Panelzahra Chavoshpour-Natanzi

Mehdi Sahihi

Encapsulation of quercetin-loaded β-lactoglobulin for drug delivery using modified anti-solvent method

Keywords:

Many scientists use proteins as attractive bio-availability enhancers for natural compounds and pharmaceuticals which have poor water solubility, due to their natural abundance, amphiphilic nature, and desirable biocompatibility. Here, we investigate the preparation, characterization, and application of β-Lactoglobulin (BLG) based nanoparticles for encapsulation of quercetin, systematically. We used anti-solvent method that is common for nano particle preparation of water-soluble proteins. The procedure involves partial unfolding of protein molecules, limited aggregation in the presence of anti-solvent, crosslinking via chemical linker, and refolding of the constituent monomers. The results showed that acetone anti-solvent has significant effect on accumulation of BLG-quercetin nanoparticles. Adjustment of acetone content to the value of 10% v/v (acetone/water) followed by mild evaporation led to a notable improvement in Encapsulation Efficiency (EE%) and Loading Efficiency (LE%), which raised LE to 13.9%. In addition, reducing glutaraldehyde amount to 50% of equivalent, led to toxicity reduction of the drug carrier system.

The nanoparticles with a mean particle size of about 180-300 nm and semispherical appearance were approved using Atomic Force Microscopic (AFM) and Field Emission Scanning Electron Microscopy (FESEM) methods. Protein nanoparticles may be digested at different stages of the gastrointestinal tract, depending on acidity, ionic strength, or specificity of proteases (pepsin and trypsin). This study suggested that BLG as a resistant protein to peptic digestion forms nanoparticles that are digestible (compared to untreated BLG) by pepsin. As a result, satisfactory controlled release was achieved under simulated fast condition, i.e., digestion in simulated gastric fluid (SGF) at pH = 2 and then in simulated intestinal fluid (SIF). Finally, the mechanism of drug release into the buffer environment was well-fitted by the Korsmeyear-Peppas kinetic model. The conclusions of this study may apply not only to quercetin-BLG system, but also to a wide variety of encapsulation systems involving water-soluble protein and hydrophobic target compound, with adequate LE and reduced toxicity.

Introduction

Drug delivery systems (DDS) are developed to improve the therapeutic properties of pharmaceuticals. These systems release drug at a certain and definite place and affect the distribution and kinetics of drug release in the body [START_REF] Benita | Microencapsulation: Methods and industrial applications[END_REF]. Nanoparticles (NPs) are widely used in drug delivery and have multiple advantages such as small size, controlled release, protection of drug molecules and ability to pass across the blood-brain barrier [START_REF] Yun | Nanoparticles for oral delivery: Targeted nanoparticles with peptidic ligands for oral protein delivery[END_REF]. These properties have made them superior in comparison to conventional DDS.

Nanostructures including polymers, lipids, polysaccharides, and proteins have been explored as DDS. The selection of nanoparticle materials depends on several factors such as NPs size and intrinsic properties of the drug [START_REF] Kreuter | Nanoparticles[END_REF].

The most important challenges are nano-formulations, interaction of immune system proteins with NPs and the creation of a protein crown around them, which plays a key role in the ultimate performance of NPs. Protein based NPs have caught the interest of researchers in the recent years due to their desirable properties such as low toxicity, biodegradability, biocompatibility and possibility of preparing various formulations [START_REF] Lohcharoenkal | Protein nanoparticles as drug delivery carriers for cancer therapy[END_REF].

Protein defined charge and their hydrophilic and hydrophobic domains [START_REF] Bengoechea | formation of protein nanoparticles by controlled heat treatment of lactoferrin: Factors affecting particle characteristics[END_REF]) make them a good choice for nanoparticle formulations including gelatin [START_REF] Jahanshahi | Gelatin nanoparticle fabrication and optimization of the particle size[END_REF], albumin [START_REF] Kratz | Antitumour activity of acid labile transferrin and albumin doxorubicin conjugates in in vitro and in vivo human tumour xenograft models[END_REF], gliadin [START_REF] Ezpeleta | Gliadin nanoparticles for the controlled release of all-trans-retinoic acid[END_REF] and milk proteins [START_REF] Livney | Milk proteins as vehicles for bioactives[END_REF].

One of the most important whey proteins is β-Lactoglobulin (BLG) that is a member of the lipocalin superfamily [START_REF] Nacka | Induction of new physicochemical and functional properties by the glycosylation of whey proteins[END_REF]. It has made up of 162 amino acids with a molecular weight of about 18.3 kDa [START_REF] Ragona | EF loop conformational change triggers ligand binding in β-lactoglobulins[END_REF]. Previous studies showed that BLG can bind and transport numerous amphiphilic and hydrophobic ligands [START_REF] Apenten | Stability parameters for β-lactoglobulin thermal dissociation and unfolding in phosphate buffer at pH 7.0[END_REF][START_REF] Divsalar | Comparative analysis of refolding of chemically denatured β-lactoglobulin types A and B using the dilution additive mode[END_REF][START_REF] He | αs-casein inhibits the pressure-induced aggregation of β-lactoglobulin through its molecular chaperone-like properties[END_REF][START_REF] Ricchiuto | Structural and dynamic roles of permanent water molecules in ligand molecular recognition by chicken liver bile acid binding protein[END_REF]. Interaction of BLG with polyphenols [START_REF] Kanakis | Milk β-lactoglobulin complexes with tea polyphenols[END_REF]Sahihi, Ghayeb, & Bordbar, 2012;[START_REF] Sahihi | Interaction of β-lactoglobulin with resveratrol: Molecular docking and molecular dynamics simulation studies[END_REF], phospholipids [START_REF] Lefevre | Interaction of β-lactoglobulin with phospholipid bilayers: A molecular level elucidation as revealed by infrared spectroscopy[END_REF], antioxidants [START_REF] Sahihi | Interaction of β-lactoglobulin with resveratrol: Molecular docking and molecular dynamics simulation studies[END_REF], fatty acids [START_REF] Mohammadi | Interaction of curcumin and diacetylcurcumin with the lipocalin member β-lactoglobulin[END_REF], vitamin D and cholesterol [START_REF] Wang | Binding of vitamin D and cholesterol to β-lactoglobulin[END_REF], aromatic hydrocarbons [START_REF] Invernizzi | In vivo aggregation of bovine β-lactoglobulin is affected by Cys at position 121[END_REF] and so on has been investigated, previously. Besides, BLG demonstrates a significant resistance to peptic digestion due to its compact folded conformation and abundance of rigid β-sheets in its structure. The results of previous studies showed that only 9% of BLG is degraded after 4 h of incubation with pepsin [START_REF] Teng | Cationic β-lactoglobulin nanoparticles as a bioavailability enhancer: Protein characterization and particle formation[END_REF]. On the other hand, it is much more readily degraded by trypsin in the small intestine [START_REF] Sahu | Encapsulation of curcumin in Pluronic block copolymer micelles for drug delivery applications[END_REF].

Flavonoids are a large group of phenolic components of plants. Quercetin, one of the most wellknown flavonoids, has been included in the human diet for a long history and is present in various fruits and vegetables [START_REF] Hertog | Content of potentially anticarcinogenic flavonoids of 28 vegetables and 9 fruits commonly consumed in The Netherlands[END_REF]. The use of quercetin has been widely related with various health benefits, including antioxidant, anti-inflammatory, antiviral and anticancer properties as well as its function to ease some cardiovascular diseases. Despite the great benefits of quercetin, it has some disadvantages such as poor water solubility, low bioavailability, chemical instability and short biological half-life which may reduce its efficiency when is used in the food and pharmaceuticals [START_REF] Cai | Bioavailability of quercetin: Problems and promises[END_REF].

In the past decade, many studies have been done on protein NPs. Antçnio et al., prepared soy protein NPs using anti-solvent method [START_REF] Antçnio | Bovine serum albumin nanoparticles containing quercetin: Characterization and antioxidant activity[END_REF]. The soy protein NPs were also used to load folic acid [START_REF] Teng | Nanoparticles synthesized from soy protein: Preparation, characterization, and application for nutraceutical encapsulation[END_REF]. The results showed better stability of folic acid compared to its free state and confirmed that 57% of the drug was encapsulated in nanoparticles. Reduction of particles size and increasing the amount of drug loading are important in NPs preparation. Therefore, they synthesized soy protein-polysaccharide complexes that could improve the properties of soy protein NPs. The results showed that vitamin D loading capacity was about 80.5%-90.5% and the size of particles was around 162-243 nm. Also, the formed complex showed good stability in the various ranges of pH (Teng, Luo, Wang, Zhang, & Wang, 2013). Rahiminejad et al., developed the bovine serum albumin (BSA) protein nanoparticles and evaluated different conditions such as pH, temperature, and initial protein concentration to achieve suitable particle size [START_REF] Rahimnejad | Production of biological nanoparticles from bovine serum albumin for drug delivery[END_REF]. Recent studies led to the preparation of BLG NPs and loading of various drugs into it due to its unique structure and function as an ideal carrier to transport of bioactive molecules. Recently, curcumin was encapsulated into the BLG NPs and was examined in different conditions of anti-solvent content, the amount of crosslink agent and various ratios of curcumin/BLG NPs. Also, the release of the drug in simulated gastric fluids (SGF) and simulated intestinal fluids (SIF) was investigated. The results showed that encapsulated curcumin has better resistance to digestion than free curcumin [START_REF] Teng | Insight into curcumin-loaded β-lactoglobulin nanoparticles: Incorporation, particle disintegration, and releasing profiles[END_REF].

The anti-solvent method is one of the most common methods to prepare the Nps of proteins that are soluble in water and unstable in some organic solvents (a wide range of albumins and globulins). However, this method has drawbacks that limit its using. For example, the loading efficiency of the prepared protein NPs is mostly lower than the other methods. The second weakness lies in toxicity of chemical materials that are necessary for NPs preparation. The presence of glutaraldehyde and acetone as a cross-linker and anti-solvent, respectively, are concerns for the safety of this method [START_REF] Ezpeleta | Gliadin nanoparticles for the controlled release of all-trans-retinoic acid[END_REF]. The anti-solvent method contains four steps, i.e., preparation of protein solution; acetone addition; glutaraldehyde addition and evaporation. In the recent studies, the typical protocol for preparation of protein NPs was modified due to increase the amount of curcumin loaded into protein NPs and reduce the toxicity of DDS [START_REF] Teng | Insight into curcumin-loaded β-lactoglobulin nanoparticles: Incorporation, particle disintegration, and releasing profiles[END_REF].

The physical and chemical properties of the used protein and drug have various effects on the preparation and characteristics of NPs. In fact, the formation of nanoparticles depends on increasing of protein unfolding and decreasing its hydrophobic intramolecular interactions. During the formation of the nanoparticles, the protein undergoes conformational changes depending on its composition, concentration, crosslinking agent and preparation conditions such as pH, ionic strength and type of the solvent (D'Mello, Das, Das, Pathak, & Thassu, 2009). Also, a drug can be loaded either by encapsulation inside the nanoparticle or by interaction with the protein through covalent or noncovalent interactions. It is well known that the loading rate of the drug in nanoparticles, will affect on the physical and chemical properties of the drug [START_REF] Vandervoort | Preparation and evaluation of drug-loaded gelatin nanoparticles for topical ophthalmic use[END_REF]. Therefore, our purpose is fabrication of small nanoparticles with narrow size distribution as a carrier for DDS. BLG can be used for the development of protein NPs due to its importance as a suitable drug carrier. In the present paper, we used the modified anti-solvent method for preparation of BLG NPs in different conditions such as pH, acetone content, initial protein concentration and quercetin/BLG ratios. Then, it was introduced as a DDS to transfer of quercetin; and the release of quercetin in SGF and SIF was also investigated.

Materials and methods

Materials.

Bovine BLG (90% purity), pepsin (3200-4500 units/mg protein), trypsin (10000 units/mg protein), and quercetin (98% purity) were purchased from Sigma-Aldrich (St. Louis, MO, USA). Potassium hydrogen phosphate, potassium dihydrogen phosphate, hydrochloric acid, sodium acetate, acetic acid, sodium hydroxide, acetone, ethanol, tween 80 and glutaraldehyde were purchased from Merck chemical Co. All of the chemicals were analytical grade and were used without further purification.

Preparation of quercetin-loaded BLG NPs

BLG NPs were prepared by modified desolvation method [START_REF] Teng | Nanoparticles synthesized from soy protein: Preparation, characterization, and application for nutraceutical encapsulation[END_REF]. The whole process was done in 800 rpm constant stirring. BLG was dissolved in deionized water at 5, 10 and 15 mg/ml and quercetin was dispersed in acetone at 2 mg/ml, and were equilibrated for 1 h. Pure acetone was added dropwise to BLG dispersion (Up to 1.5-fold of the initial volume of BLG solution) and an appropriate amount of quercetin solution was added to achieve 5, 10, and 15%, w/w quercetin/protein ratios. Additional pure acetone was then added to total volume of 10 mL to decrease the particle concentration [START_REF] Weber | Desolvation process and surface characterisation of protein nanoparticles[END_REF] and the solutions were equilibrated for 30 min. The final content of acetone before crosslinking was about 95% v/v. Two levels (50, and 100% equivalent) of glutaraldehyde as a chemical cross-linker were applied.

Theoretically, each milligram of BLG needs 40 μg glutaraldehyde for stoichiometric crosslinking [START_REF] Teng | Cationic β-lactoglobulin nanoparticles as a bioavailability enhancer: Protein characterization and particle formation[END_REF]. After 16 h of crosslinking, various solutions with final acetone content ranged from 10 to 90% v/v were prepared. It can be inferred that the evaporation process with continuous decreasing in acetone content, may be critical for encapsulation of quercetin. Hence, after 1 h of equilibration, the acetone was evaporated slightly at room temperature under reduced pressure using a vacuum oven (Frapajoohesh, IRAN) to remove acetone. Evaporation step lasted about 3 h and additional water was then added to achieve a final volume of 5 mL. The final dispersion was stored at 4 °C for further analyzes. The initial and final pH values of the dispersions were about 7.

Quantitative analysis

For quantitative analysis; the BLG-quercetin NPs were prepared based on the above procedure. Also, 100% equivalent of glutaraldehyde was used and mixed with aqueous acetone to achieve various acetone contents. After equilibration for 1 h, the dispersion was centrifuged (9000 g, 30 min, room temperature). The insoluble quercetin was recovered in the precipitate and dissolved in pure acetone, whereas the supernatant was subjected to ultrafiltration by centrifugation (5000 g, 15 min, room temperature) using a Macrosep centrifuge tube (MW cutoff 10 kDa; Pall Corp., Ann Arbor, MI, USA). The filtrate containing non-bound quercetin was recovered and diluted with pure acetone. The concentrations of the subsequent mixtures were measured using UV-Vis spectroscopy (Lambda 265, PerkinElmer) at λ = 375 nm.

Characterization of quercetin-loaded BLG NPs

Surface charge, size and morphology of BLG NPs were measured using Zeta potential (ZP) and DLS (dynamic light scattering) (HORIBA SZ-100) or AFM (Dualscop C-26, DME Germany) methods, respectively. Particle size and surface charge determination are essential for appropriate characterization of NPs. DLS and ZP measurements have gained popularity as simple, easy and reproducible methods to determine particle size and surface charge, respectively. AFM method was used under tapping mode to measure the topological shape of BLG NPs. The prepared BLG NPs were spread and dried onto Lamel surface. Sample topologies were generated by recording the vertical movements during scanning and the particle images were analyzed with the DME-SPM software.

The quercetin-loaded BLG NPs were characterized by Fourier-transform infrared (FT-IR) and Xray diffraction (XRD) analyses. Samples were freeze-dried and mounted onto a Jasco FT/IR 6300 spectrometer (Jasco Inc., Easton, MD, USA). The infrared transmittance was recorded at wavenumbers between 1000 and 4000 cm -1 . At least 100 scans were undertaken for each sample.

The spectra were averaged, smoothed, and corrected for their baselines using Spectra Manager software. Also, XRD patterns of pure quercetin, quercetin-loaded BLG NPs and blank BLG NPs were obtained using the X-ray diffract meter (D8 ADVANCE, Germany) with Ni-filtered Cu Kα radiation. The measurements were performed at a voltage of 40 kV and 25 mA. Scanning electron microscopy (SEM) was used to observe the morphology of the nanoparticles.

Approximately 40 μL of the dispersion (after evaporation and water supplementation) was cast dried on an aluminum pan, mounted on a conductive carbon tape, coated with gold/platinum using a sputter coater, and observed under SEM (MIRA3TESCAN-XMU).

Encapsulation Efficiency (EE%) and loading efficiency (LE%)

The EE for each sample was calculated after concentration determination of insoluble and free unbounded quercetin (please see section 2.2) as follows [START_REF] Teng | Nanoparticles synthesized from soy protein: Preparation, characterization, and application for nutraceutical encapsulation[END_REF]):

In addition, after the ultrafiltration by centrifugation mentioned above, the retentate containing the quercetin-encapsulated nanoparticles was collected and lyophilized. The LE was calculated as follows:(2)Weight of encapsulated quercetin = total amount of quercetin -(non-bound and precipitated quercetin)

In vitro release of quercetin

Release in PBS. Prepared samples with the following parameters were chosen for in vitro release study: quercetin loading of 10, and 15% (w/w), initial acetone content of 10% (v/v) and glutaraldehyde levels that showed the optimal EE for each quercetin loading ratio. Samples were taken after evaporation but prior to supplementation of water. All of the used buffers (PBS, SGF and SIF) contained 5 mg/mL Tween 80. Also, the PBS was prepared at pH = 7.2 and 0.1 mol/L of phosphate salts. Two milliliters of the above mentioned samples was mixed with 2 mL of PBS and incubated at 37 °C for 30 min. The mixture was injected into a sealed dialysis tube (MW cutoff = 10 kDa), which was then placed in a flask containing 60 mL of PBS (preheated at 37 °C).

The flask was then incubated in a reciprocal shaking bath at 37 °C under constant shaking at 120 rpm. At predetermined time intervals, aliquots of 2 mL were withdrawn from the flask and measured for absorbance at 375 nm, which was converted to the mass of released quercetin.

Release in SGF and SIF. The nanoparticle dispersion with quercetin loading of 10% was chosen for this study. Two milliliters of the sample were incubated at 37 °C and then were diluted with 4 mL of two preheated buffers, i.e., SGF-2 or SGF-5 (same as SGF-2 but its pH was adjusted to 5.0). These buffers mimicked the gastric environment at fasting and fed states, respectively [START_REF] Fotaki | Biorelevant dissolution methods and their applications in in vitro-in vivo correlations for oral formulations[END_REF]. SGF and SIF were prepared based on previously published methods [START_REF] Marques | Simulated biological fluids with possible application in dissolution testing[END_REF][START_REF] Remondetto | Iron availability from whey protein hydrogels: An in vitro study[END_REF][START_REF] Teng | Insight into curcumin-loaded β-lactoglobulin nanoparticles: Incorporation, particle disintegration, and releasing profiles[END_REF] and BLG/protease ratio was about 100:1. After 15 min of mixing, the dispersion was subjected into a dialysis bag and was placed in a flask containing 20 mL of SGF without pepsin enzyme. At predetermined time intervals, aliquots of 2 mL were withdrawn from the flask and measured for absorbance at λ = 375 nm, which was converted to the mass of released quercetin.

On the other hand, another batch of the nanoparticle dispersions were mixed with SGF-2 and digested for 60 min at 37 °C in the reciprocal shaking bath. It was then mixed with SIF buffer and eventually injected into the dialysis bag. Afterwards, the dialysis bag was placed in 20 mL SIF flask without trypsin enzyme and the absorption of released quercetin was measured using UV-Vis spectroscopy method.

Results and discussion

Concentration effect on the size, shape and stability of BLG NPs

In this study, BLG solutions with initial concentrations of 5, 10 and 15 mg/mL were used to prepare the NPs with size of 180-298 nm. The results of DLS method are presented in Table 1. The results show that, smaller BLG NPs can be obtained in 10 mg/mL initial protein concentration. Zeta potential allows us to study the stabilization of colloidal systems. The stability of the colloidal suspensions of nanoparticles depends on the charged species present at the particle surface that impair the aggregation and the consequent collapse. Since the stability of the colloidal system is due to the balance between the attractive and repulsive forces; the system will be stable when the repulsive forces are stronger. This stability may be achieved through steric repulsions or electrostatic interactions. Usually, it is accepted that the zeta potential between -30mV and +30 mV indicates an unstable suspension, while for values higher than +30 mV or lower than -30mV it is assumed that you have a stable system [START_REF] Bhattacharjee | DLS and zeta potential-What they are and what they are not[END_REF]. Zeta potentials of BLG NPs at different initial protein concentrations were evaluated and the results showed that the initial protein concentration of 10 mg/mL makes the most stable NPs with ZP of about -85.8 mV (Table 1). The effect of drug concentration on the size of DDS was also evaluated. In the presence of 5% and 15% (w/w) of quercetin/BLG, the particle size was increased, which was reasonable. According to the ZP data, stability of the system is reduced after loading of the drug, which can be due to the presence of quercetin on the surface of the NPs and reducing the surface charge. AFM images also showed that the nanoparticles were formed by smooth surface and semispherical shape (Fig. 1, Fig. 2). Previous studies revealed that the smaller nanoparticles have higher stability than the larger ones and can escape from the vascular system via cavities in the lining of blood vessel [START_REF] Müller | Albumin nanospheres as carriers for passive drug targeting: An optimized manufacturing technique[END_REF].

pH effect

After particle size optimization in 10 mg/mL of initial protein concentration; the pH effect on morphology of BLG NPs was evaluated. In fabrication of protein NPs, both gravity and repulsive forces exist between particles, and balance between these forces produces nanoparticles of a certain shape. Due to dependence of both gravity and repulsive forces on pH [START_REF] Sahihi | Structure-function relationship of β-lactoglobulin in the presence of sodium dodecylbenzenesulfonate[END_REF], the shape of BLG NPs is significantly affected by pH value of the aqueous solution. AFM imaging results indicated that protein nanoparticles at pH = 4 and 9 do not have the semispherical appearance. Hence, the pH = 7 was selected as optimized pH due to importance of NPs morphology (Fig. 3).

Characterization of quercetin-loaded NPs

The SEM images of BLG NPs are shown in Fig. 4. FESEM images exhibit particles with smooth surface and semispherical shape. Two main groups of particles were identified in the images, i.e., larger particles with an average particle size of about 200 nm and smaller particles with size of about 40-50 nm (Fig. 4). Fig. 4 demonstrates that the former type of particles was possibly assembled from the latter one. Such aggregates might have existed in the nanoparticle dispersion before drying process. The structural characteristics of food proteins are often studied by Fourier transform infrared (FT-IR) spectroscopy in order to determine their structure-function relationship. Each compound has a characteristic set of absorption bands in its infrared spectrum. Characteristic bands found in the infrared spectra of proteins and polypeptides include the Amide I and Amide II which arise from amide bonds. The absorptions related to Amide I and Amide II bands lead to stretching vibrations of C=O and bending vibrations of the N-H bonds, respectively. Locations of the both bands are sensitive to the secondary structure contents of a protein due to their role in hydrogen bonds that are formed between different elements of protein secondary structure [START_REF] Byler | Examination of the secondary structure of proteins by deconvolved FTIR spectra[END_REF][START_REF] Surewicz | New insight into protein secondary structure from resolution-enhanced infrared spectra[END_REF].

In the present work, quercetin loading into BLG NPs in 15% (w/w) quercetin/BLG was investigated using FT-IR method. Fig. 5 shows 4.4 nm and 12 nm shift of Amide I (1654.2 cm -1 , C = O stretching) and amide II (1522.52 cm -1 , NH bending and CN stretching) bands of BLG NPs in the presence of quercetin, respectively. These changes suggest that carbonyl or amine groups of protein chains play key role in protein-quercetin interaction. In addition, the broad region in about 3300 cm -1 (OH-group) and its changed intensity in the presence of quercetin, suggests formation of hydrogen bonds between the protein and quercetin (loading quercetin into BLG NPs) [START_REF] Teng | Nanoparticles synthesized from soy protein: Preparation, characterization, and application for nutraceutical encapsulation[END_REF]. On the other hand, encapsulation of quercetin with high ratio of quercetin to BLG (100:1) removes the quercetin peaks in FT-IR spectrum of the quercetin-NPs complex. (between 1600 and 1700 cm -1 ) is mainly due to C=O stretching vibration and is directly related to the backbone conformation. Amide II (between 1500 and 1600 cm -1 ) comes from the N-H bending vibration.

Solid substances may reveal crystalline and/or amorphous characteristics. XRD method can distinguish systems/materials between crystalline and amorphous, effectively. The crystalline substances present with defined peaks despite of the amorphous compounds [START_REF] Patel | Revealing facts behind spray dried solid dispersion technology used for solubility enhancement[END_REF]. In general, amorphous solids are more soluble than crystalline forms due to free energy of dissolution process. Amorphous solids have randomy arranged molecules, so low power consumption is required to separate them. Accordingly, their rate of dissolution is faster than crystal form [START_REF] Riekes | Evaluation of oral carvedilol microparticles prepared by simple emulsion technique using poly (3-hydroxybutyrate-co-3-hydroxyvalerate) and polycaprolactone as polymers[END_REF]. The XRD patterns of quercetin, blank BLG NPs and quercetin-loaded BLG NPs are given in Figs. 6 andS1. Quercetin shows defined peaks at angles 7°, 8°, 12.5°, 14°, 18°, 29° and 32° which are characteristics of crystalline structure (Fig. 1(a)), while, BLG bands do not show any peaks due to its amorphous nature (Fig. S1 (b)). Fig. 6 reveals that the intensity of quercetin peaks is decreased in quercetin-BLG NPs complex. One explanation is that quercetin molecules were encapsulated or dispersed in the polymer matrix during the desolvation process [START_REF] Wu | Preparation, physicochemical characterization, and antioxidant effects of quercetin nanoparticles[END_REF].

Fig. 6. X-ray powder diffraction of quercetin-loaded BLG NPs.

Binding of quercetin to BLG NPs as a function of acetone content

In water/acetone binary system containing BLG NPs, quercetin molecules could be find in three forms, i.e., insoluble quercetin, dissolved quercetin and BLG-bound quercetin molecules that were measured in the precipitate, filtrate and retentate, respectively. Fig. 7 shows the distribution of quercetin in BLG NPs as a function of acetone content. The data were obtained after rapidly diluting the cross-linked dispersion with appropriate water/acetone mixtures. As can be seen from this figure, the percentage of free quercetin was increased significantly at acetone content >40% v/v. The results were similar to a relevant study on BLG monomers, which reported that the refined binding capability were decreased by 30% or higher concentration of ethanol [START_REF] Duclairoir | formation of gliadin nanoparticles: Influence of the solubility parameter of the protein solvent[END_REF][START_REF] Dufour | Alcohol-induced changes of β-lactoglobulin-retinolbinding stoichiometry[END_REF]. The results suggest a weak interaction between the ligand and BLG NPs. On the other hand, 30-40% of quercetin molecules were detected in the precipitate in the presence of 10-25% acetone. This observation was probably due to: (i) quercetin as a hydrophobic compound exhibits low solubility in 10-25% acetone and

(ii) most of the protein molecules were partly or fully folded, so there were insufficient hydrophobic sites to associate with quercetin. [START_REF] Teng | Nanoparticles synthesized from soy protein: Preparation, characterization, and application for nutraceutical encapsulation[END_REF]. In addition, most of the ligand binding sites lose their activity at high level of acetone during preparation of the NPs [START_REF] Zhang | Investigation of the interaction of naringin palmitate with bovine serum albumin: Spectroscopic analysis and molecular docking[END_REF]. Therefore, the quercetin-BLG association might have taken place mostly on the hydrophobic sites exposed by desolvation, rather than the native binding sites of BLG. Fig. 7. Effect of acetone content on the distribution of quercetin in BLG NPs dispersion. BLG concentration was 10 mg/mL, quercetin concentration was 1 mg/mL and the nanoparticles were cross-linked with 100% equivalent of glutaraldehyde.

In 40% of acetone, a considerable percentage of quercetin molecules (90%) are in protein associated form. This phenomenon is possibly due to two factors: (i) the high polarity of 40% acetone compared to higher concentrations, force quercetin molecules to associate with other hydrophobic molecules (BLG) and minimize their contact with water, (ii) a great number of hydrophobic sites on BLG molecules are exposed in 40% acetone in comparison with 25% acetone [START_REF] Teng | Nanoparticles synthesized from soy protein: Preparation, characterization, and application for nutraceutical encapsulation[END_REF], which cause the association and stabilization of more quercetin molecules.

Due to the acetone content dependence of quercetin distribution, it can be judged that the evaporation process is critical for encapsulation of quercetin. We hypothesized that the LE of BLG NPs might be improved by lowering the acetone content after crosslinking and equilibrating the dispersion for a period of time to allow sufficient quercetin-BLG binding. Hence, the dispersion should be evaporated mildly.

Effect of acetone content and glutaraldehyde level on EE% and LE%

The EE of quercetin-loaded BLG NPs as a function of acetone content and glutaraldehyde levels was investigated. Fig. 8 reveals that the change in EE does not show a direct and regular relationship with acetone content. However, it can be realized that in all cases, the highest amount of EE is observed in 90% and/or 10% of acetone. These irregular changes are observed in both values of 50% and 100% equivalents of glutaraldehyde. All of the EE values refer to initial concentrations of the drug in various acetone contents and different levels of glutaraldehyde have been presented in Table 2. The results show the similar changes for the values of LE, too. for the nanoparticles mixed with 15%, 10% and 5% (w/w) quercetin/BLG NPs, respectively.

Regarding to the maximum amount of EE in 90% of acetone, it can be suggested that this loading capacity is due to high solubility of quercetin in acetone as well as trapping large number of quercetin molecules during the evaporation process at hydrophilic sites and their encapsulation.

The samples containing 10% of acetone showed the LE values about 11.9%, 8.7% and 3.7%, for 15%, 10% and 5% w/w quercetin/NPs, respectively. As a result, all soluble quercetin (free and encapsulated) have been inserted into the capsules due to the high solvent polarity and leads their strong interactions with BLG NPs.

On the basis of these results, adjustment of the lowest acetone content is critical for achieving the optimal values for LE and EE. Moreover, a lower glutaraldehyde levels could be applied for preparation of BLG NPs. As it is shown in Figs. 8 and 50% and 100% of glutaraldehyde levels were investigated for all of the quercetin/BLG NPs ratios and acetone contents (the results related to 5% and 15% (w/w) of acetone are shown in Table S1 and Fig. S2). Table 2 shows that at 50% of glutaraldehyde, EE% for samples with 10% and 90% of acetone were higher than 100% of glutaraldehyde, or had a few difference. In fact, by decreasing the glutaraldehyde level, with the highest EE values, the toxicity of drug delivery system can be reduced, effectively.

In vitro release of quercetin from BLG NPs

In PBS: Fig. 9(a) shows release of quercetin from BLG NPs in a PBS/Tween 80 system. It is remarkable that quercetin degrades rapidly in PBS, but its stability could be greatly improved in the presence of nonionic surfactants such as Tween 80 [START_REF] Tønnesen | Studies on curcumin and curcuminoids[END_REF]. Two systems were chosen to investigate quercetin release in PBS buffer system based on the EE and LE values in previous section. These conditions consist of 50% of glutaraldehyde, 10% of acetone content, and 10% and 15% w/w of quercetin/BLG NPs. The results indicate that release rate for nanoparticles with low quercetin loading is higher than the other case with high quercetin loading due to the following reasons: (i) the particles with higher quercetin loading exhibit greater sizes, and have lower quercetin specific surface area (ii) solubility of quercetin in the PBS/Tween 80 system is constant in a given environment and desolvation of quercetin is slowed as its concentration reaches to the equilibrium value; and (iii) higher loading indicates higher concentration of quercetin accumulated in the outer buffer, which slows the diffusion of quercetin through the dialysis membrane. acetone content, and 10% quercetin/BLG NPs.

In vitro drug release kinetics

In this study, five kinetic models have been used to investigate the mechanism of quercetin release from BLG NPs, which are briefly described as below:

• i)

Zero order kinetics model follows the equation as (Qt/Q0) = k0t, where k0 is the zeroth order rate constant; Qt denotes the amount of released quercetin and Q0 denotes the initial amount of quercetin. In this model the drug release is independent of its concentration [START_REF] Najib | The kinetics of drug release from ethylcellulose solid dispersions[END_REF].

• ii)

First order kinetics model follows the equation as Ln (Qt/Q0) = -k1t, where k1 is the first order rate constant. The release rate is concentration dependent [START_REF] Desai | Investigation of factors influencing release of solid drug dispersed in inert matrices ii quantitation of procedures[END_REF].

• iii)

Korsmeyer-Peppas model follows the equation as Qt/Q∞ = kt n where Qt/Q∞ is fraction of released drug at time t, k is the release rate constant and n is the release exponent. The n value is used to characterize different release for cylindrical shaped matrices [START_REF] Korsmeyer | Mechanisms of solute release from porous hydrophilic polymers[END_REF]).

• iv)

Hxson-Crowell model follows the equation as Q 1.3 = -kst where ks is constant incorporating the surface volume relation [START_REF] Hixson | Dependence of reaction velocity upon surface and agitation[END_REF].

• v)

Higuchi model follows the equation as Q/Q0 = kH.t 1.2 where kH is Higuchi matrix release kinetics constant. The drug release from matrix is directly proportional to square root of time and is based on the Fickian diffusion [START_REF] Higuchi | Mechanism of sustained-action medication. Theoretical analysis of rate of release of solid drugs dispersed in solid matrices[END_REF].

The quercetin release in PBS for 5%, 10% and 15% (w/w) quercetin/BLG NPs were investigated by all five kinetic models, and the related results are shown in Fig. S3 and Table 3. The R 2 values for Korsmeyer-Peppas model (Fig. 3(c)) are slightly higher than the other models and show its better performance to predict the quercetin release from the NPs. In this model, if the n value is 0.45, the release follows the Fickian diffusion mechanism. If n is between 0.45 and 0.89, polymer matrix loss is effective in drug release and finally, if the value of n is 0.89; releasing is time independent. Hence, the polymer matrix loss is effective in the present case according to the amount of n = 0.57, 0.57 and 0.49, for 5%, 10% and 15% (w/w) samples, respectively [START_REF] Higuchi | Mechanism of sustained-action medication. Theoretical analysis of rate of release of solid drugs dispersed in solid matrices[END_REF]. Hixson-Crowell 0.0001 (mg 1/3 /h) 0.7084 0.0001 (mg 1/3 /h) 0.6064 0.0002 (mg 1/3 /h) 0.8214 Higuchi 0.0027 (mg/h 1/2 ) 0.8373 0.0023 (mg/h 1/2 ) 0.7914 0.0029 (mg/h 1/2 ) 0.9347

In SGF and SIF: The release profiles of quercetin in simulated gastric fluids (SGF) and simulated intestinal fluids (SIF) are shown in Fig. 9. The releasing profile for nanoparticles with 10% of quercetin loading was chosen for SGF and SIF experiments, due to its higher releasing rate than 15% (w/w) in PBS.

Releasing in SGF was investigated at two different pHs: pH = 2 that represents the gastric condition in the fasting state and pH = 5 that corresponds to the fed state [START_REF] Fotaki | Biorelevant dissolution methods and their applications in in vitro-in vivo correlations for oral formulations[END_REF].

After 1 h of digestion, the mixture was transferred to SIF to determine the release profile under the simulated intestinal condition. It was noteworthy that after 2 h, about 40% of encapsulated quercetin was released in SGF at pH = 5 (Fig. 9(b)). BLG is known for its resistance to peptic digestion that is its major advantage over other proteins with respect to the transportation and delivery of nutraceuticals and drugs [START_REF] Reddy | Structural and conformational basis of the resistance of β -lactoglobulin to peptic and chymotryptic digestion[END_REF]. This characteristic was confirmed by Teng and et al., in which only 9% of BLG was degraded after 4 h of incubation with pepsin [START_REF] Teng | Cationic β-lactoglobulin nanoparticles as a bioavailability enhancer: Protein characterization and particle formation[END_REF][START_REF] Otte | Hydrolysis of bovine βlactoglobulin by various proteases and identification of selected peptides[END_REF]. We hypothesized from this result that the BLG NPs were actually decomposed in SGF at pH = 5, although the individual BLG molecules remained intact. When NPs were dispersed in SGF at pH = 2 (Fig. 9(b)), the BLG NPs exhibited significantly lower rate of release than at pH = 5, and 25% of encapsulated quercetin being released in 2 h. After being transferred to SIF (Fig. 9(c)), the remaining quercetin molecules continued to release from the nanoparticles. This was probably due to degradation of residual BLG NPs as well as the molecules, because of the known capability of trypsin to digest BLG [START_REF] Otte | Hydrolysis of bovine βlactoglobulin by various proteases and identification of selected peptides[END_REF]. The significant difference in the releasing pattern of dispersions were treated at pH = 2 and pH = 5 is probably due to the different residual concentration of quercetin after the first digestion step. At the end of the twostep digestion, about 80% of quercetin was recovered from the two buffers (SGF and SIF). Based on these results, BLG NPs might not be suitable for the controlled release of quercetin in the fed state, but they could release quercetin in a controlled and sustained manner if administrated during the fasting state.

Conclusions

In the present paper, encapsulation and quercetin release process of BLG NPs were systematically evaluated. The results showed that acetone anti-solvent had a significant effect on accumulation of BLG NPs. At the acetone content of about 10% v/v, the quercetin loading process had a great influence on EE% and LE% and increased the loading efficacy to about 13.9%. In addition, optimizing the amount of glutaraldehyde and reducing itscontent from 100% to 50% of equivalent led to preparation of low toxic DDS.

The DLS and zeta potential results, after optimizing the initial protein concentration and pH, approved the preparation of nanoparticles with mean particle size of about 180-300 nm and good stability for BLG NPs. Also, the AFM and FESEM images showed semispherical appearance for the NPs. This study suggested that BLG as a resistant protein to peptic digestion could form nanoparticles that were digestible by pepsin at pH = 5, due to breakage of amide bonds that had been formed by glutaraldehyde. As a result, satisfactory controlled release was achieved under simulated fast condition, i.e., digestion in simulated gastric fluid (SGF) at pH = 2 and then in simulated intestinal fluid (SIF).

The results of this study are applicable not only to the BLG-quercetin DDS but also to the other drug delivery systems including water-soluble proteins and hydrophobic compounds with increased satisfactory loading and reduced DDS toxicity.

Fig. 1 .

 1 Fig. 1. AFM images of BLG NPs with initial protein concentration of: a) 5 mg/mL b) 10 mg/mL c) 15 mg/mL.

Fig. 3 .

 3 Fig. 3. AFM images of BLG NPs at different pHs: a) pH = 4 b) pH = 7 c) pH = 9.

Fig. 4 .

 4 Fig. 4. FESEM images of quercetin-loaded BLG nanoparticles (coexistence of larger and smaller particles).

Fig. 5 .

 5 Fig. 5. FT-IR spectra of empty BLG NPs, quercetin/BLG NPs and quercetin. The amide I band

Fig. 8 .

 8 Fig. 8. Effect of acetone and glutaraldehyde contents on the EE% of quercetin/BLG NPs at 10% of quercetin/BLG mixing ratio.

Fig. 9 .

 9 Fig. 9. Time-dependent release of quercetin from BLG nanoparticles in a) PBS/Tween 80 buffer, DDS consists of 50% glutaraldehyde, 10% acetone content, and 10% and 15% w/w, quercetin/BLG NPs in, b) SGF-2 and SGF-5, DDS consists of 50% glutaraldehyde, 10% acetone content, and 10% quercetin/BLG NPs and c) DDS consists of 50% glutaraldehyde, 10%

Table 1 .

 1 DLS and Zeta potential Data for BLG NPs at 100% glutaraldehyde.

	Initial

protein concentration (mg/mL) [Quer]/[BLG] (w/w) Particle size Zeta potential (mV)

	5	-	298.9 ± 41.5 -32.3
	10	-	152.3 ± 26.4 -85.8
	15	-	180.6 ± 7.1 -71.7
	10	5%	250.9 ± 21.5 -64.7
	10	15%	268.8 ± 34.4 -63.5

Table 2 .

 2 Characteristics of quercetin-loaded BLG nanoparticles at 10% quercetin/BLG mixing ratio.

	acetone%	100%glu	LE%	50%glu	LE%
		EE%		EE%
	10	78.8 ± 1.102	8.7 ± 0.123	86.1 ± 1.54	9.5 ± 0.171

Table 3 .

 3 Curve fitting of quercetin release profile from BLG NPs.

	[Quer]/[ BLG]	5%		10%		15%
	Kinetic Model	k	R 2	k	R 2	k	R 2
	Zero order	0.0002 (mg/h)	0.7145 0.0003 (mg/h)	0.6064 0.0005 (mg/h)	0.8214
	First order	0.0264 (mg/h)	0.6189 0.0217 (mg/h)	0.6786 0.0160 (mg/h)	0.8552
	Korsmeyer-peppas 1.3674 (h)	0.9659 1.5240 (h)	0.9517 1.2153 (h)	0.9543

Acknowledgement

The authors are grateful to Institute of Physics Polish Academy of Sciences, Warsaw, Poland, and University of Isfahan for financial support of this work.


Simon Briole
email: simon.briole@umontpellier.fr

Augustin Colette
email: augustin.colette@ineris.fr

Emmanuelle Lavaine
email: emmanuelle.lavaine@umontpellier.fr

The Heterogeneous Effects of Lockdown Policies on Air Pollution *

Keywords: C23, I18, Q53 air pollution, P M 2.5, lockdown, spatial heterogeneity, machine learning, Covid-19

While a sharp decline in air pollution has been documented during early Covid-19 lockdown periods, the stability and homogeneity of this effect are still under debate. Building on pollution data with a very high level of resolution, this paper estimates the impact of lockdown policies on P M 2.5 exposure in France over the whole year 2020. Our analyses highlight a surprising and undocumented increase in exposure to particulate pollution during lockdown periods. This result is observed during both lockdown periods, in early spring and late fall, and is robust to several identification strategies and model specifications. Combining administrative datasets with machine learning techniques, this paper also highlights strong spatial heterogeneity in lockdown effects, especially according to long-term pollution exposure.

Introduction

A growing body of evidence highlights a sharp decline in air pollution in many countries during early Covid-19 lockdown periods [START_REF] Venter | COVID-19 lockdowns cause global air pollution declines[END_REF][START_REF] Berman | Changes in US air pollution during the COVID-19 pandemic[END_REF][START_REF] Mahato | Effect of lockdown amid COVID-19 pandemic on air quality of the megacity Delhi, India[END_REF][START_REF] Dang | Does the COVID-19 lockdown improve global air quality? New cross-national evidence on its unintended consequences[END_REF][START_REF] Brodeur | On the effects of COVID-19 safer-at-home policies on social distancing, car crashes and pollution[END_REF]. This effect appears to be driven by sharp reductions in human mobility and economic activity [START_REF] Faridi | The effect of COVID-19 pandemic on human mobility and ambient air quality around the world: A systematic review[END_REF]. However, some recent studies tend to mitigate this result and the stability and homogeneity of this effect is still under debate [START_REF] Adam | Air quality changes in cities during the COVID-19 lockdown: A critical review[END_REF][START_REF] Schneider | Differential impact of government lockdown policies on reducing air pollution levels and related mortality in Europe[END_REF][START_REF] Bartoňová | The Covid-19 pandemic and environmental stressors in Europe: synergies and interplays[END_REF]. In particular, these studies suggest that the effects of lockdown policies are likely be very heterogeneous depending on the geographic area and the type of air pollutant considered. Understanding the heterogeneity in lockdown effects on air pollution and analyzing the mechanisms mediating this heterogeneity is key given the large detrimental effects of air pollution on health and economic outcomes [START_REF] Aïchi | Pollution de l'air: le coût de l'inaction[END_REF][START_REF] Deryugina | The mortality and medical costs of air pollution: Evidence from changes in wind direction[END_REF]. This paper investigates the effects of lockdown policies on P M 2.5 and N O 2 exposure in France, a country where P M 2.5 emissions primarily originate from the residential and tertiary sector. In such a context, the theoretical impact of lockdown policies on P M 2.5 is unclear. On the one hand, the curtailment of economic activities and reduced human mobility [START_REF] Dang | Does the COVID-19 lockdown improve global air quality? New cross-national evidence on its unintended consequences[END_REF] during lockdown periods tend to decrease the level of P M 2.5 . On the other hand, increases in residential heating or biomass burning [START_REF] Sicard | Amplified ozone pollution in cities during the COVID-19 lockdown[END_REF] as well as increases in O 3 [START_REF] Adam | Air quality changes in cities during the COVID-19 lockdown: A critical review[END_REF] may enhance the formation of P M 2.5 .

Like in many countries, France was hit by two Covid-19 epidemic waves in 2020, one in early spring and the other in late fall, and implemented lockdown policies during the two corresponding periods. We show that these two periods coincided with strong increases in P M 2.5 concentration, by about 25% with respect to non-lockdown periods. By contrast, nitrogen dioxide (N O 2 ), which is mainly related to transport emissions, decreased drastically during both periods.

To reach these conclusions, our analyses draw on daily air pollution data available for the whole French territory over the 2015-2020 period. This dataset provides daily measures of P M 2.5 and N O 2 exposure with a very high level of resolution (2x2km grid level). Our estimation strategy builds on the comparison between air pollution during lockdown and non-lockdown periods, controlling for the same baseline difference in previous years. This approach allows us to control for any seasonal and geographic correlations between pollutant emissions, meteorological conditions and air pollution at a very fine scale. This paper contributes to the growing literature studying the causal impact of lockdown policies on P M 2.5 . Causal evidence of lockdown-induced pollution remains scarce and primarily based on the analysis of early phases of the pandemic [START_REF] Brodeur | On the effects of COVID-19 safer-at-home policies on social distancing, car crashes and pollution[END_REF][START_REF] Dang | Does the COVID-19 lockdown improve global air quality? New cross-national evidence on its unintended consequences[END_REF]. In this paper, we leverage long-term air pollution data to build a measure of excess pollution exposure, defined as the deviation in 2020 P M 2.5 pollution exposure with respect to a counterfactual (prelockdown) period -namely the average of pollution exposure over the 2015-2019 period. This strategy deals not only with geographic correlations but also with seasonal correlations between pollutant emissions, meteorological conditions and air pollution. On top of this, our analyses build on a massive dataset of nearly 50 millions observations, defined at the 2x2km grid level, a much finer geographic scale than the one used by previous papers which typically build on county-level or national-level analyses.

Our results highlight the importance of documenting the heterogeneity in the effects of lockdown on air pollution. While most of the existing evidence point to a positive effect of lockdown on air quality, we document a sharp increase in P M 2.5 in France during lockdown periods. Building on Machine Learning techniques, we also show that the impact of lockdown is stronger in the areas with the highest levels of long-term exposure to air pollution. These results are consistent with the fact that P M 2.5 emissions in France primarily originate from the residential and tertiary sector as well as with the fact that people spent much more time at home than usual during the two lockdown periods [START_REF] Brandily | A poorly understood disease? The impact of COVID-19 on the income gradient in mortality over the course of the pandemic[END_REF]. They also suggest that the effects of lockdown policies on air pollution can vary a lot both across and within countries and crucially depends on the type of pollutant considered and its sources of emissions.

The remainder of this paper is organised as follows. Section 2 presents background information on air pollution, lockdown policies and the data exploited. Section 3 provides graphical evidence on the evolution of air pollution in France in 2020. Section 4 presents the estimation strategy and the main results from our regression analyses. Finally, Section 5 concludes with a brief discussion of the main results outlined in this paper.

2 Background and data

Air Pollution

Our analyses draw on air pollution data provided by the French National Institute for Industrial Environment and Risks (INERIS ), available over the 2000-2020 period for the whole of metropolitan France. This gridded reanalysis pollution data combines numerical modeling data from the CHIMERE chemistry-transport model [START_REF] Menut | CHIMERE 2013: a model for regional atmospheric composition modelling[END_REF] with measures of air quality from monitoring stations to correct for ground observations. Gridded reanalysis pollution data are computed by INERIS in order to build population-wide measures of background pollution exposure. 1 They provide hourly measures of exposure to the four main regulated pollutants: P M 2.5 , P M 10 , N O 2 , and O 3 . These measures are available at a very fine geographical level, namely at the 2km x 2km level. We aggregate pollution data at the daily level, for each of the 134,459 grid cells located in metropolitan France.

Our analyses focus on exposure to P M 2.5 and N O 2 , whose negative effects on human health have long been documented in the epidemiological and economic literature. 2 The thresholds recommended by the World Health Organization with respect to P M 2.5 are 5 µg/m3 for annual average exposure and 15 µg/m 3 for daily average exposure. The thresholds for N O 2 are 10 µg/m 3 for annual exposure and 25 µg/m 3 for daily exposure [START_REF] Who | WHO global air quality guidelines: particulate matter (PM2. 5 and PM10), ozone, nitrogen dioxide, sulfur dioxide and carbon monoxide[END_REF]. P M 2.5 exposure in France has slightly but continuously decreased over the last decade, in line with the global trends observed in European countries [START_REF] Sicard | Urban population exposure to air pollution in Europe over the last decades[END_REF][START_REF] Salesse | Inequality in exposure to air pollution in France: bringing pollutant cocktails into the picture[END_REF] and in the US [START_REF] Currie | What do economists have to say about the Clean Air Act 50 years after the establishment of the Environmental Protection Agency?[END_REF][START_REF] Currie | What caused racial disparities in particulate exposure to fall? New evidence from the Clean Air Act and satellite-based measures of air quality[END_REF]. Despite this encouraging trend, average exposure to P M 2.5 in France in 2020 is 7.8 µg/m 3 , which is well above the recommended threshold. 3 Beyond the annual averages, the daily thresholds set by the WHO are very regularly exceeded over the 2015-2020 period, even when considering weekly averages P M 2.5 exposure (Figure A1). Figure A2 also shows that there is a strong spatial heterogeneity in P M 2.5 exposure over the French territory.

More than 55% of P M 2.5 emissions in France originate from the residential and tertiary sector, while 15% originate from the transport sector [START_REF] Lavaine | Health, air pollution, and animal agriculture[END_REF][START_REF] Citepa | Inventaire des émissions de polluants atmosphériques et de gaz à effet de serre en France -Format Secten[END_REF]. By contrast, N O x emissions primarily originate from the transport sector (58%). For both pollutants, the agricultural and industrial sectors respectively account for 10-17% of emissions. As outlined in Figure A1, which depicts weekly average levels of P M 2.5 exposure in France over the 2015-2020 period, there is a strong seasonality in P M 2.5 concentration, due to both anthropogenic emissions and weather conditions.

Weather Data

On top of pollutant emissions, air quality conditions are also determined by changes in weather conditions. 4 To account for these factors, we match our pollution data with weather data from the the French national institute for meteorological data monitoring (Météo France). We match each grid cell from pollution data to the closest weather station, 5 and we derive the following daily weather variables for each grid cell: total precipitations, surface maximum temperatures, surface minimum temperatures, wind speed and wind direction. For this last parameter, we build dummies for each of four directions: North (below 45• or above 315•), East (between 45• and 135•),South (between 135• and 225•) and West (between 225• and 315•).

Socio-economic data

To investigate the heterogeneity of our results, we also match our pollution data with the Filosofi 2017 dataset, an administrative fiscal dataset produced by the French National Institute for Statistics (INSEE ). This gridded dataset provides socio-economic indicators at a very local level, namely at the 1x1km grid level, for the whole French population in 2017. For each grid cell, the dataset provides the number of inhabitants and their age distribution, the average standard of living (i.e., the disposable household income divided by the number of consumption units), the share of poor households, the share of owner households and the share of single-parent households. This dataset also includes detailed information on housing conditions, allowing us to compute for each grid cell the the share of households living in houses, the share living in collective dwellings, the share living in subsidized housing, the total surface area of dwellings and the age of houses.

Lockdown policies

Lockdown periods in France in 2020

Like in many European countries, France was hit by two distinct Covid-19 epidemic waves in 2020. These two waves respectively peaked in April, with 15,479 excess deaths observed over this single month, and November, with 12,537 excess deaths [START_REF] Brandily | A poorly understood disease? The impact of COVID-19 on the income gradient in mortality over the course of the pandemic[END_REF]. 6 In both cases, the French government reacted by taking extraordinary containment measures. As COVID-19 first spread in the country in early 2020, the government decided of a national lockdown on March 17 and that eventually lasted until May 11. This first lockdown was the most stringent: all workers stayed home except if their activity was deemed essential for the country. A second lockdown was decided on October 30 and continued until December 15. This second lockdown was slightly less stringent than the previous one and got repealed quicker, with the end of a first phase after a month when all shops opened again. Using Google mobility data, [START_REF] Brandily | A poorly understood disease? The impact of COVID-19 on the income gradient in mortality over the course of the pandemic[END_REF] show that, all over the 2020 year in France, time spent at home appears much higher when a lockdown policy is in place, and slightly more so during the first lockdown than the second.

Oxford Stringency Index

To better account for the variety in the nature and intensity of policy responses taken by the French government over the 2020 year, and to the likely resulting variations in air pollution, we also exploit the Oxford Stringency Index (OSI). This index was developed by [START_REF] Hale | A global panel database of pandemic policies (Oxford COVID-19 Government Response Tracker)[END_REF] to measure the overall strictness of lockdown restrictions at a given point in time in a given country.

It is constructed as the mean of eight policy measures, namely school closing, workplace closing, canceling of public events, restrictions on gathering, closed public transportation, stay-at-home requirements and travel restrictions (both internally and internationally). The OSI is computed as the mean of the standardized policy measures (between 0 and 1), so that each policy measure contributes equally to the index, independently from its number of levels. The OSI is then rescaled to have values between 0 (no response) and 100 (maximum response in every possible policy measure).

Figure A3 in the appendix shows the evolution of this index in France over the 2020 year. It can be noted that the period in between the two lockdown periods is not characterized by the absence of restriction measures, confirming the interest of using a more continuous measure of policy restrictions.

The Effects of Lockdown Policies on Air Pollution: Graphical Evidence

In the remainder of the paper, we explore the effects of lockdown policies on air pollution. Before moving on to our econometric investigations, we start by providing simple graphical evidence on the evolution of exposure to P M 2.5 and N O 2 over the 2020 year. Figure 1 first depicts the evolution of the daily national exposure to P M 2.5 in France in 2020, contrasting lockdown periods (in black) with regular periods (in gray). The figure reveals a marked increase in the national exposure to P M 2.5 during the two lockdown periods. In particular, it shows a clear discontinuity in P M 2.5 exposure, with a jump right after the start of each lockdown period, respectively in March 17 and October 30.7 Such discontinuity is less visible N O 2 exposure, and the average levels of exposure don't seem to be sharply different during lockdown periods, as opposed to regular periods of 2020 (Figure 2).

While Figure 1 suggests a positive effect of lockdown restrictions on P M 2.5 exposure, it could also reflects the strong seasonality in P M 2.5 concentrations highlighted in Figure A1. To take one step further, we compute for each grid cell the difference between the level of exposure to P M 2.5 a given day of the year in 2020 and the average level observed during that same day of the year over the 2015-2019 period. This allows us to account for spatial and temporal regularity in terms of Figures 3 and4 replicate Figures 1 and2, but plotting this outcome expressed in difference instead of the raw level of exposure. These two figures first confirm that both P M 2.5 and N O 2 concentration levels are lower in 2020 than in previous years, a result that have been widely documented in the recent literature [START_REF] Venter | COVID-19 lockdowns cause global air pollution declines[END_REF]. However, Figure 3 also reveals that lockdown periods systematically coincide with sudden and sustained increases in P M 2.5 differential exposure levels, in line with analyses based on raw exposure levels. It seems harder to conclude on the relationship between N O 2 differential exposure levels and lockdown policies from this graphical analysis.

The next section presents results from econometric analyses aiming at testing the robustness and exploring the heterogeneity of these effects.

The Effects of Lockdown Policies on Air Pollution: Regression Analysis 4.1 Econometric approach

Our objective is to estimate the effects of restrictions imposed by lockdown policies on P M 2.5 exposure. As a baseline approach, we compare the levels of P M 2.5 exposure observed in 2020 in each grid cell during lockdown vs. regular periods, controlling for local weather conditions and grid cell fixed effects. In practice, we estimate the following model:

Y it = α + β 1 Lockdown t + β 2 W it + µ i + ϵ it (1)
where Y it represents P M 2.5 exposure in grid i on day t of year 2020 and Lockdown t is a dummy indicating lockdown periods. µ i represents the full set of grid fixed effects. This parameter allows us to control for any geographic differences in P M 2.5 exposure that is constant over time across grid cells. W it represents the set of weather control variables described in Section 2.2. 8 We cluster all standard errors at the day level, which is the level at which our "treatment" variable (i.e., the lockdown dummy) varies.

While our baseline approach accounts for the confounding effects of local weather conditions as well as for any geographic differences in P M 2.5 exposure that is constant over time, it could be biased by seasonal effects on pollution emissions or concentrations. In particular, human activities may not be constant throughout the year, with some periods corresponding systematically to an increase in pollutant emissions and others to a reduction in emissions. These seasonal effects may also vary over space, depending on the type of area considered (e.g., rural vs urban, North vs South, etc.). To account for these factors, we estimate a model that allows P M 2.5 exposure to depend on grid-specific × day-of-the-year fixed effects (κ it ). 9 We compute Y * it , the difference between P M 2.5 exposure in 2020 in grid cell i on day-of-the-year t and the average P M 2.5 exposure in that same grid cell and day-of-the-year over the 2015-2019 period. We then estimate the following (implicit) difference-in-difference (DiD) model:10

Y * it = α + β 1 Lockdown t + β 2 W * it + ϵ * it (2)
where Y * it = Y it,2020 -Ȳit,2015-2019 . This model therefore compares pollution exposure in lockdown vs. regular days in 2020 vs. 2015-2019. It implicitly controls for year, day-of-the-year, grid cell and grid cell × day-of-the-year fixed effects. It therefore accounts for the global decreasing trend in P M 2.5 observed over our period of observation. It also accounts for any seasonal correlation between human activities and pollution, allowing this correlation to vary at a very local level (i.e., 2x2km grid cell). The parameter of interest β 1 captures the causal effects of lockdown on P M 2.5 exposure under the assumption that, absent lockdown (and once controlled for local weather shocks), the difference in P M 2.5 between lockdown and regular periods observed in 2020 would have been similar to that same difference in previous years (2015)(2016)(2017)(2018)(2019). In Appendix B, we provide extensive evidence that our results are robust to several alternative identification strategies and/or specifications: our main conclusions hold with a model based on a regression discontinuity design (Section B1), with an explicit DiD model (Section B3), when changing weather controls (Section B2) or when relying on randomization-based inference (Section B4).

While our main analyses compare days of lockdown with days of regular periods in a binary way, we also implement regressions using the Oxford Stringency Index. To do so, we estimate Equations ( 1) and (2) using this index instead of the dummy indicating lockdown periods. This allows us to capture more variability in the restriction measures implemented all over the 2020 year.

Average effects

Table 1 shows the results of the estimation of Equations ( 1) and (2), using a dummy indicating lockdown periods on the one hand and the Oxford Stringency Index on the other hand. As can be seen in column (1), P M 2.5 exposure levels are higher during lockdown than regular periods in France, once controlled for local weather conditions and grid cell fixed effects. The point estimate is significant at the 1% level and suggests that on average, there was a 2.5 µg/m 3 higher exposure during lockdown periods. This result is confirmed by the estimation of a model that accounts for seasonal effects in pollution emissions and meteorological conditions. As can be seen in column

(2), P M 2.5 exposure levels are 1.9 µg/m 3 higher during lockdown than during regular periods of 2020, compared to the same baseline difference in previous years. This lockdown-induced increase in P M 2.5 is consistent with the fact that P M 2.5 emissions in France primarily originate from the residential and tertiary sector as well as with the fact that people spent much more time at home than usual during the two lockdown periods [START_REF] Brandily | A poorly understood disease? The impact of COVID-19 on the income gradient in mortality over the course of the pandemic[END_REF]. We further investigate the stability of this effect across lockdown periods. Interestingly, results presented in Table 2 show a very high stability in the effects of lockdown policies on P M 2.5 exposure: in both specifications, the effect is virtually the same across the two lockdown periods. This result is important with respect to the external validity of our conclusions. It also further reduces concerns that meteorological factors may drive the estimated effects.

Analyses based on the Oxford Stringency Index, which accounts for restriction measures in a more flexible way than the simple lockdown dummy, provide very similar results. The estimates presented in columns (3) and ( 4) both suggest a positive and significant effect of these measures on P M 2.5 exposure, both in level and in difference with respect to the 2015-2019 period. The point estimate in the last column implies that a 45 points increase in the index (i.e., the average difference in the index between lockdown and regular periods) would result in a 1.8 µg/m 3 increase in P M 2.5 differential exposure between lockdown and regular periods, compared to the baseline difference in previous years. 2) implies that N O 2 exposure levels are 1.9 µg/m 3 lower during lockdown than during regular periods of 2020, compared to the same baseline difference in previous years. This lockdown-induced reduction in N O 2 is consistent with the fact that N O 2 emissions in France primarily originate from the transport sector and with the sharp decline in transport emissions observed in France during lockdown periods due to reduced human mobility. It is also consistent with previous studies on the effects of lockdown on N O 2 exposure [START_REF] Venter | COVID-19 lockdowns cause global air pollution declines[END_REF][START_REF] Berman | Changes in US air pollution during the COVID-19 pandemic[END_REF][START_REF] Mahato | Effect of lockdown amid COVID-19 pandemic on air quality of the megacity Delhi, India[END_REF][START_REF] Schneider | Differential impact of government lockdown policies on reducing air pollution levels and related mortality in Europe[END_REF].

Heterogeneous effects

The implementation of Covid-19 lockdown policies coincides with an increase in P M 2.5 exposure in France in 2020. An important question, however, is whether this effect have been homogeneous over the territory. In this section, we build on Machine Learning techniques to explore this issue and to shed light on the distribution of treatment effects over the territory according to socio-economic indicators and long-term pollution levels.

Machine Learning analysis

In this section, we take a Machine Learning approach to explore the spatial heterogeneity of lockdown effects in a data-driven manner, allowing us to include a high number of heterogeneity dimensions without being subject to the risk of overfitting. More specifically, we implement the generalized random forest (GRF) procedure introduced by Athey et al. (2019). This approach has been implemented in several recent studies exploring the heterogeneity of treatment effects in a variety of contexts (see e. We conducted this test by considering Y * it , namely the difference between P M 2.5 exposure in 2020 in a given grid cell on a given day-of-the-year and the average P M 2.5 exposure in that same grid cell and day-of-the-year over the 2015-2019 period, as our main outcome. To implement this test, we randomly selected a subsample representing 5% of the total number of observations in our main sample (i.e., 2,146,677 observations) for computational reasons. The detailed results of this test are given in Table 4. They show that the null hypothesis that β = 0 is unambiguously rejected for our main outcome variable, highlighting the presence of a significant spatial heterogeneity in the effects of lockdown on P M 2.5 exposure. Further evidence of this spatial heterogeneity is provided by Figure C1, which depicts the distribution of conditional average treatment effects (CATEs). As the figure reveals, CATEs vary considerably, taking a range of values from 0 to +6.

To further explore the sources of treatment effect heterogeneity, it is possible to identify the variables that are most often used by the causal forest procedure to grow trees and predict individual treatment effects. More specifically, for each heterogeneity variable, it is possible to count the proportion of splits on this variable used by the procedure, giving a higher weight to a split the earlier it occurs in the development of a tree. When we conduct this analysis, we find that the most important sources of treatment heterogeneity relate to long-term pollution exposure (both P M 2.5 and N O 2 ). 13To illustrate the importance of long-term pollution exposure, Figures 5 (a These figures reveal a clear positive and linear relationship between the impact of lockdown on P M 2.5 exposure as predicted by the GRF procedure and long-term pollution exposure in the grid cell, for both P M 2.5 and N O 2 long-term exposure. Analyses based on a classical regression approach confirm the significance of these heterogeneous effects (Tables C1 andC2). These analyses also show that the correlation between lockdown effects and long-term exposure is much stronger when considering

P M 2.5 rather than N O 2 .
Finally, on top of long-term pollution levels, the effects of lockdown on P M 2.5 exposure appear to be heterogeneous along some socio-economic indicators. As illustrated in Figures C2,C3 and C4, the predicted impact of lockdown tends to be stronger in grid cells with younger inhabitants, with a higher share of households living in collective dwellings and with higher household income.

Altogether, these results suggest that the positive impact of lockdown on P M 2.5 exposure tend to be stronger in urban than rural settings.

Discussion and conclusion

While a recent literature highlights the positive effects of lockdown policies on air quality, evidence based on causal methodologies remains scarce and focuses on the early implementation of lockdown policies. This paper builds on daily air pollution data available at a very fine geographical level in France to estimate the impact of lockdown on P M 2.5 and N O 2 exposure. Building on an implicit DiD strategy, we contrast excess pollution during days of lockdown to excess pollution during days of regular periods of 2020, compared to the same baseline difference in previous years.

Our results first point to a general decrease in P M 2.5 and N O 2 exposure in 2020 compared to previous years, especially in the most polluted areas. More surprisingly, our analyses also highlight a strong increase in P M 2.5 during both lockdown periods, with exposure levels about 2 µg/m 3 (+25%) higher than during the rest of the year. This result holds when accounting for seasonality in human activities and meteorological conditions in a very flexible way, or when using alternative identification strategies or specifications.

Based on machine learning techniques, we also find strong spatial heterogeneity in this effect, with the increase during lockdown periods being more pronounced in areas with a high level of long-term pollution exposure. This result is consistent with the fact that P M 2.5 emissions primarily originate from the residential and tertiary sectors in France as well as with the fact that people spent much more time at home than usual during lockdown periods. To the extent that long-term exposure is able to capture it, the increase of residential heating in areas with high energy poverty may be another source of explanation for this strong pattern of heterogeneity.

Our results are contrast with previous finding in the literature documenting strong improvement in air quality related to lockdown policies implemented during early phases of the Covid-19 crisis.

They highlight the necessity to account for the spatial and temporal heterogeneity of lockdown effects on air pollution, especially with respect to the main sources of pollution. Understanding the impact lockdown policies on P M 2.5 and N O 2 exposure is crucial from a health perspective.

An extensive literature documents the detrimental of these pollutants on mortality, hospitalizations related to cardiovascular, respiratory or metabolic problems and associated economic outcomes [START_REF] Deryugina | The mortality and medical costs of air pollution: Evidence from changes in wind direction[END_REF][START_REF] Aïchi | Pollution de l'air: le coût de l'inaction[END_REF]. In addition to usual health outcomes, P M 2.5 exposure could also play an important role in the severity of Covid-19 symptoms [START_REF] Persico | The effects of increased pollution on COVID-19 cases and deaths[END_REF][START_REF] Isphording | Pandemic meets pollution: poor air quality increases deaths by COVID-19[END_REF]. Finally, the oxidative potential of P M 2.5 emitted during lockdown periods could be strong. While assessments of the chronic and acute effects of particulate matter on human health tend to be based on mass concentration, with particle size and composition, a recent literature shed light on the oxidative potential concentration mostly associated with anthropogenic sources, in particular with fine-mode secondary organic aerosols largely from residential biomass burning and coarse-mode metals from vehicular non-exhaust emissions [START_REF] Daellenbach | Sources of particulate-matter air pollution and its oxidative potential in Europe[END_REF].

Besides, a review about air quality changes during lockdown periods highlights the enhanced formation of secondary P M 2.5 during these periods [START_REF] Adam | Air quality changes in cities during the COVID-19 lockdown: A critical review[END_REF]. Future research should further explore the causal impact of secondary P M 2.5 exposure on health during lockdown periods. [START_REF] Chernozhukov | Generic Machine Learning Inference on Heterogeneous Treatment Effects in Randomized Experiments, with an Application to Immunization in India[END_REF], which seeks to fit the Conditional Average Treatment Effect (CATE) as a linear function of the out-of-bag causal forest estimates. This test is performed on our main outcome that measures P M2.5 differential exposure in 2020 (as compared to 2015-2019), using a random subsample representing 5% of our main sample. The first row of the table shows the main β coefficient of this regression and its standard errors (in parentheses), clustered at the day-of-the-year level. The next 5 rows show the 5 most important variables determining the heterogeneity of lockdown effects. * p<0.10, ** p<0.05, *** p<0.01. One potential threat to the validity of our main identification assumption relates to the existence of shocks that would correlate with both air quality and lockdown policies, which could bias our main estimates. In particular, a recent literature highlighted a positive association between air pollution and the number of COVID-19 cases and related-mortality.14 Higher levels of air pollution could therefore indirectly induce governments to implement more stringent lockdown.

Main Figures

To further check the robustness of our main results, we estimate a Regression Discontinuity in Time (RDiT) model around lockdown dates. This alternative identification takes advantage of the fact that the implementation of lockdown policies represent a sudden and exogenous shock [START_REF] Dang | Does the COVID-19 lockdown improve global air quality? New cross-national evidence on its unintended consequences[END_REF]. In this approach, observations just before the lockdown starting dates provide the counterfactual for observations immediately after the lockdown dates. It relies on the assumption that the exact starting date of the lockdown policy is randomized in the close neighborhood of the actual date. 15In practice, we estimate the following model using the rdrobust stata package [START_REF] Calonico | rdrobust: Software for regression-discontinuity designs[END_REF]:

Y it = α + τ 1 t≥t 0 + δ f f (t) + δ i g(t)1 t≥t 0 + ϵ it (3)
where Y it represents P M 2.5 exposure in grid i in 2020 on day t, t 0 indicates the cutoff (lockdown starting date) and 1 t≥t 0 is a dummy indicating lockdown implementation. f (.) and g(.) are flexible functions that we allow to differ on each side of the time cutoff. We cluster standard errors at the day level. We use the optimal data-driven bandwidth selection procedures proposed by [START_REF] Calonico | Optimal bandwidth choice for robust bias-corrected inference in regression discontinuity designs[END_REF].

B3 Explicit DiD

Our main econometric model can be viewed as an implicit difference-in-difference (DiD) design where the coefficient of interest is β 1 . It estimates the difference in excess pollution (time dimension) between days of lockdown ("treatment group") and days of regular period ("comparison group'").

This model identifies the causal effect of lockdown policies on excess pollution under the assumption that, absent lockdown, the evolution of pollution between 2015-2019 and 2020 would have been similar on average between days of lockdown and days of regular periods, after accounting for grid-specific seasonality and local weather conditions.

To further check the robustness of our results, we take advantage of the panel nature of our data to estimate an explicit DiD model, which includes day-of-the-year × grid fixed effects and uses P M 2.5 exposure level as the main dependent variable. Formally, we estimate the following model, on a 5% random subsample of observations from our main sample:

Y ity = α + β 1 Lockdown t + β 2 Lockdown t × 1 y=2020 + β 3 W ity + µ it + δ y + ϵ ity (4)
where Y ity represents P M 2.5 exposure in grid i on day t of year y and Lockdown t is a dummy indicating lockdown periods. µ it represents the full set of day-of-the-year × grid fixed effects. W ity represents the set of weather control variables described in Section 2.2. Note that 1 y=2020 is included in the set of year fixed effects δ y and that day and grid fixed effects are included in day × grid fixed effects µ it . We cluster all standard errors at the day level.

As shown in Table B4, the nature of the result is unchanged when implementing this explicit DiD model: on average, P M 2.5 is 1.57 µg/m 3 higher during days of lockdown.

CEE-M Working Papers

  g.,[START_REF] Carter | Heterogeneous impact dynamics of a rural business development program in Nicaragua[END_REF];[START_REF] Allcott | The welfare effects of social media[END_REF];[START_REF] Haaland | Labor market concerns and support for immigration[END_REF];Sylvia et al. (2021);[START_REF] Briole | The Making of Civic Virtues: A School-Based Experiment in Three Countries[END_REF]). In our setting, it makes it possible to predict treatment effects for each grid cell individually using all available information on its characteristics and to test the existence of heterogeneity in lockdown effects. 11 To train our procedures, we use two measures of long-term pollution exposure defined at the grid level, namely average exposure to P M 2.5 and N O 2 over the 2009-2019 period, as well as all the socio-economic indicators described in Section 2. Denoting Y our main outcome of interest, L the dummy indicating lockdown periods and Z the set of baseline covariates, this procedure starts by growing two regression forests to construct estimates Y (Z) and L(Z) of E(Y |Z) and E(L|Z). Building on these two estimates, the procedure then grows a causal forest to construct an estimate S(Z) of the conditional average treatment effect s 0 (Z) = E(Y 1 -Y 0 |Z), where Y 1 and Y 0 represent grid cells' potential outcomes in treated and non-treated states. Finally, following Athey & Wager (2019) and Chernozhukov et al. (2018), it is possible to test for the existence of heterogeneity in s 0 (Z) by regressing Y -Y (Z) on C = S(L -L(Z)) and SD = (S(Z) -S)(L -L(Z)), where S represents the average of S(Z), and by looking at the significance of the regression coefficient of SD, which provides an estimate of Cov(S(Z), s 0 (Z))/V ar(S(Z)). Let's denote this regression coefficient by β. Rejecting H 0 : β = 0 implies rejecting that the actual variance of s 0 (Z) is zero. It also implies rejecting that the causal forest estimates of treatment effects do not represent relevant predictors of the actual treatment effects. 12

  ) and 5 (b) respectively plot the distribution of long-term P M 2.5 and N O 2 exposure by deciles of the CATEs distribution.

Figure 1 :

 1 Figure 1: P M 2.5 exposure in France in 2020

Figure 2 :

 2 Figure 2: N O 2 exposure in France: 2020

Figure 3 :

 3 Figure 3: P M 2.5 exposure in France: 2020 vs 2015-2019

Figure 4 :Figure 5 :

 45 Figure 4: N O 2 exposure in France: 2020 vs 2015-2019

Figure A2 :

 A2 Figure A2: Spatial distribution of P M 2.5 exposure in France

Figure A3 :

 A3 Figure A3: Evolution of the Oxford Stringency Index in France in 2020

Figure C1 :

 C1 Figure C1: Conditional Average Treatment Effects distribution

Figure

  Figure C2: Conditional Average Treatment Effects and Inhabitants Age

Figure C3 :

 C3 Figure C3: Conditional Average Treatment Effects and share of Households in Collective Dwellings

Figure C4 :

 C4 Figure C4: Conditional Average Treatment Effects and Household Income

Table 3

 3 replicates the analyses presented in Table 1 with N O 2 as the outcome. The results presented in this table suggest that lockdown restriction measures affect negatively the level of N O 2 exposure. The point estimate presented in column (

Table 1 :

 1 Effects of lockdown on P M 2.5 exposure in 2020

		(1)	(2)	(3)	(4)
		P M 2.5 2020 2020 vs 2015-2019	2020	2020 vs 2015-2019
	Lockdown dummy	2.5048 * * *	1.9054 * * *
		(.44992)	(.49143)
	Oxford Stringency Index			.02052 * *	.03905 * * *
				(.00998)	(.00843)
	Weather controls	✓	✓	✓	✓
	Observations	49211994	49211994	46119437	46119437
	Standard errors in parentheses
	* p < 0.10, * * p < 0.05, * * * p < 0.01

Table 2 :

 2 Effects of lockdown on P M 2.5 exposure in 2020: distinguishing the two lockdown periods

		(1)	(2)
		P M 2.5 2020 2020 vs 2015-2019
	First lockdown	2.5921 * * *	1.8955 * * *
		(.61298)	(.72495)
	Second lockdown	2.4362 * * *	1.9135 * * *
		(.55303)	(.61200)
	Observations	49211994	49211994
	Standard errors in parentheses
	* p < 0.10, * * p < 0.05, * * * p < 0.01

Table 3 :

 3 Effects of lockdown on N O 2 exposure in 2020

		(1)	(2)	(3)	(4)
		N O 2 2020 2020 vs 2015-2019	2020	2020 vs 2015-2019
	Lockdown dummy	-1.2756 * * *	-1.9966 * * *
		(.35583)	(.27802)
	Oxford Stringency Index			-.04621 * * *	-.01303 *
				(.0064)	(.00677)
	Weather controls	✓	✓	✓	✓
	Observations	49211994	49211994	46119437	46119437
	Standard errors in parentheses
	* p < 0.10, * * p < 0.05, * * * p < 0.01

Table B1

 B1 The first panel of the table shows the estimation for the first lockdown, which started on March, 17. The second panel of the table shows the estimation for the second lockdown, which started on October, 30. RDD results are consistent with the main results outlined in this paper, as a discontinuous increase in P M 2.5 exposure is observed right after the implementation of each lockdown period. Figures1(a) and 1(b), which respectively depicts the effects of the first and

	shows the result of the estimation of Equation (3) using different functional forms of
	the running variable: a linear model (column (1)), a quadratic model (column (2)) and a cubic
	model (column (3)).

Table B1 :

 B1 Effects of lockdown on P M 2.5 exposure in 2020: RDD estimations

		(1)	(2)	(3)
		P M 2.5	P M 2.5	P M 2.5
	First lockdown
	RD Estimate	5.3573 * * * 3.5473 * * *	3.3465 * * *
		(1.1934)	(.65153)	(.69797)
	Observations	1236434	1236434	1236434
	Second lockdown
	RD Estimate	1.8269 * *	.99007	2.1329 * * *
		(.93159)	(1.222)	(.76227)
	Observations	1224741	1224741	1224741
	Model	Linear	Quadratic	Cubic
	Note:
	This table shows the estimation of lockdown effects using a Regression
	Discontinuity in Time approach design. The bandwidth has been com-
	puted using the optimal data-driven procedure proposed by Calonico
	et al. (2020). Standard errors (in parentheses) are clustered at the day
	level. * p<0.10, ** p<0.05, *** p<0.01.

Table B3 :

 B3 Effects of lockdown on P M 2.5 exposure: without weather controls

		(1)	(2)	(3)	(4)
		P M 2.5 2020 2020 vs 2015-2019	2020	2020 vs 2015-2019
	Lockdown dummy	3.9309 * * *	2.559 * * *
		(.48366)	(.56552)
	Oxford Stringency Index			.03899 * * *	.05258 * * *
				(.01169)	(.01014)
	Weather controls	.	.	.	.
	Observations	49211994	49211994	46119437	46119437
	Standard errors in parentheses

* p < 0.10, * * p < 0.05, * * * p < 0.01

Table B4 :

 B4 Effects of lockdown on P M 2.5 : Explicit DiD model p < 0.10, * * p < 0.05, * * * p < 0.01

		(1)	(2)
		P M 2.5	P M 2.5
	Lockdown × 2020 1.5732 * * *
		(.36577)
	OSI × 2020		.02573 * * *
			(.00806)
	Observations	17190826 17036461
	Standard errors in parentheses

*

Table C2 :

 C2 Effects of lockdown on P M 2.5 : Heterogeneity by N O 2 long-term exposure level p < 0.10, * * p < 0.05, * * * p < 0.01 34

		(1)	(2)	(3)	(4)
		P M 2.5 2020 2020 vs 2015-2019	2020	2020 vs 2015-2019
	Lockdown dummy	1.4667 * *	.79774
		(.58172)	(.71047)
	Oxford Stringency Index (OSI)			-.0015	.00032
				(.01132)	(.01204)
	N O 2 exposure 2009-2019		-.14905 * * *		-.30326 * * *
			(.01651)		(.05116)
	N O 2 exposure 2009-2019 × Lockdown	.07926 * *	.0834 * *
		(.03691)	(.04176)
	N O 2 exposure 2009-2019 × OSI			.00168 * *	.00294 * * *
				(.00083)	(.00086)
	Observations	49211628	49211628	46119094	46119094
	Standard errors in parentheses

*

  Augustin Colette & Emmanuelle Lavaine « The Heterogeneous Effects of Lockdown Policies on Air Pollution »

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By contrast, we do not exploit directly measures based on local station data (industrial or traffic), whose purpose is to measure pollution emissions -rather than exposure -at a local level. These monitoring stations are sparse and strategically placed to capture locally produced emissions (e.g., from road traffic or industrial activities).

This literature highlights in particular the negative role played by fine particulate matter[START_REF] Pope | Lung cancer, cardiopulmonary mortality, and long-term exposure to fine particulate air pollution[END_REF][START_REF] Lepeule | Chronic exposure to fine particles and mortality: an extended follow-up of the Harvard Six Cities study from 1974 to 2009[END_REF][START_REF] Lelieveld | The contribution of outdoor air pollution sources to premature mortality on a global scale[END_REF][START_REF] Ciarelli | Long-term health impact assessment of total PM2. 5 in Europe during the 1990-2015 period[END_REF][START_REF] Deryugina | The mortality and medical costs of air pollution: Evidence from changes in wind direction[END_REF]. For example, the Environmental Protection Agency (EPA) estimates that P M2.5 is responsible for over 90% of air pollution-related health damages in the US (US Environmental Protection Agency, 2011). A growing body of evidence also documents the adverse economic effects of air pollution on non-health outcomes, including labor supply, cognitive performance and labor productivity, educational attainment or crime. See[START_REF] Aguilar-Gomez | This is air: The "nonhealth" effects of air pollution[END_REF] for a recent review of this evidence.

Average exposure to N O2 in France in 2020 is 8.3 µg/m 3 .

In a critical review of more than 200 papers,[START_REF] Gkatzelis | The global impacts of covid-19 lockdowns on urban air pollutiona critical review and recommendations[END_REF] highlight the significant effects of meteorological conditions on pollutant concentrations.[START_REF] Barré | Estimating lockdown-induced European NO2 changes using satellite and surface observations and air quality models[END_REF] further show the importance of accounting for weather conditions to estimate N O2 changes induced by lockdown policies.

There are 875 weather stations in our dataset. The average distance between a grid cell from our pollution data and the closest weather station is 11.8km. The maximum distance is 50 km, but more than 99% of grid cells are located less than 27kms away from the closest weather station.

Overall in 2020, there was 49,495 deaths in excess in French urban areas in comparison with the average of 2018 and 2019[START_REF] Brandily | A poorly understood disease? The impact of COVID-19 on the income gradient in mortality over the course of the pandemic[END_REF].

Analyses based on a formal Regression Discontinuity in Time (RDiT) approach confirm the existence of a significant discontinuity in P M2.5 at both time cutoffs (see Appendix B1).

For computational reasons, our main estimations include a continuous specification of our 4 weather variables (total precipitations, surface maximum temperatures, surface minimum temperatures, wind speed) as well as a dummy for each of the four possible wind directions. In Appendix B2, we provide evidence that our results are unchanged when including a very large set of weather fixed effects, based on bins for each of the four variables and their interactions.

Note that day-of-the-year fixed effects and grid fixed effects are included in κit.

In Appendix B3, we show that our results are robust to estimating a formal (explicit) DiD model.

The analyses conducted in this section use the R package grf, version 2.0.2[START_REF] Tibshirani | Grf: Generalized Random Forests (version 2.0.2). R[END_REF]).

Conversely, when H0 is not rejected, this does not necessarily imply that there is no significant heterogeneity in treatment effects, it may also mean that the causal forest procedure does not produce relevant predictions of treatment effects.

These two variables respectively account for 72% and 16% of the splits. Other variables that appear in at least 2-3% of the splits relate to the age distribution of inhabitants, to their average income and to the proportion of households living in collective dwellings.

See for example Coker et al. (2020); Wu et al. (2020); Isphording & Pestel (2021); Persico & Johnson (2021); Weaver et al. (2022) or Becchetti et al. (2022).

RDiT methods have been widely implemented in the economic literature that estimate the causal impact of specific shocks on air quality[START_REF] Davis | The effect of driving restrictions on air quality in Mexico City[END_REF][START_REF] Auffhammer | Clearing the air? The effects of gasoline content regulation on air quality[END_REF][START_REF] Chen | Green infrastructure: The effects of urban rail transit on air quality[END_REF][START_REF] Gallego | The effect of transport policies on car use: Evidence from Latin American cities[END_REF][START_REF] Dang | Does the COVID-19 lockdown improve global air quality? New cross-national evidence on its unintended consequences[END_REF]. However, these methods may suffer from methodological limitations, especially in the presence of time varying treatment effects or autoregression[START_REF] Hausman | Regression discontinuity in time: Considerations for empirical applications[END_REF].

INERIS for providing us access to the data used in this work. We also thank the support of the ADEME grant AQACIA 2162D0019 -Air-COV project.

Appendix A Descriptive Statistics

B2 Weather controls

Our main econometric approach control for weather conditions in a very parsimonious way to avoid excessive computation time. In this appendix section, we provide evidence that controlling for weather conditions in a much more flexible way doesn't change the nature of our main results. The high granularity and comprehensive scope of our data makes it possible to include a very large set of weather condition fixed effects. For each of our 4 weather variables (daily maximum temperatures, daily minimum temperatures, daily total precipitation and daily average wind speed), we generate indicators for the quartiles of these variables. We then generate a set of indicators for all possible interactions of these temperature (min and max), precipitation, wind speed and wind direction variables and include it in our main specification as W it . This regression model thus controls for more than 1,000 possible combinations of weather conditions. Table B2 reproduces the main results presented in Table 1 with a model including the large set of weather control variables, estimated on a 5% random subsample of the main sample. Those results reinforce the assumption that our estimates are not driven by unobserved meteorological factors that would be correlated with both lockdown implementation and P M 2.5 concentration. Finally, our estimates are also robust to the omission of weather controls (Table B3).

B4 Permutation tests

We further check the robustness of our results to an alternative (randomization-based) inference approach by performing permutation tests. These tests randomly reassign the treatment status (i.e., lockdown) over days of the 2020 year. We then compare the observed difference in our outcome (P M 2.5 exposure) between lockdown and regular days with the distribution of this difference in the placebo tests. This comparison allows us to assess whether the observed difference is likely to have been produced by chance -and not by the effects of lockdown policies. We implement these tests on a 5% random subsample of observations, using the ritest command [START_REF] Heß | Randomization inference with Stata: A guide and software[END_REF] and simulating 100 permutations. As can be seen in Table B5, none of the 100 permutations performed provides a greater difference in our outcome than the one that is actually observed. This result further confirms that the likelihood that our estimated effect of lockdown policies is caused by chance is close to 0.