Pedro Dias Longhitano

Khaoula Tidriri
email: khaoula.tidriri@grenoble-inp.fr

Christophe Bérenguer

Benjamin Echard
email: benjamin.echard.2@volvo.com

Pedro D Longhitano
email: pedro.longhitano@volvo.com

Bruno Castanier

Marko Cepin

David Bigaud

Christophe Berenguer
email: christophe.berenguer@grenoble-inp.fr

A closed-loop prescriptive maintenance approach for an usage dependent deteriorating item -Application to a critical vehicle component

Keywords: Maintenance, decision making, multi-objective optimization, degradation and reliability models, automotive sector

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

Introduction

The digitalization of the economy in the past decades has made data availability grow and become more important. Within the maintenance field, new technologies are raising and the possibilities opened with the Internet of Things are countless. At the same time, customers are more demanding on maintenance performance and added value, wanting to reduce their exploitation costs while having no unplanned stops. Consequently, in recent years, advanced maintenance strategies, such as predictive maintenance (PdM) and prescriptive maintenance (PsM), gathered a lot of attention from researchers.

Although no formal and widely accepted definition of PsM can yet be found in the literature, it is understood as a maintenance integrated framework where the best action to take is quantitatively chosen, based on criteria that take into account all the functionalities of the system, [START_REF] Iung | De la maintenance prédictive à la maintenance prescriptive: Une évolution nécessaire pour l'industrie du futur[END_REF]. PsM differs from PdM because it considers a comprehensive set of actions for prescription, going beyond the maintenance actions classically considered in maintenance policies (e.g. repair, inspections and replacements), such as changing aspects of system usage to reduce the full exploitation cost.

One of the main difficulties of implementing PsM solutions is that prognostic models are usually built to estimate remaining useful life (RUL) [START_REF] Tang | Remaining useful life prediction of lithium-ion batteries based on the Wiener process with measurement error[END_REF], but they do not take into account the decision making process that follows in real-life applications. Similarly, researchers who focus on decision making for maintenance consider prognostics as a given input, [START_REF] Lesobre | A usage-informed preventive maintenance policy to optimize the maintenance free operating period for multicomponent systems[END_REF], which does not always properly take into account the specificity of the prognostic information, as e.g. the impact of different decisions on the state of health of the system, etc.

Such a situation where the prognostics step and the health management process are not tightly interlinked may be limiting the performance of the 2 P. Longhitano, K. Tidriri, C. Bérenguer, B. Echard whole prognostics and health management (PHM) loop, [START_REF] Atamuradov | Prognos-Fig. 6. Waste Cost Comparison tics and health management for maintenance practitioners-review, implementation and tools evaluation[END_REF], and does not allow to make decisions to fully exploit the possible different usage modes for the system, to choose what tasks to prioritize and to reduce the overall exploitation cost. PsM actions go beyond maintenance, inspection and replacement dates, and consider all functionalities and cost sources of a system. Going into this direction, [START_REF] Wang | Joint optimization of condition-based maintenance and inventory control for a k-out-of-n:f system of multi-state degrading components[END_REF] have worked on deciding maintenance dates as well as deriving rules for inventory control, using degradation information to jointly manage replacement schedules and spare parts. Another example of expanding the usual maintenance decisions can be found in [START_REF] Obando | An architecture for controlling the remaining useful lifetime of a friction drive system[END_REF] where the authors have developed methods to control the torque of a friction drive system in order to expand its RUL.

For industrial vehicles applications, a method for scheduling jointly both missions and maintenance operations for a fleet of vehicles was proposed by [START_REF] Robert | Joint assignment of missions and maintenance operations for a fleet of deteriorating vehicles[END_REF] ; however, the proposed approach has not modelled important operational aspects of the problem and has not addressed the fact that, in practical problems, maintenance and systems exploitation decisions happen in two very different time scales. Those aspects will be addressed in this paper, and a full closed loop decision making algorithm for a particular vehicle component will be presented, scheduling maintenance and managing the vehicles of a fleet, and hence considering both the prognostic and the decision making problems.

Accordingly, the rest of the paper is organized as follows. Section 2 addresses the problem formulation, presenting its main aspects. Section 3 details the modeling of the system degradation and the different actions that can be applied to the fleet. Section 4 presents the full decision-making algorithm. In Section 5, the proposed approach is illustrated through simulations. Finally, Section 6 concludes the paper.

Problem Statement

The goal of the present work is to propose the optimal exploitation strategy for a fleet of vehicles, in order to provide fleet owners with the necessary tools for deciding which vehicles to send to a given mission, as well as when to perform maintenance operations.

Missions are defined as the deliveries that a vehicle has to make from one point to another. The points in space to be visited are associated with a deadline. All the distances from point to point are considered to be known, as well as the duration of the displacements from one point to another. Distances are stored in a matrix D and durations in a matrix T .

Most vehicle owners have maintenance contracts that include periodic visits to workshops to perform routine maintenance operations such as oil changes and revisions. To avoid extra visits to the workshop -which would possibly lead to downtime and add costs -it is beneficial to perform necessary components replacements during those regular visits. The maintenance date decision comes down to choosing which of those already planned visits to use for components replacements.

There is a trade-off behind this decision-making process. If a component is not changed when it should have been, the owner takes the risk to have a breakdown which will create huge costs. On the other hand, if he changes it too early he wastes a still usable component. This trade-off will be addressed and quantified in the proposed model and decision-making scheme in future sections.

Both maintenance operations and mission planning are conversely connected. Sending vehicles that are more degraded to do less severe missions -those which are less likely to cause big increases in the degradation -can postpone maintenance operations. On the other hand, knowing that a given component will be changed for sure in the next visit to the workshop should also change the way missions are planned. If a vehicle owner is guaranteed to have a brand new component in a few days, he should use the current component as much as possible in this remaining period, avoiding wastes and sparing other vehicles.

The PsM solution goal is to provide the best mission schedule for a fleet of vehicles and decide maintenance dates, considering the effect one has on the other. In this work, we propose a PsM solution focused on a single critical component of a vehicle, i.e. the brake-pad.

We consider the following structured policy for a fleet of M vehicles. At each decision time τ k , two decisions have to be made:

• Maintenance Date Decision : assuming that the two next scheduled workshop visits of vehicle i will happen at t wkp1 i and t wkp2 i , it is necessary to decide whether or not to replace the brake-pad at t wkp1 i , based on the current brake-pad thickness level, Y ki . • Missions scheduling : missions are then dispatched among trucks so as to minimize an overall cost function

The model associated to this policy and its solution are developed in the next sections.

Model Development

Working Assumptions

The main working hypotheses are:

• A decision epoch τ k arises when a new set of missions has to be accomplished.

A closed-loop prescriptive maintenance approach for a usage dependent deteriorating item 3 For example, every day a fleet owner has to make deliveries and therefore, decisions will happen at the beginning of each day, before sending vehicles from the headquarter. • T , D are known and displacements durations are considered to be deterministic. A version of this problem where distances and durations are considered as stochastic can be tackled in future works to have a more realistic solution. • t wkp1 i and t wkp2 i are known for every vehicle i at τ k as well as Y k . Both t wkp1 i and t wkp2 i are determined by a maintenance contract and therefore, no decision making process can affect those quantities. • Only immobilizations caused by problems with the brake-pad are considered.

Component Deterioration Model

The brake system is critical in any vehicle. One of its key elements is the brake-pad, a component of disk brakes used in several applications. Due to its simplicity and importance,the brake-pad has been chosen as a use case for this work.

The most common failure mode of the brakepad is due to wear and tear with usage. A brakepad is considered defective whenever its thickness falls under a given threshold. In this paper, this event is considered as a failure and will require the vehicle to be stopped.

Fig. 1 shows an example of how thickness evolved for a brake-pad.

For a given mode of operation, the brake-pad thickness evolution exhibits a mean trend close to be directly proportional to the traveled distance, but also a temporal and item-to-item variability. One of the most common classes of stochastic process used to model this type of degradation phenomena is the Wiener process with a linear drift [START_REF] Tang | Remaining useful life prediction of lithium-ion batteries based on the Wiener process with measurement error[END_REF]. In this paper, the chosen version of such a model is:

Y (x) = Y 0 + λx + σ B B(x) + (1)
where Y is the brake-pad thickness, x is the traveled distance, Y 0 is the initial thickness, λ is the negative drift, considered to be constant and estimated through data, B(x) is the standard Brownian motion, σ B is its variance and is a measurement noise considered to be Gaussian. Those parameters can be estimated directly from data as explained in [START_REF] Tang | Remaining useful life prediction of lithium-ion batteries based on the Wiener process with measurement error[END_REF].

This model correlates degradation to traveled distance and therefore can be used to connect degradation and mission planning, as well as to base the maintenance date decision, as it will be seen in the following sections.

Maintenance Date Decision

We assume that, at a decision epoch τ k , the two next scheduled dates of workshop visit t wkp1 i and t wkp2 i are known for each vehicle i. The maintenance decision at hand is then to choose whether the next workshop visit date t wkp1 i has to be retained for a brake-pad replacement or whether this operation can be postponed at least until t wkp2 i . If a replacement happens too early at t wkp , a cost related to the wasted thickness is incurred:

C bk Y 0 (Y (t wkp ) -Y crit ) (2)
where Y (t wkp ) is the measured thickness at the moment of the replacement and Y crit is the critical failure threshold of a single brake-pad.

It is important to highlight that, differently from delay, distance and degradation costs, Eqn. 2 is not computed on the fleet level, but evaluated independently for every vehicle.

Deciding not to change the brakes at t wkp1 and to wait until t wkp2 corresponds to a risk of a vehicle immobilization between the present date and t wkp2 whose cost can be estimated by:

C f ail P [Y (t wkp2 ) < Y crit |Y (t wkp1 )] (3)
where P[Y (t wkp2 ) < Y crit |Y (t wkp1 )] is the probability of failing before t wkp2 , given that Y (t wkp1 ) is known and C f ail is the total cost of an immobilization, which accounts for corrective maintenance costs and the impact of the immobilization on the deliveries, including extra delays, the cost of changing other vehicles plans throughout the work session, etc.

A brake-pad will be replaced at t wkp1 if:

C bk Y 0 (Y (t wkp1 ) -Y crit ) < C f ail P[Y (t wkp2 ) < Y crit |Y (t wkp1 )]
(4)

Costs for Missions Assignment

In the following section, the costs used in the optimization of mission schedules are presented. P. Longhitano, K. Tidriri, C. Bérenguer, B. Echard

It is important to keep in mind that some of those costs are not monetarily paid at every τ k , but guide the optimization process to reduce the long term exploitation cost.

Degradation Cost

Whenever a fleet of vehicles follows a mission schedule, the expected average thickness of the fleet decreases. The total thickness variation over the fleet can be expressed as:

N i=1 Y ki - N i=1 E[Y k+1 i ] = N i=1 λ i X i (5)
where N represents the vehicles that will not undergo brake-pad replacements in the next workshop visit (vehicles with a maintenance date decided must be used as much as possible before replacement). Y ki is the thickness of the brake-pad of vehicle i before performing the scheduled missions, Y k+1 i is the thickness of the brake-pad of vehicle i after performing the scheduled missions, since this quantity is stochastic, the expectation operator E is used. X i is the distance vehicle i will travel while following this mission schedule.

Therefore, the fleet expected degradation cost of a mission schedule can be written as:

C deg = C bk Y 0 N i=1 λ i X i (6)
where C bk is the cost of a brake-pad.

Operational Costs

Traditionally, scheduling missions is mainly impacted by fuel consumption and deadlines. To be able to quantitatively decide between two different schedules we have to model those cost sources.

As the focus of this article lies in the optimization of planning and maintenance, fuel consumption costs are considered to be directly proportional to the traveled distance. In the future, this PsM algorithm can be easily adapted to account for offline consumption estimations similar to [START_REF] Basso | Energy consumption estimation integrated into the electric vehicle routing problem[END_REF]. For now, the cost related to distances C dist is given by:

C dist = C Km M i=1 X i (7)
where C Km is a fuel price based constant, M represents the whole fleet, and X i is the distance that will be traveled by vehicle i.

While planning missions, it is important to consider the deadlines. In real life, penalties for late deliveries can be applied in several different ways. In this paper, penalties are considered to be proportional to the delay. Therefore, the delay cost is:

C delay = C d P i=1 max[t i -l i , 0] (8)
where C d is a constant that is related to the cost of penalties, P is the total number of points to be visited, t i is the arrival time at point i and l i is the deadline of point i. Notice that in this formulation, the duration of the displacement between two points is considered to be deterministic, so, once mission plan is decided, the arrival instant t is known. This assumption means that uncertainties on the delivery date caused by traffic or unplanned breakdowns are not considered, which is justified since this paper considers only immobilizations due to brake-pad wear, which should not occur while following the PsM schedules.

C dist and C delay are completely defined by distance matrix D, duration matrix T , the deadlines of each delivery point and a mission plan.

Waste Cost

As explained in Section 2, once a maintenance date is decided for a given vehicle, it must be used as much as possible before the replacement, avoiding waste and sparing other vehicles. To do so, a dynamic cost is used. Its construction starts by defining t * .

t * i = t -t mainti (9)
where t mainti is the maintenance date of vehicle i, and t is the present time. Then the cost of not using vehicles that will undergo brake replacements, C w , is:

C w = C bk Y 0 N * i=1 (E[Y i ] -Y crit )A(t * i ) (10)
where N * are the vehicles that will undergo a brake-pad change at t maint , E[Y i ] is the expected thickness of vehicle i after completing the scheduled missions, Y crit is the critical failure threshold of a brake-pad and A(t * i ) is an activation function. Similarly to the degradation, delay and distance cost, C w is computed at the fleet level.

A(t * i ) could be any monotonic increasing function, so that it grows with t * , meaning that the cost of not using the vehicle becomes more important the closer the replacement date is. The chosen activation function is:

A(t * ) = S(αt * + β) (11)
A closed-loop prescriptive maintenance approach for a usage dependent deteriorating item 5 Notice that N * accounts for the vehicles that will undergo replacements and should be more used, while N considers those vehicles for which a replacement date was not yet defined, and therefore, whose thickness should be spared and maximized, and finally M is the ensemble of all vehicles in the fleet.

C w is a dynamic cost, depending on the maintenance date. Minimizing it will make vehicles that will have their brake-pad changed, more used, avoiding waste and sparing other vehicles.

Closed Loop Decision Making

Based on the model developed in the previous section, a closed loop PsM decision making procedure for the joint maintenance and missions assignment can now be implemented. The PsM solution is represented in Fig 3.

The solution is composed of two main parts, a scheduler and a maintenance date decision maker. The scheduler will receive the list of missions to be accomplished, alongside with the related information (matrices D, T and respective deadlines), and the last available degradation measurement. It will then proceed to find the best schedule possible, in order to reduce the long-term overall exploitation cost.

This mission schedule will be followed by the fleet and new degradation measures will be collected. These measurements will be used as an input by the maintenance date decision maker which will decide if a vehicle will replace its brake-pads in the next workshop visit. Replacement dates are then updated and used to change the scheduler cost function.

In the following sections, the scheduler and the maintenance decision maker are explained in detail.

Scheduler

The scheduler is responsible for finding the optimal mission schedule π. The optimization criterion that accounts for the overall exploitation

C(π) = C delay + C dist + C w + C deg (12)
In a fleet with identical vehicles, minimizing C deg implies minimizing the traveled distance, and therefore, in terms of Eq. 12, any schedule that reduces the total distance and respect deadlines will be equivalent. On the other hand, it is beneficial not only to reduce the total degradation cost, but also to use less degraded vehicles to perform shorter missions, postponing brake-pad replacements. To address this fact, the optimization problem is:

min π C(π) -γY min ( 13
)
where γ is a positive constant, determined empirically, through simulations and Y min is the minimal expected thickness in the fleet, after following the mission plan π. The term -γY min will privilege schedules that not only reduce the overall exploitation cost but also postpone maintenance operations, using less degraded vehicles to perform more demanding missions.

Since this problem of scheduling missions is a variation of the travel salesman problem, it is NP-hard. The optimizer used was based on genetic programming, a heuristic method that, even though fast, is not guaranteed to find the optimal solution every time.

Maintenance Date Decision Algorithm

To make the decision of choosing the next workshop visit for brake-pad replacement, it is needed to evaluate Eq. 4 and thus to estimate P[Y (t wkp2 ) < Y crit ] and Y (t wkp1 ). To this aim, it is necessary to make the hypothesis that P[X/T ] -distribution of the distance traveled given a specific time window -is known, since Y correlates with the distance traveled by a vehicle and not time.

Once P[X/T ] is known, Monte-Carlo methods can be used to decide the maintenance date. P. Longhitano, K. Tidriri, C. Bérenguer, B. Echard

Table 1. Fleet initial conditions Y 0 λ σ B (%) (km -1 ) (km -1 ) Vehicle 1 100 -1e-3 1e-1 Vehicle 2 100 -8e-4 1e-1 Vehicle 3 100 -8e-4 1e-1 Vehicle 4 100 -8e-4 1e-1
Whenever a degradation measure is available and therefore the current value of Y is known, the algorithm estimates the average Y (t wkp1 ) by making random samplings of P[X/T ] to infer the average distance traveled at t wkp1 . Similarly, P[Y (t wkp2 ) < Y crit ] is estimated using random samples of P[X/T ], in that case, the number of trajectories in which an immobilization occurred before t wkp2 is compared to the number of trajectories in which it did not, so that this probability can be empirically estimated.

In real life applications, P[X/T ] can be estimated based on the vehicle's usage history and the client's business model.

Numerical Experiments and Results

To test the PsM solution, a comparison between the proposed algorithm and other exploitation strategies is made through simulations, to see how they can affect the long term cost.

Missions and Fleet Parameters

The simulations emulate the exploitation of a fleet of vehicles that have to perform the same missions every week. Those fleets are identical and have the parameters presented on Table 1.

Matrix D and T are chosen so that every point in space is equidistant (equals to 100 km) and every possible displacement has the same duration (equals to 1 hour). This choice is done in order to have a configuration where different schedules would lead to optimal distance and delay costs. In such configuration, the scheduler can have more impact on the costs related to degradation and maintenance since more schedules are acceptable in terms of delay and distance costs. The set of missions chosen is presented in Table 2. Point 0 has no deadline attached, representing a headquarters, from where vehicles will have to start their missions and to where they will go back after finishing them. Points 5 to 11 should be visited until 12 hours after the vehicles depart from the headquarters. Points 1 to 4 have tighter deadlines in order to force all the vehicles to be used.

The constants used in the optimization cost function are given in Table 3. In the simulation, whenever a truck performs a schedule of missions, the thickness of the brakepad evolves according to the model (1).

Fleet strategies

Three different strategies are compared through simulations, all of them start in the same initial conditions, presented at table (1) and have to perform the missions of Table 2 every week, scheduling mission and brake-pad replacements in different ways:

Strategy 1 consists in using the PsM algorithm in close-loop as represented in Fig 3 . To decide replacement dates, P[X/T ] must be estimated. This distribution is obtained through a first simulation, performed with different degradation levels for a fleet with the initial parameters of Table 1.

Strategy 2 emulates a strategy used by some real clients. Every week, the fleet follows the same schedule. This fixed schedule does not take the degradation model into consideration, only accounting for delay and distance costs and minimizing the total duration of missions. This schedule then minimizes the total distance, the delays and finishes all deliveries as soon as possible, as real fleet managers do. Clients with certain types of maintenance contract receive an alert to schedule brake-pad replacements whenever thickness falls under a warning threshold Y w . To emulate a client maintenance strategy, replacements will occur whenever a regular visit to the workshop happens and thickness is already below Y w .

Strategy 3 consists in using an open-loop version of the PsM algorithm. A schedule of missions is built using the PsM scheduler once, therefore taking into account the degradation parameters of A closed-loop prescriptive maintenance approach for a usage dependent deteriorating item 7 each truck. This schedule will be followed every week. Maintenance will happen in the same way as for strategy 2, whenever a regular visit to the workshop happens and thickness is already below Y w .

Simulation Analysis

Schedules

Table 4 shows fixed schedule followed by Strategy 2. It completes the missions as fast as possible, and since all points are equidistant and it starts with the point that presents the earlier deadlines, both distance and delay costs are optimized. On the other hand, since this planning does not take into account the degradation cost, it uses Vehicle 1 -which has the highest absolute deterioration rate |λ| -to perform more missions than necessary. The normalized degradation cost associated with this schedule is C deg = 0.005. With the fixed schedule followed by Strategy 3 presented in Table 5, it can be seen that, similarly to Strategy 2, this schedule minimizes distance traveled and does not cause any delay. On the other hand, since this schedule was found by the PsM scheduler, it takes degradation into account and therefore, avoids using Vehicle 1 as much as possible.

Strategy 1 does not follow a fixed schedule. Fig 4 shows the histogram of traveled distances for each vehicle of the fleet. It can be seen that Vehicle 1 was not used for more than one mission in most weeks, reducing the degradation cost to C deg = 0.003. The schedules of missions in which it is used more than once can be explained by the fact that the genetic algorithm does not converges to the optimal schedule every time and in a few occasions, due to the randomness of the algorithm, a sub-optimal schedule was used.

Long Term Cost

To compare the different strategies, it is necessary to compute the long term exploitation cost, which is composed of delay, distances and maintenance costs. Delay and distances costs are obtained directly from Eq.7 and Eq. 8.

C deg is not a cost paid daily by fleet managers, it is only a measure of how well exploited the fleet was in terms of health management.

The real cost paid by fleet managers is the replacement and immobilization costs.

In the simulations, whenever a replacement of brake-pad happens, maintenance cost is increased by C bk and whenever an immobilization happens, maintenance cost is increased by C f ail . Notice that the only possible cause for immobilization considered is related to the brake-pad wear, not accounting for failures cause by other components. C f ail includes all the expenses related to the immobilization, including extra delays, so that, adding it to the simulation cost is its only consequence.

Operational costs are identical for the three fleets. No delay cost is payed and distance cost is equal every week to C dist = 0.19, which means that the scheduler is able to reduce the traveled distance and the delay for the fleet in every mission schedule.

Figures 5 and6 show the maintenance cost and the waste cost (as calculated in Eq. 2).

We can notice that no immobilization occurred with any of the strategies. On the other hand, with Strategy 2, more replacements were necessary than for the other strategies. This is due to the fact that its fixed schedule has a higher C deg and shows that considering the knowledge on the Strategy 2 and Strategy 1 use schedules derived from the PsM algorithm. Even following sub-optimal schedules sometimes, Strategy 1 performed better, postponing maintenance operations and avoiding waste. This is due to the use of dynamic scheduling that accounts for maintenance dates and often uses more degraded vehicles to perform the least demanding missions.

Conclusion and future work

In this paper, a PsM solution was proposed for a fleet of vehicles. The actions to be analyzed were related to the plan of mission and the maintenance date, considering the impacts one has on the other. The component chosen for this task was the brake-pad, modeled with a wiener process. While scheduling missions, different operational costs that can be inferred from basic mission characteristics and from the degradation model, were modelled. For the maintenance date part, a Monte-Carlo method was used, based on the hypothesis that P[X|T ] is known. To improve it, methods for online estimation of P[X|T ] can be added in the future. Also, in future works a stochastic version of matrix D and T should be considered. Finally, through simulation, the PsM solution was compared to two different exploitation strategies, showing it outperforms the strategy 2 and that its usage on close loop can outperform its usage in open loop (Strategy 3). Because of the probabilistic nature of the degradation phenomena, more tests are needed to quantify exactly how much improvement is achieve through the PsM solution.

In future works, more complex operational constraints can be studied and component models that allow for more complex actions, such as parameters changes, replacements for used components, etc, may be used.

Fig. 1 .

 1 Fig. 1. Example of a brake pad degradation path

Fig. 2 .

 2 Fig. 2. Example of an activation function

Fig. 3 .

 3 Fig. 3. PsM structure

Fig. 4 .

 4 Fig. 4. Histogram of traveled distances -Strategy 1

8

  Fig. 5. Maintenance Cost Comparison

Table 2 .

 2 Point to be visited

	Point	Deadline (h)
	Point 0	-
	Points 1, 2, 3 & 4	1
	Points 5, 6, 7, 8, 9, 10 & 11	12
	Table 3. Normalized Constant Values For
	Simulations
	Constant	Value
	C bk	1
	C Km	0.0015
	C d	0.4
	C f ail	14.2
	Y crit	0

Table 4 .

 4 Fixed Schedule -Strategy 2

		Points Visited
	Vehicle 1	0, 3, 10, 6, 0
	Vehicle 2	0, 1, 9, 11,0
	Vehicle 3	0, 2, 5, 7, 0
	Vehicle 4	0, 4, 8, 0

Table 5 .

 5 Fixed Schedule -Strategy 3

		Points Visited
	Vehicle 1	0, 1, 0
	Vehicle 2	0, 2, 5, 7, 0
	Vehicle 3	0, 3, 6, 10, 11, 0
	Vehicle 4	0, 4, 9, 8, 0


A Riviere

T Nothof

R Greiner

Sylvain Tranchimand

Nicolas Noiret

F Robert

M Mireaux
email: mmireaux@ccpa.com

In vitro assessment of enzymatic phytate dephosphorylation during digestive process of different feeds and feed ingredients

Keywords: in vitro digestion model, phytate, phytase, phosphorus, feed ingredient IPx, myo-inositol phosphate with x phosphate residues, M, maize, RM, rapeseed meal, SBM, soybean meal, SD, standard deviation, W, wheat

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

Introduction

Phosphorus (P) is an essential nutrient in animal nutrition. It has an important structural role in bone mineralization, as a component of the crystalline structure of the skeleton, as well as in the form of phospholipids in cell membranes. As part of energy-rich compounds such as nucleotides for instance phosphorus also plays an essential role in metabolism or its regulation. 2,3,4,5,, also called phytate, was reported as the main storage form of phosphorus in cereals, legumes and nuts [START_REF] Humer | Phytate in pig and poultry nutrition[END_REF]. However, phytate phosphorus is poorly available for monogastrics because of the low phytate dephosphorylating activity in their gastro-intestinal tract and the inability of phytate to be absorbed per se. Therefore, most of the phytate phosphorus is metabolized by the colon microflora or excreted and accumulates in soil. As a consequence strong effects on fluxes of phosphorus in the landscape and enrichment of water bodies with phosphorus have been reported resulting in eutrophication with many harmful environmental impacts such as shifts in species and variations in water quality and micro-organism composition [START_REF] Correll | The role of phosphorus in the eutrophication of receiving waters: A review[END_REF][START_REF] Smith | Eutrophication: impacts of excess nutrient inputs on freshwater, marine, and terrestrial ecosystems[END_REF]. Phytate has also a strong antinutritional effect by forming indigestible complexes with nutrients, such as mineral divalent cations and proteins or dietary amino acids and may therefore increase their endogenous losses [START_REF] Woyengo | Review: Anti-nutritional effects of phytic acid in diets for pigs and poultry -current knowledge and directions for future research[END_REF]. Thus, not only phosphorus has to be supplemented in diets as an inorganic feed additive in order to be bioavailable, but also other nutrients have to be incorporated at higher levels, both of which represent a significant cost in animal nutrition. Since their first commercialization in 1991, phytate-degrading enzymes, also called phytases, represent a widely recognized solution as feed additives by allowing phytate dephosphorylation during digestion [START_REF] Lei | Nutritional benefits of phytase and dietary determinants of its efficacy[END_REF].

Therefore, supplementation of phytase improves the bioavailability of both the organically bound phosphorus and the nutrients complexed by phytate.

Feed enzymes suppliers recommend a standard inclusion of 500 U of phytase per kg of feed in most pig and poultry feeds. However, differences in apparent activity of phytases were observed depending on the activity assay applied. In addition, the efficacy of phytases might also be altered by in vivo feed composition [START_REF] Dersjant-Li | Phytase in non-ruminant animal nutrition: a critical review on phytase activities in the gastrointestinal tract and influencing factors[END_REF]. Therefore, phytases need to be studied in a model of the digestive tract under identical conditions to allow a proper comparison of their efficacies in the dephosphorylation of phytate. As in vivo evaluations of phosphorus uptake and assimilation are tedious, require a lot of time and repetitions, and are not always very sensitive and reproducible due to inner variations, in vitro models appear to be convenient alternatives [START_REF] Shastak | Determination and estimation of phosphorus availability in growing poultry and their historical development[END_REF].

Conditions applied in vitro might be very different from those in vivo, therefore these models do not perfectly mimic the digestive process. However, they enable studying the enzymatic dephosphorylation of phytate under a broad variety of conditions more rapidly and more easily than in in vivo trials. A three-step in vitro model simulating the gastrointestinal tract of poultry was already described to investigate the dephosphorylation of phytate occurring in wheat in the presence of several phytases, taking temperature, retention time, pH, and proteolytic enzymes into account [START_REF] Menezes-Blackburn | Performance of seven commercial phytases in an in vitro simulation of poultry digestive tract[END_REF]. Therefore, this digestion model was adapted in order to study the enzymatic dephosphorylation of phytate from different feed ingredients or complete diets.

Materials and methods

Materials

The phytase used in this study was a recombinant enzyme from Buttiauxella expressed in Trichoderma reesei (Danisco, Copenhagen, Denmark). This solid phytase preparation was extracted (10% w/v) with sodium acetate buffer (20 mM, pH 5.5) for 2 h at 20 °C and centrifuged (25000g, 4 °C, 30 min) prior to characterization and use of the extract in the in vitro degradation model.

All feed ingredients (wheat, maize, soybean meal and rapeseed meal) and components of diets (inorganic salts, amino acids and premix) were ground to 0.5 mm using an ultra-centrifugal mill ZM 500 (Retsch®, Haan, Germany) with a 24-tooth rotor. Three complete diets were designed in order to mimic traditional poultry feeds (Table 1): a wheat-maize-soybean-meal-based diet (W.M.SBM), a maize-soybean-meal diet (M.SBM) and a wheat-maize-rapeseed-meal diet (W.M.RM). The initial phytate and inorganic phosphorus contents, along with the endogenous phytase activities of each feed ingredients and complete diets were measured prior to the use in the digestion simulation.

Phytic acid dodecasodium salt (Sigma 274321), pancreatin from porcine pancreas (4 × USP, Sigma P1750), and pepsin from porcine gastric mucosa (>250 U/mg, Sigma P7125) were obtained from Sigma (Darmstadt, Germany). Ultrasep ES 100 RP18 column was purchased from Bischoff (Leonberg, Germany) and AG ® 1-X4 anion exchange resin (100-200 mesh) from Bio-Rad (München, Germany). All reagents were of analytical grade.

Standard phytase activity assay

The microbial phytase activity assay was performed according to a previously described method [START_REF] Greiner | Purification and characterization of two phytases from Escherichia coli[END_REF]. Briefly, 10 μL of an appropriately diluted phytase solution was added to 350 μL of a 2.9 mM solution of phytic acid dodecasodium salt in sodium acetate buffer (100 mM, pH 5.5) and incubated at 37 °C. After a 30 min incubation, the released inorganic P was measured by using a modification of the ammonium molybdate method [START_REF] Heinonen | A new and convenient colorimetric determination of inorganic orthophosphate and its application to the assay of inorganic pyrophosphatase[END_REF]: 1.5 mL of a stop solution of 10 mM ammonium heptamolybdate / 2.5 M sulfuric acid / acetone (1:1:2 v/v/v) was added to the mixture, followed after 2 min by a 100 µL addition of a 1 M citric acid solution. The absorbance of the formed phospho-molybdate complex was measured at 355 nm. Prior to the phytase activity assay, the linearity of the phosphorus release from phytic acid dodecasodium salt was confirmed under the conditions used . P release was measured every five minutes during thirty minutes and the coefficient of determination of P release over time was higher than 0.99. Blanks were performed by adding the stop solution prior to enzyme addition. One unit of phytase activity was defined as the amount of phytase releasing 1 μmol of inorganic P in 1 min under test conditions.

Simulation of monogastrics' digestive tract

The simulation model was based on one previously described [START_REF] Menezes-Blackburn | Performance of seven commercial phytases in an in vitro simulation of poultry digestive tract[END_REF]. This three-step model was adapted into a monogastric digestion simulation. Step 1 (humidification) was performed by incubating 1 g of ground matrix (feed ingredient or complete diet) at 40 °C for 15 min with 6 mL of sodium acetate buffer (50 mM, pH 5.0) containing different amounts of phytase activity (0, 250, 500, 750, and 1000 U/kg feed). Step 2 (acidic treatment) was performed by adding to the previous digesta 560 μL of 1 M HCl and 1040 μL of sodium acetate buffer (50 mM, pH 3) containing 21 mg/mL of pepsin. The entire mixture was incubated at 40 °C for 10 min. Step 3 (alkaline treatment) was performed by adding to the previous digesta 1.3 mL of 1 M NaHCO3 and 1.3 mL of 14.8 mg/mL aqueous pancreatin solution. The entire mixture was incubated at 40 °C for 15 min. All incubations were performed under continuous shaking to guarantee a homogeneous distribution of all ingredients.

The samples obtained from the simulated digestion were freeze-dried overnight (Christ, Osterode am Harz, Germany), and then extracted with 20 mL of 2.4 % HCl for 3 h at room temperature. The resulting suspensions were centrifuged (30 min, 4 °C, 12000g) and the supernatants were collected and used for myo-inositol phosphate quantification (AOAC Method 986.11, 1990).

Quantification of myo-inositol phosphates

Two milliliters aliquots of the supernatants were diluted with 60 mL water. The entire solution was applied to a column (0.7 × 15 cm) containing 0.5 g of AG ® 1-X4 anion exchange resin (100-200 mesh). The column was washed with 25 mL of water and 25 mL of 25 mM HCl. Then myoinositol phosphates were eluted with 25 mL of 2 M HCl. The obtained eluates were concentrated in a vacuum evaporator and dissolved in 1 mL of water. Then 20 μL of the samples were analyzed by HPLC (Pharmacia, Uppsala, Sweden) on an Ultrasep ES 100 RP18 (2 × 250 mm) column using refractive index (RI) detection in order to quantify IP3 to IP6. (PN 3150 RI Detector, Postnova Analytics, Landsberg am Lech, Germany). The elution was performed in isocratic mode at 40 °C with a 0.2 mL/min flow rate of solvent (formic acid / methanol / water / tetrabutylammonium hydroxide, 44:56:5:1.5 v/v, pH 4.25) [START_REF] Sandberg | HPLC method for determination of inositol tri-, tetra-, penta-, and hexaphosphates in foods and intestinal contents[END_REF]. A 1.67 mM aqueous solution of myo-inositol hexakisphosphate ester (IP6) was used as a standard.

Evaluation of feed ingredients and feeds prior to digestive process

In order to measure the inorganic phosphorus and phytate contents of feed ingredients and feeds, 1 g of matrix was extracted for 3 h with 20 mL of 2.4 % HCl at 20 °C. The mixture was centrifuged (30 min, 4°C, 12000g, Beckman, Krefeld, Germany) and the supernatants were collected and used for inorganic P and phytate quantification. IP3 to IP6 were measured as described in 2.4. Inorganic phosphorus content was measured by using the modification of the ammonium molybdate method [START_REF] Heinonen | A new and convenient colorimetric determination of inorganic orthophosphate and its application to the assay of inorganic pyrophosphatase[END_REF] previously described: briefly, 1.5 mL of a stop solution of 10 mM ammonium heptamolybdate / 2.5 M sulfuric acid / acetone (1:1:2 v/v/v) was added to 400 µL of supernatant, followed after 2 min by a 100 µL addition of a 1 M citric acid solution and the absorbance of the formed phospho-molybdate complex was measured at 355 nm.

The intrinsic phytase activity of feed ingredients and feeds was measured by direct incubation of 1 g in a 5 mM solution of sodium phytate in acetate buffer (100 mM, pH 5.5) for 30 min at 37°C [START_REF] Greiner | Determination of the activity of acidic phytate-degrading enzymes in cereal seeds[END_REF]. 50 µL of the mixture is sampled every 5 min and diluted with water, prior to measuring the released inorganic P as already described.

Calculation of phosphorus release from phytate

The amount of phosphorus released from IPx was calculated based on the myo-inositol phosphates (IP6 -IP3) quantified in the feed ingredients and in the feed before and after in vitro digestion. Indeed, the values obtained by direct phosphate quantification were higher than those obtained from phytate dephosphorylation. This might be due to a dephosphorylation of other phosphorylated compounds present in the feed or feed ingredients [START_REF] Lowry | The determination of inorganic phosphate in the presence of labile phosphate esters[END_REF] or an interaction between the phosphate released and other constituents of the feeds or feed ingredients.

The initial IP2 and IP1 contents of feed ingredients was reported insignificant [START_REF] Pointillart | Phytates, phytases: leur importance dans l'alimentation des monogastriques[END_REF] and therefore only their IP3 to IP6 contents were considered. The phosphorus initially bound to the myo-inositol ring (IP3 to IP6) could be calculated according to Equation 1. Equation 1Calculation of initial phytate bound phosphorus (mole)

• ••••••• ! • •" = # $ * &' ( ! • •" = # $ * &' ( ! • •" ) (*+ ) (*,
Where k is the number of P bound to the inositol ring. The HPLC system used is not capable of quantifying IP2, IP1 and myo-inositol and their quantification is of little interest, because IP4 and/or IP3 and not IP1 nor IP2 generally accumulate during digestion [START_REF] Greiner | Activity of Escherichia coli , Aspergillus niger , and rye phytase toward partially phosphorylated myo-inositol phosphates[END_REF][START_REF] Schlemmer | Degradation of phytate in the gut of pigspathway of gastrointestinal inositol phosphate hydrolysis and enzymes involved[END_REF]. After in vitro digestion however the concentrations of IP2, IP1 and myo-inositol need to be considered in order to calculate P released from the myo-inositol ring. Thus, the inositol amount calculated according to Equation 2 before and after in vitro digestion and defined as (IP<3) might either be present as myo-inositol, IP1 or IP2. Equation 2Material balance (mole) of inositol phosphates and calculation of IP<3 content after digestion It is considered that

# &' ( ) (*, ! • •" = # &' ( ) (*+ ! • •" Thus, # &' ( ) (*+ ! • •" = # &' ( ) (*+ -!•" + # &' ( / (*, -!•" + 012 34253627
It is defined

# &' ( / (*, -!•" + 012 34253627 = (&' < 3) -!•"
Thus,

(&' < 3) -!•" = # &' ( ) (*+ ! • •" -# &' ( ) (*+ -!•"
Because the real-life situation will be in between the two extremes (100 % as myo-inositol or 100 % as IP2), the accumulation of IP1 exclusively was used as an intermediate situation to estimate the P released from the myo-inositol ring. (Equation 3) Equation 3Material balance (mole) of originally phytate-bound phosphorus and calculation of P released after digestion

Pphytate initial = Pphytate final + Preleased With '>ℎ16@6A -!•" = # $ * &' ( -!•" ) (*, = # $ * &' ( -!•" ) (*+ + # $ * &' ( -!•" / (*, but # $ * &' ( -!•" / (*, 35 B4$42C4 Its highest value is 2 * ∑ &' ( -!•" / (*,
and its lowest value is 0.

An accumulation of IP1 was considered, i.e. IP2 = 0 and myo-inositol = 0 as an intermediate situation

# $ * &' ( -!•" / (*, = 1 * # &' ( -!•" = 1 * (&' < 3) -!•" / (*, SO ' G•"••H•I ~# $ * &' ( ! • •" ) (*+ -# $ * &' ( -!•" ) (*+ -1 * (# &' $ 6 $=3 34363@7 -# &' $ 6 $=3 K34@7
)

Data management

The statistical replicate of this work (n) is the calculation of P release based on the measured IP6 to IP3 at the end of a laboratory run of digestion simulation for one ingredient and one phytase dose. Each experiment was performed multiple times. The initial phytate phosphorus content for each ingredient used to calculate P release for the different replicates were the average of at least 2 measurements but 3 for soybean meal, 5 for maize and 7 for wheat. Data were analyzed using R version 4.0.2 (R Core Team 2020) by ANOVA to evaluate the impact of ingredients, phytase dose and their interactions on P liberation. Linear and quadratic effects of phytase dose were tested. Data with absolute values of standard residues above 3 were excluded. Rapeseed meal P release (in mg of P/kg of rapeseed meal) data had to be excluded from the ANOVA analysis because of their high variability which led to non-normal distribution of the residues (Shapiro-Wilk test). A Kruskal-Wallis test was performed on the initial IPx contents of feed ingredients and diets followed by a Dunn test for multiple pairwise comparisons. An effect was considered significant at P-values below 0.05 (P ≤0.05).

Results

Phytate phosphorus content and endogenous phytase activity of the feed ingredients and complete diets.

The range of phytate phosphorus content (1.8 to 9.8 g/kg) was wide among feed ingredients (Table 2). The values obtained for the complete diets agreed to those determined for the individual ingredients considering their relative proportions. Furthermore, huge differences in endogenous phytase activities was observed among the different feed ingredients. Wheat had a very high (>1700 U/kg) endogenous phytase activity, higher than the highest phytase dose (1000 U/kg) added as a supplement to the in vitro digestion system. In maize and soybean meal however, the endogenous phytase activities were low (<100 U/kg). An intermediate endogenous phytase activity (244 ± 124 U/kg) was found in rapeseed meal. The obtained phytate phosphorus contents and endogenous phytase activities of the feed ingredients are in good agreement with those already reported [START_REF] Eeckhout | Total phosphorus, phytate-phosphorus and phytase activity in plant feedstuffs[END_REF][START_REF] Selle | Total and phytate-phosphorus contents and phytase activity of Australian-sourced feed ingredients for pigs and poultry[END_REF][START_REF] Viveros | Phytase and acid phosphatase activities in plant feedstuffs[END_REF], except for rapeseed meal. The endogenous phytase activity for rapeseed meal was found to be higher than the published data. Moreover, in the complete diets the endogenous phytase activities obtained were higher than expected from the phytase activities of the single ingredients, although repetition of the measurements would be necessary to validate the results.

Myo-inositol phosphate hydrolysis during digestion simulations of feed ingredients

Differences in phytate dephosphorylation were observed with the different feed ingredients using the in vitro approach (Figure 1). An almost complete IP6 dephosphorylation was obtained with wheat even without exogenous phytase addition. The high endogenous phytase activity of wheat could easily explain this observation. For maize and soybean meal, the lowest exogenous phytase dose tested (250 U/kg) was sufficient for a complete IP6 hydrolysis. Both feed ingredients exhibited a relatively low endogenous phytase activity but also a low phytate content compared to rapeseed meal. The initial contents of P bound to IPx significantly differed between feed ingredients (p=0.008) with maize having a significantly lower content than rapeseed meal, the other feed ingredients being intermediate. Due to the high phytate content compared to the other feed ingredients a complete IP6 dephosphorylation was not achieved during in vitro digestion of rapeseed meal even at the highest dose (1000 U/kg) of exogenous phytase: about a 0.06 portion of the initial IP6 content remained after digestion.

The profiles of the partially phosphorylated myo-inositol phosphates (IP5 to IP3) generated during in vitro digestion were comparable among wheat, maize, soybean meal and rapeseed meal.

IP5 didn't accumulate and was rapidly further dephosphorylated. The first phytate dephosphorylation product accumulating was IP4. After the complete disappearance of IP6, IP4 was further hydrolyzed to IP3 which accumulated later on.

The proportion of released phosphorus was found to be very different among the feed ingredients (P<0.001, Table 3). Phosphorus release from phytate in wheat was high even without phytase addition (a 0.47 portion of its initial P content bound to IPx). This result was expected because of its very high endogenous phytase activity (1749 ± 71 U/kg). In comparison, phosphorus release from phytate in other ingredients only reached 0.15 to 0.19 portions of their initial P content bound to IPx. Addition of exogenous phytase increased the liberation of phosphorus by up to 1.7fold in wheat at the highest dose (1000 U/kg) tested, resulting in the release of a 0.80 portion of the phosphorus initially bound to the myo-inositol ring. In the presence of 1000 U/kg of exogenous phytase, P release for maize reached 0.68 of the phosphorus initially bound to the myo-inositol ring, 0.74 for soybean meal and 0.40 for rapeseed meal.

Myo-inositol phosphate hydrolysis during digestion simulations of feeds

The three-step simulation process was also applied to three different feeds composed of the feed ingredients tested (Table 1): a wheat-maize-soybean-meal-based diet (W.M.SBM), a maizesoybean-meal diet (M.SBM) and a wheat-maize-rapeseed-meal diet (W.M.RM).

The sequential hydrolysis of IP6 were found to be similar among the three evaluated feeds (Figure 2). IP3 was also observed to accumulate.

P released is significantly increased in the presence of the highest dose (1000 U/kg) of exogenous phytase compared to the in vitro digestion without exogenous phytase (P<0.05, Table 4): P release increased by a 3.3-fold (W.M.SBM), a 4.6-fold (M.SBM) and a 2.7-fold (W.M.RM).

Phosphorus release from IPx was found to be increasing with increasing doses of exogenous phytase and more than a 0.6 portion of the phosphorus initially bound to the myo-inositol ring was released in the presence of 1000 U/kg exogenous phytase for all three diets studied. The amount of phosphorus released in the in vitro digestion model is dependent on the initial IPx phosphorus content of the feeds (P<0.001). Feeds with higher initial phytate phosphorus concentration resulted in higher phosphorus releases although no significant difference between initial phytate contents was found between feeds (p=0.102).

Discussion

Phytase efficacy is affected by many factors, among others the availability of phytate for enzymatic hydrolysis. Solubility of phytate during the digestive process, broadly reviewed for both poultry and pigs (Selle andRavindran, 2008, 2007), is one of the factors influencing this availability, since only soluble phytate could act as a substrate for the phytases used as feed additives. Thus, phytate location within the feed matrix may also contribute to the availability of phytate for enzymatic hydrolysis. Phytate within the plant matrix needs to be released in order to be available for the exogenous phytases added to feeds. Phytate location in cereal and oilseeds was studied and it was found that distribution differs between grains [START_REF] Erdman | Oilseed phytates: Nutritional implications[END_REF][START_REF] O'dell | Distribution of phytate and nutritionally important elements among the morphological components of cereal grains[END_REF]. In wheat and rapeseed, phytate is mainly distributed within the outer layer (aleurone layer and outer bran) of the grain, whereas the endosperm contains almost no phytate. Unlike other oilseeds, no specific site of phytate location was identified in soybean seed. For maize nearly 90 % of its phytate phosphorus is present in the germ. Despite this wide variety of phytate locations among the tested feed ingredients and total diets, no significant differences in the relative appearance of partially phosphorylated myo-inositol phosphates (IP5 to IP3) were found in the in vitro digestion model: IP5 was quickly further dephosphorylated and IP4 was the first dephosphorylation product accumulating during IP6 hydrolysis followed by IP3. This result was expected, since the relative concentration of the different dephosphorylation products of phytate over time is mainly dependent on the phytase used and the viscosity of the system (Greiner, unpublished results). Only one single exogenous phytase was applied in the present study and the viscosities when using different feed ingredients or diets were similar.

The initial phytate phosphorus content seems to be a limiting factor of the enzymatic phytate dephosphorylation: the higher the initial phytate content, the more phytate is released into the liquid phase of the digestive tract in the model and therefore more phytate is available for the phytase to act on. Under in vivo conditions, when feeds are not ground, release of phytate from the feed matrix might be more pronounced than in the in vitro system depending on the location of the phytate within the matrix and the particle size of the feed particles. Furthermore, the higher viscosity under in vivo conditions might influence the release of phytate into the liquid phase and therefore the amount of phytate accessible to the phytase.

The concentration of phosphate may also affect enzymatic phytate dephosphorylation, because phosphate was reported to act as a competitive inhibitor for several phytases [START_REF] Greiner | Purification and characterization of two phytases from Escherichia coli[END_REF].

Assuming that the inhibition constants for the exogenous phytase used in this study is similar to those reported for the E. coli phytases (between 11.9 and 13 mM) [START_REF] Greiner | Purification and characterization of two phytases from Escherichia coli[END_REF], the concentration of phosphate in the feed ingredients and diets is too low for an inhibition. During in vitro digestion however, the concentration of phosphate increased to a level where inhibition may occur.

As expected, the role of the intrinsic feed phytase in enzymatic phytate dephosphorylation was higher, the higher its level was but also the lower the activity of the added phytase was. Only for wheat exhibiting a much higher intrinsic phytase activity than the other feed ingredients, a noticeable role of the intrinsic phytase in enzymatic phytate dephosphorylation was observed. It is very likely that the intrinsic phytase dephosphorylates phytate in the feed matrix, because phytase and phytate are co-located within the feed matrix, whereas phytate need to be released from the feed matrix to be accessible to the exogenous phytase. Thus, the minor role of the intrinsic phytases might be explained by a fast release of phytate into the liquid phase of the in vitro system. It is also likely that the intrinsic plant phytases are more prone to inactivation under gastric and intestinal conditions compared to the added exogenous phytase (Selle andRavindran, 2008, 2007). When incorporated to the feed for animal nutrition, these endogenous phytases are also prone to inactivation due to the fabrication process.

For the digestive process in the absence of exogenous phytase, the absolute P release depends both on the initial myo-inositol phosphate content and on the intrinsic phytase activity of the ingredient used (Table 2-3). Some of the obtained values present a high variability and would need confirmation. It is especially the case for rapeseed meal which data had to be excluded from the analysis of variance. This high variability is probably partly due to experimental error, but a higher variability caused by the plant matrix cannot be excluded. Indeed, phytate is harder to extract from rapeseed meal than from soybean meal [START_REF] Morgan | In vitro versus in situ evaluation of the effect of phytase supplementation on calcium and phosphorus solubility in soya bean and rapeseed meal broiler diets[END_REF]. Despite this variability, some hypothesis can be made. The maize and soybean meal used in this study exhibited low intrinsic phytase activities (44 and 86 U/kg respectively) and therefore a low P release from the myo-inositol ring was observed (264 ± 271 and 751 ± 234 mg/kg respectively). The wheat used, with its significantly higher intrinsic phytase activity (1749 U/kg) resulted in a higher P release (997 ± 436 mg/kg) despite its low initial phytate content. A 0.46-fold decrease in its initial P content bound to the myo-inositol ring was observed. The rapeseed meal used had the highest initial content of myo-inositol-bound P (9.8 g/kg) and a high P release from IPx was obtained (1619 ± 1761 mg/kg).

However, it represents only a 0.17-decrease of its initial myo-inositol-bound P content, because of its relatively low intrinsic phytase activity (244 U/kg). The same trends were also observed for the three complete diets (W.M.SBM, W.M.RM and M.SBM) used in this study.

The intrinsic phytase activities determined for the different diets are always higher than the sum of the intrinsic phytase activities of their individual ingredients (Table 2). A similar phenomenon was observed when mixing pea flour with wheat flour [START_REF] Chouchene | Evidence of a synergistic effect between pea seed and wheat grain endogenous phytase activities[END_REF]. A synergistic effect between the pea and wheat phytases was given as an explanation for the observed effect. Considering the high phytate concentration relative to the intrinsic phytase content in the phytase activity assay and the short time of incubation, a synergistic effect is very unlikely. During the assay at maximum a 0.03 part of the P bound to phytate was released and therefore the phytases present in the mixture only act on IP6 and therefore independently. Either a compound present in one ingredient acting as activator of the intrinsic phytase of another ingredient or phytase inhibitors present in the different ingredients being inactivated in the diets might explain the observation.

Conclusion

An in vitro digestive simulation process was a successful tool to assess the efficacy of a bacterial phytase used as a feed supplement in order to dephosphorylate phytate present in different feed ingredients and complete diets. Phytase efficacy was dependent on the feed or feed ingredient, partially due to their initial amount of phytate. The intrinsic plant-derived phytase had only a measurable role in phytate dephosphorylation when its activity was high such as in wheat and low doses of exogenous bacterial phytase was added. In the in vitro system, feed ingredients were ground and other elements might have a greater influence under in vivo conditions: release of phytate from the feed matrix might vary depending on the location of the phytate within the matrix, the particle size of the feed particles or the viscosity of the digesta. In conclusion, the in vitro digestion model applied was proven to be a simple and useful tool to assess the enzymatic dephosphorylation of phytate during digestion with different parameters and could be used to study specific parameters affecting the enzymatic dephosphorylation of phytate under digestive conditions.

Figure 1

 1 Figure 1 Remaining phytate (IP6) and myo-inositol penta-, tetra-and triphosphate (IP5-3) arising from partial phytate hydrolysis in the digesta after in vitro simulations with the different feed ingredients, expressed in percentage of the initial concentrations of IPs. Error bars present the confidence interval of the mean.

  Without addition of exogenous phytase, 0.75 (M.SBM), 0.54 (W.M.RM) and 0.39 (W.M.SBM) portions of the initial IP6 remained in the digesta of the in vitro simulation. The extent of phytate dephosphorylation is linked to the endogenous phytase activities (129, 864 and 883 U/kg for M.SBM, W.M.RM and W.M.SBM respectively) and initial IPx phosphorus content of

	the different diets (2.3, 4.3 and 2.6 g/kg).

Accumulation of the partially phosphorylated myo-inositol phosphates was in good agreement to IPx accumulation using the individual ingredients. No accumulation of IP5 was observed during in vitro digestion in the presence and absence of exogenous phytase, IP4 was the first intermediate accumulating and after the complete dephosphorylation of IP6, IP4 was further hydrolyzed to IP3.

  SP7284, product supplied by CCPA (Janze, France). Composition (expressed per kg of feed): vitamin A (6000 UI), vitamin D3 (1200 UI), vitamin E (10 UI), vitamin B2 (2.50 mg), D-calcium panthotenate (5 mg), vitamin B12 (0.02 mg), niacinamide (13 mg), FeSO4•H2O (80 mg), CuSO4•5H2O (13 mg), ZnSO4•H2O (105 mg), MnO (40 mg), Ca(IO3)2 (0.50 mg), Na2SeO3 (0.26 mg), sepiolite (4.30 mg) on calcium carbonate.Phytate phosphorus content and endogenous phytase activities in feed ingredients and complete diets, compared to previously reported values in the literature. (values are means of n measurements).

	Table 1 Table 2
	Composition (in g/kg) of the complete diets studied
			W.M.SBM a	M.SBM a	W.M.RM a
	Wheat Maize		310.0 306.2 Present study	-566.0	310.0 306.2 Values from the literature b
	Soybean meal	Phytate P a	250.0 Inorganic P	300.0 Endogenous	-Phytate P a	Inorganic P	Endogenous
	Rapeseed meal	(g/kg)	(g/kg)	-	-phytase (U/kg)	250.0 (g/kg)	(g/kg)	phytase (U/kg)
	Distiller's dried grains with solubles Soybean oil Wheat 2.1 ± 0.1 (n=10) Sodium carbonate Maize 1.8 ± 0.1 (n=9)	50.0 25.0 0.4 ± 0.01 (n=2) 1.5 0.3 ± 0.01 (n=2)	50.0 25.0 1749 ± 71 (n=2) 1.5 44 ± 5 (n=2)	50.0 1.3-3.2 25.0 1.5 1.6-2.6	0.6-1.1 0.3-0.5	255-1912 0-75
	Dicalcium phosphate Calcium carbonate Sodium chloride Soybean meal 3.9 ± 0.2 (n=5) D/L-Methionine L-Lysine Rapeseed meal 9.8 ± 0.3 (n=6)	8.0 6.0 2.3 1.0 ± 0.02 (n=2) 16.0 10.0 2.1 ± 0.01 (n=2)	8.0 6.0 2.3 16.0 (n=1) 86 10.0 244 ± 124 (n=2)	8.0 6.0 2.8-5.4 2.3 16.0 10.0 3.4-8.8	2.1-4.0 2.1-7.2	0-149 0-43
	L-Threonine			6.0			6.0		6.0
	Premix b Monensin W.M.SBM c	2.6 ± 0.1 (n=2)	4.0 5.0 2.6 ± 0.1 (n=2)		883 (n=1)	4.0 5.0	-	4.0 5.0	-	-
	Total Calculated nutrient content M.SBM c 2.3 ± 0.1 (n=2)	1000 2.5 ± 0.1 (n=2)	1000 (n=1) 129	-	1000	-	-
	-Metabolizable energy (kcal/kg) W.M.RM c 4.3 ± 0.2 (n=2) 3.3 ± 0.3 3009.0 (n=2)	3053.0 864 (n=1)	-	2943.0	-	-
	-Crude protein (g/kg)		191.0		196.0		161.0
	-Ca (g/kg)			7.9		8.0		2.6
	-Total P (g/kg)			5.2		5.2		5.3
	-Available P (g/kg)		2.5		2.8		3.5

a W.M.SBM, wheat-maize-soybean-meal-based diet (W.M.SBM); M.SBM, maize-soybean-meal diet (M.SBM); W.M.RM, wheat-maize-rapeseed-meal diet (W.M.RM) b a IP3 to IP6 bound phosphorus concentration b

[START_REF] Eeckhout | Total phosphorus, phytate-phosphorus and phytase activity in plant feedstuffs[END_REF][START_REF] Selle | Total and phytate-phosphorus contents and phytase activity of Australian-sourced feed ingredients for pigs and poultry[END_REF][START_REF] Viveros | Phytase and acid phosphatase activities in plant feedstuffs[END_REF]

c W.M.SBM, wheat-maize-soybean-meal-based diet (W.M.SBM); M.SBM, maize-soybean-meal diet (M.SBM); W.M.RM, wheat-maize-rapeseed-meal diet (W.M.RM)

b Initial IPx phosphorus contents for proportion calculation are 2104 mg/kg for wheat, 1771 for maize, 3930 for soybean meal and 9773 for rapeseed meal c The absolute P release data for rapeseed meal were excluded from the ANOVA analysis because of their high variability. cd-vw : Within column, means without common superscript differ (P<0.05)

Acknowledgments

This study was completed at the Max Rubner Institut (Haid-und-Neu-Strasse, Karlsruhe, Germany). The authors thank the whole Team of the Department of Food Technology and Bioprocess Engineering (Karlsruhe, Germany) for their input to this study.

Funding statement

Arnaud

Riviere was supported by a CIFRE (Industrial Agreements of Training by Research) PhD studentship funded by the ANRT (National Association of Research and Technology, Paris, France) and Deltavit, CCPA Group (Janzé, France).

Declaration of Competing Interest

The authors confirm that there are not conflicts of interest in this research