Adjélé Wilson

Claire Punginelli

Andrew Gall

Cosimo Bonetti

Maxime Alexandre

Jean-Marc Routaboul

Cheryl A Kerfeld

Rienk Van Grondelle

Bruno Robert

John T M Kennis

Adje ´le ´wilson

Diana Kirilovsky
email: diana.kirilovsky@cea.fr.

Robert Haselkorn

D K Wrote

A photoactive carotenoid protein acting as light intensity sensor

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

Intense sunlight is dangerous for photosynthetic organisms. Cyanobacteria, like plants, protect themselves from light-induced stress by dissipating excess absorbed energy as heat. Recently, it was discovered that a soluble orange carotenoid protein, the OCP, is essential for this photoprotective mechanism. Here we show that the OCP is also a member of the family of photoactive proteins; it is a unique example of a photoactive protein containing a carotenoid as the photoresponsive chromophore. Upon illumination with blue-green light, the OCP undergoes a reversible transformation from its dark stable orange form to a red ''active'' form. The red form is essential for the induction of the photoprotective mechanism. The illumination induces structural changes affecting both the carotenoid and the protein. Thus, the OCP is a photoactive protein that senses light intensity and triggers photoprotection.

cyanobacteria ͉ nonphotochemical quenching ͉ photoprotection ͉ phycobilisome T o maximize the use of sunlight, photosynthetic organisms collect as much light as possible using an antenna made up of pigments attached to special proteins. However, excess light is harmful because it can induce the formation of dangerous oxygen species in the photochemical reaction centers. Under full sunlight conditions, a safety valve must be opened to convert the excess into heat and to reduce the amount of energy funneled to reaction centers. It is well known that in plants carotenoids play an essential role in photoprotective mechanisms within the chlorophyll-membrane antenna of photosystem II (PSII) [START_REF] Horton | Regulation of light harvesting in green plants[END_REF][START_REF] Niyogi | Photoprotection revisited: genetic and molecular approaches[END_REF][START_REF] Demming-Adams | Antioxidants in photosynthesis and human nutrition[END_REF][START_REF] Holt | Carotenoid cation formation and the regulation of photosynthetic light harvesting[END_REF][START_REF] Standfuss | Mechanisms of photoprotection and non-photochemical quenching in pea light harvesting complex at 25Å resolution[END_REF][START_REF] Pascal | Molecular basis of photoprotection and control of photosynthetic light harvesting[END_REF][START_REF] Ruban | Identification of a mechanism of photoprotective energy dissipation in higher plants[END_REF]. In contrast, the mechanism of thermal energy dissipation in cyanobacteria, which plays a key role in global carbon cycling, remained elusive. Only within the last few years has a photoprotective mechanism associated with the soluble phycobilisome antenna of PSII in cyanobacteria been demonstrated [START_REF] Bissati | Photosystem II fluorescence quenching in the cyanobacterium Synechocystis PCC 6803: involvement of two different mechanisms[END_REF][START_REF] Wilson | A soluble carotenoid protein involved in phycobilisome-related energy dissipation in cyanobacteria[END_REF][START_REF] Wilson | Light induced energy dissipation in iron-starved cyanobacteria. Roles of OCP and IsiA proteins[END_REF][START_REF] Scott | Mechanism of the down regulation of photosynthesis by bluelight in the cyanobacterium Synechocystis PCC 6803[END_REF][START_REF] Rakhimberdieva | Carotenoid-induced quenching of the phycobilisome fluorescence in photosystem II-deficient mutant of Synechocystis sp[END_REF][START_REF] Rakhimberdieva | Phycobilin/ chlorophyll excitation equilibration upon carotenoid-induced non-photochemical fluorescence quenching in phycobilisomes of the cyanobacterium Synechocystis sp PCC 6803[END_REF][START_REF] Rakhimberdieva | Protein-protein interactions in carotenoid triggered quenching of phycobilisome fluorescence in Synechocystis sp PCC 6803[END_REF]. A specific soluble carotenoid protein, the orange carotenoid protein (OCP), plays an essential role in this process [START_REF] Wilson | A soluble carotenoid protein involved in phycobilisome-related energy dissipation in cyanobacteria[END_REF][START_REF] Wilson | Light induced energy dissipation in iron-starved cyanobacteria. Roles of OCP and IsiA proteins[END_REF]. In its absence, thermal dissipation is abolished, rendering the cells more sensitive to high light intensities; this is manifested as a faster decrease in PSII activity in a mutant lacking the OCP [START_REF] Wilson | A soluble carotenoid protein involved in phycobilisome-related energy dissipation in cyanobacteria[END_REF]. Surprisingly, the role of the carotenoid in the OCP is completely different from the role of the photoprotective carotenoids in plants. The OCP appears to act as a photoreceptor, responding to blue-green light; this induces energy dissipation, resulting in a detectable quenching of the cellular fluorescence, known as nonphotochemical-quenching (NPQ), through interaction with the phycobilisome [START_REF] Wilson | A soluble carotenoid protein involved in phycobilisome-related energy dissipation in cyanobacteria[END_REF][START_REF] Scott | Mechanism of the down regulation of photosynthesis by bluelight in the cyanobacterium Synechocystis PCC 6803[END_REF]. In mutants containing the OCP but lacking phycobilisomes, blue-green light was unable to induce the photoprotective mechanism [START_REF] Wilson | A soluble carotenoid protein involved in phycobilisome-related energy dissipation in cyanobacteria[END_REF][START_REF] Wilson | Light induced energy dissipation in iron-starved cyanobacteria. Roles of OCP and IsiA proteins[END_REF].

The OCP, a 35 kDa protein that contains a single noncovalently bound carotenoid [START_REF] Holt | A carotenoid protein from cyanobacteria[END_REF][START_REF] Wu | The orange carotenoid protein of Synechocystis PCC 6803[END_REF][START_REF] Kerfeld | Water-soluble carotenoid proteins of cyanobacteria[END_REF][START_REF] Kerfeld | Structure and function of the water-soluble carotenoid-binding proteins in cyanobacteria[END_REF], is the product of the slr1963 gene in Synechocystis PCC 6803 [START_REF] Wu | The orange carotenoid protein of Synechocystis PCC 6803[END_REF]. Highly conserved homologs of the OCP are found in most of the cyanobacterial genomes. The structure of the Arthrospira maxima OCP has been determined to 2.1 Å resolution [START_REF] Kerfeld | The crystal structure of a cyanobacterial water-soluble protein[END_REF]. It consists of two domains: a unique ␣-helical N-terminal domain and a mixed ␣-helical/␤sheet C-terminal domain. The embedded keto carotenoid, 3Јhydroxyechinenone (hECN), composed of a conjugated carbonyl group located at the terminus of a conjugated chain of 11 carbon-carbon double bonds in an all-trans configuration. The carotenoid spans both protein domains with its keto terminus nestled within the C-terminal mixed ␣/␤ domain. Absolutely conserved Tyr-44 and Trp-110 make hydrophobic contacts with the hydroxyl terminal end of the carotenoid, whereas two other absolutely conserved residues, Tyr-203 and Trp-290, form hydrogen bonds to the carbonyl moiety at the keto terminus of the pigment [START_REF] Kerfeld | The crystal structure of a cyanobacterial water-soluble protein[END_REF] (refer also to Fig. 3A).

Results

To isolate the OCP, C-terminal His-tagged OCP mutants were constructed in Synechocystis PCC 6803, using kanamycin or spectinomycin resistance for mutant selection [supporting information (SI) Figs. S1 andS2]. In the WT and the kanamycin resistant mutant, blue-green light induced similar fluorescence quenching, indicating that the presence of the His-tag did not affect the activity of the OCP. In the spectinomycin resistant mutant, the fluorescence quenching was slightly decreased relative to the WT (Fig. 1 A); this correlates with a lower concentration of the OCP in this mutant (probably because of a destabilization of the mRNA) (Fig. 1B). In addition, a mutant was constructed in which the slr1963 gene containing a Cterminal His-tag was expressed using the psbA2 promoter region as the promoter. In this strain, large quantities of the OCP were present (see Fig. 1B) and a very large fluorescence quenching was observed (see Fig. 1 A), confirming the relationship between OCP concentration and excitation energy quenching. The OCP was isolated using affinity Ni-chromatography followed by an ion-exchange column (Fig. S3). The absorption spectrum of the His-tagged OCP isolated from Synechocystis 6803 is essentially identical to that of A. maxima (compare Fig. 2B dark form with the spectrum in Fig. 2 in ref. [START_REF] Polivka | Spectroscopic properties of the carotenoid 3Ј-hydroxyechinenone in the orange carotenoid protein from the cyanobacterium Arthrospira maxima[END_REF]. As in the latter strain, it mainly binds hECN (Fig. S4).

In darkness or dim light the OCP appears orange (OCP o ) and its absorption spectrum presents a typical carotenoid shape, reflecting the strongly allowed S 0 -S 2 transition with three distinct vibrational bands; the 0-0 vibrational peak is located at 496 nm (see Fig. 2 A andB). The position and shape of this transition corresponds to that of hECN locked into an all-trans conformation by the surrounding protein [START_REF] Polivka | Spectroscopic properties of the carotenoid 3Ј-hydroxyechinenone in the orange carotenoid protein from the cyanobacterium Arthrospira maxima[END_REF], in agreement with the crystallographic structure [START_REF] Kerfeld | The crystal structure of a cyanobacterial water-soluble protein[END_REF]. Strikingly, upon illumination with blue-green light (400-550 nm) at 10°C, the OCP o is completely photoconverted to a red form, OCP r . The red-shifted spectrum of OCP r with a maximum at 500 nm loses the resolution of the vibrational bands (see Fig. 2 A andB). To elucidate whether the conversion of the OCP o to OCP r occurs in whole cells under NPQ-inducing conditions, absorbance spectra of whole cells of the overexpressing OCP strain and the ⌬OCP strain, lacking the OCP (9), were measured before and after illumination with high intensities of blue light at 11°C and the light-minus-dark difference spectra calculated. Our results strongly suggested that OCP r is accumulated in vivo under the conditions inducing energy dissipation and fluorescence quenching (Fig. 1C).

In darkness, OCP r spontaneously reverts to the orange form (Fig. 2C). This step is not accelerated by illumination (Fig. S5). The back-reaction kinetics (red to orange) shows a large temperature dependence, the half-time of recovery varying from 30 sec at 32°C to Ϸ45 min at 11°C. In vivo, the recovery NPQ kinetics also show a large temperature dependence; however, the kinetics are slower [START_REF] Bissati | Photosystem II fluorescence quenching in the cyanobacterium Synechocystis PCC 6803: involvement of two different mechanisms[END_REF][START_REF] Wilson | A soluble carotenoid protein involved in phycobilisome-related energy dissipation in cyanobacteria[END_REF][START_REF] Rakhimberdieva | Protein-protein interactions in carotenoid triggered quenching of phycobilisome fluorescence in Synechocystis sp PCC 6803[END_REF] than the OCP r to OCP o dark conversion, suggesting that the OCP r form is more stable in vivo than in vitro or that the fluorescence quenching remains longer than the OCP r form. In contrast, the initial rate of the light photoconversion was temperature-independent (Fig. 2D). Thus, at a fixed light intensity, the steady-state concentration of OCP r depended on the temperature. This is reflected in vivo, where a larger NPQ was observed at 7°C than at 33°C (Fig. S6). The kinetics of OCP r formation strongly depended on light intensity (Fig. 2E). This correlates with the observed dependency on light intensity of the blue-light induced NPQ in whole cells [START_REF] Wilson | A soluble carotenoid protein involved in phycobilisome-related energy dissipation in cyanobacteria[END_REF].

Collectively, these results strongly suggested that OCP r is the active form of the OCP and that pigment-protein interactions are critical to this activity. To confirm this, a C-terminal His-tagged W110S-OCP mutant and an overexpressing C-terminal His-tagged W110S OCP mutant were constructed and characterized. High intensities of blue-green light induced no fluorescence quenching in the mutant (Fig. 3B), indicating that Trp-110 is critical to the OCPs photoprotective function. This was substantiated by construction of an overexpressing W110S-OCP mutant in which very little quenching was induced, although large quantities of OCP were present (see Fig. 3 B andC). The absorbance spectrum of the isolated mutated OCP was similar to that of the WT OCP (Fig. 3D). Moreover, each isolated mutant OCP contains a carotenoid molecule as judged by comparison to WT OCP (similar A 467 /A 280 ratio, data not shown). High intensities of blue-green light converted only a very small portion of the OCP o to OCP r , even after 15 min of illumination at 10°C (see Fig. 3D). Thus, there is a direct correlation between the accumulation of OCP r and the induction of the fluorescence quenching.

Resonance Raman spectroscopy was used to observe lightinduced structural changes of the hECN. The Raman spectra of the OCP o from A. maxima and Synechocystis PCC 6803 are nearly identical, indicating that the carotenoid-peptide interactions in these two proteins are remarkably homologous (Fig. 4A). Thus, the X-ray structure from the former strain may be used as a model for the OCP of the latter. This has been confirmed by the determination of the 1.65 Å structure of the Synechocystis PCC6803 OCP (C.A.K., unpublished results). Before illumination, the resonance Raman spectra of OCP-bound hECN shows that this carotenoid is in an all-trans conformation, in good agreement with the X-ray structure [START_REF] Kerfeld | The crystal structure of a cyanobacterial water-soluble protein[END_REF]. The relatively high intensity of the bands in the 4 region, however, indicates that this conformation is not planar, but highly distorted around the C-C bonds [START_REF] Robert | Insights into the molecular dynamics of plant light-harvesting proteins in vivo[END_REF]. Upon illumination the position of C ϭ C stretching mode shifts from 1,528 cm Ϫ1 to 1,521 cm Ϫ1 , indicating that the apparent conjugation length of hECN increased by about one conjugated bond [START_REF] Rimai | Vibrational spectra of some carotenoids and related linear polyenes. A raman spectroscopy study[END_REF], in agreement with the observed red-shift (see Fig. 4A). Trans-cis isomerisation of hECN should shift down the position of this band, and should result in the appearance of new bands in the spectra because of the change in the molecular symmetry. As this is not observed, we can conclude that hECN is still all-trans in its red form. Of course, we cannot formally discard presence of end chain isomerisation (such as 7-cis), whose effect on the Raman spectra (and on the electronic absorption spectra) is limited. The decrease of intensity of the 950 cm Ϫ1 indicates that upon photoconversion, hECN reaches a less distorted, more planar structure [START_REF] Rimai | Vibrational spectra of some carotenoids and related linear polyenes. A raman spectroscopy study[END_REF]. Similar differences were observed using the OCP from A. maxima (data not shown). Further studies will be necessary to elucidate the specific nature of the changes in the carotenoid.

Light-induced Fourier transform infrared (FTIR) difference spectroscopy was applied to probe the light-induced structural changes in the protein of the OCP. Upon illumination, large changes in the OCP FTIR spectra can be observed Ϸ1,650 and 1550 cm Ϫ1 , where the Amide I and Amide II protein modes are expected to contribute. In the light-minus-dark FTIR spectra, these protein contributions, with specific frequencies for each type of protein secondary structure (loops, ␣-helix, and ␤-sheet) [START_REF] Krimm | Vibrational spectroscopy and conformation of peptides, polypeptides, and proteins[END_REF], may be formally attributed to the protein modes on the basis of their sensitivity to D 2 O exchange (hECN molecules contain only one, nonconjugated, exchangeable proton) (Fig. 4B). The differential signal at 1,677(Ϫ)/1,697(ϩ) cm Ϫ1 is assigned to portions of the protein without secondary structure: that is, the loops. The ␣-helix and ␤-sheet carbonyl region shows an intense and broad negative band centered at 1,643 cm Ϫ1 , which has a corresponding induced absorption at 1,663(ϩ) and 1,618(ϩ)cm Ϫ1 assigned to ␣-helix and ␤-sheet, respectively. Light-induced Amide I changes in the OCP are large, suggesting a major rearrangement of the protein backbone. An up-shift of the Amide I vibrations of ␣-helix corresponds to a weakening of the NH Ϫ C ϭ O hydrogen bonds that connect the turns, indicating a less rigid helical structure in a significant part of OCP upon formation of the red form. A down-shift of the Amide I vibrations of ␤-sheet corresponds to a shortening (ie, a strengthening) of the NH Ϫ C ϭ O H-bonds between the ␤ strands, resulting in a compaction of the ␤-sheet domain upon formation of the red form. The Amide I frequency-shift pattern observed here for OCP is strikingly similar to that observed in the LOV2 domain of phototropin, a flavin-binding blue-light photoreceptor [START_REF] Iwata | Light-induced structural changes in the LOV2 domain of Adiantum Phytochrome 3 studied by low-temperature FTIR and UV-visible spectroscopy[END_REF].

Ultrafast spectroscopy was applied to examine the primary photochemistry of the OCP and the efficiency of product formation. Fig. 5A shows the result of a global analysis of the time-resolved data. Four kinetic components are required for an adequate fit. The 100-fs component corresponds to internal conversion of the initially excited, optically allowed, S 2 state of the carotenoid to the low-lying, optically forbidden S 1 state coupled to an intramolecular charge-transfer (ICT) state. The 1-ps and 4.5-ps components correspond to decay of the S 1 and ICT states, respectively [START_REF] Polivka | Spectroscopic properties of the carotenoid 3Ј-hydroxyechinenone in the orange carotenoid protein from the cyanobacterium Arthrospira maxima[END_REF]. After decay of the hECN excited states on a ps timescale, a photoproduct remains at very low amplitude (Fig. 5B). The spectral signature of this product species is similar to that of the light-minus-dark spectrum of the OCP (see Fig. 5A). However, the primary product is slightly red-shifted with respect to that of the light-minus-dark, indicating that these states may be similar but not identical and that relaxation takes place on timescales longer than nanoseconds. The amplitude of the product state at 565 nm is only 1% of that of the original carotenoid bleach near 475 nm immediately after excitation (see Fig. 5A), consistent with the assumption that the OCP is a low quantum-yield photoactive protein.

Discussion

Previously, we demonstrated that the OCP is specifically involved in a photoprotective phycobilisome-associated NPQ mechanism [START_REF] Wilson | A soluble carotenoid protein involved in phycobilisome-related energy dissipation in cyanobacteria[END_REF]. Here, we show that the OCP is a photoactive protein sensing light intensity. Light induces the conversion between a dark stable orange form (OCP o ) and a metastable stable red form (OCP r ). The accumulation of the OCP r is essential for the induction of the photoprotective mechanism. The OCP r is present in whole cells under illuminations inducing the NPQ mechanism. Moreover, high intensities of blue-green light induced almost no fluorescence quenching in an OCP mutant in which the OCP photoconvertion was nearly abolished. The OCP o to OCP r conversion occurs with a very low quantum yield (Ϸ0.03); this is likely to be because the OCP protein is involved in a photoprotective process that must be induced only under high light conditions. Moreover, the ratio of the two forms under illumination depends on light intensity and temperature: more red active OCP r at high light intensities and low temperatures. This provides a mechanism for the protein to sense photoinhibitory conditions: high light and light plus cold. Indeed, in vivo, greater fluorescence quenching is induced by increasing the light intensity and by lowering the temperature. Retinal, a carotenoid derivative, is the chromophore of rhodopsins, a family of photoactive membrane-embedded proteins that are used throughout the animal and microbial kingdom as light receptors [START_REF] Spudich | Retinylidene proteins: structures and functions from archaea to humans[END_REF]. Because retinal and hECN share structural similarities, it is worth considering whether OCP photoactivation could be similar to that of rhodopsin. However, our results suggest a completely different mechanism. Retinal is covalently bound to the protein by a protonated Schiff-base linkage to a Lys residue. The hECN in the OCP is close to an absolutely conserved Arg, but there is no covalent bond [START_REF] Kerfeld | The crystal structure of a cyanobacterial water-soluble protein[END_REF]. Light induces an isomerisation of the retinal initiating the photocycle involving proton transfer between the Schiff-base and a carboxylate residue of the rhodopsin. In the OCP, no isomerisation was detected. Thus, although the specific changes in the carotenoid of OCP remain to be elucidated, they are clearly different from those occurring in retinal.

Light-driven structural changes in the carotenoid correlate with the protein conformational changes observed by FTIR; the structural rearrangement in the OCP may be a precondition for interaction with the phycobilisome or other proteins. Collectively, our data suggest a mechanism analogous to that of other blue-light responsive proteins, such as PYP and LOV domaincontaining proteins. In each of these, blue light causes changes in the chromophore that induces disruption of hydrogen bonding networks and large conformational changes in the protein required for the light-responsive function [START_REF] Rubinstenn | Structural and dynamic changes of photoactive yellow protein during its photocycle in solution[END_REF][START_REF] Harper | Structural basis of a phototropin light switch[END_REF]. By analogy, we posit that the absorption of blue light by the OCP alters the strength of one or both of the hydrogen bonds between the carotenoid and the protein. The resulting conformational changes in the protein could render the carotenoid more accessible and form a signal propagation pathway from the carotenoid to the surface of the OCP.

The C-terminal domain of the OCP (between residues 196 to 296) is structurally similar to the 7.8 kDa core linker protein (Noam Adir, personal communication; Fig. 6A), although lacking significant sequence homology. The linker protein consisting of a three-stranded ␤-sheet and one ␣-helix was cocrystallized The OCP r is essential for the induction of the photoprotective mechanism. (A) Shown is 100% conserved Tyr and Trp interacting with the carotenoid. (B) Decrease of Fm' during exposure of WT (red squares), overexpressing W110S OCP mutant (green circles), and His-tagged W110S OCP resistant mutant (blue triangles) cells to 740-mol photons m Ϫ2 s Ϫ1 of bluegreen light (400 -550 nm). (C) Immunoblot detection in membranephycobilisome fractions from WT (1), overexpressing W110S OCP mutant (2), and His-tagged W110S OCP (3). Each lane contained 1.5-g chlorophyll (D). Absorbance spectra of the dark orange form (OCP o ; black) and the light form (OCP r ; red). The OCP o was illuminated during 15 min at 1,200-mol photons m Ϫ2 s Ϫ1 and at 10°C. Wavenumber (cm -1 ) Intensity (a.u.) A 1700 1600 1500 1400 1300 1200 1100 1000 with allophycocyanin (APC) trimers that constitute part of the core of the phycobilisome [START_REF] Reuter | Structural analysis at 22 A of orthorhombic crystals presents the asymmetry of allophycocyanin-linker complex, APLC 7.8 , from phycobilisomes of Mastigocladus laminosus[END_REF]. The structure revealed that the linker protein is bound within the central aperture of the APC trimer and directly interacts with the ␤84 chromophores of two APC subunits. Therefore, we hypothesize that the C-terminal OCP domain, by interacting with the center of an APC trimer, may bring the carotenoid into proximity of the APC chromophores. In addition, the Trp-290 and Tyr-203 residues, which interact with the carbonyl of the carotenoid, belong to the central strand of the ␤-sheet and to the ␣-helix of the C-terminal domain, respectively (Fig. 6B). Modifications in this domain caused by light-induced carotenoid changes could then possibly regulate the interaction between the carotenoid and the APC chromophores Carotenoid molecules are able to quench excitation energy from tetrapyrrole molecules in vitro through energy transfer to their optically forbidden S 1 state, coupled to an intramolecular charge-transfer state [START_REF] Berera | A simple artificial light-harvesting dyad as a model for excess energy dissipation in oxygenic photosynthesis[END_REF]. It was recently proposed that this mechanism is at the origin of the NPQ process in higher plants [START_REF] Ruban | Identification of a mechanism of photoprotective energy dissipation in higher plants[END_REF]. Hydroxyechinenone, which contains a conjugated carbonyl group, clearly exhibits such an intramolecular charge transfer state [START_REF] Polivka | Spectroscopic properties of the carotenoid 3Ј-hydroxyechinenone in the orange carotenoid protein from the cyanobacterium Arthrospira maxima[END_REF]. Therefore, we hypothesize that the OCP is not only the sensor of light but also the fluorescence quencher. Absorption of light by the hECN induces conformational changes of the carotenoid, shifting the absorption spectra toward the red region of the visible spectrum. The red shift is likely necessary to tune the optically forbidden S 1 state of hECN to a position to allow the energy transfer from the phycobilisome to the OCP. This mechanism is reminiscent of the gear-shift mechanism proposed to explain the role of zeaxanthin in higher plant NPQ [START_REF] Frank | Mechanism of nonphotochemical quenching in green plants: Energies of the lowest excited singlet states of violaxanthin and zeaxanthin[END_REF]. Possibly, an increase of charge-transfer character of the hECN excited states upon formation of OCP r plays a role as well.

Although the molecular mechanism of the orange to red conversion and the exact role of the OCP in the cyanobacterial photoprotective mechanism await elucidation, our results suggest several mechanistic hypotheses that open an unexplored frontier in research on the functions of carotenoids: this is a unique report of a carotenoid protein functioning as a photoactive protein sensing light intensity.

Materials and Methods

His-Tagged Strains Construction. The Synechocystis PCC 6803 genome region containing the slr1963 and slr1964 genes was cloned. Then, the slr1964 gene was interrupted by a kanamycin-resistance or a spectinomycin-resistance cassette and nucleotides encoding for 6 His were added in the slr1963 gene. Synechocystis 6803 WT cells were transformed by these plasmids (see Fig. S2 A). To obtain a strain overexpressing the OCP, the genome region containing the slr1963 and slr1964 genes was cloned in the pPSBA2 ampicillin-resistant vector [START_REF] Lagarde | Increased production of zeaxanthin and other pigments by application of genetic engineering techniques to Synechocystis sp strain PCC 6803[END_REF]. Nucleotides encoding for 6 His were added in the 3 Ј side of the slr1963 gene and a 1.3-kb kanamycin resistance gene was inserted. The plasmid obtained was used to transform the WT and the Cter6HSp/Sm mutant (see Fig. S2B). The point mutation (W to S) was added in the slr1963 gene in the normally-expressing and overexpressing plasmids by site-directed mutagenesis. More details can be found in SI Materials and Methods.

Purification of the Orange Carotenoid Protein. In this study, we used OCP isolated from the Km-resistant and Sp-resistant His-tagged OCP mutants. His-tagged OCP mutant cells (1-mg chl.ml Ϫ1 ) in 0.1-M Tris⅐HCl pH ϭ 8 buffer were broken in mild light using a French Press. The membranes were pelleted and the supernatant was loaded on a column of Ni-ProBond resin. The OCP was further purified on a Whatman DE-52 cellulose column. To quantify the OCP present in the different strains, membrane-phycobilisome fractions were isolated [START_REF] Wilson | Light induced energy dissipation in iron-starved cyanobacteria. Roles of OCP and IsiA proteins[END_REF] and were analyzed by SDS page on 12%/2M urea in a Tris/Mes system [START_REF] Kashino | An improved SDS-PAGE system for the analysis of membrane protein complexes[END_REF]. The OCP was detected by a polyclonal antibody against OCP [START_REF] Wilson | Light induced energy dissipation in iron-starved cyanobacteria. Roles of OCP and IsiA proteins[END_REF]. Carotenoids were extracted as previously described [START_REF] Polivka | Spectroscopic properties of the carotenoid 3Ј-hydroxyechinenone in the orange carotenoid protein from the cyanobacterium Arthrospira maxima[END_REF] and separated by HPLC. Mass analysis was realized. More details can be found in SI Materials and Methods.

Spectroscopy Measurements. The kinetics of fluorescence changes were monitored in a modulated fluorometer (PAM) as previously described [START_REF] Bissati | Photosystem II fluorescence quenching in the cyanobacterium Synechocystis PCC 6803: involvement of two different mechanisms[END_REF].

Transient absorption spectroscopy used 475-nm 50-fs laser pulses at 1 kHerz and energy per pulse of Ϸ200 nj. The data were subjected to global and target analysis [START_REF] Van Stokkum | Global and target analysis of time-resolved spectra[END_REF] (see also SI Materials and Methods).

FTIR samples of the OCP in H2O and D2O were made with Ϸ2 l of 5-mM OCP spread between two tightly fixed CaF2 windows without any spacer. Lightminus-dark spectra were recorded using an FTIR spectrometer (IFS 66s Bruker) equipped with a nitrogen cooled photovoltaic mercury-cadmium-telluride detector (20 MHz, KV 100, Kolmar Technologies). A blue LED emitting at 470 nm was used for photoconversion.

Resonance Raman spectra, in resonance with the carotenoid electronic transitions, were recorded with a Jobin Yvon U1000 spectrometer equipped with liquid-nitrogen-cooled controlled-drift detector (Spectrum One, Jobin-Yvon). A coherent Argon laser (Innova 100) was used for excitation at 496.5 nm (OCP o ) or 528 nm (OCP r ). During spectral measurements, the temperature of the sample was maintained at 10 K to avoid photoconversion of OCP o into OCP r or relaxation of OCP r into OCP o . The dark form of OCP was flash frozen in a liquid nitrogen bath.

Fig. 1 .

 1 Fig.1. Relationship between blue-green light induced NPQ and the OCP in whole cells. (A) Decrease of maximal fluorescence (Fm') during exposure of WT (red squares), over-expressing OCP mutant (blue circles), His-tagged OCP/K m resistant mutant (green romboids) and His-tagged OCP/Sp resistant mutant (black triangles) cells to 740-mol photons m Ϫ2 s Ϫ1 of blue-green light (400 -550 nm). The graph is the average of four independent experiments and the error bars show the maximum and the minimum fluorescence value for each point. The cells were diluted to 3-g chlorophyll/ml. (B) Coomassie bluestained gel electrophoresis and immunoblot detection (bottom panel) in membrane-phycobilisome fractions from His-tagged OCP/Sp resistant mutant (1), His-tagged OCP/K m resistant mutant (2), WT (3), and over-expressing OCP mutant (4). The arrow indicates the OCP. Each lane contained 1.5-g chlorophyll. (C) OCP r is present in whole cells under NPQ-inducing conditions. Difference light-minus-dark absorbance spectrum of the isolated OCP (red) compared with the double difference absorbance spectrum: light-minus-dark overexpressing OCP cells spectrum minus light-minus-dark ⌬OCP cells [strain without OCP (9)] (average of five independent experiments). The illumination of cells and spectra recording were realized at 11°C.

Fig. 2 .

 2 Fig.2. Isolated OCP is responsive to blue-green light : Photoconversion and dark recovery. (A) Photograph of isolated OCP o and OCP r . To obtain OCP r the isolated protein was illuminated with a blue-green light at 740-mol photons m Ϫ2 s Ϫ1 at 12°C for 2 min. (B) Absorbance spectra of the dark orange form (OCP o ; black) and the light red form (OCP r ; red). (C) Darkness red OCP r to orange OCP o conversion (decrease of the absorbance at 580 nm) and (D) photoconversion from the OCP o to the OCP r form using a 350-mol photon m Ϫ2 s Ϫ1 blue-green light intensity (increase of the absorbance at 580 nm) at different temperatures: 32°C (violet), 28°C (rose), 24°C (blue), 19°C (green), 15°C (red), and 11°C (black). (E) OCP r accumulation at 11°C and different light intensities: 20 (black), 50 (red), 120 (green), 210 (blue), 350 (rose), 740 (orange), and 1,200 (violet)-mol photons m Ϫ2 s Ϫ1 of blue-green (400 -550 nm). The protein concentration was OD 0.2 at 495 nm.

  Fig. 3.The OCP r is essential for the induction of the photoprotective mechanism. (A) Shown is 100% conserved Tyr and Trp interacting with the carotenoid. (B) Decrease of Fm' during exposure of WT (red squares), overexpressing W110S OCP mutant (green circles), and His-tagged W110S OCP resistant mutant (blue triangles) cells to 740-mol photons m Ϫ2 s Ϫ1 of bluegreen light (400 -550 nm). (C) Immunoblot detection in membranephycobilisome fractions from WT (1), overexpressing W110S OCP mutant (2), and His-tagged W110S OCP (3). Each lane contained 1.5-g chlorophyll (D). Absorbance spectra of the dark orange form (OCP o ; black) and the light form (OCP r ; red). The OCP o was illuminated during 15 min at 1,200-mol photons m Ϫ2 s Ϫ1 and at 10°C.

Fig. 4 .

 4 Fig. 4. Changes in the carotenoid and the protein upon illumination. (A) Resonance Raman spectra of Synechocystis PCC 6803 OCP r and OCP o and Arthrospira maxima OCP o in the 1,740 to 820 cm Ϫ1 range and (B) light-minusdark FTIR spectra of OCP in H 2O (black) and in D2O Ϸ5 (red line) and 50 (blue line) seconds after illumination with a blue LED in the carbonyl region between 1,730 and 1,600 cm Ϫ 1 (Amide I region). The OCP r minus OCP o Amide I differential pattern is assigned to H-bond loosening (upshift) of the loops and ␣-helices carbonyl modes together with a H-bond strengthening (downshift of carbonyl modes) of the ␤-sheet.

Fig. 5 .Fig. 6 .

 56 Fig. 5. Primary photochemistry of OCP revealed by femtosecond spectroscopy. OCP was excited with 50-fs flashes at 475 nm and the absorbance changes were monitored between 400 and 675 nm at time delays up to 3 ns. (A) Global analysis of time resolved data in the form of Evolution-Associated Difference Spectra (EADS). Four kinetic components with time constant of 100 fs (black), 1 ps (red), 4.5 ps (blue), and a long-lived component (green, expanded 30ϫ). (B) Kinetic trace recorded at 565 nm (symbols) and the result of the global analysis (solid line). After decay of carotenoid excited-state signals on the picosecond timescale, a nondecaying photoproduct is formed at low yield. Note that the time axis is linear up to 10 ps and logarithmic thereafter. The vertical axis is split into two linear axes to show the long-lived product.

͉ www.pnas.org͞cgi͞doi͞10.1073͞pnas.0804636105 Wilson et al.

͉ www.pnas.org͞cgi͞doi͞10.1073͞pnas.0804636105 Wilson et al.

͉ www.pnas.org͞cgi͞doi͞10.1073͞pnas.0804636105 Wilson et al.

ACKNOWLEDGMENTS. We thank G. Ajlani and W. Vermaas for the gift of the plasmid pPSBA2 and D.W. Krogmann for stimulating discussions. We acknowledge Annie Marion-Poll, Jean-Pierre Boutin, and Lucien Kerhoas for discussions and advice about carotenoid analysis. This work was supported by grants from I'Agence Nationale de la Recherche, France (programs CAROPROTECT and BIOPHYSMEMBPROTS) (to A.W., D.K., A.G., and B.R.), and the INTRO2 European Union FP6 Marie Curie Research Training Network.


Tristan Mary-Huard
email: maryhuar@agroparistech.fr

Julie Aubert
email: julie.aubert@agroparistech.fr

Nadera Mansouri
email: nadera.mansouri@jouy.inra.fr

Olivier Sandra
email: olivier.sandra@jouy.inra.fr

Jean-Jacques Daudin
email: daudin@agroparistech.fr

Nadera Mansouri-Attia

Statistical methodology for the analysis of dye-switch microarray experiments

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

Background

DNA microarray technology is a high throughput technique by which the expression of the whole genome is studied in a single experiment. Experiments must be well organized and design issues are crucial, see [START_REF] Yang | Design issues for cDNA microarray experiments[END_REF][START_REF] Churchill | Fundamentals of experimental design for cDNA microarrays[END_REF]. In dual label experiments Cy3 and Cy5 are used as fluorescent dyes allowing to compare two RNA samples on the same slide. It is now well known that there exists a differential effect of the two dyes [START_REF] Yang | Normalization for cDNA microarray data: a robust composite method addressing single and multiple slide systematic variation[END_REF][START_REF] Kerr | Statistical Analysis of a gene expression microarray experiment with replication[END_REF], that can be gene-specific. An efficient way to remove this technical artifact is to use balanced reverse dye designs [START_REF] Dobbin | Statistical design of reverse dye microarrays[END_REF]. Balanced reverse dye designs can be divided into three classes along a line of strengthening balancing constraints:

1. Balanced reverse dyes for which each biological sample is hybridized only one time and therefore present with only one dye, on only one array (Table 1.1). These designs are globally balanced but not individually balanced.

2. Individually-balanced design for which each biological sample is divided into two parts, one hybridized with Cy3 on one array and the other with Cy5 on another array. Each biological sample is hybridized exactly two times (Table 1.2).

3. Dye-swaps for which each couple of biological samples from two conditions are hybridized on two arrays with reverse dyes. Dye-swaps are constrained to be couple-balanced (Table 1.3).

Dye-swap design is mostly used when the technical error is higher than the biological variability, either to reduce the technical variance, or when gene-specific dye-bias is of concern [START_REF] Martin-Magniette | Evaluation of the gene-specific dye bias in cDNA microarray experiments[END_REF][START_REF] Dobbin | Characterizing dye bias in microarray experiments[END_REF]. When the biological variability is greater than the technical error, globally balanced designs are statistically more efficient [START_REF] Dobbin | Statistical design of reverse dye microarrays[END_REF]. However the number of biological samples is sometimes limited, therefore this design is not always possible in practice.

The term Dye-switch is used for the first and sometimes also for the second classes. Dye-switch designs of the second class are sometimes described and proposed in papers dealing with microarrays experiments. For example loop designs are often members of this class [START_REF] Oleksiak | Variation in gene expression within and among natural populations[END_REF][START_REF] Whitehead | Neutral and adaptive variation in gene expression[END_REF], although the distinction between the first and the second class is not always clearly made.

A major point to notice is that the statistical analysis may be very different for the three classes of design. The analysis of the first and third classes is straightforward and well described in articles (see for example [START_REF] Kerr | Statistical Analysis of a gene expression microarray experiment with replication[END_REF][START_REF] Kerr | Analysis of variance for gene expression microarray data[END_REF][START_REF] Wit | Statistics for Microarrays: Design, Analysis and Inference Chichester[END_REF]): the experimental units are mutually independent (we consider as usual that the two conjugate arrays of the dyeswaps are summed up to only one experimental unit), and simple statistical procedures such as Student T-tests (or regularized T-tests) can be performed. On the contrary, if we consider the second class of designs, the experimental units are not independent, a feature that must (or must not) be accounted for. The literature about the statistical study of such designs is limited: some papers proposed some theoretical contributions for their analysis [START_REF] Landgrebe | Efficient two-sample designs for microarray experiments with biological replications[END_REF][START_REF] Landgrebe | Efficient design and analysis of two colour factorial microarray experiments[END_REF], but simple guidelines for experimenters and practical considerations (computational burden, choice of a strategy for parameter estimation) are not available.

We consider here the simplest individually-balanced dyeswitch design: two conditions A and B are compared in a two-color cDNA microarray experiment, with n biological samples for each condition. The design is the following: each RNA sample (A 1 to A n for condition A, and B 1 to B n for condition B) is divided into two parts, one labelled with Cy5 and the second labelled with Cy3. Then 2n microarrays are hybridized with respectively A 1 Cy5 and B 1 Cy3, B 1 Cy5 and A 2 Cy3, A 2 Cy5 and B 2 Cy3, and so on till B n Cy5 and A 1 Cy3, (see Table 1.2). There are 2n samples, 4n labelled samples, 2n microarrays, and each sample is hybridized two times (one with Cy5 and one with Cy3) on two different arrays. We propose a simple, efficient and robust method for the statistical analysis of this experiment.

Model on the measure of the expression of genes

After the normalization step, X i is the expression measure on the log-scale, for a given gene, corresponding to condition A on array i. Let j(i) denote the sample number corresponding to condition A and array i.

Similarly, Y i is the expression measure for the condition B sample on the same array, and j'(i) the sample number corresponding to condition B and array i. In the following the gene index is not present in order to simplify the mathematical expressions, but it is important to note that all the terms in the following models are gene-specific. Here we use an analysis of variance (ANOVA) model for the expression measure as introduced by [START_REF] Kerr | Analysis of variance for gene expression microarray data[END_REF].

The model for X i and Y i is the following: where • µ A and µ B are the population mean expression measures for condition A and B.

• δ l(i) is a two-level fixed effect corresponding to the dye effect. δ l(i) = δ 1 (resp. δ 2 ) for all the samples labelled with Cy5 (resp. Cy3). This term accounts for the gene-specific dye bias.

• B j(i) represents an independent gaussian random term with mean 0 and standard deviation σ B , corresponding to the random effect of sample j(i). This variable is specific to the biological sample and is called biological error, related

X B M T Y B M T i A l i j i i i i B l i j i i i = + + + + = + + + + ′ ′ ′ m d m d ( ) ( ) ( ) ( )
, to the variability of the biological material inside each population A and B.

• M i represents an independent gaussian random term with mean 0 and standard deviation σ M . M i is the effect of the spot associated to the gene under concern in microarray i and has the same value for the two samples which are hybridized on array i. This error term takes into account the spatial heterogeneity in each array that affects both Cy3 and Cy5 measurements.

• T i represents an independent gaussian random term with mean 0 and standard deviation σ T , corresponding to the technical variability, including the steps of labelling, hybridization and measure of intensity of fluorescence. This variable has a specific value for each combination gene×dye×sample, even if the samples are hybridized on the same array and at the same spot, so that T i and are independent random variables. T i and M i are the two components of the so-called technical error.

Model on the difference of expression on one array

Let D i = X i -Y i , i = 1,.
..,2n. Using equation ( 1) we obtain: which may be written

D i = µ + BD i + (-1) i+1 δ + TD i where • µ = µ A -µ B
is the true differential expression between conditions A and B for the gene under concern,

• BD i = B j(i) -B j'(i) is a random variable with mean 0 and standard deviation σ B ,

• TD i = T i -is an independent random variable with mean 0 and standard deviation σ T ,

• δ = δ 1 -δ 2 is the difference between the Cy3 and Cy5 dye effects. This term accounts for the gene-specific dye bias.

Each variable D i follows a Gaussian distribution with mean E(D i ) = µ + (-1) i+1 δ and variance . All the covariances cov(D i , D j ) are equal to zero except the following ones:

with the convention that 2n + 1 = 1.

In this study, we present and compare different strategies for the statistical analysis of individually-balanced designs. The article is organized as follows. In the Results section, five statistical procedures to analyze individually balanced designs (Table 1.2) are compared on both simulated and real data. The Conclusion section draws the main conclusions and gives some useful guidelines for the analysis of individually-balanced designs. The details of the computation are given in the Methods section.

Results

Statistical procedure comparison

In this section, we investigate the efficiency of five test procedures for the differential analysis of datasets corresponding to the design of Table 1.2. The procedures are the following (see the Methods section for more details):

• Naive Method NM: for each gene, the naive test statistic is computed.

• Unbiased Paired Method (UP): for each gene, the unbiased paired statistic is computed. Notice that from the Methods section, the theoretical value of C must be positive. In practice, the estimated value may be negative. In such a case, C is truncated at 0.

• Unbiased Unpaired Method (UU): for each gene, the unbiased unpaired statistic is computed. As for the previous method, the value of C XY must be positive. If not, C XY is truncated at 0. Furthermore, the unbiased variance estimator is . Since

C XY is non-negative, the variance estimator may have a negative value. In such a case, the variance can be fixed at a given threshold (0.001 in the following).

′ T i D B B T T i A B ji j i li l i i i = - + - + - + -′ ′ ′ m m d d ( ) ( ) ( ) ( ) 2 ′ T i 2 V D i B T ( ) = + 2 2 2 2 s s cov( , ) D D i i B + = 1 2 s T n D S N = 2 2 T n D S C UP = + 2 2 2 ( ) T n X Y S X S Y C XY UU = - + - 2 2 2 S S C X Y X Y 2 2 2 + -
• Mixed Model with ML estimation (ML): for each gene, model ( 1) is adjusted with the Maximum Likelihood algorithm.

• Mixed Model with REML estimation (REML): for each gene, model ( 1) is adjusted with the Restricted Maximum Likelihood algorithm.

It is important to consider both the ML and REML algorithms for the mixed model since each algorithm has its own advantages. While ML is known to provide biased estimates of the variance components, computations are faster and the algorithm does converge. REML gives unbiased estimates of the parameters, but may not converge if the number of observations is small. Both ML and REML computations were performed using the R package Maanova [START_REF] Kerr | Analysis of variance for gene expression microarray data[END_REF].

Simulations

To study the behavior of the 5 procedures, we performed a simulation study using model [START_REF] Yang | Design issues for cDNA microarray experiments[END_REF]. We considered 3 different values for (0.5, 1,

for the number of samples in one condition (5, 10, 20, 30) and 5 possible values for the differential expression µ = µ A -µ B (0, 1, 2, 3, 4). The parameter σ T was fixed at 1. For each combination of the parameters, 10,000 genes were simulated.

Control of the Type I error rate

We first consider the case µ = 0. Table 2 shows the actual Type I error rate level of the 5 test procedures, when the requested nominal level is 5%. Different behaviors can be observed: NM and ML result in a type I error rate higher than the nominal level, and procedure UU is conservative. UP results in an actual level that is close to the expected one, whatever the conditions. In most cases, REML enables an efficient control of the type I error. Yet, when the biological variability is high and the number of samples is low, REML yields a high type I error because of inconsistent estimations of the variance (see the next section). When = 2 and n = 5, the discrepancy between the theoretical and the actual level is even worse for REML than for the other methods.

From these first observations we conclude that we can discard procedures NM and ML, since in differential analysis an effective control of the Type I error rate is necessary.

Performance analysis

We now compare the performance of the 3 remaining procedures to detect differentially expressed genes. Table 3 shows the proportion of detected differentially expressed genes, for different values of the parameter set. It clearly appears that the power of procedure UU is low compared with procedures UP and REML. This may be the consequence of the Student approximation (each test statistic is compared with the quantile of a Student distribution with 2n -2 degrees of freedom), that could be more erroneous in the case of the UU statistic.

An interesting point is that UP results are more stable than the REML results. If we consider sample sizes n larger than 20, we observe that the absolute values of the approximate REML T-test range from 0 to 32, except for some genes where the absolute value is larger than 400. These outliers come from an erroneous estimation of the variance of the mean difference, that is evaluated to be (almost) 0. This does not happen with (UP) since the estimated variance is max(S 2 , S 2 + 2C), i.e. the variance is overestimated to avoid outliers. Notice that despite this overestimation in many cases the power of UP is larger than the power of REML.

Computational burden and convergence

We now consider the important question of computational time for the 2 competitive procedures UP and REML. Since microarray experiments can involve hun-

s B 2 s M 2 s B 2
s B 2 s B 2 s B 2 s B 2
dreds of thousands of genes, it becomes critical to use efficient algorithms for the statistical analysis of the data. Table 4 gives the user CPU time associated to each procedure for the complete analysis of 10,000 genes. While the computational time is constant whatever the condition for the (UP) procedure, (REML) is 8 to 330 times longer than (UP), depending on the number of samples.

Furthermore, REML can result in inconsistent estimates of the variance, as shown in the previous sections, or may not converge. Table 4 provides the number of genes for which the REML algorithm did not converge.

Embriogenomic data

The impact of pregnancy on the cattle endometrium transcriptom is investigated in [START_REF] Mansouri | Identification of differentially regulated genes in the endometrium of cyclic and pregnant cows using a high-throughput transcriptome analysis[END_REF]. In Mammals, the implantation of the embryo is a key event in the establishment of a pregnancy. A microarray experiment has been made to analyze the gene expression of the bovine pregnant endometrium and determine key pathways that control the endometrium physiology during the implantation process. The expression of 13300 genes in the endometrium of cows (n = 5) has been investigated. Only 5 animals were available for each condition so that the dye-switch design of Table 1.2 was used. Gene profiling has been established to analyze the impact of pregnancy by comparing the endometrium of cyclic (day 20 of cycle) versus pregnant animals (day 20 of pregnancy). In the following, the results of the five statistical procedures defined above are compared using this dataset.

The Venn diagram of Figure 1 shows the number of genes declared differentially expressed (DE) by 4 methods using the Bonferroni method with a 5% level. The UU method gives the least number of DE genes (4) and is not presented in the diagram. REML (which did not converge for 3 genes) gives the greater number of DE genes (93), among which 23 are also found by the other methods, and 70 are specifically found by REML (70 REML specific genes). 70 genes are found DE by ML (22 ML specific genes), and 58 by the naive method (9 Naive specific).

Finally 33 genes are declared DE by UP, and all of them are also found by one, two or all of its competitors. Therefore UP provides the less discordant results. The higher number of DE genes obtained with the naive and the ML methods was expected, since it is known from the theory and the simulation study that these methods yield more false positives than the nominal risk. Figure 2 (right) shows that the ML and UP estimates of the standard error are coherent but that the ML estimate are lower than the ones obtained by the UP method. This point is in keeping with the statistical theory which assesses that the UP estimate of the variance is unbiased while the ML estimate has a negative bias.

The high number of DE genes specifically found with REML is odd. Figures 2 and3 show that this comes from very low estimates of variance for some genes, so that these genes are declared DE not because the mean difference of expression between the two conditions is high, User CPU time of procedures (UP) and (REML), for σ 2 = 0.5 and different numbers of samples. The last column provides the average number of genes for which REML did not converge.

Venn diagram for the embriogenomics experiment

but because this mean difference is divided by a very low standard error. So most of the 70 genes only found by the REML method are due to too low estimates of the gene variance obtained by the REML algorithm. This observation is in keeping with the results of the simulation study. Therefore the UP method or the naive method should be preferred in this particular experiment. The use of REML without a sharp biological analysis of the results gene by gene would be misleading.

Teleost fish dataset

An important application of the methodology proposed in the previous section is the analysis of loop design experiments. Loop and interwoven loop designs were initially proposed in [START_REF] Churchill | Fundamentals of experimental design for cDNA microarrays[END_REF] to compare p treatments, where p is 3 or higher. Figure 4 displays a particular interwoven loop design where 3 different 2-by-2 loop comparisons of treatments are combined in a single experiment. The 3 loop comparisons are

• N1 → S1 → N3 → S3 → N5 → S5 → N2 → S2 → N4 → S4 → N1 • S1 → G1 → S3 → G3 → S5 → G5 → S2 → G2 → S4 → G4 → S1 • N1 → G2 → N3 → G4 → N5 → G1 → N2 → G3 → N4 → G5 → N1
Each of these comparisons corresponds to the design of Table 1.2 discussed in the previous section. Such experimental designs have been studied both theoretically [START_REF] Wit | Near-optimal designs for dual channel microarray studies[END_REF] and practically [START_REF] Oleksiak | Variation in gene expression within and among natural populations[END_REF][START_REF] Whitehead | Neutral and adaptive variation in gene expression[END_REF]. Here, we briefly present the Teleost fish data of [START_REF] Oleksiak | Variation in gene expression within and among natural populations[END_REF].

The Teleost fish experiment aims to compare 3 populations of fish (Northern Fundulus heteroclitus, Southern Fundulus heteroclitus and Fundulus grandis). Five individuals were examined in each population to determine the variation in gene expression between populations. Each individual is used to probe four cDNA microarrays, according to the design of Figure 4. The raw data consist of 120 measurements (15 individuals × 4 slides × 2 duplicates per slide) for 907 genes.

In [START_REF] Oleksiak | Variation in gene expression within and among natural populations[END_REF], the signal is modelled as follows (after per slide duplicate averaging):

Y ijkg = m + A i + D j + (AD) ij + G g + (AG) ig + (DG) jg + (V G) kg + e ijkg ,
where A, D, G and V stand for Array, Dye, Gene and Variety, respectively. Then the 4 measurements corresponding to a given individual are averaged, and an F statistic is computed per gene to check whether the variety effect is significant or not.

This strategy roughly amounts to the UU test procedure of section when the number of treatments is higher than 2.

The main difference is that in model ( 4), the model does not include the array random effect which takes into account the dependency between two measures on the same array. According to the results of section, this implies that the variance estimator is biased, leading to a loss of power.

As an alternative, we perform the statistical analysis using the UP procedure. Each pairwise comparison between 2 varieties is made, and a gene is declared differentially expressed if at least 2 of the 3 tests are significant. Each test is performed at the level 0.02, meaning that for a given gene, the nominal level is roughly 0.001 (3 × 0.02 2 for 2 of the 3 tests to be significant under H 0 at level 0.02). This is a good compromise between the 0.01 threshold adopted in the original articles with no correction for multiple testing, and the 0.5 × 10 -4 (0.05/907) threshold given by a 5% level per test combined with a Bonferronni multiple testing correction. While the drawback of our strategy is to replace one test by three, the advantage is that the variance estimate is unbiased. Table 5 gives the Oleksiak original list of differentially expressed genes found with the original method and the UP list of genes found with the UP procedure.

Among the 15 genes originally identified, 5 are also declared differentially expressed with the (UP) method. At a first glance, the (UP) procedure seems less powerful than the original method since only 9 genes are found here compared with the 15 genes of the original article. But due to the threshold adopted by the authors in [START_REF] Oleksiak | Variation in gene expression within and among natural populations[END_REF], the expected number of false positives is 9 for the Oleksiak list, whereas for the (UP) list we expect only 1 false positive. Therefore most of the 10 extra genes found in [START_REF] Oleksiak | Variation in gene expression within and among natural populations[END_REF] may be false positives. To examine the discriminant effect of the 9 genes of the (UP) list, we performed as in the original publication a clustering of the individuals, according to the significative genes. The corresponding tree is given in Figure 5. A cutoff of the tree at 0.15 gives the following 3 classes : {S1, S2, S4, S5, N1}, {G1, G2, G3, G4, G5, S3}, {N2, N5, N3, N4}.

These 3 classes roughly correspond to the three populations of interest, up to 2 misclassified observations. In the original article, the partition in 3 classes gave {N1, N2, N3, N4, N5}, {S1, S4}, {G1, G2, G3, G4, G5, S2, S3, S5}.

With only 9 genes (rather than 15), the classification obtained with (UP) is improved compared with the classification of the original method.

Discussion

Random terms taking into account the array and the sample effects must be included in the statistical model at the gene level for dye-switch experiments. We showed on simulations that the naive paired T-test, which does not take into account the biological sample effect, leads to more false positives than expected, especially when the biological sample effect is high. It may be safely used only when the biological variance is lower than the technical variance. The REML estimate for mixed model provides an approximatively correct false positive rate, at the price of high computational complexity, lack of convergence for low or medium sample sizes and sometimes spurious results. To the contrary, the UP method we propose is easy to implement and not computationally intensive. The method is protected against spurious results, leading to a more robust and powerful analysis than REML when the biological variability is high and the number of samples low, an usual situation in microarray experiments.

Mean difference versus standard error for the REML-differentially expressed genes of the embriogenomics experiment For small sample size experiments, it is advised to use regularized T-test, see [START_REF] Baldi | A Bayesian Framework for the Analysis of Microarray Expression Data: Regularized t-Test and Statistical Inferences of Gene Changes[END_REF][START_REF] Delmar | VarMixt: efficient variance modelling for the differential analysis of replicated gene expression data[END_REF][START_REF] Smyth | Linear models and empirical Bayes methods for assessing differential expression in microarray experiments[END_REF][START_REF] Tusher | Significance analysis of microarrays applied to transcriptional response to ionizing radiations[END_REF]. Regularization strategies are based on statistical methods that take the individual variance of each gene as input and give a regularized variance for each gene as output. The UP procedure proposed in this paper gives an estimate for the variance of the differential expression for each gene, so it allows a further application of all these regularization methods.

Conclusion

In this paper the proposed estimate of the variance of the differential expression is assessed for the comparison between two conditions in a dye-switch design. The same methodology could be extended to more complex designs involving more than two conditions and duplicate hybridizations of the same biological sample on different arrays.

Methods

Paired test procedure

According to expression (2), an unbiased estimator of µ is . The variance of this estimator is

To perform a statistical test on parameter µ, we need to estimate .

Naive variance estimate

The naive estimate of is which is used to perform paired T-tests. But in a dyeswitch experiment the variables D i -are not centered, since the means of D i and are µ + (-1) i+1 δ and µ, respectively. Hence we consider the alternative estimator where

D D n i = ∑ 1 2 V V D D = ( ) V V n D n V D D D n n D i i i i B = = +       = + ∑ ∑ ∑ + ( ) ( ) cov( , ) ( 1 2 1 4 2 2 1 4 2 2 2 2 1 2 s s s s s s T B B T i i n n n V D D D 2 2 2 2 1 4 1 2 4 2 1 2 2 ) ( ) ( ( ) cov( , )) +     = + = + + V D V D 1 2 1 2 n D D i i - - ∑ ( ) D D S n D D i i i 2 2 1 2 2 = - - ∑ ( ) , ( ) D n D i D n D i i i i i i = = ∑ ∑ 1 1 is odd is even if is odd otherwise , . ( )
The Teleofish experiment design Figure 4 The Teleofish experiment design. The expectation of this alternative estimator is S 2 is a downward biased estimator of V( ). The higher compared with , the higher the bias:

From this naive estimate of the variance we can derive a first T-test statistic to be used for the differential analysis:

Unbiased variance estimate Let . We have From this and equation ( 5) we can deduce the following unbiased estimate of :

Finally, the "unbiased paired t-statistic" for testing the null hypothesis

H 0 = {µ 1 = µ 2 } is E n D D n E D E D n i i i i i i 1 2 2 1 2 2 1 2 2 2 2 - -         = - -     = - i B T n n n n n + - +       = - × × - + ∑ 2 2 2 2 2 2
)

. = + s s B T D s B 2 s T 2 V D E S B T B T ( ) ( ) / / . = + +         2 1 2 2 1 2 2 s s s s T n D S N = 2 2 C D D D D n i i i i i = - - - + + ∑ 1 2 4 1 1 ( ) ( ) ( ) ( ) E C n E D D D D D D D D n i i i i i i i i i B ( ) [ ] ( ) ( ) ( ) ( ) = - - - + = - + + + + ∑ 1 2 4 1 2 4 1 1 1 1 s 2 2 2 2 2 2 2 2 1 2 2 - - + × ×       = ∑ n n n n B B B i B s s s s . V D S n S C D 2 2 1 2 2 = + ( )
Clustering tree for the Teleofish dataset Figure 5 Clustering tree for the Teleofish dataset. Clustering tree for the Teleofish dataset, obtained from the second list of differentially expressed genes of Table 5.

which is approximately distributed as a Student distribution with 2n -2 df under H 0 .

Unpaired test procedure

Let (respectively ) be the mean of the 2 results obtained with the same biological sample (in 2 different arrays and with the 2 dyes) for condition A (respectively condition B). From model (1) one obtains where j is the biological sample index (recall that sample j is different for the two conditions), i(j) and i'(j) are the arrays on which sample j has been hybridized. and may be correlated as a result of a possible common array effect. and are uncorrelated because the two different biological samples of the same condition cannot be present together on the same array. From result (5) we have:

The ) .

B M M T T j ij i j ij i j X j ′ Y j X j ′ X j V X Y V n D B T ( ) ( ). - = = + 1 2 4 2

E S S

X Y B T M ( ) .

Figure 1

 1 Venn diagram for the embriogenomics experiment. Comparison of the DE genes obtained by four methods. Vertical right rectangle: REML, horizontal low rectangle: UP, bone: N and circle: ML.

  Comparison of the standard errors obtained with ML, REML and UP for the REML-DE genes of the embriogenomics experiment Figure 2 Comparison of the standard errors obtained with ML, REML and UP for the REML-DE genes of the embriogenomics experiment. Left: REML estimates (yaxis) versus UP estimates (x-axis) of the standard error. Center: REML estimates versus ML estimates. Right: UP estimates versus ML estimates.

Figure 3

 3 Mean difference versus standard error for the REML-differentially expressed genes of the embriogenomics experiment. Standard error of the difference obtained by REML (y-axis) versus mean difference between the two conditions (x-axis). Black points are not found DE by other methods than REML.

Table 1 : Three different balanced reverse dye designs for the comparison of 2 treatments

 1

	1 array	1	2	3	4	5	6	7	8	9	10
	Cy5 A1 B5 A3 B9 A5 B6 A7 B10 A9 B9
	Cy3 B3 A2 B8 A4 B2 A6 B1 A8 B4 A10
	2 array	1	2	3	4	5	6	7	8	9	10
	Cy5 A1 B1 A2 B2 A3 B3 A4 B4 A5 B5
	Cy3 B1 A2 B2 A3 B3 A4 B4 A5 B5 A1
	3 array	1	2	3	4	5	6	7	8	9	10
	Cy5 A1 B1 A2 B2 A3 B3 A4 B4 A5 B5
	Cy3 B1 A1 B2 A2 B3 A3 B4 A4 B5 A5
	Three different balanced reverse dye designs for the comparison of 2
	treatments (A and B), with an equal number of slides. A i stands for the i th biological sample in condition A. (1) Globally balanced design, with
	10 biological samples per condition. (2) Individually-balanced design
	with 5 biological samples per condition. (3) Dye-swap design with 5
	biological samples per condition.

Table 2 : Actual level of the 5 test procedures in one simulation of 10 000 genes

 2

				= 0.5				= 2
	M e t h o d	5	1 0	2 0	3 0	5	1 0	2 0	3 0
	Naive	6.9 (0.2)	7.3 (0.2)	7.3 (0.2)	7.5 (0.2)	13.2 (0.3)	13.9 (0.3)	14.0 (0.3)	14.2 (0.3)
	Unbiased Paired	5.2 (0.2)	5.2 (0.2)	5.2 (0.2)	5.3 (0.2)	8.2 (0.3)	6.9 (0.2)	6 (0.2)	5.8 (0.2)
	Unbiased Unpaired	2.1 (0.1)	1.3 (0.1)	1.0 (0.1)	1 (0.1)	4.6 (0.2)	3.4 (0.2)	2.7 (0.1)	2.9 (0.2)
	ML	8.5 (0.3)	8.6 (0.3)	8.3 (0.3)	8.3 (0.3)	12.5 (0.4)	11.1 (0.3)	9.9 (0.3)	9.8 (0.3)
	REML	4.7 (0.2)	4.2 (0.2)	4.5 (0.2)	4.9 (0.2)	14.7 (0.4)	8.5 (0.3)	5.9 (0.2)	5.5 (0.2)

Actual mean level (standard error) of the 5 test procedures, for low ( = 0.5, left) and high ( = 2, right) values of biological variance, and different number of samples n in each condition (in column). The requested nominal threshold is 5%.

Table 3 : Power of the UU, UP and REML test procedures

 3

				µ = 1			µ = 3
	Nb Samples		UU	UP	REML	UU	UP	REML
		s B 2
	5	0.5 5.6	13.6	10.6	55.5	92.1	86.75
	5	2	2.8	5.0	12.95	17.9	29.4	34.75
	10	0.5 13.2 39.3 33.97	77.8	100.0 99.64
	10	2	3.5	7.8	9.06	45.0	63.5	63.06
	20	0.5 35.0 80.1 78.13	98.8	100.0 100.0
	20	2	7.3	14.5 13.93	82.6	94.8	94.53
	30	0.5 51.9 95.5 95.05 100.0 100.0 100.0
	30	2	12.1 22.5 21.74	96.2	99.6	99.53
	Power (probability of rejecting H 0 × 100) of the different test
	procedures to detect a low (µ = 1, left) or high (µ = 3, right)
	differential expression.

Table 4 : CPU times of procedures UP and REML

 4

	n	UP CPU	REML CPU	No REML CV
	5	2.3	787	56.9
	10	2.6	212	5
	20	2.8	467	0
	30	3.2	1046	0.16

Table 5 : Lists of genes for the Teleofish experiment

 5

	Oleksiak list [8]

Lists of genes whose expression was significantly different between populations. The first 5 genes are found differentially expressed by both methods.

  It is easy to see that the second sum in C XY has the same mean. Therefore an unbiased estimate of is , and the approximate unpaired t-sta-

																											The overestimation is more dramatic as	increases.
														T UP =		n 2	(	S	D + 2 2 C	)	This estimate may be corrected:	may be estimated
																											using the empirical covariance between	and	. Let
					X j												Y j
																											with the convention that	. The mean of the first
																											sum is
	X	j	=	m	A	+	+ d d ( 1	2	)/	2	+	B	j	+	M i j ( )	+	M i j ′ ( )	)/	2	+	(	T i j ( )	+	T i j ′ ( )	)/	2
	Y	j		=	m	B	+	( d d d 1 +	2	) /	2	+ ′ +	( )	+	′ ( )	) /	2	+ ′ + ′ ′ ( ( ) ( )	) /	2
																											tistic is
					usual unpaired estimate of		is equal to
										, where								and
																			, whose common mean (under the
	homoscedastic model (1)) is equal to
	Therefore
	This method overestimates the true variance

(page number not for citation purposes)

Acknowledgements

The authors thank Douglas L. Crawford who provided the Teleofish dataset.

Authors' contributions

TMH and JJD conceived the method and prepared the manuscript. TMH and JA implemented part of the software and performed the statistical analysis. NM made the Embriogenomics experiment under the direction of OS. All authors contributed to the discussion and approved the final manuscript.


Caroline Rondel
email: caroline.rondel@ensiacet.fr

Isabelle Alric
email: isabelle.alric@ensiacet.fr

Jean-François Blanco
email: jeanfrancois.blanco@ensiacet.fr

Françoise Silvestre
email: francoise.silvestre@ensiacet.fr

Synthesis and properties of lipoamino acid/fatty acid mixtures. Influence of the amphiphilic structure

Keywords: Surfactants, amino acids, acylation, critical micelle concentration (CMC), foaming properties

The acylation of amino acids by acid chlorides with from 8 to 12 carbon atoms, in alkaline aqueous medium following Shotten-Baumann reaction, results in sodium salts of N α -acylamino acids and fatty acids mixture. These lastest are present in proportion from 40 to 60%. These compositions represent mixtures of amphiphilic anionic surfactants. They contribute together to the properties of the formulation. Measurements of the surface-active properties of these formulations, such as critical micelle concentration (CMC), surface tension at the CMC (TS), foaming capacity (FC) and foaming stability (FS), show that surfactant mixtures with the longest chain have the most desirable properties. They are comparable to commercial petroleum-based surfactants. Thus, the CMC, TS and CM values of the formulation obtained starting from leucine and dodecanoyl chloride (310 mg/L, 30.1 mN/m and 200%, respectively) are similar, even better than, sodium dodecylsulfate (290 mg/L, 39.1 mN/m and 230%, respectively).

Introduction

Surfactants, or surface-active agents, are among the most widespread and widely used chemical products in the world today. In 2002, total surfactant production volume worldwide was 11 million tonnes. Derivatives of plant origin accounted for approximately 20% of this production. Within a context of sustainable development, there is an urgent need to produce environmentally-friendly surfactants.

These surfactants can be obtained from molecules that mimic natural amphiphilic structures.

The association of a polar amino acid (hydrophilic moiety) and a non polar long chain compound (hydrophobic moiety) to built amphiphilic structures allows to obtain molecules with a high surface activity [START_REF] Infante | Amino acid-based surfactants[END_REF]. Thus, lipoamino acids obtained from natural raw materials are the choice surface-active molecules for applications in the food, pharmaceutical and cosmetic industries. As a result of their structure, they have a low degree of toxicity, improved resistance to hard water, antimicrobial activity [START_REF] George | A comparative study on the surface activity and micellar behavior of some N-acylamino acid based surfactants[END_REF], are gentle and not irritating to the skin and are easily biodegradable [START_REF] Infante | Amino acid-based surfactants[END_REF][START_REF] Infante | Non-conventional Surfactants from Amino Acids and Glycolipids: Structure, Preparation and Properties[END_REF].

If we consider the chemical structure of an amino acid, the fatty chain can be introduced via the amine or carboxylic function. However, the reactivity of the amine function in aqueous medium is widely higher than the one of carboxylic acid. We were interested in N α -acylamino acids obtained by fat chain grafting on the amine function of amino acid. Many synthesis pathways use organic solvents [START_REF] Infante | Non-conventional Surfactants from Amino Acids and Glycolipids: Structure, Preparation and Properties[END_REF][START_REF] Molinero | Synthesis and properties of Na-lauroyl-L-arginine dipeptides from collagen[END_REF][START_REF] Prabhudesai | Chemical synthesis of amino acidcontaining lipids. I. Lipids derived from monobasic amino acids. Fette, Seifen[END_REF][START_REF] Perez | Synthesis, Aggregation, and Biological Properties of a New Class of Gemini Cationic Amphiphilic Compounds from Arginine, bis(Args)[END_REF]. Another pathway consists of synthesis by acylation using an acid chloride in water, following the Schotten-Baumann reaction [START_REF] George | A comparative study on the surface activity and micellar behavior of some N-acylamino acid based surfactants[END_REF][START_REF] Desai | Surface activity and micellar behavior of sodium salts of N-acyl glycine, glycylglycine, and diglycylglycine[END_REF][START_REF] Berger | Preparation of N-acyl derivatives of amino acid mixtures obtained from cereal protein hydrolyzates for cosmetics. N° FR9221318 9. Takehara M[END_REF]. In parallel, in operating conditions (alkaline aqueous medium), the acid chloride hydrolyses in carboxylate ion (Figure 1). It is therefore necessary to determine the quantity of fatty acid formed during the secondary reaction in order to determine the composition of the final mixture. The aim is to acylate the greatest proportion of amino acid possible. To do this, an excess of acid chloride in relation to amino acids, is added. The presence of sodium (do)decanoate and octanoate contributes also to the mixture properties, because they have an amphiphilic capacity.

We were particularly interested in the acylation of a neutral amino acid with a non-ionic side chain (leucine), of an amino acid with a negatively-charged side chain (glutamic acid) and a basic amino acid with a positively-charged side chain (arginine), and acid chlorides with from 8 to 12 carbon atoms. The N α -acylamino acids/fatty acid sodium salts ratio of the mixture obtained was determined by NMR and UV spectroscopy methods. Then, we studied the surfactant properties of these different formulations. Indeed, only few of these surfactants

Experimental Procedures

Materials L-leucine (99%), L-glutamic acid (99%), L-arginine (98%), octanoyl chloride (>97%), decanoyl chloride (98%), dodecanoyl chloride (98%), o-phtaldialdehyde (OPA), sodium phosphate, sodium tetraborate, sodium dodecyl sulphate (SDS), β-mercaptoethanol and hexadecyl-trimethylammoniumbromid (CTAB) were purchased from Sigma-Aldrich (Saint Quentin Fallavier, France). D 2 O (99.90%) was supplied by Eurisotop (Gif-sur-Yvette, France). Preparation of N α -acylamino acid sodium salts Sodium hydroxide (2.72 g/68 mmol) -except for synthesis with glutamic acid (4.08 g/102 mmol) -and amino acid (34 mmol) were dissolved in 30 mL of water in a 250-mL two-necked flask equipped with a cooling agent and mechanical stirring. The mixture was stirred at room temperature. Acid chloride (51 mmol) was added after the amino acid and the sodium hydroxide were totally dissolved. The reaction temperature was thus maintained at 50°C for 3 h. At the end of the reaction, the pH was adjusted to 2-3 with a 4N hydrochloric acid solution. Water was eliminated using a rotary evaporator. A purification step of reaction mixture in order to eliminate the sodium chloride was then performed. For that purpose, 50 mL of ethanol was added to the mixture. Then, the ethyl-alcoholic solution was heated under reflux for 30 min. The mixture is vacuum-filtered. The dry matter and mineral content of the solid (obtained after the former filtration) was determined using the AFNOR standard, NF VO3-706, and the insoluble fraction was analysed by infrared spectrometry. The ethanol was then eliminated from the filtrate using the rotary evaporator. The residue obtained was dissolved in a saturated sodium hydroxide aqueous solution (4 to 6 g) and in 10 to 20 mL of ethanol. The N α -acylamino acid and fatty acid of sodium salts mixture were precipitated after adding 30 mL of acetone [START_REF] George | A comparative study on the surface activity and micellar behavior of some N-acylamino acid based surfactants[END_REF]. Finally, a filtration is performed in order to recover and vacuum dry the product mixture.

Determination of the dry matter and mineral content by AFNOR standard, NF VO3-706 2.5 g of product was put down in porcelain crucible. It was placed in an incubator at 105°C until to a constant weight. Then, it cooled in a desiccator. The percentage in dry matter is determined by the relation: m dry : masse of the dry product after a stay in an incubator at 105°C (g) m ashes : masse of ashes from dry product after calcination at 550°C (g) Analysis of amino groups and determination of the acylation rate Free amino acid groups were quantified using the reliable OPA method (12), described by Frister et al. [START_REF] Frister | OPA method modified by use of N,Ndimethyl-2-mercaptoethylammonium chloride as thiol component[END_REF]. The sample to be analysed was dissolved in a buffer solution of 12.5 mM sodium tetraborate and 2% SDS (w:w) at pH 8.5. 2 mL of a reagent solution prepared the same day were added to 1 mL of unknown solution. The reagent solution was prepared by introducing the following into a 50 mL volumetric flask: 25 mL 0.1 M sodium tetraborate solution (pH 9.2), 2.5 mL 20% SDS (w:w), 40 mg OPA dissolved in 1 mL methanol, 100 µg β-mercaptoethanol. The final volume was completed up to 50 mL with demineralised water.

The absorbance of the mixture was measured at 340 nm after 2 min incubation. The number of amine groups was calculated using a calibration curve obtained with L-leucine. The acylation rate (AR) was determined using the following formula:

AR = (Ni-Nf)/Ni*100
where Ni is the number of free amine groups in the amino acid before acylation, and Nf is the number of free amine groups in the final product determined by OPA.

Nuclear magnetic resonance ( 1 H and 13 C NMR) analysis All the NMR measurements were performed with in 7.05 Tesla Bruker AVANCE 300 spectrometer. All the proton and carbon-13 spectra were acquired at 300.1312 MHz and 75.4764 MHz, respectively, in a 5 mm direct probe (PH QNP-300SB F/P/C-H-D -05 -Zgrad -BTO 2000). The experiments were carried out at 293.1 ± 0.1 K. The sample (20-50 mg of salt) was dissolved in 0.6 mL of D 2 O. The chemical shifts were referenced to tetramethylsilane (TMS) for 1 H and 13 C nuclei. The proton spectra were collected with a solvent suppression experiment (Pulse programme 1 H: zgpr) with a 90° (P1=2.70 µs ; PL1=0 dB and PL9=45 dB) pulse as 32K points over 6.172 KHz spectral width.

All the carbon-13 spectra were acquired using standard proton-decoupled carbon-13 acquisition with pulse-gradient (Pulse programme 13 C: zgpg30). For this purpose, a carbon-13 length pulse of typically 9.70 µs (PL=-1 dB) and 18.115 KHz proton decoupling were applied during acquisition. The number of scan is 1,536 for carbon-13 experiments and 64 for proton analysis.

Measurement of the Critical Micelle Concentration (CMC)

Surface tension was measured using a GBX-TEN 089 tensiometer equipped with a Wilhelmy plate. Mixtures consisting of N α -acylamino acid and fatty acid sodium salts (2.5 g/L) were dissolved in a 0.1 M sodium phosphate buffer solution at pH 7.0 to obtain 200 mL of solution.

Drops of 400 µL of this solution were added to 50 mL of the same phosphate buffer solution.

Surface tension was continuously measured and recorded at 20°C until a constant surface tension value was observed. The CMC was obtained at the breaking point of the surface tension curve in relation to the logarithm of the mixture concentration.

Measurement of foaming properties

Foaming properties were measured using the method described by Padmashree et al. [START_REF] Padmashree | Effect of the traditional processing on the functional properties of cowpea (Vigna catjang) flour[END_REF]. 3 g of surfactants were mixed with 300 mL of water in a graduated 1-L cylinder. The solution was stirred at 1600 r/min. The volume was measured 30 s after stirring. The foaming capacity (FC) was expressed as the percentage of volume according to the following formula:

Results and discussion

Purification of acylation reaction products

The aim of this step is to eliminate all compounds that have no surface-active properties (sodium chloride, amino acids). After the elimination of water, the reaction products are dissolved in ethanol under reflux. By simple filtration of the medium, the totality of sodium chloride, not soluble in ethanol is eliminated. The mineral matter determination of solid obtained gives values of about 100% for synthesis performed with leucine and glutamic acid and above 60% for the synthesis carried out with arginine. In the last case, the infrared showed that the precipitate also contained an arginine fraction, slightly soluble in ethanol.

The second step of purification consists in obtaining the surface-active molecules under salt form and it permits to eliminate the amino acids that have not reacted. These latest do not precipitate during acetone addition. Therefore, the final mixture contains only the N αacylamino acid sodium salts and the fatty acid sodium salts. In the case of mixture obtained starting from glutamic acid, the precipitation of this amino acid is observed in acetone. The surfactant mixtures are thus contaminated by glutamic acid (Table1).

Determination of the conversion rate of the acylation reaction and the final formulation composition

In the operating conditions involving 1.5 equivalent of acid chloride for 1 equivalent of amino acid in presence of 2 equivalents of sodium hydroxide (3 for the synthesis with glutamic acid in reason of the presence of two carboxylic functions), the conversion in relation to amino acid (η AA ) is determined by OPA method, for the different reactions. η AA are raised for arginine (77-90%) and for leucine (87-88%) and lowered for glutamic acid (53-75%) (Table1). This lower conversion rate is due to higher basicity of reaction medium during the synthesis with glutamic acid, because of the presence of its two carboxylate functions, favouring the chloride hydrolysis. The influence of hydrophilic element is perceptible in the case of arginine acylation because the acylation rate is proportional to the fatty chain length.

The N α -acylation by acid chloride is an efficient way to constitute amphiphilic compounds.

The ratio of N α -acylamino acids to the total quantity of N α -acylamino acids and fatty acid salts formed in the final composition (R AA ) and the fatty acid salts to the total quantity of N αacylamino acids and fatty acid salts formed in the final composition (R FA ) is determined by NMR. A preliminary study of 1 H (zgpr) and 13 The values of integration on the 1 H spectra are determined in order to allow the calculation of the assay of our mixtures. I 1 and I 2 the value of the integral corresponding to one proton of N α -acylamino acid sodium salts and fatty acid sodium salts, respectively. For the three N αacylleucine acids, the N α -octanoylarginine acid and the N α -decanoylarginine acid-based mixtures, the integrals chosen correspond to the CH 2 (protons H3) in alpha of the amide function (integral I 1 ) or in alpha of carboxylic function (integral I 2 ) for the N α -acylamino acid sodium salts or the fatty acid sodium salts, respectively (Figure 2). Concerning the N αdodecanoylarginine acid sodium salt and the three N α -acylglutamic acid sodium salt-based mixtures, the integrals chosen correspond to the terminal methyl group (protons H1) of the hydrophobic part of our components (integral I 1 +I 2 ) and to the proton (H4) signals grafted on the asymmetric carbon of the N α -acylamino acid sodium salts (integral I 1 ). The integrals I 1 and I 2 of the spectrum of the mixture containing the N α -octanoylglutamate sodium salt and the octanoate sodium salt are illustrated on Figure 3. The assay of the mixture is expressed by the yield (R AA and R FA ) calculated with the following formula: 1. The yield (R AA ) obtained after purification are different from conversion rate (η AA ) obtained by OPA before purification. According to our experimental conditions, R AA can not exceed 66%. The lower yields observed for the derivates of glutamic acid may be explained by a content of sodium hydroxide greater during the synthesis with this amino acid that would lead to a premature hydrolysis of the chloride acid. The chain length does not seem to have any influence on the yield of the synthesis, regarding the uncertainty of about 10% on these values.

Measurement of the critical micelle concentration

A linear decrease in surface tension is observed when the concentration of the mixture is increased for all surfactants, up to the CMC (Figure 4 ), beyond which there is no observable change in surface tension. This behaviour is common to surfactants in solution. The high CMC values observed for the N α -octanoylamino acid-based formulations are due to the fact that the N α -octanoylamino acids have a less hydrophobic chain than that of N α -decanoylamino and N α -lauroylamino acids (Table 2). In fact, a longer, more hydrophobic chain results in lower surface tension. This is attributed to the increase in the affinity of lipophilic molecules for interfaces [START_REF] Sanchez-Vioque | Emulsifying properties of acylated rapeseed (Brassica napus L.) peptides[END_REF]. Regardless of the nature of the hydrophilic head of the amino acid, N αlauroylamino acids have the lowest CMC. The charge of the polar head also seems to have an influence on the CMC. For the same chain length, the CMC of the leucine derivates mixture is inferior to the one of arginine derivates, which is inferior to the one of glutamic acid derivates. The N α -acylleucine sodium salts have an anionic hydrophilic head, whereas N αacylarginine sodium salts have an amphoteric one and N α -glutamic acid sodium salts have one with two negative charges. Likewise, the higher values of CMC for the glutamic acid derivates are explained by the presence of residual glutamic acid. This amino acid has no surface-active properties, so its presence increases the CMC values N α -lauroylamino acid-and N α -decanoylamino acid-based formulations have a surface tension at the CMC comparable and sometimes even lower than that of SDS and CTAB. They therefore have interesting surface-active properties.

Measurements of foaming properties

The results of foaming properties are given on Table 3. Regardless of the amino acid used, the shorter the chain is, the lower the FC will be, implying that less foam will be produced. By extending the length of the chain, the lipophilic character of the molecule is increased and the tension at the water/air interface is lowered at the same time. The N α -lauroylarginine sodium salt-based mixtures and the N α -decanoylarginine sodium salt-based mixtures have a good foaming capacity. Indeed, the anionic and amphoteric surfactants are known for their good foaming capacity [START_REF] Benoit | Hair and/or body hygienic powder comprising surfactants[END_REF]. The foam volume value obtained for these mixtures is comparable to the value obtained with commercial SDS. This is proof that these are good foaming agents.

Moreover, some N α -acylamino acids are sold as cosmetic ingredients for shower gels and cleansers (17). The stirring with N α -acylglutamate sodium salts have less good foaming capacity for the same reasons that previously (presence of sodium glutamate in the mixture).

A second major parameter when studying foaming properties concerns their stability (Figure 5). Foams are thermodynamically unstable systems. Their stability and their fracture depend on a series of complex phenomena that begin with the hydrodynamic drainage of the liquid, the dilution of the aqueous film and the coalescence of bubbles [START_REF] Franses | Adsorption and surface tension behavior of gemini surfactants at air-water, oil-water, and solid-water interfaces. In Gemini surfactants. Synthesis, interfacial and solution phase behavior and applications[END_REF]. An arginine hydrophilic head combined with a C10 or C12 hydrophobic chain confer good stability on N α -acylarginine due to the amphoteric nature of their polar head. Indeed, the amphoteric surfactants improve the foaming capacity, as well as the foaming stability [START_REF] Basheva | Role of Betaine as Foam Booster in the Presence of Silicone Oil Drops[END_REF].

  were studied: Takehara et al. (9-11) and George et al. (2) were interested in the surface-active properties of few N α -acylamino acid salts.

  of the initial product (g) m dry : masse of the dry product after a stay in an incubator at 105°C (g) After the determination of the dry matter rate, the crucibles are placed in an oven at 550°C for 3 hours. The percentage of mineral is figured by the following relation:

  foam volume was recorded at 5, 30, 60, 120 and 300 min after stirring. Foaming stability (FS) was calculated using the following formula:

  C (zgig) signals, completed with 2D studies (COSY, HSQC, HMBC) led to the attribution of the HNMR signals. To allow quantitative HNMR determination, all NMR measurements have been carried out with a delay time D1 = 60 sec. This delay time permits the full relaxation of all the nuclei concerned by the assay.

R

  AA and R FA are gathered in Table

Figure 1 :

 1 Figure 1: Two competitive reactions: acylation and hydrolysis of acid chloride

Figure 2 :Figure 3 : 1 H 1 || 3 Figure 4 :Figure 5 :Table 2 :

 23113452 Figure 2 : N α -acylamino acid and alcanoate sodium salts

Table 3 : Foaming capacity (%) of N α -acylamino acid-based formulations and references

 3