Federico Perche

Olivier Lambert

Mathieu Berchel

Paul-Alain Jaffres

Chantal Pichon

Gene transfer

Lyoph 3 1. Introduction

Gene therapy aims to use nucleic acids as medicine for curing genetic deficiencies and a large variety of acquired diseases [START_REF] Edelstein | Gene therapy clinical trials worldwide to 2007--an update[END_REF]. Nucleic acids include large plasmid DNA (pDNA), small DNA as antisense oligonucleotides and RNA as ribozymes, siRNA and mRNA. pDNA encodes either proteins, oligonucleotides, ribozymes or siRNA. Their electrostatic complexes with cationic polymers or lipids are proposed as non-viral delivery systems. Accordingly, the development of lipoplexes (complexes with cationic lipids) and polyplexes (complexes with cationic polymers) has drawn much attention over last fifteen years [START_REF] Templeton | Nonviral delivery for genomic therapy of cancer[END_REF][START_REF] Mintzer | Nonviral vectors for gene delivery[END_REF]. A third emerging class of Lipid-Polycation-DNA complexes termed LPD or lipopolyplexes concerns ternary complexes made with liposomes, cationic peptides or polymers and nucleic acids. LPD made with 1,2-dioleoyl-3-trimethylammonium-propane (DOTAP) : cholesterol liposomes plus protamine sulfate or dioleoyl phosphatidylethanolamine (DOPE) : cholesteryl hemisuccinate liposomes plus polylysine were the first ones developed by Huang et al., [START_REF] Gao | Potentiation of cationic liposome-mediated gene delivery by polycations[END_REF][START_REF] Li | In vivo gene transfer via intravenous administration of cationic lipid-protamine-DNA (LPD) complexes[END_REF]. LPD were also used to deliver siRNA for silencing the epidermal growth factor receptor in lung cancer cells [START_REF] Chen | Novel cationic lipid that delivers siRNA and enhances therapeutic effect in lung cancer cells[END_REF]. LPD were used as adjuvant for protein-based vaccines [START_REF] Dileo | Lipidprotamine-DNA-mediated antigen delivery to antigen-presenting cells results in enhanced anti-tumor immune responses[END_REF][START_REF] Vangasseri | Lipid-protamine-DNA-mediated antigen delivery[END_REF] and carrier for mRNAbased vaccines [START_REF] Hoerr | In vivo application of RNA leads to induction of specific cytotoxic T lymphocytes and antibodies[END_REF][START_REF] Weide | Plasmid DNA-and messenger RNA-based anti-cancer vaccination[END_REF]. We also reported that LPD were efficient system for mRNA-based vaccine. For this purpose, mRNA encoding tumor antigen was complexed with a PEGylated histidine-rich polylysine and the resulting polyplexes were encapsulated in L-histidine-(N,Ndi-n-hexadecylamine)ethylamide : cholesterol liposomes [START_REF] Mockey | mRNA-based cancer vaccine: prevention of B16 melanoma progression and metastasis by systemic injection of MART1 mRNA histidylated lipopolyplexes[END_REF]. The histidine groups of these molecules promote membrane destabilization in acidic medium allowing nucleic acid delivery in the cytosol [START_REF] Midoux | Efficient gene transfer by histidylated polylysine/pDNA complexes[END_REF][START_REF] Kumar | Single histidine residue in head-group region is sufficient to impart remarkable gene transfection properties to cationic lipids: evidence for histidine-mediated membrane fusion at acidic pH[END_REF]. LPD are ternary complexes that are usually prepared extemporaneously before their use, a procedure that limits storage of large quantities and would be difficult to handle by medical personnel for in vivo applications.

In the present study, we examined whether LPD dehydration would be an interesting storage option. We measured the transfection efficiency (TE) recovery of reconstituted LPD Lyoph 4 upon either lyophilisation or evaporation. pDNA was first condensed with PEGylated histidylated polylysine and subsequently a liposomal formulation was added to form LPD.

For LPD100, O,O-dioleyl-N-(3N-(N-methylimidazolium iodide)propylene) phosphoramidate)

(1) : O,O-dioleyl-N-histamine Phosphoramidate (3) liposomes were used [START_REF] Mevel | Novel neutral imidazole-lipophosphoramides for transfection assays[END_REF][START_REF] Mevel | Synthesis and transfection activity of new cationic phosphoramidate lipids: high efficiency of an imidazolium derivative[END_REF] (Scheme 1).

The lipophosphoramidate 2 possesses an N-methylimidazolium polar head conferring a permanent positive charge for DNA condensation. The imidazole group of the neutral colipid 3 which can acquire a cationic charge when the pH of the medium drops bellow pH 6 was used to favour endosome destabilisation and pDNA delivery in the cytosol. We previously reported that lipoplexes formed with those liposomes exhibited efficient transfection [START_REF] Mevel | Novel neutral imidazole-lipophosphoramides for transfection assays[END_REF][START_REF] Mevel | Synthesis and transfection activity of new cationic phosphoramidate lipids: high efficiency of an imidazolium derivative[END_REF].

Lipophosphoramidates have a chemical structure which is bio-inspired from the natural phospholipids present in the cell membranes and most of these synthetic vectors proved to exhibit a moderate or low toxicity according to in vitro [START_REF] Lamarche | Lipophosphoramidates as lipidic part of lipospermines for gene delivery[END_REF][START_REF] Mevel | Dicationic lipophosphoramidates as DNA carriers[END_REF] and in vivo [START_REF] Picquet | Cationic lipophosphoramidates and lipophosphoguanidines are very efficient for in vivo DNA delivery[END_REF][START_REF] Gall | A novel cationic lipophosphoramidate with di-unsaturated lipid chains : synthesis, physico-chemical and transfection activities[END_REF] transfection assays. The best preservation of LPD100 TE was obtained after evaporation rather than lyophilisation. Moreover, TE of evaporated LPD100 was preserved upon one month storage. When LPD100 were prepared with dehydrated pDNA/PEGylated histidylated polylysine complexes and fresh liposomes, TE was as efficient as with fresh ones.

Materials and Methods

Preparation of liposomes

Liposomes 100 (lip 100) were prepared by mixing at a molar ratio of 1:1, 1 mL of 5.4 mM O,O-dioleyl-N-[3N-(N-methylimidazolium iodide)propylene] Phosphoramidate (1) in ethanol and 1 mL of 5.4 mM O,O-dioleyl-N-histamine Phosphoramidate (2) in ethanol [START_REF] Mevel | Novel neutral imidazole-lipophosphoramides for transfection assays[END_REF][START_REF] Mevel | Synthesis and transfection activity of new cationic phosphoramidate lipids: high efficiency of an imidazolium derivative[END_REF]. Ethanol solution was evaporated until formation of a film. The film was hydrated for 12 h at 4°C in 1 mL of 10 mM hepes buffer, pH 7.4, vortexed and then the suspension was sonicated for 15 min at 37 kHz at 20°C using a Bioblock ultrasonic bath (Bioblock Scientific, Illkirch, France). Lyoph 5

Plasmid DNA

pTG11033 was a plasmid DNA of 9514 bp (kindly given by Trangène S.A., Strasbourg, France) encoding the luciferase gene of Photinus pyralis (Firefly luciferase, FLuc) under the cytomegalovirus (CMV) promoter. Supercoiled DNA was isolated from E. Coli DH5α supercompetent bacteria (Invitrogen, Cergy Pontoise, France) by alkali lysis and purification with QIAGEN Mega Kit Endotoxin free Plasmid (Qiagen, Courtaboeuf, France).

Polymer

PEGylated histidylated poly-L-Lysine (PEG-HpK) was synthesized as previously described [START_REF] Mockey | mRNA-based cancer vaccine: prevention of B16 melanoma progression and metastasis by systemic injection of MART1 mRNA histidylated lipopolyplexes[END_REF][START_REF] Midoux | Efficient gene transfer by histidylated polylysine/pDNA complexes[END_REF].

Lipopolyplexes

Polyplexes (PX) were prepared at a DNA / polymer weight ratio of 1:3 (μg : μg) by adding dropwise PEG-HpK (15 μg in 5 μL 10 mM Hepes buffer, pH 7.4) to DNA (5 μg in 25 μL 10 mM hepes buffer, pH 7.4) and mixing for 4 sec. After 30 min at 20°C, LPD were formed by adding liposomes (5 μL at 5.4 mM; 10 μg) to PX, a gentle mixing and letting the solution stand for 15 min at 20°C. For transfection assays with fresh LPD, the solution was adjusted to 1 mL with serum-free medium, made 0.15 M NaCl with a 5 M NaCl solution. For LPD dehydration, the solution was adjusted to 500 µL with 10 mM Hepes buffer, pH 7.4.

When indicated, the solution was adjusted to 0.15 M NaCl with a 5 M NaCl solution and / or was diluted with a 50% saccharose solution (Sigma). For transfection assays with dehydrated LPD, the solution was reconstituted by adding 500 µL of water and 500 µL serum-free medium.

Lyophilization

PX and LPD (5 µg of plasmid DNA) at a final volume of 500 µL in polypropylene cryotubes closed with a cap pitted with holes made with a 25G  5/8" needle (Terumo, Guyancourt, France) were frozen progressively (-1°C per min) in isopropanol (>99.5%, Lyoph 6

Fischer Scientific) using a Mr Frosty container (Dominique Dutscher, Brumath, France) placed in a -70°C freezer during 12h and freeze-dried at -55°C, 0.05 mbar with an Alpha 1-2 LD Plus lyophilizer (Christ, Osterode, Germany) and a vacuubrand rotary vane vacuum pump RZ 2.5 (Vacuubrand GMBH + CO KG, Wertheim, Germany) during 18h without secondary dessication.

Evaporation

PX and LPD dehydration was carried out at a final volume of 500 µL in 1.5 mL polypropylene tube during 8h in a Speedvac (Speedvac SC110A, Savant; Refrigerated Vapor Trap RVT 400, Savant) at 35°C, 10 mbar. When indicated, PX and LPD were frozen progressively (-1°C per min) in isopropanol before evaporation.

DNA quantitation

The quantity of DNA in reconstituted PX and LPD was determined by fluorescence measurement in the presence of 12 µg/mL of ethidium bromide (Promega, Charbonnières-les-Bains , France) and 0.05 mg/mL 500 kDa dextran sulfate (Sigma) in 96 wells plates. The fluorescence intensity was measured at 620/10 nm upon excitation at 531/25 nm with Victor I spectrophotometer (1420 Multilabel Counter Victor, Wallac) after 30 min of agitation on an agitating plate.

Lipid quantitation

The lipid concentration in reconstituted LPD was determined by fluorescence measurement in the presence of Nile Red in 96 well plates. LPD (10 µL in 70 µL of 10 mM HEPES, pH 7.4) were mixed with 20 µL of a Nile Red solution (1 µM in methanol, Sigma).

The mixture was agitated for 5 min at room temperature on an agitating plate. The fluorescence intensity was measured at 620/10 nm upon excitation at 531/25 nm with Victor I spectrofluorophotometer.

Size and ζ potential measurements

Lyoph 7

The size and ζ potential of PX and LPD were measured at 7 µg/mL DNA by dynamic light scattering and electrophoretic mobility with ZetaSizer 3000 (Malvern Instruments, Orsay, France), respectively as previously described [START_REF] Midoux | Efficient gene transfer by histidylated polylysine/pDNA complexes[END_REF]. 20µL of liposomes or LPD containing 10µg DNA were diluted into 1.2 mL of 10 mM HEPES buffer pH 7.4.

Cells and cell culture

Human embryonic kidney 293T7 cells were grown at 37°C in a humidified atmosphere containing 5% CO 2 in MEM medium containing 10% heat inactivated fetal bovine serum (PAA Laboratories, Les Mureaux, France), 2 mM L-glutamine (Fischer Bioblock, Illkirch, France), 100 U/mL penicillin (Fischer Bioblock) and 100 U/mL streptomycin (Fischer Bioblock) [START_REF] Brisson | Subcellular trafficking of the cytoplasmic expression system[END_REF]. The cells were cultured in the presence of geneticin (400 mg/mL) to maintain selection of T7 transformants. Cells were mycoplasma-free as evidenced by bisbenzimidazole (Hoechst 33258, Molecular Probes) [START_REF] Chen | In situ detection of mycoplasma contamination in cell cultures by fluorescent Hoechst 33258 stain[END_REF].

Transfections

Two days before transfection, cells were seeded in 24 well culture plates at density of 1.2 x10 5 cells/cm². At the time of transfection cells were 80% confluent. Cells were then incubated for 4 h at 37°C with 0.5 mL (2.5 µg DNA) transfection solution. Then, the transfection medium was removed, replaced by fresh complete culture medium and cultured for 44 h before measurement of the luciferase activity.

Luciferase activity

Luciferase activity was measured using a Lumat LB9507 luminometer (Lumat LB9507, Berthold, Wildbach, Germany) and luciferase activity (Relative Light units, RLU) was expressed per milligrams of proteins according to [START_REF] Midoux | Specific gene transfer mediated by lactosylated poly-L-lysine into hepatoma cells[END_REF]. The amount of proteins was determined by modified bicinchoninic assay and the luciferase activity was normalized to RLU per milligram extracted protein.

Lyoph 8

Results

Lyophilisation of lipopolyplexes

LPD were slowly frozen and lyophilized in Hepes buffer. The transfection of HEK293T cells with a plasmid encoding luciferase was used as read-out to test the preservation of LPD activity upon dehydration. As shown in figure 1, when LPD100 and LPD23 were freeze-dried without salt or any cryoprotectant, the luciferase activity obtained with reconstituted LPD was two orders of magnitude lower than that with fresh ones. When LPD23 were freeze-dried in the presence of 0.15 M NaCl, the luciferase activity decreased also strongly (Fig. 2). This was also the case with LPD100 (not shown). This strong decrease was not associated with a lower amount of DNA and lipids in reconstituted LPD. Indeed, the quantities of DNA and lipids before lyophilisation and after rehydration of freeze-dried LPD were equal (data not shown). Table 1 shows the effect of lyophilisation on LPD size. Fresh LPD100 exhibited an average size of 118 ± 37 nm in the absence of salts. At physiological salt concentration, fresh LPD100 formed aggregates of 1.7 µm. Upon lyophilisation in the presence of salt, the size of reconstituted LPD100 was ~50% smaller than fresh ones. Sugars are often employed as excipient for liposomes cryopreservation. When 2 mg D-Mannitol were added to LPD23 solution before lyophilisation, TE of reconstituted LPD was better (15% of that obtained with fresh LPD) than when lyophilisation was carried out in the absence of D-Mannitol (Fig. 2). As checked by agarose gel electrophoresis, all pDNA did not migrate in the presence of 2 mg D-Mannitol meaning that sugar did not dissociate LPD (not shown). TE of LPD23 lyophilized in the presence of 0.15 M NaCl plus 2 mg D-Mannitol was a little bit more (20%) protected (Fig. 2). This was also the case for LPD100 (not shown). Note that under the latter conditions, the size of reconstituted LPD23 was small (168 nm) compared to that of LPD100 (Table 1). This small size could negatively affect their TE in vitro but it could be an advantage for transfection in vivo.

Lyoph 9

Evaporation of lipopolyplexes

Whilst rarely employed, evaporation with speedvac can be used for LPD dehydration.

Taking into account that freezing step causes LPD aggregation, and evaporation of unfrozen LPD produces giant liposomes [START_REF] Pick | Liposomes with a large trapping capacity prepared by freezing and thawing of sonicated phospholipid mixtures[END_REF], the evaporation of unfrozen or frozen LPD100 was tested. The evaporation of unfrozen LPD100 carried out in the presence of 0.15 M NaCl did not drastically destroy their TE (Fig. 3). The luciferase activity was about half that of fresh LPD100 for a hydration time of 1h or 2h but was only of one third for 5 min or 30 min hydration time. The optimal hydration time for LPD recovery was at least 1 h. Next, we compared LPD evaporation in the presence of either salt, D-Mannitol or salt plus D-Mannitol.

Evaporation of LPD100 in the presence of 0.15 M NaCl gave the best TE recovery (Fig. 4).

The luciferase activity was half of that obtained with fresh LPD. For LPD23, TE recovery was 10% at the best (Fig. 4 insert). This protocol was reproducible since the TE of three different LPD100 preparations made at three different times was not statically different (Fig. 5). In contrast, TE recovery was lower when LPD were frozen before evaporation. The presence of D-Mannitol allowed reconstitution of small LPD100 (440 nm versus 1.7 µm) (Table 1). Note that TE of the latter was 10% of that obtained with the fresh ones (Fig. 4). Reconstituted frozen LPD100 evaporated in the presence of salts exhibited a smaller size than fresh ones (~700 nm versus 1.7 µm) (Table 1).

Lipopolyplexes stability

TE of fresh LPD was not conserved after 1 month storage at 4°C. Compared to fresh LPD100, TE were indeed 13%. We evaluated the stability of reconstituted LPD after evaporation in the presence of 0.15 M NaCl (Fig. 6 mettre 1 mois direct). The stability was checked after 1 month in solution at 4°C or -20°C. TE of LPD was also tested after reconstitution from powder conserved 1 month at -20°C. A good preservation of LPD100 (60% recovery) was observed after 1 month at -20°C either as solution or powder. Lyoph 10

Lipopolyplexes made with dehydrated polyplexes

LPD were prepared with dehydrated PX (PEG-HpK polyplexes) and fresh liposomes to assume that the lost of TE of dehydrated LPD did not come from dehydration sensitivity of PX. It has been reported that lyophilisation of PX made with PEI or block copolymers did not impair TE [START_REF] Hobel | Polyethylenimine PEI F25-LMW allows the long-term storage of frozen complexes as fully active reagents in siRNA-mediated gene targeting and DNA delivery[END_REF][START_REF] Brus | Stabilization of oligonucleotide-polyethylenimine complexes by freeze-drying: physicochemical and biological characterization[END_REF][START_REF] Werth | A low molecular weight fraction of polyethylenimine (PEI) displays increased transfection efficiency of DNA and siRNA in fresh or lyophilized complexes[END_REF][START_REF] Miyata | Freeze-dried formulations for in vivo gene delivery of PEGylated polyplex micelles with disulfide crosslinked cores to the liver[END_REF]. As expected, TE of PEG-HpK PX was preserved after lyophilisation or evaporation (Fig. 7). TE of LPD100 made with freeze-dried PX were comparable and were only reduced by 30% to 40% compared to that of fresh LPD (Fig. 7 insert). Interestingly, TE of LPD100 reconstituted with evaporated PX was even 2-fold higher than fresh LPD100 (Fig. 8). Note that the optimal hydration time of PX was about 1 h.

Discussion

LPD prepared by the addition of a selected liposomal formulation on preformed polyplexes (PX) are promising non-viral nucleic acids delivery systems. Here, PX were formed between a PEGylated histidylated polylysine and pDNA and LPD were prepared by the addition of liposomes 100. We previously shown that Lipoplexes with 100 exhibited powerful DNA transfection [START_REF] Kumar | Single histidine residue in head-group region is sufficient to impart remarkable gene transfection properties to cationic lipids: evidence for histidine-mediated membrane fusion at acidic pH[END_REF][START_REF] Mevel | Novel neutral imidazole-lipophosphoramides for transfection assays[END_REF][START_REF] Mevel | Synthesis and transfection activity of new cationic phosphoramidate lipids: high efficiency of an imidazolium derivative[END_REF]. Usually, LPD are prepared extemporaneously before their use, a procedure that limits storage of large quantities and would be difficult to handle by medical personnel. Therefore, the preparation of efficient dehydrated LPD would be an interesting option since only hydration will be carried out before in vivo administration. For this purpose, lyophilisation has been applied to lipoplexes [START_REF] Chen | An overview of liposome lyophilization and its future potential[END_REF][START_REF] Clement | Large-scale production of lipoplexes with long shelf-life[END_REF][START_REF] Zhong | Characteristics comparison before and after lyophilization of transferrin modified Procationic-Liposome-Protamine-DNA complexes (Tf-PLPD)[END_REF], polyplexes [START_REF] Sun | Growth inhibition of the pulmonary metastatic tumors by systemic delivery of the p27 kip1 gene using lyophilized lipid-polycation-DNA complexes[END_REF][START_REF] Terakita | The influence of water on the stability of lyophilized formulations with inositol and mannitol as excipients[END_REF][START_REF] Grit | Chemical stability of liposomes: implications for their physical stability[END_REF][START_REF] Li | Lyophilization of cationic lipid-protamine-DNA (LPD) complexes[END_REF][START_REF] Mao | Chitosan-DNA nanoparticles as gene carriers: synthesis, characterization and transfection efficiency[END_REF], LPD [START_REF] Hobel | Polyethylenimine PEI F25-LMW allows the long-term storage of frozen complexes as fully active reagents in siRNA-mediated gene targeting and DNA delivery[END_REF][START_REF] Sun | Growth inhibition of the pulmonary metastatic tumors by systemic delivery of the p27 kip1 gene using lyophilized lipid-polycation-DNA complexes[END_REF] and siRNA-liposomes complexes [START_REF] Terakita | The influence of water on the stability of lyophilized formulations with inositol and mannitol as excipients[END_REF][START_REF] Grit | Chemical stability of liposomes: implications for their physical stability[END_REF]. In this last case, dehydration increased the stability of siRNA-liposomes complexes by immobilization and elimination of water which is a powerful oxidant (hydrolysis) and associated water. It has been also observed that the absence of cryoprotectant produces higher particles-sizes that reduce subsequently the transfection efficiency [START_REF] Yadava | Effect of lyophilization and freezethawing on the stability of siRNA-liposome complexes[END_REF]. A rapid freezing of lipoplexes in liquid nitrogen before lyophilisation has been reported to preserve their activity after rehydration [START_REF] Li | Lyophilization of cationic lipid-protamine-DNA (LPD) complexes[END_REF][START_REF] Anchordoquy | Physical stability of nonviral plasmid-based therapeutics[END_REF][START_REF] Maitani | Effect of sugars on storage stability of lyophilized liposome/DNA complexes with high transfection efficiency[END_REF]. Here, Lyoph 11 we decided to slowly freeze LPD according to [START_REF] Higgins | Factors influencing cryoprotective activity and drug leakage from liposomes after freezing[END_REF][START_REF] Mohammed | Lyophilisation and sterilisation of liposomal vaccines to produce stable and sterile products[END_REF]. In addition, LPD were lyophilized in Hepes buffer to prevent acidification during water elimination [START_REF] Hobel | Polyethylenimine PEI F25-LMW allows the long-term storage of frozen complexes as fully active reagents in siRNA-mediated gene targeting and DNA delivery[END_REF]. But, the TE recovery of our LPD dramatically decreased after lyophilisation. Dehydration submits LPD to dehydration stress, vacuum stress, temperature stress and rehydration stress. These stresses can decrease when a cryoprotectant is added to protect both sides of the liposomal membrane. For this purpose, sugars and especially disaccharides which are naturally used by many organisms to increase resistance to dehydration, are employed as excipients for cryopreservation of liposomes [START_REF] Crowe | Lessons from nature: the role of sugars in anhydrobiosis[END_REF]. In prokaryotes, protection by cryoprotectants is explained by mechanisms including water replacement hypothesis [START_REF] Potts | Desiccation tolerance of prokaryotes[END_REF]. The particle isolation hypothesis has been proposed to explain stability of lipid/DNA complexes after lyophilisation in the presence of sugars [START_REF] Allison | Stabilization of lipid/DNA complexes during the freezing step of the lyophilization process: the particle isolation hypothesis[END_REF]. These sugars included inulin [START_REF] Hinrichs | The choice of a suitable oligosaccharide to prevent aggregation of PEGylated nanoparticles during freeze thawing and freeze drying[END_REF], dextran [START_REF] Hinrichs | The choice of a suitable oligosaccharide to prevent aggregation of PEGylated nanoparticles during freeze thawing and freeze drying[END_REF], dextrose, galactose, mannose [START_REF] Li | Lyophilization of cationic lipid-protamine-DNA (LPD) complexes[END_REF], sucrose [START_REF] Maitani | Effect of sugars on storage stability of lyophilized liposome/DNA complexes with high transfection efficiency[END_REF][START_REF] Molina | Maintenance of nonviral vector particle size during the freezing step of the lyophilization process is insufficient for preservation of activity: insight from other structural indicators[END_REF], trehalose [START_REF] Brus | Stabilization of oligonucleotide-polyethylenimine complexes by freeze-drying: physicochemical and biological characterization[END_REF][START_REF] Li | Lyophilization of cationic lipid-protamine-DNA (LPD) complexes[END_REF][START_REF] Mohammed | Lyophilisation and sterilisation of liposomal vaccines to produce stable and sterile products[END_REF][START_REF] Anchordoquy | Maintenance of transfection rates and physical characterization of lipid/DNA complexes after freeze-drying and rehydration[END_REF], alkylglycosides [START_REF] Bendas | Synthetic glycolipids as membrane-bound cryoprotectants in the freezedrying process of liposomes[END_REF] and D-Mannitol [START_REF] Cortesi | Effect of DNA complexation and freezedrying on the physicochemical characteristics of cationic liposomes[END_REF].

Unfortunately, TE of LPD100 dramatically dropped (90% to 80%) upon lyophilisation in the presence of 2 mg D-Mannitol as well as in presence of salt plus 2 mg D-Mannitol. Higher concentration of D-Mannitol should have a better effect. But, we used this sugar concentration to prevent dilutions which have to be done after reconstitution to preserve isotonicity of solutions before administration [START_REF] Molina | Maintenance of nonviral vector particle size during the freezing step of the lyophilization process is insufficient for preservation of activity: insight from other structural indicators[END_REF]. We found that lyophilisation of PX formed with PEG-HpK polymer preserved their TE. When LPD were prepared with freeze-dried PX and fresh liposomes, 60% to 70% of TE was preserved for the two types of LPD meaning that dehydration of liposomes was the major hurdle. Nevertheless, PX dehydration should be a minimal option for storage.

Although lyophilisation is the main technique used for lipoplexes, PX and LPD dehydration, evaporation by speedvac is more seldom [START_REF] Montanari | Avoiding failed reconstitution of ultradeformable liposomes upon dehydration[END_REF]. Speedvac is made of a centrifuge and a vacuum pump. The vacuum is inferior to that of a freeze-drier, so the vacuum stress is lower. Evaporation is carried out in a confined area at room temperature while lyophilisation Lyoph 12 is done at -50°C. So, speedvac evaporation could be less stressing for LPD. In contrast to lyophilisation, we observed that evaporated LPD100 retained 50% TE upon reconstitution.

LPD evaporation in the presence of 0.15 M NaCl without prior freezing and was found to be the optimal protocol for LPD100. Under this condition, the reconstitution of LPD is obtained just by adding water. Remarkably, LPD100 retained 60% transfection effciciency after one month at -20°C either as solution or powder.

The mixture of the two lipophoramidates (1 and 2) remaining miscible upon hydration is likely in favour of the high TE recovery upon LPD100 dehydration.

LPD with a small size and a good TE recovery in vitro could be obviously used for in vivo administration. Among them, ??? of salts and fresh liposomes exhibited good recovery.

Despite their low TE recovery ?? could be effective in vivo due to their smaller size.

Conclusion

The storage of LPD100 with preservation of the transfection efficiency was obtained after dehydration by evaporation.

Figure legends Scheme 1 :

 1 Figure legends

Figure 1 :

 1 Figure 1: Effect of LPD lyophilization on the transfection efficiency. 293T7 cells were

Figure 2 :

 2 Figure 2: Effect of evaporation on the transfection efficiency of LPD. 293 T7 cells were

Figure 3 :

 3 Figure 3: Effect of NaCl and saccharose on the transfection efficiency of evaporated

Figure 4 :

 4 Figure 4: Reproductibility of the transfection efficiency of LPD after evaporation. 293

Figure 5 :

 5 Figure 5: LPD stability. 293 T7 cells were transfected with fresh LPD 100, LPD 100 kept at

Figure 6 :

 6 Figure 6: Effect of PX dehydration on the transfection efficiency of PX and LPD. 293T7

Figure 7 :

 7 Figure 7: Effect of PX evaporation on the transfection efficiency of LPD. 293 T7 cells

Figure 8 :

 8 Figure 8: Measure of pDNA by fluorescence either complexed or complexed and treated

Table I : LPD and PX size and ζ potential values.

 I

	LPD	Size (nm)	ζ (mV)		DNA
					recovery
					%
		fresh LDP
	-NaCl	136 ± 5.4	14.1 ± 2.5	90 ± 1.5
	+ NaCl	1141 ± 179	0.6 ± 8.2	90 ± 1.5
	10% saccharose	144 ± 2.5	19 ± 2.6	87 ± 2
	20% saccharose	152.5 ± 3	20.1 ± 3.3	87.5 ± 3
	NaCl 10%	1458 ± 15	-0.2 ± 4.2	±
	saccharose
	freeze-dried LPD
	-NaCl	370 ± 200	11.5 ± 2.8	41 ± 0.6
	+ NaCl	684 ± 85	-1.9 ± 2.1	69 ± 7
	10% saccharose	475 ± 60	10.1 ± 2	39 ± 0.8
	20% saccharose	702 ± 490	10.8 ± 1.5 35.5 ± 1.6
	NaCl 10%	1140 ± 142	5.3 ± 3.4	53 ± 2
	saccharose
		evaporated LPD
	-NaCl	±	±		6.5 ± 1.7
	+ NaCl	785 ± 140	3.5 ± 3.7	42.4 ± 2
	10% saccharose	283 ± 5	15.5 ± 3.8 24.5 ± 0.7
	20% saccharose	180 ± 31	10.4 ± 6.2 15.3 ± 1.5
	NaCl 10%	786 ± 20	2.7 ± 8.6 41.2 ± 1.2
	saccharose
		LPD made with
		dehydrated PX
	+ NaCl	658 ± 42	±		±
	PX	Size (nm)	ζ (mV)	DNA recovery
					%
		fresh
	-NaCl	181 ± 1	±		±
	+ NaCl	1263 ± 14	±		±
		freeze-dried
	-NaCl	nd	±		±
	+ NaCl	500 ± 704	±		±
	10% saccharose	±	±		±
	20% saccharose	±	±		±
	NaCl 10% saccharose	±	±		±

Acknowledgements

We warmly thank Dr Arabinda Chaudhuri (Indian Institute of Chemical Technology, Hyderabad, India) for the synthesis of L-histidine-(N,N-di-n-hexadecylamine)ethylamide.

Remercier Ulysse Asseline.

This work was supported by grant from Ligue Nationale contre le Cancer (Région Centre). FP was a recipient of a fellowship from Ligue Nationale contre le Cancer.

Lyoph 13


Gauthier Roubaud

Pierre Bondareff

Giorgio Volpe

Sylvain Gigan

Sébastien Bidault
email: sebastien.bidault@espci.fr

Samuel Grésillon
email: samuel.gresillon@espci.fr

†institut Langevin

Far-Field Wavefront Control of Nonlinear Luminescence in Disordered Gold Metasurfaces

Keywords: Wavefront shaping, plasmonics, metasurfaces, nonlinear luminescence, disordered

come

media Disorder in complex media has recently undergone a paradigm shift with the ability to control multiply-scattered light using wavefront shaping: from a major drawback when considering aberrations and attenuation through diffusion, disorder becomes a powerful tool to engineer wave propagation in space [START_REF] Vellekoop | Focusing coherent light through opaque strongly scattering media[END_REF][START_REF] Popoff | Measuring the Transmission Matrix in Optics: An Approach to the Study and Control of Light Propagation in Disordered Media[END_REF][START_REF] Park | Subwavelength light focusing using random nanoparticles[END_REF] and time. [START_REF] Aulbach | Control of Light Transmission through Opaque Scattering Media in Space and Time[END_REF][START_REF] Katz | Focusing and compression of ultrashort pulses through scattering media[END_REF][START_REF] Mosk | Controlling waves in space and time for imaging and focusing in complex media[END_REF][START_REF] Mounaix | Spatiotemporal Coherent Control of Light through a Multiple Scattering Medium with the Multispectral Transmission Matrix[END_REF][START_REF] Rotter | Light fields in complex media: Mesoscopic scattering meets wave control[END_REF] A scattering medium can be programmed as an adaptable lens, [START_REF] Vellekoop | Focusing coherent light through opaque strongly scattering media[END_REF][START_REF] Popoff | Measuring the Transmission Matrix in Optics: An Approach to the Study and Control of Light Propagation in Disordered Media[END_REF][START_REF] Park | Subwavelength light focusing using random nanoparticles[END_REF][START_REF] Vellekoop | Phase control algorithms for focusing light through turbid media[END_REF][START_REF] Conkey | Genetic algorithm optimization for focusing through turbid media in noisy environments[END_REF][START_REF] Boniface | Transmission-matrixbased point-spread-function engineering through a complex medium[END_REF] a pulse shaper [START_REF] Mounaix | Spatiotemporal Coherent Control of Light through a Multiple Scattering Medium with the Multispectral Transmission Matrix[END_REF][START_REF] Mounaix | Temporal recompression through a scattering medium via a broadband transmission matrix[END_REF] or an optical processor. [START_REF] Dong | Optical Reservoir Computing Using 16 Multiple Light Scattering for Chaotic Systems Prediction[END_REF] On the other hand, plasmonic resonators, with their ability to confine and enhance electromagnetic fields at deep subwavelength scales, [START_REF] Gresillon | Experimental observation of localized optical excitations in random metal-dielectric films[END_REF][START_REF] Li | Self-similar chain of metal nanospheres as an efficient nanolens[END_REF] provide complementary degrees of freedom in controlling the propagation of light.

Designing metallic antennas and surfaces with coupled plasmonic modes indeed allows farfield phase modulation to tune local electric fields. [START_REF] Aeschlimann | Adaptive subwavelength control of nano-optical fields[END_REF][START_REF] Volpe | Controlling the Optical Near Field of Nanoantennas with Spatial Phase-Shaped Beams[END_REF][START_REF] Devilez | Mode-balancing far-field control of light localization in nanoantennas[END_REF][START_REF] Volpe | Deterministic Subwavelength Control of Light Confinement in Nanostructures[END_REF][START_REF] Gjonaj | Active spatial control of plasmonic fields[END_REF][START_REF] Kao | Coherent Control of Nanoscale Light Localization in Metamaterial: Creating and Positioning Isolated Subwavelength Energy Hot Spots[END_REF][START_REF] Kao | Digitally" Addressable Focusing of Light into a Subwavelength Hot Spot[END_REF][START_REF] Veksler | Multiple Wavefront Shaping by Metasurface Based on Mixed Random Antenna Groups[END_REF][START_REF] Zhang | Nanoscale Switching of Near-Infrared Hot Spots in Plasmonic Oligomers Probed by Two-Photon Absorption in Photopolymers[END_REF] It is, for instance, possible to turn on or off the field enhancement in a nanoparticle dimer [START_REF] Volpe | Controlling the Optical Near Field of Nanoantennas with Spatial Phase-Shaped Beams[END_REF] or to switch between several hotspots in a more complex nanoantenna. [START_REF] Aeschlimann | Adaptive subwavelength control of nano-optical fields[END_REF][START_REF] Devilez | Mode-balancing far-field control of light localization in nanoantennas[END_REF][START_REF] Volpe | Deterministic Subwavelength Control of Light Confinement in Nanostructures[END_REF][START_REF] Zhang | Nanoscale Switching of Near-Infrared Hot Spots in Plasmonic Oligomers Probed by Two-Photon Absorption in Photopolymers[END_REF] However, the use of simple resonators strongly limits the number and position of hotspots that can be controlled. Deterministic 2D surfaces can be engineered to provide extra degrees of freedom for wavefront shaping [START_REF] Kao | Coherent Control of Nanoscale Light Localization in Metamaterial: Creating and Positioning Isolated Subwavelength Energy Hot Spots[END_REF] but their fabrication by focused ion beam milling is difficult and costly; and their programmability is very sensitive to fabrication errors. [START_REF] Kao | Digitally" Addressable Focusing of Light into a Subwavelength Hot Spot[END_REF] As an alternative, we propose to use disordered gold metasurfaces that are easy and cost-effective to fabricate and which feature both strong local field enhancements, or hotspots, at numerous positions of the sample, as well as delocalized plasmonic modes [START_REF] Gresillon | Experimental observation of localized optical excitations in random metal-dielectric films[END_REF][START_REF] Stockman | Localization versus Delocalization of Surface Plasmons in Nanosystems: Can One State Have Both Characteristics?[END_REF][START_REF] Seal | Coexistence of Localized and Delocalized Surface Plasmon Modes in Percolating Metal Films[END_REF][START_REF] Krachmalnicoff | Fluctuations of the Local Density of States Probe Localized Surface Plasmons on Disordered Metal Films[END_REF][START_REF] Castanie | Distance dependence of the local density of states in the near field of a disordered plasmonic film[END_REF][START_REF] Awada | Experimental study of hot spots in gold/glass nanocomposite films by photoemission electron microscopy[END_REF] that can be coherently modulated. [START_REF] Gunn | Polarization and Phase Control of Remote Surface-Plasmon-Mediated Two-Photon-Induced Emission and Waveguiding[END_REF][START_REF] Gunn | Measurement and Control of Ultrashort Optical Pulse Propagation in Metal Nanoparticle-Covered Dielectric Surfaces[END_REF][START_REF] Aeschlimann | Nano-Optical Control of Hot-Spot Field Superenhancement on a Corrugated Silver Surface[END_REF][START_REF] Bondareff | Probing Extended Modes on Disordered Plasmonic Networks by Wavefront Shaping[END_REF] Furthermore, disordered or aperiodic metasurfaces made of coupled resonators exhibit stronger local field enhancements than comparable regular arrays. [START_REF] Gopinath | Deterministic aperiodic arrays of metal nanoparticles for surface-enhanced Raman scattering (SERS)[END_REF][START_REF] Savo | Localization of electromagnetic fields in disordered metamaterials[END_REF] We demonstrate here that optical hotspots in disordered plasmonic surfaces are coherently optimized using wavefront shaping; proving that electric near-fields can be engineered using a far-field phase modulation.

Disordered gold films are fabricated by depositing gradually a nanometer-scale layer of gold on a glass substrate: partial dewetting of the metal leads to the formation of random islands that can exhibit electrical percolation if a given filling fraction of gold, ff , is reached on the surface (called percolation threshold, see supporting information for more details). [START_REF] Voss | Fractal (Scaling) Clusters in Thin Gold Films near the Percolation Threshold[END_REF] These rough metallic surfaces have been extensively used as substrates for surface-enhanced spectroscopy [START_REF] Moskovits | Surface roughness and the enhanced intensity of Raman scattering by molecules adsorbed on metals[END_REF][START_REF] Hartstein | Enhancement of the Infrared Absorption from Molecular Monolayers with Thin Metal Overlayers[END_REF][START_REF] Biteen | Enhanced Radiative Emission Rate and Quantum Efficiency in Coupled Silicon Nanocrystal-Nanostructured Gold Emitters[END_REF] as they feature strong local field enhancements [START_REF] Gresillon | Experimental observation of localized optical excitations in random metal-dielectric films[END_REF][START_REF] Awada | Experimental study of hot spots in gold/glass nanocomposite films by photoemission electron microscopy[END_REF] for a spectral range that is significantly broader than comparable regular arrays of plasmonic resonators. [START_REF] Gadenne | Optical Properties of Nanostructured Random Media[END_REF][START_REF] Gopinath | Photonic-Plasmonic Scattering Resonances in Deterministic Aperiodic Structures[END_REF] In practice, the modulation of optical hotspots is monitored in-situ by measuring nonlinear photoluminescence (NPL) from gold under a femtosecond pulsed excitation. While the physical origin of NPL in gold nanostructures is still under debate, [START_REF] Beversluis | Continuum generation from single gold nanostructures through near-field mediated intraband transitions[END_REF][START_REF] Haug | Hot-Electron Intraband Luminescence from Single Hot Spots in Noble-Metal Nanoparticle Films[END_REF][START_REF] Molinaro | Two-Photon Luminescence of Single Colloidal Gold Nanorods: Revealing the Origin of Plasmon Relaxation in Small Nanocrystals[END_REF] this technique has been shown to provide a direct estimation of near-field enhancements when there is one hotspot per diffraction-limited area. [START_REF] Volpe | Controlling the Optical Near Field of Nanoantennas with Spatial Phase-Shaped Beams[END_REF][START_REF] Ghenuche | Spectroscopic Mode Mapping of Resonant Plasmon Nanoantennas[END_REF] Interestingly, photo-emission electron microscopy measurements on disordered gold metasurfaces demonstrated that the number of hotspots per wavelength squared is between 1 and 2 for a given excitation wavelength and polarization. [START_REF] Awada | Experimental study of hot spots in gold/glass nanocomposite films by photoemission electron microscopy[END_REF] Fig. 1-a describes the employed optical setup: the wavefront of a linearly-polarized femtosecond pulsed laser is shaped by a spatial light modulator (SLM). An inverted microscope with a highnumerical aperture (N A =1.4) conjugates the SLM with the plane of a gold metasurface over a given area (later referred to as wavefront-shaped area). The femtosecond excitation is collimated after the microscope objective and the size of the SLM macropixels are chosen such that their image on the sample surface is comparable to the diffraction limit. Finally, nonlinear luminescence emitted by the gold surface is imaged on a high-sensitivity sCMOS camera. This optical setup is therefore optimized to tune independently the phase of the incoming wave on the sample surface for a homogeneous excitation, while measuring the NPL intensity. However, taking into account the limited numerical aperture of the microscope, tuning the excitation phase at scales similar to the diffraction limit will necessarily induce small fluctuations of the excitation intensity on the sample surface. We demonstrate below that the influence of this effect on the ability to optimize nonlinear luminescence emitted by disordered gold metasurfaces using phase-only wavefront shaping is negligible when the size Figure 1: Wavefront-shaping to optimize nonlinear luminescence in disordered gold metasurfaces (a) Experimental setup: a phase-modulated femtosecond excitation is conjugated with the plane of a disordered gold surface in an inverted microscope (insert: typical scanning electron microscopy image, scale bar is 100 nm). Nonlinear photoluminescence intensity (INPL) is then imaged on a high-sensitivity camera after spectral filtering. (b) Principle of the random iterative algorithm: half of the pixels of an initial random phase pattern are randomly selected. During the first iteration, these pixels have their phase modulated over four values 0, π/2, π and 3π/2. If one phase provides a higher NPL intensity in the center of the wavefront-shaped area than the initial random phase-mask, it is then selected as the new optimized phase pattern (outlined in blue). In the following iterations, half of the pixels are randomly chosen and a similar selection is performed. If the phase patterns of iteration n do not provide a higher NPL signal, the wavefront of the iteration n -1 is retrieved for the n + 1 iteration. (c) Typical evolution of the NPL intensity in the center of the wavefront-shaped area during optimization (data for each phase value of each iteration in red and evolution of the maximum intensity in blue). Examples of 2D and 3D NPL images (d) and corresponding phase-masks (e) before (i) and after (ii) optimization for a gold metasurface close to the percolation threshold (scale bars are 1 µm). In this case, the wavefront-shaped area is a 20 µm square. The red circles mark the center of the wavefront-shaped area in which nonlinear luminescence is optimized during the random iteration algorithm.

of the wavefront-shaped area on the sample is significantly larger than the diffraction limit.

An iterative random optimization algorithm 9,10 is used to increase the nonlinear lumines-cence signal in the center of the wavefront-shaped area, as described in Fig. 1-b. Starting from an initially random phase pattern, half of the pixels of the SLM are randomly selected to define a modulation mask (represented in red in Fig. 1-b). This mask is tuned over 4 phases between 0 and 3π/2. If, for one of these 4 phases, the strongest NPL intensity in the center of the wavefront-shaped area is larger than with the initial random phase pattern, this modified wavefront is selected (outlined in blue in Fig. 1-b). For the second iteration, a randomly chosen half of the pixels of this new phase pattern are again modulated over 4 phases: if a larger NPL intensity is found, a new optimized wavefront is selected for the next iteration; while, if the signal decreases, the next iteration is performed on the last phase pattern that provided the largest NPL intensity. Fig. 1-c shows a typical increase of the NPL intensity during the optimization algorithm: a maximum is found after several tens of iterations with most iterations leading to a signal reduction. The duration of the optimization procedure is limited to 15 min (130 iterations) in order to avoid mechanical instabilities in the optical setup (see supporting information -SI -for more details). This means that the optimization procedure may not be optimal, not only because random algorithms cannot reach a global maximum, 10 but also because of the limited experimental duration and because the algorithm only considers 4 possible phases. However, in more than 75% of the measurements, the highest observed NPL signal is obtained before the 100th iteration. Fig. 1-d shows an example of NPL images before and after wavefront optimization for a plasmonic metasurface close to the percolation threshold (ff =0.64), as well as the corresponding initial and final phase masks. In this case, the wavefront-shaped area is a 20 µm square, which is about 4 times the interaction length observed for delocalized plasmonic modes in gold surfaces with a filling fraction close to the percolation threshold. [START_REF] Bondareff | Probing Extended Modes on Disordered Plasmonic Networks by Wavefront Shaping[END_REF] We observe a significant increase of the nonlinear luminescence specifically at the chosen position of the sample (center of the wavefront-shaped area) with a factor of 91. We can also note that other positions of the sample typically exhibit a small reduction of the NPL intensity, demonstrating the complex interplay of local optical hotspots and delocalized modes that in-fluence the nonlinear emission process. A general trend in these experiments is the increased homogeneity of the final phase mask compared to the initial random one. This indicates that the optimization procedure is efficient and comes partially from the low number of phases that are generated (4 different phases between 0 and 3π/2). It might also be linked to the limited number of delocalized modes that coherently interfere to enhance the NPL signal.

It is important to stress that the optimized nonlinear luminescence signal corresponds to a diffraction-limited area (see Fig. S1 in the SI for more details): since, in plasmonic nanostructures, large luminescence intensities originate from strong local field enhancements, [START_REF] Beversluis | Continuum generation from single gold nanostructures through near-field mediated intraband transitions[END_REF][START_REF] Michaels | Ag Nanocrystal Junctions as the Site for Surface-Enhanced Raman Scattering of Single Rhodamine 6G Molecules[END_REF] this result indicates that far-field wavefront shaping indeed controls and enhances near-field optical hotspots in disordered gold metasurfaces.

The local electric field enhancements [START_REF] Gresillon | Experimental observation of localized optical excitations in random metal-dielectric films[END_REF][START_REF] Krachmalnicoff | Fluctuations of the Local Density of States Probe Localized Surface Plasmons on Disordered Metal Films[END_REF][START_REF] Awada | Experimental study of hot spots in gold/glass nanocomposite films by photoemission electron microscopy[END_REF] as well as the interaction lengths of delocalized plasmonic modes [START_REF] Bondareff | Probing Extended Modes on Disordered Plasmonic Networks by Wavefront Shaping[END_REF] are sensitive to the filling fraction of noble metals in disordered surfaces. Therefore, we performed several tens of iterative random optimizations for different thicknesses of deposited gold as shown on Fig. 2 (maintaining a 20 × 20 µm 2 square as the wavefront-shaped area). These data demonstrate unequivocally the influence of the nanoscale morphology of gold islands on the ability to enhance nonlinear luminescence using far-field wavefront shaping. Indeed, Fig. 2-a It is interesting to note that significant enhancement factors are also observed at low filling fractions where the metasurface features a high density of isolated gold islands. In this case, plasmon polaritons do not propagate on continuous metallic nanostructures but through coupled plasmonic modes as studied in 1D arrays of regular nanoparticles. [START_REF] Maier | Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides[END_REF][START_REF] Koenderink | Complex response and polariton-like dispersion splitting in periodic metal nanoparticle chains[END_REF][START_REF] De Waele | Tunable nanoscale localization of energy on plasmon particle arrays[END_REF] Our measurements demonstrate that wavefront shaping can be exploited in extended 2D arrays of isolated plasmonic resonators. However, Fig. 2-b clearly shows that the added structural complexity and disorder of percolated films, which combine continuous metallic particles and coupled plasmonic modes, leads to a significant gain in NPL intensities and enhancement factors. This is in agreement with previous studies that demonstrated stronger local modulations of the electric field [START_REF] Krachmalnicoff | Fluctuations of the Local Density of States Probe Localized Surface Plasmons on Disordered Metal Films[END_REF][START_REF] Awada | Experimental study of hot spots in gold/glass nanocomposite films by photoemission electron microscopy[END_REF] and plasmonic modes delocalized over longer distances around percolation (5-6 µm interaction lengths at ff =0.64 compared to 2-3 µm at low filling fractions). [START_REF] Bondareff | Probing Extended Modes on Disordered Plasmonic Networks by Wavefront Shaping[END_REF] The experimental data provided in Fig. 1 and Fig. 2 indicate that tuning the phase when exciting delocalized modes in disordered plasmonic metasurfaces, several microns away from the area of interest, leads to a coherent increase of a chosen optical hotspot and, therefore, of the corresponding NPL intensity. This phenomenon should be strongly sensitive to the number of accessible delocalized modes and therefore to the size of the wavefront-shaped area. [START_REF] Bondareff | Probing Extended Modes on Disordered Plasmonic Networks by Wavefront Shaping[END_REF] We investigate in Fig. 3 the sensitivity of the random optimization procedure with respect to the size of the wavefront-shaped area (averaged over 20 realizations), for a fixed gold filling fraction close to percolation. We observe two regimes: a first increase of the luminescence signal when the size of the wavefront-shaped area is tuned between 2 µm and 6 µm; followed by a reduction and a second increase from 10 µm to 40 µm, above which the signal tends to saturate. In practice, the origin of the large NPL intensities with small and large wavefront-shaped areas are significantly different: when the modified phase-mask is comparable in size with the diffraction limit at 790 nm (Fig. 3-a-i), the iterative optimization of the luminescence signal originates largely from fluctuations of the excitation intensity due to spherical aberrations (grey area in Fig. 3-b); while, when the wavefront-shaped area is significantly larger than the diffraction limit (Fig. 3-a-ii and iii), the random algorithm essentially exploits phase-only modulations (white area in Fig. 3-b).

Considering the numerical aperture of the optical setup and the wavelength of the femtosecond laser, the diffraction limit is of the order of 700 nm; comparable in size with the image, on the sample plane, of the macropixels of the SLM on which the phase of the incoming field is modulated (square of typically 360 × 360 nm 2 ). In practice, a sharp phase difference between two consecutive macropixels will weakly diffract the excitation field in the plane of the sample, leading to low intensity oscillations at the interface between pixels over a typical distance of several times the diffraction limit. Therefore, the image of the phase-only SLM on the disordered gold surface is not a pure phase-mask but features small fluctuations of the electromagnetic field amplitude. These fluctuations are strongly reduced when the macropixel size is increased. But the size at which they disappear is comparable to the interaction length of delocalized modes on the plasmonic metasurface, making the optimization procedure inherently a complex mix of amplitude and phase modulations. Importantly, the optimization algorithm is random and selects any phase mask that increases the NPL intensity, either thanks to constructive interferences between delocalized plasmonic modes or between electric fields diffracted by several macropixels leading to a higher excitation intensity in the center of the wavefront-shaped area. Therefore the NPL intensity may increase without involving delocalized plasmonic modes.

Hence, we experimentally verify that, for a small wavefront-shaped area, the dominant effect is a local increase of the excitation intensity, while this not the case for large wavefront-shaped area. For this purpose, we measure the two-photon fluorescence image of a homogeneous polymer film doped with fluorescein, using phase patterns that were selected by the random algorithm on the gold metasurface. 1.5, corresponding to less than a factor 2 for the NPL signal. The enhancements of NPL intensities observed on the gold metasurface in Fig. 3-b, for large wavefront-shaped areas, are therefore essentially due to phase modulations. This can be understood when considering that when half of the pixels of a large phase-mask are randomly selected by the algorithm for each iteration, the probability that these pixels are at a diffraction-limited distance from the center of the wavefront-shaped area is weak. For small phase-masks, most selected pixels can influence the intensity at the center of the wavefront-shaped area. To further evidence that the optimized gold NPL intensity for large phase-masks is due to a complex phase pattern selected for a given morphology of the disordered metasurface, we measure the evolution of the signal as we displace the sample using a piezoelectric stage. After optimization, the gold NPL signal typically drops by 80% over a few hundred nanometers, while an optimized fluorescein TPF signal is independent of the sample position. This further evidences that intensity fluctuations do not influence significantly the NPL optimization process for large wavefront-shaped areas. It also confirms the subwavelength origin of the optimized NPL intensities.

The data of Fig. 4 indicate that the experimental enhancement factors measured in Fig.

3 could be slightly overestimated compared to a hypothetical phase-only wavefront shaping process during which the excitation intensity remains perfectly homogeneous. However, the limited duration of the iterative process and the limited number of phases in the algorithm suggest, on the contrary, underestimated enhancement factors. It is therefore interesting to investigate whether the measured values of Fig. 3 qualitatively agree with the considered underlying phase-only optimization mechanism: electric fields from phase-modulated delocalized modes that coherently add up to enhance an initial optical hotspot. We therefore develop a simple phenomenological model of the enhancement of the NPL intensity in the center of the wavefront-shaped area.

In brief, we suppose that, before optimization, the electric fields due to delocalized modes in the area of interest have random phases and can be neglected in the initial NPL emitted by the center of the wavefront-shaped area. After optimization, we consider that the electric fields of all the delocalized modes are now in phase and can be coherently added to the initial excitation field impinging on the center of the wavefront-shaped area. To take into account that plasmon polaritons propagating on disordered surfaces are multiply scattered, [START_REF] Akkermans | Mesoscopic Physics of Electrons and Photons[END_REF] we consider that each ij macropixel of the SLM produces a surface cylindrical wave that is exponentially damped because of absorption. With r ij the distance between the center of the considered macropixel and the center of the wavefront-shaped area, the amplitude of the electric field of the damped cylindrical wave in the center of the wavefront-shaped area can be written as ηE 0 e -r ij /L λ/2πr ij , with E 0 the amplitude of the electric field of the wavefront-shaped collimated excitation of wavelength λ = 790nm, η the coupling efficiency of the excitation field to the damped cylindrical wave and L the interaction length of the delocalized modes. [START_REF] Bondareff | Probing Extended Modes on Disordered Plasmonic Networks by Wavefront Shaping[END_REF] As the size of the SLM macropixels on the sample surface are significantly larger than the nanoscale morphology of the disordered metasurface, we assume that an averaging effect leads to similar interaction lengths and coupling efficiencies for all pixels.

Importantly, L was estimated experimentally around 5 µm in similar samples. [START_REF] Bondareff | Probing Extended Modes on Disordered Plasmonic Networks by Wavefront Shaping[END_REF] If we define the enhancement factor of the NPL signal ρ as the ratio between optimized and initial intensities, then

ρ = 1 + η ij e -r ij /L λ 2πr ij 2p , (1)
where p = 2.8 is the nonlinear intensity dependence of the luminescence signal (see Fig. S2). 3-b for phase patterns smaller than 10 µm, confirming the influence of intensity fluctuations when the size of the wavefront-shaped area is similar to the diffraction limit. Importantly, the coupling efficiency η is defined for the amplitude of the electric field. Therefore, the experimental data for large wavefront-shaped areas indicate a coupling efficiency in intensity of about 0.01%. This is significantly lower than typical coupling efficiencies of ∼1% that were estimated for propagating surface plasmons in rough gold surfaces. [START_REF] Salomon | Local excitation of surface plasmon polaritons at discontinuities of a metal film: Theoretical analysis and optical near-field measurements[END_REF] This discrepancy can be due to a non-optimum wavefront-shaping process because of the limited number of phases and the fixed number of iterations of the algorithm; but also to a limited number of delocalized modes that are capable of modifying the electric field in the center of the wavefront-shaped area (as already discussed when considering the final phase pattern in Fig. 1-d).

Conclusion

By tuning the phase of a far-field excitation when coupling to delocalized plasmonic modes, we were able to optimize near-field optical hotspots in disordered gold metasurfaces by wavefront shaping. This process is performed using a random iterative algorithm and monitored by a typical two-order of magnitude enhancement of the nonlinear photoluminescence of gold in a chosen diffracted-limited area. We demonstrate that this process is the most efficient at the percolation threshold, when the sample exhibits the highest level of morphological complexity and disorder. Importantly, the hypothesis of a phase-only modulation is only valid when the wavefront-shaped area is significantly larger than the diffraction limit. Although intensity fluctuations hinder the quantitative estimation of maximum enhancement values for the nonlinear luminescence signal, our experiments agree qualitatively with a simple phenomenological model using optical parameters of disordered gold films already reported in the literature. Interestingly, this model highlights the important parameters that favor the enhancement of optical hotspots and, therefore, of NPL intensities using wavefront shaping:

increasing the interaction length L (by using silver instead of gold [START_REF] Bondareff | Probing Extended Modes on Disordered Plasmonic Networks by Wavefront Shaping[END_REF] ) and increasing the coupling efficiency η to delocalized modes (for instance, by tuning the wettability of the deposited metal in order to increase the thickness and, thus, the scattering cross-section of resonant nanostructures on the metasurface). While these results already open exciting opportunities for the modulation of optical hotspots in complex gold metasurfaces; their extension to a matrix formalism, in order to couple desired near-field properties with a known far-field excitation, would allow the development of fully programmable disordered plasmonic substrates that provide surface-enhanced spectroscopic information from chosen and well-defined areas of a given sample.

  presents the distributions of NPL signals before and after optimization for a disordered metasurface far from percolation (ff =0.29), one close to percolation (ff =0.64) and one significantly above it (ff =0.76): we observe that both the initial and final intensities are significantly larger close to percolation. By fitting these distributions with log-normal probability density functions, it is possible to infer average initial and final NPL intensities as well as standard errors. This allows the definition of an average enhancement factor, whose dependence with respect to the gold filling fraction is plotted in Fig. 2-b alongside the average NPL intensities after optimization. Close to percolation, the final nonlinear signals are more than one order of magnitude larger than far from it and also correspond to the largest enhancement factors, reaching nearly two orders of magnitude when ff =0.64.

Figure 2 :

 2 Figure 2: Influence of the nanometer-scale morphology of the disordered metasurface. (a) Semi-logarithmic distributions of NPL intensities before (light color bars) and after (dark color bars) 20 optimization procedures for three different filling fractions of gold (ff =0.29, orange bars; ff =0.64, green bars; ff =0.76, purple bars -typical corresponding transmission electron microscopy images are shown to the right). The initial NPL intensities are estimated over 10 4 pixels around the optimized position (in the center of the wavefront-shaped area). The final NPL intensities are estimated as the largest value in the 9 pixels around the center of the wavefront-shaped area after optimization. (b) Optimized nonlinear luminescence intensities and average NPL enhancement factors as a function of the gold filling fraction. The average enhancement factors are estimated using the means of the log-normal distributions of Fig. 2-a. The error bars for the optimized nonlinear luminescence intensities are the standard errors of the log-normal distributions. The error bars for the enhancement factors are the standard errors of the optimized intensity divided by the mean initial intensity (for which the standard error is negligible).

  size of wavefront-shaped area[µm]

Figure 3 :

 3 Figure 3: Influence of the size of the wavefront-shaped area on the NPL enhancement factor. (a) Examples of optimized phase masks when the wavefront-shaped area is a 4 µm (i), 20 µm (ii) or 40 µm (iii) square. (b) Evolution of the average enhancement factors (measured over 20 realizations) as a function of the size of the wavefront-shaped area, for a fixed filling fraction close to the percolation threshold. The error bars are estimated similarly to Fig. 2-b. The gray area highlights the experimental conditions for which fluctuations of the excitation intensity play an important role on the measured NPL enhancement factor. The solid lines are theoretical estimations of the enhancement factors as a function of the size of the wavefront-shaped area using a simple phenomenological model with two parameters: the interaction length L of the delocalized plasmonic modes in the metasurface and the coupling efficiency η to these delocalized modes. Blue line: L = 5µm / η = 0.011. Green line: L = 5µm / η = 0.013.

Fig. 4 -

 4 a shows typical images of the gold NPL and fluorescein TPF intensities when the square wavefront-shaped area is 4 µm wide. It also provides distributions of the NPL and TPF signals measured on the optimized area after 18 independent iterative procedures, compared to the distributions of initial NPL and TPF signals, for the same size of the wavefront-shaped area. On the fluorescent sample, we systematically observe an increased TPF intensity in the center of the wavefront-shaped area after optimization with an average enhancement of 4. Considering the different nonlinear intensity dependence of the TPF (quadratic) and gold NPL (2.8 power dependence) signals (see Fig.S2), this corresponds to an increased nonlinear luminescence on the gold surface of a factor 7. It is interesting to note that the random algorithm can be directly implemented with the homogenous fluorescent film providing average TPF enhancements of 6 (see Fig.S3), further evidencing the issue of intensity fluctuations on the optimization process. However, this process cannot fully account for the enhancement observed in Fig.3-bfor a 4 µm wavefront-shaped area, meaning that the optimization algorithm mixes intensity fluctuations and phase modulations to enhance the NPL signal.

Fig. 4 -

 4 Fig. 4-b provides a similar comparison between gold NPL and fluorescein TPF signals for 24 optimization procedures with a 20 µm wide phase pattern. In about 75% of the measurements, the TPF intensity in the optimized area is comparable with the rest of the sample.In practice, the TPF intensity distribution indicates a moderate average enhancement of

Figure 4 :

 4 Figure 4: Influence of excitation intensity fluctuations on the wavefront optimization of the NPL signal. Typical images of the NPL intensity on a disordered gold metasurface after optimization (top left) and of the TPF signal of a homogeneous fluorescent sample using the optimized phase pattern (bottom left), as well as distributions of the NPL (red data, top right) and TPF signals (blue data, bottom right) before (light color bars) and after (dark color bars) iterative optimization for two sizes of the wavefront-shaped area: 4 µm (a) and 20 µm (b). Scale bars are 1 µm. (c) Three examples of the evolution of the NPL (red data) and TPF (blue data) signals, in the center of the wavefront-shaped area after optimization, when the sample is moved while the phase pattern is kept constant.

Equation 1

 1 assumes that the excitation cross-section of the sample leading to the emission of nonlinear luminescence is the same for a plane-wave excitation or for 2D propagating waves. Since the number and position of pixels are defined by the wavefront-shaped area, this equation provides a simple phenomenological dependence of the average enhancement factors as a function of the size of the wavefront-shaped area. The solid lines in Fig.3-b correspond to modeled enhancement factors for L = 5 µm and η = 0.011 (blue line) and η = 0.013 (green line), respectively. Our phenomenological model therefore agrees qualitatively with a two-order of magnitude enhancement of the NPL intensities using phase-only wavefront shaping in areas larger than 20 µm. A discrepancy of about one order of magnitude is observed when comparing the experimental data points and the calculated values in Fig.

Acknowledgement

The authors thank A. Goetschy for discussions. This work was supported by the French Direction Générale de l'Armement (DGA) under project 2017706. Work at Institut Langevin was supported by LABEX WIFI (Laboratory of Excellence within the French Program "Investments for the Future") under references ANR-10-LABX-24 and ANR-10-IDEX-0001-02 PSL*. Work at Laboratoire Kastler Brossel was supported by the European Research Council (ERC) under project 278025. S.G. is a member of the Institut Universitaire de France (IUF).

Supporting Information Available

Experimental procedures and complementary measurements of the size of the optimized NPL signal, of the nonlinear dependence of the luminescence of gold with respect to the excitation intensity and of the optimization of the TPF from a homogeneous fluorescent surface due to fluctuations of the excitation intensity.