the fit are similar. Thanks to the analytically fitted curves, it is possible to reproduce the material behavior induced by laser-matter interaction using any mechanical simulation software. In the directillumination regime, the temporal laser pulse and pressure profile do not have the same shape, as can be seen in figure 9. There is indeed a sharp peak at the beginning of the plateau that makes it irrelevant to describe the ablation pressure using only its maximal value. As an illustration, figure 14 represents the maximum of this pressure peak P max and the pressure at the end of the pulse duration, P Tpul , obtained analytically as a function of the intensity, together with the maximum pressure P max calculated from the experimental FSV using formula [START_REF] Antoun | Spall Fracture[END_REF]. The pulse duration does not affect the maximum pressure, however, longer pulses induce lower pressures at time T pul . In the entire range studied, the maximum pressures calculated from the experimental FSVs are in between the fits of the maximum pressure and the pressure at T pul . It is therefore important to take the entire temporal pressure profile into account when using it as an input to simulate the target's behavior under laser shock. For the purposes of this study, the profile was divided into four temporal zones, the initiation, the rise, the maximum, and the relaxation (figure 15). For each zone, an analytic formula has been fitted in order to reproduce the simulation over the entire area of validity. The intensities were set between 1 and 10 GW cm -2 for 7 to 20 ns FWHM Gaussian pulses. It should be noted that only the 7 ns simulations can be compared with experiments.

T 0 is defined as the time needed for the initiation of the ablation phenomena. For a Gaussian pulse, the intensity increase is slow, since the energy deposited needs some time to ablate the surface and create a plasma which will absorb the laser energy. The initial reflectivity of the aluminum surface, which controls T 0 , is set to 0.5. Once the aluminum is sufficiently ablated, the pressure rises drastically until it reaches its maximal value, P max . After this maximum is reached at T max , the medium slowly relaxes. The following equations describe the analytic formulation which enables the reproduction of the profile pressure using only the pulse duration T pul and the maximum intensity, I, for Gaussian pulses.

• Initiation t ≤ T 0 : P(t) = 0 with T 0 = 0.8+0.87T pul I 0.35 • Linear rise t ≤ T l : P(t) = P i ( t-T0 T l -T0 ) with T l = T max - 1 2 T pul and P i = 0.82P max • Maximal pressure T l ≤ t ≤ T r P(t) = P max e - ( t-Tmax 1.1T pul ) 2 with T r = T max + 1 2 T pul • Final release zone t ≥ T r : P(t) = P i ( Tr-Trδ t-Trδ ) n .
The maximal pressure peak is reached at T max , with T max = 1.7 T pul (I -(1.3 -0.13 T pul ))

0.012 , the highest values being achieved with P max = 2.2 I 0.57 . The coefficients n and δ, required for the calculation of the final relaxation are defined by equation (A12) in appendix A.2. It can be seen from these formulas that the maximum of the pressure does not depend on the pulse duration for a Gaussian pulse (this might not be true for other pulse shapes). The pulse duration has an influence on the pressure duration, which is to make its temporal shape longer. The maximum pressures calculated from the experimental FSVs presented in 7 using formula (1) [START_REF] Tollier | Study of the laser-driven spallation process by the velocity interferometer system for any reflector interferometry technique[END_REF] were plotted together with the maximum values of P max calculated via the fit in figure 16. These two methods of maximum pressure determination are in very good agreement until the water breakdown phenomenon occurs.

1053 nm.

For water-confined regimes at 1053 nm, the temporal pressure profiles obtained from the simulation with intensities ranging from 1 to 6 GW cm -2 and top-hat pulses from 10 to 40 ns were separated into four zones (figure 17). The analytic equations of the pressure profile dependence on the laser intensity, I (GW cm -2 ) and the pulse duration T pul [ns] are as follows:

-Quadratic rising t ≤ T 0 : P

(t) = P max ( 1 - ( 1 -t T0 ) 2 )
with T 0 = 2.4 I and P max = 2I 0.53 ) .

The pressure temporal profiles are not Gaussian shapes, however the maximum pressure P max is close to the pressure at the end of the laser pulse, P pul . The maximal pressures P max calculated from the fit are plotted as a function of the incident intensities together with the P max calculated by equation (1) from the experimental FSVs. Similarly to the WCR at 532 nm, the two methods of P max determination are in good agreement. The pulse duration ∆T has no influence on P max , however, a longer pulse duration induces a longer pressure, therefore it is important to take into account the entire temporal profile of the pressure given by the above equations.

Conclusions

In this paper, we presented the experimental FSVs of pure aluminum, as measured by VISAR in three different laser labs. This work synthesizes a significant range of input parameters covering two irradiation regimes (direct and water confined), three wavelengths (from 532 to 1053 nm), two laser pulse shapes (Gaussian and top-hat), four laser-pulse durations (from 7 to 40 ns) and five focal-spot sizes (from 1 to 5 mm) with round and square shapes. Although the experiments were conducted with several laser configurations, the results collected demonstrated good consistency. More precisely, it was shown that with similar wavelengths and pulse durations, the shape of the focal spot does not have an effect on the maximal FSV. Due to the good agreement of the simulation results with the experimental data, the reliability of the ESTHER code was extended to a broader range of validity, making it now possible to obtain physical data characterizing the plasma produced (table 2). We have presented analytic fits of the temporal pressure profiles that can be used in any mechanical simulation software to simulate the behavior of aluminum targets under laser shock. In a future investigation, the influence of changing the pulse duration and spatial shape at 532 nm will be investigated.

Figure 1 .

 1 Figure 1. A schematic view of the experimental setups (a) in water-confined regime performed at Héphaïstos, HiLASE and GCLT, (b) in direct-interaction regime performed at GCLT.

Figure 2 .

 2 Figure 2. (a) Temporal pulse of 7 ns at Hephaïstos. (b) Typical CCD image of a ϕ = 4 mm round top-hat focal spot.

Figure 3 .

 3 Figure 3. (a) Top-hat temporal profile of a 10 ns pulse at HiLASE. (b) Spatial shape profile for a ϕ = 3.5 mm square top-hat laser spot.

Figure 4 .

 4 Figure 4. (a) Top-hat temporal profile obtained for 10, 20 and 40 ns requests at GCLT. (b) Typical CCD image of a ϕ = 5.1 mm round top-hat focal spot.

Figure 5 .

 5 Figure 5. A comparison of the simulated (colored dashed lines) and experimental (black lines) results for 99.999% pure aluminum, thickness = 100 µm, GCLT, 1053 nm, direct illumination, ϕ = 1.1 mm: (a) ∆T = 10 ns, (1) I = 16.7 GW cm -2 , (2) I = 112.0 GW cm -2 , (b) ∆T = 20 ns, (1) I = 8.1 GW cm -2 , (2) I = 133.6 GW cm -2 , (c) ∆T = 40 ns, (1) I = 24.7 GW cm -2 , (2) I = 71.1 GW cm -2 . Uncertainty of the simulation ε = 15% (grey area).

Figure 6 .

 6 Figure 6. FSVmax versus laser intensity I. 99.999% pure aluminum, thickness = 100 µm, GCLT-1053 nm, direct illumination, ϕ = 1.1 and 2.5 mm, ∆T = 10 ns, 20 ns and 40 ns.

Figure 7 .

 7 Figure 7. A comparison of the simulatied (colored dashed lines) and experimental (black lines) results for pure aluminum, thickness = 500 µm, WCR. (a) Hephaïstos, 532 nm, ∆T = 7 ns, ϕ = 4 mm, (1) I = 2.4 GW cm -2 , (2) I = 5.9 GW cm -2 , (b) GCLT, 1053 nm, ∆T = 10 ns , ϕ = 5 mm, (1) I = 2.3 GW cm -2 , (2) I = 5.0 GW cm -2 , (c) GCLT, 1053 nm, ∆T = 20 ns, ϕ = 5 mm, (1) I = 1.4 GW cm -2 , (2) I = 2.3 GW cm -2 , (d) GCLT, 1053 nm, ∆T = 40 ns, ϕ = 5 mm, (1) I = 0.4 GW cm -2 , (2) I = 1.1 GW cm -2 . Uncertainty of the simulation ε = 15 % (grey area).

Figure 8 .

 8 Figure 8. FSVmax versus laser intensity I. Pure aluminum, thickness = 500 µm, WCR: (a) Hephaïstos, 532 nm, ϕ = 3 and 4 mm, ∆T = 7 ns; (b) GCLT: 1053 nm; HiLASE: 1029 nm; ϕ = 5 and 3.5 mm, ∆T = 10 ns; (c) GCLT, 1053 nm, ϕ = 5 mm, ∆T = 20 ns; (d) GCLT, 1053 nm, ϕ = 5 mm, ∆T = 40 ns.

Figure 9 .

 9 Figure 9. P abl versus time. 99.999% pure aluminum, thickness = 100 µm, GCLT, 1053 nm, direct illumination, ϕ = 1.1 mm: (a) ∆T = 10 ns, (1) I = 16.7 GW cm -2 , (2) I = 112.0 GW cm -2 ; (b) ∆T = 20 ns, (1) I = 8.1 GW cm -2 , (2) I = 133.6 GW cm -2 ; (c) ∆T = 40 ns, (1) I = 24.7 GW cm -2 , (2) I = 78.1 GW cm -2 .

Figure 10 .

 10 Figure 10. P abl versus time. 99.999% pure aluminum, thickness = 500 µm, WCR: (a) Hephaïstos, 532 nm, ∆T = 7 ns, ϕ = 4 mm, (1) I = 2.4 GW cm -2 , (2) I = 5.9 GW cm -2 ; (b) GCLT, 1053 nm, ∆T = 10 ns, ϕ = 5 mm, (1) I = 2.3 GW cm -2 , (2) I = 5.0 GW cm -2 ; (c) GCLT, 1053 nm, ∆T = 20 ns, ϕ = 5 mm, (1) I = 1.4 GW cm -2 , (2) I = 2.3 GW cm -2 , (d) GCLT, 1053 nm, ∆T = 40 ns, ϕ = 5 mm, (1) I = 0.4 GW cm -2 , (2) I = 1.1 GW cm -2 .

Figure 11 .

 11 Figure 11. Temperature versus position. 99.999% Pure aluminum, thickness = 100 µm, GCLT, 1053 nm, direct illumination, ϕ = 1.1 mm: (a) ∆T = 10 ns, (1) I = 16.7 GW cm -2 , (2) I = 112.0 GW cm -2 , (b) ∆T = 20 ns, (1) I = 8.1 GW cm -2 , (2) I = 133.6 GW cm -2 , (c) ∆T = 40 ns, (1) I = 24.7 GW cm -2 , (2) I = 78.1 GW cm -2 .

Figure 12 .

 12 Figure 12. Temperature versus position. 99.999% pure aluminum, thickness = 500 µm, WCR (a) 532 nm, ∆T = 7 ns, ϕ = 4 mm, (1) I = 2.4 GW cm -2 , (2) I = 5.9 GW cm -2 , (b) GCLT, 1053 nm, ∆T = 10 ns, ϕ = 5 mm, (1) I = 2.3 GW cm -2 , (2) I = 5.0 GW cm -2 , (c) GCLT, 1053 nm, ∆T = 20 ns, ϕ = 5 mm, (1) I = 1.4 GW cm -2 , (2) I = 2.3 GW cm -2 , (d) GCLT, 1053 nm, ∆T = 40 ns, ϕ = 5 mm, (1) I = 0.4 GW cm -2 , (2) I = 1.1 GW cm -2 .

Figure 13 .

 13 Figure 13. Analytic temporal pressure profile corresponding to a 40 ns top-hat pulse at 1053 nm with an incident laser intensity of 250 GW cm -2 under direct laser illumination.

)•Figure 14 .

 14 Figure 14. Maximum pressures calculated according to the analytic fit and formula (1), together with the pressure at the end of the pulse duration calculated according to the analytic fit for 10, 20 and 40 ns top-hat pulses at 1053 nm under direct illumination.

Figure 15 .

 15 Figure 15. Analytic temporal pressure profile corresponding to a 7 ns FWHM Gaussian pulse at 532 nm with an incident laser intensity of 5 GW cm -2 under the WCR.

4. 2 .

 2 Water-confined regime 4.2.1. 532 nm. With the 7 ns Gaussian-shaped laser pulse, the pressure profile is also a Gaussian until the final release.

Figure 16 .

 16 Figure 16. Maximum pressures calculated by analytic fits and formula (1) for 7 ns Gaussian pulses at 532 nm in the WCR.

Figure 17 .

 17 Figure 17. Analytic temporal pressure profile corresponding to a 20 ns top-hat pulse at 1053 nm with an incident laser intensity of 3 GW cm -2 under the WCR.

Figure 18 . 4 with T 1 =

 1841 Figure 18. Maximum pressures calculated according to analytic fits and formula (1) for 10, 20 and 40 ns top-hat pulses at 1053 nm in the WCR.-Plateau T 0 ≤ t ≤ min(T 1 , T pul ) : P(t) = P min + (Pmax -P min ) (T1-t T1-T0) 4with T 1 = max(12, 16 -I) and P min = 1.79 I 0.453 -Linear connection T 1 ≤ t ≤ min(T pul ) : P(t) = P40ns-Pmin 40-T1 (t -T 1 )

Table 2 .

 2 Plasma characterization of water-confined laser shock at λ = 532, 1029 and 1053 nm, ∆T = 7, 10, 20, and 40 ns for pure aluminum, thickness = 500 µm. Laser parameter λ = 523 nm -∆T = 7 ns λ = 1029 nm-∆T = 10 ns λ = 1053 nm-∆T = 10 ns λ = 1053 nm-∆T = 20 ns

Table 1 .

 1 Parameters used for the Steinberg-Cochran-Guinan (SCG) material model[START_REF] Steinberg | A constitutive model for metals applicable at high-strain rate[END_REF] with an aluminum target (99.999%, laminated).

	Material	Y 0 (MPa)	Ymax (MPa)	β	n	ε i	G 0 (GPa)	G ′ p	G ′ T (GPa/K)
	Aluminum	120	160	4000	0.27	0	27.1	1.8	-1.7 × 10 -2

Appendix A. Parameters for temporal pressure profile scaling law

A.1. Direct illumination regime

The parameters P max , P i (pressure at time equals T i ), p, n and δ (figure 13) were adjusted for the entire intensity and pulse duration range. The results are given below, with I and T pul in ns and GW cm -2 , respectively. ) .

(A5)

The parameters P max and p do not depend on the pulse duration, therefore they were adjusted for the longest pulse duration, i.e 40 ns. The minimal pressure, P m , corresponds to the pressure obtained at the end of this pulse duration. The other three parameters related to the relaxation, P i , n, and δ are given by the following equations. They depend on the pulse duration T pul . P i = 0.11 + 0.011I * for I * ≤ 240 -3.4 T pul (A6)