Radiative sky cooling of silicon solar modules: evaluating the broadband effectiveness of photonic structures J. Dumoulin, 1 E. Drouard, 2 and M. Amara 1 1) Univ. Lyon, CNRS, INSA de Lyon, Ecole Centrale de Lyon, CPE Lyon, Université Claude Bernard Lyon 1, INL UMR 5270, 69621 Villeurbanne, France.

2) Univ Lyon, Ecole Centrale de Lyon, INSA de Lyon, CNRS, CPE Lyon, Université Claude Bernard Lyon 1, INL, UMR5270, 69134 Ecully, France.

(*Electronic mail: mohamed.amara@insa-lyon.fr) (Dated: 6 December 2022) Photovoltaic solar cells are designed to efficiently absorb solar photons but convert only a limited proportion of them into electricity. Under real operating conditions, the remaining energy causes solar modules to heat up to 50-60 °C, which is detrimental to their power conversion efficiency and lifetime. In recent years, there has been a growing interest in the so-called radiative sky cooling strategy. This approach consists in optimizing the thermal radiation of cells or modules -with the help of photonic structures -by taking advantage of the atmospheric transparency in the 8-13 range.

In this paper, we present an in-depth analysis of radiative sky cooling applied to silicon based photovoltaic modules. A simulation of a preliminary design of a photonic structure for possible radiative sky cooling of a module is also proposed.

Radiative sky cooling (RSC) has a significant theoretical benefit 1,2 and practical applications [START_REF] Zhu | Radiative cooling of solar absorbers using a visibly transparent photonic crystal thermal blackbody[END_REF][4][START_REF] Zhao | Performance analysis of enhanced radiative cooling of solar cells based on a commercial silicon photovoltaic module[END_REF][START_REF] Long | Simultaneously enhanced solar absorption and radiative cooling with thin silica micro-grating coatings for silicon solar cells[END_REF][START_REF] Li | Investigating the Effect of Radiative Cooling on the Operating Temperature of Photovoltaic Modules[END_REF][START_REF] Lee | Visibly Clear Radiative Cooling Metamaterials for Enhanced Thermal Management in Solar Cells and Windows[END_REF][START_REF] Wang | Radiative cooling of commercial silicon solar cells using a pyramid-textured PDMS film[END_REF][START_REF] Akerboom | Passive Radiative Cooling of Silicon Solar Modules with Photonic Silica Microcylinders[END_REF] are starting to emerge in the field of crystalline silicon (c-Si) photovoltaic (PV) devices. Those propose various photonic approaches that aim to modify the thermal emissivity profile, thereby enhancing RSC. In our recent paper 1 , we have demonstrated that the ideal thermal emissivity of solar modules beyond the band gap should correspond to the profile shown in figure 1. As we can see, this allows a double thermal benefit by : i) reflecting all photons in the parasitic solar absorption (PSA) range, which corresponds to the range 1.1-4 µm ii) enhancing thermal emission in the mid-infrared (MIR) range, that is for wavelengths > 4 µm. Furthermore, maintaining good absorption in the PV conversion (0.3-1.1 µm) range is essential to ensure that cooling is not at the expense of photovoltaic performance. These claims are in the agreement of those available in literature. Among the growing number of proposals, some of them come close to the desired properties 4,[START_REF] Li | Investigating the Effect of Radiative Cooling on the Operating Temperature of Photovoltaic Modules[END_REF][START_REF] Lee | Visibly Clear Radiative Cooling Metamaterials for Enhanced Thermal Management in Solar Cells and Windows[END_REF][START_REF] Wang | Radiative cooling of commercial silicon solar cells using a pyramid-textured PDMS film[END_REF][START_REF] Fathabadi | Novel Silica-Based PV Glass Cover Providing Higher Radiative Cooling and Power Production Compared with State-of-The-Art Glass Covers[END_REF] . Prospective work dedicated to multi-junction devices has even started to emerge [START_REF] Heo | Determining the Effectiveness of Radiative Cooler-Integrated Solar Cells[END_REF] .

Despite the fact that some approaches are very promising, several aspects must be carefully addressed for the resulting technologies to be effective. In particular, there is still a need of clear methodological guidelines in order to comprehensively assess the benefit of a given photonic approach. First and foremost, current studies are sometimes carried out on devices that do not have the properties of a solar module [START_REF] Zhu | Radiative cooling of solar absorbers using a visibly transparent photonic crystal thermal blackbody[END_REF][START_REF] Long | Simultaneously enhanced solar absorption and radiative cooling with thin silica micro-grating coatings for silicon solar cells[END_REF][START_REF] Akerboom | Passive Radiative Cooling of Silicon Solar Modules with Photonic Silica Microcylinders[END_REF][START_REF] Zhao | Radiative cooling of solar cells with micro-grating photonic cooler[END_REF][START_REF] Silva-Oelker | Numerical study of sodalime and PDMS hemisphere photonic structures for radiative cooling of silicon solar cells[END_REF] . In fact, the thermal emissivity of the latter should be used as the starting point [START_REF] Gentle | Is enhanced radiative cooling of solar cell modules worth pursuing?[END_REF] . Notably, the emissivity of a conventional c-Si module is quite different from that of a c-Si solar cell [START_REF] Riverola | Midinfrared emissivity of crystalline silicon solar cells[END_REF] . In the MIR range, the thermal emissivity depends only on the module cover glass (an optimization at the cell scale is thus ineffective). In the PSA range, the thermal emissivity depends partly on the cell but also on the glass and the EVA. Secondly, the impact of a change in the module's emissivity profile on its power conversion efficiency is not always thoroughly assessed. In simulations, this requires to cover the entire PV-PSA-MIR range and to make use of a coupled physical model for the PV module. Impor-W a v e l e n g t h ( µm )

S o l a r i r r a d i a n c e A t m o s p h e r i c i r r a d i a n c e

T h e r m a l e m i s s i v i t y tantly, some studies neglect the influence of one or more of the PV [START_REF] Li | A Comprehensive Photonic Approach for Solar Cell Cooling[END_REF][START_REF] Jaramillo-Fernandez | A Self-Assembled 2D Thermofunctional Material for Radiative Cooling[END_REF] , PSA [START_REF] Wang | Radiative cooling of commercial silicon solar cells using a pyramid-textured PDMS film[END_REF][START_REF] Perrakis | Combined nano and micro structuring for enhanced radiative cooling and efficiency of photovoltaic cells[END_REF] , or MIR [START_REF] Slauch | Optical approaches for passive thermal management in c-Si photovoltaic modules[END_REF][START_REF] Li | A Comprehensive Photonic Approach for Solar Cell Cooling[END_REF] ranges despite the fact that all three ranges influence the thermal and electrical behaviour.

As for the physical modeling, some studies do not include a coupling between the thermal and electrical properties [START_REF] Li | A Comprehensive Photonic Approach for Solar Cell Cooling[END_REF] , or do not assess the benefit on the electrical properties at all [START_REF] Zhao | Performance analysis of enhanced radiative cooling of solar cells based on a commercial silicon photovoltaic module[END_REF][START_REF] Long | Simultaneously enhanced solar absorption and radiative cooling with thin silica micro-grating coatings for silicon solar cells[END_REF][START_REF] Andueza | Enhanced thermal performance of photovoltaic panels based on glass surface texturization[END_REF] .

The objective of the present study is twofold. First, we investigate the importance of considering the PV conversion range in the analysis of RSC. To this extent, some practical guidelines are introduced to evaluate the ability of a given photonic approach to enhance thermal performance while also maintaining good electrical conversion efficiency. This complements previous theoretical work 1 , now providing a clear picture over the entire PV-PSA-MIR range. On this basis, we then propose a preliminary design of a photonic structure. Its benefit on thermal and electrical performance is comprehensively quantified, to serve as a benchmark methodology for this purpose.

To evaluate the impact of a change in emissivity on the electrical and thermal behaviour, it is of interest to consider several devices. Thus, we consider two commercial solar modules and one ideal module, with respect to their external luminescence efficiency Q lum e and absorption in the PV range α PV 1. Quasi-ideal : Q lum e = 1.0, α PV = 0.96 2. IBC Kaneka [START_REF] Green | Pushing to the Limit: Radiative Efficiencies of Recent Mainstream and Emerging Solar Cells[END_REF][START_REF] Yoshikawa | Silicon heterojunction solar cell with interdigitated back contacts for a photoconversion efficiency over 26%[END_REF] : Q lum e = 1.6.10 -2 , α PV = EQE 3. PERC [START_REF] Müller | Loss analysis of 22% efficient industrial PERC solar cells[END_REF] : Q lum e = 1.6.10 -4 , α PV = EQE

The term EQE relates to the External Quantum Efficiency of the aforementioned references. Solar modules with different properties are considered because this changes their electro-thermal behavior, and so does the impact of a change in the thermal emissivity. For instance Q lum e strongly affects both the power conversion efficiency and its sensitivity to increased temperature [START_REF] Dupré | Physics of the temperature coefficients of solar cells[END_REF] . The physical model used to evaluate the electro-thermal behavior is based on our selfconsistent model developed in our previous work 1 . Unless otherwise stated, reference environmental conditions are used (solar spectrum AM1.5G, standard U.S. atmosphere, 15 • C, no wind). More details about the physical model and the EQE can be found in the supplementary material.

Figure 2 summarized the power enhancement due to an increase of the RSC as a function of the power loss due to a lower light absorption in the PV range. The calculation takes into account a thermal emissivity profile equal to 75% [START_REF] Gentle | Is enhanced radiative cooling of solar cell modules worth pursuing?[END_REF] in the MIR range, and equal to 20% in the PSA range [START_REF] Li | A Comprehensive Photonic Approach for Solar Cell Cooling[END_REF] .

At first, for the quasi-ideal cell, the benefit of RSC is canceled when the absorption in the PV range is decreased by only 3%. More generally, the electrical power loss is of about -3 W.m -2 /%, i.e. per each percent of absorption loss in the PV conversion range. Such a power decrease is huge compared to the previously established power increase resulting from the improvement of the thermal emissivity profile 1 : +0.2 W.m -2 /% in the MIR range (i.e., a 15 times smaller sensitivity), +0.1 W.m -2 /% in the PSA range (30 times smaller sensitivity). For the more realistic scenarios (IBC Kaneka and PERC cells), the benefit of the RSC is canceled for a slightly higher deterioration of absorption in the PV range (6% and 7.5%, respectively). This is likely because of their lower efficiency which increases their operating temperature. Thus, their electrical power enhancement due to RSC is higher. Additionally, they also show a slightly lower sensitivity to the electrical power loss per each percent of absorption: -2.5 W.m -2 /% for the IBC Kaneka case, -2 W.m -2 /% for the PERC case. Overall, this highlights that the constraint on the absorption in the PV range is higher for solar cells with a good efficiency.

Based on the previous results, more general quantitative criteria for the optimization of radiative properties of silicon modules can be proposed. These criteria noted f PSA and f MIR establish a link between the electrical power gain associated with an improvement in the emissivity in the PSA or MIR ranges and the electrical power loss related to the absorption degradation in the PV conversion range. We define these two quantities as follows

f PSA = δ ε PSA ↓ δ α PV ↑ = δ P elec δ α PV ↑ . δ P elec δ ε PSA ↓ -1 f MIR = δ ε MIR ↓ δ α PV ↑ = δ P elec δ α PV ↑ . δ P elec δ ε MIR ↓ -1
P elec is electrical power, α PV the average absorptivity in the PV conversion range, ε PSA the average emissivity in the range of parasitic solar absorption, and ε MIR the average emissivity in the MIR range. The signs ↑ and ↓ indicate an increase and a decrease respectively. The derivatives with respect to a given spectral range are calculated by keeping the properties constant in the other ranges. Thus the average degradation ∆α PV of the tolerable PV absorption during a reduction of parasitic absorption ∆ε PSA is given by ∆ε PSA = f PSA .∆α PV . Similarly, the average ∆α PV degradation of the tolerable PV absorption during an increase in the MIR emissivity ∆ε MIR is given by ∆ε MIR = f MIR .∆α PV . With the help of environmental condition, namely ambient temperature, solar irradiation and wind velocity, it is possible to calculate the mean value of f MIR and f PSA . The box plot given by figure 3 illustrates the obtained results. When comparing the three scenarios, the general trend is consistent with what might be expected from figure 2 : the quasi-ideal scenario exhibits the highest constraint on the PV range, while the PERC case hase the lowest constraint. The IBC is slightly more sensitive to the PV range, with an average value of about 20 for f MIR and 35 for f PSA . This shows that the sensitivity to the PV range should be of special concern especially when improving the emissivity in PSA range. In fact, any (average) improvement of emissivity in the PSA range must be accompanied by a 35 times smaller decrease in the (average) PV absorption range. Otherwise, there will be no benefit to electrical power. Note that environmental conditions change the values of f PSA and f MIR , leading to a large dispersion of the values. However, the most notable effect is due to wind velocity (value of h). As the latter increases, the baseline operating temperature decreases and therefore the electrical power is less affected by any change in radiative cooling properties. Hence, the value of f PSA and f MIR increase with wind velocity. This effect can be seen in figure 3, where two groups of data points are visible in each case. Note that these results assume that the decrease in PV absorption is not correlated to absorption by non-active materials in the module. The latter phenomenon would induce a higher operating temperature for the same decrease in PV absorption, and thus an increase in sensitivity. The importance of such a broadband analysis and the high sensitivity to a small decrease of the PV absorption is illustrated through a preliminary design of photonic structure for RSC. Among several approaches proposed in the literature at air/glass or glass-EVA interfaces, such as metallo dielectric filters, transparent conductive oxide based hot mirrors or full dielectric hot mirrors, the last one clearly appears as the most able to limit the decrease of the PV absorption. Derived from the multilayer dielectric mirror located at the air/glass interface of a silicon module proposed by Li et al. [START_REF] Li | A Comprehensive Photonic Approach for Solar Cell Cooling[END_REF] that decreases its temperature by 5.7 • C, a 32 layers based on two materials, TiO 2 and SiO 2 , has been designed under normally incident light using Transfer Matrix Method [START_REF] Larouche | Openfilters: open-source software for the design, optimization, and synthesis of optical filters[END_REF] given the ideal absorption / emissivity profile of figure 1. The final thickness is about 1446 nm. The resulting spectra, shown in figure 4, are used to calculate the electrical and thermal behavior in the three scenarios formerly introduced.

f A S P f M I R f A S P f M I R f A S P f M I R Q u a s i -i
More precisely, as reported in table I, if this calculation only takes into account the PV absorption and PSA reflection ("PV-PSA" in Table 2), the module temperature and electrical performances are significantly enhanced. However, these enhancements are reduced if the MIR part of the spectrum is taken into account. This shows the importance of performing a broadband calculation to estimate the benefit of a given photonic structure. This is due to the decrease of the thermal emissivity induced by the filter mainly above 13 µm (see figure 4). Overall, the proposed photonic structure still allows to decrease the operating temperature and to enhance the electrical power.

In conclusion, we have investigated the use of radiative cooling to improve the operating temperature of silicon-based modules. The main results can be summarized as follows:

• It is mandatory to include the PV part of the spectrum for any optimization procedure of the module RSC, i.e. the optimization of the absorption / emission beyond the bandgap. In fact, even of a few percent degradation of solar absorption will cancel any benefit of enhanced RSC. • We have introduced a new criterion that quantifies and links absorptivity and reflectivity in the different part of the solar spectrum and solar module thermal emission. This criterion serves as a guideline to determine if a given structure is worth studying in more detail. • It was revealed that the reflectivity profile in between [λ gap -4 µm] is strongly linked with any modification of the module emissivity. • Based on our criterion, we have found a new photonic structure which simultaneously enhances RSC and maintains electrical conversion performance. Notably, we have highlighted the importance of the broadband calculation in order to assess its benefits.

The takeout message is that we can no longer optimize the optical properties of the module only on the infrared part of the spectrum. A thorough quantification of the photon balance over the entire PV-PSA-MIR range is mandatory. Finally, future research is oriented towards the extension of this analysis to other proposed solutions for the RSC.

SUPPLEMENTARY MATERIAL

See supplementary material for the physical model, the EQE of the selected solar cells. In addition, we provide the details of dielectric coating material, thickness, and structure.

PI d e a l p r o f i l eFIG. 1 .

 1 FIG.1. Incoming solar and atmospheric irradiance. The absorbed irradiance (blue) corresponds to the US standard atmosphere. The red line depicts the real thermal emissivity profile of silicon-based solar modules (data extracted from Li et al.[START_REF] Li | A Comprehensive Photonic Approach for Solar Cell Cooling[END_REF] ). The black line of the graph shows the ideal emissivity for RSC.

  FIG.2. Electrical power gain obtained thanks to an ideal emissivity profile as a function of the absorption loss in the PV range. Results are given for the Quasi-ideal, the IBC Kaneka, and the PERC devices.

FIG. 3 .

 3 FIG. 3. Values of f MIR and f PSA in different boundary conditions. Each point is calculated by a set of three conditions: T amb =(15, 25) • C, h=(5, 15) W.m -2 K -1 , I sun =(500, 1000) W.m -2

TABLE I .

 I Electrical and thermal behaviors of solar module due ton RSC with two optimization scenarios.

	Cell	∆T [ • C]	∆J gen [mA.cm -3 ]	∆P elec [W.m -2 ]
		PV-PSA a BB b PV-PSA BB PV-PSA BB
	Quasi-ideal	-5.3	-3.7 +0.3 +0.3 +5.2	+4.1
	IBC Kaneka	-5.1	-3.6 +0.4	+0.4 +5.6	+4.7
	PERC	-4.6	-3.0 +0.4 +0.4 +5.8 +4.6
	a PV & PSA spectral domains
	b PV & PSA & MIR spectral domains (Broadband)

J. Dumoulin, E. Drouard, and M. Amara, "Radiative sky cooling of solar cells: fundamental modelling and cooling potential of single-junction devices," Sustainable Energy and Fuels 5

, 2085-2096 (2021).


Anaïs Bénarouche

Vanessa Point

Frédéric Carrière
email: carriere@imm.cnrs.fr

Jean-François Cavalier
email: jfcavalier@imm.cnrs.fr

lipase by Orlistat for investigating simultaneously lipase adsorption and substrate hydrolysis at the lipid-water interface

Keywords: CMC, critical micellar concentration, DGL, dog gastric lipase, FFA, free fatty gastric lipase, HCEL, human carboxylester lipase, HPL, human pancreatic lipase, MAG, monoacylglycerol, TAG, triacylglycerol enzyme kinetics, interfacial enzymology, lipase, lipolysis, monomolecular film, lipase inhibition

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

Introduction

Inhibiting digestive lipases to reduce fat absorption has become the main pharmacological approach for the treatment of obesity during the last decade [START_REF] Carrière | Inhibition of gastrointestinal lipolysis by Orlistat during digestion of test meals in healthy volunteers[END_REF][START_REF] Lengsfeld | Physiology of Gastrointestinal Lipolysis and Therapeutical Use of Lipases and Digestive Lipase Inhibitors[END_REF]. The FDA-approved lipase inhibitor Orlistat is currently found in two different drug products, Xenical™ (Roche) which can be obtained only under medical prescription, and Alli™ (GlaxoSmithKline) which is an overthe-counter product. Orlistat is an active site-directed inhibitor that forms a stoichiometric longlived acyl-enzyme complex with human gastric (HGL) and pancreatic (HPL) lipases [START_REF] Borgstrom | Mode of action of tetrahydrolipstatin: a derivative of the naturally occurring lipase inhibitor lipstatin[END_REF][START_REF] Hadváry | Inhibition of pancreatic lipase in vitro by the covalent inhibitor tetrahydrolipstatin[END_REF][START_REF] Gargouri | Inactivation of pancreatic and gastric lipases by THL and C12: 0-TNB: a kinetic study with emulsified tributyrin[END_REF] after the nucleophilic attack of the catalytic serine residue on the β-lactone group [START_REF] Hadváry | The lipase inhibitor tetrahydrolipstatin binds covalently to the putative active site serine of pancreatic lipase[END_REF][START_REF] Lüthi-Peng | Identification of the active-site serine in human pancreatic lipase by chemical modification with tetrahydrolipstatin[END_REF] (Scheme 1).

By covalently blocking the digestive lipase's active site, Orlistat inhibits the hydrolysis of dietary triacylglycerols (TAGs) and thus reduces the production and subsequent intestinal absorption of monoacylglycerols (MAGs) and free fatty acids (FFAs). The inhibitory efficacy of Orlistat is tightly associated with its amphiphilic structure. It can be found at the lipid-water interface as well as in mixed micelles with surfactants. The inhibition of HPL [START_REF] Lüthi-Peng | Identification of the active-site serine in human pancreatic lipase by chemical modification with tetrahydrolipstatin[END_REF], HGL [START_REF] Gargouri | Inactivation of pancreatic and gastric lipases by THL and C12: 0-TNB: a kinetic study with emulsified tributyrin[END_REF] and human carboxyl ester lipase (HCEL) [START_REF] Borgstrom | Mode of action of tetrahydrolipstatin: a derivative of the naturally occurring lipase inhibitor lipstatin[END_REF] by Orlistat is thus drastically increased upon adding bile salts above their critical micellar concentration (CMC). Tiss et al. [START_REF] Tiss | Inhibition of human pancreatic lipase by tetrahydrolipstatin: Further kinetic studies showing its reversibility[END_REF][START_REF] Tiss | A comparative kinetic study on human pancreatic and Thermomyces lanuginosa lipases: Inhibitory effects of tetrahydrolipstatin in the presence of lipid substrates[END_REF] reported that the dependence of HPL inhibition on the presence of bile salts in the incubation medium may be attributable to the formation of mixed micelles of Orlistat and bile salts. This micellar solubilisation probably increases the availability of this inhibitor in solution and thus favours its interaction with pancreatic lipase, which active site becomes accessible in solution in the presence of bile salts [START_REF] Belle | Probing the opening of the pancreatic lipase lid using sitedirected spin labeling and EPR spectroscopy[END_REF]. Orlistat is also soluble in oil and can partition between the oil core and the lipid-water interface. Increasing the interfacial area by an emulsification process promotes a stronger diffusion of Orlistat from the oil core towards the interface [START_REF] Tiss | Surface behaviour of bile salts and tetrahydrolipstatin at air/water and oil/water interfaces[END_REF][START_REF] Tiss | Transfer of orlistat through oilwater interfaces[END_REF]. Taking into account these findings, it was concluded that the partitioning of Orlistat between the oil and aqueous phases, as well as its rate of transfer, may contribute importantly to the inhibition of lipolysis along the gastrointestinal tract [START_REF] Tiss | Surface behaviour of bile salts and tetrahydrolipstatin at air/water and oil/water interfaces[END_REF].

Another factor that may be of importance is the reversibility of lipase inhibition by Orlistat (Scheme 1B). Although it is often written in literature reviews that Orlistat is an irreversible lipase inhibitor, it was shown in early studies that HCEL inhibition was reversible [START_REF] Borgstrom | Mode of action of tetrahydrolipstatin: a derivative of the naturally occurring lipase inhibitor lipstatin[END_REF]. The authors reported that the stoichiometric acyl-enzyme complex 1 formed between the β-lactone ring of Orlistat and the active site serine residue of HCEL was spontaneously slowly hydrolyzed [START_REF] Borgstrom | Mode of action of tetrahydrolipstatin: a derivative of the naturally occurring lipase inhibitor lipstatin[END_REF][START_REF] Stalder | Tetrahydrolipstatin: Degradation products produced by human carboxyl-ester lipase[END_REF]. Full recovery of HCEL activity was then measured concomitantly with the release of the corresponding β-lactone-cleavage Orlistat form (i.e., compound 2 in Scheme 1).

Compound 2 would also be subjected to further chemical modifications (rapid isomerization, i.e. compound 3; and/or hydrolysis, i.e. compound 4) leading to the -lactone final degradation product 6 together with traces of the N-formylleucyl ester thereof, i.e. corresponding to 5 [START_REF] Borgstrom | Mode of action of tetrahydrolipstatin: a derivative of the naturally occurring lipase inhibitor lipstatin[END_REF][START_REF] Stalder | Tetrahydrolipstatin: Degradation products produced by human carboxyl-ester lipase[END_REF][START_REF] Stalder | Tetrahydrolipstatin: Thermal and Hydrolytic Degradation[END_REF]. Moreover, it was also demonstrated by the authors that these degradation products had no inhibitory activity toward lipases [START_REF] Stalder | Tetrahydrolipstatin: Thermal and Hydrolytic Degradation[END_REF], therefore emphasizing the unique structure-inhibitory activity relationship of the Orlistat molecule. More recently, a similar reactivation phenomenon was also observed with pancreatic lipase [START_REF] Tiss | Inhibition of human pancreatic lipase by tetrahydrolipstatin: Further kinetic studies showing its reversibility[END_REF]. Tiss et al. reported that the HPL inhibition by Orlistat could be rapidly and partially reversed (by around 40%) in the presence of an emulsion of short-or long-chain TAGs and bile salts below their CMC [START_REF] Tiss | Inhibition of human pancreatic lipase by tetrahydrolipstatin: Further kinetic studies showing its reversibility[END_REF]. Lipolysis and lipase inhibition are thus two competitive processes that can occur simultaneously in vitro, as well as in vivo [START_REF] Carrière | Inhibition of gastrointestinal lipolysis by Orlistat during digestion of test meals in healthy volunteers[END_REF], when the lipase is in presence of both substrate and inhibitor. The net efficacy of the inhibitor depends on the relative rates of lipolysis and inhibition reactions, on the possible reactivation of inhibited enzyme, as well as on the relative proportions of lipid substrate and inhibitor. It was also shown that the nature and the emulsification state of dietary lipids had a large impact on these rates and on the resulting efficacy of Orlistat in the course of test meals hydrolysis [START_REF] Carrière | Inhibition of gastrointestinal lipolysis by Orlistat during digestion of test meals in healthy volunteers[END_REF].

In the present work, initially dedicated to dog gastric lipase (DGL) inhibition by Orlistat, a reversibility of DGL inhibition was also observed using the monomolecular film technique.

More interestingly, conditions were found for observing both lipase adsorption onto the lipid film spread at the air-water interface, reactivation of Orlistat-inhibited DGL and hydrolysis of the 1,2-dicaprin film. These unexpected findings allowed us to monitor simultaneously two essential steps of interfacial catalysis by a lipase using Orlistat as a tool. Contrary to "classical" enzymes acting on soluble substrates and often following the Michaelis-Menten model, lipases are soluble enzymes acting on an insoluble substrate, TAGs that form oil-in-water emulsions, membrane bilayers, micelles and vesicles [START_REF] Aloulou | Exploring the specific features of interfacial enzymology based on lipase studies[END_REF][START_REF] Singh | Structuring food emulsions in the gastrointestinal tract to modify lipid digestion[END_REF][START_REF] Golding | The influence of emulsion structure and stability on lipid digestion[END_REF]. In this context, lipases first need to bind the lipid-water interface before hydrolyzing their substrates. This mechanism of action often includes conformational changes at the enzyme level, such as the opening of a lid controlling the access to the active site and generating an interfacial recognition site [START_REF] Aloulou | Exploring the specific features of interfacial enzymology based on lipase studies[END_REF][START_REF] Cavalier | Inhibition of human gastric and pancreatic lipases by chiral alkylphosphonates. A kinetic study with 1,2-didecanoyl-sn-glycerol monolayer[END_REF][START_REF] Delorme | Effects of Surfactants on Lipase Structure, Activity and Inhibition[END_REF]. It is usually rather difficult to analyze the various reaction steps of interfacial catalysis in a single experiment, and lipase assays often give access to global and apparent kinetic parameters resulting from all these steps. Since measuring the enzyme partitioning between the aqueous phase and the substrate interface is a difficult task in the course of the lipolysis reaction, lipase assays are often performed in presence of a large excess of substrate interfacial area assuming that all enzyme is bound at the interface. Lipases can however act according to a hopping mode and a continuous exchange between the water phase and the interface can occur with a specific equilibrium constant [START_REF] Haiker | Rapid exchange of pancreatic lipase between triacylglycerol droplets[END_REF]. With lipid monolayers as substrate, it was shown that only part of the enzyme binds to the lipid film spread at the air-water interface using either a radio-labelled lipase (continuous assay) [START_REF] Pieroni | Hydrolysis of mixed monomolecular films of triglyceride/lecithin by pancreatic lipase[END_REF][START_REF] Gargouri | Inhibition of lipases by proteins: A binding study using dicaprin monolayers[END_REF] or an ELISA for detecting the lipase in the bulk phase and lipid film after their separation (end-point assay) [START_REF] Cavalier | Inhibition of human gastric and pancreatic lipases by chiral alkylphosphonates. A kinetic study with 1,2-didecanoyl-sn-glycerol monolayer[END_REF][START_REF] Aoubala | Interfacial binding of human gastric lipase to lipid monolayers, measured with an ELISA[END_REF][START_REF] Marguet | Interfacial and or molecular recognition by lipases of mixed monomolecular films of 1,2-dicaprin and chiral organophosphorus glyceride analogues?[END_REF][START_REF] Tiss | Interfacial binding and activity of lipases at the lipid-water interface: effects of Gum Arabic and surface pressure[END_REF].

Using DGL as a model enzyme, the new experimental model described here aims at monitoring both lipase adsorption and activity using mixed monomolecular films of 1,2-dicaprin and Orlistat with the surface barostat technique. DGL can be used as a model lipase because gastric lipase is the first enzyme involved in fat digestion in the stomach, and like pancreatic lipase it shows a strong preference for TAGs and diacylglycerols (DAGs); while some other lipases prefer substrates forming aggregates in solution like MAGs [START_REF] Bakala N'goma | Understanding the lipid-digestion processes in the GI tract before designing lipid-based drug-delivery systems[END_REF]. Moreover, DGL has 85.7% amino acid sequence identity with HGL and both enzymes have superimposable 3-D structures [START_REF] Roussel | Crystal structure of the open form of dog gastric lipase in complex with a phosphonate inhibitor[END_REF] and similar lipase activities [START_REF] Fernandez | In vitro gastrointestinal lipolysis of four formulations of piroxicam and cinnarizine with the self emulsifying excipients Labrasol and Gelucire 44/14[END_REF].

Materials and methods

Chemicals.

1,2-didecanoyl-sn-glycerol (1,2-dicaprin, reference 800810P) from Avanti Polar Lipids Inc. was purchased from Coger (Paris, France) and was > 99% purity. All other chemicals, including Orlistat, 2-(N-morpholino)ethane sulfonic acid (MES), NaCl, CaCl2 and sodium acetate were purchased from Sigma-Fluka-Aldrich (St-Quentin-Fallavier, France) and were > 98% purity. Chloroform (anhydrous for analysis, stabilized with amylene) was purchased from Sigma-Aldrich-Fluka (St-Quentin-Fallavier, France) and was of HPLC grade.

Enzymes.

Crude recombinant dog gastric lipase (DGL) was provided by Meristem Therapeutics (Clermont-Ferrand, France) [START_REF] Gruber | Large-scale production of a therapeutic protein in transgenic tobacco plants: effect of subcellular targeting on quality of a recombinant dog gastric lipase[END_REF] and purified as previously described [START_REF] Roussel | Crystal structure of the open form of dog gastric lipase in complex with a phosphonate inhibitor[END_REF]. For protein digestion before mass spectrometry analysis, trypsin of sequencing grade was purchased from Sigma-Aldrich-Fluka (St-Quentin-Fallavier, France).

Protein digestion and MALDI-TOF mass spectrometry analysis.

Protein in-gel digestion was performed with sequencing grade trypsin as previously described [START_REF] Point | Analysis of the discriminative inhibition of mammalian digestive lipases by 3-phenyl substituted 1,3,4oxadiazol-2(3H)-ones[END_REF]. MALDI-TOF analyses were performed on a Bruker Microflex II mass spectrometer (Daltonik, Deutchland) using a saturated solution of -cyano-4-hydroxycinnamic acid in acidified water (0.1% TFA) and acetonitrile (30:70, v/v) as matrix. Mass spectra were acquired in the positive ion mode, using the FlexAnalysis™ software program (Bruker, Daltonik, Deutchland). Theoretical and experimental monoisotopic peptide masses were obtained using the BioTools™ software program (Bruker, Daltonik, Deutchland) with a mass tolerance ranging from 50 to 100 ppm.

Kinetics of DGL adsorption and activity using the monomolecular film technique.

Measurements were performed at room temperature (25 °C) using the KSV5000 barostat equipment (KSV, Helsinki, Finland) monitored by the KSV Device Server Software v. 1.20 (KSV Instruments Ltd., Helsinki, Finland) running under Windows XP ® . The principle of this method has been described previously by Verger et al. [START_REF] Verger | Action of phospholipase A at interfaces[END_REF]. It involves the use of a Teflon "zero-order" trough with two compartments: a reaction compartment (volume 38.5 mL; surface area, 31.2 cm 2 ) and a reservoir compartment (volume 126.3 mL; surface area, 210.5 cm 2 ) connected to each other by a small surface channel. Before each experiment, the Teflon trough was cleaned with tap water, and then gently brushed in the presence of distilled ethanol, before being washed again with tap water and abundantly rinsed with Milli-Q™ water. The Teflon trough was filled with 10 mM sodium acetate buffer (pH 5.0) containing 100 mM NaCl and 20 mM CaCl2, prepared with Milli-Q™ water and filtered through a 0.45 µm Millipore ® membrane. Residual surface-active impurities were removed before each experiment by simultaneous sweeping and suction of the surface [START_REF] Pieroni | Hydrolysis of mixed monomolecular films of triglyceride/lecithin by pancreatic lipase[END_REF]. The monolayer was formed at the airwater interface by spreading a few microliters of a lipid solution (1 mg mL -1 in chloroform) until the desired initial surface pressure (Πi), measured with a Wilhelmy plate (perimeter 3.924 cm) [START_REF] Wilhelmy | Ueber die Abhängigkeit der Capillaritäts Constanten des Alkohols von Substanz und Gestalt des benetzten festen Körpers[END_REF], was reached. The waiting time for the spreading solvent evaporation and for the film to reach equilibrium varied from 10 to 20 min depending on the spreading volume and the initial surface pressure.

When using mixed monomolecular films of 1,2-dicaprin containing various mole fraction of Orlistat (Orlistat, %), a Teflon barrier was placed transversally over the small channel connecting the two compartments of the "zero-order" trough in order to block surface communication between these compartments. Surface pressure was first determined by placing the Wilhelmy plate in the reaction compartment where the mixed film was spread at the desired Πi. The stability of each mixed 1,2-dicaprin/Orlistat monolayer was initially checked by recording over 90 min the variations in surface pressure. In all cases, no significant change in surface pressure ( 0.2 mN m -1 ) was observed during the time course of the experiment. The Wilhelmy plate was then switched to the reservoir compartment where only 1,2-dicaprin film was subsequently spread at the same Πi. The barrier between the two compartments was then removed in order to allow communication of the two films, and the enzyme solution (1.1 mg mL -1 DGL in 10 mM MES pH 6.0 containing 150 mM NaCl) was injected with an Hamilton syringe (from 6-50 µL for final concentrations ranging from 5-60 nM, respectively) into the subphase of the reaction compartment. With medium chain lipids such as 1,2-dicaprin, soluble lipolysis products (i.e., monocaprin and capric acid) are released upon the action of the lipase and a drop in surface pressure is recorded. Using the barostat mode of the KSV5000 device, an automatically-driven Teflon mobile barrier moves over the reservoir compartment to compress the monomolecular lipid film and compensate for the substrate molecules removed from the film by the enzyme hydrolysis, thus keeping the surface pressure (i.e. Πi continuously measured on the reservoir compartment) constant. With the surface barostat technique, the lipid substrate packing in the monomolecular film (i.e. the molecular area and surface concentration of substrate) is thus assumed to remain constant during the time-course of hydrolysis, and it is then possible to obtain accurate steady-state kinetic measurements with minimal perturbation caused by increasing amounts of reaction products. The reaction compartment was stirred with a 1-cm magnetic bar rotating at 250 rpm. The system is designed so that the agitation of the aqueous phase with a magnetic stirring bar does not disturb the stability of the surface film. The data recorded from inhibition kinetics were analyzed according to a model previously established for lipase inhibition [START_REF] Cavalier | Inhibition of human gastric and pancreatic lipases by chiral alkylphosphonates. A kinetic study with 1,2-didecanoyl-sn-glycerol monolayer[END_REF]. DGL activity (mole cm -2 min -1 M -1 ) was expressed as the number of moles of substrate hydrolyzed per time unit (min), per surface unit (cm 2 ) of the reaction compartment of the "zero-order" trough and for an arbitrary lipase concentration of 1 M. [START_REF] Verger | Action of phospholipase A at interfaces[END_REF].

Treatment of kinetics data of substrate hydrolysis by DGL at the lipid-water interface using the monomolecular film technique

Under steady state conditions (i.e., when time tends to infinity, Figure 2A) the maximal reaction rate vS = dy/dt (cm s -1 ) is calculated from the slope of the experimental kinetic curves y = f(t); where y is the movement of the mobile barrier (cm) monitored by the barostat and t, time (min). The enzyme velocity vm (molecule cm -2 s -1 ) in the monolayer system can be deduced from Eq. 1 [START_REF] Panaiotov | Enzymatic reactions at interfaces: Interfacial and temporal organization of enzymatic lipolysis[END_REF]:

S l v v s s m   = Eq. 1
where S is the surface concentration of 1,2-dicaprin (molecule cm -2 ) at Πi = 25 mN m -1 , derived from the equilibrium surface pressure-area isotherm; S is the surface area of the reaction compartment (cm 2 ); and l is the width (cm) of the reservoir compartment. It is assumed here that the molecular area of substrate is constant and remains the same as in initial conditions, thus neglecting changes due to enzyme penetration and Orlistat degradation products before the steady state velocity regime is reached. Using the nomenclature of the Verger-de Haas interfacial kinetic model [START_REF] Panaiotov | Enzymatic reactions at interfaces: Interfacial and temporal organization of enzymatic lipolysis[END_REF][START_REF] Verger | Enzyme reactions in a membrane model. 1. A new technique to study enzyme reactions in monolayers[END_REF], the expression of vm in the monolayer system can be rewritten as (Eq. 2)

:

S E M cat m K k v    = * * Eq. 2
where kcat is the interfacial catalytic rate constant (s -1 ); K*M is the interfacial Michaëlis-Menten constant (molecule cm -2 ); and  is the interfacial concentration (molecule cm -2 ) of the DGL adsorbed onto the film. When acting on mixed 1,2-dicaprin/Orlistat monomolecular films, the residual lipase activity (RAE*(%), %) is then deduced from Eq. 2 as the ratio of the respective enzyme velocities in presence (vm( Orlistat )) and in absence (vm( Orlistat =0)) of inhibitor (Eq. 3):

0) (α ) (α (%) * Orlistat Orlistat 100 RA =  = m m E v v Eq. 3
2.6. DGL adsorption/penetration onto mixed 1,2-dicaprin/Orlistat monomolecular films.

Mixed monomolecular films of 1,2-dicaprin/Orlistat were formed only over the reaction compartment of the "zero-order" Teflon trough (volume 38.5 mL; surface area, 31.2 cm 2 ) at an initial surface pressure (Πi) of 25 mN m -1 as described above. After injecting DGL into the aqueous subphase with an Hamilton syringe (from 6.8 to 50 µL DGL stock solution for final concentrations ranging from 8.4 to 60 nM, respectively), the surface pressure increase due to the adsorption/penetration of the lipase into the mixed monolayer was continuously recorded (every 5 seconds) until the equilibrium surface pressure was reached. The aqueous subphase, composed of the same acetate buffer (pH 5.0) as described above, was continuously stirred with a 1-cm magnetic bar rotating at 250 rpm.

Treatment of kinetic data of DGL adsorption onto mixed 1,2-dicaprin/Orlistat monolayers.

The apparent kinetic parameters of DGL adsorption (ka, M -1 s -1 ) and desorption (kd, s -1 ) onto the mixed 1,2-dicaprin/Orlistat films were calculated according to the methodology we recently reported [START_REF] Bénarouche | New insights into the pH-dependent interfacial adsorption of dog gastric lipase using the monolayer technique[END_REF]. Briefly, the experimental data (i.e., surface pressure increase (Π) with time) were fitted to the Langmuir adsorption isotherm equation adapted to surface pressure measurements (Eq. 4):

Π (t) = Πi + Πmax..[1 -exp (-t)]
Eq. 4

where Π (t) is the surface pressure measured as a function of time; Πi is the initial surface pressure; Πmax is the maximum variation of surface pressure reached upon DGL binding;  is the fraction of the total free adsorption (binding) sites coverage; and  = (ka.CE0 + kd) with CE0

(mol L -1 ) being the DGL concentration in the subphase of the trough.

Curve-fitting the experimental data points to Eq. 4 using KaleidaGraph 4.1 software (Synergy Software) allowed calculating  values for multiple CE0 concentrations at each Πi investigated.

Values of ka and kd were then determined from the slope and y-intercept, respectively, of the linear plot of  versus CE0 (Figure S2 in Supplementary Material). The adsorption equilibrium coefficient, KAds, which represents the binding affinity between the protein and the lipid film, was obtained from the ratio of the measured rate constants (KAds = ka/kd = 1/KD).

Using the mathematical equations derived from the interfacial kinetic model of Verger et al. [START_REF] Verger | Action of phospholipase A at interfaces[END_REF][START_REF] Verger | Enzyme reactions in a membrane model. 1. A new technique to study enzyme reactions in monolayers[END_REF][START_REF] Verger | Interfacial enzyme kinetics of lipolysis[END_REF][START_REF] Verger | Comparative studies of lipase and phospholipase A2 acting on substrate monolayers[END_REF], it became possible to estimate, by indirect calculation, the theoretical value of the enzyme interfacial concentration (, molecule cm -2 ) based on Eq. 5, where Strough / Vtrough represents the surface area-volume ratio (cm -1 ) of the reaction compartment of the Teflon trough:

                 + =  trough trough D E E V S K C ) 1 ( 0 * Eq. 5
Finally, the mathematical expression of the molecular area (AE*, Å 2 molecule -1 ) occupied by the enzyme adsorbed onto the mixed films at a surface pressure of 25 mN m -1 maintained constant by the mobile barrier movement, is:

( )   ( ) ( ) * * * occupancy surface θ A A E trough E lipid lipid trough E S n S  =     - =
Eq. 6

Alipid (Å 2 molecule -1 ) is the mean molecular area of the mixed film at a given Orlistat value deduced from the surface pressure (Π)-molecular area isotherms at Πi = 25 mN m -1 ; nlipid is the number of molecules spread at the air-water interface at the same Πi; and  is the fractional surface coverage determined in Eq. 4.

Eq. 6, thus obtained by means of our mathematical approach based on Verger's kinetic model, therefore allowed access to an estimation of the values of AE* (see reference [START_REF] Bénarouche | New insights into the pH-dependent interfacial adsorption of dog gastric lipase using the monolayer technique[END_REF] for more details).

 Results and Discussion

Covalent inhibition of DGL by Orlistat.

It was first check that DGL was inhibited by Orlistat through a covalent interaction with the catalytic serine residue as previously demonstrated with HCEL and HPL [START_REF] Borgstrom | Mode of action of tetrahydrolipstatin: a derivative of the naturally occurring lipase inhibitor lipstatin[END_REF][START_REF] Tiss | Inhibition of human pancreatic lipase by tetrahydrolipstatin: Further kinetic studies showing its reversibility[END_REF][START_REF] Stalder | Tetrahydrolipstatin: Thermal and Hydrolytic Degradation[END_REF]. After pre-incubation of DGL with a 40-fold molar excess of Orlistat for 30 min, a tryptic digestion of the inhibited DGL and a peptide mass fingerprint (PMF) by MALDI-TOF mass spectrometry [START_REF] Pappin | Rapid identification of proteins by peptide-mass fingerprinting[END_REF] were performed under previously described conditions [START_REF] Point | Analysis of the discriminative inhibition of mammalian digestive lipases by 3-phenyl substituted 1,3,4oxadiazol-2(3H)-ones[END_REF]. PMF was then compared with the one of the non-inhibited lipase (Figure S1 in Supplementary Material). With DGL alone, a m/z of 2,904.9 Da corresponding to the T 142 GQDKLHYVGHS 153 QGTTIGFIAFSTNPK 168 peptide containing the catalytic Ser 153 residue was detected (Figure S1A). When DGL was incubated with Orlistat, a mass increase of +500.7 Da was observed in the PMF spectrum for the peptide containing the active site serine (Figure S1B), which confirmed that a covalent bond had been formed between Orlistat (495.39 Da) and the catalytic serine residue of the gastric lipase, taking into account the precision of the MALDI-TOF technique and the molecular mass of DGL (48,449 ± 103 Da) recorded using the same instrument.

Enzyme kinetics of DGL on mixed 1,2-dicaprin films containing Orlistat.

In order to get more insight into the mechanism of inhibition of DGL in presence of Orlistat, the monolayer technique [START_REF] Verger | Action of phospholipase A at interfaces[END_REF] and surface pressure measurements were further used to monitor the interfacial interactions between DGL and monomolecular films of 1,2-dicaprin spread at the air-water interface and containing various mole fractions (Orlistat, %) of Orlistat.

As a prerequisite to study DGL inhibition at the lipid-water interface, compression isotherms of various mixed 1,2-dicaprin/Orlistat monolayers were first performed in order to determine their interfacial properties (Figure 1A). The surface pressure (Π)-molecular area curves deduced from compression isotherms were comparable to those previously published [START_REF] Tiss | Surface behaviour of bile salts and tetrahydrolipstatin at air/water and oil/water interfaces[END_REF]. For pure compounds, the mean value of the characteristic parameters (surface pressure, Πcoll; molecular area, Acoll) obtained at the collapse point were: Πcoll = 44.9 mN m -1 / Acoll = 40.6 Å 2 molecule -1 for 1,2-dicaprin (Figure 1A, isotherm 1); and Πcoll = 28.8 mN m -1 / Acoll = 62.1 Å 2 molecule -1 for Orlistat (Figure 1A, isotherm 8). A working surface pressure of Πi = 25 mN m -1 was selected from these isotherms because it is below the collapse pressure of all films and DGL was found to be active on pure 1,2-dicaprin with linear kinetics at this surface pressure (Figure 2A).

The mean molecular area of mixed monomolecular films of 1,2-dicaprin/Orlistat was further determined for various Orlistat mole fractions at this selected surface pressure of 25 mN m -1 . Only slight deviations from ideal mixing (straight dashed line joining the molecular areas of the pure compounds) were observed. Orlistat induced either low expansion effects at Orlistat above 10% (Figure 1B), or on the contrary low condensing effects at Orlistat below 2.0%

(Figure 1C). Such variations amounted to only +7.3% at Orlistat = 25% and +8.2% at Orlistat = 0.3%. For Orlistat ranging from 0 to 1.5%, the mean molecular area (50.0 1.6 Å 2 molecule -1 ) remained close to that of pure 1,2-dicaprin (52.2 Å 2 molecule -1 ) at 25 mN m -1 .

After the characterization of mixed 1,2-dicaprin/Orlistat monolayers, DGL interaction with these monolayers and lipolytic activity was then investigated using the surface barostat technique. As shown in Figure 2A, the forward movement of the mobile barrier (i.e.

consumption of 1,2-dicaprin substrate and rapid desorption of lipolysis products) increased progressively with time to reach a steady-state regime after a lag period (1) increasing with Orlistat. 1 value was defined as the intercept with time axis of the asymptote reached under steady state conditions (Figure 2A). In the absence of Orlistat, the mobile barrier moved forward after a 1 lag time of around 3.5 min following enzyme injection below the monolayer (Figure 2A, curve 1). When Orlistat was mixed with 1,2-dicaprin, 1 value increased and ranged from 18

to 80 min while increasing Orlistat (Table 1). Moreover, the forward movement of the mobile barrier was preceded by a transient backward movement (Lbarrier, mm -Figure 2A) that could reflect an increase in the occupation of the surface of the reaction compartment by either the enzyme adsorbed onto the monolayer or some reaction products before their desorption. This increase in the surface area was quantified as S = Lbarrier  l, l (=61 mm) being the width of the reservoir trough. Like 1 values, S was also found to increase with Orlistat (Table 1).

After making these observations, 1 and S values, as well as the enzyme velocity at steady-state regime (vm), were further used for describing DGL interaction with the mixed monolayers, its inhibition by Orlistat, and its activity on 1,2-dicaprin. Using Eq. 3, DGL residual activity on 1,2-dicaprin (RAE*(%)) was deduced from the experimental calculated vm (Eq. 1) and plotted as a function of Orlistat. As depicted in Figure 2B, only small amounts of Orlistat were required to significantly inhibit the DGL activity. The mole fraction of Orlistat which reduced the enzyme activity to 50% of its initial value (  Orlistat) was found to be around 1.4%. Similar findings were obtained in previous studies [START_REF] Cavalier | Inhibition of human gastric and pancreatic lipases by chiral alkylphosphonates. A kinetic study with 1,2-didecanoyl-sn-glycerol monolayer[END_REF][START_REF] Ransac | Inactivation of pancreatic and gastric lipases by tetrahydrolipstatin and alkyl-dithio-5-(2-nitrobenzoic acid). A kinetic study with 1,2didecanoyl-sn-glycerol monolayers[END_REF][START_REF] Gargouri | Covalent inhibition of digestive lipases: an in vitro study[END_REF], with for instance an   Orlistat of 0.25% in the case of HGL [START_REF] Ransac | Inactivation of pancreatic and gastric lipases by tetrahydrolipstatin and alkyl-dithio-5-(2-nitrobenzoic acid). A kinetic study with 1,2didecanoyl-sn-glycerol monolayers[END_REF] acting on mixed 1,2-dicaprin/Orlistat monolayers spread at 20 mN m -1 .

These results reflect a high affinity of gastric lipase for Orlistat present within a substrate monolayer. Tiss et al. have proposed that the hydrophilic parts of Orlistat, i.e. the reactive -lactone ring and the N-formyl-L-Leucine group could extend more deeply in the aqueous subphase than 1,2-dicaprin molecules, because of their larger polar head groups size [START_REF] Tiss | Surface behaviour of bile salts and tetrahydrolipstatin at air/water and oil/water interfaces[END_REF]. Such interfacial orientation might be a plausible explanation for the strong affinity of lipases for Orlistat, present in mixed film even at low mole fractions, and therefore responsible for its high inhibitory efficiency.

Interestingly for Orlistat values below 1.0%, experimental RAE*(%) were consistently higher than 100% (i.e., RAE*(%) for Orlistat = 0%), with a maximum (RAE*(%) = 140%) at Orlistat = 0.3%.

It was checked that increasing DGL concentration from 8.4 to 60.0 nM did not modify the profile of the experimental inhibition curves obtained for Orlistat  1.0% (Figure 2C). One hypothesis to explain this phenomenon is that the presence of Orlistat or its transient degradation products in the mixed films could trigger DGL activity at low Orlistat before a clear Orlistat-dependent inhibition profile is observed at higher Orlistat (Figure 2B). It was previously observed that the activity of lipolytic enzymes could be remarkably influenced by using mixed monolayers rather than pure substrate monolayers [START_REF] Pieroni | Hydrolysis of mixed monomolecular films of triglyceride/lecithin by pancreatic lipase[END_REF][START_REF] Piéroni | Hydrolysis of mixed monomolecular films of phosphatidylcholine/triacylglycerol by pancreatic phospholipase A2[END_REF][START_REF] Vainio | Action of lipoprotein lipase on mixed triacylglycerol/phosphatidylcholine monolayers. Activation by apolipoprotein C-II[END_REF][START_REF] Arimoto | Activation and inhibition of lipoprotein lipase in mixed monolayers of medium or long chain-triglycerides and phospholipids[END_REF][START_REF] Peters | Influence of Surface Properties of Mixed Monolayers on Lipolytic Hydrolysis[END_REF]. For instance, porcine pancreatic lipase (PPL) activity on trioctanoylglycerol was doubled by progressively diluting the TAG film with non-hydrolysable dilauroylphosphatidylcholine (DLPC) [START_REF] Pieroni | Hydrolysis of mixed monomolecular films of triglyceride/lecithin by pancreatic lipase[END_REF]. DGL activity on 1,2-dicaprin could thus be increased by a more favourable presentation of the substrate to the enzyme in mixed films containing traces of Orlistat and/or its degradation products. Paradoxically, it would be the first time that this phenomenon is observed when the lipid substrate is mixed with small amounts of a lipase inhibitor. Another hypothesis could be however artefacts of calculation.

Measuring an increase in residual lipase activity (more than 100% activity on 1,2-dicaprin alone) could result from an increase in substrate molecular area, higher changes in surface pressure when it is hydrolyzed and thus a larger forward movement of the mobile barrier. It is however difficult to imagine such an increase in 1,2-dicaprin molecular area at constant surface pressure, while the lipase and transient Orlistat degradation products are also present at the interface. In the present work, molecular area of 1,2-dicaprin was considered to be constant for calculations and equal to that estimated from a pure film of substrate (A1,2-dicaprin = 52.2 Å 2 molecule -1 ) when all Orlistat molecules have been hydrolyzed.

Increasing the lipase concentration also resulted in a significant reduction of 1 lag time values up to 72-89% at 60 nM (Table 1), but did not significantly impact the observed hydrolytic step (i.e., RAE*% values -Figure 2C). It is noteworthy that, whatever the lipase concentration in the 8.4-60 nM range, the experimentally determined Lbarrier were found to remain nearly constant for a given Orlistat value. The corresponding calculated mean S values were 1.30 0.02 cm 2 , 2.28 0.10 cm 2 and 3.36 0.11 cm 2 at Orlistat = 0.3%, 0.5% and 1.0%, respectively. According to the interfacial kinetic model developed by Verger et al. [START_REF] Verger | Action of phospholipase A at interfaces[END_REF][START_REF] Verger | Comparative studies of lipase and phospholipase A2 acting on substrate monolayers[END_REF], 1 lag times as well as the increase in the surface area of the film (i.e. S) during lipolysis, were interpreted as being due to the rate-limiting step of enzyme adsorption (E  E*) onto the monolayer. In these conditions, the concomitant increase in 1 lag time and Lbarrier (up to  -10 mm at Orlistat = 1.5% -Figure 2A) with Orlistat, may be associated with DGL adsorption onto the mixed monolayer. However, since the inhibition by Orlistat has been shown to be reversible with some lipases (Scheme 1), compound 2 resulting from the hydrolysis of Orlistat (Scheme 1C) might also be responsible for the transient increase in the surface area. This more polar molecule resulting from the opening of the -lactone ring might remain at the interface and occupied a larger molecular area. To check these hypotheses, additional experiments with a pure monomolecular film of Orlistat were performed.

Evidence for the reversibility of DGL inhibition by Orlistat.

A pure film of Orlistat was spread over both the reaction and the reservoir compartments of the zero-order trough. After DGL injection (60 nM final concentration) below the monolayer, an important backward movement of the mobile barrier was first recorded (up to -34.4 mm -Figure 2D) followed by a slow and linear forward movement of the mobile barrier. This later finding is consistent with a slow hydrolysis of Orlistat by DGL followed by the formation of soluble degradation products according to the pathway described in Scheme 1. DGL inhibition by Orlistat therefore appears as a reversible process as previously shown with HCEL and HPL [START_REF] Borgstrom | Mode of action of tetrahydrolipstatin: a derivative of the naturally occurring lipase inhibitor lipstatin[END_REF][START_REF] Tiss | Inhibition of human pancreatic lipase by tetrahydrolipstatin: Further kinetic studies showing its reversibility[END_REF][START_REF] Stalder | Tetrahydrolipstatin: Degradation products produced by human carboxyl-ester lipase[END_REF]. Since Orlistat degradation leads to a forward movement of the mobile barrier, one can therefore conclude that the initial backward movement of the barrier is mainly due to enzyme adsorption and not to the accumulation at the interface of insoluble Orlistat degradation products.

From these experiments, it was possible to estimate the velocity of pure Orlistat degradation by DGL (vm = 5.34 (0.18)  10 9 molecule cm -2 s -1 ). This value represents around 0.40% of the lipolytic rate reached by DGL on pure 1,2-dicaprin film at the same enzyme concentration (CE0 = 60 nM). Making the assumption that DGL would act at the same rate on Orlistat in mixed monolayers, all Orlistat molecules could be hydrolyzed by the lipase in 1.4 min, 2.3 min and 4.5 min at Orlistat of 0.3%, 0.5% and 1.0%, respectively. Although these theoretical time values are lower than the 1 lag times observed at the same Orlistat before recording DGL activity on mixed 1,2-dicaprin/Orlistat monolayers (from 4.3 to 7.2 min -Table 1), they are in the same order of magnitude. This strongly supports the hypothesis that 1 lag time correlates with DGL inhibition by Orlistat and subsequent reactivation, i.e. Orlistat consumption before the 1,2-dicaprin substrate becomes a more accessible ligand for DGL. This is the first time that the reversibility of lipase inhibition by Orlistat is observed using the monomolecular film technique and mixed films of 1,2-dicaprin and Orlistat. Previous studies of this kind conducted on other mammalian digestive lipases (i.e., HGL, HPL and PPL) reported a rapid and total inactivation of the lipases without mention that the enzyme could restore some of its original activity after a long lived transient molecular poisoning induced by Orlistat [START_REF] Cavalier | Inhibition of human gastric and pancreatic lipases by chiral alkylphosphonates. A kinetic study with 1,2-didecanoyl-sn-glycerol monolayer[END_REF][START_REF] Ransac | Inactivation of pancreatic and gastric lipases by tetrahydrolipstatin and alkyl-dithio-5-(2-nitrobenzoic acid). A kinetic study with 1,2didecanoyl-sn-glycerol monolayers[END_REF][START_REF] Gargouri | Covalent inhibition of digestive lipases: an in vitro study[END_REF]. Further studies are now required to determine whether DGL is unique among lipases or the reactivation of other lipases was previously missed using the monomolecular film technique.

This second hypothesis is supported by the fact that the reversibility of HPL inhibition has been shown using the pH-stat technique [START_REF] Tiss | Inhibition of human pancreatic lipase by tetrahydrolipstatin: Further kinetic studies showing its reversibility[END_REF].

Using the reversible inhibition of DGL for monitoring lipase adsorption and activity in the course of a single experiment.

At this stage of the study, it appeared that the backward and forward movements of the mobile barrier observed after injecting DGL below a mixed 1,2-dicaprin/Orlistat film were associated with lipase adsorption onto the film and substrate hydrolysis, respectively. The first step of lipase adsorption was characterized by 1 lag time and S (the surface covered by the backward shift of the barrier). Because of the much higher affinity of DGL for Orlistat than for 1,2-dicaprin, no apparent lipase activity was recorded before the reversible inhibition of DGL by Orlistat led to a complete conversion of Orlistat into -hydroxyacid degradation products (Scheme 1C) that were further removed from the lipid interface. After that, a rapid hydrolysis of 1,2-dicaprin molecules by "reactivated" DGL was observed and characterized by the enzyme velocity at steady-state regime (vm).

To confirm these assumptions, a series of independent experiments were performed under the same conditions used for hydrolysis kinetics (i.e.: Πi = 25 mN m -1 ; [DGL] = 8.4 nM; Orlistat = 0.3, 0.5, 1.0 or 1.5% in mixed films), except that the surface pressure was not kept constant using the barostat mode after injecting the lipase in the subphase. Variations in surface pressure were thus recorded with time as usually performed for determining adsorption kinetics on a non-hydrolysable monomolecular film [START_REF] Bénarouche | New insights into the pH-dependent interfacial adsorption of dog gastric lipase using the monolayer technique[END_REF]. In each case, an increase in the surface pressure was first observed after DGL injection, up to a plateau value that was maintained for a few minutes before a drastic drop in surface pressure occurred (Figure 3A). It was hypothesized that these typical bell-shaped variations were resulting from (i) the adsorption of DGL onto the mixed monolayer and (ii) the subsequent hydrolysis of 1,2-dicaprin and desorption of lipolysis products.

The inflexion point on the  = f(t) curves was then determined and the corresponding time was defined as the induction time (2) for observing lipolysis product desorption and thus enzyme activity (Figure 3A). Interestingly, 2 values were found to be almost equal to the 1 values determined in previous experiments with the barostat mode, 1 being the lag time for measuring steady-state kinetics of 1,2-dicaprin hydrolysis (Figures 3B-C). Both 1 and 2

showed an increase that was proportional to Orlistat values (Figure 3C). Moreover, by varying the DGL concentration from 8.4 to 60 nM, 1 and 2 lag times not only remained almost identical but also displayed the same hyperbolic decay pattern which reached a minimum plateau value at 40 nM (Figure 3D). In the absence of Orlistat, 1 and 2 values were around 3.5 min. at CE0 = 8.4 nM and not experimentally observed above this concentration.

From the results obtained here after injection of DGL below mixed 1,2-dicaprin/Orlistat monolayers, it becomes obvious that the forward movement of the mobile barrier observed using the surface barostat mode (Figure 2A) and the significant drop in surface pressure observed in the absence of surface pressure control (Figure 3A) are both related to the hydrolysis of 1,2-dicaprin film by the DGL. The observation of a lag time (1) or induction time (2) for measuring 1,2-dicaprin hydrolysis is associated with the presence of Orlistat mixed with the substrate monolayer. Using two independent experimental set-ups for determining 1 and 2, it appeared that these characteristic time values were nearly identical and varied linearly with Orlistat values (Figure 2C). Both lag times are therefore characteristic of the inhibition period occurring before Orlistat is fully hydrolyzed. The lipolytic activity, recorded after Orlistatdependent lag times, thus reflects a complete (at low Orlistat values, Figure 2A) or partial (Figure 2D) reactivation of the DGL inhibited after adsorption onto the mixed lipid film. The partial reactivation of DGL after inhibition by Orlistat suggests the formation of two distinct DGL-Orlistat complexes. The first one (E*Io; Figure 4) being formed rapidly by covalent interaction (opening of the -lactone ring) and later on, further hydrolyzed to restore lipase activity (fast and reversible inhibition step); while the second one (E*I2; Figure 4) may involve a different mode of interaction between Orlistat and DGL (probably covalent, based on mass spectrometry analysis as shown in Figure S1 in Supplementary Material) and leads to a slow and irreversible lipase inhibition (or at least a long-life lipase-inhibitor complex stable during the assay period).

Such a hypothesis was previously raised by Tiss et al. to explain the partial reversibility of human pancreatic lipase inhibition by Orlistat in bulk assays [START_REF] Tiss | Inhibition of human pancreatic lipase by tetrahydrolipstatin: Further kinetic studies showing its reversibility[END_REF].

Determination of DGL apparent interfacial kinetic parameters.

Based on the kinetic model presented in Figure 4 and assuming that the surface pressure increase recorded in presence of Orlistat was due to DGL binding to the mixed film, adsorption kinetics at Πi = 25 mN m -1 were recorded for DGL concentrations ranging from 8.4 to 60 nM and Orlistat values of 0.3, 0.5 and 1.0%. The adsorption (ka) and desorption (kd) rate constants corresponding to the interaction of DGL with the mixed film were determined by curve-fitting experimental data points (only those corresponding to an increase in surface pressure up to the inflection point) to Eq. 4 [START_REF] Bénarouche | New insights into the pH-dependent interfacial adsorption of dog gastric lipase using the monolayer technique[END_REF]. ka and kd values obtained for the three different Orlistat values (0.3%, 0.5% and 1.0%) appeared to be similar (Figure S2 in Supplementary Material) and mean values were therefore estimated: mean ka = 7.94 (0.21) × 10 4 M -1 s -1 and mean kd = 6.56 (0.42) × 10 -4 s -1 .

As depicted in Figure 5A, the resulting adsorption equilibrium coefficient KAds = (ka/kd) remained almost constant in the 0.3-1.0% Orlistat range (Table S1 in Supplementary Material).

From these findings and the fact that mixed 1,2-dicaprin/Orlistat monolayers show a quasi-ideal mixing for Orlistat values between 0.0% and 1.5% (Figure 1C), the, extrapolation of KAds value to Orlistat = 0 (i.e., the y-intercept of the linear plot [KAds = f(Orlistat)]) was made to estimate the interfacial binding affinity (KAds ( Orlistat =0) = 1.22 (0.05) × 10 8 M -1 ) between DGL and pure 1,2-dicaprin monolayer at a surface pressure of 25 mN m -1 . It is worth noticing that KAds ( Orlistat =0)

is nearly identical to the interfacial binding affinity determined by Chahinian et al. using DGL and a solid hydrophobic surface (KAds = 1.54 × 10 8 M -1 ) at the same pH value of 5.0 [START_REF] Chahinian | How gastric lipase, an interfacial enzyme with a Ser-His-Asp catalytic triad, acts optimally at acidic pH[END_REF], and it is in the same order of magnitude as the recently reported interfacial binding affinity between DGL and the non-hydrolysable DLPC monolayer (KAds = 0.32 × 10 8 M -1 ) at the same pH (5.0) and the same surface pressure (Πi = 25 mN m -1 ) [START_REF] Bénarouche | New insights into the pH-dependent interfacial adsorption of dog gastric lipase using the monolayer technique[END_REF].

Estimation of the amount of DGL adsorbed onto mixed monolayers.

From the experimentally-determined adsorption kinetic parameters (ka, kd, KAds), it was then possible to estimate, by means of Eq. 5, the theoretical surface concentration of adsorbed DGL (, molecule cm -2 ) onto the mixed films for each of the three Orlistat mole fractions tested (Table S1 in Supplementary Material).

As previously observed with KAds (Figure 5A),  values did not vary significantly as a function of Orlistat (Figure 5B). An extrapolation to Orlistat = 0 was then made to estimate the apparent interfacial concentration of DGL ( ( Orlistat =0) = 66.1 (0.28) × 10 10 molecule cm -2 ) adsorbed on a pure 1,2-dicaprin monomolecular film spread at 25 mN m -1 over a buffer at pH 5.0. Knowing the area of the reaction compartment and the amounts of DGL injected in the subphase, it was estimated that around 10.6% of DGL was adsorbed onto the lipid film, while 89.4% DGL would remain in the bulk phase, assuming that the adsorption of the lipase onto the Teflon surface of the trough is negligible. This was previously shown in the case of human gastric lipase (HGL) using an ELISA for estimating HGL recovery in the bulk phase and monolayer [START_REF] Cavalier | Inhibition of human gastric and pancreatic lipases by chiral alkylphosphonates. A kinetic study with 1,2-didecanoyl-sn-glycerol monolayer[END_REF][START_REF] Aoubala | Interfacial binding of human gastric lipase to lipid monolayers, measured with an ELISA[END_REF][START_REF] Marguet | Interfacial and or molecular recognition by lipases of mixed monomolecular films of 1,2-dicaprin and chiral organophosphorus glyceride analogues?[END_REF]. Using Eq. 6, the surface areas occupied by a single molecule of the adsorbed protein (AE*, Å 2 molecule -1 ) onto the latter mixed films were calculated (Table S1 in Supplementary Material), and the corresponding values were plotted as a function of the relative surface increase (mean S/S -Table 1) related to Orlistat (Figure 5C). From both S/S and AE* values deduced from two independent experiments, the limiting area ( ( Orlistat =0) = 738 22 Å 2 molecule -1 ) occupied by the first DGL molecules adsorbed onto 1,2-dicaprin film could be estimated by extrapolating AE* at zero relative surface increase (i.e., S/S = 0 corresponding to Orlistat = 0; Figure 5C) according to the method reported by Bougis et al. [START_REF] Bougis | Penetration of phospholipid monolayers by cardiotoxins[END_REF].

It is noteworthy that these data,  ( Orlistat =0) and A ( Orlistat =0), are very close to those recently estimated (*-DLPC = 49.0 × 10 10 molecule cm -2 ; AE*-DLPC = 674 Å 2 molecule -1 ) for DGL adsorption onto a DLPC monolayer at the same pH and Πi [START_REF] Bénarouche | New insights into the pH-dependent interfacial adsorption of dog gastric lipase using the monolayer technique[END_REF]. All these findings therefore reinforce the validity of our experimental approach to quantify the DGL binding onto mixed 1,2-dicaprin/Orlistat monolayers. In the present case and based on the calculated molecular area of 738 Å 2 for DGL interacting with 1,2-dicaprin monolayer, the lipase surface occupancy (4.9% 0.02%) was similar to the one previously determined (3.3% 0.07%) when using DLPC films [START_REF] Bénarouche | New insights into the pH-dependent interfacial adsorption of dog gastric lipase using the monolayer technique[END_REF]. Lipase surface occupancy with a lipid film spread at the air-water interface was therefore much lower than the surface occupancy observed with the same enzyme (DGL) adsorbed onto a hydrophobic solid surface [START_REF] Chahinian | How gastric lipase, an interfacial enzyme with a Ser-His-Asp catalytic triad, acts optimally at acidic pH[END_REF] (99.1% surface occupancy; 505 × 10 10 molecule cm -2 at pH 5.0 taking into account a mean section of approximately 196 × 10 -15 cm 2 for DGL molecule). As previously performed in the case of DGL interacting with a DLPC monolayer [START_REF] Bénarouche | New insights into the pH-dependent interfacial adsorption of dog gastric lipase using the monolayer technique[END_REF], it was estimated that the cross-section of DGL 3-D structure (PDB file 1K8Q in Protein Data Bank) fitting with the molecular area of 738 Å 2 for DGL interacting with 1,2-dicaprin monolayer at pH 5 and 25 mN m -1 would be located at around 12.0 Å from the protein surface when the lipase was oriented with the active site entrance facing the interface plane (Figure 6). One can thus speculate that the penetration depth of DGL in the 1,2-dicaprin monolayer is found within this range, and that the enzyme penetrates the interface in a compact form and not through a limited portion of the enzyme molecule.

By replacing the calculated value of  ( Orlistat =0) in Eq.

Conclusion

The reversibility of gastric lipase inhibition by Orlistat was shown here for the first time using the surface barostat technique and 1,2-dicaprin monolayers as substrate. This inhibition process is rather unique since Orlistat seems to form two distinct lipase-inhibitor complexes at the lipid interface. A fast covalent and reversible inhibition first allows blocking transiently the lipase activity before Orlistat is degraded and enzyme activity restored. When Orlistat mole fraction exceeds 1%, the lipase activity is however not fully restored, suggesting a secondary and irreversible binding mode for Orlistat in DGL active site. While the complete understanding of DGL inhibition by Orlistat at the interface still deserves some investigations, it seems that the presence of Orlistat mixed with 1,2-dicaprin has no significant effect on DGL adsorption/desorption equilibrium. Using mixed 1,2-dicaprin/Orlistat monolayers, it was thus possible for the first time to determine the adsorption and desorption rate constants as well as the kcat/K*M ratio for a lipase, DGL, acting on a monomolecular film of substrate spread at the air-water interface. In conclusion, the methods and results reported here are giving access to essential kinetic parameters describing the mechanism of action of lipases on an insoluble substrate and bring new insight on the reversible inhibition of gastric lipase by Orlistat. It should be stressed however that the mechanism of DGL inhibition by Orlistat investigated here may result from specific biochemical properties of this lipase, and should not be stated as a general mode of action before additional data are obtained with other lipases.

  2 and using the experimentally determined rate of 1,2-dicaprin hydrolysis by DGL in the absence of Orlistat (vm ( Orlistat =0) -Figure2A, curve 1), it was possible to estimate the kcat/K*M ratio between the interfacial catalytic rate constant (kcat; s -1 ) and the interfacial Michaëlis-Menten constant (K*M; molecule cm -2 ) for DGL acting on pure 1,2-dicaprin monolayer. As shown in Figure7, kcat/K*M displayed a hyperbolic variation as a function of increasing DGL concentration, and reached a plateau value of around 10.7 (0.09) × 10 -15 cm 2 molecule -1 s -1 above 40 nM DGL. Such finding, also observed in 1 and 2 variations as a function of the lipase concentration in Figure3D, suggests that 40 nM would correspond to the limiting lipase concentration beyond which no more DGL molecule is adsorbed onto the 1,2-dicaprin monolayer.

1 .

 1 Scheme 1. Structure of Orlistat (A), its mode of action in lipase inhibition (B) and its

Figure 1 .

 1 Figure 1. (A) Surface pressure versus molecular area (Π-A) curves of mixed 1,2-

Figure 2 .

 2 Figure 2. Monomolecular film experiments using the surface barostat mode at 25 mN m -1 and

Figure 3 .

 3 Figure 3. Determination of 1 and 2 characteristic times. (A) Typical variation in surface

Figure 5 .

 5 Figure 5. Variation of (A) the adsorption equilibrium coefficient (KAds) and (B) the surface

Figure 6 .

 6 Figure 6. Putative orientation of DGL penetrating into a 1,2-dicaprin monolayer spread at 25 mN m -1 . The structure of the DGL is shown as ribbon (panel A) and molecular surface (panels

Figure 7 .

 7 Figure 7. Variation of the interfacial specificity constant (kcat/K*M) of DGL acting on pure

a

  ND: not determined. Mean S/S (S = 31.2 cm 2 ) represents the relative surface increase in the reaction compartment of the "zero-order" Teflon trough. Data are presented as mean values  standard deviations of three independent assays (CV% < 5.0%).

Figure 6 44Figure 7

 67 Figure 1

Table 1 .

 1 Values of 1 lag time and S surface increase determined for various lipase concentration (CE0 = 8.4 to 60 nM) during DGL kinetics with 1,2-dicaprin monolayer containing variable mole fractions (Orlistat) of Orlistat at Πi = 25 mN m -1 . a

	Orlistat	8.4 nM	1 (min) 20 nM 40 nM	60 nM	S (cm 2 ) 8.4 nM 20 nM 40 nM 60 nM	Mean S/S
	0.3%	18.3 0.7	8.8 0.4 5.7 0.1 4.3 0.2	1.34	1.28	1.30	1.32	4.2%
	0.5%	26.0 0.6 12.0 0.4 7.5 0.3 7.2 0.1	2.35	2.28	2.12	2.38	7.3%
	1.0%	53.5 1.7 15.7 0.7 9.9 0.2 6.1 0.3	3.34	3.54	3.30	3.26 10.8%
	1.5%	74.6 2.5	ND	ND	ND	5.37	ND	ND	ND 17.2%

Acknowledgements

A. Bénarouche was supported by a PhD fellowship from the Ministère de l'Enseignement Supérieur et de la Recherche. This work was supported by the CNRS and by the LISA Carnot Institute (Convention ANR n°07-CARN-009-01). Authors would like to thank Dr. R. Lebrun and R. Puppo (at the Proteomics platform of the Institut de Microbiologie de la Méditerranée, Marseille, France) for their precious help and support with the mass spectrometry experiments.

Supplementary Material

Supplementary Data (Figures S1-S2 and Table S1) associated with this article can be found in the online version.


Quentin Desvaux
email: quentin.desvaux@inria.fr

«Metabolism studies: materiality and relationality in

Keywords: territorial metabolism, Grenoble Alpes Métropole, construction waste sector, power relations, governance

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

Analysis of the circulation of material flows on the territory of Grenoble Alpes Métropole: the influence of power relations in the building sector

Quentin Desvaux

To cite this version:

Quentin Desvaux. Analysis of the circulation of material flows on the territory of Grenoble Alpes Métropole: the influence of power relations in the building sector. 2022 -International Symposium on Metabolism studies: materiality and relationality in the Anthropocene, Jun 2022, Lyon, France. pp.1-3. hal-03885905

Based on the directives of its CODEC 1 , the waste department of Grenoble Alpes Métropole has initiated an ambitious policy aiming to reappropriate waste deposits through the transformation of local production systems. Given the convergence of these territorial issues of governance and change in the industrial system with the global issues of resource scarcity and various forms of pollution, a collaboration has emerged as a CIFRE 2 thesis between Grenoble Alpes Métropole, the CREG laboratory and the STEEP research team. This research work in political economy allows an open disciplinary approach (Figuière et al., 2018) in order to analyze the waste management sectors in the metropolitan area from two complementary approaches: a functional approach that reveals the interdependent relationships between society and its environment through the analysis of flows, and a relational approach to integrate neo-Marxist interpretations of the structure of flows and reflect the historical and social processes responsible for the asymmetries of power (Herbelin, 2018).

The use of the metabolic approach in a previous work for the analysis of the bio-waste sector highlighted the loss of some flows from the territory to a private industrial deconditioning facility 3 whose profitability is based on the concentration of many regional flows. The metabolic approach thus 1 Wastes and Circular Economy Contract of Objectives.

2 Industrial formation and research agreement.

3 A deconditioning facility is a piece of equipment that separates organic materials from the packaging that contains them, thus allowing waste producers to avoid the sorting gesture.

made it possible to reveal a deep contradiction between the willingness of the authority to valorize these wastes in an organic way and the implementation of a non-inclusive sorting obligation at the source. This contradiction is then responsible for the dependency of the territory on this infrastructure.

Following the model of this contradiction, the government is currently developing creating a national recycling sector for construction materials that is not very coherent given the lack of infrastructure for the production materials from recycled sources. By ignoring the hierarchy of treatment methods (i.e.

first reuse) which are generally supported by local structures, this strategy of concentration, based on an efficient management of flows and the free collection of waste, promotes the domination of private operators and runs against the challenge of territorialization of the stocks, the responsibility of waste producers and the transformation of the economic system.

This communication aims to provide answers to the following questions: How can the local authority integrate collective and local initiatives for the recovery of waste stocks of the building sector in a context of regulations that favor the logic of (inter)national circulation of flows? What governance should be put in place to encourage the emergence of small infrastructures and to promote their access to waste flows?

By anchoring the metabolic approach in the epistemological framework of political economy, this work aims, on the one hand, to report on the vulnerabilities of the construction waste sector, and on the other hand, to analyze the power relationships that structure this sector. This perspective is a useful addition to the quantitative approaches used in territorial ecology as it focuses on the needs of the stakeholders at the origin of the logic of material flows in a given territory (Bevione, 2021). This analysis of the territory and the interactions between its stakeholders thus questions the interactions between society and the biosphere and becomes part of a process of co-construction of the territory that goes beyond the management of material flows (Debuisson, 2014)

  in order to legitimize Grenoble Alpes Métropole in its public policy choices. Figuière, C., Boidin, B., Diemer, A., 2018. L'Économie Politique du Développement Durable. De boeck, 304 p. Herbelin, A., 2018. Ecologie territoriale et trajectoires de transitions : le cas du Rhône-Médian. Thèse de doctorat en Géographie, sous la direction de Buclet N. & Barles S., Grenoble, Université Grenoble Alpes, 471 p. https://tel.archives-ouvertes.fr/tel-02276808/document

	References:
	Bevione, M., 2021. L'analyse des interactions entre flux et acteurs pour la compréhension des enjeux
	socio-écologiques à l'échelle d'un territoire : application à la production du fromage AOP
	Beaufort dans la vallée de la Maurienne. Thèse de doctorat en Aménagement du territoire, sous la
	direction de Buclet N., Grenoble, Université Grenoble Alpes, 201 p.
	Debuisson, M., 2014. Les modes d'interaction pour une dynamique territoriale soutenable : un apport

à l'écologie territoriale. Thèse de doctorat de l'UTT Développement Durable en Sciences de l'Homme et Société, sous la direction de Buclet N., Troyes, Université de Technologie de Troyes, 504 p. https://tel.archives-ouvertes.fr/tel-01162416