Walaa Ibraheem

Capucine Chaar

Emilie Camiade

Virginie Hervé

Delphine Fouquenet

Anne-Emmanuelle Roux

Mustapha Si-Tahar

Elhadi Ahmed

Jérôme Thibonnet

Emilie Thiery

Julien Petrignet
email: julien.petrignet@univ-tours.fr

Synthesis, antibacterial and cytotoxic evaluation of cytosporone E and analogs

Keywords: natural phthalide, pharmacomodulations, antibacterial activity, cytotoxicity

The history of antibacterial discovery has revealed that natural products, especially secondary metabolites, represent privileged chemical matters for the antibacterial discovery. Among these metabolites, several natural phthalides exhibit interesting antibacterial activities, such as cytosporone E isolated from endophyte ascomycetes Diaporthe and Cytospora sp. We describe herein the synthesis and the pharmacomulations on the positions 3, 4 and 6 of cytosporone E, then the in vitro antibacterial evaluation of these compounds against Staphylococcus aureus including resistant strains, Escherichia coli and Pseudomonas aeruginosa. The evaluation of the cytotoxicity of the most active compounds against human bronchial epithelial cells was performed in order to check their safety.

Introduction

The discovery and the improvement of antibiotics has led to make considerably decrease the mortality rate by bacterial infections. However, the over-use of these drugs has resulted in a selection pressure on the bacteria, which have gradually mutated and thus led to the appearance of new generations of multi-resistant bacteria against all families of known antibiotics. [1][2] In spite of the alert launched by the World Health Organization (WHO) and public authorities, the overuse of antibiotics is still topical and multi-resistant bacteria are becoming a worldwide public health problem which keep increasing the next decades if nothing is done. [3] Thus, Gram-positive Staphylococcus aureus and Gram-negative Pseudomonas aeruginosa are two representative pathogens of the multi-antibiotic resistance, which are very often the cause of nosocomial infections. They appeared as respectively high and critical threats according a recent report published by the WHO. [3] The research of new families of antibiotics, for which the structure can be inspired by natural compounds, is a strategy of interest to solve the problem of multidrug resistant bacteria (MDR). [4] In the last decade, our group developed synthetic pathways for the preparation of natural lactones such as phthalides, an important class of small oxygenated heterocycles which are widely represented in the area of natural compounds.[5] [START_REF]Progress in the chemistry of organic natural products[END_REF] Of the known natural phthalides reported in the literature, some of them exhibit interesting antibacterial activities, such as corollosporine, [START_REF] Liberra | [END_REF] spirolaxine [8] or cytosporone E. [9] It is noteworthy the preparation of analogs of paecilocin A, [10] corollosporine [11] and spirolaxine [12] was performed in order to improve their antibacterial activities (Figure 1). The cytosporone E was reported to exhibit antibacterial activities against Gram-positive, Gramnegative and drug-resistant strains [13] with a reasonable cytotoxicity according to the cell line. [13c, 13d] To the best of our knowledge, the preparation of new analogs of this natural compound was never performed in order to improve its antibacterial activities. Considering the natural reported analogs of cytosporone E, the substituent on the position 3 has a strong influence on the biological activities since the introduction of hydroxyl group or the shortening of the heptyl chain to a methyl were deleterious for the antibacterial activity. [13d, 14] We can then assume that certain modifications of the heptyl chain could conversely increase the antibacterial properties. In addition, previous works suggested the hydroxyl on the position 5 is essential for the antibacterial activity since 5-dehydroxycytosporone E did not showed any antimicrobial activity. [9,15] One can then wonder what would be the impact on the antibacterial properties of the replacement of both hydroxyls on positions 4 and 6 (Figure 2).

Besides, it was reported that the absolute configuration of C-3 has no impact on the antibacterial properties of cytosporone E since each enantiomer and the racemic mixture exhibited the same antibacterial activities. [16] Herein, we report in this paper a short and flexible synthesis of racemic cytosporone E and various analogs pharmacomodulated on the positions 3, 4 and 6, then the in vitro antibacterial evaluation of these new compounds against representative bacteria (including resistant strains) and the evaluation of the cytotoxicity of the most active compounds.

Results and discussion

Synthesis

The literature abounds with numerous approaches for the preparation of phthalides, which are summarized in two recent reviews. [5] Noteworthy, the synthesis of C3functionnalized phthalides based on an iodine-magnesium exchange on ortho-iodobenzoate derivatives promoted by iPrMgCl.LiCl, followed by a condensation on an aldehyde, was reported as a straightforward and efficient strategy. [10,17] We considered including this methodology as a key step for the preparation of cytosporone E and its analogues (Scheme 1).

Therefore, the ortho-iodobenzoate 2 was synthesised from 1 in presence of iodine and a stoichiometric amount of silver trifluoroacetate with 63% yield. [18] A solution of iPrMgCl.LiCl in THF was prepared according to the reported procedure,[17b] and used for the magnesium-iodine exchange after titration with standard method. The substrate scope could be extended to aliphatic and various aromatic aldehydes, with average to good overall yields in phthalides 3a-l. The total demethylation was finally performed with an excess of boron tribromide (BBr3) in DCM between -20°C and room temperature to afford the trihydroxylated derivatives 4a-k with modest to good yields ranged from 15 to 90 % (Scheme 1). Because of its strong Lewis-acid nature, the boron tribromide mediated demethylation step was not compatible with p-dimethylaminophenyl group 3l (formation of an amino-boron complex). An alternative synthetic pathway for the preparation of 3l was performed (Scheme 2), based the ortho-metalation of activated aromatic ester with TMPMgCl.LiCl. [19] Thus, the hydroxyl functions of ethyl gallate 5 were protected by t-butylbenzyloxycarbonyl (Boc), which also plays the role of directing group. The ortho-metallation of 6 was performed with a commercial solution of TMPMgCl.LiCl at -40°C in THF, and was followed by the addition of p-dimethylaminobenzaldehyde. The phthalide 7 was obtained with an average yield of 52%, and the Boc-deprotection (TFA, 20°C, 15 min.) afforded the expected analogue 4l. We then performed the pharmacomodulation of the C-4 and C-6 hydroxyl substituents of the cytosporone E. The replacement of these hydroxyl by two hydrogen was achieved by the synthesis of the compound 12 (Scheme 3). The latter was prepared in a four step sequence starting from commercial 2-amino-4-methoxybenzoic acid 8 which transformed into the corresponding iodobenzoic acid 9 via a Sandmeyer reaction. The acid was then esterified into the corresponding methyl ester 10, and the phthalide 11 was obtained using the iodinemagnesium exchange strategy with iPrMgCl.LiCl and octanal as electrophile. Finally, the demethylation of 11 was performed with an excess of BBr3 to afford 12. At this stage, 12 was easily transformed in presence of SO2Cl2 in toluene into the corresponding dichlorinated compound 13, an analogue of spiromastilactone A, a recently discovered natural marine phthalide which exhibit a strong antiviral activity and a weak cytotoxicity. [20]

1 2 3a-l 4a-l R 2 O R 2 O OR 2 O O 3a (R 2 = Me), 70% 4a (R 2 = H), 52% R 2 O R 2 O OR 2 O O 3b (R 2 = Me), 21% 4b (R 2 = H), 90% R 2 O R 2 O OR 2 O O 3c (R 2 = Me), 41% 4c (R 2 = H), 89% R 2 O R 2 O OR 2 O O 3d (R 2 = Me), 49% 4d (R 2 = H), 71% R 2 O R 2 O OR 2 O O 3e (R 2 = Me), 59% 4e (R 2 = H), 67% R 2 O R 2 O OR 2 O O 3f (R 2 = Me), 35% 4f (R 2 = H), 33% OR 2 R 2 O R 2 O OR 2 O O 3g (R 2 = Me, R 3 = n-Bu), 33% 4g (R 2 = H), 44% OR 2 OR 3 R 2 O R 2 O OR 2 O O 3h (R 2 = Me), 26% 4h (R 2 = H), 32% Cl R 2 O R 2 O OR 2 O O 3i (R 2 = Me), 67% 4i (R 2 = H), 42% CF 3 R 2 O R 2 O OR 2 O O OCF 3 3j (R 2 = Me), 33% 4j (R 2 = H), 45% R 2 O R 2 O OR 2 O O 3k (R 2 = Me), 54% 4k (R 2 = H), 68% CF 3 R 2 O R 2 O OR 2 O O 3l (R 2 = Me), 46% 4l (R 2 = H), 0% (a) (b) (c)

Antibacterial activities

The antibacterial activities of 3a, 4a-l against Gram-positive Staphylococcus aureus (methicillin sensitive strain) and two Gram-negative bacteria (Escherichia coli and Pseudomonas aeruginosa) were evaluated via broth microdilution method in accordance with the guidelines of the Clinical and Laboratory Standards Institute. [START_REF]Methods for Dilution Antimicrobial Susceptibility Tests for Bacteria That Grow Aerobically; Approved Standard-Ninth Edition[END_REF] Imipenem and penicillin G were used as positive controls for this antibacterial assays. The Minimal Inhibitory Concentrations (MIC) of these compounds are reported in Table 1.

Table 1. Antibacterial activity of compounds 3a, 4a-l, 12 and 13 against S. aureus, E. coli and P. aeruginosa by broth microdilution Entry Compound MIC in µg.mL -1 (µM

) [a] R R 1 S. aureus ATCC29213 E. coli ATCC25922 P. aeruginosa PAO1 1 3a OMe n-heptyl >200 >200
NT [b] 2 4a OH n-heptyl 6.25 ( 22) >200 50 (176) [c] 3 4b OH n-undecyl 100 (298) >200 >200 NT [b] NT [b] Imipenem --NT [b] NT [b] 8 ( 26) [a] Assay experiments were performed in triplicates at three independent times. [b] NT means not tested. [b] MBC = 100 µg.mL -1 Although the importance of the trihydroxybenzene motif for the antibacterial activity was already assumed,[13a] it was confirmed herein as trimethylated cytosporone E 3a did not show any antibacterial activity against the three strains (Entry 1). The synthetic cytosporone E 4a showed a good antibacterial activity against S. aureus with a MIC of 6.25 µg.mL -1 (22 µM) but no activity against E. coli below 200 µg.mL -1 (Entry 2). These MIC values were consistent with those previously reported in the literature for the cytosporone E produced from the endophytic fungi. Interestingly, 4a exhibited a moderate antibacterial activity against P. aeruginosa, with a bactericidal mode of action, as the minimal bactericidal concentration (MBC) was found to be at 100 µg.mL -1 (MBC/MIC < 4). It is noteworthy the extracted cytosporone E from the fungi did not exhibit activity below 150 µg.mL -1 against P. aeruginosa according to the literature data. [13b] The nature of the substituent on the position 3 (R 1 ) was found to be essential for the antibacterial activity. While none of the analogs 4b-l showed antibacterial activity against E. coli and P. aeruginosa at concentrations below 200 µg.mL -1 , pharmacomodulations of the heptyl chain of 4a had positive or negative effect on the antibacterial activity against S. aureus according to the nature of the substituent. Indeed, the elongation (4b), the shortening (4c) or the ramification (4d) of the alkyl chain were deleterious as the MIC value decreased to 100 µg.mL -1 (Entries 3-5). The replacement of the heptyl chain by a benzene ring (4e) had also a negative effect on the antibacterial activity, such as para-substituted phenyl group with hydroxy (4f), chlorine (4h) or dimethylamino (4l) (Entries 6-9, 13). Interestingly, a good antibacterial activity (MIC = 12.5 µg.mL -1 ) was obtained with 4-trifluoromethyl (4i) and 4-trifluoromethoxy phenyl (4j) (Entries 10 and 11). We noticed that the position of the trifluoromethyl substituent on the aromatic ring (4k) had a slight effect on the antibacterial activity (Entry 12). The hydrogenated and chlorinated analogs 12 and 13 did not exhibit any activity against the Gramnegative strains. Besides, they were found to exhibit respectively a moderate and a good activity against S. aureus (Entries 14 and 15).

The antibacterial activities of compounds 4a, 4i-k, 12 and 13 toward methicillinsensitive S. aureus (MSSA ATCC 29213) were then compared to two methicillin-resistant strains of S. aureus (MRSA NCTC 12493 and ATCC BAA-1026). The MIC and MBC of this assay are reported in the Table 2. We observed that 4a exhibited the same antibacterial activities toward MSSA and MRSA strains with a MIC = 6.25 µg.mL -1 and MBC = 12.5 µg.mL -1 , such ratio (MBC/MIC = 2) suggested a bactericidal effect (Entry 1). Trifluoromethylated compounds 4i-k showed similar antibacterial profiles, with no significant difference of activity between the sensitive and the resistant strains (Entries 2-4). 4i and 4k were found to be 2 times more active on against MRSA than MSSA. However, we were surprised to observe than 12 and 13 were strongly more active against MRSA strains compared to the sensitive one. Indeed, 12 was eight times less active than 4a on the MSSA strain, but exhibited the same MIC and MBC values than 4i-k toward the resistant strains (Entry 5). The chlorinated compound 13 showed a MIC of 12.5 µg.mL -1 toward MSSA and was ten times more active on both MRSA strains. The MBC values suggested that 13 was bacteriostatic, unlike the others analogs tested. These MIC values were compared to those obtained with penicillin G, for which the MRSA strains are resistant (MIC > 64 µg.mL -1 , Entry 7).

Cytotoxicity

The cytotoxicity of compounds which exhibited the best antibacterial activities against MRSA (4a, 4i-k, 12 and 13) was evaluated against Beas-2B cells. This human bronchial epithelial cell-line is known to be very sensitive toward exogenous compounds. Starting from a mother solution of each compound diluted in DMSO at 3 mg.mL -1 , dilutions to 25, 12.5, 6.25, 3.1 μg.mL -1 (and 1.5 μg.mL -1 for compound 13) were made using FK12 medium without FCS.

The cells were incubated during 48h in the presence of different concentration of each compound and the cell viability was evaluated by MTS assays. The IC50 are reported in the Table 3 and was compared to their MIC against MRSA expressed in µM. While 4j, 4k and 12 have IC50 values close to their MIC value, compounds 4a, 4i and 13 have an interesting biological profile since their IC50 value is three to four times higher than their MIC against MRSA. The cytotoxicity of 4a and 4i were then compared to each other at range of concentrations between 25 and 3.1 μg.mL -1 (Figure 3A). It is noteworthy the cells alone were considered the maximum with 100% cell viability, but due to the sensibility of the cells to the solvent, the control was performed with DMSO at 1/30 th . It has been confirmed that 4a was not cytotoxic at its MIC value, since more than 80% of cell viability was observed at concentrations below 6.25 µg/mL. 4i showed a similar profile since more than 80% cell viability was observed at concentrations below 6.25 µg/mL, with a decrease in the cell-toxicity at 25 µg/mL (66% of cell viability against 29% for 4a).

We finally evaluated the cytotoxicity of 13, the most promising product under two different conditions (Figure 3B). The first condition consisted to use, as previously, a solution of 13 in DMSO at 3 mg/mL to perform the dilution range (see experimental section). In such conditions, an ambiguity subsisted on the toxicity at it MIC against MRSA (1.25 µg.mL -1 ) since 74% of cell viability was observed. In this assay, DMSO alone exhibited slight cytotoxicity since 74% of cell viability was observed. In the second condition, the DMSO was replaced by the NADES (NAtural Deep Eutectic Solvent) glycerol/choline chloride to prepare the mother solution of 13 at 3 mg.mL -1 . The dilution range was then performed in the same way, and we were pleased to observe more than 80% cell viability at 1.25 µg.mL -1 of 13 and no cytotoxic effect of the solvent alone, thus suggesting that 13 is not cytotoxic to its MIC against MRSA.

Conclusions

To conclude, we have developed a synthetic pathway for the preparation of racemic cytosporone E 4a and various analogs (4b-l, 12 and 13) of this natural phthalide pharmacomodulated on positions 3, 4 and 6. All compounds were screened for their antibacterial activities against S. aureus, E. coli and P. aeruginosa using broth microdilution.

This study revealed that these analogs did not show any antibacterial activity against the Gramnegative strains. However, several compounds showed significant antibacterial activity against methicillin-sensitive S. aureus, and were found to be 2 to 10 times more active on the methicillin-resistant of S. aureus compared to the sensitive strain. Among the most active derivatives, 4a, 4i and 13 were evaluated for their cytotoxicity against human bronchial epithelial cells at different concentrations and found not toxic at their MIC value. Therefore, these new compounds constitute an interesting line of work in the fight against the antimicrobial resistance.

Experimental section

4.1 Chemistry

General chemical methods.

All reactions were carried out under argon atmosphere. TLC spots were examined under UV light. The aldehydes were distilled before using. Silica gel (Geduran Si 60, 40-63 µm by Merck)

was used for column chromatography. Acetonitrile, dichloromethane and chloroform (stabilized with amylene) were distilled from calcium hydride, tetrahydrofuran and diethyl ether were distilled from sodium/benzophenone. Other chemicals were obtained from commercial sources and were used without further purification.

NMR spectra were obtained at 300 MHz for [START_REF] Ohba | [END_REF] A dry and argon-flushed round bottom flask was charged with a solution of methyl 3,4,5trimethoxybenzoate 1 (5.0 g, 22.1 mmol, 1 equiv.) and silver trifluoroacetate (5.1 g, 23.0 mmol, 1.04 equiv.) in dry chloroform (60 mL). Iodine (5.8 g, 23.0 mmol, 1.04 equiv.) was added in small portions over a period of 30 minutes and the dark pink solution was stirred overnight at room temperature. The reaction mixture was filtered over a pad of Celite ® , the filtrate was diluted with CH2Cl2 (50 mL) and was washed with a 5% aqueous solution of Na2S2O3 (100 mL). The aqueous phase was washed with dichloromethane (3 x 50 mL). The combined organic phases were washed with brine (100 mL), dried over MgSO4 and solvent was removed under reduce pressure. The residue was purified by column chromatography on silica gel using CH2Cl2 as eluent to afford the iodinated ester 2 (4.39 g, yield = 63%) as a white solid.

Preparation of iPrMgCl•LiCl solution[17b]

A dry and argon-flushed Schlenk tube was charged with anhydrous lithium chloride (2.1 g, 50 mmol, 1 equiv.) and magnesium turnings (1.3 g, 55 mmol, 1.1 equiv.). The solids were stirred under vaccum for 4 hours at 150°C. After cooling, dry THF (25 mL) was added followed by a solution of isopropyl chloride (4.6 mL, 50 mmol, 1 equiv.) in THF (25 mL). This suspension was stirred overnight at room temperature, and the resulting light grey solution was titrated according to Paquette method. [23] 4.1.4 Typical procedure for the preparation of compounds 3a-l A dry and argon-flushed flask equipped with a magnetic stirrer and a septum was charged with a solution of 2 (1 equiv.) in dry THF (10 mL) and was cooled at -78°C. A solution of iPrMgCl•LiCl (1.3 equiv.) was added dropwise and the reaction mixture was stirred for 30 minutes at -78°C. The corresponding aldehyde (1.3 equiv.)was added and the reaction mixture was slowly warm to room temperature and stirred overnight. The reaction mixture was hydrolysed with water (20 mL) and extracted with EtOAc (3 x 20 mL). The combined organic layers were washed with brine (20 mL), dried over MgSO4, and concentrated under reduced pressure. The residue was purified by column chromatography on silica gel.

4. 5,-one (3a)

Following the above procedure using 2 (350 mg, 1.0 mmol, 1 equiv. [START_REF]Progress in the chemistry of organic natural products[END_REF]155.5,147.6,146.8,135.4,121.4,102.5,80.2,61.2,60.7,56.4,33.4,31.7,29.2,29.0,24.7,22.6,14.0. 4.1.4.2. 4,5,-one (3b)

Following the above procedure using 2 (800 mg, 2.27 mmol, 1 equiv. 6, 155.5, 147.6, 146.8, 135.4, 121.4, 102.6, 80.2, 61.1, 60.8, 56.4, 33.4, 31.9, 29.59, 29.58, 29.51, 29.4, 29.3, 24.7, 22.7, 14 6, 155.5, 147.6, 146.8, 135.4, 121.4, 102.5, 80.1, 61.1, 60.7, 56.3, 33.1, 26.7, 22.3, 13.8 4, 155.4, 147.5, 146.8, 135.9, 121.1, 102.4, 78.7, 61.0, 60.7, 56.3, 42.9, 25.1, 23.5, 21.6 4. 1.4.6. 4,5,isobenzofuran-1(3H)-one (3f)

Following the above procedure using 2 (400 mg, 1.14 mmol, 1 equiv. 147.98, 147.64, 147.36, 135.44, 130.07, 124.04, 121.84, 119.87, 113.45, 102.60, 76.17, 74.04, 61.22, 60.32, 56.59, 55.99, 32.39, 19.31, 14. 7, 147.3, 140.3, 134.8, 130.7 (q, J = 32 Hz), 127.6 (2C), 125.6 (q, J = 3.2 Hz, 2C), 122.9 (q, J = 270 Hz) 120.4, 102.6, 80.0, 61.0, 60.3, 56.4. 19 1, 156.3, 147.8, 147.5, 137.6, 134.8, 131.1 (q, J = 32.5 Hz), 130.4, 129.2, 125.8 (q, J = 3.7 Hz), 124.2 (q, J = 3.9 Hz), 124.1 (q, J = 270 Hz), 120.5, 102.

Typical procedure for the preparation of compounds 4a-k

A dry and argon-flushed flask equipped with a magnetic stirrer and a septum was charged with a solution of phthalide 3a-k (1 equiv.) in dry CH2Cl2 (5 mL) and was cooled at -30°C. A solution of BBr3 (6 equiv.) was added and the reaction mixture was stirred overnight. The reaction mixture was hydrolysed with water (20 mL) and extracted with EtOAc (3 x 20 mL).

The combined organic layers were washed with brine (20 mL), dried over MgSO4, and concentrated under reduced pressure. The residue was purified by column chromatography on silica gel.

4. 5,-one (4a)

Following the above procedure using 3a (322 mg, 1.0 mmol, 1 equiv.), BBr3 (6 mL, 1 M in CH2Cl2, 6 mmol, 6 equiv.) and CH2Cl2 (5 mL). Chromatography on silica gel with dichloromethane/methanol (95:5) as eluent was performed to get the desired compound 4a, (45 mg, yield = 52%) as a white solid. . Mp = 170-173°C. = 170.2, 146.8, 139.7, 138.8, 129.5, 117.1, 102.0, 79.2, 32.9, 31.6, 29.2, 29.0, 24.5, 22.4, 13.4. 4.1.5.2. 4,5,6-trihydroxy-3-undecylisonenzofuran-1(3H)-one (4b) Following the above procedure using 3b (96 mg, 0.25 mmol, 1 equiv.), BBr3 (1.5 mL, 1 M in CH2Cl2,1.5 mmol, 6 equiv.) and CH2Cl2 (5 mL). Chromatography on silica gel with dichloromethane/methanol (95:5) as eluent was performed to get the desired compound 4b (80 mg, yield = 90%) as a white solid. Mp = 157-160°C. 1, 146.8, 139.7, 138.7, 129.5, 117.2, 102.0, 79.2, 33.0, 31.7, 29.5 (2C), 29.4, 29.33, 29.2 (2C), 24.6, 22.4, 13.4. HRMS (ESI): m/z calcd for [M+H] + C19H28 O5: 337.20095; found: 337.20048. 4.1.5.3. 3-butyl-4,5,6-trihydroxyisobenzofuran-1(3H)-one (4c)

Following the above procedure using 3c (70 mg, 0.25 mmol, 1 equiv.), BBr3 (1.5 mL, 1 M in CH2Cl2, 1.5 mmol, 6 equiv.) and CH2Cl2 (5 mL). Chromatography on silica gel with dichloromethane/methanol (95:5) as eluent was performed to get the desired compound 4c (54 mg, yield = 89%) as a white solid. Mp = 132-135°C. 1 H NMR (300 MHz, acetone-d6) δ = 9.09 (s, 1H), 8.39 (s, 1H), 8.29 (s, 1H), 6.83 (s, 1H), 5.44 (dd, J = 7.6, 2.9 Hz, 1H), 2.25 (m, 1H),

1.71 (m, 1H), 1.32 (m, 4H), 0.90 (t, J = 6.8 Hz, 3H). 13 C NMR (75 MHz, acetone-d6) δ = 170. 3, 146.9, 139.7, 138.9, 129.4, 117.0, 102.0, 79.3, 32.6, 26.7, 22.2, 13.4 75MHz, acetone-d6) δ = 170. [START_REF] Ventola | The antibiotic resistance crisis: part 1: causes and threats[END_REF]146.8,139.7,138.8,130.1,116.8,102.0,77.9,42.4,25.1,23.0,21.3. HRMS (ESI): m/z calcd for [M+H] + C12H14 O5: 239.09140; found: 239.0909.

4. 1.5.5. 4,5,6-trihydroxy-3-phenylisobenzofuran-1(3H)-one (4e)

Following the above procedure using 3e (120 mg, 0.40 mmol, 1 equiv.), BBr3 (2.4 mL, 1 M in CH2Cl2, 2.4 mmol, 6 equiv.) and CH2Cl2 (5 mL). Filtration over a plug of silica using ethyl acetate as eluant was performed to get the desired compound 4e (70 mg, yield = 67%) as black solid. Mp = 234-237°C. 4.1.5.6. 4,5,6-trihydroxy-3-(4-hydroxyphenyl)isobenzofuran-1(3H)-one (4f)

Following the above procedure using 3f (100 mg, 0.33 mmol, 1 equiv.), BBr3 (1.98 mL, 1 M in CH2Cl2, 1.98 mmol, 6 equiv.) and CH2Cl2 (5 mL). Filtration over a plug of silica using ethyl acetate as eluant was performed to get the desired compound 4f (33 mg, yield = 33%) as dark solid. Mp > 250°C (decomposition). 1 H NMR (300 MHz, acetone-d6) δ = 9.12 (s, 1H), 8.40 (s, 1H), 8.20 (s, 1H), 7.38-7.31 (m, 5H), 6.93 (s, 1H), 6.40 (s, 1H). 13 C NMR (75 MHz, acetone- 170.2, 157.9, 147.4, 140.2, 139.5, 129.1 (2C), 129.0, 128.2, 116.7, 115.2 (2C) 4.1.5.7. 3-(2,3-dihydroxyphenyl)-4,5,6-trihydroxyisobenzofuran-1(3H)-one (4g)

d6) δ =
Following the above procedure using 3g (100 mg, 0.25 mmol, 1 equiv.), BBr3 (2 mL, 1 M in CH2Cl2, 2 mmol, 8 equiv.) and CH2Cl2 (5 mL). Chromatography on silica gel with dichloromethane/methanol (90:10) as eluent was performed to get the desired compound 4g (30 mg, yield = 44%) as dark brown solid.

Mp = 180-190°C. 1 H NMR (300 MHz, acetone-d6) δ = 8.45 (s, 5H), 6.92 (s, 1H), 6.86 (dd, J = 7.9 Hz, 1.5 Hz, 1H), 6.78 (s, 1H), 6.67 (t, J = 7.9 Hz, 1H), 6.43 (dd, J = 7.9 Hz, 1.5 Hz, 1H).

13

C NMR (75 MHz, acetone-d6) δ = 171. 3, 148.1, 145.8, 144.2, 140.6, 139.8, 129.5, 124.9, 120.8, 118.8, 118.0, 116.3, 103.2, 75.9. HRMS (ESI): m/z calcd for [M+H] + C14H10 O7:

29104993; found: 291.04940.

4. 1.5.8. 3-(4-(chlorophenyl)-4,5,6-trihydroxy-isobenzofuran-1(3H)-one (4h)

Following the above procedure using 3h (100 mg, 0.29 mmol, 1 equiv.), BBr3 (1.74 mL, 1 M in CH2Cl2, 1.74 mmol, 6 equiv.) and CH2Cl2 (5 mL). Chromatography on silica gel with dichloromethane/methanol (95:5) as eluent was performed to get the desired compound 127l (27mg, yield = 32%) as a brownish white solid. Mp = 185-188°C. 170.0, 147.5, 140.1, 139.4, 136.4, 133.9, 129.3 (2C), 128.6, 128.5 (2C), 116.5, 102.1, 79.4. HRMS (ESI): m/z calcd for [M+H] + C14H10ClO5: 293,0211; found: 293.0217.

4. 1.5.9. 4,5,6-trihydroxy-3(4-(trifluoromethyl)

phenyl)isobenzofuran-1(3H)-one (4i)
Following the above procedure using 3i (160 mg, 0.43 mmol, 1 equiv.), BBr3 (2.58 mL, 1 M in CH2Cl2, 2.58 mmol, 6 equiv.) and CH2Cl2 (5 mL). Chromatography on silica gel with dichloromethane/methanol (95:5) as eluent was performed to get the desired compound 4i (60 mg, yield = 42%) as brownish white solid. Mp = 233-236°C. 4. 1.5.10. 4,5,phenyl)isobenzofuran-1(3H)one (4j):

Following the above procedure using 3j (150 mg, 0.39 mmol, 1 equiv.), BBr3 (2.34 mL, 1 M in CH2Cl2, 2.34 mmol, 6 equiv.) and CH2Cl2 (5 mL). Chromatography on silica gel with dichloromethane/methanol (95:5) as eluent was performed to get the desired compound 4j (60 mg, yield = 45%) as a white solid.

Mp = 155-158°C. 4. 1.5.11. 4,5,6-trihydroxy-3(3-(trifluoromethyl)

phenyl)isobenzofuran-1(3H)- one (4k)
Following the above procedure using 3k (282 mg, 0.77 mmol, 1 equiv.), BBr3 (4.62 mL, 1 M in CH2Cl2, 2.62 mmol, 6 equiv.) and CH2Cl2 (5 mL). Chromatography on silica gel with dichloromethane/methanol (90:10) as eluent was performed to get the desired compound 4k

(170 mg, yield = 68%) as brown solid. Mp = 233-236°C. 8, 147.4, 140.0, 139.1, 138.9, 132.1, 130.2 (q, J = 32 Hz), 129.5, 128.4, 125.4 (q, J = 3.7 Hz), 124.3 (q, J = 270.0 Hz), 124.2 (J= 3.7

Hz), 116.5, 102. 4.1.6. Ethyl 3,4,oxy benzoate [START_REF]Progress in the chemistry of organic natural products[END_REF].

A dry and argon-flushed round bottom flask was charged with a solution of ethyl gallate 5 (2.97 g, 15 mmol, 1 equiv.) in dried dichloromethane (50 mL) and stirred at 0°C, then trimethylamine (1.5 mL, 20 mmol, 1.3 equiv.), DMAP (244 mg, 2 mmol, 0.1 equiv.) and Boc2O (11.7g, 54 mmol, 3.6 equiv.) were added. The reaction mixture was stirred overnight at room temperature and saturated aqueous solution of NH4Cl (40 mL) was added. The aqueous phase was washed with dichloromethane (3 x 100 mL). The combined organic phases were washed with brine (100 mL), dried over MgSO4 and solvent was removed under reduce pressure. The residue was purified by column chromatography on silica gel using petroleum ether/diethyl ether (85:15) as eluent to afford the compound 6 (7.2 g, yield = 97%) as a white solid. Mp = 77-80°C. 1 H NMR (300 MHz, CDCl3) δ = 7.84 (s, 1H), 4.36 (q, J = 7.2 Hz, 2H), 1.69-1.46 (m, 27H), 1.37 (t, J = 7.1 Hz, 3H). 13 C NMR (75 MHz, CDCl3) δ = 164.5 150. [START_REF] Ventola | The antibiotic resistance crisis: part 1: causes and threats[END_REF]148.8,143.7,138.9,128.2,121.7,84.5,84.4,61.6,27.6,25.5,

phenyl)-1-oxo-1,3-dihydroisobenzofuran- 4,5,6-triyl)tricarbonate (7)
A dry and argon-flushed round bottom flask was charged with a solution of 6 (400mg, 0.8 mmol, 1 equiv.) in dry THF (4 mL). The mixture was stirred under argon atmosphere at -20°C and TMP.MgCl.LiCl (0.88 mL, 0.88 mmol, 1.1 equiv.) was added dropwise. The reaction mixture was stirred for 3 hours at -40°C and 4-(dimethyl amino)benzaldehyde (180 mg, 1.2 mmol, 1.5 equiv.) was added. The reaction mixture was stirred for 3 hours at -40°C and saturated aqueous solution of NH4Cl (30 mL) was added at -40°C. The aqueous phase was washed with dichloromethane (3 x 30 mL). The combined organic phases were washed with brine (50 mL), dried over MgSO4 and solvent was removed under reduce pressure. The residue was purified by flash chromatography using petroleum ether: diethyl ether (80:20) as eluent to afford compound 7 (250 mg, yield= 52%) as a white solid. Mp = 110-113°C 6, 151.4, 149.9, 148.6, 148.5, 145.2, 140.3, 139.4, 138.8, 129.1 (2C), 124.6, 120.5, 117.1, 112.2 (2C), 84.9, 84.8, 84.7, 82.3, 40.3 (2C), 27.6 (3C), 27.5 (3C), 27.4 (3C) [START_REF]Progress in the chemistry of organic natural products[END_REF]148.2,141.0,139.9,130.0,129.8,129.7,118.0,115.8,102.9,81.2,42.5. HRMS (ESI): m/z calcd for

[M+H] + C16H15NO5: 302.10230; found: 302.10189.

4. . [24] A dry and argon-flushed three-neck round bottom flask equipped with a magnetic stirrer, condenser, a bubbler and a bromine funnel was charged with a 50% aqueous solution of sulfuric acid (75 mL) and 4-methoxyantranilic acid 8 (6 g, 36 mmol, 1 equiv.) at 0°C. A solution of sodium nitrite (2.75 g, 30 mmol, 1.1 equiv.) in water (10 mL) was added dropwise and the temperature was kept below 5°C. After 10 minutes of stirring at 0°C, a solution of potassium iodide (8.25 g, 50 mmol, 1.4 equiv.) in water (20 mL) was added dropwise. The reaction mixture was stirred at room temperature for 2 hours then heated to 70°C until the nitrogen release was ceased. The reaction mixture was cooled to room temperature and then extracted with ethyl acetate (3 x 50 mL). The organic phases were combined and washed with water (2 x 50 mL) and brine (1 x 50mL), dried over MgSO4 and concentrated under reduced pressure to afford 9 (5.32 g, yield = 53%) as yellow solid. 1 H NMR (300 MHz, CDCl3) δ = 8.05 (d, J = 8.9 Hz, 1H), 7.58 (d, J = 2.5 Hz, 1H), 6.94 (dd, J = 8.9 Hz, 2.5 Hz, 1H), 3.87 (d,J = 7.8 Hz,3H). 13 C NMR (75 MHz, DMSO-d6) δ = 166. 9,161.4,132.1,131.3,127.2,113.7,96.0,. [25] A dry and argon-flushed round bottom flask equipped with a magnetic stirrer and a septum was charged with a solution of 9 (5 g, 18 mmol, 1 equiv.) in dry acetonitrile (40 mL). Iodomethane (1.46 mL, 23.4 mmol, 1.3 equiv.) and DBU (3.95 mL, 19.8 mmol, 1.1 equiv.) were successively added and the reaction mixture was stirred overnight at room temperature. The solvent was removed and the residue was diluted in ethyl acetate (50 mL). The organic phase was washed with water (3 x 50 mL), a aqueous solution of HCl 1 M (2 x 50mL), a aqeous saturated solution of NaHCO3 (2 x 50mL)

and brine (50mL). The organic phase was the dried over MgSO4, filtered and solvent was evaporated under reduced pressure. The residue was purified by column chromatography on silica gel using petroleum ether/ethyl acetate (95:5) as eluent to afford 10 (3.11 g, yield = 60%) as clear oil. 162.0,132.5,131.6,127.0,113.6,95.6,55.6,. A dry and argon-flushed flask equipped with a magnetic stirrer and a septum was charged with a solution of 10 (500 mg, 1.7 mmol, 1 equiv.) in dry THF (10 mL) and was cooled at -78 °C. A solution of iPrMgCl•LiCl

(2.35 mL, 0.94 M solution in THF, 2.2 mmol, 1.3 equiv) was added dropwise and the reaction mixture was stirred for 30 minutes at -78°C. Then octanal (345 µL, 2.2 mmol, 1.3 equiv.) was added and the reaction mixture was slowly warm to room temperature and stirred overnight.

The reaction mixture was hydrolysed with water (20 mL) and extracted with EtOAc (3 x 20 mL). The combined organic layers were washed with brine (20 mL), dried over MgSO4 and concentrated under reduced pressure. The residue was purified by column chromatography on silica gel using petroleum ether/ethyl acetate (90:10) as eluent to afford 11 (230 mg, yield = 52%) as clear oil. 8, 165.0, 153.3, 127.6, 118.9, 116.5, 106.3, 81.1, 56.2, 35.2, 32.1, 29.7, 29.5, 25.2, 23.0, 14.5 [START_REF] Ventola | The antibiotic resistance crisis: part 1: causes and threats[END_REF]161.5,153.2,127.6,118.3,117.3,108.1,81.0,34.7,31.7,29.3,29.1,24.7,22.6,14.1. HRMS (ESI): m/z calcd for [M+H] + : 249.1485;found. 249.1489. 4.1.13. 4,6-Dichloro-3-heptyl-5-hydroxylisobenzofuran-1(3H)-one (13). A dry and argon-flushed flask equipped with a magnetic stirrer and a septum was charged with a solution of 12 (60 mg, 0.24 mmol, 1 equiv.) in toluene (5 mL), diisopropylamine (1 μL, 0.007 mmol, 0.03 equiv.) and sulfuryl chloride (36 μL, 0.44 mmol, 1.8 equiv.) were added successively. The reaction mixture was stirred at 70°C for 1 hour, then cooled to room temperature and hydrolysed with methanol (5 mL) and extracted with EtOAc (3 x 20 mL). The combined organic layers were washed with brine (20 mL), dried over MgSO4 and concentrated under reduced pressure.

C15H20O3

The residue was purified by column chromatography on silica gel using dichloromethane (100%) as eluent to afford 13 (26 mg, yield = 43%) as white solid. Mp = 119-122°C. Tested compounds were dissolve in DMSO to get a mother solution of 3 mg/mL and then further dilutions were made in Mueller Hinton (MH) to get a range of tested concentration (200, 100, 50, 25, 12.5, 6.25. 3.125 µg.mL -1 ). Broth microdilution method and numerations were used for the determination of minimal inhibitory and bactericidal concentrations (MIC and MBC). Subculturing of PAO1 Lux strain was performed on TSA agar from an aliquot stored at -80°C.

After one night at 37°C, few colonies were suspended in 3 mL of LB medium and incubated at 37°C, with agitation at 200 rpm, overnight. The next day, several dilutions were made in LB medium to obtain OD between 0.3-0.6. This dilution was then incubated at 37°C, with agitation for approximately 3 hours, then it was centrifuged at 3000 g for 10 minutes, at 6°C. Then the bacterial pellet was suspended in MH and adjusted to an OD of 0.4, corresponding to 2.10 8 CFU/mL, which was then diluted to obtain a bacterial suspension containing 2.10 5 CFU/mL

The inoculum size was verified by plating 100 μL 3-fold dilutions on TSA agars and incubating overnight at 37°C for CFU counts.

MIC and MBC evaluation

Hundred microliter/well of the bacterial suspension was inoculated into 96-well microtiter plate (Greiner Bio-One; Cellstar/S. aureus and E. coli), (Fisher Scientific, Illkirch-Graffenstaden, France/PAO1). 100 µL/well of MH (control) or molecules was added in duplicate for each condition. The microtiter plate was incubated in Eon thermo-regulated spectrophotometer plate reader (BioTek Instruments / S. aureus and E. coli), (Tecan, Lyon, France / PAO1) for 24 h at 37°C in ambient air with continuous shaking. The absorbance at OD 600 nm was read at 30 min intervals. After MIC determination, corresponding to the first well without bacterial growth, the MBC was evaluated. For that purpose, 50 µL of each well were 5-fold diluted and each of dilutions were plated on a LB agar plate, which was then incubated at 37°C for 24 h.

The MBCs were recorded as the lowest dilution that produced a ≥ 99.99% reduction in growth (≥4-log10 reduction in CFU/mL) in comparison to the initial inoculum (Figure 32). This test were performed in triplicate at three independent times.

Cytotoxicity assays

Culture, maintenance and preparation of Beas-2B cells

The Beas-2B line is a line of human bronchial epithelial cells transformed with the SV40 virus.

These cells are adherent and become immortal. A culture medium F12Mix+Glutamax (Ref 31765-027 Gibco) was used, to which was added Fetal Bovine Serum (FBS) at 10% final as well as Penicillin-Streptomycin (P/S) at 1% final. This medium was called complete F12K medium. The cells were stored in complete F12K culture medium to which was added 10% DMSO, at -196°C. For their preparation, the cells were first thawed rapidly at 37°C with stirring. They were then diluted in 10 mL of complete medium before centrifugation at 150 g for 5 minutes, at 20°C. Once the supernatant has been removed, the cells were cultured in 75 cm² dishes in the presence of 15 mL of complete medium, then incubated at 37°C under a humid atmosphere in the presence of 5% CO2. After 48 hours of incubation, the medium was replaced with new complete medium. The medium was removed as the cell were at confluence and the cells were detached from the dish by the action of trypsin, an endoprotease which hydrolyzes peptide bonds. After rinsing the cell layer with 2 mL of trypsin, 3 mL were added and the flask was incubated 1 at 2 minutes at 37°C, under a humid atmosphere in the presence of 5% CO2.

After cell detachement the action of the trypsin was neutralized by the addition of 7 mL of complete medium. The cells were then transferred to a Falcon tube and 100 μL are taken in order to determine the total number of cells by the Malassez cell counting technique.

Centrifugation of the tube was carried out for 5 minutes at 150 g, at 20°C. The supernatant has been removed and the cells were placed in culture at a rate of 300,000 in 15 mL of complete medium in a 75 cm² dish. The dish was then incubated at 37°C in a humid atmosphere in the presence of 5% CO2.

Principle of the MTS test[26]

Cellular cytotoxicity is linked to cell survival. The latter can be evaluated by a colorimetric A determination was carried out by measuring the absorbance of the formazan at 490 nm. The cytotoxicity was calculated as following: Cell viability (%) = [OD of exposed cells / (OD of control cells)] x 100. A compound was described as non-cytotoxic when the resulting cell viability is greater than 80%. The cells were seeded in a 96-well plate at a rate of 10 000 cells in 150 μL of medium. Some wells were not inoculated to serve as a positive control (control cells) for MTS. The cells were incubated for 48 hours in a humid atmosphere in the presence of 5% CO2, at 37°C. After incubation and verification of the confluence of the cells, the wells were washed with 200 μL of medium without FBS, then 100 μL of each compound were deposited per well, at a rate of 6 wells per compound (or dilution) tested. The MTS was diluted to 1/6 in FK12 without FBS and 100 μL were deposited in each well. The plate was then incubated for 1 hour in a humid atmosphere in the presence of 5% CO2, at 37°C. After the incubation was completed, the plate was placed in the Tecan spectrometer to measure the absorbance of the wells at 490 nm. The results were normalized against the control MTS and expressed as a percentage. This test was perfomed in duplicata at two independent times

Figure 1 :

 1 Figure 1: Natural antibacterial phthalides with their reported pharmacomodulations.

Figure 2 :

 2 Figure 2: Structure and biological activities of cytosporone E and some natural analogs

Scheme 2 :

 2 Scheme 2: Synthesis of the analog 4l. (a) Boc2O, Et3N, DMAP, CH2Cl2, 0°C to rt, overnight, 97%; (b) TMPMgCl.LiCl, THF, -20 °C, 3h then 4-dimethylaminobenzaldehyde, -40 °C, 3h, 52%; (c) CF3COOH, rt, 15 min, 81%.

Scheme 3 :

 3 Scheme 3: Synthesis of the analogs 12-13 (a) NaNO2, H2SO4, 0°C, 20 min. then KI, rt, 2h, 53%; (b) MeI, DBU, acetonitrile, rt, 1h, 60%; (c) iPrMgCl.LiCl, THF -78 °C, 30 min then octanal, -78 °C to rt, overnight, 65%; (d) BBr3 (1M in CH2Cl2, 3 equiv.), CH2Cl2, -20°C to rt, overnight. 56%; (e) SO2Cl2, iPr2NH, toluene, 1h, 50°C, 43%.

Table 2 .

 2 Minimum Inhibitory and Bactericidal Concentrations (in µg.mL -1 ) of compounds 4a, 4i-k, 12 and 13 against MSSA and MRSA

Figure 3 :

 3 Figure 3: Evaluation of phthalides cytotoxicity on Beas-2B cells by MTS at different concentrations. A: Compounds 4a and 4i (n = 2). B: compound 13 dissolved in DMSO (n= 2) and in NaDES glycerol-choline chloride (n = 3).

  1 H NMR (300 MHz, methanol-d4) δ = 7.66(d, J = 8.2 Hz, 2H), 7.49 (d, J = 8.1 Hz, 2H), 6.89 (s, 1H), 6.46 (s, 1H).13 C NMR (75 MHz, methanol-d4) δ = 170.8, 146.6, 140.0, 139.0, 138.0, 129.1 (q, J = 32.3 Hz), 127.4, 126.6 (2C), 123.8 (q, J = 3.8 Hz, 2C), 122.9 (q, J = 270.0 Hz), 114.0, 100.4, 79.0.19 F NMR (282 MHz, methanol-d4) δ = -64.1. HRMS (ESI): m/z calcd for [M+H] + C15H9F3O5: 327.04748; found: 327.04696.

4. 2 . 1 . 1 .

 211 Bacterial culture S. aureus and E. coli strains were cultured on Luria-Bertani (LB) plates overnight. Several isolated colonies were suspended in 5 mL of MH media and grown overnight at 37°C, under agitation (200 rpm). Optical density (OD) was measured and then several dilutions of this fresh suspension were prepared in MH medium to obtain 2.10 5 CFU/mL (CFU for colony forming unit). The inoculum size was verified by plating 5-fold dilutions on LB plates and incubating overnight at 37°C for CFU counts.

  method based on the detection of the conversion of a tetrazolium derivative (MTS) by cells metabolically active, CellTiter 96 ® Aqueous One Solution Cell Proliferation Assay Promega was used. Succinate dehydrogenases in cells reduce the yellow tetrazolium compound MTS, also called (3-(4,5-dimethylthiazol-2-yl)-5-(3-carboxymethoxyphenyl)-2-(4-sulfophenyl)-2Htetrazolium, yellow into purple formazan, soluble in the culture medium. Thus, after incubation for 1 hour, the intensity of the purple color is directly proportional to the number of living cells.

NMe 2 Scheme 1 :

 21 Synthesis of the cytosporone E and analogs. (a) I2, CF3COOAg, CHCl3, rt., 24h, 63%;(b) iPrMgCl.LiCl, THF -78 °C, 30 min then R 1 CHO -78 °C to rt, overnight, 18-69%; (c) BBr3 (1M in CH2Cl2, 6 to 10 equiv.), CH2Cl2, -20°C to rt, overnight. 15-90%.

Table 3 .

 3 Summary

	Compound	IC50 Beas-2B cells	MIC against MRSA
		(µM)	(µM)
	4a	66.4	22.3
	4i	87.1	19.2
	4j	41.5	36.5
	4k	31.3	38.3
	12	58.4	50.4
	13	15.9	3.9

of cytotoxicity against Beas-2B cells and activity against methicillinresistant S. aureus of compounds 4a, 4i-k, 12 and 13

  ), iPrMgCl•LiCl(1.73 mL, 0.75 M solution in THF, 1.3 mmol, 1.3 equiv), octanal (203 µL, 1.3 mmol, 1.3 equiv.) and THF(10 mL). Chromatography on silica gel with Petroleum ether/EtOAc (85:15) as eluent was performed to get the desired compound 3a (225 mg, yield = 70%) as a white solid. Mp = 57-

	60°C. 1 H NMR (300 MHz, CDCl3) δ = 7.10 (s, 1H), 5.44 (dd, J = 7.9 Hz, 3.0 Hz, 1H), 3.96 (s,
	3H), 3.93 (s, 3H), 3.90 (s, 3H), 2.20-2.12 (m, 1H), 1.74-1.65 (m, 1H), 1.45-1.19 (m, 10H), 0.85
	(t, J = 6.0 Hz, 3H). 13 C NMR (75 MHz, CDCl3) δ = 170.

  equiv.) and THF(20 mL). Chromatography on silica gel with Petroleum ether/EtOAc (70:30) as eluent was performed to get the desired compound 3d (310 mg, yield = 49%) as a white solid. Mp = 55-58°C.1 H NMR (300 MHz, CDCl3) δ = 7.11 (s, 1H), 5.48 (dd, J = 10.1 Hz, 1.7

	Hz, 1H), 3.97 (s, 3H), 3.93 (s, 3H), 3.91 (s, 3H), 2.02-1.90 (m, 2H), 1.56-1.48 (m, 1H), 1.06 (d,
	J = 6.0 Hz, 3H), 0.96 (d, J = 6.0 Hz, 3H). 13 C NMR (75 MHz, CDCl3) δ = 170.
	. HRMS (ESI): m/z calcd for [M+H] +
	C15H20O5: 281.13835; found: 281.13790.

4.

5,

Following the above procedure using 2 (800 mg, 2.28 mmol, 1 equiv.), iPrMgCl•LiCl

(6.6 mL, 0.45 M solution in THF, 2.97 mmol, 1.3 equiv.)

, isobutyraldehyde

(314 µL, 2.96 mmol, 1.3

  Following the above procedure using 2 (400 mg, 1.14 mmol, 1 equiv.), iPrMgCl•LiCl(1.48 mL, 1.0 M solution in THF, 1.48 mmol, 1.3 equiv.), benzaldehyde (150 µL, 1.48 mmol, 1.3 equiv.) and THF (10 mL). Chromatography on silica gel with Petroleum ether/EtOAc (90:10) as eluent was performed to get the desired compound 3e (200 mg, yield = 59%) as a white solid.

	. HRMS (ESI): m/z calcd
	for [M+H] + C15H20O5: 281.13835; found: 281.13792.
	4.1.4.5. 4,5,6-Trimethoxy-3-phenylisobenzofuran-1(3H)-one (3e)

Mp = 98-101°C.

1 H NMR (300 MHz, CDCl3) δ = 7.39-7.32 (m, 3H), 7.29-7.24 (m, 2H), 7.21

(s, 1H), 6.35 (s, 1H), 3.94 (s, 3H), 3.91 (s, 3H),

3.45 (s, 3H)

.

13

C NMR (75 MHz, CDCl3) δ = 170.4, 155.9, 147.

9, 147.5, 136.3, 135.7, 129.2, 128.6 (2C), 127.4 (2C), 120.8, 102.6, 81.2, 61.0, 60.3, 56.4

. HRMS (ESI): m/z calcd for [M+H] + C17H16O5: 301.10705; found: 301.10664.

  .87 mmol, 1.3 equiv.) and THF(20 mL). Chromatography on silica gel with Petroleum ether/Et2O (85:15) as eluent was performed to get the desired compound 112g (240 mg, yield = 42%) as a yellow oil.1 H NMR (300 MHz, CDCl3) δ = 7.20 (s, 1H), 2H), 6.83 (s, 1H), 6.41 (dd, J = 7.3 Hz, 1.8 Hz, 1H), 4.14 (dd, J = 6.7 Hz, 2.3 Hz, 1H), 3.98 (dd, J = 6.9

	Hz, 2.2 Hz, 1H),3.94 (s, 3H), 3.90 (s, 3H), 3.86 (s, 3H), 3.50 (s, 3H), 1.82-1.71 (m, 2H), 1.57-
	1.42 (m, 2H), 0.96 (t, J = 7.4 Hz, 3H). 13 C NMR (75 MHz, CDCl3) δ = 170.83, 155.81, 153.06,
	Mp = 95-103°C. 1 H NMR (300 MHz, CDCl3) δ = 7.19 (s, 1H), 7.17 (d, J = 8.8 Hz, 2H), 6.87
	(d, J = 8.8 Hz, 2H), 6.32 (s, 1H), 3.94 (s, 3H), 3.91 (s, 3H), 3.80 (s, 3H), 3.48 (s, 3H). 13 C NMR
	(75 MHz, CDCl3) δ = 170.4, 160.2, 158.8, 147.9, 147.4, 135.5, 128.8 (2C), 128.3, 121.0, 114.0
	(2C), 102.6, 81.1, 61.1, 60.4, 56.4, 55.3. HRMS (ESI): m/z calcd for [M+H] + C18H18O6:
	331.11761; found: 331.11702.
	4.1.4.7.4,5,6-3-(2-Butoxy-3-methoxyphenyl)-4,5,6-trimethoyisobenzofuran-1(3H)-one
	(3g)

), iPrMgCl•LiCl (2.96 mL, 0.5 M solution in THF,

1.48 mmol, 1.3 equiv.), p-anisaldehyde (180 µL, 1.48 mmol, 1.3 equiv.)

and THF

(10 mL)

. Chromatography on silica gel with Petroleum ether/EtOAc (85:

15)

as eluent was performed to get the desired compound 3f (130 mg, yield = 35%) as a white solid.

Following the above procedure using 2 (500 mg, 1.44 mmol, 1 equiv.), iPrMgCl•LiCl

(3.74 mL, 0.5 M solution in THF, 1.87 mmol, 1.3 equiv.)

, 2-butoxy-3-methoxybenzaldehyde (389 mg, 1

  , 101.8, 80.4. HRMS (ESI): m/z calcd for [M+H] + C14H11O6: 275.0550; found: 275.0546.

  3, 79.3. 19 F NMR (282 MHz, acetone-d6) δ = -63.1. HRMS (ESI): m/z calcd for [M+H] + C15H9F3 O5: 327.04748; found: 327.04700.

Acknowledgements

We acknowledge Prof. Leslie Delaye-Boudescoque for her helpful discussion and for providing the NaDES solvent. We would also like to thank Dr. Frédéric Montigny (University of Tours) for mass spectra and HRMS and the French Ministry for Research and Innovation for the financial support.


As climate change worsens, intensified natural events are expected to happen in the future. Among these events, floods can be the most destructive and can cause significant damages on many levels. It is therefore necessary to put in place cost-effective flood forecasting models in order to obtain accurate dynamic simulations for flood risk assessment. However, current models are affected with large uncertainties and need to be constrained with independent data that must be acquired from in situ measurements or remote sensing derived observations. If the network of hydrometric stations was well developed, flow rate and/or stage time series should be provided at a relatively sufficient spatial and temporal coverages and used as inputs for flood models. However, in many areas around the world, stream gauges are sparsely distributed and can be lacking in ungauged basins [85]. To compensate the lack of in situ data, we propose to exploit earth observation (EO) and particularly make use of Synthetic Aperture Radar (SAR) imagery due to its ability to provide frequent updates of flooded areas at a large scale, regardless of atmospheric conditions. Moreover, the specular reflection of the emitted backscatter on open water bodies allows a relatively straightforward detection of water on the SAR image. Thus, these images hold an added value and a potential to improve the predictive accuracy of flood forecasting models through data assimilation (DA). Widely used in the fields of hydrology, hydraulics and geosciences, DA aims to optimally combine uncertain model predictions and uncertain observations. This relies on the estimation of optimal model states and/or parameters and allows thereby for the reduction of model uncertainties. DA can be carried out sequentially, for example in near-real time, by updating model states and/or parameters using observations as they become available, or in a reanalysis by assimilating all observations at once, i.e., retrospectively. Another major challenge tied to the hydrodynamic modelling is the lack of hydraulic parameter data that are needed as inputs, such as the riverbed shape and elevation. While the knowledge of such information is critical for flood models, it is rarely available from remote sensing observations, digital elevation models (DEMs), or ground data measurements. Most studies have estimated river discharges and depths assuming the bathymetry and bed roughness to be known a priori. The complexity of implementing DA to estimate these hydraulic parameters have long been seen has a pitfall.

In this study, we propose to assimilate probabilistic flood maps derived from SAR data into the SW2D-DDP model, a 2-dimensional shallow water equations model with depth-dependent porosity, in order to retrieve the unknown bathymetry of a river. The porosity functions in this model, enable a straightforward representation of the riverbed geometry using porosity parameters. We assume the bed shape to be trapezoidal, and the bed roughness to be known a priori. The DA framework is thus based on integrating PFMs into the SW2D-DDP model via a Tempered Particle Filter (TPF) and takes into account the SAR observation and the SW2D-DDP model related uncertainties. The data assimilation algorithm is applied using as a test case the 2012 flood event that hits the Severn River around the city of Tewkesbury at the confluence of the Severn and Avon Rivers. We thus proposed to retrieve via data assimilation a simplified spatially distributed riverbed geometry (i.e., riverbed depth) along with the model downstream boundary condition in the form of a rating curve. The results are very encouraging as the model predictions reach water level RMSEs below 0.5 m as a result of the assimilation although the retrieved river depths are not matching the real one.

Paper

  Title: ASSIMILATION OF PROBABILISTIC FLOOD MAPS INTO LARGE SCALE HYDRAULIC MODELS TO RETRIEVE MISSING RIVER GEOMETRY DATA USING A TEMPERED PARTICLE FILTER Authors: 1. Vita Ayoub, Luxembourg Institute of Science and Technology 2. Renaud Hostache, Institut de Recherche pour le développement 3. Marco Chini, Luxembourg Institute of Science and Technology 4. Ramona Pelich, Luxembourg Institute of Science and Technology 5. Patrick Matgen, Luxembourg Institute of Science and Technology 6. Carole Delenne, Université de Montpellier Abstract :


Hirotada Hashimoto

Nicolas Grenier
email: nicolas.grenier@lisn.upsaclay.fr

Makoto Sueyoshi

David Le Touzé

Comparison of MPS and SPH methods for solving forced motion ship flooding problems

Keywords: Particle methods, MPS, SPH, Ship flooding, Forced roll test, Trapped air 1. INTRODUCTION

In order to assess the safety of damaged ships quantitatively, advanced numerical simulation methods are required for the prediction of ship dynamic behavior coupled with floodwater. For the prediction of fast and complicated free-surface flows in immediate flooding, particle methods are promising because largely deformed free-surface can be naturally and accurately followed without numerical diffusion. In this paper, systematic comparisons of the MPS (Moving Particle Semi-implicit) and SPH (Smoothed Particle Hydrodynamics) methods are made on ship flooding problems. Firstly, numerical simulations based on the MPS and SPH methods are performed on forced roll tests of a twodimensional damaged compartment and are compared with a dedicated model experiment. Secondly, similar comparisons are made for a three-dimensional flooded compartment. Through these comparisons between MPS and SPH methods and to model-scale experiments, the capability of particle methods in simulating complicated flooding flows is investigated and the difference of prediction accuracy of the MPS and SPH methods is discussed. For the case of two-dimensional damaged compartment, it is also studied what effects has a single-phase approximation in comparison

to simulations where air is modelled, and how the trapped air in damaged compartments influences the water flow evolution. Results from this study show that both particle methods are capable to simulate complex flooding flows in good quantitative agreement with respect to experiments and with similar execution times while there is no possibility to draw superiority of one method. However when dealing with air modelling, using a simplified approach limits computational times but induces quite large discrepancies compared to fully modelling the air phase.

Collision and grounding accidents of ships are frequently reported even nowadays while human and environmental security issues are carefully looked by societies. Securing the survivability against flooding is one of the most important requirements in ship design [START_REF] Bačkalov | Ship stability, dynamics and safety: Status and perspectives from a review of recent STAB conferences and ISSW events[END_REF]. Since the quantitative prediction of ship transient behavior induced by the floodwater inflow is essential to ensure the safety of damaged ships, advanced numerical simulation methods are strongly desired especially for immediate flooding leading to capsizing. These methods must be able to accurately predict the strongly nonlinear freesurface flow occurring into damaged compartments through damage openings and progressive flooding into all floodable compartments. In addition, the dynamic coupling between floodwater and ship motion must also be considered. Therefore, the development of advanced numerical methods in time domain, which enable to simulate dynamic motions of damaged ships from the initial stage of water flooding to the final equilibrium or catastrophic state, is crucial to fully account for the complexity of these floodwater flows. This problem can be studied either experimentally (see, e.g., [START_REF] Acanfora | An Experimental Investigation on the Dynamic Response of a Damaged Ship with a realistic arrangement of the flooded compartment[END_REF][START_REF] Siddiqui | Experimental studies of a damaged ship section in forced heave motion[END_REF]) or using conventional mesh-based CFD (Computational Fluid Dynamics) methods (see, e.g., [START_REF] Gao | Numerical study of damaged ship flooding in beam seas[END_REF][START_REF] Sadat-Hosseini | URANS simulations for a flooded ship in calm water and regular beam waves[END_REF][START_REF] Gao | On damaged ship motion and capsizing in beam waves due to sudden water ingress using the RANS method[END_REF]) while progressive flooding is still often studied with linearized algebraic formulations [START_REF] Braidotti | A Comparison of Different Linearized Formulations for Progressive Flooding Simulations in Full-Scale[END_REF]. For solving violent flows of flooding, e.g. abrupt flooding through damaged openings or progressive flooding with sloshing and up-and downflooding, particle methods, thanks to their Lagrangian formalism which naturally includes nonlinear transport term and preserves sharp interfaces, present interesting features to describe nonlinear freesurface flows. Beyond providing an accurate and perfectly non-diffusive description of complex fluid interfaces, the Lagrangian nature of particle methods permits to avoid the discretization of the convection term of Navier-Stokes equations, thus providing a source of accuracy when flows are dominated by inertia, as are violent flows (no numerical diffusion on this term). The two main particle methods to simulate complex free-surface flows are the SPH (Smoothed Particle Hydrodynamics) and MPS (Moving Particle Semi-implicit) methods, which are closely related. Regarding complex flooding flow problems, several studies can be found with these methods. González et al. [START_REF] González | Numerical prediction of the dynamic behavior of a ro-ro ship after a hull side damage[END_REF] simulated the shallow water flow in flooded car deck by SPH. Skaar et al. [START_REF] Skaar | The use of a meshless CFD method in modelling progressive flooding and damaged stability of ships[END_REF] predicted progressive flooding of a complicated two-dimensional ship section by SPH. Le Touzé et al. [START_REF] Touzé | SPH simulation of green water and ship flooding scenarios[END_REF] and Oger et al. [START_REF] Oger | Advances in SPH for naval hydrodynamics[END_REF] simulated flooding in ship internal compartments by SPH. Zhang et al. [START_REF] Zhang | Investigation on a damaged ship model sinking into water based on three dimensional SPH method[END_REF] and Guo et al. [START_REF] Guo | A 3-D SPH model for simulating water flooding of a damaged floating structure[END_REF] predicted sinking of a simple 3-D damaged model by SPH. Later, Ming et al. [START_REF] Ming | Numerical simulation of a damaged ship cabin flooding in transversal waves with Smoothed Particle Hydrodynamics method[END_REF] predicted sinking of a similar compartment in beam waves. Cao et al. [START_REF] Cao | Multi-phase SPH modelling of air effect on the dynamic flooding of a damaged cabin[END_REF] included the influence of air on a two-dimensional damaged cabin simulated by a multiphase SPH method. Hashimoto et al. [START_REF] Hashimoto | Numerical simulation method for damaged ships under flooding condition[END_REF][START_REF] Hashimoto | A numerical simulation method for transient behavior of damaged ships associated with flooding[END_REF] predicted transient and dynamic behaviors of a damaged PCTC (Pure Car and Truck Carrier) in flooding situations, with a hybrid scheme using ordinary potential theory for intact hull and the MPS method for damaged hull.

The numerical technique, solving an equation of ship motion and the Navier-Stokes equation by the MPS method simultaneously in the framework of weakly nonlinear analysis, is useful for ship motions coupled with fluid flows [START_REF] Hashimoto | Numerical simulation method for coupling motions of a ship and tank fluid[END_REF][START_REF] Bulian | Coupled simulation of nonlinear ship motions and a free surface tank[END_REF]. Zhang et al. [START_REF] Zhang | Numerically simulated flooding of a freely-floating two-dimensional damaged ship section using an improved MPS method[END_REF] studied flooding of different ship sections with the MPS method and analyzed impact of damage position on ship motion and flooding.

Although the existing works mentioned above well demonstrated that particle methods are promising approaches for the safety assessment of damaged ships in flooding condition, there are few comparative researches between the MPS and SPH methods. Souto-Iglesias et al. [START_REF] Souto-Iglesias | On the consistency of MPS[END_REF][START_REF] Souto-Iglesias | On the consistency of MPS[END_REF] investigated the consistency of MPS and discussed the differences with SPH. Several groups showed comparison results of the MPS and SPH methods for standard dam-break or sloshing tests [START_REF] Abdelrazek | Comparison between SPH and MPS Methods for Numerical Simulations of Free Surface Flow Problems[END_REF][START_REF] Bakti | Comparative Study of Standard WC-SPH and MPs solvers for Free Surface Academic Problems[END_REF][START_REF] Amaro | A Comparison Between Weakly-Compressible Smoothed Particle Hydrodynamics (WCSPH) and Moving Particle Semi-Implicit (MPS) Methods for 3D Dam-Break Flows[END_REF]. Khayyer et al. [START_REF] Khayyer | An enhanced ISPH-SPH coupled method for simulation of incompressible fluid-elastic structure interactions[END_REF][START_REF] Khayyer | Multi-resolution ISPH-SPH for accurate and efficient simulation of hydroelastic fluid-structure interactions in ocean engineering[END_REF] compared accuracy of both methods to compute fluid-structure interactions. Here, a systematic comparative study between the MPS and SPH methods is conducted on forced roll tests of a two-dimensional damaged compartment, and on a three-dimensional flooded compartment situation.

Through comparison with dedicated experimental tests at model scale for various conditions, capability of the two particle methods to predict flooding flows is discussed and the accuracy of each particle method is carefully investigated. In a first stage the MPS and SPH methods are compared with each other in the two-dimensional situation without taking the air phase into account, showing discrepancies with the experimental results. The importance of the air phase was highlighted for flooding problems [START_REF] Gao | Numerical study of damaged ship's compartment sinking with air compression effect[END_REF] and water slamming [START_REF] Khayyer | A Multiphase Compressible-Incompressible Particle Method for Water Slamming[END_REF]. Thus in a second stage, it is shown how modeling the trapped air in damaged compartments permits to recover closely the experimental results. This is done in two different ways: either by numerically modelling the local equations in both phases or by using a simple Boyle's law model. Then, a complicated three-dimensional flow is simulated by the MPS and SPH methods and is compared with the experimental result in terms of hydrodynamic forces and flow configurations in the compartment. Finally, conclusions are drawn regarding the capabilities and differences of the two methods for investigating realistic complex geometry flooding situations.

The present paper is organized as follows. In section 2.1 and 2.2, a brief review of the MPS and SPH methods is provided and some details are given on the two related numerical solvers used for the comparison study. Experimental setup and measurement procedure used for the validation of these particle methods are shown in section 3.1 and 3.2. Comparison results between the MPS, SPH and experimental results are presented for the two-dimensional situation in section 4.1. The trapped air effect and its numerical treatment are studied in section 4.2. The results for a realistic threedimensional flooding situation are described and discussed in section 4.3. Finally, the main conclusions of the paper are given in section 5.

MPS AND SPH METHODS

MPS solver

The moving particle semi-implicit (MPS) method was proposed by Koshizuka and Oka [START_REF] Koshizuka | Moving particle semi-implicit method for fragmentation of incompressible fluid[END_REF] for solving incompressible fluid flows. The governing equations used in the MPS method, dealing with incompressible flow approximation, are the incompressible Navier-Stokes equations written in Lagrangian formalism (Eq.1-3).

= 0

(1)

= - 1 〈∇ 〉 + 〈∇ 〉 + (2) = (3)
In (Eq. 1-3), variables are the density , time , velocity , pressure , kinematic viscosity coefficient , gravity acceleration and position .

The spatial differential operators in (Eqs. 1-2) are discretized with the particle interpolations in (Eqs. [START_REF] Gao | Numerical study of damaged ship flooding in beam seas[END_REF][START_REF] Sadat-Hosseini | URANS simulations for a flooded ship in calm water and regular beam waves[END_REF][START_REF] Gao | On damaged ship motion and capsizing in beam waves due to sudden water ingress using the RANS method[END_REF], with use of a weighting function, w(r), and summation over the neighbor particles j included in a compact neighborhood Ωi around particle i. The inter-particle distance is denoted = -.

Each particle represents a volumic fluid element (equivalent to a material cell in mesh-based methods).

〈∇ 〉 = - - ! " ∈$ % , ' (4)
〈∇ 〉 = 2 ) *( -)! - ∈Ω , ≠ (5)
) = ∑ 2 ! ∈Ω , ≠ ∑ ! ∈Ω , ≠ (6)
is the number of dimensions of the considered problem and is the particle number density in the initial configuration.

In the MPS method, the gravity and viscous terms in (Eq. 2) and the flow kinematics (Eq. 3) are evolved explicitly in time, and the Pressure Poisson Equation (Eqs. 7-8) is solved implicitly, i.e. we have a semi-implicit time stepping:

〈∇ 〉 123 = 2 ) * 123 -123 ! -= -Δ * - ∈$ % , ' (7)
* = ! * ∈Ω , ≠ (8)
where 123 is the pressure at next time step to be solved implicitly, Δ the time step, * the intermediate step particle number density and * the intermediate step particle position. Once the pressure known, its gradient is calculated by (Eq. 4) and is used to update the position of particles while satisfying the incompressibility assumption (Eq. 1).

An in-house solver based on the MPS method, named MPS-Hydro, is used for the MPS simulations (see [START_REF] Sueyoshi | Numerical simulation of wave-induced nonlinear motions of a two-dimensional floating body by the moving particle semi-implicit method[END_REF][START_REF] Sueyoshi | Numerical Simulation of Tank Sloshing with Thin Plate Structures by Using a Particle Method[END_REF] for the algorithm of the solver). The weighting function used in this study is the one of (Eq. 9), with 6 the effective radius. It is modified from the conventional one [START_REF] Koshizuka | Moving particle semi-implicit method for fragmentation of incompressible fluid[END_REF] to have a finite value even when the effective radius goes to zero.

In MPS-Hydro, wall boundaries are imposed by mirror-particles [START_REF] Hashimoto | A numerical simulation method for transient behavior of damaged ships associated with flooding[END_REF][START_REF] Sueyoshi | Numerical Simulation of Tank Sloshing with Thin Plate Structures by Using a Particle Method[END_REF] and the wall reflection algorithm which inverts the velocity vector of a fluid particle when it comes within the threshold of minimum distance to the wall surface. The compressibility of fluids [START_REF] Ikeda | Numerical Analysis of Jet Injection Behavior for Fuel-Coolant Interaction using Particle Method[END_REF] and quasi-compressibility [START_REF] Tanaka | Stabilization and smoothing of pressure in MPS method by Quasi-Compressibility[END_REF] are introduced in solving the Pressure Poisson Equation to stabilize the calculation.

During the last decade the MPS method has been largely improved, especially solving the free-surface instability which was the recognized defect of the standard MPS method, see, e.g., [START_REF] Gotoh | On the state-of-the-art of particle methods for coastal and ocean engineering[END_REF].

SPH solver

The Smoothed Particle Hydrodynamics (SPH) method [START_REF] Lucy | A numerical approach to the testing of the fission hypothesis[END_REF][START_REF] Gingold | Smoothed particle hydrodynamics: theory and application to nonspherical stars[END_REF] was first applied to free-surface flows by Monaghan [START_REF] Monaghan | Simulating free surface flows with SPH[END_REF]. Differently from the MPS where we make the incompressible flow assumption, the weakly-compressible approach is used in the original SPH framework to solve the Navier-Stokes equations (Eqs. 14-15), with a closure barotropic equation of state (Eq. 16).

where > is the polytropic coefficient (set to 7 for water).

In the weakly-compressible approach, the sound speed is artificially lowered to save computational

= -〈∇. 〉 (14)
= -1 〈∇p〉 + 〈∇ @〉 + (15)

A = B > C8 ; D -1E (16)
time (up to the limit where the Mach number Ma is equal to 0.1; Ma is based on a reference velocity derived here from a Froude number equal to unity (F = GHI) and the reference length H equal to domain depth), without influencing the incompressible part of the flow at aim in our problems [START_REF] Marrone | Prediction of energy losses in water impacts using incompressible and weakly compressible models[END_REF].

The weighting function w chosen in the present SPH scheme is the Wendland kernel [START_REF] Wendland | Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree[END_REF]:

The classical SPH space operators applied to pressure gradient, velocity divergence and velocity Laplacian (discretized after Monaghan [START_REF] Wendland | Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree[END_REF]) lead to:

〈∇ 〉 = * + ∇! J - ∈$ % ( 18
) 〈∇. 〉 = * - . ∇! J - ∈$ % ( 19
) 〈∇ 〉 = - . - ∇! J " ∈Ω ( 20
)
where Vi is the volume of particle i. However, this naive fully-explicit SPH implementation (called the strong formulation) into the previous system (Eqs. 14-15) leads to unstable formulation. A simple way to stabilize it is to add an artificial viscosity, but pressure field may be noisy. A more accurate alternative is to rewrite the equations in conservative form and to derive a weak formulation of the system (Eqs. [START_REF] Ming | Numerical simulation of a damaged ship cabin flooding in transversal waves with Smoothed Particle Hydrodynamics method[END_REF][START_REF] Cao | Multi-phase SPH modelling of air effect on the dynamic flooding of a damaged cabin[END_REF] based on a Finite Volume numerical analysis (see [START_REF] Vila | On Particle Weighted Methods and Smooth Particle Hydrodynamics[END_REF]) and a Riemann solver.

This leads to the following discrete system [START_REF] Vila | On Particle Weighted Methods and Smooth Particle Hydrodynamics[END_REF][START_REF] Oger | SPH accuracy improvement through the combination of a quasi-Lagrangian shifting transport velocity and consistent ALE formalisms[END_REF] for the inviscid part of the system (hyperbolic Euler equations):

where Φ is the vector of conservative variables: Φ = ( , L) M . N is the flux solution (for both continuity and momentum equations) of the Riemann problem based on left Φ and right Φ states corresponding to particles i and j, and along direction O = P! QP! Q ⁄ . In the present work, this function N is based on an approximate Riemann solver called acoustic, and its accuracy is enhanced

!( ) = 7 T U 81 - 6 ; V 81 + 4 6 ; 0 ≤ ≤ 6 0 6 ≤ (17)
J Φ = *2X Φ , Φ , O ∇! J J -+ J Y ∈Ω (21)
with the MUSCL scheme. Y is the vector of source terms, including gravity and viscous effects.

Besides, in this specific formulation of SPH it is needed to evolve in time the volume of each particle.

An equation similar to the continuity equation is used and discretized as follow:

Time forwarding of both (Eq. 21) and (Eq. 22) is explicit and is based on a Runge-Kutta scheme (of 4 th order).

The SPH solver used in this study is SPH-Flow. Boundary conditions are enforced by a Boundary

Integral Method with CutFace Approach (BIM-CFA) [START_REF] Chiron | Fast and accurate SPH modelling of 3D complex wall boundaries in viscous and non viscous flows[END_REF] which requires neither particles on the boundary nor ghost particles. This method reduces implementation complexity and allows to simulate more easily complex geometries. Special care is taken for the parallel implementation of the whole SPH scheme to keep an efficient scalability (almost perfect up to tens of thousands of cores [START_REF] Oger | On distributed memory MPI-based parallelization of SPH codes in massive HPC context[END_REF]).

Comparison of MPS and SPH features to study flooding

In previous paragraphs, both particle methods were introduced with their respective main features. To underline which ones are specific to study flooding scenarios, the following Table 1 sum-up these characteristics.

Table 1: Features for flooding simulations

Features MPS SPH

Solid boundaries

Mirror-particles [START_REF] Hashimoto | A numerical simulation method for transient behavior of damaged ships associated with flooding[END_REF][START_REF] Sueyoshi | Numerical simulation of wave-induced nonlinear motions of a two-dimensional floating body by the moving particle semi-implicit method[END_REF] Integral approach (BIM-CFA) [START_REF] Chiron | Fast and accurate SPH modelling of 3D complex wall boundaries in viscous and non viscous flows[END_REF] Total force calculation Pressure integration on solid boundaries [START_REF] Sueyoshi | Numerical simulation of wave-induced nonlinear motions of a two-dimensional floating body by the moving particle semi-implicit method[END_REF] Pressure integration on solid boundaries with integral approach (BIM-CFA) [START_REF] Chiron | Fast and accurate SPH modelling of 3D complex wall boundaries in viscous and non viscous flows[END_REF] Free-surface handling Conventional method using Naturally handled by the

J = * - . ∇! J J - ∈Ω (22)
the free surface parameter [START_REF] Koshizuka | Moving particle semi-implicit method for fragmentation of incompressible fluid[END_REF] method [START_REF] Colagrossi | Theoretical considerations on the free-surface role in the smoothed-particle-hydrodynamics model[END_REF] Two-phase modeling (details in

MODEL-SCALE EXPERIMENT

The nonlinear behavior of a damaged ship in serious flooding situations is so complicated that it is difficult to directly compare the MPS and SPH methods in time history of ship motion. In that sense, sophisticated situation/experiment is preferable at first for the validation of the particle methods and for the comparative study between the MPS and SPH methods, so that prescribed forced roll tests are conducted instead of water flooding tests. Model-scale experiments for investigating the validity of the numerical methods are performed for a simple two-dimensional damaged model and a realistic three-dimensional flooded model. For the comparison between MPS and SPH methods, a two-dimensional model of a damaged car deck section is selected. A schematic view of the model is given in Fig. 1 and its dimensions are shown in Table 2. The model was made by acrylic with thickness of 0.008m. The model has upper and lower compartments and monotonous side damage is presented along the right broadside for both compartments. Front and rear broadsides are kept closed by acrylic walls (not represented in Fig. 1).

Two-dimensional damaged model

Forced roll tests were conducted at a two-dimensional wave basin at Osaka University. The experimental setup is shown in Fig. 2. The height of roll axis is 0.3m from the bottom of model. A pressure sensor with diameter of 1 cm is installed on the inner sidewall at (x, y) = (-0.242m, 0.160m). The sampling rate for the measurement is 100 Hz. The test conditions are shown in Table 3. The roll period is decided from the designed natural roll period of a PCTC. The body-fixed coordinate system (Fig. 3) is used for the analysis of forced roll test. The moment of inertia of the model and measurement system is omitted by subtracting the forced roll test result in the air conducted with the same amplitude and period. 4. The body-fixed coordinate system is used for the analysis of hydrodynamic forces as in the twodimensional cases, see Fig. 7. The forced roll tests were repeated for the empty and partially filled conditions. The measured hydrodynamic force without floodwater is subtracted from that with floodwater to extract the hydrodynamic force produced by the floodwater, to be directly compared with MPS and SPH calculations.

NUMERICAL RESULTS

Two-dimensional damaged model

The geometry adopted to numerically represent the test configuration is presented in Fig. 8. This numerical tank is composed of straight beaches. This simple geometry is adopted to reduce wave reflections from the ends of the tank and to ease the comparison of flow solvers. More efficient beaches could be implemented but may require more complex tuning depending on particle methods. Fluid viscosity is neglected in both numerical solvers, which is a reasonable assumption when modeling such fast dynamics flows. The forced roll motion is prescribed with a sinusoidal function (Eq. 23). In numerical simulations, it is represented by imposing velocities to the wall particles/elements forming the damaged body. The velocities can be obtained as the differential of the sinusoidal function.

Z = Z [ \ ] 2 T ^_ ` (23)
Comparisons in time series of hydrodynamic force and local pressure between the experimental and numerical results of MPS and SPH methods are presented in Fig. 9-11, for single-phase simulations as a first stage. Regarding execution times of both methods in the present context, we can draw similar conclusions as observed for SPH method. Using an incompressible semi-implicit method permits in practice a gain up to 10 in terms of time steps compared to its explicit weakly-compressible counterpart (this gain is linked to artificial Mach number, 0.1: in implicit method, time step can be driven only by convective velocity which is ten times higher than speed of sound). However this gain is counterbalanced by the additional cost of solving the Pressure Poisson Equation (Eqs. 7-8) and imposing the Dynamic Free-Surface Boundary Condition. So we found very comparable CPU costs for both methods, SPH and MPS, in the end for present single-phase application.

Trapped air modeling

From the comparisons in Section 4.1, the existence of trapped air in the compartment could be the reason of discrepancies between the particle methods and experiment, mainly existing in the twocompartment cases studied. Therefore, in a second stage we accounted for the trapped air effect with different approaches in the MPS and SPH methods as follows.

In MPS-Hydro, the trapped air is assumed to be a single-air pocket and the instantaneous pressure of the compressed air is calculated by Boyle's law. For the numerical implementation, percentage of water particles present at the entrance of the lower damage opening is monitored and used for the judgement whether the lower damage opening is fully submerged or not (i.e. whether the air inside will be trapped or escape to the outside). When it is submerged, the instantaneous air volume (area in two-dimensional case) is measured based on water particle presence in the compartment. It is assumed the shape of trapped air when the compartment just gets submerged is circular and the initial pressure can then be determined as the average hydrostatic pressure at the depth of circle center. The timedependent pressure of the trapped air is then calculated based on Boyle's law (cf. Eq. 24) and it is imposed to free-surface particles and non-wetted wall particles when solving the pressure Poisson equation until the lower damage opening partially exposes to the air. This partial exposure is defined as the existence ratio of water is 80% or less in this study.

[

( ) = [ a a( ) (24)
where [ , [ , a, a denote air pressure, initial air pressure, area of trapped air, initial area of trapped air (in 2-D, otherwise the circle becomes a sphere and the area a volume).

Once it emerges, zero pressure is imposed to the free-surface particles as usual manner. With use of Boyle's law, the effect of air entrapped in the damaged compartment can be considered in a singlephase simulation. It should be noted that with this strategy the CPU cost does not increase because the air pressure is easily imposed to the free-surface particles instead of zero pressure as Dirichlet condition. Of course the counterpart is that this modeling is approximate compared to the actual real two-phase evolution.

Within SPH-flow, the approach to model trapped air is indeed different: the choice is made to fully simulate the air phase presence, as in the literature [START_REF] Grenier | An Hamiltonian SPH formulation for Interfacial and Free-Surface Flows using a Shepard Kernel[END_REF], by solving the two-phase Navier-Stokes equations. Thus an additional set of particles is required to discretize the air domain. These particles evolve in time with the same SPH system of equations (Eqs. [START_REF] Souto-Iglesias | On the consistency of MPS[END_REF][START_REF] Souto-Iglesias | On the consistency of MPS[END_REF] as water particles but the equation of state (Eq. 16) for this gas phase is set with appropriate parameters (polytropic coefficient γ equal to 1.4 and adequate speed of sound to reproduce air compressibility and to be able to describe properly situations where air bubbles are trapped [START_REF] Marrone | Analysis of free-surface flows through energy considerations: Single-phase versus two-phase modeling[END_REF]). Special treatment to ensure mass conservation is also performed at the interface to be compatible with the use of a Riemann solver [START_REF] Hammani | Detailed study on the extension of the δ-SPH model to multi-phase flow[END_REF]. Surface tension effects are not taken into account in the present case due to the rather large scales involved. In order to avoid excessive computational time, the speed of sound of air is artificially decreased to 50m/s.

Real compressibility of air is no more respected but compared to actual convective velocities in the air, this condition ensures a weak-compressibility assumption.

Note that air phase is modelled by a simple air pocket model in MPS (only its surface area is a matter of importance while air pocket has no velocity) while interface jump conditions are applied locally in SPH allowing to solve the flow equations everywhere in air phase (inside and outside air pocket). Note also that Boyle's law (in MPS) is an isentropic law while Tait's equation of state (in SPH) is adiabatic, which could result in slight discrepancies during compression or expansion of high intensity which is not expected in the present study. The comparisons of hydrodynamic force between the two particle methods and the experiment are shown in Figs. [START_REF] Hashimoto | Numerical simulation method for damaged ships under flooding condition[END_REF][START_REF] Hashimoto | A numerical simulation method for transient behavior of damaged ships associated with flooding[END_REF], for the inter-particle distances of 6 mm and 3 mm, respectively. It is observable that both particle methods show similar trend, as it was the case for the two-dimensional cases. The finer resolution using the smaller dx shows better agreement with the experiment in the hydrodynamic force, and the estimated amplitudes of Fy and Mx are generally acceptable. However, discrepancy can be found in their phase. This might be because the effect of air movement is neglected in these threedimensional simulations. Two-phase flow simulations or the Boyle's law approach, presented in

CONCLUSIONS

In order to investigate the capability of particle methods for ship flooding problems, systematic comparisons between the MPS and SPH methods are performed on forced roll tests of a twodimensional damaged and a three-dimensional flooded compartments. For the two-dimensional situations, it is demonstrated that the MPS and SPH methods, using the same inter-particle distance and numerical tank definition, show high similarity in general for all the tested conditions. Although there are minor differences between the two methods in the hydrodynamic force and local pressure, it is difficult to exhibit a ranking of the MPS and SPH methods from comparison results with the experiment. Actually, in single-phase simulations both particle methods are in good agreement with the experiment when trapped air effect is negligibly small. When trapped air is present with a significant role, the two-phase SPH model still provides accurate result in close agreement with the experiment, while the MPS model with Boyle's law yields only a qualitative agreement but without increasing the CPU cost with respect to single-phase simulation. The comparison of the MPS and SPH method is also made for a three-dimensional realistic flooded compartment, and the capability of the particle methods for simulating complex floodwater flows is demonstrated.

section 4. 2 )

 2 Local modification of freesurface boundary condition to handle over-pressure from trapped air pocket Full discretization of air phase[START_REF] Hammani | Detailed study on the extension of the δ-SPH model to multi-phase flow[END_REF]

Fig. 1 :

 1 Fig. 1: 2-D damaged compartment model (front and rear broadsides not represented)

Fig. 2 :

 2 Fig. 2: Experimental setup (2-D)

Fig. 3 :Fig. 4 :Fig. 5 :Fig. 6 :

 3456 Fig. 3: Coordinate system for the forced roll test (2-D)

Fig. 7 :

 7 Fig. 7: Coordinate system for the forced roll test (3-D)

Fig. 8 :

 8 Fig. 8: Numerical tank configuration

Fig. 9 :Fig. 10 :Fig. 11 :Fig. 12 :

 9101112 Fig. 9: Comparison of hydrodynamic forces, moment and relative pressure for one-compartment damage condition with φa = 20 deg, Tφ = 2.5 s. Numerical results are for single-phase simulations.

Fig. 13 :Fig. 14 :Fig. 15 :

 131415 Fig. 13: Comparison of hydrodynamic forces, moment and relative pressure for two-compartment damage condition with φa = 20 deg, Tφ = 2.5 s. Numerical results include partly (MPS) or fully (SPH) the air phase.

Fig. 17 :

 17 Fig. 17: Comparison of hydrodynamic force and moment with φa = 20 deg, Tφ = 2.8 s. Numerical results are for single-phase simulations, with dx = 3.0 mm.

section 4 . 2 ,Fig. 18 : 3 Fig. 19 :

 4218319 Fig. 18: Side views of floodwater situation. Numerical results are for single-phase simulations, with dx = 3.0 mm.

Table 2 :

 2 Dimension

			of the model (2-D)
	B	H	Hbottom	Hlower
	0.5 m	0.35 m	0.035 m	0.085 m
	Hupper	L	R	T
	0.085 m	0.28 m	0.035 m	0.008 m

Table 3 :

 3 Test conditions(2-D)

	servo
	motor
	roll axis
	load cell

Table 4

 4

		: Test condition (3-D)
	amplitude: φa (deg)	period: Tφ (s)	draft: d (m)	height of x-axis (m)
	20	2.8	0.07	0.164

Table 5 :

 5 Simulation parameters (MPS-Hydro)

	time step (s)	ratio re/dx	multiplication coefficient [34]
	0.0002 -0.00025	2.1 & 4.0	1.01
	Table 6: Simulation parameters (SPH-flow)
	Courant number	speed of sound	ratio re/dx
	0.375 (Runge-Kutta 4)	20 m/s	4.0

Table 7 :

 7 Simulation parameters (MPS-Hydro)Here both simulations are performed with different inter-particle distances to check the influence of spatial resolution on the result. The thickness of the ramp and deck floor is 6 mm, so the maximum inter-particle distance should be quite smaller than this value if ghost particles were used for wall boundary condition. However, both in MPS-Hydro and SPH-flow codes we can use an inter-particle distance of 6 mm, same value as the minimum thickness of the model, thanks to the mirror-particles wall boundary condition in MPS and BIM-CFA method in SPH-flow.

	Initial dx [m]	0.006	0.003
	Time step [s]	0.00075	0.000625
	Multiplication coefficient [34]	1.01	1.01
	Number of wall particles	101305	449542
	Number of water particles	105216	842976
	Table 8: Simulation parameters (SPH-flow)
	Initial dx [m]	0.006	0.003
	Number of water particles	104932	837891
	Ratio re/dx	2.459

Fig. 16: Comparison of hydrodynamic force and moment with φa = 20 deg, Tφ = 2.8 s. Numerical results are for single-phase simulations, with dx=6.0mm.

ACKNOWLEDGEMENT

This work was supported by a Grant-in Aid for Scientific Research of the Japan Society for Promotion of Science (No.25289317) and by the Japan Society for the Promotion of Science under the strategic young researcher overseas visits program for accelerating brain circulation on "International Collaboration on Strongly Nonlinear Fluid-Structure Interactions and Nurturing Younger Researchers in Ocean Engineering".

We can notice that raw data is close to filtered data (see Fig. 10) for late periods after transient stage.

We remind that data is averaged over the six last periods for computations and eight last for experiments. Besides, it can be noted that acoustic components are present in the weakly-compressible SPH raw data as expected. One of the effects of the averaging is to filter out these components, which is legitimate since filtering out this acoustic part permits theoretically to recover the incompressible solution.