Yohan Reynaud
email: yohan.reynaud@improve-innov.com

Michel Lopez
email: michel.lopez@improve-innov.com

Alain Riaublanc
email: alain.riaublanc@inra.fr

Isabelle Souchon
email: isabelle.souchon@inra.fr

Didier Dupont
email: didier.dupont@inra.fr

Tofu Seitan

Soya Juice Pea

Hydrolysis of plant proteins at the molecular and supra-molecular scales during in vitro digestion

Keywords:

The digestion of plant protein is highly dependent on multiple factors, with two of the most important being the protein source and the food matrix. The present study investigated the effects of these two factors on the digestion of seitan (a wheat-based food), tofu, soya juice, and a homemade emulsion of soy oil and water that was stabilised with pea protein. The four plant matrices and their respective protein isolates/concentrates (wheat gluten, soya protein, pea protein) were subjected to in vitro static digestion following the INFOGEST consensus protocol. We monitored the release of α-amino groups during digestion. We found that food matrix had a strong influence on protein digestion: soya juice was more hydrolysed than fresh tofu (51.1% versus 33.1%; P = 0.0087), but fresh tofu was more hydrolysed than soya protein isolate (33.1% versus 17.9%; P < 0.0001). Likewise, the pea-protein emulsion was better hydrolysed than the pea-protein isolate (P = 0.0033). Differences were also detected between the two solid foods investigated here: a higher degree of hydrolysis was found for tofu compared to seitan (33.1% versus 11.8%), which was perhaps a function of the presence of numerous dense protein aggregates in the latter but not the former. Furthermore, freeze-drying more than doubled the final degree of hydrolysis of seitan (P < 0.0001), but had no effect on tofu (P = 1.0000). Confocal microscopy revealed that protein networks in freeze-dried seitan were strongly altered with respect to the fresh product; instead, protein networks in freeze-dried and fresh tofu were largely similar. Finally, we found that the protease:protein ratio had a strong effect on the kinetics of proteolysis: a 3.7-fold increase in the concentration of the soya protein isolate with respect to that of the soya juice decreased the final degree of hydrolysis from 50.3 to 17.9% (P = 0.0988).

Introduction

Compared to animal protein, proteins derived from plants are known for their reduced environmental and economic impacts [START_REF] González | Protein efficiency per unit energy and per unit greenhouse gas emissions : Potential contribution of diet choices to climate change mitigation[END_REF]. However, their two principal drawbacks are the lack of certain essential amino acids to fulfil human nutritional needs and the presence of anti-nutritional factors, i.e. proteins or associated compounds (enzyme inhibitors, fibre, saponins, and tannins) that hinder the digestive process. Moreover, plant albumins are generally thought to be resistant to proteolysis due to their compact structure, a high number of disulfide bonds, and their capacity for self-association [START_REF] Carbonaro | Structural aspects of legume proteins and nutraceutical properties[END_REF]. To improve the nutritional properties of plant-based protein sources, proteins from legumes and cereals are often mixed to create an amino-acid profile that is more nutritionally complete.

To estimate protein quality, the most commonly used reference indicators are the Protein Digestibility-Corrected AA Score (PDCAAS) and the more recently proposed Digestible Indispensable Amino Acid Score (DIAAS), which takes into account the digestibility of the limiting amino acid. These values are typically determined through in vivo experiments, which are not always desirable due to the ethical and economic considerations involved. As an alternative, efforts have been made to develop in vitro systems that could help to investigate questions associated with digestion. For example, one recent study investigated the relationship between in vitro-based measures of digestibility and PDCAAS values of chickpea flour and its protein fractions. The authors found that measurements of peptide-bond hydrolysis gave the highest correlation with in vivo-generated results (Tavano, Neves, & Júnior, 2016). Admittedly, in vitro protocols do not perfectly reproduce all aspects of digestive physiology-for instance, endopeptidases, neurohormonal control, and intestinal absorption are lacking, and the geometry of the gastrointestinal tract and gastric mixing are poorly mimicked. They do, however, have the advantage of being rapid and economical ways to estimate protein degradation under digestive conditions, particularly compared to in vivo experiments on animals or clinical studies, which require more resources and are accompanied by ethical concerns [START_REF] Bohn | Correlation between in vitro and in vivo data on food digestion. What can we predict with static in vitro digestion models?[END_REF]. Moreover, in a well-controlled in vitro system, the volume of bolus and the quantity of endogenous secretions are known, which enables the precise determination of their contributions to the monitored parameters. Sampling can be performed frequently without extensive disruptions to the system, and inter-trial variability is usually lower than the inter-individual variation of in vivo trials. Finally, potential structural changes during digestion can be easily detected.

One of the most important factors in determining the digestibility, bioaccessibility, and ultimate bioavailability of food components for an organism is the food matrix. For example, protein digestion varies considerably among cheese matrices [START_REF] Lorieau | Impact of the dairy product structure and protein nature on the proteolysis and amino acid bioaccessiblity during in vitro digestion[END_REF], but to a lesser extent among plant-based food matrices [START_REF] Rozan | In Vivo and in Vitro Digestibility of Soybean, Lupine, and Rapeseed Meal Proteins after Various Technological Processes[END_REF]. Food processing, such as heat treatment, has also been shown to improve plant protein digestibility, as a consequence of heat-induced protein dissociation or unfolding and/or the elimination or deactivation of thermolabile antinutritional factors, such as trypsin inhibitors [START_REF] Liu | Effects of protein concentration and heat treatment on concentration of digestible and metabolizable energy and on amino acid digestibility in four sources of canola meal fed to growing pigs[END_REF]. In the present study, we aimed to further investigate the matrix effect on protein digestion of plant-based foods. Specifically, we used the in vitro INFOGEST digestion protocol [START_REF] Minekus | A standardised static in vitro digestion method suitable for foodan international consensus[END_REF] to perform comparisons of food products that differed in many key aspects: structure (liquid versus solid), protein source (wheat, soya, pea), and the presence/absence of a food matrix (whole food preparation versus protein isolate/concentrate). We analysed four manufactured foods-seitan, tofu, soya juice, and pea emulsion-that represented three of the most widely produced crops worldwide (among legumes, cereals, and pulses, in tonnes): wheat (8-12% Prot (w/ w); 2rd), soybean (40-45% Prot (w/w); 4th), and green pea (22-24% Prot (w/w); 30th) (FAOSTAT, 2017). Seitan is an east Asian wheat-based food, mostly constituted of gluten and starch that has undergone mild thermal treatment. Soya juice and tofu share the same base ingredient, but we included both here to investigate the effects of their highly different macrostructures: soya juice is obtained simply from soaking soya beans in water, while tofu, also called soya bean curd, undergoes one more step of chemical and thermal coagulation (induced by the addition of glucono-δ-lactone, magnesium chloride, or calcium sulfate; [START_REF] Fukushima | Soy proteins for foods centering around soy sauce and tofu[END_REF]. The green pea emulsion was created via ultrapressure homogenisation of a commercial pea protein isolate (also included in the study) and soya oil in water, and was designed to mimic as closely as possible the nutrient composition and structure of soya juice. With these four foods our study was able to examine differences in the digestion of solids (seitan, tofu) and liquids (soya juice, pea emulsion). All of these results were then compared to those obtained from digestion of the corresponding protein isolate/concentrate for each food-wheat gluten, soya protein (two concentrations, representing soya juice and tofu), and commercial pea protein isolate. To our knowledge, this is one of the first time that digestion of a protein isolate (soya) has been compared to the digestion of the same protein in two different food matrices made with the same batch i.e. a liquid soya juice and a solid tofu. Also, this is the first time that seitan has been studied regarding to the digestive degradation of its proteins.

Materials and methods

Preparation of products

Protein isolates & concentrates

As sources of isolated/concentrated protein, we used readymade commercial pea isolate (Pisane M9, Lot: N16231O04, Cosucra, Belgium) and wheat gluten; concentrated soya proteins were prepared in our laboratory. Wheat gluten and two batches of husked soya beans were graciously provided by Nutrition & Santé (Revel, France). Proteins were extracted from soya beans using a pH precipitation protocol that combined steps from two previous studies [START_REF] Li | Effect of concentration, ionic strength and freeze-drying on the heat-induced aggregation of soy proteins[END_REF][START_REF] Sorgentini | Comparative study of foaming properties of whey and isolate soybean proteins[END_REF]. Briefly, husked soya beans were milled with an ultracentrifugal mill (ZM2000, Retsch GmbH, Germany) using a 0.5-mm sieve and an airstream to avoid heating. Then, the remaining flour was dehulled with hexane (52750, Sigma-Aldrich, USA; 1:4 hexane:flour ratio (w/w)) three times using an overhead shaker at 48 tr.min -1 (Reax 2, Heidolph, Germany) and vacuum filtration (WhatMan Phase Separator 70 mm, GE Healthcare, USA). Finally, residual hexane was allowed to evaporate under a fume hood overnight. The defatted soya flour was extracted for 2 h at room temperature with distilled water (10:1 water:flour ratio) that had been adjusted to pH 8.0 with 2 N (NH 4 ) 2 CO 3 (T122523, Brenntag AG, Germany). The suspension was then centrifuged at 10,400 g for 15 min at 20 °C (Sorvall, Lynx-4000 superspeed centrifuge, Thermo Fisher Scientific, USA); the supernatant was adjusted to pH 4.5 with 1 N HCl before being stored at 4 °C for 2 h. The mixture was again centrifuged at 10,400 g for 20 min at 4 °C and the pellet was washed with distilled water, resolubilised by neutralisation to pH 8.0 with 2N (NH 4 ) 2 CO 3 , and freeze-dried. Final tofurelated and soya juice-related protein isolates contained, respectively, 83.3% and 80.2% protein (conversion factor: 5.50).

Food matrices

In addition to the protein isolates described above, this study was conducted using two solid food matrices and two liquid food matrices that we prepared ourselves. The wheat gluten was used to make seitan; the two soya bean batches were used to prepare tofu and soya juice. Soya juice was UHT (Ultra-High Temperature) packed. A portion of the tofu and seitan was minced, freeze-dried (Eurolyo, France), and then rehydrated (with the same quantity of distilled water previously lost) under agitation for 30 min. These were labelled freeze-dried tofu and freeze-dried seitan, respectively. The pea emulsion was prepared using the commercial pea isolate and commercial soya oil (Emile Noël, France). After assessing the protein and fat content of the pea isolate, both ingredients were added to water in proportions designed to replicate the protein and fat content of soya juice. The pre-emulsion was created using a disperser (T-50 Homogeniser, Ultra-Turrax, IKA, Germany) and a 15 G Dispersing Element (IKA, Germany) for 1 min at 10000 rpm. The solution was then homogenised two times using a table-top homogeniser (PandaPLUS 2000, GEA, USA) at 1000 bar. Temperature was checked at the end of processing and never exceeded 46 °C.

Food characterisation

Nutrient content

Dry matter (DM) content was determined by oven-drying at 105 °C overnight. Similarly, ash content was measured according to AOAC 923.03 (AOAC, 1990). Crude fat content was determined by the Randall method after 12 h incubation in 1 M HCl [START_REF] Iso | Céréales, produits céréaliers et aliments des animaux -Détermination de la teneur en matières grasses brutes et en matières grasses totales par la méthode d'extraction de Randall Méthode NF ISO 11085[END_REF]. Total nitrogen content was measured using the Kjeldahl method according to [START_REF] Thiex | Determination of crude protein in animal feed, forage, grain, and oilseeds by using block digestion with a copper catalyst and steam distillation into boric acid: Collaborative study[END_REF]. To calculate crude protein content, conversion factors of 5.36 for pea proteins, 5.50 for soya, and 5.50 for wheat proteins were used according to [START_REF] Mariotti | Converting nitrogen into protein -Beyond 6.25 and Jones' factors[END_REF]. Starch content was measured using a polarimeter (European Commission, 2009). Non-starch polysaccharide content was checked [START_REF] Englyst | Simplified method for the measurement of total non-starch polysaccharides by gas-liquid chromatography of constituent sugars as alditol acetates[END_REF], but as seed coats were removed from food during processing, only traces were found.

2.2.2. Structure of solid foods 2.2.2.1. Confocal laser scanning microscopy of solid food before and after freeze-drying. Sections of 0.1-mm thickness were cut with a sharp razor blade and placed on microscopy slides between two gene frames with 10 µL of fluorescent probes for protein (Alexa Fluor 546, Thermo Fisher Scientific, Inc., USA) and fat (Nil Red, Thermo Fisher Scientific, Inc., USA). Slides were examined using a confocal microscope (green laser) (Eclipse A1+, Nikon, Japan) in spectral mode. Pictures taken (presented here) were representative of the whole slide.

2.2.2.2. Scanning electron microscopy (SEM) of freeze-dried food. Freezedried products were ground into small particles 0.1-1 mm in diameter. Observation was made with an Environmental Quanta 200 FEG (FEI Company, USA) accelerated at 5 kV and under vacuum pressure of 40 Pa. Pictures shown here were considered representative of the sample.

In vitro digestion protocol

Set-up

This study used the INFOGEST in vitro digestion protocol [START_REF] Minekus | A standardised static in vitro digestion method suitable for foodan international consensus[END_REF], with a specific focus on proteolysis [START_REF] Egger | The harmonized INFOGEST in vitro digestion method: From knowledge to action[END_REF]. The enzymes used were protease, i.e. pepsin (P6887, Sigma-Aldrich, USA) during the gastric phase and porcine pancreatin (P7545, Sigma-Aldrich, USA) during the intestinal phase. Enzyme activity was determined according to EC 3.4.23.1 for pepsin and EC 3.4.21.4 for trypsin of porcine pancreatin, following the protocol described in the supplementary data of [START_REF] Minekus | A standardised static in vitro digestion method suitable for foodan international consensus[END_REF]. Biliary acid content in porcine bile (B8631, Sigma-Aldrich, USA) was checked using a colorimetric reaction-based kit (ref. 1 2212 99 90 313, DiaSys Diagnostic System GmbH). Digestions were conducted in an orbital shaking water bath (1092, GFL, Germany) at 37 °C and 150 rpm. Five mL of a commercial skim milk powder (Régilait, France) (1/10 dissolution in H 2 O, w/v) was also digested two times as a control.

Oral phase

Solid foods were ground using a manual mincer until they passed through a 2-mm sieve (Edington Mincer Pro, Product Code 86002, Berkshire, UK), and were then incubated for digestion. In order to simulate the oral phase, 5 g (of solids) or 5 mL (of liquids) were mixed with 4 mL of 1.25x concentrated simulated saliva fluid (1.25x SSF), 975 µL of distilled water, and 25 µL of 0.3 M CaCl 2 in a 50-mL Schott bottle for two minutes. Each digestion was performed with the same initial amount of food. Incubations of isolates or concentrates contained the same amount of protein as found in those of the related food. Digestions were performed at least in triplicate, in addition to a digestion without enzyme for each group.

Gastric phase

Then, 8 mL of 1.25x concentrated simulated gastric fluid (1.25x SGF) and 5 µL of 0.3 M CaCl 2 were added to the oral bolus, and the pH of the mixture was gently adjusted to 3 using 1 M HCl. Distilled water was added to create a final volume of 19 mL. After allowing the mixture to reach 37 °C, 1 mL of pepsin solution (40 000 U.mL -1 ) was rehydrated and added to the digestion reactor to obtain a final concentration of 2 000 U.mL -1 .

Intestinal phase

After 2 h of the gastric phase, 11 mL of 1.25x concentrated simulated intestinal fluid (1.25x SIF), 40 µL of 0.3 M CaCl 2 , and 2.5 mL of bile solution (160 mmol.L -1 ) were added to the chyme. The pH of the mixture was adjusted to 7 using 1 M NaOH and the reactor was filled with distilled water to reach a final volume of 35 mL, without considering the volume of the food. When the temperature reached 37 °C, 5 mL of pancreatin solution (800 U.mL -1 diluted in SIF) were added. The incubation lasted 2 h.

Sampling and pH regulation

pH was adjusted between each step and checked every 30 min using a glass electrode (N61, SI Analytics GmbH, Germany). We considered the mixture to be homogenous, and took 500-µL samples before incubation with enzymes and 10, 30, 60, and 120 min after the gastric and intestinal phases started. Two initial samplings were performed during the oral phase. At each step, < 3 mL of content were collected, representing 15% and 7.5% of the chyme volume during the gastric and intestinal period, respectively. Immediately after each sample was taken, enzymatic reactions were blocked with enzymatic inhibitors. For gastric samples, we used 10 µL of 0.5 mg.mL -1 Pepstatin A (P5318, Sigma-Aldrich, USA), diluted in 9:1 methanol:acetic acid; for intestinal samples, we added 30 µL of 0.1 M Pefabloc SC (76307, Sigma-Aldrich, USA), diluted in distilled water. Samples were then vortexed for 5 s, put on ice, and stored at -20 °C until further analysis was carried out.

Release of α-amino groups and determination of degree of hydrolysis (DH)

The concentration of α-amino groups was determined using the ninhydrin reaction described in [START_REF] Moore | A modified ninhydrin reagent for the photometric determination of amino acids and related compounds[END_REF][START_REF] Sarin | Quantitative monitoring of solid-phase peptide synthesis by the ninhydrin reaction[END_REF]. Ninhydrin reagent (250 mL) was prepared by mixing 0.75 g of D (-) fructose (F0127, Sigma-Aldrich), 1.5 g of ninhydrin (151173, Sigma-Aldrich), 15 g of monopotassium phosphate (PHR1330, Sigma-Aldrich), and 9.914 g of sodium phosphate, dibasic anhydrous (71639, Sigma-Aldrich). The mixture was adjusted to pH 6.7, completed with milliQ water, and stored in the dark until use. For each digest, the sample was centrifuged (5000 g for 10 min at 20 °C), and the supernatant was diluted with milliQ water and mixed with the prepared ninhydrin reagent at a ratio of 1:2 (v/v ninhydrin reagent:diluted solution). After heat treatment at 95 °C for 16 min, the solution was cooled on ice for 20 min. Dilution solvent (3:2 milliQ water:96% ethanol with 0.2% w/v of potassium iodate (215929, Sigma-Aldrich)) was added at a 5:1 ratio (v/v diluent:solution diluted). Absorbance at 570 nm was quantified with a Spark 20 M microplate reader (TECAN, Switzerland). A calibration curve was constructed using data generated with known concentrations of glycine in distilled water (ranging from 0.04 to 0.21 mM; G8898, Sigma-Aldrich). The analysis was performed in duplicate for each sample.

To determine the total amount of α-amino groups released from food, we used the ninhydrin protocol described above on food samples that had first undergone total acid hydrolysis (2 mg of total protein incubated with 1.5 mL of 6 M HCl solution at 110 °C for 24 h, then cooled and diluted with water). Two measures of degree of hydrolysis (DH) were calculated from these data, using the following formulas:

• DH using the total amount of food nitrogen in the mix, N tot food : DH (t) = (N(t)-N(0))/(N tot food -N(0)) × 100, where N(t) was the concentration of α-amino groups in the mixture at time t, corrected for endogenous input, and N(0) was the concentration of α-amino groups at time 0 (before the addition of pepsin).

• DH using the total amount of nitrogen from α-amino groups released after total acid hydrolysis, N 100% , according to [START_REF] Petitot | Modification of pasta structure induced by high drying temperatures. Effects on the in vitro digestibility of protein and starch fractions and the potential allergenicity of protein hydrolysates[END_REF]: DH N100% (t) = (N(t)-N(0))/(N 100% -N(0)) × 100, where N(t) and N (0) are the same as described above.

Data & statistical analysis

Data are presented as mean ± SD (standard deviation). Gastric and intestinal steps were analysed independently. DH kinetics were compared using the repeated option of the SAS PROC MIXED procedure (SAS University Edition, v. 3.71; SAS Institute Inc., Cary, NC, USA), with time of digestion, food, and their interactions (written as time × food on figures) as fixed effects. If the effect of the interaction was significant, the LSMEANS procedure was used, followed by Tukey adjustment, to test differences between foods of interest at specific time points. The alpha level for our statistical tests was 0.05.

Results and discussion

Nutritional and characterisation

Table 1 shows the composition of the different foods investigated here. Liquids were intentionally prepared to have a fat and protein content that was comparable to their solid counterparts Seitan was characterised by a high starch content (3.0 g.100 g -1 ), whereas tofu contained more fat (8.5 g.100 g -1 versus 2.1 g.100 g -1 for seitan).

Qualitatively, three distinct structures were identified in seitan and tofu (Fig. 1): (i) a hydrated gel with proteins that were more or less homogeneous, with droplets in the micrometer range, (ii) highly dense nuclei of proteins (diameter ~10 mm), (iii) and shadow areas containing water, perhaps created by shearing. Globally, seitan was more heterogeneous in composition than tofu.

As the seitan and the tofu were produced from wheat gluten or soya flour respectively, intact cells were still present in the final food. After the material had been freeze-dried, both matrices appeared more homogeneous. This might have been due to the fact that the freezing process degraded cell walls and ducts, thus facilitating the diffusion of fluorescent markers through the cell networks [START_REF] Harnkarnsujarit | Effects of freezing on microstructure and rehydration properties of freeze-dried soybean curd[END_REF]. Likewise, the cell damage caused by freezedrying also gave other components, such as enzymes, easier access to macronutrients. Since tofu had appeared more homogeneous than seitan prior to freeze-drying, we considered the resulting structural changes in seitan to be more consequential than those in tofu. Instead, in freeze-dried tofu, the lipids seemed to have coalesced. These qualitative observations were consistent with images taken with SEM (Fig. 2), in which porosity seemed to be higher in the freeze-dried seitan than in freeze-dried tofu.

Degree of hydrolysis (DH)

The degree of hydrolysis was calculated two different ways: using the total amount of food nitrogen (N tot food ) or the total amount of nitrogen in α-amino groups released after the total acid hydrolysis of food (N 100% ). These two evaluations of the degree of hydrolysis were referred to as DH and DH N100% , respectively.

All DH N100% values were higher than DH values, which could be explained by the difference between the total amount of food nitrogen put in the reactor (N tot food and the total amount of α-amino-group nitrogen released after the total acid hydrolysis of food (N 100% ). N 100% was always lower than N tot food , with the magnitude of the difference ranging from 22 to 50% depending on the food in question (Fig. 3). One contributing factor could have been that the total acid hydrolysis led to the destruction of some amino acids (Trp, Cys, Thr, Ser), which were therefore not taken into account in the determination of N 100% (FAO & WHO, 1991). Moreover, some nitrogen atoms that are not involved in α-amino groups in some amino acids (Gln, Asn, Lys, His) may been included in the measurement of N tot food and thus increased this value compared to the real amount of complete hydrolysis. Finally, some differences likely arose from the fact that we used different foods, with differences in amino acid profiles and food matrices that could affect the kinetics of acid hydrolysis. Non-negligible differences were observed between different foodstuffs regarding the amounts of α-amino groups released after total hydrolysis. For this reason, hydrolysis kinetics were presented and analysed using the total amount of food nitrogen (N tot food ).

In the case of liquid foods, around 27-28 mg of N tot food were initially incubated, corresponding to 14-16 mg of α-amino-group nitrogen of totally hydrolysed food (Fig. 3). During the intestinal step, around 65 mg of nitrogen and 14 mg of α-amino group nitrogen were contributed by the addition of pancreatin. In terms of α-amino-group nitrogen, pancreatin therefore represented 31-33% of the total nitrogen in the intestinal mixture and 46-50% of the theoretical maximum amount of α-amino-group nitrogen that could be observed, excluding the contributions of pepsin and bile.

Overall, the amounts of α-amino-group nitrogen detected here were lower than those previously reported from other studies. Most of those studies used the O-Phthalaldehyde (OPA) method, which has become popular in recent years for the evaluation of digestive proteolysis. However, this method has some limits: the risk of false positives caused by ε-amino groups is higher than for the ninhydrin method [START_REF] Church | Spectrophotometric assay using o-phthaldialdehyde for determination of proteolysis in milk and isolated milk proteins[END_REF][START_REF] Turgeon | Comparaison de trois méthodes pour la mesure du degré d'hydrolyse de protéines laitières modifiées enzymatiquement[END_REF] and OPA is more dangerous to handle than ninhydrin. Our use of ninhydrin could explain the lower of α-amino groups measured here compared to other studies that used OPA or 2,4,6-trinitrobenzenesulfonic acid (TNBS), as was previously shown in the digestion of pea protein [START_REF] Panasiuk | Determination of α-amino nitrogen in pea protein hydrolysates: A comparison of three analytical methods[END_REF].

Effect of the food structure on proteolysis

Degree of hydrolysis (DH) of food matrices

This section describes only the degree of hydrolysis (DH) of food items; protein isolates/concentrates are analysed in section 3.3.4 in the context of their corresponding foods.

The gastric proteolysis of fresh seitan (Fig. 4A) began late, after 30 min (DH = 0.3 ± 0.0%) of incubation, and reached a final DH of 0.4 ± 0.1% in this stage. Just after the addition of pancreatin, DH increased directly and progressively until it reached 11.8 ± 1.2% at 60 min, at which point it remained stable (120 min: 11.8 ± 2.6%) (Fig. 5A). The DH kinetics of freeze-dried seitan were largely similar to those of fresh seitan; the main exception was found in the intestinal step, when after 30 min the DH of freeze-dried seitan surpassed that of fresh seitan (see section 3.3.3 for more details).

With fresh tofu, gastric hydrolysis began just after the addition of pepsin (Fig. 4B); the DH was 0.5 ± 0.3% after 1 min. At 120 min, the DH arrived at 1.9 ± 0.4%. During the intestinal step (Fig. 5B), the addition of pancreatin induced a direct increase in DH (1 min: DH = 13.4 ± 5.9%), but with a large degree of variation among replicates. DH remained stable around this value for the next 10 min (DH = 12.0 ± 3.5%). Finally, from 30 min to 120 min after the addition of pancreatin, DH continued to rise linearly to a final value of 33.1 ± 4.0%. DH kinetics of freeze-dried tofu were similar to those of fresh tofu (see section 3.3.3 for more details).

Gastric hydrolysis of the pea emulsion (Fig. 4C) increased linearly, from 0.5 ± 1.0% at 1 min to a maximum of 4.9 ± 0.6%. One minute after the addition of pancreatin, the DH increased by more than a factor of seven (35.7 ± 19.4%), but again with extensive variation between tests. As we observed for tofu, during the 10 first minutes of the intestinal phase (Fig. 5C), the DH of the pea emulsion remained relatively stable around 35%. From that point until the end of the phase, the DH doubled linearly, increasing from 35.0 ± 20.6% to 73.6 ± 12.1%.

The DH of soya juice evolved similarly to that of the pea emulsion. In the simulated stomach (Fig. 4D), hydrolysis began immediately, and after 120 min of incubation, arrived at a maximum value of 4.5 ± 2.1%. In the intestinal environment (Fig. 5D), in the first minute following the addition of pancreatin the DH increased to 34.7 ± 14.0% and remained constant (about 30%) for 30 min, at which point the DH increased to reach a final value of 51.1 ± 15.5%.

Overall, the two solid matrices, seitan and tofu, exhibited a lower degree of proteolysis than the two liquid matrices, pea emulsion and soya juice. This might be due to the relative inhibition of pepsin diffusion within a solid matrix compared to a liquid one, as previously demonstrated between water and whey protein isolate gels [START_REF] Luo | Pepsin diffusivity in whey protein gels and its effect on gastric digestion[END_REF]. Indeed, natural proteolysis typically occurs in heterogeneous phases (solid-liquid) rather than in solution. Among the four foods, seitan demonstrated the least amount of Values of DH the gastric phase were low compared to final values in the intestinal phase. The differences we observed here between the DH in gastric and intestinal phases of in vitro digestion, which were based on similar quantities of protein, were consistent with those obtained from the gastric digestion of pasta (DH 8% after 180 min of pepsin incubation; [START_REF] Petitot | Modification of pasta structure induced by high drying temperatures. Effects on the in vitro digestibility of protein and starch fractions and the potential allergenicity of protein hydrolysates[END_REF] or whey protein (DH around 3-4%; [START_REF] Mat | Monitoring protein hydrolysis by pepsin using pH-stat: In vitro gastric digestions in static and dynamic pH conditions[END_REF]. Following standard practice, we also digested a skim milk powder (diluted 1:10 in water) in order to compare our results to previous studies. As was reported by [START_REF] Mat | In vitro digestion of foods using pH-stat and the INFOGEST protocol: Impact of matrix structure on digestion kinetics of macronutrients, proteins and lipids[END_REF], we found that about 60% of dairy proteins were digested using the in vitro INFOGEST protocol (L. [START_REF] Egger | Digestion of Proteins in Milk: Comparing different in vitro systems with in vivo data[END_REF][START_REF] Picariello | Role of intestinal brush border peptidases in the simulated digestion of milk proteins[END_REF].

Solid and liquid soya-based foods

The effect of the food × time interaction was significant during gastric digestion (P = 0.0429), with the DH of soya juice increasing more quickly (-0.3 ± 0.0% to 4.5 ± 2.1%) (Fig. 4D) than that of tofu (0.0 ± 0.0% to 1.9 ± 0.4%) (Fig. 4B). This result is consistent with the observation that β-conglycinin persists in tofu but not in soya juice after pepsin digestion [START_REF] Adachi | Soybean Beta-conglycinin as the main allergen in a patient with food-dependent exercise-induced anaphylaxis by tofu: Food processing alters pepsin resistance[END_REF]. One possible explanation could be linked to the lower proportion of soluble nitrogen, which is accessible to enzymes, in tofu compared to in soya juice [START_REF] Rui | Protein bioaccessibility of soymilk and soymilk curd prepared with two Lactobacillus plantarum strains as assessed by in vitro gastrointestinal digestion[END_REF]. Gastric conditions have also been reported to cause more significant structural alterations to soya juice than to tofu [START_REF] Liu | Structural characterization of soybean milk particles during in vitro digestive / non-digestive simulation[END_REF]; this could also facilitate further intestinal digestion and lead to higher rates of hydrolysis.

During intestinal digestion, the effect of food was significant (P = 0.0087), but the food × time interaction was not (P = 0.6894); this meant that even if DH values were significantly different between tofu and soya juice, the kinetics of hydrolysis were similar. The final DH values highlighted the cumulative effect of the differences between the two products: soya juice was 51.1 ± 15.5% hydrolysed (Fig. 5D), whereas tofu was only 33.1 ± 4.0% hydrolysed (Fig. 5B).

Effect of freeze-drying

Significant differences were found between fresh and freeze-dried seitan at the end of the intestinal step, with fresh seitan demonstrating a lower DH (11.8 ± 2.6%) than freeze-dried (26.3 ± 0.9%) (P < 0.0001). Instead, this was not the case for tofu (fresh: 33.1 ± 4.0% versus freeze-dried: 33.9 ± 6.7%; P = 1.0000).

Freeze-drying seemed to increase the substrates' accessibility to enzymes by modifying the food structure, but not necessarily altering pepsin proteolysis sites. Although a previous study highlighted pore deformation and wall-thickness changes in tofu during freeze-drying, and leaching during rehydration, no effect was reported on the protein digestion of tofu [START_REF] Harnkarnsujarit | Effects of freezing on microstructure and rehydration properties of freeze-dried soybean curd[END_REF]. Freeze-drying could also affect the bioaccessibility of other compounds, as was reported for polyphenol in apples, by altering the microstructure [START_REF] Dalmaua | Effects of freezing, freeze drying and convective drying on in vitro gastric digestion of apples[END_REF].

Comparison between protein concentrates/isolates and food matrices

With soya-based foods and protein isolates, we found that the food matrix had a significant effect on protein digestion: the gel matrix of tofu seemed to protect peptide bonds from hydrolysis by trypsin (and, to a lesser extent, chymotrypsin), whereas emulsification during the process of making soya juice appeared to expose them.

The effect of the food time interaction was significant for tofu and its related preparations during both the gastric and intestinal steps, with the final DH of the tofu-associated protein isolate (17.9 ± 1.8%) markedly lower than that of fresh or freeze-dried tofu (33.1 ± 4.0% and 33.9 ± 6.7%, respectively; P < 0.0001 for both) (Fig. 5B). The likely explanation for this is that, compared to the unprocessed protein of the isolate, denaturation occurring during processing probably made the protein in the food matrix more sensitive to digestive proteases by opening protein structures [START_REF] Desphande | Structure Digestibility Relationship of Legume 7S Proteins[END_REF]. However, for soya juice and its related isolate, there was no significant food × time interaction (gastric phase: P = 0.7191; intestinal phase: P = 0.2417) (Fig. 4D and Fig. 5D), which suggests that the protein in soya juice and in the soya juice-related isolate was digested in the same way. This is consistent with previous work performed on humans in which researchers found that, although the gastro-jejunal absorption of nitrogen appeared to be lower for soya juice (49%) than for soya protein isolate (63%), the difference was not statistically significant [START_REF] Baglieri | Gastro-jejunal digestion of soya-bean-milk protein in humans[END_REF]).

For pea protein, the only differences between the protein isolate and the emulsion were found during the intestinal step: when analysed over the entire stage, the DH of the emulsion was significantly higher than the DH of the protein isolate (P = 0.0033) (Fig. 5C). However, no significant differences were detected at any of the individual sampling times. It should be noted that the coefficients of variation (ratio of the mean to the standard deviation) were particularly high for the pea emulsion, likely influenced by the high relative proportion of pancreatin in the intestinal phase, as discussed in section 3.2. A 1-liter batch of emulsion was prepared before each assay. We considered each batch to be homogenous, but since only small quantities were used in each assay (5 mL), it is possible that there were variations among the samples used, which then introduced variation into our results. Regardless, for pea protein, a simple solubilisation of the isolate appeared to be less conducive to protein hydrolysis than an emulsification. The high-pressure processing used for emulsification could explain the higher rate of protein digestion in this preparation, as previously described for pea isolates [START_REF] Laguna | In vitro gastrointestinal digestion of pea protein isolate as a function of pH, food matrices, autoclaving, high-pressure and re-heat treatments[END_REF]. This type of processing may cause an increase in protein solubilisation and in the number of lipid droplets, thus increasing the exposure of protein to enzymes.

With respect to wheat protein, isolated gluten was more accessible to enzymes than gluten in a food matrix, as indicated by the higher DH in the simulated stomach for wheat gluten compared to fresh seitan starting from 30 min after the addition of pepsin (0.7-1.1% versus 0.2-0.4%; P < 0.0086) (Fig. 4A). A similar difference was observed between gluten and freeze-dried seitan at 30 and 60 min, but not at 120 min. Then, during the intestinal step, the DH kinetics of gluten were similar to those of fresh seitan, but freeze-dried seitan was significantly more hydrolysed. The reduction in gastric DH observed for seitan compared to gluten could be due to the heat treatment used in the seitan-making process, which has been previously reported to lead to lower protein hydrolysis during in vitro digestion of gluten products [START_REF] Rahaman | Effect of heat, pH and shear on digestibility and antigenic characteristics of wheat gluten[END_REF][START_REF] Wu | Effects of chemical composition and baking on in vitro digestibility of proteins in breads made from selected gluten-containing and gluten-free flours[END_REF].

Protein source and effect on proteolysis

Effect of protein source on the proteolysis of solids

When we compared fresh tofu and seitan, the food × time interaction was significant (P < 0.0001) in both the simulated stomach and small intestine. From 10 min after gastric output until the end of intestinal digestion, fresh tofu was more hydrolysed than fresh seitan (P < 0.0276), with the exception of just after the addition of bile, just before the addition of pancreatin, and 10 min into the intestinal digestion. The final values for DH in the intestinal phase illustrate the difference between these two solid foods: 33.1 ± 4.0% for fresh tofu, 11.8 ± 2.6% for seitan.

These observations may be explained by the higher solubility of soya protein compared to gluten. The supposed higher porosity (Fig. 2) of seitan compared to tofu does not seem to have resulted in higher hydrolysis. The protein aggregates that we observed in confocal images of seitan appeared to be denser than those of tofu (Fig. 1), which could explain this limited proteolysis. Other factors, such as the presence of starch in seitan and its absence in tofu, could also contribute to a higher degree of resistance to hydrolysis [START_REF] Nawrocka | Raman studies of gluten proteins aggregation induced by dietary fibres[END_REF].

Effect of protein source on the proteolysis of liquids

The proteolysis of pea and soya emulsions proceeded similarly: there was no significant interaction observed between protein source and time either during the gastric (P = 0.9509) or the intestinal step (P = 0.1850). Furthermore, during the gastric phase, no differences were detected between pea and soya isolates (P = 0.1200). However, the two isolates did exhibit significant differences during the intestinal phase (P = 0.0419): soya isolate appeared to be hydrolysed more quickly than pea isolate, even if none of the differences at individual sampling times were considered significant. This result was surprising given that a recent study, using the same conditions of in vitro digestion, found that around 25% fewer α-amino groups were released from a soya isolate compared to a pea isolate [START_REF] Corgneau | Nutritional quality evaluation of commercial protein supplements[END_REF].

Importance of the protease:protein ratio

When we compared the two types of soya protein isolates (representative of tofu and soya juice, respectively), we found a significant effect of the food × time interaction on the kinetics of gastric DH (P = 0.0186). Starting from 30 min after the addition of pepsin (P < 0.0684), the protein isolate that was representative of tofu seemed to be less hydrolysed (0.7-2.6%) than the one that represented soya juice (3.3-5.2%).

The DH of the soya protein isolates also differed during the intestinal phase (P = 0.0039), but not globally (overall interaction effect was not significant: P = 0.2523). At the end of the intestinal step, the DH of the tofu-related isolate appeared to be lower (17.9 ± 1.8%) than the soya juice-related isolate (50.3 ± 7.6%), but this difference did not reach the level of statistical significance (P = 0.0988).

The slower and more limited hydrolysis that we observed for the tofu-associated isolate could be explained by the fact that it was 3.7times more concentrated with respect to food protein content than the isolate that represented soya juice. It is also possible that some of these differences arose from inconsistencies between the batches of soya beans used to make the tofu and soya juice.

Conclusions

The present study on in vitro protein digestion of different food products enabled us to examine multiple factors that affect the digestion of proteins, and, through various comparisons, to untangle their relative effects. Here, the food matrix played an important role in the digestion of proteins, as demonstrated for both pea emulsion and tofu. By comparing the digestion of the proteins alone, only solubilised in water, to the same proteins inside a food matrix, we were able to observe clear differences in the progression of the degree of hydrolysis. In both cases, fresh tofu and pea emulsion were better hydrolysed than their respective protein isolates. However, this effect was dependent on the food matrix and protein of origin, because it was not found for seitan and soya juice. The food matrix also affected how proteases digested food proteins. Globally, we observed that solid foods had a lower degree of hydrolysis than liquid ones. More specifically, after gastric and intestinal digestion, soya juice was better hydrolysed (51%) than tofu (33%). We were also able to document how a treatment that affects the food matrix-freeze-drying, which in seitan appeared to increase the flexibility of the protein network-also increased the degree of hydrolysis. With respect to protein source, it was not possible to make generalisations; protein digestion of the soya juice-related isolate was significantly different from that of the pea isolate, but emulsions of both isolates were digested similarly. Another of our comparisons enabled us to evaluate the effect of different concentrations of the same protein: when incubated with the same amount of digestive enzyme, a larger quantity of soya protein substrate (representative of tofu) was hydrolysed more slowly than a smaller amount of the same protein (representative of soya juice). To conclude, efforts to characterise proteolysis-related data during in vitro digestion represent a useful starting point in screening and comparing the responses of different kinds of plant-based food protein to digestive processes.

  da Silva https://doi.org/10.1016/j.foodres.2020.109204 Received 3 September 2019; Received in revised form 20 March 2020; Accepted 27 March 2020

Fig. 1 .

 1 Fig. 1. Representative images from confocal laser scanning microscopy of seitan and tofu, before and after freeze-drying. Proteins were labelled in green and lipids in red (scale bar is 100 µm).

Fig. 2 .

 2 Fig. 2. Representative images from scanning electron microscopy of seitan and tofu (scale bar is 100 µm).

Fig. 3 .

 3 Fig.3. Amount of total food nitrogen in the reactor (N tot food ) compared to the total amount of nitrogen in α-amino groups released after total acid hydrolysis (N 100% ) (bars are shown with standard deviations, n = 2 total hydrolyses). The black line indicates the amount of α-amino nitrogen contributed by pancreatin in the intestinal phase. Percentages above bars are relative differences between N tot food and N 100% : (N tot food -N 100% )/(N tot food ). SMP: Skim milk powder.

Fig. 4 .

 4 Fig. 4. Profiles of degree of hydrolysis, calculated with N tot food (DH), of protein during in vitro gastric digestion. Bars represent mean ± SD; n = 3-7 digestions. Panels show the DH of foods before and 1, 5, 10, 30, 60, and 120 min after incubation with pepsin. A) Seitan group; B) Tofu group; C) Pea group; D) Soya juice group. Letters (ab) above bars indicate results of statistical comparison with post-hoc Tukey tests.

Fig. 5 .

 5 Fig. 5. Profiles of the degree of hydrolysis, calculated with N tot food (DH), of protein during in vitro intestinal digestion. Bars represent mean ± SD; n = 3-6 digestions. Panels show the DH of foods before and 1, 5, 10, 30, 60, and 120 min after incubation with pancreatin. A) Seitan group; B) Tofu group; C) Pea group; D) Soya juice group. Letters (ab) above bars indicate results of statistical comparison with post-hoc Tukey tests.

Table 1

 1 Nutritional composition of studied products (g per 100 g (wet base)).

	Protein source (N factor)	Food	DM	Ash	Protein	Fat	Starch	Name and protein content of the related protein isolate/concentrate
	Wheat (5.50)	Seitan	38.4	1.3	27.4	2.1	3.0	49.8 (Gluten)
	Soya (5.50)	Tofu	25.0	1.3	11.0	8.5	0	83.3 (Tofu-related protein isolate)
		Soya juice	8.0	0.5	3.0	2.1	0	80.2 (Soya juice-related protein isolate)
	Pea (5.36)	Pea emulsion	5.22	0.25	3.0	2.1	0	73.6 (Pea protein isolate)

Acknowledgements

We thank Dominique Chevalier from Nutrition & Santé for kindly providing food products and advice. We are grateful to Lindsay Higgins for correcting the English of the manuscript. We also gratefully acknowledge Sophie Legall for quantifying non-starch polysaccharide dosages and Thomas Auxenfans for taking pictures on the scanning electron microscope.

Funding information

The present article is part of a CIFRE thesis (CIFRE n°2016/0719) funded by IMPROVE SAS and INRA.

Disclosure

The authors have no competing interests.


Tanissia Djemai
email: tanissia.djemai@irit.fr

Patricia Stolf
email: patricia.stolf@irit.fr

Thierry Monteil
email: monteil@laas.fr

Jean-Marc Pierson
email: jean-marc.pierson@irit.fr

A Discrete Particle Swarm Optimization approach for Energy-efficient IoT services placement over Fog infrastructures *

Keywords: Fog, IoT, DPSO, Heuristics, Energy, QoS, iFogSim

The Internet of Things (IoT) encompasses both large-scale deployed physical infrastructures and software layers that enable intuitive and transparent creation of applications. This highly distributed, energy-greedy environment must ensure the quality of deployed services while taking into account the heterogeneity of capabilities and protocols as well as users and objects mobility. Deployment infrastructure has been redesigned to provide the necessary features, including paradigms such as software-defined networks and Fog computing. The purpose of this article is to study IoT services placement in a Fog architecture. We propose a model of the infrastructure and IoT applications as well as a placement strategy taking into account system's energy consumption and applications delay violations minimization with a Discrete Particles Swarm Optimization algorithm (DPSO). Simulations have been done with iFogSim simulator. Results have been compared with heuristics coming from the literature: Binary Partical Swarm optimization (BPSO), Dicothomous Module Mapping (DCT), CloudOnly, IoTFogOnly, IoTCloud (IC) and FogCloud (FC) placement approaches.

I. INTRODUCTION

Nowadays, we depict around 15 billions of deployed connected objects. A study published by CISCO [START_REF] Evans | The Internet of Things How the Next Evolution of the Internet Is Changing Everything[END_REF] predicts an increase of devices reaching 50 billions in 2025. The proliferation of equipment such as smartphones, wearables, autonomous vehicles and their associated services leads to high heterogeneity, scalability, delays and mobility issues and that is making Internet of Things (IoT) services placement in the cloud less attractive. Fog Computing is defined as the process of extending cloud capabilities with networks nodes [START_REF] Bonomi | Fog Computing and Its Role in the Internet of Things[END_REF], [START_REF] Iorga | Fog Computing Conceptual Model Recommendations of the National Institute of Standards and Technology[END_REF] and seems to be a promising solution to support requirements induced by IoT applications. Indeed, Fog computing has emerged as a powerful paradigm answering new application needs such as short response delays and high bandwidth demand by providing computing and storage capacities closer to end users. Adding to that, a large scalable and distributed infrastructure such as Fog computing is at first sight more suitable to handle objects heterogeneity and dynamic of IoT applications but in contrast, their placement and management in such infrastructure can be quite challenging and disadvantageous if not well designed. Using such a distributed large scale and dynamic topology can be easily energy and network-greedy if the trade-off between services Cloud-placed, Fog-placed is not well balanced. Adding to that, objects and users positions are also parameters that should be considered for IoT services, which also interact with real physical environment through sensors and actuators devices. Energy consumption is a high interest field for cloud community, considering that data centers consume 4% of global world energy [27]. Fog Computing, by combining both data centers, communications infrastructures and IoT systems makes the energy issue more complex to study, inheriting various issues of evaluation and optimization of the latter in networks and IoT systems. A report from the International Energy Agency (IEA) [START_REF] Iea | Energy Efficiency of the Internet of Things[END_REF] estimates the annual energy consumption of 5 types of IoT applications, home automation, smart lighting and smart street lighting, smart roads, smart appliances, to 46 TWh in 2025. Since services placement problem is NP-hard, we propose to use an evolutionary semistochastic meta-heuristic to efficiently place IoT services in a Fog infrastructure minimizing the energy consumption and applications delay violations while ensuring nodes capacities constraints and services placement constraints. This paper's contributions can be summarized as follows :

• Using a Discrete Particle Swarm Optimization for IoT services placement in a Fog computing infrastructure. • Considering different applications topologies and classes with their delay constraints. • Evaluating with real topology values and different networks technologies using iFogSim simulator.

The remainder of this paper is structured as follows. In section II we establish a brief Fog computing and services placement's state of the art. Then, we introduce Particle Swarm approach.

In section III and IV, we expose respectively the problem mod-eling and the Discrete Particle Swarm Optimization (DPSO) model used for IoT services placement. Finally, section V reports experimental results using iFogSim.

II. RELATED WORK

A. Fog computing and services placement

Fog Computing is a relatively young concept [START_REF] Bonomi | Fog Computing and Its Role in the Internet of Things[END_REF]. Since 2012, several Fog research areas have emerged, including the development of simulation tools such as iFogSim and Edge-CloudSim [3] [23], platforms for the industry, such as Iox [START_REF]Cisco company, Cisco Fog Computing with IOx[END_REF] and Edgex [START_REF] Sonmez | EdgeCloudSim: An environment for performance evaluation of Edge Computing systems[END_REF]. [START_REF] Yi | A Survey of Fog Computing: Concepts, Applications and Issues[END_REF] determines the degree of relevance of the Fog according to the type of applications and their use cases: connected vehicles, health care, smart tracking, smart grids, [START_REF] Guevara | Multiple Workflows Scheduling in Multi-tenant Distributed Systems: A taxonomy and Future Directions[END_REF] defines classes of services to facilitate deployment policies. There are also many works on Fog-Cloud and Fog-IoT layers interactions, moving loads from a Fog node to the Cloud, assigning users to Cloud and Fog services, increasing capacity mobile devices as part of Mobile Cloud Computing (MCC) [START_REF] Fernando | Mobile cloud computing: A survey[END_REF] and Mobile Edge Computing (MEC) [START_REF] Abbas | Mobile Edge Computing: A Survey[END_REF]. [START_REF] Meng | Delay-Constrained Hybrid Computation Offloading With Cloud and Fog Computing[END_REF], deals with the offloading of Fog tasks to the Cloud under delay constraints. Other works like [START_REF] Zhang | Computing Resource Allocation in Three-Tier IoT Fog Networks: A Joint Optimization Approach Combining Stackelberg Game and Matching[END_REF] tackle the issue of fog node allocation to different service providers by combining principles of game theory with Stackelberg's bidding.

Several approaches for IoT service placement in the Fog have been addressed. [START_REF] Taneja | Resource aware placement of IoT application modules in Fog-Cloud Computing Paradigm[END_REF] presents a generic placement algorithm of IoT services in the Fog based on a dichotomous search on all the available Fog nodes. [START_REF] Brogi | QoS-Aware Deployment of IoT Applications Through the Fog[END_REF] proposes a method which identifies deployment's eligibility, taking into account business policies and resources states. [START_REF] Minh | Toward service placement on Fog computing landscape[END_REF] proposes to maximize the placement of tasks in the Fog without taking into account the requirements of services and excludes cloud usage in certain cases. Following the same objective of fog resource usage maximization [START_REF] Skarlatemail | Optimized IoT service placement in the fog[END_REF] proposes a genetic algorithm approach. [START_REF] Bittencourt | Mobility-Aware Application Scheduling in Fog Computing[END_REF] studies scheduling problem in Fog computing, Considering user mobility influence on application performance and compares three different scheduling policies, namely concurrent, FCFS, and shows that delay-priority strategies, can be used to improve execution [START_REF] Pham | Towards task scheduling in a cloudfog computing system[END_REF] try to minimize application makespan and monetary cost.

About energy in Fog Computing and IoT, [START_REF] Jalali | Greening IoT with Fog: A Survey[END_REF] defines elements that should come into consideration to reduce cloud-IoT system energy consumption such as network access technology, applications type, Fog servers energy consumption with no workload, virtualization techniques and their management. [START_REF] Gray | Power consumption of IoT access network technologies[END_REF] shows that IoT applications energy consumption in the Fog is directly impacted by access technologies. It is shown that application can be more energy-greedy if it is accessed via a 4G network rather than a wired network with Ethernet technology, sending rates also influences, and in some cases wired technologies are less efficient than wireless. [START_REF] Bozorgchenani | An Energy-Aware Offloading Clustering Approach (EAOCA) in fog computing[END_REF] proposes a strategy of clustering Fog nodes to minimize their energy consumption. [START_REF] Liu | Multiobjective Optimization for Computation Offloading in Fog Computing[END_REF] tries to minimize energy, time and execution cost for mobiles tasks; it studies offloading rather than initial services placement and model the problem with queues system modeling. In [START_REF] Aparicio-Pardo | A cost model for green fog computing and networking[END_REF], model for video traffic's energy consumption in a Fog system is proposed but services placement is supposed to be already done. [START_REF] Mebrek | Efficient green solution for a balanced energy consumption and delay in the IoT-Fog-Cloud computing[END_REF] adopted an object assignment problem rather than service one by addressing IoT devices to Fog nodes assignment problem with an evolutionary algorithm to reduce mobile energy consumption under delay constraints. Due to computing and networking capacities evolution, agent-based evolutionary algorithms are receiving more attention and have emerged as strong optimization approaches. Meta-heuristics such as Genetic Algorithm (GA), Ant Colony Optimization (ACO) or Particle Swarm Optimization (PSO) seem to be the ideal approaches for distributed and dynamic computing systems. To the best of our knowledge, Particle Swarm Optimization was only used in cloud paradigm. [START_REF] Salman | Particle swarm optimization for task assignment problem[END_REF] used PSO for task assignment problem in order to reduce total execution time and compare PSO results with classical GA. In the same field, [START_REF] Izakian | A Discrete particle swarm optimization approach for grid j ob scheduling[END_REF] proposes a DPSO approach for grid job scheduling aiming to minimize makespan and flowtime and shows that this approach gives better results than other evolutionary methods such as GA and ACO. [START_REF] Singh | Energy efficient routing of WSN using particle swarm optimization and V-LEACH protocol[END_REF] proposes an energy-efficient routing protocol for Wireless network using PSO. Differently from previous works and considering good results given by the PSO approach in cloud paradigm, we aim to place different types of IoT applications in a Fog infrastructure while minimizing both system's energy consumption and applications delay violations using a Discrete Particles Swarm (DPSO) metaheuristic under devices capacities constraints. To the best of our knowledge, there is no other work in the literature that aims at minimizing both energy consumption and applications delay violations.

B. Particle Swarm Optimization approach overview

Particle Swarm approach [START_REF] Kennedy | Particle Swarm opritmization[END_REF] is a semi-stochastic population-based optimization method inspired by the collective behavior of social animals such as flock of birds and fish school. In order to find an acceptable solution to a combinatorial problem, the PSO manipulates a population of particles set called a Swarm. This particle swarm explores the problem search space to find an acceptable solution.

Considering a D-dimensional combinatorial continuous problem, the k th swarm's particle X k is a D-dimensional vector representing a feasible solution. Each particle X k is identified by a subset of particles' neighbours, its position in the search space X k t and its motion speed called velocity V k t which varies from one iteration t to the next. The speed variation of each particle X k is a function of particle's previous position X k

(t-1)
, its personal best known position P b k and its neighbours best position N b k (eq (1)).

X k t = f ( X k t-1 , V k t-1 , P b k , N b k ) (1)
PSO was initially proposed for continuous problems but rapidly, in order to resolve binary decision problems such as services placement, Kennedy and Eberhart introduced Binary Particle Swarm Optimization (BPSO) [START_REF] Kennedy | A discrete binary version of the particle swarm algorithm[END_REF]. Its main difference with PSO lies in particles positions and velocities definitions which are defined respectively as binary placement and probabilities matrices. For this purpose, the sigmoid function sig(.) is introduced to map all real valued elements of velocity v t k (i, j)in [0, 1] with i, j ∈ N.

• ∀X k particle of the swarm and its corresponding velocity V k , defined respectively as a binary placement and probability matrices, are updated according to equations ( 2), ( 3) and ( 4) as follows:

V t+1 k = ωV t k + ϕ 1 ω t 1 (P b t k -X t k ) + ϕ 2 ω t 2 (N b t k -X t k ) (2) x t+1 k (i, j) = 1 if rand() ≥ sig(v t+1 k (i, j)) 0 if rand() < sig(v t+1 k (i, j)) (3)
sig(v t+1 k (i, j)) = 1 1 + exp -v t+1 k (i,j) (4)
• ϕ 1 and ϕ 2 are respectively known as cognitive and social constants that modulate the magnitude of particle's next step to its personal best and neighbours best solutions.

According to the literature [START_REF] Marini | Particle Swarm opritmization (PSO).A tutorial[END_REF] ϕ 1 and ϕ 2 are usually in [0, 4] and it has been shown in [START_REF] Kennedy | Particle Swarm opritmization[END_REF] that ϕ 1 = ϕ 2 = 2 works well for most applications. • To avoid particle's big oscillations problem, literature introduces two approaches: Velocity clamping that bounds the velocity vector elements v k (i, j) ∈ [-V max , V max ] or a restriction coefficient ω to ponderate velocity elements values. This limitation prevents particles from moving too rapidly from one search space region to another. This value is usually initialized as a function of the problem range [START_REF] Eberhart | Comparing inertia weights and constriction factors in particle swarm optimization[END_REF], [START_REF] Marini | Particle Swarm opritmization (PSO).A tutorial[END_REF].

• ω 1 and ω 2 are two matrices with elements ω 1 (i, j), ω 2 (i, j) taken randomly in [0, 1], aiming to introduce randomness in particles motions behaviour through search space. This approach was designed for discrete problems as DPSO where values of X k are in N. For placement problems DPSO, that we will detail in section IV, is more interesting in term of memory space usage during implementation and we can easily switch from BPSO to DPSO modeling. [START_REF] Izakian | A Discrete particle swarm optimization approach for grid j ob scheduling[END_REF].

III. PROBLEM FORMULATION

A. Physical topology

We consider a Hierarchical Three-Layered Fog infrastructure M, constituted of M physical nodes. The first layer is composed of a set C of cloud data center's nodes (level 0), the second one is a set F of Fog nodes ( level 1 to l -1) and the last layer regroups a set T of IoT devices or connected things (level l) to which sensors and actuators are directly connected. The physical topology is represented by an oriented graph G M = (M, L) with L the set of links between nodes. Each node m i ∈ M with i ∈ [0, M -1] has the following characteristics:

• A Level lev i in the topology from 0 to l.

• Processing capacity cpu i in MIPS.

• Memory capacity ram i in MB.

• Power consumption characteristics p idle i that represents the power consumption of the device when it is not used and p max i the device's power consumption when it is used to its maximal capacity. Each link l k ∈ L that binds nodes m i and m j has the following characteristics:

k = (i, j) with i, j ∈ [0, M -1] If point to point (i, j 1 , .., j n ) with j n ∈ [0, M -1], n ∈ N If multi-points • ntw k represents links network technology. • bw k is the bandwidth in Mb/s.
• lc k is the latency in ms.

• ste k is the state which can be "On" or "Off". l k can be a physical or a virtual link. If l k is a virtual link, we assume that devices' routing algorithm gives us one optimum path between two machines composed of a set Θ lk of physical links.

∀v ∈ Θ lk

• bw k = min v∈Θ l k (bwv) • lc k = v∈Θ l k (lcv)

B. IoT Applications

According to works [START_REF] Mahmud | Modelling and Simulation of Fog and Edge Computing Environments using iFogSim Toolkit[END_REF], [START_REF] Giang | Developing IoT applications in the Fog: A Distributed Dataflow approach[END_REF] and [START_REF] Guevara | Multiple Workflows Scheduling in Multi-tenant Distributed Systems: A taxonomy and Future Directions[END_REF], IoT applications are special workflows that should be deployed in distributed systems and can be modeled as Directed Acyclic Graphs (DAG). Indeed, an IoT application gets data from the physical environment through sensors equipment, those information are processed by software services and then instructions are transmitted to actuators in order to act on devices. From the previous definition we can decompose the IoT application view as follows:

1) Sensors and Actuators: In application's DAG representation, sensors nodes and actuators nodes represent respectively sources and ends of the DAG data flow.

2) Processing services: Each processing service s i is defined by:

• tec i : the service deployment technology which can be a virtual machine, a container, OSGi plugin, Java Virtual Machine(JVM) or a combination of them. • mi i : the CPU requested by service i in million instructions.

• ram i : the maximum RAM requested by service i in MB.

• d exe i : the maximum execution delay for service i in ms. 3) Links and dependencies between IoT processing services: Each oriented edge e (i,j) ∈ E going from service s i to service s j represents data dependency between s i and s j and carries the following information:

• data (i,j) is the data size sent from s i to s j in kB.

• d com (i,j) is the maximum communication delay between s i and s j . 4) IoT application Direct Acyclic Graph models: We consider a Directed Acyclic Graph G A = (S, E) which represents a set A = {a 0 , ..., a A-1 } of IoT applications where each application a i has a size n i of processing services.

S is the set of size N composed of processing services from all applications that we have to place with N = A-1 i=0 n i . E is the set of edges representing data dependencies between the applications graph nodes.

5) IoT applications service classes and priority:

Establishing a prioritization between applications classes shows usually good results for standard workflows management in cloud data centers [START_REF] Guevara | Multiple Workflows Scheduling in Multi-tenant Distributed Systems: A taxonomy and Future Directions[END_REF]. Each IoT application belongs to a class as identified in [START_REF] Guevara | Class of service in fog computing[END_REF] with its associated priority. In addition to services' execution time and communication delay, each application a i has a global maximum response delay D max ai , from a sensor to its corresponding actuator, that should not be exceeded. This value is taken according to delay-sensitivity in each application class.

C. Problem statement

We aim to place a set A = {a 0 , a 1 , ..., a A-1 } of heterogeneous IoT applications in a three-Layered Fog infrastructure's nodes M = {m 0 , ..., m M -1 } while minimizing a cost function f under nodes capacities constraints.

f : N N -→ R represents system's total energy consumption E T pondered by total applications delay violations λ.

The total applications delay violations λ, defined in eq [START_REF]Cisco company, Cisco Fog Computing with IOx[END_REF], represents the count of all sensor to actuator delay violations in the applications set A.

A delay violation of an application a i occurs when the processing and communication time d ai , from its sensor to its attached actuator exceeds the allowed time D max ai which is given by the application's class requirements. λ = ai∈A w ai with :

w ai = 1 if D max ai < d ai 0 if not (5)
The total energy consumption E T is the sum of consumption from the computations and from network communications.

E T = E N + E C . (6)
For one data flow processing, i.e from sensor to actuator, we compute energy consumption as follow:

E C = N -1 i=0 M -1 j=0 Y t k (i, j) mi i cpu j (p max j -p idle j ) + p idle j (7)
E N = (i,l)∈S (j,p)∈M [Y t k (i, j)Y t k (l, p) data (i,l) bw (j,p) + lc (j,p) ][p max j + p max p -p idle j -p idle p ] (8)
with Y t k (i, j) is the binary decision variable for the placement of service s i in the device m j from the decision agent 1 k at time t. 1 Swarm based algorithms manipulate a set of potential solutions that evolve during algorithm life time. Depending on the idea of the swarm approach, the terminology of this potential group of solutions varies from one approach to another. To give a method-agnostic naming to a swarm single element we use "decision agent" term.

Y t k (i, j) = 1 if service s i is on machine m j 0 if not ( 9
)
The problem is equivalent to place the set of all services S = {s 0 , s 1 , ..., s N -1 } of G A=(S,E) , which is the DAG of all applications to place at the same time, on physical topology nodes set M. ∀k, t ∈ N :

f = min i∈[0,N -1],j∈[0,M -1] [(1 + λ)E T ] (10)
s.t ram i ≤ ram j ∀i ∈ [0, N -1], ∀j ∈ [0, M -1]..(i) mi i ≤ cpu j ∀i ∈ [0, N -1], ∀j ∈ [0, M -1]..(ii) j∈[0,M -1] y t k (i, j) = 1, ∀i ∈ [0, N -1]...(iii) • (
i) and (ii) are respectively memory and computing constraints for placing service i on machine j. • (iii) means that a service s i should be placed only in one device.

IV. A DISCRETE PSO FOR IOT SERVICES PLACEMENT

We have a particles swarm P = {X 0 , ..X P -1 } of size P , each X k ∈ P will evolve over a set T max of iterations.

A. Particle position and velocity's representations

As it is shown in Figure 1, X k ∈ N N represents the position of the k th particle in the DPSO swarm and it is a N size vector with values

x k (i) ∈ [0, M -1], ∀i ∈ [0, N -1]. X t k
is the particle's position at iteration t. x t k (i) = z means that at iteration t service s i is placed in the z th machine m z with z ∈ [0, M -1]. Which can be written as follows:

x t k (i) = z ⇐⇒ Y t k (i, z) = 1 ∧ ∀j ∈ {0, .
., N -1} -{z}, Y t k (i, j) = 0. The particle's velocity V k is an NxM matrix. It determines the motion speed of the particle X k . Each element v k (i, j) ∈ R defines the possibility of service s i to be placed in the machine m j .

B. Particle's motion equation

Particle positions are updated through iterations according to the following:

1) We compute each particle new velocity matrix according to Eq [START_REF] Iea | Energy Efficiency of the Internet of Things[END_REF].

v t+1 k (i, j) = ω (t+1) v t k (i, j) + ϕ 1 ω t+1 1 (i, j)[f (P b t k ) -f (X t k )] + ϕ 2 ω t+1 2 (i, j)[f (N b t k ) -f (X t k )] (11)
We may stress that variables ω 1 , ω 2 , ϕ 1 , ϕ 2 , ω, N b, P b keep the same meaning as in the BPSO equation [START_REF] Iorga | Fog Computing Conceptual Model Recommendations of the National Institute of Standards and Technology[END_REF]. The difference lies in the particle representation which is a vector rather than a binary matrix and this representation is better to use less memory space with vector data structures. Adding to that, considering the saturation problem of the sigmoid function in the BPSO, we prefer to use real valued velocities matrices V k . We have also introduced the fitness into velocity updating equation rather than using particle vector index. ω modulates the influence of the previous speed in the new speed computation. According to literature [START_REF] Marini | Particle Swarm opritmization (PSO).A tutorial[END_REF], [START_REF] Kennedy | Particle Swarm opritmization[END_REF], [START_REF] Eberhart | Comparing inertia weights and constriction factors in particle swarm optimization[END_REF] its value should vary in [ω min , ω max ] with ω min = 0.4 and ω max = 0.9 and the linear decrease strategies have shown best results for algorithm stabilization. For our strategy, we have chosen to update ω according to [START_REF] Chen | A particle swarm optimizer with multistage linearly-decreasing inertia weight[END_REF] as follows:

ω t = ω max - (ω max -ω min ) T max * t (12)
2) After new velocity computation, we deduce particle's new position vector with Eq (13)

x t k (i) = Z ⇐⇒ v t k (i, Z) = max ∀j∈[0,M -1] v t k (i, j) (13
) 3) Physical topology constraints can reduce placement possibilities for a service s i . Each service s i ∈ S has its authorized subset of physical machines. To ensure this constraint in the DPSO, if a service s i can't be placed in a device m j ∈ M:

∀k ∈ [0, P -1], ∀t ∈ [0, T max -1] ⇒ v t k (i, j) = -∞ (14)

C. Initial population

The initial swarm particles X 0 0 , .., X 0 P -1 are distributed uniformly in search space.

∀s i ∈ S, x 0 k (i) should be taken uniformly in service s i admissible set of machines.

Initial velocities V 0 k are initialized to 1 and -∞ elements matrices as described in Algorithm 2.

D. Neighboring Topology

Neighbourhood topology defines particles swarm communications. In its original version [START_REF] Kennedy | Particle Swarm opritmization[END_REF], PSO algorithm allows all particles to exchange their solutions to determine a global best solution. This global approach leads particles to be trapped in a local optimum. To avoid this problem, the swarm can be divided into sub-groups and communications will be allowed only between particles in the same sub-group [START_REF] Zavala | A comparison study of PSO neighborhoods[END_REF]. According to literature, we can define geometrical sub-groups which are deduced based on closest particles considering a certain metric (e.g fitness function) or we can define social subgroups that are defined based on particles swarm index and this last has shown better results than the geometrical approach [START_REF] Marini | Particle Swarm opritmization (PSO).A tutorial[END_REF], [START_REF] Kennedy | Particle Swarm opritmization[END_REF], [START_REF] Zavala | A comparison study of PSO neighborhoods[END_REF]. Based on that, we define a social circular neighbourhood of two particles as shown in Figure 2.

We present the overall DPSO approach in Algorithm 1

Data: • Topology nodes set M of size M

• Applications services set S of size N • P , Tmax, ϕ1, ϕ2, ω 0 ,ω 0 1 ,ω 0 2

Result: • Best placement particle vector Gbest • Total system energy ET • Total applications delay violations λ begin V 0 , P 0 = unif ormInit() t=0 ω 0 = 0.9 while t < Tmax do for

X t k ∈ P t do updateVelocity(X t k ) updatePosition(X t k ) if (f (X t k ) < f (P bk)) P bk ← X t k for Xw ∈ N eighbors(Xk) and w ∈ [0, P -1] do if (f (X t k ) < f (N bw)) N bw ← X t k end end (Gbest ← X t z ) ⇐⇒ f (X t z ) = min ∀k,z∈[0,P -1] {f (X t k )} t++; end end Algorithm 1: DPSO for services placement Data: • Topology size M • Services size N • Population size P Result: • Initial particles Swarm P 0 • Initial velocities set V 0 begin for k ∈ [0, P -1] do for i ∈ [0, N -1] do choose uniformly j ∈ [0, M -1] with mj allowed device for service si x 0 k (i) ← j end for i ∈ [0, N -1] do for j ∈ [0, M -1] do if mj is an allowed device for sj v 0 k (i, j) = 1 elsif v 0 k (i, j) = -∞ end end P bk ← X 0 k for Xw ∈ N eighbors(Xk) and w ∈ [0, P -1] do N bw ← X t k end end (Gbest ← X 0 z ) ⇐⇒ f (X 0 z ) = min ∀k,z∈[0,P -1] {f (X 0 k )} end

V. EXPERIMENTAL RESULTS

A. Test methodology

In order to prove the efficiency of the proposed method and to observe the impact of different Fog Layers-interplay strategies on both delay and energy consumption, the DPSO has been compared to BPSO, CloudOnly, IoTFogOnly, IoTCloud (IC), FogCloud (FC) and Dicothomous Modules Mapping (DCT) placement heuristics. Those methods are implemented in JAVA in iFogSim [START_REF] Gupta | iFogSim: A toolkit for modeling and simulation of resource management techniques in the Internet of Things, Edge and Fog computing environments[END_REF] which is a Fog environment simulator based on CloudSim tool [START_REF] Calheiros | CloudSim: A Novel Framework for Modeling and Simulation of Cloud Computing Infrastructures and Services[END_REF]. Experiments have been conducted on an Intel core i7-7700 CPU@3.60GHz x8. For a given fixed Fog topology, we vary applications set size and compare the different approaches considering system's total energy consumption in MJoules and applications delay violations number as a QoS metric.

B. Strategies

We briefly define the implemented placement approaches as follows: (1) CloudOnly -For a placement of all services in cloud nodes. (2) IoTFogOnly -IoTFogOnly tries to place all services from the same application, under capacity and dependency constraints, in IoT closest node to application's user device then it moves to Fog layer closest node. (3) FogCloud (FC) -FogCloud places as much as possible services from same application in the same Fog layer node, under dependency and capacity constraints, then it uses cloud layer placement. ( 4) IoTCloud (IC) -It places as much as possible services in the IoT layer, under dependency and capacity constraints, then it uses cloud nodes. (5) Dicothomous Module Mapping (DCT) -This method is coming from [START_REF] Taneja | Resource aware placement of IoT application modules in Fog-Cloud Computing Paradigm[END_REF], it sorts services and nodes respectively by the increasing order of their computation needs and computation capacities then a Dicothomous search over nodes is applied for each service. We adapted this strategy to respect services data dependencies. These algorithms are the baseline for the comparison with BPSO and DPSO. No other work in the literature minimizes both energy and applications delays violations. ( 6) BPSO -Is the implementation of Binary Particle Swarm algorithm as described in section II. ( 7) DPSO -For the proposed DPSO, Algorithm 1, the following ranges of parameter values have been tested: ϕ 1 , ϕ 2 in [START_REF] Bonomi | Fog Computing and Its Role in the Internet of Things[END_REF][START_REF] Jalali | Greening IoT with Fog: A Survey[END_REF] and P ∈ [START_REF] Giang | Developing IoT applications in the Fog: A Distributed Dataflow approach[END_REF]80]. Based on our pre-experiments results, which are in adequacy with values found in literature [START_REF] Marini | Particle Swarm opritmization (PSO).A tutorial[END_REF], [START_REF] Izakian | A Discrete particle swarm optimization approach for grid j ob scheduling[END_REF], DPSO performs its best under the following settings: ϕ 1 = 2, ϕ 2 = 2 P = 40.

C. Input Data 1) A varying set of IoT applications:

We consider in our work and experimentation, two types of Graphs that were given in [START_REF] Mahmud | Modelling and Simulation of Fog and Edge Computing Environments using iFogSim Toolkit[END_REF] and shown in Figure 3.

• Master-Worker: The Master is the only service that communicates with the source and then sends data instructions to workers services. After the response, the master sends orders to actuators. • Sequential Unidirectional DataFlow (SUD): It represents a sequential data flow from one service to another one. The first service gets data from sensors; the last one communicates with the actuators.

We place A applications with A ∈ [4, 32] and a step of h = 4. Each application a i has a size n i = 3 of services. We took average services workload in Million instructions demand and network data size (kB) exchanged between them proportionally to information found in applications examples given in [START_REF] Mahmud | Modelling and Simulation of Fog and Edge Computing Environments using iFogSim Toolkit[END_REF]. Each application a i is characterized by its DAG structure, Quality Of Service (QoS) requirements and priority. We used table I to generate a set of IoT applications of different classes that have been identified in [START_REF] Guevara | Class of service in fog computing[END_REF] with their associated priority (0 is the highest priority) and QoS requirements. 50% of master-slave and 50% of Sequential Unidirectional dataflow applications graphs are generated. In each graph application category, 25% of interactive Real-Time (RT) applications, 25% of Streaming applications (ST), 25% of Mission Critical applications (MC) and 25% Best Effort applications (BE) are deployed. Each application has one sensor/actuator pair placed randomly on infrastructure IoT devices. Infrastructure sensors send simultaneously data item every 5ms. We stop simulation when all sensors have sent 500 data packets.

2) A fixed three layered Physical topology: According to [START_REF] Wang | A Fog-based Architecture and Programming Model for IoT Applications in the Smart Grid[END_REF], [START_REF] Gupta | Fog Computing IoT: Overview, Architecture and Applications[END_REF] we fix an average topology of three layers: Cloud layer, Proxy server, Gateways layer and IoT devices layer. Different access network technologies (4G LTE, WiFi, LPWAN, Wired) are used as real system. For data center and proxy server nodes, we use power information measured in a local data center composed of 4 physical nodes (Intel dual Xeon E5 2699 v3 18-cores). Processor specification Fig. 4: The fixed topology used for the experimentation comes from Intel web site and MIPS evaluation from 7-zip benchmark results [44], [START_REF]CPU benchmark[END_REF]. For Fog infrastructure routers, we took information of CISCO IR809 and IR829 [START_REF]Cisco iox[END_REF]. For IoT device layer, we consider two types of equipments : an average capacity smartphone similar to Samsung galaxy S5 and a Raspberry pi 3+ B [START_REF]Raspberry benchmark[END_REF], [START_REF]Samsung Galaxy S5 Review[END_REF]. Also, considering simulator constraints, the physical topology is a k-ary tree that represents a hierarchical multi-layer topology as detailed in Figure 4 and Table II. We use 4G-LTE and LoRa networks which are considered as attractive technologies for IoT environments. We also used more classical networks technologies (Wi-Fi and wired) highly deployed all over the world. Considering 50 independent runs, Figure 5 shows both average number of delays violations (a) and system's energy consumption (b) obtained by each method for different size of heterogeneous applications sets, with hatched bar part representing network energy consumption and the non hatched one is for computation energy consumption. From 5, we can see that DPSO offers the best delay-Energy trade-off, followed by BPSO that is less efficient, which is due to Sigmoid function saturation issues that leads at some points to reduce its exploration capacity. Then, DCT strategy is the third one. CloudOnly strategy is energy and network greedy. Using cloud for services that could be hosted on smaller devices can drastically increase energy consumption and response delay. In contrast, using only IoT and Fog layers like IoTFogOnly approach decreases network resources usage but services execution will take more time and induce performance degradation. Moreover, Fog and IoT layers are usually not sufficient to host all services computation, memory and storage needs (we stress that for our experiments nodes use time sharing overbooking scheduling strategy [START_REF] Toms | Improving Cloud Infrastructure Utilization through Overbooking[END_REF]. If the CPU request of a service is smaller than the CPU capacity of the node, allocation will be possible even if the total CPU requirement of all services on that node is higher than its capacity. Services will access the processor during a quantum in a time sharing way). IoTFogOnly strategy, by using only IoT and Fog layers, reduces energy consumption by reducing Network communications and uses less power greedy devices but in contrast the execution time increases and that leads to more delays violations when applications sets size increases, as we can notice it in (a). Taking more time for execution can also leads in some cases to consume more energy. Including cloud layer in the placement strategy is necessary. With IC and FC approaches, which respectively uses only IoT-cloud and Fog-clod layers, we can notice that the first method is more energy greedy by adding cloud and network distance while it slows the overall computation capacities with powerless IoT nodes. In contrast, the approach is more interesting in term of delay by using IoT nodes proximity to place some services and exploiting cloud fast computation ability. FC strategy reduces energy consumption with smaller execution time while using more powerful execution of service but in contrast it increases actuator response time. We deduce that using only two layers is not efficient to ensure a good delay-energy trade-off. DCT approach uses the 3 layers for the placement which gives good energy values but in contrast delay violations are higher than DPSO. The approach encourages placement in IoT and Fog layers and takes cloud layer in last choice and with the time sharing scheduling strategy it becomes almost similar to IoTFogOnly placement but still better than this last because it sorts respectively services and nodes by their increasing computation needs and capacities and so it uses fairly the exploited layers.

Figure 6 plots services load per each layer for each placement method. It confirms what was said previously and shows that DPSO makes a fair load balancing of services between all layers to deal with delay constraints and energy consumption minimization. DCT uses fairly IoT and Fog layer and does not use cloud layer because services can be placed on these nodes. Then, the scheduler will use time sharing between services. Even if simple heuristics are faster than evolutionary algorithms such as DPSO we can see that the QoS and energy gain are more interesting than other strategies.

DPSO takes for the placement of a 3 services application, with half of the time dedicated to simulation, 109s while CloudOnly, IoTFogOnly, IC, FC and DCT takes respectively 84ms, 211ms, 114ms, 241ms and 167ms. In contrepart, DPSO energy delays violations average gain are respectively 80% and 31% for CloudOnly, 38% and 31% for IoTFogOnly, 61% and 31% for FC, 38% and -15% for IC, 9% and 7% for BPSO and -30% and 15% for DCT.

From what was observed previously, we can say that DPSO exploits smartly both Fog and Cloud layers advantages respectively by reducing response delay violations and offering fast and powerful computation capacity while reducing as much as possible system energy consumption.

CONCLUSION

In this paper, we proposed a DPSO approach for IoT services placement in a physical Fog topology, we compared results with BPSO, CloudOnly and with different layersinterplay combination placement approaches through iFogSim. The main contribution of our proposal is in the conjunction of the following features: evaluation of total system energy consumption using a swarm intelligence based algorithm, defining applications' class with delay constraints, proposing an algorithm to map IoT services in a Fog infrastructure minimizing energy consumption. DPSO finds a good tradeoff between cloud, Fog and IoT layers usage. Experimentation shows that DPSO prefers the middle layers devices, then depending on the application it chooses between IoT device and Cloud. For our future works, we plan to include network technologies specifics and applications priority in the placement policy logic. We will implement a multi-objective version of the DPSO with estimation strategies in order to improve computation time and solutions accuracy. We will also deal with a dynamic context by integrating objects mobility.

Fig. 1 :

 1 Fig. 1: Position of the k th particle after t iterations.

Algorithm 2 :Fig. 2 :

 22 Fig. 2: Neighbouring topology.

Fig. 3 :

 3 Fig. 3: DAG structures used for IoT applications generation

Fig. 5 :Fig. 6 :

 56 Fig. 5: Total delay violations and Energy consumption for each placement method

TABLE I :

 I IoT applications classes and priority

	QoS / Class	Best-	Streaming	Real-	Mission
		Effort	(ST)	Time	Critical
		(BF)		(RT)	(MC)
	Delay-	-	150	50	20
	sensitivity
	(ms)
	Bandwidth	Low	High	High	High
	demand
	Communication	Low	Medium	High	High
	frequency
	CPU demand	Low	Low-	Medium-	Medium-
			Medium	High	High
	Data Location Remote Local-	Local-	Local-
			Vicinity-	Vicinity-	Vicinity-
			Remote	Remote	Remote
	Mobility	High-	High-	High-	High-
		medium-	medium-	medium-	medium-
		low	low	low	low
	Examples	File	Augmented	video	health
		shar-	reality	stream-	track-
		ing	games	ing	ing
	Priority	3	2	1	0

TABLE II :

 II Fixed Topology Nodes Features j ∈ [0, 3]

	L Name N Devices MIPS RAM	uBW (Mbs)	P max -
					(MB)		P idle
	0 cloud 4	Cloud	120000 64000 10000	318-
							145
	1 Fog	1	Proxy	60000 8000	10000	169-70
			server
	2	2	d0(LoRa)	6750	1000	10000	10-45
			d1(Wired) 6750	1000	10000	10-45
		2	d2(Wi-