# Dynamic modeling of in vitro lipid digestion: Individual fatty acid release and bioaccessibility kinetics

Thuy Minh Giang, Sebastien Gaucel, Pierre Brestaz, Marc Anton, Anne

Meynier, Ioan-Cristian Trelea, Steven Le Feunteun

► To cite this version:

Thuy Minh Giang, Sebastien Gaucel, Pierre Brestaz, Marc Anton, Anne Meynier, et al. Dynamic modeling of in vitro lipid digestion: Individual fatty acid release and bioaccessibility kinetics. Food Chemistry, 2016, 194, pp.1180-1188. 10.1016/j.foodchem.2015.08.125. hal-01532511

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1 Dynamic modeling of *in vitro* lipid digestion: Individual fatty acid release and bioaccessibility kinetics

3

4

5 T.M. Giang¹,², S. Gaucel¹,², P. Brestaz³, M. Anton³, A. Meynier³, I.C. Trelea¹,² and S. Le Feunteun*¹,²

7

8 ¹ INRA, UMR782 Génie et Microbiologie des Procédés Alimentaires, F-78850 Thiverval
9 Grignon, France

10 ² AgroParisTech, UMR782 Génie et Microbiologie des Procédés Alimentaires, F-78850

11 Thiverval Grignon, France

12 ³ INRA, UR1268 Biopolymères Interactions Assemblages, F-44300 Nantes, France

13

14 *Corresponding author: steven.le-feunteun@grignon.inra.fr, +33(0)13814596
15 Abstract

16 The aim of this study was to gain knowledge about the role of triacylglycerol (TAG)
17 composition in fatty acids (FA) of o/w emulsions on both the pancreatic lipolysis kinetics and
18 the bioaccessibility of released products (i.e. contained within the bile salt micellar phase). A
19 mathematical model was developed and its predictions were compared to a set of
20 experimental data obtained during an *in vitro* digestion of a whey protein stabilized emulsion.

21 Modeling results show that FA residues of TAG were hydrolyzed at specific rates, inducing
22 different bioaccessibility kinetics. The estimated lipolysis rate constants of the studied FA
23 (C8:0, C10:0 >> C18:1 n-9 >> C12:0 > C14:0 > C16:0 ≈ C16:1 n-7 > C22:6 n-3) were in
24 close agreement with the available literature on the substrate specificity of pancreatic lipase.

25 Results also suggest that lipolysis products are very rapidly solubilized in the bile salt mixed
26 micelles with no fractionation according to the FA carbon chain.

27

28 **Keywords:** Emulsion, Digestion, Pancreatic lipase, Substrate specificity, DHA, Simulation.

29
## 1. Introduction

Human digestion of lipid emulsion is influenced by both physiological parameters and emulsion properties. Triacylglycerol (TAG) digestion occurs essentially in the intestine where about 80% of the lipolysis reaction take place (Carriere, Barrowman, Verger, & Laugier, 1993). The reaction is mediated by the pancreatic lipase-colipase complex at the oil-water interface and releases the *sn*-2-monoacylglycerol (MAG) and two free fatty acids (FFA) (Golding & Wooster, 2010). Lipolysis products are then incorporated into bile salt micelles before being transported to the gut wall and absorbed by the organism (Smith & Morton, 2010). Hence, physiological parameters such as the concentrations of pancreatic lipase, colipase and bile salts can all modify lipid digestion. The structural characteristics of emulsions are also important to consider when evaluating lipolysis kinetics. For instance, the nature of emulsifiers influences the properties of the oil-water interface and can therefore affect lipase adsorption onto droplets. The size of the oil droplets is another key parameter since fine emulsions with high interfacial areas facilitate the enzyme activity compared to coarse emulsions with low interfacial areas (Armand et al., 1999; Golding & Wooster, 2010; Li & McClements, 2010).

The TAG composition in fatty acid residues (FA), characterized by their carbon chain length and degree of unsaturation, also has a strong impact. Several studies have demonstrated that human and porcine pancreatic lipases exhibit a certain fatty acid specificity (Berger & Schneider, 1991; Desnuelle & Savary, 1963; Mukherjee, Kiewitt, & Hills, 1993; Yang, Kuksis, & Myher, 1990). For instance, it is well known that pancreatic lipase is more active on medium chain TAG (MCT, up to C10) than on long chain TAG (LCT, from C12) (Armand et al., 1992; Desnuelle & Savary, 1963; Golding et al., 2011; Li & McClements, 2010), and that its activity depends on the number and positions of unsaturations (Mukherjee et al., 1993; Yang et al., 1990). Long chain polyunsaturated fatty acids, such as docosahexaenoic acid
(C22:6 n-3, DHA), have also been reported to be among the most resistant FA to pancreatic lipase (Bottino, Vandenburg, & Reiser, 1967; Yang et al., 1990), possibly because of the short distance of the first double bond from the ester linkage (Akanbi, Sinclair, & Barrow, 2014; Bottino et al., 1967; Lawson & Hughes, 1988).

Moreover, the extent of FFA and MAG that can be solubilized into the bile salt micelles also seems to be product dependent (Freeman, 1969; Hofmann, 1963). For instance, the molar saturation ratio (mole of incorporated products/mole of bile salts) in a sodium glycodeoxycholate solution at 37°C has been reported to vary from 0.07 for stearic acid (C18:0) to 1.86 for lauric acid (C12:0) with intermediate values for long chain unsaturated FFA such as oleic (C18:1 n-9) and linoleic acids (C18:2 n-6) (Freeman, 1969). Such values, which can be partly reasoned in terms of molecular polarities and amphiphilic properties, are however dependent on numerous parameters such as the type of bile acid used or the pH of the solution (Freeman, 1969; Hofmann, 1963). Moreover, if the addition of *sn*-1-monoolein within the bile salt solution has been reported to improve the bile salt solubility of FFA, the opposite has been observed with the addition of oleic acid (Freeman, 1969). Given the variety of lipolysis products and bile acids that coexist during the intestinal digestion of edible oil, it therefore seems difficult to predict the bioaccessibility of lipolysis products.

Modeling has proven to be a powerful tool for a better understanding of the intestinal digestion kinetics. Various models of lipid digestion have been published over the last decades. Several models are based on the Michaelis-Menten equation. Verger and co-workers were the first to adapt such approach to the biphasic nature of the lipolysis reaction by taking into account the interfacial concentrations of the substrates and enzymes (Verger & de Haas, 1976; Verger, Mieras, & de Haas, 1973). Several variants have been proposed since, as for instance by Jurado, Camacho, Luzón, Fernández-Serrano, & García-Román (2008) for a bacterial lipase. These models are however quite complex and often require parameter values
that are difficult to determine experimentally, in particular for the digestion of edible oils composed of different TAG species. In a much simpler approach, intestinal lipolysis can also be described by a first order kinetic model (Ye, Cui, Zhu, & Singh, 2013). If such models can be useful in comparing the initial enzyme activity in different conditions, they do not take into account the interfacial area of oil droplets. This is why Li & McClements (2010) proposed a model in which the rate constant is expressed per unit of interfacial area, and that accounts for a progressive decrease of the oil droplet size. This model provided good fits of pH-stat measurements performed on different emulsions with the assumptions that the number of droplet remains unchanged and all droplets have the same size at any given time. Recently, we resorted to a similar modeling approach to show, by integrating experimentally measured droplet sizes, that the reduction of the interfacial area induced by droplet coalescence was the main reason why our *in vitro* intestinal lipolysis seemed to stop before the substrate was fully exhausted (Giang et al., 2015).

Nevertheless, all the above models assume a unique reaction rate constant without considering the FA composition of the studied oils. Hence, they cannot be used to reproduce the release kinetics of individual FA. In the present study, we develop a mathematical model of intestinal lipolysis that takes the composition of the oil substrate into account. It predicts the lipolysis kinetics of each FA residue and their *in vitro* bioaccessibility, defined as the concentration of FA (FFA + *sn*-2-MAG) measured within the bile salt micellar phase. The model is applied to a set of experimental data measured during the *in vitro* gastro-intestinal digestion of a whey protein stabilized emulsion. The estimated values for the model parameters (FA specific lipolysis rate constants and bile salt micellar fractions) are compared with the available literature and discussed according to their biochemical meanings.

## 2. Material and method
## 2.1. Materials

The oil containing medium-chain triacylglycerols (MCT), Miglyol 812S, was purchased from Sasol GmbH, Germany. The main fatty acids contained in this oil were C8:0 (54% w/w) and C10:0 (43%). The oil containing long-chain triacylglycerols (LCT), DHAsco, was obtained from Martek, via DSM Nutritional Products Ldt, Switzerland. It contained docosahexahenoic acid (DHA, C22:6 n-3) as major fatty acid (40% w/w) along with C12:0 (4%), C14:0 (12%), C16:0 (12%) and C18:1 n-9 (24%). Whey protein powder (Prolacta 95) was purchased from Lactalis Ingredients, France. Pepsin (P7012, 2,500 U mg⁻¹), mucin (M2378), pancreatin (P7545, 8×USP specifications), pancreatic lipase (L3126, 120 U mg⁻¹) and bile extract (B8631) were from porcine origin and obtained from Sigma-Aldrich, France. Water was Milli-Q water.

Solvents for liquid chromatography were chloroform for HPLC (Carlo Erba), methyl alcohol for HPLC (99.9%, Carlo Erba) and ammonia solution (30%, Carlo Erba). Acetone (Pure RE, Carlo Erba), sulfuric acid (RPE 96%, Carlo Erba), cyclohexane and heptadecanoic acid (Sigma) were used for the preparation of fatty acid methyl esters (FAME) of the micellar phase during intestinal digestion.

## 2.2. Emulsion preparation and digestion

A whey protein stabilized emulsion with droplet diameters below 1 µm was first prepared according to the procedure previously described in Giang et al. (2015). Briefly, the oil phase (20% w/w) contained 37.5% (w/w) of MCT and 62.5% of LCT, and the aqueous phase (80% w/w) contained 4% (w/w) of whey protein powder, used as emulsifier, in a 0.1M sodium phosphate buffer (pH 7.0). After high pressure homogenization and addition of maltodextrin solution to improve the freeze-dried stability of oil droplets, the emulsion was freeze-dried.

On the day of the *in vitro* experiments, the dry emulsion was rehydrated in Milli-Q water to obtain a final oil concentration of 3.2% (w/w).
A volume of 3 mL of the rehydrated emulsion, corresponding to an oil mass of about 96 mg, was placed into hermetically sealed headspace vials (22.4 mL). The gastric and intestinal phases of the *in vitro* digestion experiments were performed sequentially at 37°C under magnetic stirring (400 rpm). The gastric phase duration was 60 min and was launched by adding 2.12 mL of simulated gastric fluid (SGF) and 40 µL of 1M HCl to reach a final pH of 2.5. The SGF solution contained 3.9 g L⁻¹ of pepsin (corresponding to 10,000 U per mL of SGF using hemoglobin as substrate), 2.4 g L⁻¹ of mucin, 120 mM of NaCl, 2 mM of KCl and 6 mM of CaCl₂. The intestinal phase duration was then launched for 300 min maximum by adding 4.86 mL of simulated intestinal fluid (SIF) and 100 µL of 1M Na₂CO₃ to reach a final pH of 6.5. The SIF solution contained 30.8 g L⁻¹ of bile extract powder, 0.82 g L⁻¹ of pancreatin (activity: 8×USP specifications), 0.41 g L⁻¹ of pancreatic lipase (corresponding to 100 U per mL of SIF using olive oil as the substrate), and the same electrolyte concentrations as the SGF.

Samples were taken at t = 0 min of the intestinal phase using a modified SIF that contained all constituents except pancreatin and lipase, and at 15, 30, 60, 120 and 300 min of intestinal digestion. One vial was used for one sampling time and one type of measurement (quantification of LCT and MCT by HPLC, quantification of the lipolysis products within the bile salt micellar phase by GC, or droplet size by laser granulometry) so that the contents of 18 vials in total were analyzed (3 methods times 6 sampling times) for one digestion. Three independent digestion experiments, further denoted as replicates, were performed.

## 2.3. Quantification of LCT and MCT by HPLC

HPLC paired with an evaporative light scattering detector (ELSD) was used to quantify the decrease in both LCT and MCT masses during the time course of the *in vitro* digestions. Total lipids were extracted according to Bligh and Dyer method with minor modifications in the
ratio CHCl₃/CH₃OH/H₂O 1/2/1, and dissolved in CHCl₃ to obtain a final lipid concentration of 0.7 mg mL⁻¹. HPLC operating conditions were similar to those described in Kenmogne-Domguia, Meynier, Viau, Llamas, & Genot (2012) using a Uptip-prep Strategy column (2.2 µm SI, 150×4.6 mm, Interchim, Montluçon, France) and 30 µL of injected lipid extract. The signal of LCT and MCT (retention times of 1.21 and 1.32 min, respectively) were deconvoluted using a specifically developed algorithm running with the Matlab™ software (The MathWorks Inc., Natick, MA), and converted into masses using a pre-established calibration curve. LCT and MCT masses were finally converted into lipolysis percentages using Equation 1:

$$lipolysis (t) = \frac{m_{TAG_0} - m_{TAG}(t)}{m_{TAG_0}} \times 100 \% \quad (1)$$

where $m_{TAG_0}$ and $m_{TAG}(t)$ are the masses (mg) of LCT or MCT initially present in the vials and measured by HPLC at time t, respectively.

## 2.4. Droplet size measurement

The volume-based distribution of oil droplet sizes was measured using a Mastersizer S (Malvern Instruments Ltd., Worcestershire, UK) equipped with a 2 mW He-Ne laser of $\lambda = 633$ nm and the 300RF lens with detection limits of 0.05 and 900 µm. The refractive index $n_0$ of the aqueous phase was 1.33 and the properties of the dispersed phase were 1.457 for the refractive index and 0.001 for the absorption. Samples were diluted with distilled water to reach an oil volume concentration near 0.01% (w/w) for the circulation in the measurement cell. The surface weighted mean diameter, $d_{32}$, was calculated using Equation 2:

$$d_{32} = \frac{\sum n_i^3 d_i^3}{\sum n_i^2 d_i^2} \quad (2)$$

where $n_i$ is the number of droplets of diameter $d_i$.
2.5. Quantification of lipolysis products within the bile salt micellar phase by GC

Intestinal aliquots were frozen immediately after sampling. The day after, they were centrifuged at 50,000 rpm for 45 min at 4°C with Aventi J26-XP (Beckman-Coulter). Three phases were observed after centrifugation: a lipidic phase at the top, a pellet at the bottom, and a major intermediate phase containing the bile salt mixed micelles and which will be further referred as the micellar phase. 500 µL of the micellar phase were sampled for the determination of its FA composition by direct trans-methylation as described previously by Berton, Genot, & Ropers (2011). Briefly, 500 µL of the micellar phase was trans-methylated in presence of 100 µL of internal standard (heptadecanoic acid 1mg/mL in acetone/MeOH 2/1 v/v). 2 mL of methanol and 400 µL of H₂SO₄ were then introduced. The mixture was mixed; the tube screw capped and then heated à 100°C for 1 h. After cooling at room temperature, 500 µL of water and 1 mL of cyclohexane were added. After mixing, and decantation, the organic phase was removed for later analysis by GC. Fatty acid methyl ester (FAME) analyses were performed on a gas chromatograph paired with a splitless injector and a FID (Clarus, Perkin Elmer). They were separated on a capillary column (DB 225, 30 m X 0.25 mm, film thickness 0.25 mm) after splitless injection. The carrier gas (H₂) was set at 2 m min⁻¹. Temperature gradient was programmed as follows: 50°C for 3 min, increase to 180°C at 15°C min⁻¹, 7 min at 180°C, increase to 220°C at 10°C min⁻¹ and finally 10 min at 220°C. The temperature of the injector and the detector were maintained at 250°C. Individual FA were identified by comparison of their retention time with those of standards FAME mix (cat 47885-U 37, Supelco); n-3 PUFA from menhaden oil (cat 4-7085 U-14, Supelco), and marine oil standard of the AOCS. Peak surfaces were integrated and corrected by response factors of individual fatty acids.

The FA composition of the native emulsion was also quantified by GC. As summarized in Table 1, 8 fatty acids representing 95.6% of the total FA mass, were considered for the
202 modeling approach: C8:0, C10:0, C12:0, C14:0, C16:0, C16:1 n-7, C18:1 n-9, and C22:6 n-3.
203 These 8 FA showed coefficients of variation of less than 10.26% over the three replicate
204 measurements. Since the emulsion was prepared from a mixture of two oils, the last 2
205 columns of Table 1 provide the fractional contributions of LCT ($\alpha_{FA_i}$) and MCT ($1-\alpha_{FA_i}$) for
206 each FA residue. Results show that almost all C8:0 and C10:0 came from the MCT oil,
207 whereas all the other fatty acids came essentially from LCT. These fractions will be used for
208 TAG mass calculations in the model.
209

210 **3. Mathematical modeling**

211 3.1. Model assumptions and equations

212 The model was built to predict the lipolysis kinetics and the concentration profiles of the
213 lipolysis products in the bile salt micellar phase, knowing that pancreatic lipase produces two
214 FFA and one sn-2-MAG per TAG molecule. However, if the GC analyses of the samples
215 make it possible to quantify the different acyl chains, they cannot be used to discriminate their
216 molecular origin, i.e. free or esterified fatty acids. In the rest of this paper, the term fatty acid
217 (FA) will therefore refer to FA carbon chains in any kinds of molecular products. The main
218 modeling assumptions were as follows:

219 A1: the hydrolysis rate of a given fatty acid residue $FA_i$ was independent of the sn-
220 position within TAG molecules, with $FA_i$ referring to the fatty acid considered (C8:0, C10:0,
221 C12:0, C14:0, C16:0, C16:1 n-7, C18:1 n-9, or C22:6 n-3).
222

222 A2: the hydrolysis rate of a given fatty acid residue $FA_i$ was proportional to the
223 interfacial area occupied by this acyl chain.

$$
\frac{dm_{FA_i}^{lip}(t)}{dt} = -k_{FA_i} \cdot A_{FA_i}(t) \quad (3)
$$
where $m_{FA_i}^{lip}$ is the mass of FA$_i$ in the oil droplets (mg), $k_{FA_i}$ is the lipolysis rate constant of FA$_i$ (mg m⁻² min⁻¹), and $A_{FA_i}(t)$ is the interfacial area occupied by FA$_i$ (m²) at time t (min).

A3: the interfacial area occupied by FA$_i$ at time t was assumed to be proportional to its molar fraction within the oil droplets.

$$A_{FA_i}(t) = \frac{n_{FA_i}^{lip}(t)}{\sum_i n_{FA_i}^{lip}(t)} \cdot A_{TAG}(t) \quad (4)$$

where $n_{FA_i}^{lip}(t)$ is the number of moles of FA$_i$ in the oil droplets (mol) at time t and $A_{TAG}(t)$ is the interfacial area of oil droplets (m²) at time t. This equation can be rewritten as

$$A_{FA_i}(t) = \frac{\frac{m_{FA_i}^{lip}(t)}{M_{FA_i}}}{\sum_i \frac{m_{FA_i}^{lip}(t)}{M_{FA_i}}} \cdot A_{TAG}(t) \quad (5)$$

where $M_{FA_i}$ is the molar mass of FA$_i$ (g mol⁻¹).

A4: oil droplets in the emulsion were considered as spheres. The droplet interfacial area is thus:

$$A_{TAG}(t) = 6 \cdot \frac{m_{TAG}(t)}{\rho \cdot d_{32}(t)} \quad (6)$$

where $m_{TAG}(t)$ is the total mass (mg) of TAG at time t, $\rho$ is the mean mass density of the TAG (taken as 0.92 mg mm⁻³) and $d_{32}(t)$ is the surface weighted mean droplet diameter measured by laser diffraction (nm).

Combining assumptions A1-A4, Eq. (3) can be rewritten:

$$\frac{dm_{FA_i}^{lip}}{dt} = -k_{FA_i} \frac{\frac{m_{FA_i}^{lip}(t)}{M_{FA_i}}}{\sum_i \frac{m_{FA_i}^{lip}(t)}{M_{FA_i}}} \cdot 6 \cdot \frac{m_{TAG}(t)}{\rho \cdot d_{32}(t)} \quad (7)$$
A5: our experimental results show that only a fraction of hydrolyzed products were transferred into the bile salt micellar phase. To calculate the masses of $FA_i$ within this phase, a “micellar fraction”, $f_{FA_i}^{mic}$, was therefore introduced with the assumption that the transfer of lipolysis products into the micellar phase is instantaneous:

$$ \frac{dm_{FA_i}^{mic}}{dt} = -f_{FA_i}^{mic} \frac{dm_{FA_i}^{lip}}{dt} \quad (8) $$

where $m_{FA_i}^{mic}$ is the mass of $FA_i$ in the micellar phase (mg).

The micellar fraction $f_{FA_i}^{mic}$ and the lipolysis rate $k_{FA_i}$ are the unknown parameters of the model. They were estimated for each $FA_i$ by adjusting the model to the experimental data (see section 3.2). To this end, model predictions for TAG masses were calculated as follows.

The total TAG mass, $m_{TAG}(t)$, is the sum of the medium chain TAG (MCT) and long chain TAG (LCT) masses:

$$ m_{TAG}(t) = m_{MCT}(t) + m_{LCT}(t) \quad (9) $$

where $m_{MCT}(t)$ and $m_{LCT}(t)$ are the MCT and LCT masses (mg) at time t, respectively, calculated according to their fractional mass contributions ($\alpha_{FA_i}$ and $1-\alpha_{FA_i}$) shown in Table 1 and by adding the adequate mass of glycerol moiety:

$$ m_{MCT}(t) = \sum_{i} m_{FA_i}^{lip}(t) \cdot (1 - \alpha_{FA_i}) + m_{Glycerol_{MCT}}(t) \quad (10) $$

$$ m_{LCT}(t) = \sum_{i} m_{FA_i}^{lip}(t) \cdot \alpha_{FA_i} + m_{Glycerol_{LCT}}(t) \quad (11) $$

where $m_{Glycerol_{LCT}}(t)$ and $m_{Glycerol_{MCT}}(t)$ are the masses of glycerol moiety coming from MCT and LCT, respectively. They were calculated via a molar balance equation by considering that there is one mole of glycerol moiety per three moles of $FA_i$.

## 3.2. Parameter estimation
The differential equations of the model (Eq. 7 and Eq. 8) were solved numerically using Matlab® software (The MathWorks Inc., Natick, MA) equipped with the Statistics Toolbox.

The surface weighted mean diameter $d_{32}(t)$ was integrated into the model using linear interpolations of the experimental values. Model outputs, namely the evolution of the MCT and LCT masses and masses of hydrolyzed products within the micellar phase, were confronted to the corresponding experimental results measured by HPLC and GC, respectively, to estimate the unknown model parameters: $k_{FA_i}$ and $f_{FA_i}^{mic}$. Standard errors, coefficients of variation and 95% confidence intervals of the estimated parameter values were computed using the nonlinear regression software in the Matlab® Statistics Toolbox and it was checked that estimated values were statistically significant at 0.05 level.

# 4. Results and Discussion

## 4.1. Experimental results

Results related to the evolution of droplet sizes during the gastric and intestinal phases were described in detail previously (Giang et al., 2015). It was found that droplet flocculation took place during the gastric phase but these aggregates where re-dispersed after the subsequent addition of bile. Fig. 1 summarizes the results related to the evolution of oil droplet sizes ($d_{32}$) during the intestinal phase together with the corresponding TAG lipolysis kinetics. Fig. 1A shows that the lipolysis rate was much higher for MCT than for LCT as the hydrolysis of MCT was completely finished after 15 min, whereas about 20% of LCT could still be detected after 300 min of intestinal digestion. In good agreement with many studies (Li & McClements, 2010; Ye et al., 2013; Zhu, Ye, Verrier, & Singh, 2013), the LCT lipolysis curve also showed two stages with a fast initial reaction rate that markedly slowed down after about 30 min. As previously shown in (Giang et al., 2015), this can be attributed to the sudden increase of the surface weighted mean diameter induced by the coalescence of oil droplets,
and which led to a sharp reduction of the interfacial area available for lipase adsorption (Fig. 1B).

Fig. 2 presents the bioaccessibility of the 8 fatty acids considered, i.e. the lipolysis product concentrations measured within the micellar phase, expressed as percentages of FA initially present in the oil phase. Three main observations can be made. First, fatty acids can be divided into two groups according to the evolution of their bioaccessibility. The first group contains the FA arising from lipolysis of MCT, C8:0 and C10:0. They were released more quickly than the second group which corresponds to the FA arising from the lipolysis of LCT (Table 1). One may also notice that the long chain FA showed two-stage shapes with a slower rate of appearance within the micellar phase after about 30 min. These results are therefore consistent with the MCT and LCT lipolysis kinetics deduced from the HPLC measurements (Fig. 1A). Second, both the rate of appearance and the concentration measured at the end of the experiment (300 min) depended on the FA considered. The rate and extent of FA appearance in the micellar phase tended to be higher for shorter FA. This confirms that all fatty acids do not behave in the same way in terms of lipolysis kinetics and/or incorporation into the bile salt micelles. Finally, since MCT were fully hydrolyzed in less than 15 min according to the HPLC measurements (Fig. 1A), the plateau value of about 65% for C8:0 and C10:0 (Fig. 2) demonstrates that only a fraction of hydrolyzed products was recovered within the micellar phase. This is in accordance with the study of Sek, Porter, Kaukonen, & Charman (2002) who showed that lipolysis products can also be found in the oil and pellet phases after the centrifugation step used to separate the micellar phase.

## 4.2. Modeling results

The model was designed to simulate the lipolysis kinetics as well as the bioaccessibility of individual FA, and considers 8 fatty acids representing 95.6% of the total FA mass. The
parameters to be estimated were the reaction rate constant ($k_{FA_i}$) and the micellar mass fraction ($f_{FA_i}^{mic}$) for each FA.

It appeared that the fatty acids coming from MCT, C8:0 and C10:0, were fully hydrolyzed in less than 15 min of intestinal digestion (Fig. 1A and Fig. 2), i.e. before the first sampling time.

The lipolysis rate constants, $k_{C8}$ and $k_{C10}$, could therefore not be estimated due to lack of intermediate data. After preliminary model simulations, they were set at the minimum value enabling to reproduce a sufficiently fast MCT lipolysis, which was found to be 10 mg m⁻² min⁻¹. According to the above considerations, 6 lipolysis rates $k_{FA_i}$ and 8 micellar fractions $f_{FA_i}^{mic}$ remained to be determined. In a first attempt, all parameters were estimated by fitting the model to the experimental data. This model version provided very good fits (data not shown) but it appeared that the $f_{FA_i}^{mic}$ values were similar for all FA except C8:0. In other words, the bile salt solubilization ratio of the lipolysis products was about the same for FA longer than C8:0. To reduce the number of unknown parameters, it was therefore decided to keep only two $f_{FA_i}^{mic}$ parameters, one for C8:0 and the other one common to all the other FA.
Hence, the final version of the model had 6 unknown lipolysis rates $k_{FA_i}$ and 2 unknown micellar fractions $f_{FA_i}^{mic}$. Fig. 3 shows that this model version still provided very good fits of the experimental data, and Table 2 shows that the parameter values were properly estimated (coefficients of variation smaller than 10%). These results are further discussed according to their biological meanings.

### 4.3. Fractions of hydrolyzed products recovered within the bile salt micellar phase
Estimated values for the micellar fraction parameters (Table 2) can be interpreted as follows. About 70% (w/w) of the C8:0 lipolysis products were released in the bile salt micellar phase, and about 56% for the other FA. The remaining amounts of products were retained in the oil and pellet phases during the centrifugation step. The order of magnitude of these values is
consistent with studies in which centrifugation was also employed to measure the micellar content in lipolysis products (Sek et al., 2002). Note also that the model assumes an instantaneous transfer of the products into the micellar phase. The very good fits of the bioaccessibility kinetics (Fig. 3) obtained under this assumption therefore strongly suggest that the solubilization of the lipolysis products in the bile salt micelles was not rate limiting.

Similar micellar fraction values for all the lipolysis products considered may seem in contradiction with previously published data. Several studies have indeed shown that lipolysis products behave differently in terms of bile salt solubility (Freeman, 1969; Hofmann, 1963), with molar saturation ratios that can vary from 0.07 up to 1.86 (Freeman, 1969). In fact, the experimental protocol used in these studies was quite different from an *in vitro* digestion protocol since mixtures of pure molecules were used to obtain these results. During the digestion of complex natural oils, a great number of interactions take place between the different lipolysis products and bile acids, and this can greatly modify the solubility of the products in the bile salt mixed micelles. In our study, the products/bile salts molar ratio was of about 1.32 at the end of the experiment, thereby indicating that the saturation ratio for our mixture of lipolysis products was even greater.

One may also wonder why the micellar fraction obtained for C8:0 is different from those obtained for the other FA products. This can probably be attributed to the greater water solubility of this fatty acid. Indeed, using the formula proposed by Tzocheva et al. (2012), it was found that C8:0 was the only free fatty acid with a significant water solubility (0.64 g L⁻¹).

More precisely, within our experimental conditions, it can be estimated that about 6 mg of caprylic acid could dissolve if our reaction medium was made of pure water. This corresponds to 31% by weight of the total C8:0 mass introduced within the digestive tubes. According to our modeling results, a common micellar fraction of 56% provides good results for all FA except C8:0, for which a micellar fraction of 70% was estimated. The additional 14% for
356 C8:0 (70 = 56 + 14) are therefore compatible with the contribution of a water soluble fraction,
357 knowing that the micellar phase is not pure water and that the total C8:0 mass accounts for
358 both FFA and *sn*-2-MAG molecular forms. According to this interpretation, the solubility of
359 the lipolysis products in the bile salt mixed micelles would therefore be approximately the
360 same for all the FA considered, C8:0 included.
361

362 4.4. FA specific lipolysis rate constants

363 The lipolysis rate constants estimated with the model are given in Table 2. The same data, but
364 expressed as normalized values relatively to oleic acid, are also presented in Fig. 4 for
365 comparison purposes with the available literature. We may first highlight the very good
366 agreement of our results with those obtained by Berger & Schneider (1991) for C12:0, C14:0,
367 C16:0 and C18:1n-9 in spite of very different experimental conditions. Indeed, if our results
368 arise from the modeling of *in vitro* intestinal digestion of emulsified lipids made of a mixture
369 of different TAG, Berger & Schneider (1991) used a protocol based on a lipase-catalyzed
370 reaction in an organic solvent with a mixture of TAG that contained 3 identical acyl residues.

371 We may also stress that, according to our results, C8:0 and C10:0 presented rate constants that
372 were at least 3 times the one estimated for oleic acid (Table 2), hence confirming the early
373 study of Desnuelle & Savary (1963) who found the highest pancreatic lipase activity for C4:0
374 and reported a strong decrease in activity (by a factor of about 2) between C10:0 and C12:0.

375 Altogether, our findings are therefore in agreement with the reported tendency of pancreatic
376 lipase to be less active on longer saturated fatty acid residues. These variations are usually
377 ascribed to substrate dependent catalytic lipase activity, although other reaction steps, such as
378 interfacial or diffusive mass transfers of substrates and products, may play a role (Verger &
379 de Haas, 1976; Verger, Mieras, & de Haas, 1973).
Besides, if DHA (C22:6 n-3) was not studied by Berger & Schneider (1991), slower rates of pancreatic lipolysis for long-chain polyunsaturated fatty acids have been reported by many authors (Akanbi et al., 2014; Bottino et al., 1967; Zhu et al., 2013). For instance, the lipolysis rate constant of DHA should be about 0.17 times that obtained for C18:1 n-9 according to Yang et al. (1990), and of about 0.6 times that obtained for C14:0 according to Mukherjee et al. (1993). These values are represented by a triangle and a circle in Fig. 4, respectively, to show that our estimated rate constant for DHA is consistent with these findings. This higher resistance of long-chain polyunsaturated fatty acids has been attributed to an inhibitory effect induced by the presence of a double bond near the carboxyl group (Akanbi et al., 2014; Bottino et al., 1967; Lawson & Hughes, 1988).

### 4.5. Evolution of the TAG composition during lipolysis

Fig. 5 presents the oil-water interfacial areas occupied by each FA residue of TAG molecules as given by the model. They were calculated by assuming proportionality with their molar concentrations within the lipid phase (Eq. 4). Therefore, the evolution of these FA specific interfacial areas is also representative of the predicted changes of the oil droplet composition during the course of digestion. Results show that about 50% of the oil surface area was occupied by MCT fatty acid residues (C8:0 and C10:0) at the beginning of the experiment. After 15 min, MCT had totally disappeared (Fig. 1A) due to higher lipolysis rate constants for C8:0 and C10:0. This induced a considerable change in the composition of the remaining oil, with only long-chain fatty acid residues remaining. At the end of the experiment, DHA was by far the dominant FA residue (more than 70% by mole) because it had the lowest lipolysis rate constant (Table 2).

As a final remark, we may highlight that our previous model (Giang et al., 2015) assumed an average lipolysis rate for the entire LCT oil fraction, which somewhat overestimated the LCT
lipolysis rate at long times. By taking into account FA specific lipolysis rate constants, the
405
newly developed model predicts an accumulation of most resistant FA residues in the
406
remaining oil (Fig 5), which leads to a progressive decrease of the average reaction rate and a
407
better agreement with experimental measurements of the remaining LCT at 300 min (Fig 3).
408
409

410 **5. Conclusion**

In the present study, our previous model (Giang et al., 2015) was extended to take into
411
account the fatty acid composition of the oil substrate, and to enable the modeling of the *in
412
vitro* bioaccessibility of the lipolysis products. The model provided very good fits of the
413
experimental data and shows that the differences observed in the bioaccessibility kinetics of
414
the studied FA originated from different FA lipolysis rate constants. It was also used to
415
simulate the compositional evolution of the remaining oil during the course of digestion.
416
Results related to the FA specific reaction rates were in good agreement with the available
417
literature and confirm a general tendency towards a greater pancreatic lipase activity on
418
shorter fatty acid residues. Our results also support the idea that lipolysis products are rapidly
419
and equally solubilized (i.e. no fractionation) within the bile salt mixed micelles, with a
420
probable additional contribution of water soluble products for fatty acids ≤ C8. The present
421
model provides a significant improvement in comparison with models which assume an
422
average lipolysis rate with a better representation of the intestinal lipid digestion mechanisms.
423
424

425 **Acknowledgements**

This work was supported by the Institut National de la Recherche Agronomique and the
426
Institut Carnot QUALIMENT (France). The authors are involved in the Food and Agriculture
427
COST (European Cooperation in Science and Technology) Action FA1005 ‘Improving health
428
properties of food by sharing our knowledge on the digestive process (INFOGEST)’.
429
431 Nomenclature

<table><thead><tr><td>Symbols</td><td>Meaning</td></tr></thead><tbody><tr><td>A<sub>TAG</sub></td><td>Interfacial area of the oil droplets (m<sup>2</sup>)</td></tr><tr><td>A<sub>FA<sub>i</sub></sub></td><td>Interfacial area occupied by the i<sup>th</sup> FA residue (m<sup>2</sup>)</td></tr><tr><td>d<sub>32</sub></td><td>Surface weighted mean droplet diameter (nm)</td></tr><tr><td>k<sub>FA<sub>i</sub></sub></td><td>Lipolysis rate constant of the i<sup>th</sup> FA residue (mg m<sup>-2</sup> min<sup>-1</sup>)</td></tr><tr><td>f<sup>mic</sup><sub>FA<sub>i</sub></sub></td><td>Micellar mass fraction of the i<sup>th</sup> FA</td></tr><tr><td>M<sub>FA<sub>i</sub></sub></td><td>Molecular mass of the i<sup>th</sup> FA (g mol<sup>-1</sup>)</td></tr><tr><td>m<sub>TAG</sub></td><td>Mass of TAG (mg)</td></tr><tr><td>m<sup>lip</sup><sub>FA<sub>i</sub></sub></td><td>Mass of the i<sup>th</sup> FA residue in oil droplets (mg)</td></tr><tr><td>m<sup>mic</sup><sub>FA<sub>i</sub></sub></td><td>Mass of the i<sup>th</sup> FA in micellar phase (mg)</td></tr><tr><td>n<sup>lip</sup><sub>FA<sub>i</sub></sub></td><td>Quantity of the i<sup>th</sup> FA residue in oil droplets (mmol)</td></tr><tr><td>n<sup>mic</sup><sub>FA<sub>i</sub></sub></td><td>Quantity of the i<sup>th</sup> FA in aqueous phase (mmol)</td></tr><tr><td>t</td><td>Time (min)</td></tr><tr><td>ρ</td><td>Average mass density of TAG (mg mm<sup>-3</sup>)</td></tr><tr><td>α</td><td>Fraction of FA residue coming from LCT</td></tr><tr><td>1-α</td><td>Fraction of FA residue coming from MCT</td></tr></tbody></table>
434 References

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508
509 **Figure Captions**

510

511 **Fig 1.** Lipolysis of MCT (squares) and LCT (triangles) during intestinal digestion (A).
512 Surface weighted mean diameters, *d*<sub>32</sub>, (circles) and interfacial areas (diamonds) of oil
513 droplets (B). Solid lines are guide for the eyes. Means and standard deviations (smaller than
514 symbol size) were calculated over 3 replicates.

515

516 **Fig 2.** Bioaccessibility of individual lipolysis products (lines are guides for eyes). Means and
517 standard deviations were calculated over 3 replicates.

518

519 **Fig 3.** Comparison between calculated and experimental evolutions of the MCT, LCT, and
520 bioaccessible product masses during intestinal digestion. Symbols are means over 3 replicated
521 experiments (squares for MCT, triangles for LCT). Solid lines show the mass evolution
522 calculated using the model. Dotted lines show the asymptotic values calculated using the
523 model.

524

525 **Fig 4.** Lipolysis rate constants for the different fatty acid residues according to the carbon
526 chain length (expressed as normalized values relatively to C18:1 n-9). Crosses represent the
527 values determined in this study by model fitting. Squares correspond to values reported by
528 Berger & Schneider (1991). The circle and the triangle for C22:6 n-3 were estimated from the
529 studies of Mukherjee *et al.* (1993) and Yang *et al.* (1990), respectively.

530

531 **Fig 5.** Evolution of the interfacial areas (normalized values) occupied by each fatty acid
532 residue during intestinal digestion (A). Zoom on the first 15 min (B).

533
<figure><img src="image_2.png" /></figure>

<figure><img src="image_3.png" /></figure>

535

536

537
<figure><img src="image_4.png" /></figure>

539
540

541

542
<figure><img src="image_5.png" /></figure>
<figure><img src="image_6.png" /><figcaption>546 Figure 4</figcaption></figure>

547

548

549
<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /></figure>
<table><caption>**Table 1.** Fatty acid composition of the native emulsion which was made of a mixture of MCT and LCT (37.5 and 62.5 % by weight, respectively).</caption><thead><tr><th rowspan="2">Fatty acid</th><th colspan="2">TAG composition</th><th colspan="2">Origin of each FA</th></tr><tr><th>Mean of 3 replicates (% by weight)</th><th>STD of 3 replicates (% by weight)</th><th>Fraction coming from LCT α<sub>FAi</sub></th><th>Fraction coming from MCT 1-α<sub>FAi</sub></th></tr></thead><tbody><tr><td>C8:0</td><td>19.76</td><td>0.71</td><td>0.02</td><td>0.98</td></tr><tr><td>C10:0</td><td>16.89</td><td>0.33</td><td>0.05</td><td>0.95</td></tr><tr><td>C12:0</td><td>2.98</td><td>0.20</td><td>0.93</td><td>0.07</td></tr><tr><td>C14:0</td><td>7.36</td><td>0.09</td><td>0.97</td><td>0.03</td></tr><tr><td>C16:0</td><td>6.40</td><td>0.13</td><td>0.92</td><td>0.08</td></tr><tr><td>C16:1 n-7</td><td>1.39</td><td>0.07</td><td>0.99</td><td>0.01</td></tr><tr><td>C18:1 n-9</td><td>14.41</td><td>0.14</td><td>0.98</td><td>0.02</td></tr><tr><td>C22:6 n-3</td><td>26.47</td><td>0.10</td><td>1.00</td><td>0.00</td></tr><tr><td>Other FA</td><td>4.31</td><td>1.72</td><td>0.89</td><td>0.11</td></tr></tbody></table>

554

555

556

<table><caption>**Table 2.** Results of the parameter estimation for the lipolysis rate $k_{FAi}$ and the micellar fraction $f_{FAi}^{mic}$ for each fatty acid.</caption><thead><tr><th rowspan="2">Fatty acid</th><th colspan="2">k<sub>FAi</sub> (mg min<sup>-1</sup> m<sup>-2</sup>)</th><th colspan="2">f<sub>FAi</sub><sup>mic</sup></th></tr><tr><th>Value</th><th>STD</th><th>Value</th><th>STD</th></tr></thead><tbody><tr><td>C8:0</td><td>10*</td><td></td><td>0.70</td><td>0.01</td></tr><tr><td>C10:0</td><td>10*</td><td></td><td></td><td></td></tr><tr><td>C12:0</td><td>1.93</td><td>0.16</td><td></td><td></td></tr><tr><td>C14:0</td><td>1.57</td><td>0.11</td><td></td><td></td></tr><tr><td>C16:0</td><td>1.34</td><td>0.10</td><td>0.56</td><td>0.01</td></tr><tr><td>C16:1 n-7</td><td>1.50</td><td>0.11</td><td></td><td></td></tr><tr><td>C18:1 n-9</td><td>3.11</td><td>0.25</td><td></td><td></td></tr><tr><td>C22:6 n-3</td><td>0.99</td><td>0.06</td><td></td><td></td></tr></tbody></table>

558

559

560

<footnote>(*) minimum value providing a complete hydrolysis of MCT in 15 min.</footnote>