Lindon W K Moodie

Rozenn Trepos

Gunnar Cervin

Kari Anne Brathen

Bente Lindgard

Rigmor Reiersen

Patrick Cahil

Henrik Pavia

Claire Hellio

Johan Svenson

Kari Anne Bråthen

Bente Lindgård

Patrick Cahill

Prevention of Marine Biofouling Using the Natural Allelopathic Compound Batatasin-Ill and Synthetic Analogues

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

Some species of terrestrial plants accumulate secondary metabolites that negatively affect other plants growing nearby. 1 These compounds, known as allelopathic phytochemicals, can direct plant community composition and development. [1][2][3] For example, some allelochemicals diffuse into the surrounding soil, either directly from the live plants or passively via degradation of dead plants, to suppress seedling growth and germination. In doing so, allelochemicals can prevent the establishment of other plant species that could otherwise compete for space or resources. 3,[START_REF] Raven | Biology of Plants[END_REF] Many phytochemicals, such as the flavonoids, lignans, proanthocyanidins, phenolic acids and stilbenes, are secondary metabolites where the phenolic functionality is highly represented. [START_REF] Yadav | [END_REF][START_REF] King | [END_REF] The roles of these phytochemicals are diverse but are often associated with plant defense, either against grazers, microorganisms or competing plant species via allelopathic routes. 7,[START_REF] Lattanzio | Phytochemistry: Advances in Research[END_REF] One such allelopathic phytochemical is the reduced stilbene derivative 3,3´-dihydroxy-5-methoxydibenzyl commonly known as batatasin-III (1). Compound 1 was first reported in the bulbils of Dioscorea batatas (yam tubers) and has since been shown to be present in many species of orchid (family Orchidaceae). [START_REF] Xu | [END_REF][10][11] The Arctic and circumboreal evergreen dwarf shrub Empetrum nigrum (crowberry, shown in Figure S1 in Supporting Information) is likewise a prolific producer of 1. As much as 6% of the dry leaf weight of E. nigrum consists of 1, and it has been shown to accumulate in the surrounding soil where it negatively influences the establishment of new individuals of both tundra plants and trees via allelopathic mechanims. 3,12,13 Terrestrial plants are not the only taxa to produce allelochemicals. A range of marine organisms produce allelochemicals, with sessile biofouling organisms and planktonic microalgae providing particularly rich sources of these compounds. As with terrestrial plants, sessile biofouling organisms such as sponges 14,15 and macroalgae 16,17 are at risk of being overgrown or outcompeted by neighboring organisms. This often intense competition for space between sympatric organisms has given rise to an arsenal of allelopathic metabolites. 14 Likewise, some planktonic microalgae form dense "blooms", using allelochemicals to suppress sympatric competitive species of microalgae. 18,[START_REF] Graneli | In Ecology of Harmful Algae[END_REF] The use of the allelopathic naphthoquinone juglone from Juglans nigra (black walnut) to prevent surface colonization by marine microorganisms is an innovative example of the evaluation of a terrestrial allelochemical in a marine setting. [START_REF] Salta | [END_REF] The growth of organisms on marine surfaces is known as biofouling (shown in Figure S2 in Supporting Information) and rapidly occurs on materials and surfaces submerged in water. 21 The biofouling film rapidly increases the weight and roughness of boats, buoys, and aquaculture equipment, leading to increased maintenance costs, damage to infrastructure and higher fuel usage. 21,22 Historically, biofouling has been successfully combatted using paints that incorporate biocides, particularly the organotin compound tributyl tin (TBT). 23 However, these biocides have had a range of negative effects on the marine environment due to their non-specific modes of action and high potency; in the case of TBT down to 1 ng/L. Accordingly, the International Maritime Organization implemented a worldwide ban on TBT in 2003, and all other general biocides were banned from use in 2008. 21,24 Marine natural compounds are currently being investigated as potential antifoulants, aiming for a lower environmental impact and ideally a repelling or deterring mode of action. 25,26 Several highly active natural antifoulants have been reported. 27 Butenolide produced by a marine Streptomyces strain, is currently being developed towards a commercial product. 28 The biofouling community is composed of both microfoulers (bacteria and microalgae) and the larger macrofoulers (for example, bivalves, ascidians, macroalgae, tubeworms, and barnacles). Being able to screen potential antifouling agents against all these representative organisms increases the chances of discovering leads for further development. 29,30 The established allelopathic effect and capacity of 1 inspired us to investigate if these effects are transferable to a marine setting. Although it seems 1 has less capacity to interfere with the direct growth of Lactuca sativa roots (IC50 at 1-2 mM 13 ) compared to that of juglone (IC50 at 0.075-0.15 mM, 31 merismatic activity), the structurally simple dibenzylic dihydrostilbene scaffold of 1 serves as a practical entry point to a library of analogues for evaluation. Vegetable tannins have been shown to display a reversible narcotic effect on Balanus amphitrite illustrating that phenolic natural compounds can possess interesting antifouling properties. 32,33 To investigate the antifouling potential of the natural dihydrostilbene scaffold, a library of 22 synthetic dihydrostilbenes with varying substitution patterns were prepared and evaluated in an extensive screen against 17 different organisms.

The compounds were screened initially against lettuce seedling (representative for many seed plants 13 ) root growth before being exposed to ten different marine bacterial strains and four microalgal strains. Macrofouling was investigated by assessing the inhibition of the barnacle Balanus improvisus cyprid metamorphosis and also against the ascidian Ciona savignyi for selected compounds. The commercial antifouling booster biocide Sea-Nine 211™ (Dow) was included in the assays as a relevant positive control.

RESULTS AND DISCUSSION

Compound Library Design and Synthesis. The compound library was based on the dihydrostilbene scaffold of 1 and was designed to probe the contributions from both hydroxyl and methoxy substituents common in naturally occurring stilbenes. 34 The library was composed of 22 dihydrostilbenes and was designed to contain compounds with a degree of substitution ranging from mono-to tetrasubstitution. The degree of substitution was also reflected in the polarity (calculated ClogP) of the compounds which ranged from 1.99 to 4.60 allowing for an evaluation of the impact of this physicochemical property on the biological activity. The compounds were assembled employing Wittig or Horner-Wadsworth-Emmons methodology, followed by hydrogenation, which are widely accepted methods for the production of substituted 1,2-diphenylethanes. 35,36 Benzyl protection was employed for the hydroxy and methoxy groups were demethylated with HBr/AcOH. The methods employed were rapid and reliable and afforded the compounds in high yields.

A recent study highlighted how bibenzyls can be readily accessed via C (sp 3 )-H activation of methyl arenes under metal-free conditions, 37 suggesting an effective yet benign "green" method to access these compounds in the future. The majority of the compounds prepared have been reported as natural products from terrestrial plant sources before (Table S1 in Supporting Information). Figure 1 presents the structures of the prepared compounds. plants indicate that this compound can interfere with both germination and seedling root elongation. These effects were not species-specific, and plants such as forbs, grasses, shrubs and trees were all effected when exposed to 1 at low mM-concentrations. 13 The inhibitory capacity of compounds 1-13 on the mean root elongation of pre-germinated seeds of Lactuca sativa (Lettuce) was established by placing seedlings on soaked filter papers treated with increasing concentrations of the compounds. The inhibitory effect of the compounds in comparison to treatment with distilled water is presented in Figure 2. Out of the 13 compounds evaluated, eight displayed an inhibitory effect on the root elongation of L. sativa seedlings at <4 mM concentrations. The IC50 values of the active compounds were determined and are presented in Table 1 Compound 1 displayed an IC50 of 1 mM which is in good agreement with previous studies that reported the IC50 at 1-2 mM. 13 Compounds 2, 4 and 6, which are less substituted in comparison to 1, were the most potent inhibitors with IC50 values of 0.5 mM. Compounds 8, 10, 11 and 12 were slightly inferior to 1 whereas compounds 3, 5, 7, 9 and 13 did not display a high enough inhibitory activity to allow for an IC50 determination. Although the latter compounds were not particularly active at 4 mM, they still displayed some inhibitory capacity in comparison to distilled water. It is clear that the allelopathic inhibitory effect is not restricted to the natural product 1. Indeed several of the synthetic analogues displayed comparable and, in some cases, superior inhibition in the root elongation assay. The structural link to activity is not obvious given that both active and inactive compounds are mono-, diand trisubstituted. However, it appeared that hydroxy groups are beneficial for the inhibitory activity. A pair-wise analysis of these analogues with their analogous methoxy counterparts supports this; compounds 2, 4 and 6 are all highly active whereas their methoxylated counterparts 3, 5, 7, and 9 are inactive (compound 8, with both a free hydroxy and a methoxy group displayed an IC50 of 2 mM). This trend was also noticeable for the four trisubstituted analogues, although not as pronounced. Methylation of the hydroxyl groups increases the hydrophobicity of the compounds and lowers the ability to engage in hydrogen bonding interactions, which could provide a link between the free hydroxyl groups and bioactivity.

There appears to be no link between the 3´,4´ and 3,5 substitution pattern as compounds 4 and 6 are equally active. The phytotoxicity of 1, 10 and 11 against both Amaranthus hypochondriacus and Lemna paucicostata have been investigated by Mata and co-workers. 38 In their study 1, 10 and 11 displayed a pronounced phytotoxic effect and caused increased cellular leakage.

Given the observed inhibitory activities of our analogues against root elongation and the recently established inhibitory effect against seed germination 13 of 1, it was decided to evaluate this natural terrestrial scaffold in a marine setting employing diverse species involved in the formation of the biofouling film. 39 For this purpose, compounds 14-22 were prepared and included in the continued studies to generate additional structural diversity.

To remain within the plant kingdom, the effect on the adhesion and growth of microalgae was initially investigated using the methods described by Trepos et al. 29,39 employing the commercial antifouling biocide Sea-nine 211™ as a positive control. Sea-Nine 211™ is a herbicide and an inhibitor of PSII electron transport. This compound degrades rapidly in the ocean, and is employed in antifouling paint formulations. 40,41 The ability of the compounds to interfere with surface adhesion and growth (A and G respectively in Table 2 With the exception of compounds 6, 18 and 20, all the investigated compounds displayed a high general inhibitory activity against microalgae. The antialgal effect was apparent both towards adhesion and growth. Several of the compounds displayed low MIC-values at sub µg/mL concentrations. In comparison with other natural antifouling compounds and their synthetic analogues evaluated against the same algal species, the current library displays superior antifouling activity towards the microalgae. 29,42,43 The inhibitory effect on the algal adhesion is particularly noteworthy. The species C. closterium, H. coffeaeformis, P. roscoffensis all display similar sensitivity towards the investigated dihydrostilbenes while P.

purpureum is more resilient. These observations are consistent with other studies identifying P. purpureum as a particularly robust microalgae. 39,43 Both C. closterium and H.

coffeaeformis are diatoms and it appears that the compounds display a similar high activity towards this class of microalgae. As both 1 and 6 were highly active in the root elongation inhibition assay, it is interesting to observe that they are relatively poor at the inhibition of microalgae growth and adhesion. It is clear that the link between structure and activity is not the same when going from the terrestrial forb L. sativa to marine microalgae. It could be interpreted that these allelopathic compounds are highly active against both types of plants but The microfouling of a surface involves contributions from both microalgae and marine bacteria 44 and can induce a considerable increase in drag as well as biocorrosion. 45,46 Ten strains of marine bacteria involved in biofouling were tested against the compound library and results are presented in Table 3. Only the inhibitory effect on bacterial growth ("G" in the Table 3.) is displayed as none of the compounds exhibited any significant inhibitory effect towards bacterial adhesion at the concentrations employed. were all inactive against the growth of bacteria up to 10 µg/mL. d Not active at >10 µg/mL. e From Trepos et al. 39 The effects of 1-22 on the marine bacteria were less prominent than was observed against microalgae. Inhibition of bacterial growth was observed for two thirds of the compounds but these effects were species-specific. For example compounds 2, 4, 6, 9, 11 and 18 were active against of half of the included bacterial strains. Vibrio carchariae, Vibrio natriegens, and

Polaribacter irgensii were sensitive to three out of the 22 compounds and represent bacteria less sensitive to this class of compounds. No direct link between the structure of the compounds and their antibacterial properties was apparent and the results suggest that the dihydrostilbenes are not general inhibitors of the adhesion or growth of marine bacteria.

Although microfouling is an important step in the development of biofouling communities, the majority of unwanted weight gain and increased drag on marine structures results from the accumulation of macrofoulers. The metamorphosis inhibition and settlement of barnacle cyprids was used to evaluate the ability of the dihydrostilbene scaffold to limit the settlement of a common macrofouling taxon. Balanus improvisus has been employed in antifouling studies of numerous natural products and represent a relevant crustacean model species for temperate and cold waters. 29,42,43 The inhibitory effect of the compounds on cyprid settlement was initially assessed at 5 µg/mL (Figure 3). The IC50 of the active compounds were subsequently determined via dose-response studies as presented in Table 4. As illustrated in Figure 6 there is a substantial spread in the potency against B. improvisus of the analyzed compounds when evaluated at 5 µg/mL. Dose-response analysis of the active compounds revealed IC50 values in the low µg/mL concentration range with a number of compounds displaying settlement inhibition at concentrations <1 µg/mL. These inhibitory activities are higher than those reported for the large majority of previously investigated antifouling natural products 26,27,47 and are comparable to commercial antifouling products including Sea-nine™. The most active compounds 2, 3, 8, 9, 12 and 20 perform similarly (IC50 = 0.9-3.5 µM) to the highly active natural drimane sesquiterpene polygodial (IC50 = 1.1 µM), 43 the 2,5-diketopiperazine barettin (IC50 = 0.9 µM), 48 bastadin-9 (IC50 = 1.0 µM) 49 and synoxazolidinone C (IC50 = 2 µM). 29 The compounds also share similar structural features and antifouling activities with the natural antifouling phenyl ethers recently reported by Wang and co-workers. 50 The high inhibitory effect on barnacle cyprid settlement illustrates that the dihydrostilbenes also exhibit potent biological effects in higher organisms. An influential physicochemical factor for the settlement inhibition of the analyzed compounds appears to be the hydrophobicity and hydrogen-bond forming capacity. With the exception of compound 13, all other compounds (11, 17, 18 and 19) displaying low or no inhibitory activity are hydrophilic, with ClogP values ranging between 1.99 and 2.59. These poorly active compounds are substituted with a minimum of three hydroxy groups yielding, not only improved water solubility, but also an increased ability, to engage in hydrogen bonding with biological targets. For inhibition of barnacle cyprid settlement, these properties reduce the activity of the dihydrostilbene scaffold, which is in direct contradiction to the relationship seen for the L.

sativa root elongation inhibition. The observation that a high number of free hydroxyl groups may lower the antifouling activity against balanides is consistent with the findings reported by

Wang and co-workers. 50 Apart from the clear connection between increased polarity and hydrogen bond capacity and a lowered inhibitory effect towards cyprid metamorphosis, there are few defined relationships between structure and activity. However, the non-toxic analogues 3, 9 and 12 contain no free hydroxyl groups and subsequently have lower water solubility. In fact, none of the more To gain additional insight into the spectrum of antifouling activity of the dihydrostilbene scaffold, selected compounds were also evaluated as inhibitors of the settlement and metamorphosis of larvae of the ascidian Ciona savignyi (Ascidiacea). Ascidians settle rapidly on marine substrata and represent a challenging macrofouling species to manage. 51 Compounds displaying a high inhibitory activity in the barnacle assay were selected for evaluation against C. savignyi. Toxic compounds, such as compounds 7 and 20, and non-toxic analogues such as 5, 9 and 22 were included in addition to 1. The compounds were evaluated for their ability to interfere with C. savignyi larval metamorphosis and settlement according to the methodology developed by Cahill and coworkers. 51,52 The dose-response behavior and inhibitory constants are presented in Figure 5 and Table 5. 43 Of particular interest, 9 exerted its inhibitory activity via a non-toxic mode of action, with active and swimming larvae still present after five days of incubation but no successfully settled or metamorphosed larvae. The remaining compounds killed the C. savignyi larvae outright, with no active or swimming larvae present after 5 days. The correlation between a high hydrophobicity and a non-toxic mode of action is not as defined as that seen for B. improvisus due to the toxicity of compounds 5 and 22. However, the overall antifouling activity of the dihydrostilbenes against the two higher marine organisms investigated is pronounced and similar.

Toxicity against other non-target higher marine organisms has been reported for 1. The potential toxic effect on the aquatic fauna by the E. nigrum, was evaluated by Brännäs et al.

using 1. 53 The toxicity of 1 against brown trout (Salmo trutta) alevins and juvenile water fleas (Daphnia magna) was established. It was shown that 1 is toxic towards freshly hatched S.

trutta alevins and juvenile D. magna at 10 µg/mL concentrations. The toxic effect correlated with pH and increased with water acidity. 53 No analogues of 1 were investigated in their study aside from phenol.

Terrestrial Versus Marine Allelopathy. Allelopathy is successfully used to control the growth and spread of competitive plant species both on land and in the ocean. In forestry it has been shown that natural 1 can impact the structure of entire plant communities. 2,3 The antagonistic relationship between phytoplankton and rooted aquatic plants has been investigated 54 and several other studies have described the allelopathic effect of marine natural products on marine algal communities. 28,55,56 Several of these characterized marine allelochemicals are of a phenolic nature, displaying structural similarities with the currently studied terrestrial compounds. 56 As such, it is clear that the allelopathic phenomenon is ongoing on land and at sea but it is nevertheless unclear if powerful terrestrial allelopathic compound also will effectively target marine organisms to the same extent. Marine algae share some similarities with higher plants, yet in a simpler and less differentiated format.

Macrofouling invertebrates share very few features with higher plants, making it more difficult to predict how they will interact with terrestrial allelochemicals.

CONCLUSIONS

The current study represents the first comprehensive evaluation of a terrestrial allelopathic natural products scaffold in a marine setting with the goal of discovering and developing new green methods to combat marine biofouling. Despite the significant biological uncertainties, the current study clearly demonstrates that the prepared dihydrostilbenes are allelopathic against L. sativa and also active against marine algae and two taxa of marine invertebrates.

The inhibitory effect towards marine microalgae is in fact more pronounced than against L.

sativa with many of the compounds displaying inhibitory properties at low ng/mL concentration via a non-toxic mechanism against both algal adhesion and growth. The observation that these compounds also target the macrofouling invertebrates by both toxic and non-toxic pathways is even more profound, motivating further research into these naturally occurring compounds. Although the exact mechanism of action is unknown, there are clearly relevant molecular targets for dihydrostilbenes that open up new avenues for environmentally friendly strategies to combat unwanted marine growth.

EXPERIMENTAL SECTION

General Experimental Procedures. NMR spectra were acquired on a Varian 7000e 400 MHz spectrometer. HRMS was recorded on an LTQ Orbitrap XL Hybrid Fourier Transform mass spectrometer from Thermo Scientific. Solvents and reagents were obtained from commercial suppliers and used without further purification. Air-sensitive reactions were carried out under an argon atmosphere. Thin-layer chromatography was carried out on aluminum-backed plates coated with silica gel and visualized under UV light at 254 nm and ethanolic vanillin dip. Chromatography was carried out on silica gel employing mixtures of petroleum ether and ethyl acetate as eluents. Batatasin-III (1) was purchased (>99 % purity determined by HPLC) from Paragon Biochemical LLC (Salt Lake City, United States of America). Wittig salts were prepared according to the protocols of Chalal et al. 57 3-Benzyloxy-5-methoxybenzyl bromide was synthesized by the method of Nawrat et al. 58 Diethyl 3,5-dibenzyloxybenzylphosphonate was prepared according to the protocol of Sun et al. 59 containing filtered (3 µm) and UV-sterilized seawater. The dishes containing eggs received eight drops of sperm suspension from each of the two other individuals. The fertilized eggs were incubated for 1 h at 18 °C and strained through a 20-µm sieve, rinsed three times with 25 mL reconstituted seawater (RSW; 33 ± 0.5 psu; Red Sea Salt, Red Sea Aquatics, Cheddar, UK). The strained eggs were transferred to a glass Petri dish containing 25 mL RSW, and incubated for 18 h at 18 °C to hatch. Hatched larvae were transferred to conical flasks and diluted with RSW to yield 10 larvae/mL immediately prior to being employed in the inhibition assay.

Lactuca sativa Seedling Roots Assay. The inhibition of L. sativa (lettuce) seedlings through mean root elongation studies of pre-germinated seeds was determined according to González et al. 13 The compounds were dissolved in MeOH and added to five filter papers discs (Ø 50 mm) placed in Petri dishes to yield concentrations of 0 (control), 0.1, 0.5, 1.0, 2.0 and 4.0 mM. The MeOH was allowed to evaporate at room temperature before the bioassays were initiated and 1 mL of distilled water was added to moisten the filter paper before placing pre-germinated seedlings on the soaked filter papers. Three Petri dishes were employed for each compound concentration and six seedlings were placed in each dish. The root length (mm) was measured after three days of growth, after which the average root length per dish, followed by the average root length across all three dishes was calculated to yield an estimate of root length per compound concentration. Finally the inhibitory concentration yielding a 50% reduction in root length, compared to the control was calculated and reported as the IC50.

Antialgal Assays. Microplates containing the compounds in ranging concentrations were prepared from MeOH stock solutions as described by Trepos et al. 29 Microalgal stock solutions were prepared for each strain via chlorophyll analysis according to Chambers et al. 60 Aliquots (100 µL) of the algal stock solutions (0.1 mg chlorophyll a/mL) were transferred to the pre-treated microplate wells and the plates were grown at 20 °C for 5 days under constant light exposure (140 µmol m -2 s -1 ). Microalgal growth was assessed by analysis of liberated chlorophyll-a following centrifugation and addition of MeOH (100%). The released chlorophyll-a was quantified using a fluorometric method described by Chambers et al. 60 The lowest concentration yielding a decrease in chlorophyll-a content was defined as the minimum inhibitory concentration (MIC) for algal growth. Microalgal adhesion was determined in a similar manner in which the non-attached algal cells were gently removed prior to addition of 100 µL of 100% methanol to release chlorophyll-a from the remaining algal biofilms. The MIC for adhesion was defined as the lowest compound concentration inducing a reduction in optical density. When inhibition was observed, a toxicity test was performed by transferring the content of the wells into a flask of fresh medium. The growth of the initially inhibited strains was measured after 5 days of additional incubation and the mode of action of classified as biostatic if an increase in chlorophyll-a content was observed. 43 The commercial antifouling agent Sea-nine™ served as a positive control.

Antibacterial Assays. Adhesion and growth of the bacterial strains was assessed according to Thabard et al. 63 Briefly, aliquots (100 µL) of bacterial suspension (2 × 10 8 colony forming units/mL) were aseptically added to the pre-treated microplate wells and the plates were incubated at 26 °C for 48 h. Bacterial growth was investigated spectroscopically and the lowest concentration yielding a decrease in OD at 630 nm was defined as the MIC for bacterial growth. The adhesion of bacteria was determined by staining the residual attached bacterial biofilms with 0.3% aqueous crystal violet (v/v) after emptying and rinsing the incubated wells with 100 µL of FSW after 48 h of incubation. The stained bacterial biofilms were visualized at 595 nm according to Sonal and Bholse. 64 The MIC for adhesion was defined as the lowest concentration inducing a reduction in OD at 595 nm. Toxicity experiments were performed as described for the microalgae. The commercial antifouling agent Sea-nine™ served as a positive control.

Balanide Settlement Inhibition. The compounds were prepared as stock solutions in DMSO and serially diluted to generate final concentrations ranging from 0.1 to 10 µg/mL in untreated polystyrene Petri dishes, containing 10 mL filtered (0.2 μm) seawater. Newly molted cyprids (18 -22) were added to each test dish, which were subsequently incubated at ambient temperature (20 -25 °C) for 5 days. The extent of cyprid metamorphosis was assessed under a dissecting microscope and juvenile settled barnacles, as well as live and dead cyprids, were counted. The concentration preventing 50% of the cyprid settlement on the Petri dish surface was defined as the IC50 values. An initial screen was performed at 5 µg/mL for all the compounds and a full IC50 determination was only performed on those compounds displaying >50% inhibition at that concentration. Each test concentration of the compounds was replicated four times (n = 4), and dishes with 10 μL of DMSO served as negative controls. The commercial antifouling agent Sea-nine™ served as a positive control.

Ascidian Antifouling Bioassay. The ascidian bioassay was run in twelve-well tissue culture plates (Corning® Costar®, Corning Inc., Corning, NY; Ø 23 mm), containing 7.1 mL aliquots of a larval suspension (containing 10 larvae/mL) according to Cahill et al. 52 The compounds were prepared as 20% (v/v) ethanol stock solutions and were added to wells to yield final concentrations ranging from 0.001 to 20 µg/mL. The blank control contained carrier solvent only. Three replicates were performed for each treatment concentration and control (n = 3). The plates were incubated at 18 ± 1°C, 12:12 h subdued light to dark for 5 days, after which the number of larvae that had settled and completed metamorphosis were counted. Dose-response curves were plotted using four parameter logistic curve fitting on SigmaPlot 11.0. 65 The corresponding compound concentrations that reduced the number of larvae completing metamorphosis and settlement by 50% (IC50) were calculated relative to blank controls.

Synthesis. All the prepared dihydrostilbenes are known compounds and have previously been described in the literature. General synthetic procedures are described below. All the prepared compounds matched the previously reported spectroscopic data. The complete characterization of compounds 2-22 can be found in the Supporting Information.

General Procedure for Wittig Reaction. NaH (95%, 1.05 equiv.) was added to a stirred solution of Wittig salt (1.0 equiv.) in THF (0.1 M) at 0 °C. A solution of aldehyde (1.0 equiv.)

in THF (0.1 M) was added dropwise and the reaction allowed to warm to ambient temperature. After 14 h the reaction was quenched with H2O and extracted with ethyl acetate (×2). The combined organic extracts were washed with H2O, brine and dried over Na2SO4.

The solvent was removed in vacuo, and the resulting residue purified by column chromatography (petroleum ether-ethyl acetate) to afford the product as an inconsequential mixture of E and Z isomers, as determined by 1 H NMR analysis.

General Procedure for Hydrogenation. The reaction vessel was evacuated and flushed with N2 prior to addition of Pd/C (10%) (33 mg/mmol of substrate). Ethyl acetate was added to the flask followed by a solution of substrate (1.0 equiv., mixture of E and Z isomers) in ethyl acetate (final concentration ~0.1 M). The reaction flask was evacuated and backfilled with N2 (×2) prior to evacuation and introduction of a H2 balloon (×2). After stirring overnight, the vessel was flushed with N2 and the reaction mixture filtered through a bed of Celite. The Celite was washed with ethyl acetate and the solvent removed under reduced pressure. The resulting residue was purified by column chromatography (petroleum etherethyl acetate) to afford the desired bibenzyl compound.

General Procedure for Demethylation. HBr (48 wt. % in H2O) was added to a solution of substrate in glacial acetic acid (HBr-AcOH 1:1 v/v, final concentration 0.15 M). The reaction mixture was refluxed for 3 h and cooled to room temperature. After the addition of water, the reaction mixture was extracted with diethyl ether (×3) and the combined organic extracts washed with H2O, brine and dried over Na2SO4. After the removal of solvent, the product was purified by column chromatography.

General Procedure for Horner-Wadsworth-Emmons Reaction. 59 NaH (95%, 6.0 equiv.)

was added to a cooled (0 °C) solution of phosphonate (1.0 equiv.) in THF under an inert atmosphere. The reaction was allowed to warm to ambient temperature and stirred for 30 min before addition of aldehyde (1.2 equiv.) in THF. The reaction was then refluxed at 75 °C for 1 h. After cooling to room temperature the reaction was quenched by the addition of 1 M HCl and the resulting mixture extracted into CHCl3 (×3). The combined organic layers were washed with water, brine and dried over Na2SO4. The residue was concentrated and purified by column chromatography (petroleum ether-ethyl acetate) to afford the desired alkene.

1-Methoxy-3-phenethylbenzene (3). 66 Wittig reaction: 90% yield (0.4 mmol scale), E:Z = 1.5:1; Hydrogenation: 72% yield (0.4 mmol scale);

Scheme 1 .

 1 Scheme 1. General Synthetic Strategy for the Synthesis of Compounds 2-22 Employing

Figure 1 .

 1 Figure 1. Structure of batatasin-III (1) and synthetic dihydrostilbene derivatives 2-22 included in the present study

Figure 2 .

 2 Figure 2. Root length (±SD) of L. sativa seedlings in response to the inhibitory effect of selected representative dihydrostilbene compounds. Root length estimates are based on a total of 18 seedlings (pre-germinated before incubation) divided into three incubation chambers, and analyzed after three days of incubation. Distilled water was employed as negative control and the compounds were included at concentrations ranging from 0.1 to 4 mM.

  potentially via different modes of action. No clear link between the structure of the compounds and their biological effect is seen towards the microalgae. It was unexpected to see such a diverse bioactivity amongst the tetrasubstituted analogues, with compounds 16,19 and 21 representing some of the most active antialgal compounds. Conversely the structurally related compounds 18 and 20 are among the poorer inhibitors. In an attempt to further investigate the antialgal mode of action, after incubation with the compounds for MIC calculation, algal cells were transferred to fresh medium and incubated for five days. The recovered cells displayed normal growth (data not shown) illustrating that dihydrostilbenes appear to act via a reversible biostatic mechanism as opposed to a direct toxic mode of action.

Figure 3 .

 3 Figure 3. Effects of 1-22 at 5 µg/mL on the settlement of B. improvisus cyprid larvae presented as percentages of settled (dark gray columns) and dead cyprids (light gray columns) and given as means ± standard error (n = 4). Remaining larvae were free swimming. DMSO (0.1%, v/v) in filtered seawater was used as the negative control "0".

hydrophobic analogues with ClogP values between 4 .25 and 4 . 60 ( 3 , 5 , 9 , 12 , 13 and 22 ) 8 , 16 , 20 ,

 4460359122281620 display any toxicity at 5 µg/mL. Of further interest, the toxic analogues (compounds 2, 7, and 21) all display a similar overall polarity, with ClogP values between 3.20 and 3.78. These results indicate that the investigated scaffold has a broad inhibitory activity, with the more hydrophobic compounds inhibiting cyprid settlement whilst not displaying generally toxic effects as graphically shown in Figure4. These observations suggest that the antifouling structure-activity-relationship of the dihydrostilbenes towards barnacles is dictated by overall polarity and not a defined hydroxy and methoxy substitution pattern.

Figure 4 .

 4 Figure 4. Graphical representation of the correlation between hydrophobicity (CLogP), inhibition of cyprid settlement (IC50) and cyprid toxicity for the studied compounds. Inactive compounds with IC50-values >5 µg/mL have all been given an inhibitory value of "5".

Figure 5 .

 5 Figure 5. Metamorphosis inhibition of C savignyi larvae exposed to 5, 9 and 20. Inhibition of metamorphosis is relative to corresponding blank controls and values are means (n = 3) ± standard error.

Table 1 .

 1 . Lactuca sativa Seedling Root Elongation Inhibition by Compounds

1-13

	compound	Mw	CLogP a	IC50 (mM) b	root growth at 4 mM (%) c
	1	244.29	3.35	1	7.4
	2	198.26	3.92	0.5	4.4
	3	212.29	4.51	>4	92.6
	4	214.26	3.25	0.5	5.8
	5	242.31	4.60	>4	77.9
	6	214.26	3.32	0.5	10.3
	7	228.29	3.77	>4	79.4
	8	228.29	3.77	2	14.7
	9	242.31	4.25	>4	73.5
	10	230.26	2.59	2	13.2
	11	230.26	2.59	2	19.1
	12	272.34	4.52	2	42.6
	13	272.34	4.52	>4	79.4
	a Calculated using ChemBioDraw Ultra 14.0. b The IC50 value was defined as the concentration yielding a
	50% reduction in root elongation compared to that of distilled water. c In comparison (%) to the root
	elongation seen for distilled water.

Table 2 .

 2 MIC a (in µg/mL) of Batatasin-III (1) and Analogues Against the Adhesion (A) and

				Growth (G) of Microalgae
		H. coffeaformis	P. roscoffensis	C. closterium	P. purpureum
	Compound	A	G	A	G	A	G	A	G
	1	10	10	10	10	10	10	-b	10
	2	0.01	0.01	0.01	0.01	0.01	0.1	1	1
	3	10	1	10	1	10	1	-	10
	4	10	0.01	0.1	0.1	0.1	0.1	10	10
	5	0.1	0.01	0.1	0.01	10	1	10	10
	6	-	10	-	-	-	-	-	-
	7	0.01	0.01	0.1	0.01	0.01	0.01	1	0.1
	8	0.01	0.01	0.01	0.01	0.1	0.01	1	1
	9	1	0.01	1	0.01	0.1	0.01	10	1
	10	10	1	1	0.1	1	0.01	-	1
	11	0.01	0.01	1	1	0.01	0.01	1	0.1
	12	10	1	10	1	1	1	-	10
	13	10	10	1	10	1	10	-	-
	14	10	1	10	1	0.1	0.1	-	10
	15	0.01	1	0.01	1	0.01	0.1	0.01	1
	16	0.01	0.01	0.01	0.01	0.01	0.01	0.1	1
	17	1	10	0.01	1	0.01	0.01	0.1	0.1
	18	-	10	-	10	-	10	-	-
	19	0.01	0.01	0.1	0.01	0.1	0.1	1	0.1
	20	-	10	-	10	-	10	-	-
	21	0.01	0.01	0.1	0.1	0.01	0.01	10	1
	22	0.01	1	0.01	0.1	0.1	0.01	1	1
	Sea-nine™ ,c	<0.01 <0.01	<0.01	<0.01	<0.01	<0.01	<0.01	<0.01

below) of the microalage Cylindrotheca closterium, Halamphora coffeaeformis, Pleurochrysis roscoffensis, Porphyridium purpureum is presented in Table

2

.

a Minimum inhibitory concentration. b Not active at >10 µg/mL. c Data from Trepos et al.

39

Table 3 .

 3 MIC a (in µg/mL) of Batatasin-III (1) and Analogues Against the Growth of Marine

	Bacteria b

a Minimum inhibitory concentration. b Included bacterial strains: Vibrio aestuarianus, Vibrio carchariae, Vibrio harveyi, Vibrio natriegens, Vibrio proteolyticus, Halomonas aquamarina, Roseobacter litoralis, Shewanella putrefaciens, Polaribacter irgensii and Pseudoalteromonas elyakovii. c Compound 7

, 10, 12, 16, 19, 20 and 22

Table 4 .

 4 Potency and Toxicity of 1 and Analogues Against the Barnacle B. improvisus.

a Calculated using ChemBioDraw Ultra 14.0. b Reported at 5 µg/mL. Toxicity for the negative control DMSO (0.1%, v/v) in filtered seawater was 7.5 %. c Not determined.

  Compounds 13, 18 and 19 exhibited no effect on the settling behavior of the B. improvisus cyprids at 5 µg/mL, whilst several other compounds completely inhibited settlement under the same conditions. At 5 µg/mL,

	compound	Mw	CLogP a IC50 (µg/mL)	toxicity (%) b
		244.29	3.35	1.0	7.0
		198.26	3.92	0.5	100
		212.29	4.51	0.75	0.0
		214.26	3.25	1.0	11.1
		242.31	4.60	1.0	7.7
		214.26	3.32	1.0	16.0
		228.29	3.77	1.0	100
		228.29	3.77	0.75	60.8
		242.31	4.25	0.75	5.3
		230.26	2.59	5.0	3.6
		230.26	2.59	1.5	10.0
		272.34	4.52	0.75	0.0
		272.34	4.52	>5	8.0
		258.31	3.94	1.0	2.0
		244.29	3.17	1.5	8.4
		274.31	3.20	2.5	71.9
		246.26	1.99	5.0	0.0
		260.29	2.44	>5	12.9
		260.29	2.44	>5	0.0
		288.34	3.78	0.25	100
		288.34	3.78	1.5	24.3
		302.36	4.25	1.0	10.9
	Sea-nine™	282.20	4.90	0.25	n.d. c

compounds 2, 7 and 20 killed all cyprids. In contrast, compounds 3, 9 and 12 inhibited settlement of the cyprids but did not kill themindicating a non-toxic mode of action. This finding implies that within a compound library, different mode of actions may be operating.

Table 5 .

 5 Potency of Selected Compounds Against the Ascidian C. savignyi Data taken from Ref. 53 against Ciona intestinalis. b Not determined.

	compound	IC50 (µg/mL)	IC99 (µg/mL)
	1	1.9	5.5
	5	3	21.1
	7	1.1	2.6
	9	1.1	7.2
	20	0.4	3.5
	22	4.3	44.4
	Sea-nine™	0.2 a	n.d. b

a All six of the evaluated compounds inhibited C. savignyi larval metamorphosis at low concentrations, similar to those recorded against B. improvisus. Compound 20 was the most active analogue, displaying an IC50 of 0.4 µg/mL. This inhibitory potency correlates well with the data from the barnacle assay performed in the current study, and is comparable to that recently reported by Moodie et al. for synthetic analogues of polygodial.

  1 H NMR (400 MHz, CDCl3) δ 7.34 (2H, t, J = 7.2 Hz), 7.28 -7.21 (4H, m), 6.85 (1H, d, J = 7.5 Hz), 6.83 -6.78 (2H, m), 3.83 (3H, s), 2.97 (4H, s);13 C NMR (101 MHz, CDCl3) δ 159.7, 143.5, 141.9, 129.4, 128.6, 128.5, 126.0, 121.0, 114.3, 111.4, 55.2, 38.1, 37.9; HRESIMS m/z [M +H] + 213.1270 (calcd for C15H17O, 213.1274). funding the Biocide Tool Box research programme (UOAX1410), which supported P.C. involvement in this research. R.A, Ingebrigtsen (UiT The Arctic University of Norway) and J. Lehmuskallio (http://www.luontoportti.com) are acknowledged for providing the microalgae and crowberry images. The authors would also like to thank E. Raasholm for providing the comparison of juglone vs. batatasin-III interference capacity on lettuce roots and S. Kaino, E. Robertsen and C. Weber (UiT The Arctic University of Norway) for their help on the lettuce seedling experiment.

ACKNOWLEDGMENTS

This work was partly supported with grants from the Norwegian Research Council (ES508288) and J.S. and L.W.K.M. are grateful for the support. J.S was further supported by a VINNMER M.C. incoming grant from VINNOVA (grant. 2014-01435). H.P. and G.C. were supported by the Centre for Marine Chemical Ecology (http://www.cemace.science.gu.se) at the University of Gothenburg. C.H and R.T were supported by Biogenouest (http://www.biogenouest.org) at the University of Western Brittany. The authors are grateful to the New Zealand Ministry of Business, Innovation and Employment (MBIE) for

Marine Organisms. Four pure, but non-axenic, marine microalgae (obtained from Algobank, Caen, France) and ten marine bacterial strains were used in the current study (Table 6). The strains were selected to represent fouling species encountered in both estuarine and marine environments. 60,61 The bacteria were grown at 26 °C in a marine medium, composed of 0.5% peptone (neutralized bacteriological peptone, Oxoid Ltd.) in filtered (11 μm) natural seawater. Microalgae were grown at 22 °C in F/2 medium prior to use. Cyprids of B. improvisus were reared at the Lovén Centre for Marine Infrastructure -Tjärnö, University of Gothenburg, Sweden and the settlement inhibition was investigated using methods initially described by Berntsson. 29,62 Newly moulted cyprids were collected and used for the settlement assays. Adult C. savignyi were collected and maintained at the Cawthron Institute, New Zealand as previously described. 43 Eggs and sperm were harvested from three gravid individuals and transferred to separate 50 mL glass Petri dishes (Ø 90 mm)

ASSOCIATED CONTENT

Supporting Information. Characterization of all prepared compounds and 1 H NMR and 13 C NMR data for compounds 6 and 7.

Author Contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.


Gabriel Morgado

Bogdan Nowakowski

Annie Lemarchand

The FKPP wave front as a sensor of perturbed diffusion in concentrated systems

The sensitivity to perturbations of the Fisher and Kolmogorov, Petrovskii, Piskunov front is used to find a quantity revealing perturbations of diffusion in a concentrated solution of two chemical species with different diffusivities. The deterministic dynamics includes cross-diffusion terms due to the deviation from the dilution limit. The behaviors of the front speed, the shift between the concentration profiles of the two species, and the width of the reactive zone are investigated, both analytically and numerically. The shift between the two profiles turns out to be a well-adapted criterion presenting noticeable variations with the deviation from the dilution limit in a wide range of parameter values.

Introduction

The Fisher and Kolmogorov, Petrovskii, Piskunov (FKPP) wave front is the prototype of pulled fronts, whose properties are strongly influenced by the leading edge of the profile [1,2]. From the perspective of applications, wave fronts of FKPP type are widely used in models of combustion [3] and biology [START_REF] Murray | Mathematical Biology[END_REF][START_REF] Mendez | Reaction-Transport Systems: Mesoscopic Foundations, Fronts, and Spatial Instabilities[END_REF][START_REF] Mendez | Stochastic Foundations in Movement Ecology: Anomalous diffusion, invasion fronts and random searches[END_REF], in particular to account for adaptation, mutation and selection in evolutionary strategies. Sufficiently steep initial profiles converge to the front propagating at the minimum velocity deduced from a linear stability analysis [START_REF] Van Saarloos | [END_REF]8]. The FKPP front is known to be highly sensitive to even small perturbations of many different origins. Brunet and Derrida proved that a small cutoff introduced in the leading edge of the front induces a negative correction to the front speed [9]. Fluctuations have also been shown to modify the propagation speed of pulled front [10]. The description of a reaction-diffusion system at a mesoscopic scale by a master equation [START_REF] Nicolis | Self-Organization in Nonequilibrium Systems[END_REF][START_REF] Gardiner | Handbook of Stochastic Methods for Physics[END_REF] as well as particle dynamics simulations using the Direct Simulation Monte Carlo (DSMC) method [START_REF] Bird | Molecular Gas Dynamics and the Direct Simulation of Glas Flows[END_REF] both revealed that the discrete nature of particle numbers induces analogous corrections to the front speed as a cutoff in the deterministic partial differential equations.

Roughly speaking, the cutoff can be interpreted as the inverse of the particle number in the reactive zone [START_REF] Hansen | [END_REF]. It has then been shown in the framework of a Langevin approach that the effect of a multiplicative noise on the front speed can be studied under the scope of a modified cutoff theory [15,16]. The effect of a slightly exothermic reaction on the front speed has also been studied using DSMC. Below a critical heat release, the speed remains equal to the one in the isothermal case and is imposed by the Chapman-Jouguet criterion above it [17]. In addition, the DSMC method has been used to study the impact of the perturbation of local equilibrium by a fast reaction associated with a small activation energy: Reaction-induced non Maxwellian particle velocity distributions result in positive corrections to the front speed [18]. Molecular dynamics simulations of dense fluids also lead to propagation speeds larger than the marginally stable one [START_REF] Hansen | [END_REF]. Recent articles focus on the effect of an advection term [19,20,21].

In this paper, we study a reaction-diffusion wave front of FKPP type propagating in confined systems such as biological environments or more generally in concentrated chemical systems. We focus on the impact of molecular crowding on diffusion. Indeed, diffusion may be modified at high concentrations and the usual Fick's law relating the diffusion flux of a given species to the gradient of the concentration of that single species is not always valid. Linear nonequilibrium thermodynamics is used to extend Fick's law to concentrated systems, leading to diffusion flux depending on the concentration gradients of all the chemical components of the mixture [START_REF] De Groot | Non-Equilibrium Thermodynamics[END_REF][START_REF] Bullara | [END_REF]24]. In these conditions, the partial differential equations governing dynamics involve cross-diffusion terms. Experiments demonstrate that cross-diffusion coefficients can be quite significant in many kinds of chemical systems involving for example ions, micelles, surface or polymer reactions [25,26,27,28]. A priori, cross-diffusion can lead to spatial and spatiotemporal pattern formation. Recently, hydrodynamic instabilities have been observed in reaction-diffusionconvection patterns in microemulsions [29,30]. We checked that the wavelength of a Turing pattern is not affected and can therefore not characterize the perturbation of diffusion induced by high concentrations [24,31]. The goal of the paper is first to determine the impact of cross-diffusion on the properties of FKPP wave fronts involving two chemical species A and B of different diffusivities. Then, we intend to harness the sensitivity of FKPP fronts to find a macroscopic quantity depending on the detail of the diffusion rates and thus sensitive to the deviation from the dilution limit. Literature mostly reports on corrections to the front speed [8,15,16,19,20,21,32,33]. We will first examine the impact of diffusion perturbation on the front speed and then investigate the behavior of alternative quantities with the aim of defining a criterion that could be used in experiments to check if diffusion is perturbed in a concentrated system admitting a FKPP front.

The paper is organized as follows. We present the reaction-diffusion model in Sec. 2.

Analytical expressions of different quantities characterizing the wave front in dilute and concentrated systems are derived in Sec. 3. Specifically, we look for effects of diffusion perturbation on the propagation speed, the shift between A and B profiles, and the width of the reactive zone. The analytical predictions are compared to numerical results in Sec. 4. Section 5 contains conclusions.

The reaction-diffusion model

The system is composed of three chemical species. Two of them, A and B, are reactive whereas the third species S is the solvent. The reaction scheme is given by

A + B k -→ 2 A ( 1
)
where k is a rate constant. In a dilute system, the reaction-diffusion equations associated with the mechanism are

∂ t A = kAB + D A ∂ 2 x A ( 2
)
∂ t B = -kAB + D B ∂ 2 x B ( 3
)
where A and B are the concentrations of species A and B, and D A and D B are the diffusion coefficients of A and B species, respectively. In a concentrated solution, diffusion of A and B species may be perturbed. Nevertheless, we assume that the solution is ideal, in the sense that the activity remains equal to the concentration. In the framework of linear nonequilibrium thermodynamics, we derived linear relations between generalized diffusion fluxes and forces which couple the diffusion of a species with the gradients of each constituent of the mixture [START_REF] De Groot | Non-Equilibrium Thermodynamics[END_REF]24]. After the elimination of the solvent concentration S, we have shown that the reaction-diffusion equations are given by:

∂ t A = kAB + D A ∂ x 1 - A C ∂ x A -D B ∂ x A C ∂ x B ( 4
)
∂ t B = -kAB + D B ∂ x 1 - B C ∂ x B -D A ∂ x B C ∂ x A ( 5
)
where the total concentration C = A + B + S is constant. Equations ( 4) and ( 5) converge to Eqs. ( 2) and (3) in the dilution limit (A + B)/C → 0 and are valid for sufficiently small values of (A + B)/C.

We choose inhomogeneous initial conditions in the form of a step function for species A and B:

x < 0, A(x, t = 0) = V 0 , B(x, t = 0) = 0 x ≥ 0, A(x, t = 0) = 0, B(x, t = 0) = V 0 (6)
where the constant V 0 characterizes the height of the step. The reaction-diffusion equations have wave front solutions which propagate at constant speed v α where the exponent α = d for the dilute system and α = c for the concentrated system. These FKPP fronts are also called pulled fronts because the speed is determined by the leading edge of the profile which pulls the bulk to the right [START_REF] Van Saarloos | [END_REF]9].

For identical diffusion coefficients D A = D B and initially homogeneous conditions for S and A + B = V 0 , the sum A + B does not evolve. Then, introducing the conservation 4) and ( 5), we find that the concentrated solution obeys the same unperturbed equations given in Eqs. ( 2) and (3) as the diluted system. With the aim of specifying how the properties of a FKPP wave front are perturbed as the system becomes more concentrated, we consider different diffusion coefficients D A and D B in the following.

relation A + B = V 0 into Eqs. (
3 Analytical derivation of wave front features in dilute and concentrated systems

Propagation speed

To derive an approximate analytical expression of the propagation speed, we perform a linear stability analysis around the steady state (A = 0, B = V 0 ) in the moving frame at speed v α . Linearizing the reaction-diffusion equations is supposed to be valid in the leading edge of the front. We introduce the following transformation:

ξ = x v α -t (7) A(x, t) = f α (ξ) (8) B(x, t) = g α (ξ) (9)
where α = d, c.

We first address the case of a dilute system. Equations ( 2) and ( 3) can be rewritten as

0 = kf d g d + f ′ d + ε d D A f ′′ d (10) 0 = -kf d g d + g ′ d + ε d D B g ′′ d ( 11
)
where ε d = 1/v 2 d and ′ denotes the derivation with respect to ξ. The second-order differential equations are transformed into first-order equations in the four-dimension space

(f d , f ′ d , g d , g ′ d )
. We perform a linear stability analysis around the unstable steady state and obtain the following linearized uncoupled system for (f d , f ′ d ):

df d dξ = f ′ d (12) df ′ d dξ = - v 2 d D A (kV 0 f d + f ′ d ) (13)
which leads to the eigenvalues λ ± :

λ ± = -v 2 d ± v d v 2 d -4kV 0 D A 2D A ( 14
)
The existence of wave front solutions is ensured for real eigenvalues which imposes the minimum velocity:

v * d = 2 kV 0 D A (15)
In the concentrated case, Eqs. ( 4) and ( 5) read

0 = kf c g c + f ′ c + ε c D A 1 - f ′ c C f ′′ c - (f ′ c ) 2 C -D B f c g ′′ c C + f ′ c g ′ c C (16) 0 = -kf c g c + (g c ) ′ + ε c D B 1 - g c C g ′ c - (g ′ c ) 2 C -D A g c f ′′ c C + f ′ c g ′ c C ( 17
)
where

ε c = 1/v 2 c
. Following the same procedure as in the dilute case, we find

v * c = 2 kV 0 D A (18)
Hence, the front speeds in the dilute system and the concentrated system are identical in the framework of a linear stability analysis. Consequently, the following notations are introduced:

v * c = v * d = v ( 19
)
ε c = ε d = ε ( 20
)
We checked that for sufficiently steep initial conditions and after a transient regime, the wave front propagates at the minimum speed v, as in the case of identical diffusion coefficients [START_REF] Van Saarloos | [END_REF]9]. Interestingly, in both the dilute and concentrated systems, the minimum propagation speed of the linearized system does not depend on the diffusion coefficient D B of species B and only depend on the product kV 0 D A .

Front profile

A perturbation technique is used to determine analytical expressions of quantities characterizing the wave front profile. We look for solutions of the reaction-diffusion equations in the frame moving at front speed v as a Taylor expansion in the small parameter ε [START_REF] Murray | Mathematical Biology[END_REF].

As ε tends to zero, Eqs. ( 10) and ( 11) and Eqs. ( 16) and ( 17) switch from second-order differential equations to first-order equations. The boundary conditions of the first-order equations must be compatible with the ones of the second-order equations. However, the reactive terms ±kf α g α and the first-order terms f ′ α and g ′ α equal zero at the boundaries ξ = ±∞ for all perturbation orders, which ensures the consistency of a regular perturbation procedure:

f α = f α,0 + εf α,1 + ε 2 f α,2 + ... ( 21
)
g α = g α,0 + εg α,1 + ε 2 g α,2 + ... ( 22
)
where f α,i and g α,i are the i-th order corrections with i = 0, 1, 2, ... and α = d, c. The boundary conditions obey:

f α,0 (-∞) = V 0 , f α,0 = (+∞) = 0 ( 23
)
g α,0 (-∞) = 0, g α,0 (+∞) = V 0 ( 24
)
f α,i (±∞) = g α,i (±∞) = 0, for i ≥ 1 ( 25
)
The origin of the ξ-axis is chosen such that

f α,0 (0) = V 0 2 ( 26
)
f α,i (0) = 0, for i ≥ 1 (27)
The zeroth-order solutions are straightforwardly deduced from Eqs. ( 10) and [START_REF] Nicolis | Self-Organization in Nonequilibrium Systems[END_REF] and Eqs. ( 16) and ( 17) without diffusion terms

f α,0 = V 0 1 + e kV 0 ξ
(28)

g α,0 = V 0 1 + e -kV 0 ξ ( 29
)
for α = d, c.

Instead of determining the higher-order solutions, we focus on characteristic properties of the profiles. We define the height h α = f α (0) -g α (0) as the difference of concentrations between species A and B in the moving frame at the origin ξ = 0. The height h α evaluates the shift between the profiles of species A and B due to their different diffusivities. Using

Eqs. ( 26) and ( 27), we obtain the evaluations of the height up to the first and second orders:

h α,1 = εg α,1 (0) ( 30
)
h α,2 = εg α,1 (0) + ε 2 g α,2 (0) (31)
for α = d, c. Using Eqs. (10) and [START_REF] Nicolis | Self-Organization in Nonequilibrium Systems[END_REF], we obtain the first h d,1 and second-order h d,2

approximations of the height in the dilute case:

h d,1 = V 0 16 1 - D B D A ( 32
)
h d,2 = V 0 16 1 - D B D A 1 + 1 8 1 - D B D A ( 33
)
As a result, the height h d,2 does not depend on the rate constant k and the scaled height h d,2 /V 0 only depends on the ratio D B /D A . Using Eqs. ( 16) and ( 17), we find in the concentrated case:

h c,1 = V 0 16 1 - D B D A 1 - V 0 C (34) h c,2 = V 0 16 1 - D B D A 1 - V 0 C 1 + 1 8 1 - D B D A 1 -2 V 0 C ( 35
)
We check that, in the dilution limit V 0 C → 0, the first and second-order expressions of the height in the concentrated system given in Eqs. (34) and ( 35) converge to the first and second-order expressions of the height in the dilute system given in Eqs. (32) and (33).

Up to the second order, the scaled height h c /V 0 only depends on the ratio of the diffusion coefficients D B /D A and the deviation V 0 /C from the dilution limit. The parameter V 0 /C varying in the range [0, 1], the first-order evaluation h c,1 in a concentrated system is always smaller than the corresponding quantity h d,1 given in Eq. ( 32) in the dilute system. High concentrations tend to reduce the shift between A and B profiles, at least at the first order.

The width W α of the wave front is deduced from the inverse of the steepness of the A profile at ξ = 0

W α = -vV 0 /f ′ α (0) (36)
We consider the following evaluations of the width:

W α,1 = -vV 0 f ′ α,0 (0) + εf ′ α,1 (0) (37) W α,2 = -vV 0 f ′ α,0 (0) + εf ′ α,1 (0) + ε 2 f ′ α,2 (0) (38)
deduced from the first-order and the second-order expansions of f α . For the sake of simplicity, W α,1 and W α,2 will be called first and second-order evaluations of the width, respectively. In the dilute case, the first-order W d,1 and the second-order W d,2 expressions of the width are deduced from Eqs. (10) and [START_REF] Nicolis | Self-Organization in Nonequilibrium Systems[END_REF]:

W d,1 = 8 D A kV 0 1 + 1 8 1 - D B D A -1 (39)
W d,2 = 8 D A kV 0 1 + 1 8 1 - D B D A - 1 64
D B D A 3 - D B D A -1 (40)
It is worth noting that W d,0 = 8 D A kV 0 is an approximation of the width in the case D A = D B known to be valid up to the first order [START_REF] Murray | Mathematical Biology[END_REF]. The second-order evaluation W d,2

provides the corrected expression 8

D A kV 0 1 - 1 32 of the width for D A = D B . Using
Eqs. ( 16) and (17) in the concentrated case, we obtain after tedious calculations:

W c,1 = 8 D A kV 0 1 + 1 8 1 - D B D A 1 - 3V 0 2C -1 (41)
(42)

W c,2 = 8 D A kV 0 1 + 1 8 1 - D B D A 1 - 3V 0 2C - 1 64
D B D A 3- D B D A + 9 2 -8 D B D A + 7 2 D 2 B D 2 A V 0 C - 7 2 -7 D B D A + 7 2 D 2 B D 2 A V 2 0 C 2 -1
We check that, in the dilution limit 4) and [START_REF] Mendez | Reaction-Transport Systems: Mesoscopic Foundations, Fronts, and Spatial Instabilities[END_REF] in the concentrated case.

V 0 C → 0,

Comparison between analytical and numerical results

Analytical results are derived from expansions with respect to ε = 1 v 2 . For the domain of validity of approximations to be the same for all the considered parameter values, we impose that the front speed remains constant, i.e. k, V 0 , and D A are constant. In addition, the values of k, V 0 , and D A are set such that ε is much smaller than 1:

k = 10, V 0 = 10, D A = 1 ( 43
)
According to Brunet and Derrida [9], a small cutoff δ introduced in the nonlinear reactive term ±kAB induces a negative correction to the propagation speed:

v -v s v = π 2 2(ln δ) 2 (44)
where v s is the velocity of the simulated front. More generally, FKPP wave fronts are known to be sensitive to small perturbations, including fluctuations [START_REF] Hansen | [END_REF] in stochastic descriptions, perturbation of velocity distribution function [18] in particle dynamics simulations. With the aim of unambiguously assigning the observed perturbations of a wave front to high concentrations, the effect of a cutoff on the numerical results has to be evaluated and disregarded. If sufficiently fine space and time discretizations are employed, the cutoff mainly originates from the precision of the computations involving real numbers.

Choosing double precision leads to a cutoff δ ≃ 10 -16 . Using Eq. ( 44), the relative correction to the front speed is estimated at 0.4%. The effect of space discretization is similar on wave fronts with profile widths occupying the same number of spatial cells. According to Eq. ( 39) and (41), at zeroth order, the width W d,0 = W c,0 = 8 D A kV 0 only depends on the rate constant k, the diffusion coefficient D A of species A, and the boundary condition V 0 . For the effect of the cutoff to be the same in all the numerical solutions for different parameters, we impose the cell length, ∆x = πW d,0 5000 , the total number of cells, n = 50000, and the time step, ∆t = 0.1∆x 2 D max

B

, where D max B = 16 is the maximum diffusion coefficient considered. Hence, the width occupies about 1600 cells in all cases. For the initial condition defined in Eqs. ( 6), we numerically solve Eqs. ( 2) and (3) and Eqs. ( 4) and ( 5) using

Euler method for different values of the diffusion coefficient D B in the interval 1 16 , 16 and the total concentration C in the interval [25,400].

To mimic an infinite system in the x-direction, it is necessary to counterbalance the production of species A due to the propagation of the reactive front. At each time step where the sum of the concentrations of species A in each cell reaches the initial value nV 0 /2, the first left cell is suppressed and a new cell is added to the right with no A species and a V 0 concentration for species B. This trick amounts to switching in the moving frame at the propagation speed of the wave front. The speed is numerically evaluated using the time difference between two creations of right cells after the stationary regime has been reached.

For these conditions, we find that the front speeds associated with the dilute and the concentrated cases are the same and about 0.5% smaller than the zeroth-order prediction v * d . This result is close to the estimation of the cutoff effect induced by double precision. The choice of the other parameters, such as cell length and time step, and the simulation procedure are therefore satisfying. In addition, the numerical results confirm that the propagation speed is not impacted by the perturbation of diffusion induced by high concentrations as predicted in Eq. ( 18).

Figure 1 shows the stationary concentration profiles of A and B species deduced from the numerical integration of Eqs. ( 2) and (3) in the dilute case. In agreement with Eq. ( 33), Figure 2a shows the variation of the scaled height h d /V 0 in the dilute case with respect to the ratio of the diffusion coefficients D B /D A in logarithmic scale. The first and secondorder analytical expressions h d,1 and h d,2 given in Eq. ( 32) and ( 33) are compared to the results deduced from the numerical integration of Eqs. ering that D A is set at 1 whereas D B varies, and that the perturbative term in Eq. ( 11)

is proportional to ε d D B = 1 4kV 0 D B D A
, the analytical result is correct provided that D B is smaller or equal to 1, i.e. D B < D A . It is worth noting that, as D B → 0, the height h d tends to a positive limit slightly larger than V 0 /16 as predicted by Eq. ( 33): For fixed B particles, the concentration of species B in the moving frame reaches the value h d ≃ V 0 /16, independent of the diffusion coefficient D A of species A at the abscissa ξ = 0 for which the concentration of species A equals V 0 /2. 4) and ( 5), the diffusion of a given species is affected by the diffusion coefficient of the other species which reduces the effect due to D A = D B . In the limit of large D B , both h d and h c reach the extreme value -0.5 so that the difference h d -h c tends to zero.

For D B /D A > 1,
As D B → 0, the relative height difference h d -h c h d tends to a positive limit larger than the prediction V 0 /C of the first-order approximation deduced from Eqs. ( 32) and (34).

The first-order approximation does not account for the variation of the relative height

difference h d -h c h d with respect to D B /D A .
The numerical results perfectly agree with the second-order prediction in the domain D B /D A < 1 for which perturbative analysis is valid. Interestingly, the relative difference of heights reaches 28% for small D B /D A values, making the shift between A and B profiles well adapted to the discrimination between the concentrated and the dilute system.

As mentioned in Sec. 3, the height h c only depends on D B /D A and V 0 /C. The varia-tions of the height h c in the concentrated system with respect to V 0 /C are given in Fig. 3 for two different values of D B /D A . The parameter V 0 /C quantifies the deviation from the dilution limit obtained for V 0 /C → 0. We recall that a concentrated system does not refer to large values of C but to high concentrations A + B of the solute. The results shown in Fig. 2b are given for V 0 /C = 0.25 which is a good compromise between a too small value for which concentration effects would be negligible and a too large value for which the reaction-diffusion equations (Eqs. ( 4) and ( 5)) would not be valid. In Fig. 3a, the results are given for D B /D A = 1/16 < 1, associated with a positive value of h c in agreement with the results shown in Fig. 2. We find that the shift between the profiles of A and B species decreases as the system becomes more concentrated, i.e. as V 0 /C increases.

For the small value of D B /D A chosen, the expansion technique rapidly converges and the agreement between the numerical results and the second-order approximation is excellent.

In Fig. 3b, for D B /D A = 7/3 > 1, the height h c is negative and decreases in absolute value as V 0 /C increases. As already mentioned, the perturbation analysis is less relevant and the second-order prediction deviates from the numerical results. The concentrated system is closer to the standard FKPP front with D A = D B than the dilute system is.

Figure 4a gives the variation of the front width W d of species A with respect to the ratio of the diffusion coefficients D B /D A in logarithmic scale in the dilute case. The slope s d of the A concentration profile at ξ = 0, deduced from the numerical integration of Eqs. ( 2) and (3), is evaluated according to:

s d = - 0.2V 0 ξ 2 -ξ 1 ( 45
)
where the abscissa ξ 1 and ξ 2 in the moving frame obey f d (ξ 1 ) = 0.6V 0 and f d (ξ 2 ) = 0.4V 0 .

Equation ( 36) is used to obtain an estimation of the width of the reactive front. Both the first and second-order approximations given in Eqs. (39) and (40) satisfactorily agree with the numerical results for D B /D A < 4.

An analogous procedure is followed to determine an estimation of the width W c in the concentrated system from the numerical integration of Eqs. ( 4) and [START_REF] Mendez | Reaction-Transport Systems: Mesoscopic Foundations, Fronts, and Spatial Instabilities[END_REF]

Conclusion

In this work, we have studied the effects of concentration-induced perturbation of diffusion on FKPP wave fronts. The sensitivity of FKPP wave front to small perturbations makes it a good candidate for characterizing the effects of the deviation from the dilution limit on diffusion. We assume that high solute concentrations induce specific cross-diffusion terms in the reaction-diffusion equations in the framework of linear nonequilibrium thermodynamics. We consider two chemical species A and B engaged in the reaction A + B → 2A and with different diffusion coefficients, knowing that the perturbation of diffusion vanishes in the limit of identical diffusion coefficients. The analytical results deduced from a linear stability analysis show that the propagation speed in a concentrated system is not appreciably affected by the perturbation of diffusion. The relative correction of the profile width with respect to the dilute case presents an interesting behavior: It changes sign as the ratio of diffusion coefficients varies. However, the relative correction is in the order of 6% for concentration values in the domain of validity of the reaction-diffusion equations. We have introduced the height h as the difference of concentrations between A and B species in the moving frame at the origin in order to evaluate the shift between A and B profiles due to their different diffusion coefficients. Contrary to the width, the relative correction to the height h with respect to the dilute case reaches 28% for reasonable solute concentrations. The relative correction to the height is larger than 25% when the diffusion coefficient of species B is smaller than the one of species A. The diffusion coefficient of species B has to become at least 30 times larger than the diffusion coefficient of species A for the relative correction to the height to drop below 5%. In the limit of very large diffusion coefficients of species B, the width of the profile may be chosen as an alternative criterion to detect concentration-induced perturbations since the relative correction to the width converges to about 3% in this limit. We conclude that the FKPP wave front offers the opportunity to characterize concentration-induced perturbation of diffusion. Specifically, the shift of the concentration profiles of species associated with different diffusion coefficients is a well-adapted criterion showing significant variations with the deviation from the dilution limit in a wide range of diffusion coefficients.

  the first and second-order expressions of the width in the concentrated system given in Eqs. (41) and (42) converge to the first and second-order expressions of the width in the dilute system given in Eqs. (39) and (40). In addition, the zeroth-order evaluations coincide, W d,0 = W c,0 = 8 D A kV 0 . The scaled width kV 0 D A W c only depends on D B /D A and V 0 /C as the height does. In the next section, the analytical predictions of the height and the width are compared to the corresponding numerical results deduced from Eqs. (2) and (3) in the dilute case and Eqs. (

Figure 1 : 2 .

 12 Figure 1: Snapshot of the wave front profile deduced from Eqs. (2,3) with D B /D A = 16 at time t = 400. Concentration profiles of A (black solid line) and B (black dashed line) versus spatial coordinate x ∆x . The horizontal line represents V 0 2 . The vertical segment represents the height h d at ξ = 0.

( 2 )Figure 2 :

 22 Figure 2: (a) Scaled height h d /V 0 in the dilution limit and (b) relative difference between the dilute case and the concentrated case for V 0 /C = 0.25 versus diffusion coefficients ratio D B /D A . First-order approximation (black dashed line), second-order approximation (red solid line), and numerical results (black squares).

  the height h d is negative. The second-order approximation is valid until D B /D A = 4 and diverges for larger values of D B /D A . In the explored range of D B /D A , the height h d significantly decreases. Still, the scaled height h d /V 0 is bounded by -0.5 since concentrations cannot be negative. The behavior of the height h c associated with the concentrated system is similar to the one of h d . Nevertheless, as shown in Fig. 2b, the relative height difference h d -h c h d is always positive in the entire range of D B /D A values. Hence, the shift between the concentration profiles of species A and B induced by the difference between the diffusion coefficients D A and D B is reduced in a concentrated system. Actually, according to Eqs. (

Figure 3 :Figure 4 :Figure 5 :

 345 Figure 3: Scaled height h c /V 0 versus concentration ratio V 0 /C. First-order approximation (black dashed line), second-order approximation (red solid line), and numerical results (black squares) are presented for (a) D B /D A = 1/16 and (b) D B /D A = 7/3.

Acknowledgements

This publication is part of a project that has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 711859 and from the Polish Ministry of Science and Higher Education for the implementation of an international cofinanced project.


Keywords: Fluorescence imaging, fluorescence microscopy, macroscale imaging, fluorescence endomicroscopy, dynamic contrast, reversibly photoswitchable fluorophores

Fluorescence has become a ubiquitous observable in biology. Yet it encounters limitations, which may originate from optical interferences such as ambient light, autofluorescence, and spectrally interfering fluorophores. In this review, we first report on dynamic contrast which can overcome these limitations. Then we specifically describe Out-of-Phase Imaging after Optical Modulation (OPIOM), which proved relevant for multiplexed fluorescence imaging even under adverse optical conditions with several optical setups.

Dynamic contrast for overcoming spectral interferences in fluorescence imaging R Chouket 1 , A Pellissier-Tanon 1 , A Lemarchand 2 , A Espagne 1 , T Le Saux 1 , L Jullien 1 ‡ Introduction Fluorescence exhibits favorable features for imaging in biology: [1] (i) Sensitivity. Fluorescence is red-shifted with respect to the excitation wavelength, which facilitates high contrast against a dark field by spectral filtering. Thus fluorescence imaging is highly sensitive; (ii) Labeling specificity. An exogenous fluorophore can be introduced for biomolecule labeling, which is often performed by genetic engineering so as to secure exclusive selectivity. However fluorescence suffers from several limitations for sensitive and quantitative imaging. As a general feature of fluorescence imaging, the common labels exhibit rather broad bands of absorption and emission (at least 50 nm for the half-width), which limits the number of distinguishable labels in multiplexed imaging. Beyond 3-4 labels which can be routinely discriminated, building the final image requires to process the fluorescence signals at each pixel (e.g. by linear unmixing, [2,[START_REF] Zimmermann | Spectral Imaging and Linear Unmixing in Light Microscopy[END_REF] phasor analysis, [START_REF] Clayton | [END_REF]5,6,7,8]. . . ). Hence state-of-the-art spectral unmixing in living biological samples currently makes possible to distinguish six fluorophores [9] but at significant cost in terms of photon budget and computation time. [2,10,11,12,13,14,15] As more specific limitations associated with imaging biological samples, reflection or light scattering of ambient light, and autofluorescence from endogenous fluorophores may obscure the emission from a targeted fluorescent label.

In fluorescence imaging, the detrimental interference of ambient light is most often eliminated by recording images in dark environments. When the latter conditions cannot be met, subtracting the images recorded under ambient light with and without light exciting fluorescence has been exploited. [16,17] However this approach has limited interest under a temporally varying lighting environment. Moreover it cannot be used as well if ambient light is too strong as a consequence of the shot noise, which decreases the measurement precision and degrades the signal-to-noise ratio (SNR). [18] Spectral filters are also poorly effective for selectively retrieving the label signal since the spectrum of the light sources often overlaps with the emission spectrum of the common fluorescent labels. An alternative approach to distinguish the fluorescence signal from ambient light is to tailor the excitation light. Hence camera acquisition has been synchronized with a micro to millisecond long pulsed excitation light for fluorescence imaging under room light to sunlight conditions. [19,20,21,22,23,24,25] Lock-in imaging has also been used to distinguish a fluorescence signal from ambient light. Upon applying periodic modulation of the intensity of the excitation light with an angular frequency at which any modulation of the ambient light can be neglected, the modulated component of the fluorescence can be extracted (e.g after time domain Fourier transform), thereby filtering the background up to the daylight condition. [26,27] Compared to the preceding approach, lock-in imaging benefits from a higher SNR due to frequency-domain noise filtering.

Autofluorescence is another significant concern in biological samples. It originates from endogenous fluorescent molecules found in animals (e.g. NAD(P)H, flavin, and lipopigments, and porphyrins [28,29,30,31,32,33]) and in plants (e.g alkaloids, flavonoids and phenolics, ferulic acid, [34,35,36,[START_REF] Willemse | Physico-Chemical Characterisation of Plant Residues for Industrial and Feed Use[END_REF][START_REF] Goodwin | [END_REF]39,40] lipofuscins, [41,42,43] and chlorophyll [44]). Spanning from the UV to the IR wavelength range, [45,46,47,48,49,50] autofluorescence is difficult to circumvent by spectral filtering. In such a perspective, excitation and emission filters with narrow bandpasses [51,52,53,[START_REF] Teuscher | Bio protocol 8 e[END_REF] as well as fluorescent labels emitting beyond 650 nm [START_REF] Patonay | [END_REF]56,57,58,59,50,60,61,62,63] are favorable. When the autofluorescent background is spectrally homogeneous, autofluorescence can be alternatively handled as a fluorophore and eliminated by spectral unmixing. However this approach is of limited interest in biological samples, where autofluorescence arises from diverse substances at specific locations. [64,65] It is worthy of note that most strategies reported above to overcome the limitations of fluorescence imaging have exploited discrimination of the targeted label in the spectral domain. Since the optimization of the fluorescent labels (cross section for light A c c e p t e d M a n u s c r i p t absorption, quantum yield of luminescence, half-width of absorption/emission bands) has essentially reached its physical limits and considering that fluorescence should remain a much favored observable for imaging live cells, [66] it appears attractive to complement the spectral dimension for further discriminating fluorophores.

Strategies of dynamic contrast

Fluorescence emission reports on light absorption and relaxation pathways of an excited state. As such, it contains dynamic information, which can be used for discrimination in the time domain beyond the sole wavelength.

Fluorescence lifetime imaging microscopy (FLIM)

Fluorescence lifetime imaging microscopy (FLIM) has been early introduced to discriminate fluorophores by the distinct lifetimes of their first singlet excited state, [67,68] which can be extracted with three protocols. In time-correlated single-photon counting (TCSPC), the delay times of arrival of individual emitted photons are measured and the lifetime(s) is(are) retrieved from the histogram plotting the number of photons versus time after (multi)exponential fitting. [69] Alternatively, the photons emitted following a pulse of laser excitation are detected after a series of time delays in order to reconstruct the decay lifetime(s) after analyzing the recorded intensities. [70] Eventually, in contrast to both former protocols exploiting pulsed excitation, FLIM can also be implemented in the frequency domain: the excitation light is modulated and the fluorescence lifetime is retrieved from analyzing the amplitude and phase delay of the modulated fluorescence intensity. [68,71] FLIM has been used to discriminate fluorescent emitters from time-independent ambient light in homodyne detection [26] as well as from autofluorescence by exploiting differences of lifetimes. Hence time-gated detection has been used to selectively image GFP and YFP in plant cells by eliminating autofluorescence from the chloroplast. [72] Despite complex multiexponential fluorescence decay, [73,74] the long fluorescence lifetime of quantum dots has facilitated their straightforward temporal discrimination against cell autofluorescence and scattered excitation light by timegated measurements and considerably enhanced the imaging sensitivity. [75,76] However autofluorescence has an average lifetime around 4 ns (autofluorescence exhibits lifetimes ranging from ps to several ns [77,78,79,80]), which overlaps the one of the most common organic fluorophores. Hence long-lived luminophores (e.g. lanthanidebased luminescent probes, [81] azadioxatriangulenium (ADOTA) fluorophores, [82,83] Ag clusters [84]) have been designed to detect their emission after complete decay of the autofluorescence. FLIM has also been used in multiplexed fluorescence imaging analysis for histopathological identification of different stained tissues. [85]Yet FLIMbased multiplexed imaging has remained limited by the narrow range of lifetimes of the common bright fluorophores currently used in fluorescence imaging (a same few A c c e p t e d M a n u s c r i p t nanoseconds) and it has necessitated deconvolutions [86] or the adoption of subtractive schemes. [68] Discrimination by the lifetimes of photoswitched states Recently popularized by super-resolution microscopies, [87,88,89,90] reversibly photoswitchable fluorophores (RSFs) provide more opportunities than simple fluorophores for discrimination with dynamic contrast. RSFs can be photoswitched between states of different brightness upon illumination at one or two different wavelengths. [91,92,93] Their light-driven photoswitching intervenes over a wide palette of timescales (µs to s), which facilitates RSF discrimination by analyzing the temporal response of their fluorescence to appropriate light variations. Hence several protocols (e.g. transient state imaging microscopy -TRAST, [94,95,96] optical lock-in detection -OLID, [97] synchronously amplified fluorescence image recovery -SAFIRe, [98,99] and out-of-phase imaging after optical modulation -OPIOM[100, 101, 102, 103, 104]) have exploited the time domain for selectively imaging RSFs against a spectrally interfering background, this neither by relying on deconvolution nor on subtraction schemes.

Transient state imaging microscopy (TRAST) has selectively discriminated organic fluorophores by monitoring the dynamics of their long-lived, photo-induced transient dark states. [94,95,96] TRAST has been successfully implemented in multiplexed imaging by exploiting the triplet state, which is sensitive to the presence of molecular dioxygen and heavy ions such as iodide. More specifically, fluorophore-filled liposomes containing or not triplet state quenchers have been distinguished thanks to the different lifetimes of their triplet state. [95] In Optical Lock-In Detection (OLID), a series of light perturbations drives an RSF throughout cycles of photoswitching. [97,[START_REF] Du | An improved optical lock-in detection method for contrastenhanced imaging in living cells 4[END_REF][START_REF] Wu | [END_REF] The RSF modulated fluorescence signal is selectively retrieved after cross-correlation with a reference waveform (e.g. acquired from an image zone where only the RSF is present, which cancels any interference from the background (e.g. ambient light, autofluorescence,. . . which do not exhibit any fluorescence photoswitching). OLID has been first validated with a small organic RSF (nitrospirobenzopyran) and with a reversibly photoswitchable fluorescent protein (RSFP), [97] which can reversibly photoswitch between fluorescent and nonfluorescent states. [93,107] OLID was subsequently implemented with a fluorescent cyanine, which could be photoswitched at high light intensity. [108] Whereas OLID was not linearly related to the RSF concentration in its initial version, [97] it has been revisited to make it quantitative. [109] Synchronously amplified fluorescence imaging recovery (SAFIRe) exploits long-lived dark states, which are depopulated under illumination at a secondary wavelength higher than fluorescence emission. [110,111] At constant primary excitation light, modulation of the secondary light modulates the fluorescence signal without any crosstalk. After time-domain Fourier transformation of the signal from each pixel, SAFIRe can image a targeted RSF upon eliminating autofluorescence and any signal from spectrally A c c e p t e d M a n u s c r i p t interfering fluorophores. [99] Initially validated with Ag nanodots[110] and organic fluorophores, [111,112] SAFIRe was later implemented with RSFPs. [113,114,115] It also encountered many developments such as combining SAFIRe and FRET to overcome the limitation of red-shifted illumination for dark state depopulation, [116] extending SAFIRe to simple fluorophores by exploiting stimulated emission, [117] or applying SAFIRe to fluorescence correlation spectroscopy (FCS). [118] SAFIRe is endowed to overcome the limitations of autofluorescence, ambient light, and the spectral interference of RSFs, which respond more slowly than the targeted one to the optical modulation of the secondary light. Out-of-Phase Imaging after Optical Modulation (OPIOM) has added the phase lag of the modulated signal to the frequency-dependent modulation amplitude exploited by SAFIRe as a further control parameter.[100, 102] As shown below, the OPIOM exhaustive theoretical framework has led to extract analytic conditions for generating optimum band pass filters, which can directly discriminate the individual contributions of several components in RSF mixtures.

Eventually irreversible photoswitching processes have been used for dynamic contrast.

In Bleaching-Assisted Multichannel Microscopy (BAMM), the kinetic signature of photobleaching made possible to discriminate up to three spectrally similar fluorophores with an unmixing algorithm.[119] BAMM was successfully applied to organic dyes, autofluorescent biomolecules and fluorescent proteins. [119] OPIOM in action Theoretical background OPIOM relies on time periodic illumination at one wavelength (light intensity I(t) with I 0 average value and ω angular frequency) to govern RSF photoswitching between two states of different brightness (see Fig. 1a).[100, 101] The thermodynamically stable state 1 is photochemically depopulated in favor of the thermodynamically less stable state 2 (rate constant k 12 (t) = σ 12 I(t)) and it is populated back either by photochemical conversion or thermal recovery (rate constant k 21 (t) = σ 21 I(t) + k ∆ 21 ; σ 12 and σ 21 : photoswitching action cross-sections of the RSF, k ∆ 21 : rate constant for thermal recovery of 1 from 2). Since the photoswitching rates depend on I(t), periodic light modulation modulates the concentrations of the two RSF states at ω angular frequency but with a phase delay originating from the relaxation time of RSF photoswitching. At steadystate, the amplitudes of the quadrature-delayed component of the concentrations and of fluorescence emission exhibit a resonance when the parameters of light modulation match the kinetic parameters of RSF photoswitching by fulfilling two conditions:

I 0 = k ∆ 21 σ 12 + σ 21 (1)
ω = 2k ∆ 21 (2)
A c c e p t e d M a n u s c r i p t

The resonant quadrature-delayed component of the modulated fluorescence has been chosen as the OPIOM signal (see Fig. 1c). It can be simply extracted by a robust time Fourier transform benefiting from lock-in amplification to improve the SNR. Proportional to the RSF concentration, the OPIOM signal can quantitatively discriminate a targeted RSF against another spectrally similar fluorophore or RSF endowed with different photoswitching kinetics.

= σ 12,1 = 196 m 2 mol -1 , σ 21,1 = 0 m 2 mol -1 , σ 12,2 = 0 m 2 mol -1 , σ 21 = σ 21,2 = 413 m 2 mol -1 , k ∆ 21 = 1.5 × 10 -2 s -1 with I 0 = 100k ∆ 21 /(σ 12,1 + σ 21,1 ).
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A c c e p t e d M a n u s c r i p t

Many RSFs (e.g. green fluorescent RSFPs) can be photoswitched back and forth at two different wavelengths (e.g. 480 and 405 nm with green RSFPs). Thus a secondary light can be applied to accelerate the recovery process of the photoswitched state. [120,102] In Speed OPIOM which exploits time periodic two-color illumination, the light sources at wavelengths λ 1 and λ 2 are modulated in antiphase at angular frequency ω with respective average light intensities I 0 1 and I 0 2 (see Fig. 1b).

[102] Again the Speed OPIOM signal is the quadrature-delayed response of the RSF fluorescence (see Fig. 1d). It exhibits a resonance when the illumination parameters I 0 2 /I 0 1 and ω/I 0 1 match the RSF photoswitching cross sections σ 12,i (respectively σ 21,i ) associated with photoswitching from 1 to 2 (respectively from 2 to 1) driven at λ i (i = 1, 2)

(σ 12,1 + σ 21,1 ) I 0 1 = (σ 12,2 + σ 21,2 ) I 0 2 (3)
ω = 2 (σ 12,1 + σ 21,1 ) I 0 1 . (4)
Beyond being twice higher than with OPIOM, the Speed OPIOM signal can benefit from higher frequencies of image acquisition. As shown in Eqs. [START_REF] Zimmermann | Spectral Imaging and Linear Unmixing in Light Microscopy[END_REF][START_REF] Clayton | [END_REF], increasing I 0 1 and I 0 2 at constant ratio I 0 2 /I 0 1 leads to increase ω at resonance.

Implementation

Easily adapted onto commercially available optical setups, the (Speed-)OPIOM imaging protocols can improve their performances without any significant modification. Indeed, they simply require to modulate light sources, which are usually exploited at constant intensity.

We have implemented (Speed-)OPIOM on five optical setups: two different fluorescence microscopes,[100, 102], a fluorescence macroscope,[102, 103] and a fluorescence endomicroscope. [104] OPIOM has been implemented in epifluorescence and single plane imaging microscopies (see Fig. 2a,b).[100] We first used a microdevice filled with RSFP solutions to demonstrate that it selectively gives access to quantitative information on RSFP concentrations. We then applied OPIOM in epifluorescence microscopy to show that it could image RSFPs in fixed and live cells even in the presence of spectrally interfering fluorophores. Finally, we validated OPIOM in single plane imaging microscopy upon evidencing that it could overcome the interfering autofluorescence of tissues and compartments when imaging zebrafish embryos.

Speed-OPIOM has been subsequently implemented in epifluorescence microscopy,[102] macrofluorescence imaging,[102, 103] and fluorescence endomicroscopy[104] (see Fig. 2ce). In epifluorescence microscopy, we could show that Speed OPIOM can selectively retrieve the fluorescence emission from a targeted RSFP in the presence of spectrally interfering fluorophores and autofluorescence in real time in live cells. Four fluorescent proteins with a similar spectral signature have been discriminated in cells (see Fig. 3a-e). Speed OPIOM was then demonstrated to be relevant for remote imaging with a simple and inexpensive fluorescence macroscope. In a first step, we showed that Speed-OPIOM could enhance the sensitivity and the signal-to-noise ratio for fluorescence detection in blot assays by factors of 50 and 10, respectively, over direct fluorescence A c c e p t e d M a n u s c r i p t observation under constant illumination. Then, we evidenced that Speed-OPIOM successfully overcame the strong autofluorescence of growth media that are currently used in microbiology and realized multiplexed fluorescence observation of colonies of spectrally similar fluorescent bacteria. Finally, we easily discriminated fluorescent labels from the autofluorescent and reflective background in labeled leaves, even under the interference of incident light at intensities that are comparable to sunlight. Eventually we have implemented Speed OPIOM in fluorescence endomicroscopy enabling for fullframe acquisition. Using a simple and cheap optical-fiber bundle-based endomicroscope with one-photon excitation integrating modulatable light sources, we first showed that Speed OPIOM is endowed with intrinsic optical sectioning, which restricts the observation of RSFPs at targeted positions within a sample. We also demonstrated that Speed OPIOM efficiently eliminates the interference of the autofluorescence arising from both the fiber bundle and the specimen in several biological samples.

Conclusion

Fluorescence imaging has benefited from significant advances for biological applications, which extend from the development of multiple genetically-encoded fluorophores to the introduction of new microscopies. Overcoming the diffraction limit with super-resolution microscopies has been a first illustration of this impressive progress. More recently, several fluorescence imaging protocols exploiting dynamic contrast (e.g. TRAST, OLID, SAFIRe, OPIOM) have addressed further challenges, which had been considered limiting for fluorescence imaging. In this short review, we more specifically reported on OPIOM. We showed that it is easy to implement on a variety of simple and cheap optical setups, in which it can overcome autofluorescence and ambient light or discriminate several spectrally similar fluorophores. Added to the continuous introduction of RSFs and genetic techniques for labeling, the imaging protocols exploiting dynamic contrast are expected to open new fields of applications for fluorescence imaging.

Figure 1 .

 1 Figure 1. (Speed-) Out-of-phase imaging after optical modulation (OPIOM). (a,c) In OPIOM, a time-periodic light (angular frequency ω and average intensity I 0 ) modulates the fluorescence emission from an RSF involved in an exchange between a bright and a dark state (respectively 1 and 2) (a). The OPIOM signal S OP IOM is the amplitude of the out-of-phase component of the fluorescence emission. The OPIOM image of a targeted RSF is selectively and quantitatively retrieved upon adopting resonant illumination parameters I 0 and ω, which match the RSF kinetic parameters σ 12 , σ 21 , and k ∆ 21 using Eqs. (1,2) (c); (b,d) In Speed-OPIOM, the time-periodic illumination involves two lights modulated in antiphase at angular frequency ω with respective average intensities I 0 1 and I 0 2 (b). The Speed-OPIOM signal S SpeedOP IOM is the amplitude of the out-of-phase component of the fluorescence emission. It is resonant in the space of the illumination parameters {I 0 2 /I 0 1 ,ω/I 0 1 } (d). The Speed-OPIOM image of a targeted RSF is recorded upon matching the illumination parameters I 0 2 /I 0 1 and ω/I 0 1 to the RSF kinetic parameters σ 12,1 , σ 21,1 , σ 12,2 , and σ 21,2 using Eqs. (3,4). The panels (c) and (d) display the theoretical plots of the OPIOM and Speed-OPIOM signals normalized by the RSF concentration with σ 12 = σ 12,1 = 196 m 2 mol -1 , σ 21,1 = 0 m 2 mol -1 , σ 12,2 = 0 m 2 mol -1 , σ 21 = σ 21,2 = 413 m 2 mol -1 , k ∆ 21 = 1.5 × 10 -2 s -1 with I 0 = 100k ∆ 21 /(σ 12,1 + σ 21,1 ).

Figure 2 .

 2 Figure 2. Optical setups for (Speed-)OPIOM implementation. (a) OPIOM in epifluorescence microscopy;[100] (b) OPIOM in single plane illumination microscopy (SPIM);[100] (c) Speed-OPIOM in epifluorescence microscopy;[102] (d) Speed-OPIOM in macroscale fluorescence imaging;[102, 103] (e) Speed-OPIOM in fluorescence endomicroscopy.[104]

Figure 3 .

 3 Figure 3. Speed OPIOM can independently image four spectrally similar RSFPs. Pre-OPIOM (a) and Speed OPIOM images tuned to selectively image Dronpa-2 (b), Padron (c), and Dronpa (d). In (e), overlay between the pre-OPIOM image from the Dronpa-2 acquisition and Speed OPIOM images collected in (b-d). Systems: Fixed U2OS cells expressing H2B-Dronpa-2, Mito-Padron, Dronpa-GTS, and Lyn11-EGFP. Localizations: H2B (nucleus), Lyn11 (cell membrane), Mito (mitochondria), GTS (Golgi). The images were recorded at 37 o C. Scale bars: 20 µm. Reproduced with permission from reference [102].

  A c c e p t e d M a n u s c r i p t A c c e p t e d M a n u s c r i p t A c c e p t e d M a n u s c r i p t

Acknowledgments

This work was supported by the ANR (France BioImaging -ANR-10-INBS-04, Morphoscope2 -ANR-11-EQPX-0029, HIGHLIGHT, and dISCern), the Fondation de la Recherche Médicale (FRM), the MITI CNRS (Imag'In and Instrumentations aux limites), and the Domaine d'Intérêt Majeur Analytics de la Région Ile de France (DREAM).