Franziska Schmidt

Ifsttar Bridges

Bernard Jacob Ifsttar

Claude Servant

Yves Marchadour

EXPERIMENTATION OF A BRIDGE WIM SYSTEM IN FRANCE AND POTENTIAL APPLICATIONS FOR BRIDGE MONITORING AND OVERLOAD DETECTION

Keywords: B-WIM, reinforced concrete bridges, metal bridges, orthotropic deck, trucks Pesage par pont instrumenté, pont béton armé, pont métallique, dalle orthotrope, poids lourds

B-WIM is experimented in France for 15 years now, and several publications have been written about this. But generally no real attention is given to the element »bridge«, that is what we try to do here. Indeed, this paper gives some elements about the issues and the structures to be chosen to carry out B-WIM tests. It also highlights the importance of the position of the sensors and the whole instrumentation system to obtain accurate results. To do this, it summarizes several B-WIM tests carried out in France by IFSTTAR (former LCPC) on reinforced concrete bridges and metal bridges. The issue of their structural behavior is addressed. Then, bridge builders and managers explain their interests in B-WIM, by reviewing the type of usual bridges in France and their health. A way to maintain their level of service needs to be found.

Introduction

In France, engineers do have a quite good knowledge of the structural health of the bridges: Indeed, since 1195, the procedure called "IQOA", which is the short form of "Image Qualité des Ouvrages d'Art" (this means "image of the quality of the structures") is mandatory in order to assess the health of the structures of the national road system owned by the French government [F. Thierry2010]. Each year, this procedure is applied to one third of all bridges, so theoretically all bridges should be inspected in 3 years, and each two years a general report on the structural health of state-owned bridges is published. For example, in 2010 the number of inspected bridges was 11930, with a total deck surface of 55657494 m 2 . Between one quarter and one third of the total surface (1477 structures) is located in the Parisian region. Most of these bridges are reinforced concrete bridges (5771 out of a total of 11930, with a surface of 1549629m 2 ). The second most represented sort of bridges is the prestressed bridges: their number is about 2218, with a surface equal to 2634104m 2 . This is quite ordinary, since the prestressed technology is generally reserved to long span bridges, which are quite rare. We did not realize B-WIM tests on prestresssed concrete bridges because their spans are long with not so short influence lines, which means that multiple presence events would be difficult, or even impossible, to manage. But we did realize several experimentations on reinforced concrete bridges, especially rigid frame bridge (frames and bents). In France, there are 2550 frame bridges (440000m 2 ) and 1754 bents (604000m 2 ), which explains why they are of special interest for us. The quality of the inspected bridges is classified in 5 classes: the bridges in class 1 are bridges in good visible health, needing only routine maintenance. Class 2 corresponds to bridges in good visible structural health but with equipments or protection elements with defaults or bridges with small defaults needing a specialized treatment without urgency. Class 2E corresponds to the same kind of bridges as class 2, but needing an urgent treatment. Class 3 corresponds to bridges with structural defaults and needing non-urgent repairing. Class 3 U is the worst class and regroups bridges whose structure presents important defaults and which need urgent repair works. IN 2010, most bridges were listed in class 2, see Table 1. Generally, the defaults do not concern the equipments, but are localized on the bearings or the structure. This assessment demonstrates the need for preserving these structures, by monitoring the loads applied to them and their behavior. Of course, in this paper, we are interested in the loads due to traffic. For 15 years now, IFSTTAR (former LCPC) experiments bridge Weigh-in-motion on different kinds of bridges, by buying and using a SiWIM system of the Slovenian company CESTELS. This paper has the purpose to make a short summary of these experiments and to give voice to other participants of the civil engineering domain: Claude Servant, technical director or the construction company Eiffage who contributed to the building of the viaduct de Millau, and Yves Marchadour who has been for several years the responsible for traffic and their impact on bridges at the French Ministry for Transportation.

So we begin first by a technical summary of these experiments, then we share the points of vue of bridge builders and transportation managers.

Different kind of bridges and installations

This second chapter summarizes the main experimentations of B-WIM carried out in France by the IFSTTAR, for more information see [Mohamed Bouteldja2003]. These can be divided in two sorts depending on the sort of bridge: reinforced concrete bridges and metal bridges.

Concrete bridges

Frame bridges

The institute investigated B-WIM on several frame bridges, where the most known ones are the experiments on the national roads RN19 and RN4.

The RN19 (which should now be called RD19, since several parts of this road have been given up by the state and given to the departments) goes from Paris to the Swiss border and is 170km long. The heavy traffic is about 1500 trucks/day. The studied structure is near the city Nogent-sur-Seine (kilometer 102) and carries 2 lanes, one in each direction. It is a standard frame bridge, with a span of 10 m (the width is about 11m), see Figure 1 with a photograph of this bridge and the position of the sensors. The thickness of the deck is 60 cm, which is ideal for measuring correctly the deformations. The events of multiple presences had to be removed manually, and then the results are quite acceptable, see Table 2. We observe a better result in lane 1 than in lane 2. This could be explained by bump being on the surface of the pavement of lane 2.

)
The position of the sensors is explained by the diagram of moment of this king of structure, see Figure2. Indeed, the maximum of deformation will be observed at mid-span. There is a need to avoid a node and the best results would be obtained near an antinode, see [Ieng2011]. Some other frame bridges have been tested for the use of B-WIm, especillay one bridge on the national road RN4, near Rozay en Brie. Here again, the accuracy of the system has been C(15), which is not sufficient for automatic detection. In this case n the reason for these quite poor results is the design of the bridge: it is skewed. This highlights one again the importance of the position of the sensors, related to the structure and its behavior.

Bent bridges

Bents in reinforced concrete are very frequent bridges on French roads. A simple bent is composed of a bridge sleeper fixed on the abutments, which lie on a spread footing or deep foundations. So, contrary to frames, bents are hyperstatic structures, with various degrees from 1 to 3, depending on the way the structure is linked to the foundation and the soil.

We experimented B-WIM on a bent bridge on the highway A9, near Montpellier, see Figure 3. It is a bent with hinges at the bearings. The behavior is then very similar to that of frame bridges, like represented in Figure 2. The rotation at the bearings is more important. This bridge and its dynamic behavior has been studied extensively by UCD. We just studied the accuracy of B-WIM on this bridge. The results are given in Table 3, the class obtained is D+(20). Here the reasons for these poor reasons could be more simple: indeed, there is suspicion that are have been bad links done between B-WIM signals and the corresponding static weight. To finish this paragraph on reinforced concrete bridges (frame and bent), there is a need to underline the fact that this type of bridge is really convenient for B-WIM: indeed, there is a great number of these structures on French roads, their behavior is esay to understand, it is generally easy to access to the underside of the deck, multiple presences are infrequent. But, for a bridge and structure engineer, these structures are not the most interesting ones, that is why we experimented B-WIM on some long-span metal bridges.

Steel bridges

The first metal bridge to be instrumented with the SiWIM system was the Autreville bridge on the highway A31. It is a metal bridge with an orthotropic deck, see Figure 4. In this case, we had some problems to install the sensors: indeed, the system generally distributed by CESTELS uses sensors adapted to concrete bridges, but not metal bridges. A new way to fix the sensors on the underside of the metallic deck had to be found, with the help of CESTELS. But this experimentation made it possible for us to recognize the suitability of these bridges for B-WIM. Indeed, these bridges have short influence lines, because of the transverse stiffeners (all 7-8 meters), which means that multiple presences are no real issue. Moreover, the particular transverse design of these bridges makes it possible to detect the lateral position of the wheels. But one »drawback« would be that these structures need a more sophisticated algorithm to weigh correctly through B-WIM, see [Jacob2012] or [Zhou2012]. So, several B-Wim tests were carried out on the viaduct of Millau, see Figures 5, in The decks is a caisson, and each wall of this caisson is orthotropic. Two types of steel have been used for this deck: S355 for the slab of the lateral caissons and S460 for the caissons linking the piers, the decks and the pylons and the slab of the central caissons. The general design of the caissons and the dimensions are given in Figure 6. Some results of these tests are given in Table 4, or [Romboni2011]. Two reasons for these poor results can be found: the first one is that there are numerous tanks driving on this bridge and these vehicles are well kown to be badly eighted by B-Wim (beacuse of the mouvement of the fluids). The second reason is that this king of structures needs adapted algorithms to treat the signals [Jacob2012], algorithms which are different from those incorporated in the SiWIM system. This first (long) part is aimed to highlight the importance of the structure in the B-WIM system. In the next part, we explain why, as a contributor in the management of instractrure in France, we are interested in B-WIM.

Point of vue of an infrastructure manager

The French infrastructure network is ageing: indeed, numerous structures were built quickly after the destructions of World War 2. These are not of critic age. Indeed, the structures built after 1995 are in good shape: if we use again the classification explained in the introduction, quite no structure is in class 3U. Most of them are in class 2.

For each period of construction, the general health is known, see Table 5. <1850 1850-1900 1901-1950 1951-1975 1976- With decreasing public funding, these structures need to be maintained, and so the ereparation prioritised. To do that correctly, realistic information about the sollictations (traffic in this case) and the behavior of the structure is needed. B-WIM is able to provide all this as it calculates the weights and dimensions of the trucks passing over the system and it records the strains in the structure. Thus, we have access to the real sollicitations and the real strains, which makes it possible with reliability and probabilistic methods to calculate probabilities of failure and prioritize the intervention of the public person (reparation, law on the weight and dimensions of the trucks, specific regulations on some structures or some roads...).

Table 5: Classification of the structures according to their period of construction

Class

Conclusion

In this short summary paper, we wanted to recall the experiments of B-WIM done in France and their physical and structural explanations. We wanted also to introduce the works done on these structures newly used in B-WIM which are the structures non constant transversely like the orthotropic decks. These works are presented in two other communications oat these conferences [Jacob2012] and [Zhou2012].

Figure 1 :

 1 Figure 1: Frame bridge near Nogent sur Seine, and instrumentation used for the B-WIM.

Figure 2 :

 2 Figure 2: Diagram of moents for a frame type bridge. The bearings are fixed.

Figure 3 :

 3 Figure 3: Bent bridge used for B-WIM experiments near Montpellier. (a) Photograph of the bridge, (b) Sketch of the structure.

Figure 4 :

 4 Figure 4: Sketch of the deck of the Autreville bridge.

  2009 and 2010. The viaduct is a bridge with guying, which is 2460 meters long. It goes over the valley of the Tarn, with height of 270m over the level of the river. Its decks is 32 meters large, and carries a highway of twice two lanes (so two lanes in each direction) and an espace lane in each direction. There are 7 piers, whose heights are between 77m and 245m and which are extended by pylons with a height of 87m and 11 pairs of stays. of the viaduct of Millau, with its 7 piers and pylon. The pier number 2, is the highest in the world with 245m. (b) Picture of the inside of the caisson with two extensometers used in the case of B-WIM adapted to metal bridges.

Figure 6 :

 6 Figure 6: General design of the deck of the viaduct of Millau.

Table 1 : Assessed health of French bridges (see [F. Thierry2010])

 1

	Class	1	2	2E	3	3U	Non assessed
	Percentage	11%	47.4%	22.5%	5%	1.1%	13%

Table 2 : B-WIM results on the frame type bridge of Nogent sur Seine, the classes are calculated following [(chairman)1998].

 2

		GVW	B(10)
	Lane 1	Axle groups Single axles	B+(7) B(10)	B(10)
		Axles in groups	B+(7)
		GVW	C(15)
	Lane 2	Axle groups Single axles	B(10) B(10)	C(15)
		Axles in groups	B(10

Table 3 : B-WIM results on the bent type bridge on the highway A9, near Montpellier

 3

		Number	Mean	Standard deviation	Class	General class
	GVW	94	94	2.61	C(15)
	Axle groups	91	3.77	9.59	D+(20)
	Single axles	188	1.21	6.74	B(10)	D+(20)
	Axles of groups	273	4.06	12.26	D+(20)

Table 4 : Some results obtained while testing B-WIM on the viaduct de Millau.

 4

		Mean	Standard deviation	Class
	GVW	-2.36	6.67
				D(25)
	Single axles	1.14	7.91


Béatrice Dendelé

Xavier Tekpli B,#

Kévin Hardonniere

Jørn A Holme

Laure Debure

Daniel Catheline

Volker M Arlt

Eszter Nagy

David H Phillips E

Steinar Øvrebø

Steen Mollerup

Mallory Poet

Martine Chevanne

Vincent Rioux

Marie-Thérèse Dimanche- Boitrel

Odile Sergent

Dr Dominique Lagadic-Gossmann
email: dominique.lagadic@univ-rennes1.fr

Protective action of n-3 fatty acids on benzo[a]pyrene-induced apoptosis through the plasma membrane remodeling-dependent NHE1 pathway

Keywords: docosahexaenoic acid, DPA, docosapentaenoic acid, EPA, eicosapentaenoic acid, ER, endoplasmic reticulum, HPLC, high-performance liquid chromatography, MUFA, monounsaturated fatty acid, PUFA, polyunsaturated fatty acid, PAH, polycylic aromatic hydrocarbon, SFA, saturated fatty acid lipid rafts, apoptosis, benzo[a]pyrene, eicosapentaenoic acid, docosahexaenoic acid, Na + /H + exchanger 1

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

Protective action of n-3 fatty acids on benzo[a]pyrene-induced apoptosis through the plasma membrane remodeling-dependent NHE1 pathway

INTRODUCTION

Environmental variables influence the incidence and progression of disease. Dietary fat is an environmental variable that has been associated experimentally and epidemiologically with diverse physiopathological states (e.g. inflammation, diabetes, cardiovascular disease, and cancer). However, the impact of fat on the incidence of disease appears to depend on the type of fatty acids present in diet. With regard to tumorigenesis, in vivo studies in rodents have indicated that omega-3 (n-3) fatty acid-enriched diets would protect against chemical-induced carcinogenesis whereas omega-6-enriched diets would favor it [START_REF] Actis | N-3, n-6 and n-9 dietary fatty acids modulate the growth parameters of murine salivary gland tumors induced by dimethylbenzanthracene[END_REF][START_REF] Reddy | Effect of diets high in omega-3 and omega-6 fatty acids on initiation and postinitiation stages of colon carcinogenesis[END_REF][3].

Several health benefits of dietary consumption of n-3 polyunsaturated fatty acids (PUFAs)

have been described, among them, a decrease in the risk of cardiovascular diseases [START_REF] Lemaitre | n-3 Polyunsaturated fatty acids, fatal ischemic heart disease, and nonfatal myocardial infarction in older adults: the Cardiovascular Health Study[END_REF][START_REF] Hirafuji | Cardiovascular protective effects of n-3 polyunsaturated fatty acids with special emphasis on docosahexaenoic acid[END_REF],

reduction of the risk of developing colorectal cancer [START_REF] Hendrickse | Dietary omega-3 fats reduce proliferation and tumor yields at colorectal anastomosis in rats[END_REF], inhibition of the growth of tumor cells [START_REF] Colquhoun | Eicosapentaenoic acid and docosahexaenoic acid effects on tumour mitochondrial metabolism, acyl CoA metabolism and cell proliferation[END_REF][START_REF] Kato | Docosahexaenoic acid (DHA), a primary tumor suppressive omega-3 fatty acid, inhibits growth of colorectal cancer independent p53 mutational status[END_REF][START_REF] Narayanan | A combination of docosahexaenoic acid and celecoxib prevents prostate cancer cell growth in vitro and is associated with modulation of nuclear factor-kappaB, and steroid hormone receptors[END_REF], and enhancement of healthy cell survival [START_REF] Kishida | Docosahexaenoic acid enrichment can reduce L929 cell necrosis induced by tumor necrosis factor[END_REF]. n-3 PUFAs are not synthesized de novo by human cells. The most effective way to increase the n-3 PUFA content in plasma or tissues is via dietary supplementation [START_REF] Arterburn | Distribution, interconversion, and dose response of n-3 fatty acids in humans[END_REF]. Usual dietary intake comes mainly from oily fish (salmon, mackerel, sardine, tuna), but also from some vegetable oils and seaweeds. However these products, especially fish and seafood, may also be contaminated with toxic compounds.

Indeed, most fishes are at least to some degree contaminated with diverse environmental chemicals, such as persistent organic pollutants including dioxins or polycyclic aromatic hydrocarbons (PAHs) [START_REF] Visciano | Polycyclic aromatic hydrocarbons in fresh and cold-smoked Atlantic salmon fillets[END_REF][START_REF] Domingo | Omega-3 fatty acids and the benefits of fish consumption: is all that glitters gold?[END_REF][START_REF] Domingo | Levels of PCDD/PCDFs and PCBs in edible marine species and human intake: a literature review[END_REF]. Nonetheless, several studies have indicated that the risk of exposure to chemical contaminants via these products could be partially offset by the fatty acid-associated health benefits [START_REF] Mozaffarian | Fish intake, contaminants, and human health: evaluating the risks and the benefits[END_REF][START_REF] Foran | Quantitative analysis of the benefits and risks of consuming farmed and wild salmon[END_REF]. In fact, in vivo experiments in rodents showed that n-3 PUFA supplementation could prevent the adverse effects of PAHs [START_REF] Silva | Effects of dietary n-3, n-6 and n-9 polyunsaturated fatty acids on benzo(a)pyrene-induced forestomach tumorigenesis in C57BL6J mice[END_REF][START_REF] Manna | Fish oil regulates cell proliferation, protect DNA damages and decrease HER-2/neu and c-Myc protein expression in rat mammary carcinogenesis[END_REF]. However, the underlying mechanisms for such protective actions remain to be determined.

The n-3 PUFAs have been suggested to inhibit in vivo the genotoxic effects of benzo[a]pyrene (B[a]P) in mice or 7,12-dimethylbenz[a]anthracene in rat [3,[START_REF] Manna | Dietary fish oil associated with increased apoptosis and modulated expression of Bax and Bcl-2 during 7,12-dimethylbenz(alpha)anthracene-induced mammary carcinogenesis in rats[END_REF]. The n-3 PUFAs, docosahexaenoic acid (DHA) and eicosapentaenoic acid (EPA), are known to be rapidly incorporated into plasma membrane and to increase membrane fluidity as well as to decrease the cholesterol content of lipid raft microdomains [START_REF] Shaikh | Biophysical and biochemical mechanisms by which dietary N-3 polyunsaturated fatty acids from fish oil disrupt membrane lipid rafts[END_REF]. Such an impact on membrane properties is important to consider since we have recently found that B[a]P-induced plasma membrane remodeling, more particularly changes in lipid raft biochemical characteristics, plays a key role in apoptosis via the regulation of intracellular pH. Additionally, several other compounds might also partly exert their toxic effects through plasma membrane dysfunction [START_REF] Tekpli | Importance of plasma membrane dynamics in chemical-induced carcinogenesis, Recent Pat[END_REF][START_REF] Tekpli | Membrane remodeling, an early event in benzo[a]pyrene-induced apoptosis[END_REF].

We thus hypothesized that addition of n-3 fatty acids might interfere with B[a]P-induced toxicity. More specifically we examined if DHA and EPA could modulate B[a]P-induced apoptosis by affecting the levels of DNA damage or the plasma membrane microstructure in rat liver epithelial F258 cells. This cell model was chosen since we previously showed the existence of two pathways involved in B[a]P-induced apoptosis: a p53-dependent pathway triggered by DNA damage and most interestingly, a pH-dependent apoptotic pathway related to the activation of the Na + /H + exchanger 1 (NHE-1) by membrane remodeling [START_REF] Tekpli | Importance of plasma membrane dynamics in chemical-induced carcinogenesis, Recent Pat[END_REF][START_REF] Tekpli | Membrane remodeling, an early event in benzo[a]pyrene-induced apoptosis[END_REF]. The present study shows that DHA and EPA protect F258 cells against B[a]P-induced apoptosis, most likely by inhibiting the B[a]P effects at the plasma membrane level, and hence the NHE-1-dependent pathway.

MATERIAL AND METHODS

2.1.Chemicals

B[a]P, DEVD-AMC (Asp-Glu-Asp-7-amino-4-methylcoumarin), DHA and EPA were purchased from Sigma Chemical Co (St Louis, MO, USA). Hoechst 33342 was purchased from Invitrogen (Invitrogen, France). DPA (docosapentaenoic acid) was purchased from Cayman Chemical (Ann Harbor, USA). Rabbit polyclonal anti-p53 phospho Serine 15, mouse monoclonal anti--actin, anti-CD71, and anti-CYP1A1 antibodies were from Santa Cruz Biotechnology (Tebu-bio SA, Le Perray en Yvelynes, France). Mouse monoclonal anti-NHE1 and anti-flotillin were purchased from Becton Dickinson (BD Biosciences, San Jose, CA).

Rabbit polyclonal antibody against CYP1B1 was from Alpha Diagnostics (San Antonio, USA).

Cell culture and apoptosis measurement

The F258 rat liver epithelial cell line originated from the liver of 10 day-old Fisher rats and was kindly provided by Pr. Olivier Fardel [βγ]. Cells were cultured in Williams'E medium supplemented with 10% fetal calf serum, 2 mM L-glutamine, 5 IU/mL penicillin, and 0.5 mg/mL streptomycin, at 37°C under a 5% CO 2 atmosphere, and treated 24 h following seeding as previously described [START_REF] Tekpli | Membrane remodeling, an early event in benzo[a]pyrene-induced apoptosis[END_REF][START_REF] Payen | Unaltered expression of multidrug resistance transporters in polycyclic aromatic hydrocarbon-resistant rat liver cells[END_REF][START_REF] Huc | Identification of Na+/H+ exchange as a new target for toxic polycyclic aromatic hydrocarbons[END_REF]. Cells were pre-treated with DHA (140 µM), EPA (200 µM), DHA:EPA (70:100 µM), or DPA (50 and 80 µM) for one hour, after which B[a]P (50 nM) was added and incubation continued for a further 24, 48 or 72 h. The DHA concentration used was lower than with EPA due to cytotoxicity. These concentrations were chosen in order to be as close as possible to those detected in plasma after dietary supplementation (0.5-0.7 mM) [START_REF] Wander | Oxidation of plasma proteins is not increased after supplementation with eicosapentaenoic and docosahexaenoic acids[END_REF]. All PUFAs were prepared in methanol and final concentration of this vehicle in culture medium did not exceed 0.12% (v/v); for all treatments without PUFAs, the same concentration of vehicle as for PUFAs-treated cells was included.

B[a]P stock solutions were prepared in dimethyl sulfoxide; final concentration of this vehicle in culture medium was <0.05% (v/v), and control cultures received the same concentration of vehicle as B[a]P-treated cultures. Microscopic detection of apoptosis was performed in both floating and adherent cells, using Hoechst 33342 labeling, as previously described [START_REF] Huc | Identification of Na+/H+ exchange as a new target for toxic polycyclic aromatic hydrocarbons[END_REF]. The caspase activity assay using the fluorescent substrate DEVD-AMC was performed as previously described [START_REF] Tekpli | Membrane remodeling, an early event in benzo[a]pyrene-induced apoptosis[END_REF].

Quantitative real-time reverse transcription-polymerase chain reaction (RT-PCR)

Total RNA was extracted from frozen cultured cells by the Izol-RNA Lysis Reagent (5 PRIME) and reverse transcribed using qScript cDNA Synthesis kit (Quanta Biosciences).

Quantitative analysis of the specific expression of various genes was performed by real-time PCR on an ABI PRISM 7900HT (Applied Biosystems, Foster City, CA, USA), as previously described [START_REF] Tekpli | DNA methylation of the CYP1A1 enhancer is associated with smoking-induced genetic alterations in human lung[END_REF]. After isolation, RNA concentration was measured and only the RNA with ratio of absorbance 260/280 > 1.8 were used for experiments. To assess the successful amplification of the target genes, a standard curve was made for each primer sets. In addition,

for each primer set a dissociation curve was analyzed in order to ensure that there were no contaminating products in the reaction; the product of PCR reaction was also analyzed in a 2% agarose gel. The expression levels of target genes were normalized relative to the expression of the -actin gene.

Western blotting

After treatment, cells were harvested, centrifuged, washed with PBS and lysed for 10 min on ice in Cytobuster lysis buffer (Invitrogen, Paisley, UK). The lysis buffer was complemented with protease inhibitor (cOmplete, Mini; Protease Inhibitor Cocktail, Roche Applied Science).

DNA and cell debris were removed by centrifugation. Western blot analysis was performed not only in whole cell lysates but also in the detergent resistant membrane (DRM; raft) and soluble (S; non-raft) fractions (see below for raft isolation), as previously described [START_REF] Tekpli | Membrane remodeling, an early event in benzo[a]pyrene-induced apoptosis[END_REF][START_REF] Joannard | Role for mitogen-activated protein kinases in phenobarbital-induced expression of cytochrome P450 2B in primary cultures of rat hepatocytes[END_REF].

In short, 40 µg of whole cell lysate were separated on 12% SDS-polyacrylamide gel electrophoresis. Immunoblots were then probed with rabbit polyclonal anti-p53 (100 ng/mL), -phospho Ser15-p53 (200 ng/mL), or mouse monoclonal anti-CYP1A1 (100 ng/mL), -CYP1B1 (100 ng/mL) or -actin (25 ng/mL) antibodies. Regarding raft and soluble fractions, 5 μg and 100 μg respectively were separated on 10% SDS-polyacrylamide gel electrophoresis. Immunoblots were then probed with mouse monoclonal anti-NHE1 (100 ng/mL), mouse monoclonal anti-flotillin (50 ng/mL) or -CD71 antibodies (200 ng/mL).

Regarding raft and soluble fractions, 5 µg and 100 µg respectively were separated on 10% SDS-polyacrylamide gel electrophoresis. Immunoblots were then probed with mouse monoclonal anti-NHE1, mouse monoclonal anti-flotillin or -CD71 antibodies. Examples of full gel western blots images can be seen in Supplementary Figure 8.

Immunofluorescence assay for detecting GM1

Cells were fixed 30 min at 4°C with 4% paraformaldehyde in PBS; after washing, cells were incubated for 1 h with a blocking solution (2% BSA in PBS) and subsequently, with FITCcoupled cholera toxin B (Vybrant® FITC Lipid Raft Labeling Kit; Invitrogen) (0.5 µg/mL) for 1 h. DAPI was used to stain nuclei. Fluorescent-labelled cells were captured with a DMRXA Leica microscope and a COHU high performance CCD camera using Metavue software. Data are representative of at least three independent experiments.

DNA adduct analysis by 32 P-postlabeling

DNA adducts were measured in each DNA sample (4 μg) using the nuclease P1 enrichment version of the 32 P-postlabeling method as described previously [START_REF] Arlt | Metabolic activation of benzo[a]pyrene in vitro by hepatic cytochrome P450 contrasts with detoxification in vivo: experiments with hepatic cytochrome P450 reductase null mice[END_REF][START_REF] Phillips | The 32P-postlabeling assay for DNA adducts[END_REF]. Chromatographic conditions for thin-layer chromatography (TLC) on polyethyleneimine-cellulose (Macherey-Nagel, Düren, Germany) were: D1, 1.0 M sodium phosphate, pH 6.0; D3, 4 M lithium formate and 7 M urea, pH 3.5 and D4, 0.8 M lithium chloride, 0.5 M Tris and 8.5 M urea, pH 8.0. After chromatography, TLC sheets were scanned using a Packard Instant Imager (Dowers Grove, IL), and DNA adduct levels (relative adduct labeling [RAL]) were calculated from adduct c.p.m., the specific activity of [ -32 P]ATP and the amount of DNA (pmol of DNA-P) used.

Comet assay

DNA strand breaks and alkali-labile lesions were detected by the comet assay, and the lesionspecific repair enzyme formamidopyrimidine DNA-glycosylase (FPG) was employed to characterize oxidative damage to DNA as described previously [START_REF] Landvik | 3-Nitrobenzanthrone and 3-aminobenzanthrone induce DNA damage and cell signalling in Hepa1c1c7 cells[END_REF]. Nuclei were stained with ethidium bromide and DNA damage scored (50 nuclei per sample) using the Comet IV capture system (version 4.11; Perceptive Instruments, UK). The tail intensity (% tail DNA), defined as the percentage of DNA migrated from the head of the comet into the tail, was measured for each nucleus scored. All samples were measured blind. Mean median % tail DNA was compared by t-test analysis.

High-performance liquid chromatography (HPLC) of B[a]P metabolites

For the analysis of B[a]P metabolites, culture medium (2 mL) from exposed cells was collected and stored at -20°C until further processing. The medium was diluted to 10 mL in Institute, Kansas City, MO, USA).

Lipid raft isolation

Fractionation of lipid rafts was adapted from a previously described method [START_REF] Nourissat | Ethanol induces oxidative stress in primary rat hepatocytes through the early involvement of lipid raft clustering[END_REF]. Briefly, F258 cells (2×10 8 ) were washed in ice-cold PBS and scraped in 3 mL of PBS. Pellets were lysed for 30 min at 4°C in 1 mL 2-(N-morpholino)ethanesulfonic acid)-buffered saline (MBS), supplemented with protease inhibitors, containing 1% cold Triton X-100 before homogenization with a tight-fitting dounce homogenizer. Lysates were diluted in 2 mL MBS containing 80% sucrose (w/v) and placed at the bottom of a linear sucrose gradient consisting of 8 mL 5-40% sucrose (w/v) in MBS. Samples were centrifuged at 200,000 g for 20 h at 4°C, and 11 fractions of 1 mL each were collected from the top of the gradient. As previously characterized in F258 cells [START_REF] Tekpli | Membrane remodeling, an early event in benzo[a]pyrene-induced apoptosis[END_REF], fractions 1 to 7 correspond to lipid rafts, and fractions 8 to 11 correspond to the non-raft fractions. Protein amounts were measured on each fraction according to the Lowry method (Biorad, Marnes la Coquette, France). Fatty acid and cholesterol analyses were then carried out on each fraction and the calculated amounts were then summed according to DRM [Detergent Resistant Membranes; 1 to 7] and S [Soluble; 8

to 11] fraction pools.

Fatty acid analysis

After fractionation of lipid rafts, lipids were extracted using Folch method [START_REF] Folch | A simple method for the isolation and purification of total lipides from animal tissues[END_REF]. After saponification, fatty acids were methylated with boron trifluoride (14% in methanol) at 70°C for 15 min. Fatty acid methyl esters were then extracted with pentane and analyzed by gas chromatography using an Agilent gas chromatography Technologies 6890N (Bios Analytique, Toulouse, France). Identification of fatty acid methyl ester peaks was based on retention times obtained for methyl esters prepared from fatty acid standards.

Cholesterol analysis in lipid raft fractions

The cholesterol content in DRM (raft) and S (non raft) fractions of each gradient fraction was spectrophotometrically evaluated by a cholesterol oxidase/peroxidase assay using the Infinity Cholesterol kit (Thermo Electron Corp., Eragny sur Oise, France) after lipid extraction by a 2:1 chloroform/methanol mixture (v/v).

Measurement of pH i

pH i was monitored using the pH-sensitive fluorescent probe carboxy-SNARF-1-AM (carboxy-seminaphtorhodafluor acetoxy methyl ester; InVitrogen), in HEPES-buffered solution, as previously described [START_REF] Huc | Identification of Na+/H+ exchange as a new target for toxic polycyclic aromatic hydrocarbons[END_REF]. The emission ratio 640/590 nm detected from intracellular SNARF was calculated and converted to a linear pH scale using in situ calibration.

Caspase activity measurements

Adherent and floating cells were lysed in the caspase activity buffer (50 mM HEPES pH=7,5, 150 mM NaCl, 1mM EGTA, 0.1% Tween 20, 10% Glycerol, protease inhibitors). 40 µg of crude cell lysate were incubated with 80 µM DEVD-AMC for 2 h at 37 °C. Caspase-mediated cleavage of DEVD-AMC was measured by spectrofluorimetry (Spectramax Gemini, Molecular Devices, Sunnyvale, CA, USA) at the excitation/emission wavelength pair of 380/440 mm. Three independent experiments, performed in triplicate, were carried out for each experimental condition.

Statistical analysis

All data are presented as mean ± standard error along with the number of observations, n, corresponding to independent cultures used. Analysis of variance of means followed by Newman-Keuls test was performed using Statistica software. Differences were considered significant at the level of P<0.05. *, P< 0.05; **, P<0.01; ***, P<0.001.

RESULTS

DHA and EPA inhibit B[a]P-induced apoptosis in F258 cells

In order to study the effects of DHA and EPA on B activity revealed that DHA decreased B[a]P-induced caspase activation by ~60%, while EPA had less marked effects (Fig. 1C and1D). Interestingly, co-treating cells with B[a]P and a mixture of the two n-3 PUFAs (i.e. DHA 70 µM + EPA 100 µM) elicited a higher protective effect compared to single n-3 PUFA pre-treatment at their optimal concentration (Fig. 1E).

Light microscopy observations also showed that both DHA or EPA resulted in some protection of the cells against B[a]P-induced loss of cell viability. Indeed the cell density was higher in B[a]P / n-3 PUFA co-treated cells compared with cells treated with B[a]P alone (Supplementary Fig. 1).

Effects of DHA and EPA on B[a]P metabolism

It has been reported that n-3 PUFAs can interfere with the metabolism of xenobiotics by reducing the activity of different cytochrome P450 (P450) enzymes [START_REF] Yao | The inhibitory effect of polyunsaturated fatty acids on human CYP enzymes[END_REF]. As both DHA and EPA reduced B[a]P-induced apoptosis, we tested the effects of DHA and EPA on the mRNA expression of CYP1A1 and CYP1B1 (as both P450 isoenzymes are involved in B[a]P activation). We found that EPA and DHA significantly increased B[a]P-induced CYP1A1 and CYP1B1 mRNA levels (Fig. 2A and2B), although changes were not that marked. At the protein level, P450 1A1 was undetectable as previously reported [START_REF] Holme | Different mechanisms involved in apoptosis following exposure to benzo[a]pyrene in F258 and Hepa1c1c7 cells[END_REF]; no significant effects were observed when considering P450 1B1 protein expression (Fig. 2C and2D). In order to get further insight into the effects of omega-3 fatty acids on B[a]P metabolism, we analyzed the B[a]P metabolites in the cell culture medium by HPLC. As shown in Supplementary Fig.

Effects of DHA and EPA on the lipid composition of plasma membrane microstructures

As stated above, we have recently found that B[a]P-induced plasma membrane remodeling plays a key role in apoptosis via the regulation of intracellular pH [START_REF] Tekpli | Membrane remodeling, an early event in benzo[a]pyrene-induced apoptosis[END_REF][START_REF] Huc | Identification of Na+/H+ exchange as a new target for toxic polycyclic aromatic hydrocarbons[END_REF][START_REF] Tekpli | NHE-1 relocation outside cholesterol-rich membrane microdomains is associated with its benzo[a]pyrene-related apoptotic function[END_REF]. Based on the fact that DHA and EPA can change membrane microstructure and composition [START_REF] Wassall | Polyunsaturated fatty acid-cholesterol interactions: domain formation in membranes[END_REF], we investigated possible effects of DHA and EPA on plasma membrane.

Gas chromatography was used to measure the percentage of saturated (SFA), monounsaturated (MUFA), and polyunsaturated fatty acids (PUFA) in purified lipid rafts (DRM) and in non-raft (S) fractions. We found that DHA and EPA were well incorporated in both domains, with a higher affinity for the non-raft (S) fraction (Fig. 5). DHA had a better penetration in whole plasma membrane compared to EPA. B[a]P did not affect the incorporation of the two n-3 PUFAs in the plasma membrane (Fig. 5). Interestingly, when categorizing the fatty acid detected by gas chromatography in different classes SFA (saturated fatty acids), MUFA (monounsaturated fatty acids) or PUFA and looking at the effect of DHA and EPA, we found that they modified the fatty acid content of the different sub-membrane fractions (DRM or S). Increased levels of PUFA and SFA were observed in the non-rafts (S) upon DHA or EPA exposure while a decrease was seen in the quantity of MUFA in both raft and non-raft fractions (Fig. 6A-6D). The same results were found in presence of B[a]P (data not shown).

Other effects of DHA and EPA on the plasma membrane content of single fatty acids can be found in Supplementary Fig. 4. After EPA or DHA exposure, the membrane content in oleic acid (C18:1 n-9) decreased concomitantly with an increase in the stearic acid content (C18:0).

A marked increase in docosapentaenoic acid (DPA, C22:5 n-3) in both rafts (DRM) and nonrafts (S) fractions was also observed especially after EPA treatment, but this increase was unrelated with EPA protective effects (Supplementary Fig. 5). Cholesterol is an important determinant of raft formation and it was shown previously that B[a]P significantly decreased the level of cholesterol in lipid rafts via an effect on the 3-hydroxy-3-methylglutaryl-CoA (HMG CoA) reductase expression, thereby leading to a remodeling of rafts [START_REF] Tekpli | Membrane remodeling, an early event in benzo[a]pyrene-induced apoptosis[END_REF]. This result was confirmed in the present study and we found that DHA or EPA treatment also significantly decreased the amount of cholesterol in lipid rafts; however, no further decrease was observed when cells were co-exposed with B[a]P (Fig. 7).

To examine if the changes in cholesterol-membrane content induced by DHA or EPA affected the plasma membrane integrity, we next tested the effects of these two lipids on raft distribution in cells. The GM1 distribution (a specific marker of lipid rafts) was analyzed by fluorescence microscopy using cholera toxin fragment B coupled to a fluoroprobe. As expected from our previous study, B[a]P disturbed the organization of cholesterol-enriched microdomains (rafts) as exemplified by the diffuse homogenous GM1 staining compared to control cells (Fig. 8) [START_REF] Tekpli | Membrane remodeling, an early event in benzo[a]pyrene-induced apoptosis[END_REF]. None of the PUFAs changed the GM1 distribution alone, but they both prevented the effects of B[a]P (Fig. 8).

apoptosis in rat hepatic epithelial F258 cells, mostly by interfering with the effects that B[a]P exerts on H+ homeostasis (Fig. 11A). More specifically EPA and DHA inhibit the NHE1dependent intracellular alkalinization previously shown to be induced in the B[a]P-related apoptosis [START_REF] Huc | Identification of Na+/H+ exchange as a new target for toxic polycyclic aromatic hydrocarbons[END_REF].

We found that DHA and EPA reduce B[a]P-induced apoptosis (50% reduction at optimal concentration). However, DHA appeared to be more effective in inhibiting caspase activation than EPA. Such a differential action was further emphasized by the fact that cotreating cells with B[a]P and a mixture of DHA/EPA nearly completely inhibited apoptosis.

Knowing that B[a]P induced both caspase-dependent and independent apoptotic pathways in F258 cells [START_REF] Tekpli | Membrane remodeling, an early event in benzo[a]pyrene-induced apoptosis[END_REF][START_REF] Huc | Identification of Na+/H+ exchange as a new target for toxic polycyclic aromatic hydrocarbons[END_REF][START_REF] Gorria | Lagadic-Gossmann, A new lactoferrin-and iron-dependent lysosomal death pathway is induced by benzo[a]pyrene in hepatic epithelial cells[END_REF][START_REF] Huc | Multiple apoptotic pathways induced by p53-dependent acidification in benzo[a]pyrene-exposed hepatic F258 cells[END_REF] , our results indicate that the intracellular mechanisms underlying the protective effects of these lipids might, at least partially, differ.

Recent studies have shown that DHA, but not EPA, dramatically alters cardiac mitochondrial fatty acid composition and prevents mitochondrial dysfunction [START_REF] Khairallah | Treatment with docosahexaenoic acid, but not eicosapentaenoic acid, delays Ca2+induced mitochondria permeability transition in normal and hypertrophied myocardium[END_REF][START_REF] Khairallah | Dietary supplementation with docosahexaenoic acid, but not eicosapentaenoic acid, dramatically alters cardiac mitochondrial phospholipid fatty acid composition and prevents permeability transition[END_REF]. Thus, an explanation for the differential effects of DHA and EPA on caspase activation might be that DHA, unlike EPA, may act on mitochondrial dysfunction, an event known to be necessary for caspase activation in our model [START_REF] Huc | Multiple apoptotic pathways induced by p53-dependent acidification in benzo[a]pyrene-exposed hepatic F258 cells[END_REF]. As recently reviewed, other differential effects between DHA and EPA might also contribute to the different action of these PUFAs on caspase activation [START_REF] Gorjao | Comparative effects of DHA and EPA on cell function[END_REF].

The protective action of PUFAs might have involved inhibition of B[a]P metabolism, since we have previously shown it as of importance in our cell model [START_REF] Payen | Unaltered expression of multidrug resistance transporters in polycyclic aromatic hydrocarbon-resistant rat liver cells[END_REF]. Analysis of the rate of B[a]P removal and the total amount of B[a]P metabolites formed suggested some slight modifications of B[a]P metabolism upon DHA but not upon EPA (Figure 11A). There was an increase in the expression of CYP1A1 and CYP1B1, but with apparently no major changes in the levels of P450 enzymes, although a minor increase in P450 enzymes levels cannot be completely ruled out. In contrast, in vitro assays using different human P450s have shown that PUFAs can be metabolized by these enzymes [START_REF] Konkel | Role of cytochrome P450 enzymes in the bioactivation of polyunsaturated fatty acids[END_REF], and thus function as competitive inhibitors [START_REF] Yao | The inhibitory effect of polyunsaturated fatty acids on human CYP enzymes[END_REF]. The overall result may be some minor changes in B[a]P metabolism and in the balance between activation and detoxification of the molecule. HPLC analysis of B[a]P metabolism suggested some slight effect of DHA on the quantity of some of the metabolites produced. Interestingly, an increase in the amount of B[a]P-r-7,t-8,c-9,t-10tetrahydrotetrol, a further metabolite of one of the major DNA reactive B[a]P metabolites, was observed. The DHA-related increase in B[a]P tetrol may have significant effects on the DNA damage induced by B[a]P. In fact, it could be related to the increase in the formation of B[a]P-DNA adducts detected by 32 P-postlabeling with DHA. Nevertheless, the cell response to such an increase in DNA damage as measured by p53 phosphorylation remained unchanged (Figure 11A). Since the protective effects of EPA and DHA towards B[a]Pinduced apoptosis appeared to be independent of p53 activation, which in our cell model is responsible for the genotoxic-related apoptotic pathway [START_REF] Huc | Multiple apoptotic pathways induced by p53-dependent acidification in benzo[a]pyrene-exposed hepatic F258 cells[END_REF], we looked at the membrane remodeling-related apoptotic pathway.

Several studies have shown that supplementation with n-3 PUFAs leads to modifications of the physical properties of biological membranes [START_REF] Yaqoob | The nutritional significance of lipid rafts[END_REF]. Indeed, dietary fatty acids have been found to affect lipid raft composition and organization, with consequences on cell function [START_REF] Kang | Free, long-chain, polyunsaturated fatty acids reduce membrane electrical excitability in neonatal rat cardiac myocytes[END_REF][START_REF] Xiao | Potent block of inactivation-deficient Na+ channels by n-3 polyunsaturated fatty acids[END_REF].

The most represented SFA and MUFA in F258 plasma membrane are stearic acid (C18:0) and oleic acid (C18:1), respectively. We observed that DHA and EPA increased the membrane content of stearic acid while they decreased that of oleic acid. This could be possibly attributed to an inhibitory effect on 9-desaturase (SCD1) expression (Dendelé et al., unpublished data), and lead to an improper ratio (SFA / MUFA) in membranes with consequences on membrane fluidity, protein activities and cell functions [START_REF] Miyazaki | Role of stearoyl-coenzyme A desaturase in lipid metabolism[END_REF].

Here we found that both DHA and EPA depleted cholesterol in raft microdomains, with no further effect of B[a]P. This finding is in accordance with previous studies on DHA and EPA using membrane models, suggesting that the reduction was due to the incompatibility between the highly flexible structure of PUFAs and the rigid moiety of cholesterol [START_REF] Pitman | Molecular-level organization of saturated and polyunsaturated fatty acids in a phosphatidylcholine bilayer containing cholesterol[END_REF]. We previously found that B[a]P reduced the cholesterol content of lipid rafts via the inhibition of the expression of HMG CoA reductase [START_REF] Tekpli | Membrane remodeling, an early event in benzo[a]pyrene-induced apoptosis[END_REF]. EPA and DHA may also regulate this cholesterol synthesis rate limiting enzyme [START_REF] Jossic-Corcos | Hepatic farnesyl diphosphate synthase expression is suppressed by polyunsaturated fatty acids[END_REF].

Despite a significant depletion of cholesterol in lipid rafts, it seemed that EPA and DHA did not affect the cellular repartition of lipid rafts as no changes in GM1 staining were observed following EPA or DHA exposure compared to control conditions. However, coexposure with either n-3 PUFA and B[a]P protected from B[a]P-induced GM1 redistribution.

It can be hypothesized that DHA and EPA might replace cholesterol in rafts and consequently form another type of membrane microdomain, which still contains GM1 but less cholesterol (Figure 11B). Thus, the protein content of these newly formed plasma membrane microdomains may also be different, as shown here by the marked decrease of the NHE1 protein level in detergent resistant membranes. As previously suggested, the presence of DHA or EPA in rafts might actually lead to the formation of PUFA domains within membrane lipid rafts, thereby leading to changes in protein lateral organization [START_REF] Shaikh | Biophysical and biochemical mechanisms by which dietary N-3 polyunsaturated fatty acids from fish oil disrupt membrane lipid rafts[END_REF].

Such an effect of n-3 PUFAs on the proteins present in lipid rafts has already been reported, e.g. for the epidermal growth factor receptor whose level is decreased in lipid rafts upon DHA exposure [START_REF] Rogers | Docosahexaenoic acid alters epidermal growth factor receptorrelated signaling by disrupting its lipid raft association[END_REF][START_REF] Schley | Field, (n-3) PUFA alter raft lipid composition and decrease epidermal growth factor receptor levels in lipid rafts of human breast cancer cells[END_REF]. In this context, knowing that NHE1 activity is mechano-sensitive [START_REF] Tekpli | Regulation of Na+/H+ exchanger 1 allosteric balance by its localization in cholesterol-and caveolin-rich membrane microdomains[END_REF][START_REF] Lacroix | Kinetic analysis of the regulation of the Na+/H+ exchanger NHE-1 by osmotic shocks[END_REF],

one might suppose that a decrease in NHE1 protein levels in cholesterol-rich microdomains after PUFA treatment may interfere with the NHE1-dependent apoptotic pathway induced by B[a]P. Indeed, due to this decrease, B[a]P would then be unable to exert its effect on the NHE1 plasma membrane relocation, and hence on its activation and intracellular alkalinization [START_REF] Tekpli | NHE-1 relocation outside cholesterol-rich membrane microdomains is associated with its benzo[a]pyrene-related apoptotic function[END_REF]. In support of this hypothesis we found that B[a]P-induced, NHE1-related intracellular alkalinization was prevented by both DHA and EPA. Regarding the effects of the n-3 PUFA on NHE1 activity, it is important to note that DHA and EPA alone have been reported previously to inhibit Na + /H + exchange in cardiac cells [START_REF] Goel | Effects of omega-3 polyunsaturated fatty acids on cardiac sarcolemmal Na(+)/H(+) exchange[END_REF], and similar effects were observed when we used NHE1-overexpressing PS120 cells (Supplementary Fig. 6). The

  Dendelé, Xavier Tekpli, Kévin Hardonnière, Jørn A Holme, Laure Debure, Daniel D. Catheline, Volker M Arlt, Eszter Nagy, David H Phillips, Steinar Ovrebø, et al. To cite this version: Béatrice Dendelé, Xavier Tekpli, Kévin Hardonnière, Jørn A Holme, Laure Debure, et al.. Protective action of n-3 fatty acids on benzo[a]pyrene-induced apoptosis through the plasma membrane remodeling-dependent NHE1 pathway. Chemico-Biological Interactions, 2014, 207, pp.41-51. 10.1016/j.cbi.2013.11.002. hal-00950341

H 2 O

 2 , applied to a preconditioned (5 mL methanol and 10 ml water) Sep-Pak C 18 cartridge (Millipore Corporation, Milford, MA, USA), followed by a wash with H 2 O (10 mL), and eluted with 100% methanol (5 mL). The methanol eluate was evaporated to dryness at 45°C under a nitrogen stream and suspended in 100 μL of 100% methanol. HPLC separation of B[a]P metabolites was performed on a Nova-Pak C 18 3.9x150 mm 2 column (Waters, Milford, MA, USA) with a Waters 625 LC System, equipped with a LC 240 fluorescence detector (Perkin-Elmer, Beaconsfield, UK). The B[a]P metabolites were separated by a linear gradient of 30-100% methanol in H 2 O for 40 min. For the quantitative determination of B[a]P metabolites, the following fluorescence conditions were used: 0 min, excitation 380/emission 431; 0.5 min, excitation 341/emission 381; 20 min, excitation 253/emission 410; 27 min, excitation 380/emission 431. The concentrations of B[a]P metabolite standards were determined by ultraviolet absorbance of the compounds dissolved in ethanol and using extinction coefficients from the NIH Chemical Carcinogen Repository (Midwest Research

  [a]P-induced apoptosis, F258 cells were pre-treated for 1 h with DHA (140 µM) or EPA (200 µM), and then co-treated with B[a]P (50 nM) for up to 72 h. Determination of apoptotic cells using Hoechst 33342 staining showed that both DHA and EPA reduced the number of cells exhibiting apoptotic nuclei by 50% (Fig.1A and 1B). No changes were detected in the amount of B[a]P-induced necrotic cells as determined by propidium iodide staining (data not shown). Measurement of caspase 3/7

2 ,

 2 DHA somewhat changed B[a]P metabolism, as a 2-fold increase in the quantities of B[a]Pr-7,t-8,c-9,t-10-tetrahydrotetrol and 9-hydroxyB[a]P was found upon co-exposure with B[a]P and DHA compared to B[a]P alone, which was concomitant with a decrease in B[a]P-trans-9,10-dihydrodiol. In contrast, EPA treatment did not markedly alter the quantities of B[a]P metabolites formed.3.3. Effects of DHA and EPA on B[a]P-induced DNA damagePrevious studies have reported that n-3 PUFA-enriched diets can prevent DNA damage induced by B[a]P or DMBA in vivo[3,[START_REF] Manna | Dietary fish oil associated with increased apoptosis and modulated expression of Bax and Bcl-2 during 7,12-dimethylbenz(alpha)anthracene-induced mammary carcinogenesis in rats[END_REF]. Here, we tested the effects of DHA or EPA on B[a]P-induced DNA damage measured by the comet assay and 32 P-postlabeling.The results of the comet assay showed that DHA and EPA had no effects on B[a]P-induced oxidative or non-oxidative DNA damage after a 24 h (Fig.3A) or a 48 h (data not shown) B[a]P exposure. As a positive control, we found an increase in the quantity of oxidative DNA damage elicited by a 5 µM B[a]P exposure during 48 h (Supplementary Fig.3).32 P-Postlabeling analysis revealed that DHA increased by 54% the levels of B[a]P-DNA adducts (i.e.10-(deoxyguanosine-N 2 -yl)-7,8,9-trihydroxy-7,8,9,10-tetrahydrobenzo[a]pyrene [dG-N 2 -BPDE]) after a 48 h co-exposure with B[a]P, whereas EPA had no effect (Fig.3B). As a change in DNA damage could result in changes in the activation of the p53-related apoptotic pathway, we then decided to look at this pathway. As shown in Fig.4, the phosphorylation and expression of p53 remained unchanged whatever the fatty acid tested. As no change in the activation by B[a]P of the p53-dependent apoptotic pathway could be observed upon DHA or EPA exposure, we next focused on the other apoptotic pathway involved in our cell model, that is the membrane remodeling-related apoptotic pathway triggered by B[a]P[START_REF] Tekpli | Membrane remodeling, an early event in benzo[a]pyrene-induced apoptosis[END_REF].

Fig. 2 .Fig. 4 .Fig. 5 .

 245 Fig. 2.

Fig. 6 .

 6 Fig. 6.

Fig. 7 .

 7 Fig. 7.

Fig. 8 .Fig. 9 .

 89 Fig. 8.

Fig. 10 .

 10 Fig. 10.

Fig. 11 .

 11 Fig. 11.

Acknowledgements

We thank Laurent Counillon (University of Nice-Sophia Antipolis, France) for scientific input, Rita Baera (Oslo, Norway) for skilful technical assistance and Stéphanie Dutertre and the Platform "Microscopy Rennes Imaging Center" of SFR Biosit, University of Rennes 1 (France) for immunofluorescence analysis. This study was financially supported by the Ligue Nationale contre le Cancer (FR) and Cancer Research UK. Béatrice Dendelé was a recipient of a fellowship from Région Bretagne. Xavier Tekpli was a recipient of a fellowship from the Association for Research on Cancer (ARC). Volker M. Arlt, Eszter Nagy and David H. Phillips are members of the European Union Network of Excellence ECNIS 2 (Environmental Cancer Risk, Nutrition and Individual Susceptibility).

Effects of DHA and EPA on the B[a]P-activated NHE1 pathway

The most important effect of B[a]P-induced plasma membrane remodeling in F258 cells is the activation of a pH-dependent apoptotic pathway [START_REF] Tekpli | Membrane remodeling, an early event in benzo[a]pyrene-induced apoptosis[END_REF], which is triggered by a change in NHE1 sub-localization in plasma membrane, thus leading to its activation (with a resulting alkalinization) [START_REF] Tekpli | NHE-1 relocation outside cholesterol-rich membrane microdomains is associated with its benzo[a]pyrene-related apoptotic function[END_REF][START_REF] Tekpli | Regulation of Na+/H+ exchanger 1 allosteric balance by its localization in cholesterol-and caveolin-rich membrane microdomains[END_REF]. Fig. 9 confirms that B[a]P partially induced a relocation of NHE1 from raft (DRM) to non-raft (S) fractions. Regarding the effects of DHA and EPA, we found that both PUFAs used alone led to a strong decrease of NHE1 protein level in raft microdomains, and no additional effects of B[a]P on NHE1 sub-plasma membrane localization were detected, as further stressed when performing western blotting on pooled fractions (Supplementary Fig. 6A). In order to rule out any possible effect of PUFAs on NHE1 expression that might have explained such an effect on protein level, analysis of NHE1 mRNA expression was performed by RT-qPCR and no significant change was detected whatever the condition tested (Supplementary Fig. 6B).

Regarding NHE1 function, we found that both DHA and EPA alone inhibited NHE1 activation following an intracellular acid load in PS120 cells over-expressing NHE1 (Supplementary Fig. 7). We then tested the effects of PUFAs on the B[a]P-induced, NHE1related intracellular alkalinization in F258 cells [START_REF] Huc | Identification of Na+/H+ exchange as a new target for toxic polycyclic aromatic hydrocarbons[END_REF]. As shown in Fig. 10, both PUFAs prevented the B[a]P-induced intracellular alkalinization.

Collectively, these results show that DHA and EPA inhibit NHE1 activation, which interferes with NHE1 activation by B[a]P, thereby protecting cells from apoptosis.

DISCUSSION

In vivo studies have shown that n-3 PUFAs can inhibit PAHs-related carcinogenesis


Irfan Mahmood
email: mahirfan@yahoo.com

Zero curvature representation of non-commutative and quantum Painlevé II equation with its non-vacuum solutions

Keywords: Integrable systems, Painlevé II equation, zero curvature condition, Riccati equation, Darboux transformation. 2000 Mathematics Subject Classification: 22E46, 53C35, 57S20 *

In this paper, I derive a zero curvature representation of quantum Painlevé II equation and its Riccati form which can be reduced to the classical Painlevé II when h → 0. Further I derive non-vacuum solitonic solutions of the noncommutative Painlevé II equation with the help of its Darboux transformation for which the solution of the noncommutative Painlevé Riccati equation has been taken as a seed solution.

Introduction

The Painlevé equations were discovered by Painlevé and his colleagues when they have classified the nonlinear second-order ordinary differential equations with respect to their solutions [START_REF] Painlevé | Sur les equations differentielles du second Ordre et dOrdre superieur, dont lInterable Generale est Uniforme[END_REF].The study of Painlevé equations is important from mathematical point of view because of their frequent appearance in the various areas of physical sciences including plasma physics, fiber optics, quantum gravity and field theory, statistical mechanics, general relativity and nonlinear optics. The classical Painlevé equations are regarded as completely integrable equations and obeyed the Painlevé test [START_REF] Hone | Painlevé test, singularity structure and integrability[END_REF][START_REF] Okamoto | The Painleve property, One century later[END_REF][START_REF] Balandin | On the Painlevé test for non-abelian equations[END_REF]. These equations admit some properties such as linear representations, hierarchies, they possess Darboux transformations(DTs) and Hamiltonian structure. These equations also arise as ordinay differential equations (ODEs) reduction of some integrable systems, i.e, the ODE reduction of the KdV equation is Painlevé II (PII) equation [START_REF] Joshi | The second Painlevé hierarchy and the stationarty KdV hierarchy[END_REF][START_REF] Joshi | Existence and uniqueness of tri-tronque solutions of the second Painlev hierarchy[END_REF].

The noncommutative(NC) and quantum extension of Painlevé equations is quite interesting in order to explore the properties which they possess with respect to usual Painlevé systems on ordinary spaces. NC spaces are characterized by the noncommutativity of the spatial co-ordinates. For example, if x µ are the space co-ordinates then the noncommutativity is defined by [x µ , x ν ] ⋆ = iθ µ where parameter θ µν is anti-symmetric tensor and Lorentz invariant and [x µ , x ν ] ⋆ is commutator under the star product. NC field theories on flat spaces are given by the replacement of ordinary products with the Moyal-products and realized as deformed theories from the commutative ones.

Moyal product for ordinary fields f (x) and g(x) is explicitly defined by

f (x) ⋆ g(x) = exp( i 2 θ µν ∂ ∂ x ′ µ ∂ ∂ x ′′ ν ) f (x ′ )g(x ′′ ) x=x ′ =x ′′ = f (x)g(x) + i 2 θ µν ∂ f ∂ x ′ µ ∂ g ∂ x ′′ ν + O(θ 2 ).
this product obeys associative property f ⋆ (g ⋆ h) = ( f ⋆ g) ⋆ h, if we apply the commutative limit θ µν → 0 then above expression will reduce to ordinary product as f ⋆ g = f .g.

We are familiar with Lax equations as a nice representation of integrable systems. The Lax equation and zero curvature condition both have same form on deformed spaces as they possess on ordinary space. These representations involve two linear operators, these operators may be differential operators or matrices [START_REF] Hamanaka | Towards noncommutative integrable systems[END_REF][START_REF] Paniak | Exact noncommutative KP and KdV multi-solitons[END_REF][START_REF] Kupershmidt | Noncommutative integrable systems, in nonlinear evolution equations and dynamical systems[END_REF][START_REF] Dimakis | Noncommutative Korteweg-de Vries equation[END_REF][START_REF] Legaré | Noncommutative generalized NS and super matrix KdV systems from a noncommutative version of (anti-) selfdual Yang-Mills equations[END_REF][START_REF] Hamanaka | Noncommutative Burgers equation[END_REF]. If A and B are the linear operators then Lax equation is given by A t = [B, A] where [B, A] is commutator under the star product or quantum product, this Lax pair formalism is also helpful to construct the DT, Riccati equation and BT of integrable systems. The compatibility condition of inverse scattering problem

Ψ x = A(x,t)Ψ and Ψ t = B(x,t)Ψ yields A t -B x = [B, A]
which is called the zero curvature representation of integrable systems [13-16. Further we will denote the commutator and anti-commutator by [, ] -and [, ] + respectively. Now the Lax equation and zero curvature condition can be expressed as

A t = [B, A] -and A t -B x = [B, A] -.
The Painlevé equations can be represented by the Noumi-Yamada systems [START_REF] Noumi | Higher order Painlevé equations of type Al[END_REF], these systems are discovered by Noumi and Yamada while studying symmetry of Painlevé equations and these systems also possess the affine Weyl group symmetry of type A 1 l . For example Noumi-Yamada system for Painlevé II equation is given by

   u ′ 0 = u 0 u 2 + u 2 u 0 + α 0 u ′ 1 = -u 1 u 2 -u 2 u 1 + α 1 u ′ 2 = u 1 -u 0 (1.1)
where u ′ i = du i dz and α 0 , α 1 are constant parameters. Above system (1.1) also a unique representation of NC and quantum PII equation, for NC derivation of PII equation [START_REF] Retakh | Noncommutative Toda chain , Hankel quasideterminants and Painlevé II equation[END_REF] the dependent functions u 0 , u 1 , u 2 obey a kind of star product and in case of quantum derivation these functions are subjected to some quantum commutation relations [START_REF] Nagoya | Quantum Painlevé equations: from Continuous to discrete[END_REF].

In this paper I derive an equivalent zero-curvature representation of quantum PII equation with its associated quantum Riccati equation and also I construct non-vacuum solutions of NC PII equation by using its Darboux transformation. The following section of this paper consists a brief introduction to NC and quantum PII equation. In section 3, I present a linear representation of quantum PII equation whose compatibility yields its associated zero-curvature condition. Further I derive quantum PII Riccati equation with the help of its linear system. The section 4 contains the derivation of eigenvector solution for NC PII linear system and NC PII Riccati equation. At the end of this paper I apply some Darboux transformations to construct the non-vacuum solitonic solutions of NC PII equation by taking the solution NC PII Riccati as a seed solution.

u ′′ 2 = 2u 3 2 -2[z, u 2 ] + +C (2.1)
introduced by V. Retakh and V. Roubtsov [START_REF] Retakh | Noncommutative Toda chain , Hankel quasideterminants and Painlevé II equation[END_REF] where

C = 4(β + 1
2 ) is constant. The NC PII equation (2.1) can be obtained by eliminating u 0 and u 1 from (1.1 ). The above NC PII equation (2.1) also can be represented by equivalent inverse scattering problems with special case β = -1 2 [START_REF] Bertola | Fredholm determinants and pole-free solutions to the noncommutative Painleve' II equation[END_REF] and in general with non zero constant C = 0 [START_REF] Irfan | Lax pair representation and Darboux transformation of noncommutative Painlevé's second equation[END_REF]. Let consider the following inverse scattering problem [START_REF] Irfan | Lax pair representation and Darboux transformation of noncommutative Painlevé's second equation[END_REF] for the NC PII equation

Ψ λ = A(z; λ )Ψ Ψ z = B(z; λ )Ψ (2.2)
with Lax matrices

A = (8iλ 2 + iu 2 2 -2iz)σ 3 + u ′ 2 σ 2 + ( 1 4 Cλ -1 -4λ u 2 )σ 1 B = -2iλ σ 3 + u 2 σ 1 (2.3)
where σ 1 , σ 2 and σ 3 are Pauli spin matrices given by

σ 1 = 0 1 1 0 , σ 2 = 0 -i i 0 σ 3 = 1 0 0 -1
here λ is spectral parameter, the compatibility condition of system (2.2) yields NC PII equation (2.1).

Quantum Painlevé II equation

The quantum extension of classical Painlevé equations involves the symmetrical form of Painlevé equations proposed in [START_REF] Nagoya | Quantum Painlevé equations: from Continuous to discrete[END_REF] to noncommuting objects. For the quantum Painlevé II equation let us replace the function u 0 , u 1 , u 2 by f 0 , f 1 , f 2 respectively in system (1.1 ), further parameters α 0 and α 1 belong to the complex number field C. The operators f 0 , f 1 and f 2 obey the following commutation rules

[ f 1 , f 0 ] -= 2h f 2 , [ f 0 , f 2 ] -= [ f 2 , f 1 ] -= h (2.4)
where h is Planck constant, the derivation ∂ z preserves the commutation relations (2.4) [START_REF] Nagoya | Quantum Painlevé equations: from Continuous to discrete[END_REF]. The NC differential system (??) admits the affine Weyl group actions of type A

(1) l and quantum PII equation

f ′′ 2 = 2 f 3 2 -z f 2 + α 1 -α 0 . (2.5)
can be obtained by elimination f 0 and f 1 from system (1.1 ) with the help of commutation relations (2.4) [START_REF] Nagoya | Quantum Painlevé equations: from Continuous to discrete[END_REF]. The above equation (2.5) is called quantum PII equation because after eliminating f 0 and f 2 from same system (1.1 ) we obtain P 34 that involves Planck constant h [START_REF] Nagoya | Quantum Painlevé equations: from Continuous to discrete[END_REF]. In next section I construct a linear systems whose compatibility condition yields quantum PII equation with quantum commutation relation between function f 2 and independent variable z, further we show that under the classical limit when h → 0 this system will reduce to classical PII equation.

Zero curvature representation of quantum PII equation

Proposition 1.1.

The compatibility condition of following linear system

Ψ λ = A(z; λ )Ψ, Ψ z = B(z; λ )Ψ (3.1)
with Lax matrices

A = (8iλ 2 + i f 2 2 -2iz)σ 3 + f ′ 2 σ 2 + ( 1 4 cλ -1 -4λ f 2 )σ 1 + ihσ 2 B = -2iλ σ 3 + f 2 σ 1 + f 2 I (3.2)
yields quantum PII equation, here I is 2 × 2 identity matrix and λ is spectral parameter and c is constant.

Proof:

The compatibility condition of system (3.1) yields zero curvature condition

A z -B λ = [B, A] -. (3.3)
We can easily evaluate the values for A z , B λ and [B, A] -= BA -AB from the linear system (3.2) as follow

A z = (i f ′ 2 f 2 + i f 2 f ′ 2 -2i)σ 3 + f ′′ 2 σ 2 -4λ f ′ 2 σ 1 (3.4) B λ = -2iσ 3 (3.5)
and

[B, A] = i f ′ 2 f 2 + i f 2 f ′ 2 + [ f 2 , z] --ih δ λ -i f ′ 2 f 2 -i f 2 f ′ 2 [z, f 2 ] -+ ih (3.6)
where

δ = -i f ′′ 2 + 2i f 3 2 -2i[z, f 2 ] + + ic + i[ f ′ 2 , f 2 ] -+ 4iλ h and λ = i f ′′ 2 -2i f 3 2 + 2i[z, f 2 ] + -ic + i[ f 2 , f ′ 2 ] --4iλ h.
now after substituting these values from (3.4), (3.5) and (3.6) in equation (3.3) we get

[ f 2 , z] --ih δ λ [z, f 2 ] -+ ih = 0 (3.7)
and the above result (3.7) yields the following expressions

[ f 2 , z] = 1 2 ih f 2 (3.8) and i f ′′ 2 -2i f 3 2 + 2i[z, f 2 ] + -ic + i[ f 2 , f ′ 2 ] --4iλ h = 0 (3.9)
equation (3.8) shows quantum relation between the variables z and f 2 . In equation (3.9) the term i[ f , f

′ 2 ] --2iλ h can be eliminated by using equation f

′ 2 = f 1 -f 0 from (1.1
) and quantum commutation relations (2.4). For this purpose let us replace f 2 by -1 2 λ -1 f 2 in (2.4), then commutation relations become

[ f 0 , f 2 ] -= [ f 2 , f 1 ] -= -2λ h. (3.10)
Now let us take the commutator of the both side of the equation f

′ 2 = f 1 -f 0 with f 2 from right side, we get [ f ′ 2 , f 2 ] -= [ f 1 , f 2 ] --[ f 0 , f 2 ] -
above equation with the commutation relations (3.10) can be written as

[ f ′ 2 , f 2 ] -= -4λ h. ( 3
i f ′′ 2 -2i f 3 2 + 2i[z, f 2 ] + -ic = 0.
Finally, we can say that the compatibility of condition of linear system (3.1) yields the following expressions

f ′′ 2 = 2 f 3 2 -2[z, f 2 ] + + c z f 2 -f 2 z = ih f 2 (3.12)
in above system (3.12) the first equation can be considered as a pure version of quantum Painlevé II equation that is equipped with a quantum commutation relation [z, f 2 ] -= -ih and this equation can be reduced to the classical PII equation under the classical limit when h → 0.

Remark 1.1.

The linear system (3.1) with eigenvector Ψ = ψ 1 ψ 2 and setting ∆ = ψ 1 ψ -1 2 can be reduced to the following quantum PII Riccati form

∆ ′ = -4i∆ + f 2 + [ f 2 , ∆ ] --∆ f 2 ∆
Proof:

Here we apply the method of Konno and Wadati [START_REF] Konno | Simple Derivation of Bäcklund transformation from Riccati Form of inverse method[END_REF] to the linear system (3.12) of quantum PII equation. For this purpose let us substitute the eigenvector Ψ = ψ 1 ψ 2 in linear systems (3.1) and we get

     dψ 1 dλ = (8iλ 2 + i f 2 2 -2iz)ψ 1 + (-i f ′ 2 + 1 4 C 0 λ -1 -4λ f 2 + h)ψ 2 dψ 2 dλ = (i f ′ 2 + 1 4 C 0 λ -1 -4λ f 2 -h)ψ 1 + (-8iλ 2 -i f 2 2 + 2iz)ψ 2 (3.13)
and

ψ ′ 1 = (-2iλ + f 2 )ψ 1 + f 2 ψ 2 ψ ′ 2 = f 2 ψ 1 + (2iλ + f 2 )ψ 2 (3.14)
where ψ ′ 1 = dψ 1 dz and now from system (3.14) we can derive the following expressions

ψ ′ 1 ψ -1 2 = (-2iλ + f 2 )ψ 1 ψ -1 2 + f 2 (3.15) ψ ′ 2 ψ -1 2 = -2iλ + f 2 + f 2 ψ 1 ψ - 1 2 (3.16)
. Let consider the following substitution

∆ = ψ 1 ψ -1 2 (3.17)
now taking the derivation of above equation with respect to z

∆ ′ = ψ ′ 1 ψ -1 2 -ψ 1 ψ -1 2 ψ ′ 2 ψ -1
2 after using the ( 3.15), (3.16) and (3.17) in above equation we obtain

∆ ′ = -4i∆ + f 2 + [ f 2 , ∆ ] --∆ f 2 ∆ (3.18)
the above expression (3.18) can be considered as quantum Riccati equation in ∆ because it involves commutation [ f 2 , ∆ ] -= f 2 ∆ -∆ f 2 that has been derived from the linear system (3.14).

NC PII Riccati equation and Solution to the eigenvector of NC PII system

Proposition 1.2.

The linear system (2.2) with eigenvector Ψ = χ Φ and setting Γ = χΦ -1 can be reduced to the following NC PII Riccati form

Γ ′ = -4iλ Γ + u -ΓuΓ Proof:
For this purpose once again we apply the method of [START_REF] Konno | Simple Derivation of Bäcklund transformation from Riccati Form of inverse method[END_REF] to derive NC PII Riccati equation from the linear systems (2.2). Let us consider the eigenvector Ψ = χ Φ in linear systems (2.2) and we obtain

     dχ dλ = (8iλ 2 + iu 2 -2iz)χ + (-iu z + 1 4 Cλ -1 -4λ u)Φ dΦ dλ = (iu z + 1 4 Cλ -1 -4λ u)χ + (-8iλ 2 -iu 2 + 2iz)Φ (4.1)
and

χ ′ = -2iλ χ + uΦ Φ ′ = uχ + 2iλ Φ (4.2)
where χ ′ = dχ dz and from system (4.2) we can evaluate the following expressions

χ ′ Φ -1 = -2iλ χΦ -1 + u (4.3) Φ ′ Φ -1 = -2iλ + uχΦ -1 . (4.4)
Now let consider the following substitution

Γ = χΦ -1 (4.5)
and after taking the derivation of above equation with respect to z we get

Γ ′ = χ ′ Φ -1 -χΦ -1 Φ ′ Φ -1 .
Finally by making use of Γ and Γ ′ in ( 4.3) and (4.4) and after simplification we obtain the following expression

Γ ′ = -4iλ Γ + u -ΓuΓ (4.6)
the above equation (4.6) is NC PII Riccati form in Γ where u is the solution of NC PII equation (2.1). As Γ has been expressed in terms of χ and Φ, the components of eigenvector of NC PII system (2.2), in next section we construct solution for Γ by solving the system (4.2) for χ and Φ. Proposition 1.3.

The solution of eigenvector Ψ = χ Φ can be derived from 4.2 in the following form Ψ = e -2iλ z+a 0 1 0 + e 2iλ z+b 0 0 1 where a 0 and b 0 are constants.

Proof:

In order to derive the solution for eigenvector Ψ of NC PII linear system (2.2) let us multiply first equation by Φ -1 and second equation by χ -1 from right side of that system and then after subtracting the both sides of the resulting equations we get

χ ′ + 2iλ χ -Φ ′ + 2iλ Φ Φ -1 χ -1 = 0 (4.7)
it implies that

χ ′ + 2iλ χ -Φ ′ + 2iλ Φ = 0
and finally we obtain

χ ′ = -2iλ χ (4.8)
Φ ′ = 2iλ Φ. (4.9)
Now equation (4.8) can be written as where a 0 is constant of integration, similarly from (4.9) we can calculate Φ = e 2iλ z+b 0 . (4.12)

χ ′ χ -1 = -2iλ (
finally the eigenvector Ψ of NC PII system can be written as Ψ = e -2iλ z+a 0 1 0 + e 2iλ z+b 0 0 1 .

Darboux transformations of NC PII equation

In the theory of integrable systems the applications of Darboux transformations (DTs) are quite interesting to construct the multi-soliton solutions of these systems. These transformations consist the particular solutions of corresponding linear systems of the integrable equations and their seed (initial) solutions. For example the NC PII equation (2.1) possesses following N fold DT

u[N + 1] = Π N k=1 Θ k [k]u[1]Π 1 j=N Θ j [ j] for N ≥ 1 (5.1) with Θ N [N] = Λ φ N [N]Λ χ N [N] -1
where u [START_REF] Painlevé | Sur les equations differentielles du second Ordre et dOrdre superieur, dont lInterable Generale est Uniforme[END_REF] is seed solution and u[N + 1] are the new solutions of NC PII equation [START_REF] Irfan | Lax pair representation and Darboux transformation of noncommutative Painlevé's second equation[END_REF]. In above transformations (5.

Λ φ 2N+1 [2N + 1] = Φ 2N Φ 2N-1 • • • Φ 1 Φ λ 2N χ 2N λ 2N-1 χ 2N-1 • • • λ 1 χ 1 λ χ . . . . . . • • • . . . . . . λ 2N-1 2N χ 2N λ 2N-1 2N-1 χ 2N-1 • • • λ 2N-1 1 χ 1 λ 2N-1 χ λ 2N 2N Φ 2N λ 2N 2N-1 Φ 2N-1 • • • λ 2N 1 Φ 1 λ 2N Φ and Λ χ 2N+1 [2N + 1] = χ 2N χ 2N-1 • • • χ 1 χ λ 2N Φ 2N λ 2N-1 Φ 2N-1 • • • λ 1 Φ 1 λ Φ . . . . . . • • • . . . . . . λ 2N-1 2N Φ 2N λ 2N-1 2N-1 Φ 2N-1 • • • λ 2N-1 1 Φ 1 λ 2N-1 Φ λ 2N 2N χ 2N λ 2N 2N-1 χ 2N-1 • • • λ 2N 1 χ 1 λ 2N χ with Λ φ 1 [1] = Φ 1 , Λ χ 1 [1] = χ 1
where χ 1 , χ 2 , χ 3 , ..., χ N and Φ 1 , Φ 2 , Φ 3 , ..., Φ N are the solutions of system (4.2) at λ 1 , λ 2 , λ 3 , ..., λ N . and Let us first consider the case N = 1: For this case the one fold DT of NC PII equation from (5.1 ) can be written as

u[1] = -8iλ 1 (1 -e -8iλ 1 z ) -1 e -4iλ
u[2] = Λ φ 1 [1](Λ χ 1 [1]) -1 u[1]Λ φ 1 [1](Λ χ 1 [1]) -1 or u[2] = Φ 1 χ -1 1 u[1]Φ 1 χ -1 1 . (6.3)
where u [START_REF] Hone | Painlevé test, singularity structure and integrability[END_REF] is a new solution of NC P-II equation that is generated by its seed solution u [START_REF] Painlevé | Sur les equations differentielles du second Ordre et dOrdre superieur, dont lInterable Generale est Uniforme[END_REF] and Φ 1 , χ 1 are of solutions system (4.2) at λ = λ 1 can be derived in the following forms

χ 1 = e -2iλ 1 z+a 0 Φ 1 = e 2iλ 1 z+b 0 (6.4)
. here a 0 and b 0 are constant of integration. Now after substituting the values from (6.1), (6.2) and (6.4) into (6.3) we obtain second soliton solution of NC PII equation as follow

u[2] = -8iλ 1 e 4iλ 1 z (1 -e -8iλ 1 z ) -1 . (6.5)
Now for N = 2 and with the even quasideterminants

Λ φ 2 [2], Λ χ 2 [2]
given in [START_REF] Irfan | Lax pair representation and Darboux transformation of noncommutative Painlevé's second equation[END_REF], the third soliton solution of NC PII equation can be written as

u[3] = Λ φ 2 [2](Λ χ 2 [2]) -1 u[2]Λ φ 2 [2](Λ χ 2 [2]) -1 (6.6)
for the above solution (6.6) the quasideterminants Λ φ 2 [START_REF] Hone | Painlevé test, singularity structure and integrability[END_REF] and Λ χ 2 [START_REF] Hone | Painlevé test, singularity structure and integrability[END_REF] can be derived in following forms Λ φ 2 [START_REF] Hone | Painlevé test, singularity structure and integrability[END_REF] = λ e -2iλ z+b -λ 1 e -4iλ 1 z+2iλ z+C 1 and Λ χ 2 [START_REF] Hone | Painlevé test, singularity structure and integrability[END_REF] = λ e 2iλ z+a -λ 1 e 4iλ 1 z-2iλ z+C 2 from their expressions given in [START_REF] Irfan | Lax pair representation and Darboux transformation of noncommutative Painlevé's second equation[END_REF], here C 1 = b 1a 1 + a and C 1 = a 1b 1 + a are constants of integration. Similarly we can construct remaining non-vacuum solutions of NC PII equation for N = 3 , N = 4 and so on by applying its Darboux transformations (5.1) iteratively.

Conclusion

In this paper, we have derived a zero curvature representation of quantum Painlevé II equation with its associated Riccati form and also we have derived an explicit expression of NC PII Riccati equation from the linear system of NC PII equation by using the method of Konno and Wadati [START_REF] Konno | Simple Derivation of Bäcklund transformation from Riccati Form of inverse method[END_REF]. At the end of this paper it has been shown that by using the Darboux transformation we can construct all non-vacuum solitonic solutions of NC PII equation by taking solution of NC PII Riccati equation as a initial solution. Further, one can derive Bcklund transformations for NC PII equation with the help of our NC PII linear system with its Riccati form by using the technique described in [START_REF] Konno | Simple Derivation of Bäcklund transformation from Riccati Form of inverse method[END_REF][START_REF] Khater | Bäcklund transformations and exact soliton solutions for some nonlinear evolution equations of the ZS/AKNS system[END_REF], these transformations may be helpful to construct the nonlinear principle of superposition for NC PII solutions. It also seems interesting to construct the connection of NC PII equation to the known integrable systems such as its connection to NC nonlinear Schrödinger equation and to NC KdV equation as it possesses this property in classical case.

2 .

 2 Noncommutative and quantum Painlevé II equation 2.1. Noncommutative Painlevé II equation The following NC analogue of classical Painlevé II equation

. 11 )′ 2 , f 2 ]

 1122 Now after substituting the value of [ f -from (3.11) in (3.9) we get

  4.10) the left hand side χ ′ χ -1 of above equation (4.10) represents NC derivation of log(χ) with respect to z and now the equation (4.10) can be expressed as (logχ) ′ = -2iλ now after integrating above equation with respect to z we get χ = e -2iλ z+a 0 (4.11)

  1) Λ φ N [N] and Λ χ N [N] are the quasideterminants of the particular solutions of NC PII linear system (2.2). Here the odd order quasideterminant representationS of Λ φ 2N+1 [2N + 1] and Λ χ 2N+1 [2N + 1] are presented below

6 .

 6 Non-vacuum solutions of NC PII equation Proposition 1.4. All non-vacuum solitonic solutions of NC PII equation can be derived from DTs (5.1) by taking the solution u of NC PII Riccati equation (4.6) as a seed (initial) solution u[1] of NC PII DTs (5.1) as followu[1] = -8iλ 1 (1e -8iλ 1 z ) -1 e -4iλ 1 zProof:Let us derive the non-vacuum solutions of NC PII equation with the help of its DTs (5.1) taking the solution u of NC PII Riccati equation (4.6) as seed or first soliton solution. For this purpose, we can show that that the following solution Γ = e 4iλ 1 z (6.1)

8. Acknowledgement I would like to thank V. Roubtsov and V. Retakh for their discussions to me during my Ph. D. research work. My special thanks to the University of the Punjab, Pakistan, on funding me for my Ph.D. project in France. I am also thankful to LAREMA, Université d'Angers and ANR "DIADEMS", France on providing me facilities during my Ph.D. research work.