Zouggar El Oualid

Chaouch Souad
email: chaouchsouad@yahoo.fr

Djaffar Ould Abdeslam
email: djaffar.ould-abdeslam@uha.fr

Abdelhamid Lilia
email: abdelhamidenergie@yahoo.fr

Sliding Control with Fuzzy Type-2 Controller of Wind Energy System based on Doubly Fed Induction Generator

Keywords:

The wind system based on double-fed induction generators (DFIG) has become a very important source of energy. To ensure the proper functioning of this system, many improved control algorithms have been developed for the rotor side converter (RSC). In order to independently control the active and reactive powers of the (DFIG) and obtain effective control, we use a control strategy based on coupling the type-2 fuzzy logic control with the sliding mode control (SMC). The regulation of active and reactive power is done by the orientation of the stator flux. This command has allowed us to reduce the chattring phenomenon and improve the performance of the system in terms of speed monitoring and stator side power regulation. Simulations are performed using MATLAB / Simulink to validate the effectiveness of the proposed control algorithm. The simulation results, obtained when applying this control strategy to the system, demonstrated the validity of the results and thus validated the high performance of this control technique.

INTRODUCTION

The use of wind energy conversion systems has developed into one of the most important new alternatives to conventional fossil fuels in recent years. It offers an excellent opportunity to generate electricity and contribute to respect for the environment.

Recently, the use of doubly fed induction generator in global wind farms is very important because of its high performance in terms of systematic low cost, high energy efficiency, operating over a wide range of speed variation and extracting the maximum amount of power available [START_REF] Blaabjerg | Overview of control and grid synchronization for distributed power generation systems[END_REF][START_REF] Abad | Doubly Fed Induction Machine[END_REF][START_REF] Errouissi | Offset-free direct power control of DFIG under continuous-time model predictive control[END_REF][START_REF] Zavadil | Making connections: Wind generation challenges and progress[END_REF][START_REF] Xiong | Fractional Order Sliding Mode Based Direct Power Control of Grid-Connected DFI[END_REF]. In principle, the performance of the control system and the accuracy and response of the dynamic control system can be strongly influenced by factors such as changes in model variables, measurement errors, an online control system, load conditions and non-linearity. However, the classical PID controller has been widely used to improve control system applications to consider these factors. In order to solve the problem of parametric variations for the calculation of controllers in vector control, sliding mode control is highly appreciated in many areas among them the control of the wind system. It present excellent properties, such as insensitivity to certain external disturbances and variation of parameters, sliding mode control (SMC) known for its simplicity and robustness [START_REF] Belounis | Fuzzy Sliding Mode Controller of DFIG for Wind Energy Conversion[END_REF]. Thanks to the inference system and expert knowledge, the design of the fuzzy logic controller can solve the problem of modeling and variations in system parameters. the type 1 fuzzy logic controller gives better performance in DFIG control than traditional PI controllers [START_REF] Raju | Design and Implementation of Type-2 Fuzzy Logic Controller for DFIG-Based Wind Energy Systems in Distribution Networks[END_REF] [START_REF] Djafar | Speed control of induction motor with broken bars using sliding mode control (SMC) based to on type-2 fuzzy logic controller (T2FLC)[END_REF]. in the general case the membership functions (MFs) and the bases of the rules are based on the experiences of experts or programmers. therefore, there is uncertainty in the rules and the functions depend on the choices of the experts. According to [START_REF] Mendel | On computing normalized interval type-2 fuzzy sets[END_REF][START_REF] Mendel | General type-2 fuzzy logic systems made simple: A tutorial[END_REF][START_REF] Ruiz | Join and meet operations for type-2 fuzzy sets with nonconvex secondary memberships[END_REF][START_REF] Miguel | Type-2 fuzzy entropy sets IEEE Trans-actions on Fuzzy Systems[END_REF] fuzzy logic type 2 has advantages over fuzzy logic type 1 in handling uncertainties in memberships functions and in unexpected disturbances and is very much used in traffic [START_REF] Mendel | A new look at type-2 fuzzy sets and type-2 fuzzy logic systems[END_REF], for power control [START_REF] Li | Traffic flow data forecasting based on interval type-2 fuzzy sets theory[END_REF], fault detection [START_REF] Sun | Optimal tunning of type-2 fuzzy logic power system stabilizer based on differential evolution algorithm[END_REF] and image processing [START_REF] Hassani | zslices-based general type-2 fuzzy fusion of support vector machines with application to bearing fault detection[END_REF] and control for Dual Star Induction Machine [START_REF] Melin | Edge-detection method for image processing based on generalized type-2 fuzzy logic[END_REF].

This paper is organized as follows; modelling of the wind turbine as well as the Power Mechanical Regulation of a wind turbine are provided in section II. Sliding Mode control of the active and reactive powers is presented in section III. The fuzzy logic is introduced in section IV and the results simulation are presented and discussed in section V. Finally, a conclusion of the paper is presented in the last section.

WIND TURBINE SYSTEM MODELING

The wind energy conversion system is composed of the wind turbine, gearbox, DFIG and back-to-back converter. The figure.1 shows the general structure of the wind energy conversion system with its studied control. The turbine captures the wind's kinetic energy and transforms it into a torque that turns the rotor blades. Then, the DFIG converts the mechanical power into electrical power. In this configuration, with the rotor-side converter control, it is possible to adjust the amplitude and frequency of the current in the rotor windings. So that the rotor speed can be changed over a wide range, thus allowing the system to: operate at a variable speed; recover maximum energy and improve its performance, and with the grid-side converter control, maintain the DC bus voltage at a desired reference value while keeping the reactive reference power at zero.

DFIG

Generator-side converter

Grid-side converter

Grid

Wind Turbine Model

The power contained in the form of kinetic energy in the wind crossing at a speed Vv and surface A1, is expressed by: [START_REF] Rahali | Adaptive Field-Oriented Control Using Supervisory Type-2 Fuzzy Control for Dual Star Induction Machine[END_REF] [19]

𝑃𝑃 𝑇𝑇 = 1 2 . 𝜌𝜌. 𝐴𝐴 1 . 𝑉𝑉 𝑣𝑣 3 (1)
Where, ρ is the air density (kg/m3). The wind turbine aerodynamics is characterized by the well-known non-dimensional curves of the power coefficient as a function of the peak speed ratio λ and the blade angle of inclination β [START_REF] Du | Aerodynamics analysis of wind power[END_REF]. The tip speed ratio is the ratio between the blade tip speed Ωt and the wind speed Vv can be expressed as follows [START_REF] Nunes | Influence of the Variable-Speed Wind Generators in Transient Stability Margin of the Conventional Generators Integrated in Electrical Grids[END_REF]

𝜆𝜆 = Ω 𝑡𝑡 .𝑅𝑅 𝑡𝑡 𝑉𝑉 𝑣𝑣 (2)
Where, Ωt is the angular speed of the turbine rotor.

The expression of this power coefficient has been approached for this type of turbine, by the following equation [START_REF] Abdin | Control Design and Dynamic Performance Analysis of a Wind Turbine-Induction Generator Unit[END_REF][23] [START_REF] Bedouda | Robust Control of Doubly Fed Induction Generator for Wind Turbine Under Sub-Synchronous Operation Mode[END_REF]:

𝐶𝐶 𝑝𝑝 (𝜆𝜆, 𝛽𝛽) = �0,5 -0.167(𝛽𝛽 -2)�𝑠𝑠𝑠𝑠𝑠𝑠 � 𝜋𝜋.(𝜆𝜆+0,1) 18,5-0,3.(𝛽𝛽-2 ) � -0.0018(𝜆𝜆 -3)(𝛽𝛽 -2) (3)
The figure.2 shows the relation between Cp, β and λ given by equation (3). from Figure 2, it can be seen that the power coefficient Cp is influenced by two parameters, both by the peak speed ratio λ and by the pitch angle 𝛽𝛽. With equation (2), we can see that at a certain wind speed Vv, the power coefficient Cp can be set to be its maximum value by adjusting both the pitch angle 𝛽𝛽 and the rotation speed Ωt of the turbine. As shown in Figure 2, when 𝛽𝛽 = 2 and λ = λopt, the power coefficient Cp will reach its maximum value Cp_max . The maximum theoretically achievable power coefficient is Cp_max = 0.5. Using the coefficient Cp, the wind turbine can recover only a part of that power: [START_REF] Bedouda | Robust Control of Doubly Fed Induction Generator for Wind Turbine Under Sub-Synchronous Operation Mode[END_REF] 𝑃𝑃 𝑡𝑡 = 1 2

. 𝜌𝜌. 𝜋𝜋 . 𝑅𝑅 𝑡𝑡 2 . 𝑉𝑉 𝑣𝑣 3 . 𝐶𝐶 𝑝𝑝 (𝜆𝜆, 𝛽𝛽)

Where, Rt is the radius of the wind turbine and Cp represents the aerodynamic efficiency of the wind turbine.

The value of λ corresponding to maximum of mechanical power available is called λopt (optimal). The rotor torque is obtained from the power received and the speed of rotation of the turbine:

𝑇𝑇 𝑡𝑡 = 𝑃𝑃 𝑡𝑡 Ω 𝑡𝑡 = 𝜌𝜌𝜋𝜋𝑅𝑅 𝑡𝑡 2 𝑉𝑉 𝑣𝑣 3 2Ω 𝑡𝑡 𝐶𝐶 𝑝𝑝 (𝜆𝜆, 𝛽𝛽) (5)
The power transmission train is constituted by the blades linked to the hub, coupled to the slow shaft, which is linked to the gearbox, which multiplies the rotational speed of the fast shaft connected to the generator.

The turbine rotational speed and driving torque are expressed in the fast shaft by:

Ω 𝑚𝑚 = 𝐺𝐺 Ω 𝑡𝑡 (6)
𝑇𝑇 𝑚𝑚 = 𝑇𝑇 𝑡𝑡 𝐺𝐺 (7)
Where, G is the gearbox ratio.

The complete dynamic model of the wind system is compiled using the mechanical equation:

𝐽𝐽 𝑑𝑑Ω 𝑚𝑚 𝑑𝑑𝑡𝑡 = 𝑇𝑇 𝑚𝑚 -𝑇𝑇 𝑒𝑒𝑚𝑚 -𝐷𝐷 Ω 𝑚𝑚 (8)
Where, J is the wind system inertia and D is the friction coefficient.

The block diagram of the wind turbine model is presented in Figure .3.

Mechanical Regulation of the Power of a Wind System

The relation (4) makes it possible to establish a whole of characteristics giving the power available according to the number of revolutions of the generator for various speeds of wind.

Figures 4 and5 plots the characteristics of the employed wind turbine model for simulations. It shows a generic power curve for a variable speed, and variable pitch wind turbine. At low wind speed (zone 2), the objective in this zone is to extract the maximum power with the application of a command that captures available wind energy. This command called MPPT. In zone III where the wind speed is increased, the power increases considerably, so we must apply a command that limits this power with the keep electricity production. This command based on the orientation of the blades of the wind turbine, it is called pitch control. Law of optimal ordering of a wind system at variable speed

Maximum Power Tracking Control Strategy

In practice, a measurement of the wind speed is very difficult to achieve since the anemometer is located behind the rotor of the turbine and the diameter swept by the blades of the turbine is important.

In this operation region, the objective of the speed control is to follow the path of maximum power extraction.

When the turbine is working on the maximum power point,

𝜆𝜆 𝑜𝑜𝑝𝑝𝑡𝑡 = 𝑅𝑅 𝑡𝑡 Ω 𝑡𝑡 𝑉𝑉 𝑣𝑣 , 𝐶𝐶 𝑝𝑝 = 𝐶𝐶 𝑝𝑝_𝑚𝑚𝑚𝑚𝑚𝑚
The aerodynamic torque extracted by the turbine is then given by [START_REF] Benkahla | Comparative Study of Robust Control Strategies for a Dfig-Based Wind Turbine[END_REF]:

𝑇𝑇 𝑡𝑡 = 𝜌𝜌 𝜋𝜋 𝑅𝑅 𝑡𝑡 2 2 Ω 𝑡𝑡 𝑅𝑅 𝑡𝑡 3 Ω 𝑡𝑡 3 𝜆𝜆 𝑜𝑜𝑜𝑜𝑡𝑡 3 𝐶𝐶 𝑝𝑝_𝑚𝑚𝑚𝑚𝑚𝑚 (9)
With,

𝑇𝑇 𝑡𝑡 = 𝜌𝜌 𝜋𝜋 𝑅𝑅 𝑡𝑡 5 2 𝜆𝜆 𝑜𝑜𝑜𝑜𝑡𝑡 3 𝐶𝐶 𝑝𝑝_𝑚𝑚𝑚𝑚𝑚𝑚 Ω 𝑡𝑡 2 = 𝐾𝐾 𝑜𝑜𝑝𝑝𝑡𝑡_𝑡𝑡 Ω 𝑡𝑡 2 (10)
Where:

𝐾𝐾 𝑜𝑜𝑝𝑝𝑡𝑡_𝑡𝑡 = 𝜌𝜌 𝜋𝜋 𝑅𝑅 𝑡𝑡 5 2 𝜆𝜆 𝑜𝑜𝑜𝑜𝑡𝑡 3 𝐶𝐶 𝑝𝑝_𝑚𝑚𝑚𝑚𝑚𝑚
Thus as it is illustrated in the figure (2), the maximum value of 𝐶𝐶 𝑝𝑝 can be found using a graphical method, which is 0.5 in this case. This value corresponds to β = 2 and λ = 9.15. This tip speed value is assigned as the optimum tip speed.

Based on this value, the optimum turbine speed curve at any given wind speed can be obtained. This curve is then used as a reference in the active power control.

The diagram block of the wind turbine model and its control are presented in Figure.

DFIG MODEL WITH STATOR FLUX ORIENTATION

The doubly Fed Induction Generator is classically modeled in the Park d-q frame, giving rise to the equations system [START_REF] Bedouda | Robust Control of Doubly Fed Induction Generator for Wind Turbine Under Sub-Synchronous Operation Mode[END_REF] [26]:

Wind speed (m/s) The active and reactive stator powers are given as follows:

� 𝑃𝑃 𝑠𝑠 = 𝑉𝑉 𝑠𝑠𝑑𝑑 𝐼𝐼 𝑠𝑠𝑑𝑑 + 𝑉𝑉 𝑠𝑠𝑠𝑠 𝐼𝐼 𝑠𝑠𝑠𝑠 𝑄𝑄 𝑠𝑠 = 𝑉𝑉 𝑠𝑠𝑠𝑠 𝐼𝐼 𝑠𝑠𝑑𝑑 -𝑉𝑉 𝑠𝑠𝑑𝑑 𝐼𝐼 𝑠𝑠𝑠𝑠 (12)
The rotor currents that provide independent control of the active power Ps and the reactive power Qs of the DFIG must be defined in the stator fluxoriented reference frame. Then the reference rotor currents are determined by the reference active and reactive power values.

For obvious reasons of simplification, the DFIG control is carried out in a frame dq related to the rotating field of the stator, in which the axis d is aligned, in this case, with the stator flux space vector, as shown in Figure [START_REF] Raju | Design and Implementation of Type-2 Fuzzy Logic Controller for DFIG-Based Wind Energy Systems in Distribution Networks[END_REF], and a stator flux aligned with the axis d has been adopted. In addition, the stator resistance can be neglected because this is a realistic assumption for generators used in wind power [6][27]. On the basis of these considerations, we obtain the system of equations:

⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ 𝑉𝑉 𝑠𝑠𝑑𝑑 = 0 𝑉𝑉 𝑠𝑠𝑠𝑠 =
The objective is to apply this control to control independently of the active and reactive powers generated by the doubly fed induction generator by orientation from fluxes.

The reactive power set point will be kept zero so as to keep a unit power factor on the stator side.

Adaptation of equation ( 12) to our simplifying assumptions gives:

� 𝑃𝑃 𝑠𝑠 = -𝑉𝑉 𝑠𝑠 𝐿𝐿 𝑚𝑚 𝐿𝐿 𝑠𝑠 𝐼𝐼 𝑟𝑟𝑠𝑠 𝑄𝑄 𝑠𝑠 = 𝑉𝑉 𝑠𝑠 𝑑𝑑 𝑠𝑠 𝐿𝐿 𝑠𝑠 - 𝑉𝑉 𝑠𝑠 𝐿𝐿 𝑚𝑚 𝐿𝐿 𝑠𝑠 𝐼𝐼 𝑟𝑟𝑑𝑑 (14)
The reactive power desired is

𝑄𝑄 𝑠𝑠_𝑟𝑟𝑒𝑒𝑟𝑟 = 0 (15)
Using these equations, we get the instruction:

� 𝐼𝐼 𝑟𝑟𝑠𝑠_𝑟𝑟𝑒𝑒𝑟𝑟 = - 𝐿𝐿 𝑆𝑆 𝑉𝑉 𝑠𝑠 𝐿𝐿 𝑚𝑚 𝑃𝑃 𝑠𝑠_𝑟𝑟𝑒𝑒𝑟𝑟 𝐼𝐼 𝑟𝑟𝑑𝑑_𝑟𝑟𝑒𝑒𝑟𝑟 = 𝑉𝑉 𝑠𝑠 𝜔𝜔 𝑠𝑠 𝐿𝐿 𝑚𝑚 (16)
From expressions [START_REF] Ruiz | Join and meet operations for type-2 fuzzy sets with nonconvex secondary memberships[END_REF], the relationship between the rotor currents and the voltages is obtained:

� 𝑑𝑑𝑑𝑑 𝑟𝑟𝑠𝑠 𝑑𝑑𝑡𝑡 = 1 𝐿𝐿 𝑟𝑟 𝜎𝜎 (𝑉𝑉 𝑟𝑟𝑑𝑑 -𝑅𝑅 𝑟𝑟 𝐼𝐼 𝑟𝑟𝑑𝑑 - 𝐿𝐿 𝑚𝑚 𝐿𝐿 𝑠𝑠 𝑑𝑑𝑑𝑑 𝑠𝑠 𝑑𝑑𝑡𝑡 + 𝜔𝜔 𝑟𝑟 𝐿𝐿 𝑟𝑟 𝜎𝜎𝐼𝐼 𝑟𝑟𝑠𝑠 ) 𝑑𝑑𝑑𝑑 𝑟𝑟𝑠𝑠 𝑑𝑑𝑡𝑡 = 1 𝐿𝐿 𝑟𝑟 𝜎𝜎 (𝑉𝑉 𝑟𝑟𝑠𝑠 -𝑅𝑅 𝑟𝑟 𝐼𝐼 𝑟𝑟𝑠𝑠 -𝜔𝜔 𝑟𝑟 𝐿𝐿 𝑟𝑟 𝜎𝜎 𝐼𝐼 𝑟𝑟𝑑𝑑 -𝜔𝜔 𝑟𝑟 𝐿𝐿 𝑚𝑚 𝐿𝐿 𝑠𝑠 𝜑𝜑 𝑠𝑠 ) (17)

MODEL OF GRID-SIDE CONVERTOR AND FILTER

The lateral grid-side converter (CSR) and the filter illustrated in Figure 1 can be modeled in the Park d-q frame by the following equations:

� 𝑉𝑉 𝑟𝑟𝑑𝑑 =
The active and reactive powers generated by the CSR are defined by:

� 𝑃𝑃 𝑟𝑟 = 𝑉𝑉 𝑟𝑟𝑑𝑑 𝐼𝐼 𝑟𝑟𝑑𝑑 + 𝑉𝑉 𝑟𝑟𝑠𝑠 𝐼𝐼 𝑟𝑟𝑠𝑠 𝑄𝑄 𝑟𝑟 = 𝑉𝑉 𝑟𝑟𝑠𝑠 𝐼𝐼 𝑟𝑟𝑑𝑑 -𝑉𝑉 𝑟𝑟𝑑𝑑 𝐼𝐼 𝑟𝑟𝑠𝑠 (20)

SLIDING MODE CONTROL WITH FUZZY LOGIC

SLIDING MODE CONTROL

The design of the sliding mode control is realized mainly in three complementary stages defined by [START_REF] Lei | Modeling of the wind turbine with a doubly fed induction generator for grid integration studies[END_REF] [30]:

Choice of sliding surfaces Slotine proposes [START_REF] Rouabhi | Power Quality Enhancement of Grid Connected Doubly-Fed Induction Generator Using Sliding Mode Control[END_REF] a surface of sliding which is a scalar function such that the controlled variable slips on the surface:

𝑠𝑠(𝑥𝑥) = � 𝑑𝑑 𝑑𝑑𝑡𝑡 + 𝜆𝜆� 𝑟𝑟-1 𝑒𝑒(𝑥𝑥) (21)
Where r is the relative degree of the system, λ is a positive constant and e(x) is the error between the variable and its reference. We will take r = 1 for the command of the power we get:

𝑠𝑠(𝑥𝑥) = 𝑒𝑒(𝑥𝑥) (22)
The active power will be directly proportional to the axis q rotor current and reactive power proportional to the rotor axis current d.

� 𝑠𝑠(𝑃𝑃) = 𝑒𝑒(𝑃𝑃) = 𝐼𝐼 𝑟𝑟𝑠𝑠_𝑟𝑟𝑒𝑒𝑟𝑟 -𝐼𝐼 𝑟𝑟𝑠𝑠 𝑠𝑠(𝑄𝑄) = 𝑒𝑒(𝑄𝑄) = 𝐼𝐼 𝑟𝑟𝑑𝑑_𝑟𝑟𝑒𝑒𝑟𝑟 -𝐼𝐼 𝑟𝑟𝑑𝑑 (23)
Then we will have: Conditions for convergence In order to force the chosen variables to converge to their reference values it needs that both surfaces of sliding are driven to zero.

� 𝑠𝑠(𝑃𝑃) = 0 𝑠𝑠(𝑄𝑄) = 0 ⇒ � 𝑠𝑠(𝑃𝑃) = 𝑑𝑑 𝑑𝑑𝑡𝑡 �𝐼𝐼 𝑟𝑟𝑠𝑠_ 𝑟𝑟𝑟𝑟𝑓𝑓 -𝐼𝐼 𝑟𝑟𝑠𝑠 � = 0 𝑠𝑠(𝑄𝑄) = 𝑑𝑑 𝑑𝑑𝑡𝑡 �𝐼𝐼 𝑟𝑟𝑑𝑑_𝑟𝑟𝑒𝑒𝑟𝑟 -𝐼𝐼 𝑟𝑟𝑑𝑑 � = 0 (25)

Control law design

Now consider the following command:

� 𝑠𝑠̇ (𝑃𝑃) = -𝑠𝑠𝑠𝑠𝑠𝑠(𝑠𝑠(𝑃𝑃)) 𝑠𝑠̇ (𝑄𝑄) = -𝑠𝑠𝑠𝑠𝑠𝑠�𝑠𝑠(𝑄𝑄)� (26)
Combining these equations with Equation ( 24 The algorithm of control is defined by the relation:

� 𝑉𝑉 𝑟𝑟𝑠𝑠 = 𝑉𝑉 𝑟𝑟𝑠𝑠_𝐸𝐸𝑠𝑠 + 𝑉𝑉 𝑟𝑟𝑠𝑠_𝑚𝑚𝑡𝑡𝑡𝑡𝑟𝑟 𝑉𝑉 𝑟𝑟𝑑𝑑 = 𝑉𝑉 𝑟𝑟𝑑𝑑_𝐸𝐸𝑠𝑠 + 𝑉𝑉 𝑟𝑟𝑑𝑑_𝑚𝑚𝑡𝑡𝑡𝑡𝑟𝑟 (29)
With

� 𝑉𝑉 𝑟𝑟𝑠𝑠-𝑚𝑚𝑡𝑡𝑡𝑡𝑟𝑟 = -𝑣𝑣 1 * 𝑠𝑠𝑠𝑠𝑠𝑠(𝑠𝑠(𝑝𝑝)) 𝑉𝑉 𝑟𝑟𝑑𝑑-𝑚𝑚𝑡𝑡𝑡𝑡𝑟𝑟 = -𝑣𝑣 2 * 𝑠𝑠𝑠𝑠𝑠𝑠(𝑠𝑠(𝑄𝑄)) (30)
Therefore, combining these equations with Equation (28), we obtain

� 𝑉𝑉 𝑟𝑟𝑠𝑠-𝑚𝑚𝑡𝑡𝑡𝑡𝑟𝑟 = 𝐿𝐿 𝑟𝑟 𝜎𝜎 𝑠𝑠𝑠𝑠𝑠𝑠(𝑒𝑒(𝑃𝑃)) 𝑉𝑉 𝑟𝑟𝑑𝑑-𝑚𝑚𝑡𝑡𝑡𝑡𝑟𝑟 = 𝐿𝐿 𝑟𝑟 𝜎𝜎 𝑠𝑠𝑠𝑠𝑠𝑠(𝑒𝑒(𝑄𝑄)) (31)
Finally, the global sliding control system is grouped in the figure 8.

FUZZY LOGIC CONTROL

Since Zadeh [START_REF] Merabet | Power-current controller based sliding mode control for DFIG-wind energy conversion system[END_REF] first introduced fuzzy set theory, Fuzzy logic control (FLC) has been successfully applied in various fields.

Basically, the use of fuzzy logic control for a system is based on rules that are based on the expertise and knowledge of the human being. Extension of ordinary fuzzy sets, namely type1 fuzzy sets (T1-FS) is type 2 fuzzy sets (T2-FS) [START_REF] Zadeh | Fuzzy sets[END_REF]. Fuzzy control is the examination, development, and experimentation of systems based on fuzzy rules. The first step in building a fuzzy controller is to define a knowledge base containing information on the linguistic variables and fuzzy subsets characterizing them, as well as the rules linking these variables, based on expert knowledge of the problem, to determine the output. These outputs are evaluated by the controller, based on the fuzzy inputs, resulting from the fuzzification process of the real inputs, and the fuzzy control rules. The intermediate outputs, resulting from the evaluation of fuzzy rules, remain fuzzy variables, which must be modified by the defuzzification process in order to obtain the control information not fuzzy for the final process [START_REF] Zadeh | The concept of a linguistic variable and its application to approximate reasoning-I[END_REF].

The five main elements of a type 2 fuzzy logic system (FLS), are grouped in Figure .9, as follows: Fuzzifier, rules base, Fuzzy inference engine, type reducer and Defuzzifier. -An inference engine that converts fuzzy controller inputs based on the knowledge base.

-A defuzzification interface that converts the fuzzy outputs to crisp outputs suitable to drive plants actuators.

-Fuzzy Controller design To eliminate the disadvantage of the sliding mode control which is the production of high frequency oscillation caused by its sat(S(x)) switching control, the latter has been replaced by a type-2 fuzzy controller as shown in the following figure: The first input of the fuzzy system is the current error, it is the difference between the reference value and the measured value of currents, and the second input is the error derivative of the latter. The surface of the controller is shown in Figure 12 The output of the fuzzy system is the variation of the attractive control. This output is represented by five language labels: high decrease (HD), Medium decrease (MD), low decrease (LD), Zero (Z), low increase (LI), Medium increase (MI) and high increase (HI). The MFs representing the output are shown in this table:

SIMULATION RESULTS

The mathematical model of the overall system has been simulated in Matlab-Simulink. The parameters of the wind turbine and the DFIG are given in appendix B. [6][17] In our simulation, the active power is sent to the electrical grid, while the stator reactive power setpoint will be maintained at zero (Qs= 0 VAR) to ensure a unit power factor on the stator.

To check the control laws proposed in this work and to check the decoupling between the active and reactive stator powers (Ps and Qs), we give different instructions with different moments for the power active stator, which are shown in the figure 10. In this test, an instruction was given for the active power to be injected into the electrical grid. There is a good follow-up of the instructions for the active power as well as for the reactive power of the stator which is maintained at zero by the real powers delivered by the DFIG. This technique made it possible to obtain a perfect decoupling enters the two components of the stator power.

CONCLUSION

This work, dedicated to the modeling, simulation and control of a wind energy conversion system by MPPT control for the extraction of the maximum power of the wind turbine, to independently control the active and reactive power we used the sliding mode control based on the fuzzy controller type-2. The modelling, development and analysis of control laws are presented. These controls are applied to regulate the active and reactive power of the dualpower generator to their reference values. According to the simulation results obtained, the proposed controller shows satisfactory dynamic performance, it gives a reduced response stabilization time for the DFIG quantities, it allows a fast response without exceeding and it performs a perfect control with regard to the monitoring of the power setpoints.

Figure 1 .

 1 Figure 1. Synoptic diagram of the wind system.

Figure 2 .

 2 Figure 2. Curves of coefficients of power of a 4kW pitch regulated wind turbine, for different pitch angles β.

Figure 3 .

 3 Figure 3. Wind turbine model

Figure 4 .

 4 Figure 4. Variations of the mechanical power available for a type of wind system given.

Figure 5 .

 5 Figure 5. Law of optimal ordering of a wind system at variable speed

6 .Figure 6 .

 66 Figure 6. Wind turbine model with Control

Figure 7 .

 7 Figure 7. Synchronous rotating dq reference frame aligned with the stator flux space vector

Figure 8 .

 8 Figure 8. Schematic diagram of the Sliding mode Control system.

Figure 10 .

 10 Figure 10. Fuzzy Sliding Mode control of the active and reactive power.

Figure 11 .

 11 Figure 11. Membership for inputs

Figure 12 .Figure 13 .Figure 14 .Figure 15 .Figure 16 .Figure 17 .Figure 18 .Figure 19 .

 1213141516171819 Figure 12. profile for the power active stator

  𝑤𝑤 𝑟𝑟 𝜑𝜑 𝑟𝑟𝑑𝑑 𝜑𝜑 𝑠𝑠𝑑𝑑 = 𝐿𝐿 𝑠𝑠 𝐼𝐼 𝑠𝑠𝑑𝑑 + 𝐿𝐿 𝑚𝑚 𝐼𝐼 𝑟𝑟𝑑𝑑 𝜑𝜑 𝑠𝑠𝑠𝑠 = 𝐿𝐿 𝑠𝑠 𝐼𝐼 𝑠𝑠𝑠𝑠 + 𝐿𝐿 𝑚𝑚 𝐼𝐼 𝑟𝑟𝑠𝑠 𝜑𝜑 𝑟𝑟𝑑𝑑 = 𝐿𝐿 𝑟𝑟 𝐼𝐼 𝑟𝑟𝑑𝑑 + 𝐿𝐿 𝑚𝑚 𝐼𝐼 𝑠𝑠𝑑𝑑 𝜑𝜑 𝑟𝑟𝑠𝑠 = 𝐿𝐿 𝑟𝑟 𝐼𝐼 𝑟𝑟𝑠𝑠 + 𝐿𝐿 𝑚𝑚 𝐼𝐼 𝑠𝑠𝑠𝑠

	⎧ 𝑉𝑉 𝑠𝑠𝑑𝑑 = 𝑅𝑅 𝑠𝑠 𝐼𝐼 𝑠𝑠𝑑𝑑 +	𝑑𝑑𝑑𝑑 𝑠𝑠𝑠𝑠 𝑑𝑑𝑡𝑡	-𝑤𝑤 𝑠𝑠 𝜑𝜑 𝑠𝑠𝑠𝑠
	⎨ ⎪ ⎪ ⎪ ⎪ 𝑉𝑉 𝑟𝑟𝑑𝑑 = 𝑅𝑅 𝑟𝑟 𝐼𝐼 𝑟𝑟𝑑𝑑 + 𝑉𝑉 𝑠𝑠𝑠𝑠 = 𝑅𝑅 𝑠𝑠 𝐼𝐼 𝑠𝑠𝑠𝑠 + ⎪ 𝑉𝑉 𝑟𝑟𝑠𝑠 = 𝑅𝑅 𝑟𝑟 𝐼𝐼 𝑟𝑟𝑠𝑠 +	𝑑𝑑𝑑𝑑 𝑠𝑠𝑠𝑠 𝑑𝑑𝑡𝑡 𝑑𝑑𝑑𝑑 𝑟𝑟𝑠𝑠 𝑑𝑑𝑡𝑡 𝑑𝑑𝑑𝑑 𝑟𝑟𝑠𝑠	+ 𝑤𝑤 𝑠𝑠 𝜑𝜑 𝑠𝑠𝑑𝑑 -𝑤𝑤 𝑟𝑟 𝜑𝜑 𝑟𝑟𝑠𝑠				(11)
	⎩ ⎪ ⎪ ⎪ ⎪ ⎪	𝑇𝑇 𝑒𝑒𝑚𝑚 = 𝑝𝑝	𝐿𝐿 𝑚𝑚 𝐿𝐿 𝑠𝑠	�𝐼𝐼 𝑟𝑟𝑑𝑑 𝜑𝜑 𝑠𝑠𝑠𝑠 -𝐼𝐼 𝑟𝑟𝑠𝑠 𝜑𝜑 𝑠𝑠𝑑𝑑 �
			5000
										Zone II	Pn
			4000							MPPT Control
		Mechanical Power (W)	1000 2000 3000		Zone I				Vmin	Vn	Vmax Pitch control Zonne III
			0
			1	2	3	4	5	6	7	8	9	10	11	12

𝑑𝑑𝑡𝑡

+

  𝑤𝑤 𝑠𝑠 𝜑𝜑 𝑠𝑠𝑑𝑑 𝑉𝑉 𝑟𝑟𝑑𝑑 = 𝑅𝑅 𝑟𝑟 𝐼𝐼 𝑟𝑟𝑑𝑑 +

				𝑑𝑑𝑑𝑑 𝑟𝑟𝑠𝑠 𝑑𝑑𝑡𝑡	-𝑤𝑤 𝑟𝑟 𝜑𝜑 𝑟𝑟𝑠𝑠
	𝑉𝑉 𝑟𝑟𝑠𝑠 = 𝑅𝑅 𝑟𝑟 𝐼𝐼 𝑟𝑟𝑠𝑠 +	𝑑𝑑𝑑𝑑 𝑟𝑟𝑠𝑠 𝑑𝑑𝑡𝑡	+ 𝑤𝑤 𝑟𝑟 𝜑𝜑 𝑟𝑟𝑑𝑑
	𝑇𝑇 𝑒𝑒𝑚𝑚 = -𝑝𝑝	𝐿𝐿 𝑚𝑚 𝐿𝐿 𝑠𝑠	𝐼𝐼 𝑟𝑟𝑠𝑠 𝜑𝜑 𝑠𝑠𝑑𝑑

  𝑅𝑅 𝑟𝑟 𝐼𝐼 𝑟𝑟𝑑𝑑 -𝐿𝐿 𝑟𝑟 𝑑𝑑𝑑𝑑 𝑓𝑓𝑠𝑠 𝑉𝑉 𝑔𝑔𝑑𝑑 , 𝑉𝑉 𝑔𝑔𝑠𝑠 represent the grid voltage, 𝐼𝐼 𝑟𝑟𝑑𝑑 , 𝐼𝐼 𝑟𝑟𝑠𝑠 represent the grid current, 𝐿𝐿 𝑟𝑟 represents the filter inductance and 𝑅𝑅 𝑟𝑟 represents the filter resistance. The voltage across the DC bus capacitor is obtained by integrating the current flowing through the capacitor.

	𝑑𝑑𝑉𝑉 𝑠𝑠𝑑𝑑 𝑑𝑑𝑡𝑡	=	1 𝐶𝐶	𝐼𝐼 𝑐𝑐

𝑑𝑑𝑡𝑡

+ 𝜔𝜔 𝑠𝑠 𝐿𝐿 𝑟𝑟 𝐼𝐼 𝑟𝑟𝑠𝑠 + 𝑉𝑉 𝑔𝑔𝑑𝑑 𝑉𝑉 𝑟𝑟𝑠𝑠 = 𝑅𝑅 𝑟𝑟 𝐼𝐼 𝑟𝑟𝑠𝑠 -𝐿𝐿 𝑟𝑟 𝑑𝑑𝑑𝑑 𝑓𝑓𝑠𝑠 𝑑𝑑𝑡𝑡 -𝜔𝜔 𝑠𝑠 𝐿𝐿 𝑟𝑟 𝐼𝐼 𝑟𝑟𝑑𝑑 + 𝑉𝑉 𝑔𝑔𝑠𝑠

[START_REF] Rahali | Adaptive Field-Oriented Control Using Supervisory Type-2 Fuzzy Control for Dual Star Induction Machine[END_REF]

Where,

  𝐿𝐿 𝑟𝑟 𝜎𝜎 �𝑉𝑉 𝑟𝑟𝑠𝑠 -𝑅𝑅 𝑟𝑟 𝐼𝐼 𝑟𝑟𝑠𝑠 -𝜔𝜔 𝑟𝑟 𝐿𝐿 𝑟𝑟 𝜎𝜎 𝐼𝐼 𝑟𝑟𝑑𝑑 -𝜔𝜔 𝑟𝑟

	� 𝑠𝑠̇ (𝑄𝑄) = 𝑠𝑠̇ (𝑃𝑃) = -𝑉𝑉 𝑠𝑠 𝑉𝑉 𝑠𝑠 𝐿𝐿 𝑚𝑚 𝐿𝐿 𝑆𝑆 𝜔𝜔 𝑠𝑠 𝐿𝐿 𝑚𝑚 -𝑃𝑃 ̇𝑠𝑠𝑟𝑟𝑟𝑟𝑓𝑓 -1 𝐿𝐿 𝑟𝑟 𝜎𝜎 �𝑉𝑉 𝑟𝑟𝑑𝑑 -𝑅𝑅 𝑟𝑟 𝐼𝐼 𝑟𝑟𝑑𝑑 -1	𝐿𝐿 𝑚𝑚 𝐿𝐿 𝑠𝑠	𝑑𝑑𝑡𝑡 𝑑𝑑𝑑𝑑 𝑠𝑠	+ 𝜔𝜔 𝑟𝑟 𝐿𝐿 𝑟𝑟 𝜎𝜎𝐼𝐼 𝑟𝑟𝑠𝑠 �	𝐿𝐿 𝑚𝑚 𝐿𝐿 𝑠𝑠	𝜑𝜑 𝑠𝑠 �	(24)

  𝐿𝐿 𝑟𝑟 𝜎𝜎 �𝑉𝑉 𝑟𝑟𝑠𝑠 -𝑅𝑅 𝑟𝑟 𝐼𝐼 𝑟𝑟𝑠𝑠 -𝜔𝜔 𝑟𝑟 𝐿𝐿 𝑟𝑟 𝜎𝜎 𝐼𝐼 𝑟𝑟𝑑𝑑 -𝜔𝜔 𝑟𝑟 𝑅𝑅 𝑟𝑟 𝐼𝐼 𝑟𝑟𝑠𝑠 + 𝜔𝜔 𝑟𝑟 𝐿𝐿 𝑟𝑟 𝜎𝜎 𝐼𝐼 𝑟𝑟𝑑𝑑 + 𝑠𝑠

						), we
	obtain
	� 𝐿𝐿 𝑟𝑟 𝜎𝜎 �𝑉𝑉 𝑟𝑟𝑑𝑑 -𝑅𝑅 𝑟𝑟 𝐼𝐼 𝑟𝑟𝑑𝑑 -𝐿𝐿 𝑆𝑆 𝑉𝑉 𝑠𝑠 𝐿𝐿 𝑚𝑚 𝑃𝑃 ̇𝑠𝑠𝑟𝑟𝑟𝑟𝑓𝑓 + 1 1	𝐿𝐿 𝑠𝑠 𝐿𝐿 𝑚𝑚	𝑑𝑑𝑑𝑑 𝑠𝑠	𝐿𝐿 𝑚𝑚 𝐿𝐿 𝑠𝑠	𝜑𝜑 𝑠𝑠 � = 𝑠𝑠𝑠𝑠𝑠𝑠(𝑠𝑠(𝑃𝑃))	(27)
	Using the above equations, the rotor voltages are
	obtained
	�	𝑉𝑉 𝑟𝑟𝑠𝑠 = 𝐿𝐿 𝑚𝑚 𝑉𝑉 𝑠𝑠 𝐿𝐿 𝑠𝑠

𝑑𝑑𝑡𝑡

+ 𝜔𝜔 𝑟𝑟 𝐿𝐿 𝑟𝑟 𝜎𝜎𝐼𝐼 𝑟𝑟𝑠𝑠 � = 𝑠𝑠𝑠𝑠𝑠𝑠�𝑠𝑠(𝑄𝑄)� + 𝜎𝜎𝐿𝐿 𝑟𝑟 𝐼𝐼 ̇𝑟𝑟𝑠𝑠_ 𝑟𝑟𝑟𝑟𝑓𝑓 + 𝐿𝐿 𝑟𝑟 𝜎𝜎 𝑠𝑠𝑠𝑠𝑠𝑠(𝑠𝑠(𝑃𝑃)) 𝑉𝑉 𝑟𝑟𝑑𝑑 = 𝑅𝑅 𝑟𝑟 𝐼𝐼 𝑟𝑟𝑑𝑑 -𝜔𝜔 𝑠𝑠 𝑠𝑠 𝐿𝐿 𝑟𝑟 𝜎𝜎 𝐼𝐼 𝑟𝑟𝑠𝑠 + 𝐿𝐿 𝑟𝑟 𝜎𝜎 𝑠𝑠𝑠𝑠𝑠𝑠�𝑠𝑠(𝑄𝑄)�

[START_REF] Bounar | Adaptive Fuzzy Control of Doubly-Fed Induction Machine[END_REF]

  � 𝑉𝑉 𝑟𝑟𝑠𝑠-𝐸𝐸𝑠𝑠 = 𝑅𝑅 𝑟𝑟 𝐼𝐼 𝑟𝑟𝑠𝑠 + 𝜔𝜔 𝑟𝑟 𝐿𝐿 𝑟𝑟 𝜎𝜎 𝐼𝐼 𝑟𝑟𝑑𝑑 + 𝑠𝑠 𝐿𝐿 𝑚𝑚 𝑉𝑉 𝑠𝑠 𝐿𝐿 𝑠𝑠 + 𝜎𝜎𝐿𝐿 𝑟𝑟 𝐼𝐼 ̇𝑟𝑟𝑠𝑠_ 𝑟𝑟𝑟𝑟𝑓𝑓 𝑉𝑉 𝑟𝑟𝑑𝑑-𝐸𝐸𝑠𝑠 = 𝑅𝑅 𝑟𝑟 𝐼𝐼 𝑟𝑟𝑑𝑑 -𝜔𝜔 𝑠𝑠 𝑠𝑠 𝐿𝐿 𝑟𝑟 𝜎𝜎 𝐼𝐼 𝑟𝑟𝑠𝑠

Table 1 .

 1 Membership

	E	NH	NM	NL	Z	PL	PM	PH
	ΔE
	NH	HD	HD	HD	HD	MD	LD	Z
	NM	HD	HD	HD	MD	LD	Z	LI
	NL	HD	MD	MD	LD	Z	LI	MI
	Z	HD	MD	LD	Z	LI	MI	HI
	PL	MD	LD	Z	LI	MI	HI	HI
	PM	LD	Z	LI	MI	HI	HI	HI
	PH	Z	LI	MI	HI	HI	HI	HI

for output

We have seven values of error (e) and seven values of change in error (de) then we will have 49 rules to cover all possible inputs. These are often simply written in a table as follows:

Table 2 .

 2 Rules table of the fuzzy controller

APPENDIX A

Nomenclature of the parameters for DFIG

V sd ,V sq ,V rd ,V rq

Stator and rotor voltage components in the d-q reference frame I sd , I


Yasmine Labrak

Béatrice Heurtault

Benoît Frisch

Patrick Saulnier

Elise Lepeltier

Veronique E Miron

Giulio G Muccioli
email: giulio.muccioli@uclouvain.be

Anne Des

Anne Des Rieux
email: anne.desrieux@uclouvain.be

Impact of anti-PDGFRα antibody surface functionalization on LNC uptake by oligodendrocyte progenitor cells

Keywords:

teaching and research institutions in France or abroad, or from public or private research centers.

Introduction

The myelin sheath, formed by oligodendrocytes in the central nervous system (CNS), is a crucial element in the transduction of electrical impulses along the axons and in neuron metabolic support. In demyelinating diseases, such as multiple sclerosis (MS), loss of the myelin sheath causes invalidating symptoms such as cognitive dysfunction, impaired locomotor function and disorders such as optical neuritis [START_REF] Dobson | Multiple sclerosisa review[END_REF]. In MS, demyelination results from a complex physiopathological process involving a targeted immune response towards the myelin sheath [START_REF] Franklin | Regenerating CNS myelin -From mechanisms to experimental medicines[END_REF]. Until now, the trigger of this autoimmune disease is still unknown, but the onset of MS is believed to be multifactorial (i.e. genetic, environmental, hypovitaminosis D, viral infections) [START_REF] Filippi | Multiple sclerosis[END_REF].

Endogenous repair of myelin sheaths occurs via the recruitment and differentiation of oligodendrocyte progenitor cells (OPC) into new myelinating oligodendrocytes [START_REF] Franklin | Regenerating CNS myelin -From mechanisms to experimental medicines[END_REF]. As a result, a new functional myelin sheath is rebuilt around axons, restoring efficient electrical impulse conduction. However, with time and MS progression, this mechanism becomes less efficient, mostly due to a limited oligodendrocyte repopulation and a thinner de novo myelin sheath [START_REF] Franklin | Regenerating CNS myelin -From mechanisms to experimental medicines[END_REF][START_REF] Dendrou | Immunopathology of multiple sclerosis[END_REF].

Most MS therapies focus on reducing peripheral inflammation and on lengthening remission time between relapses. However, no treatments stimulating remyelination are currently available [START_REF] Göttle | An unmet clinical need: roads to remyelination in MS[END_REF]. To reach this goal, one strategy is to enhance remyelination by promoting OPC differentiation into mature oligodendrocytes [START_REF] Lubetzki | Remyelination in multiple sclerosis: from basic science to clinical translation[END_REF]. For the last decades, researchers have been working to de-Abbreviations: Ab, anti-PDGFRα antibody; DBCO, Dibenzocyclooctyne; FACS, fluorescence associated cell sorting; IMT, 2-Iminothiolane•HCl; LNC, lipid nanocapsule; MFI, mean fluorescence intensity per cell; MS, multiple sclerosis; PDGFRα, platelet-derived growth factor receptor α; PDGFAA, platelet-derived growth factor A; OPC, oligodendrocytes progenitor cells cipher OPC differentiation pathways to find molecules that would enhance remyelination [START_REF] Lubetzki | Remyelination in multiple sclerosis: from basic science to clinical translation[END_REF]. A few drugs have been tested in preclinical or clinical settings in this context. For instance, retinoic acid and calcitriol have been studied in vitro for their differentiating potential of OPC. Bexarotene, a lipophilic retinoid X receptor gamma (RXRγ) agonist, showed some interesting results on remyelination in a recent clinical trial involving relapsing-remitting MS patients [START_REF] Brown | Safety and efficacy of bexarotene in patients with relapsingremitting multiple sclerosis (CCMR One): a randomised, double-blind, placebocontrolled, parallel-group, phase 2a study[END_REF]). However, the trial was interrupted due to two major off-target effects, hypothyroidism and hypertriglyceridemia.

Using targeted nanomedicines is one strategy to reduce side effects. In this context, lipid nanocapsules (LNC) are gaining interest. Indeed, LNC are very efficient in solubilizing lipophilic bioactive drugs, are biocompatible, can protect their cargo from degradation and facilitate their transport across membranes [START_REF] Roger | Lipid nanocapsules maintain full integrity after crossing a human intestinal epithelium model[END_REF]. Moreover, their surface can be modified to favor their interactions with a specific cell or tissue. For instance, LNC surface has been modified to target a specific cell type (Carradori et al., 2016a); [START_REF] Hirsjarvi | Tumour targeting of lipid nanocapsules grafted with cRGD peptides[END_REF][START_REF] Laine | Brain tumour targeting strategies via coated ferrociphenol lipid nanocapsules[END_REF][START_REF] Morille | Galactosylated DNA lipid nanocapsules for efficient hepatocyte targeting[END_REF], mainly by adsorption of a targeting peptide ( (Carradori et al., 2016a); [START_REF] Gazaille | Characterization of Biological Material Adsorption to the Surface of Nanoparticles without a Prior Separation Step: a Case Study of Glioblastoma-Targeting Peptide and Lipid Nanocapsules[END_REF][START_REF] Umerska | Understanding the adsorption of salmon calcitonin, antimicrobial peptide AP114 and polymyxin B onto lipid nanocapsules[END_REF]. As platelet-derived growth factor receptor α (PDGFRα) is specifically expressed at the at the surface of OPCs in the CNS [START_REF] Li | Expression of NG2 and platelet-derived growth factor receptor alpha in the developing neonatal rat brain[END_REF][START_REF] Zou | Distribution of lipid nanocapsules in different cochlear cell populations after round window membrane permeation[END_REF], we hypothesized that grafting an anti-PDGFRα antibody at LNC surface would favor the targeting of OPC.

Thus, here we compared three different approaches to graft an anti-PDGFRα at LNC surface (LNC-Ab). Two are based on thiol-maleimide chemistry but involved different approaches to link the maleimide at LNC surface (transacylation vs post-insertion), while the third one is based on copper less click-chemistry. Following an extensive characterization of the obtained LNC-Ab, we assessed their targeting ability, first using a custom-made ELISA assay and then in vitro, in rat OPC primary cultures.

Materials and methods

Materials

Labrafac® provided by Gattefosse SA (France) and Lipoïd® S100 by Lipoid Gmbh (Germany). Kolliphor HS15®, poly-d-Lysine hydrobromide (70000-150000 Da), fluorescamine, 2-Iminothiolane•HCl and propidium iodide were purchased from Sigma (United-States). 1,2-Distearoyl-sn-glycero-3-phosphorylethanolamine-PEG (2000) -Maleimide (DSPE-PEG-Maleimide) and NH 2 -PEG (5000) -Dibenzocyclooctyne (NH 2 -PEG-DBCO) were purchased from Nanocs (United-States). NH 2 -PEG (5000) -Maleimide was purchased from Creative PEGWorks (United-States). Anti-PDGFRα was purchased from BioLegend (United-States). Anti-rat-HRP, DMEM (41966-029), HEPES, Pen/Strept, DMEM 0.05% trypsin-EDTA (1x), Presto blue Cell Viability Reagent, DiD'solid, SiteClick™ Antibody Azido Modification Kit and Alexa-488-Phalloidine were purchased from Thermo Fisher Scientific (United-States). Plateletderived growth factor A (PDGFAA) and fibroblast growth factor 2 (FGF) were purchased from Peprotech (United Kingdom). rmPDGFRA/Fc chimera (soluble PDGFRα) has been purchased from R&Dsystems. Spectra-Por Float-a-lyzer G2 300 kDa dialysis membrane and Rotilabo® syringe sterile 0.22 μm filters were purchased from Carl Roth GmbH (Germany).

Preparation of anti-PDGFRα-lipid nanocapsules (LNC-Ab)

Preparation of the LNC

LNC were prepared following the protocol developed by Heurtault et al. [START_REF] Heurtault | A novel phase inversion-based process for the preparation of lipid nanocarriers[END_REF]. Briefly, 0.846 g of Solutol HS15, 0.075 g of Lipoïd®, 0.089 g of NaCl, 1.028 g of Labrafac® and 2.962 ml of water were mixed under magnetic stirring for 5 min at 50 °C. Next, three temperature cycles of heating/cooling were done between 60 °C and 90 °C, also under magnetic stirring. During the cooling of the last cycle, at 77 °C, 12.5 ml of cold water (4 °C) were added, under high-speed stirring. The resulting nanoparticle of 126 mg/ml were filtered with a 0.2 μm filter for sterilization and stored at 4 °C until use. LNC concentration was calculated by the total weight of Kolliphor HS 15, Lipoïd® and Labrafac® divided by the final volume the LNC formulation [START_REF] Xu | Size Effect on Lipid Nanocapsule-Mediated GLP-1 Secretion from Enteroendocrine L Cells[END_REF].

Fluorescent LNC, obtained by loading DiD into LNC (14,7 μg/ml of DID in LNC), were used for confocal and uptake experiments [START_REF] Bastiat | A new tool to ensure the fluorescent dye labeling stability of nanocarriers: a real challenge for fluorescence imaging[END_REF]. DiD was added before the heating/cooling cycles.

Preparation of LNC-PEG-Maleimide

To graft Ab on the surface of the LNC, two approaches based on the coupling between thiol and maleimide moieties were used. The first one consisted of the transacylation of PEG chains (Kolliphor) exposed at LNC surface using NH 2 -PEG-Maleimide (Approach 1), while the second one consisted of the post-insertion of DSPE-PEG-Maleimide in the PEG corona of the LNC (Approach 2) (Fig. 1A). For both approaches, the thiolated antibody was covalently coupled to the PEG by reaction with the maleimide moiety.

Transacylation of NH 2 -PEG-Maleimide (Approach 1): Transcylated LNC were made according to Messaoudi et al.'s protocol [START_REF] Messaoudi | Anti-epidermal growth factor receptor siRNA carried by chitosan-transacylated lipid nanocapsules increases sensitivity of glioblastoma cells to temozolomide[END_REF]. Briefly, 5 mg of NH 2 -PEG-Maleimide (1:100, molar ratio of Maleimide : Kolliphor HS®) with 2 ml of LNC and 100 μl of NaOH (10 M) were incubated under agitation for 15 min. Then 2 ml of glycine buffer (50 mM of glycine and 5 mM of HCl, pH = 2) were added. NH 2 reacted with the hydroxystearic acid moiety of the Kolliphor HS®, to form an amide bond linking the LNC to the NH 2 -PEG-Maleimide. After NH 2 -PEG-Maleimide covalent grafting at the surface of the LNC, the formulation was dialyzed for 48 h (cut-off 300 kDa) against water to remove the unbound PEG-maleimide.

Post-insertion of DSPE-PEG-Maleimide (Approach 2): Post-inserted LNC were made according to Perrier et al. protocol (Perrier et al. 2010). Briefly, DSPE-PEG-Maleimide (1:100 M Ratio of PEG-Maleimide: Kolliphor HS®) dissolved in PBS was incubated for 1 h at 60 °C under agitation. Afterward, 300 μl of this solution were added to 400 μl of LNC prepared as described in section 2.2.1. The resulting mixture underwent seven cycles of 15 min incubation at 60 °C under stirring followed by 15 min of incubation on ice.

Preparation of LNC-PEG-DBCO

NH 2 -PEG-DBCO was covalently grafted to the surface of the LNC by transacylation as described in section 2.2.2 (Approach 3) (Fig. 2). Five mg or 10 mg of NH 2 -PEG-DBCO (1:100 or 1:50 M ratio of PEG-DBCO : Kolliphor HS® ) with 2 ml of LNC and 100 μl of NaOH (10 M) were incubated under agitation for 15 min. Then, LNC-PEG-DBCO were separated from unreacted components as described in 2.2.2. 1 and2). The primary amines on the anti-PDGFRα (Ab) were thiolated with 2iminothiolane•HCl (IMT) in PBS (Fig. 1). A mixture of Ab and IMT was made using a molar ratio Ab:IMT of 10:1, with a concentration of IMT of 13.7 μg/ml. Ab and IMT were kept under agitation for 1 h during which the solution was vortexed every 15 min [START_REF] Behzadi | Cellular uptake of nanoparticles: journey inside the cell[END_REF]. Then, 200 μl of LNC were mixed with 100 μl of the Ab : IMT solution and incubated under agitation for 2 h (vortexed every 30 min). To block the remaining free maleimide at the LNC surface, cysteine•HCl was added to the suspension and was further incubated for 30 min. The resulting suspension was dialyzed for 48 h (cut-off 300 kDa) to remove unbound Ab.

Grafting of anti-PDGFRα on LNC 2.2.4.1. For LNC-PEG-Maleimide (Approach

For LNC-PEG-DBCO (Approach 3) According to supplier instructions, Ab and anti-IgG2a were azidomodified using the Thermofisher® Site-Click kit (Fig. 2). Briefly, a βgalactosidase enzyme was used to remove the terminal galactose residues of the carbohydrate chains localized on the Fc region of the an- tibody. Those terminal residues were replaced by an azide-containing sugar (GalNAz) using a β-1,4-galactosyltransferase. Then 200 μl of LNC were incubated overnight with 100 µl of a solution containing 280 μg/ ml of azido modified antibody diluted in PBS. According to the manufacturer, the average number of DBCO moieties per antibody was 3 to3.5. The resulting suspension was dialyzed for 48 h (cut-off 300 kDa) to remove unbound Ab.

Characterization of LNC-Ab

Size, polydispersity index and zeta potential of LNC-Ab were measured in milliQ water using a ZetasizerUltra® (Malvern, United Kingdom).

To determine the antibody grafting yield, following removal by dialysis of the unbound Ab from the LNC preparation (see above), primary amines of the Ab were quantified with a fluorescamine assay (Schelte et al. 2000;[START_REF] Udenfriend | Fluorescamine: A reagent for assay of amino acids, peptides, proteins, and primary amines in the picomole range[END_REF]. Briefly, 50 μl of LNC-Ab were mixed with 50 μl of HCl 12 M and incubated for 12 h at 120 °C to hydrolyze the peptidic bonds. After heating, 100 μl of NaOH 6 M were added to the mixture. Five hundred μl of a fluorescamine solution (30 mg/100 ml of dioxane), 1,5 ml of borate buffer (pH = 9, 45 mM of boric acid and 76 mM of borate) and 40 μl of sample were mixed in a quartz cuvette extemporaneously and resulting fluorescence was read at λex = 400 nm and λem = 480 nm (Spectramax® reader, Molecular Device®, United Kingdom). The calibration curve was produced using increasing amounts of Ab (2.25 to 27.5 µg/ml) in the presence of LNC as a matrix. A representative calibration curve can be found in the supplementary data (Fig. 1.S). The detection limit and the quantification limit of the method are 2.83 µg/ml and 9.83 µg/ml, respectively. The intraday day precision was 8.2% and 5.4%, and the interday precision was 6.8% and 4.5 %, when using 13.7 µg/ml and 27,5 µg/ml, respectively. The calculated accuracy is of 8.7%, and 3.5 % for 13.7 µg/ ml and 27,5 µg/ml, respectively.

To determine the amount of antibody, present in the LNC-Ab, the samples were prepared similarly to the calibration curve, where an increasing quantity of sample was reacted with fluorescamine, resulting in a sample curve that follows the equation . Grafting efficiency was then calculated with the following equation:

To obtain an estimation of the number of antibodies per LNC, the quantity of antibody was divided by the number of LNC in the sample (Table 1.S; measured by nanoparticle tracking analysis (NTA) (Ze-taview®, Particle Metrix®, Germany)) using the following equations: Na: Avogadro number = 6.022 × 10 23 mol -1 Molecular weight of Ab = 150000 g.mol -1

C O R R E C T E D P R O O F

Impact of the grafting on the interaction of anti-PDGFRα with its target

The impact of the grafting on Ab ability to interact with its target has been assessed by an ELISA optimized in our lab. A 96-well plate was coated with 100 μl of soluble PDGFRα (rmPDGFRα) diluted at different concentrations (from 0.3 to 20 nM) in PBS and incubated overnight at 4 °C. Then, the plate was washed 3 times and blocked with 300 μl of a 1% BSA solution in PBS during 1 h. Then, LNC-Ab and all other conditions were diluted in a 0,1% BSA solution at 1 nM of Ab. Following 4 h of incubation at room temperature and 3 washes, 100 µl of anti-rat-HRP antibody (1:2000 dilution) were added to the wells and incubated for 1 h at RT. TMB (3,3′,5, 5′-tetramethylbenzidine) was used as HRP substrate, and the optical density was read at 450 nm.

The Ab /rmPDGFRα association was appreciated by calculating the percentage of Ab response rate using the following equation:

where a response rate of 100% would correspond to a similar recognition of the rmPDGFRα by the modified Ab and the commercial Ab.

To evaluate PEG chain impact on Ab activity, the Ab was pegylated according to the protocols used for Approach 1 and 3.

Pegylation of Ab with NH 2 -PEG-Maleimide

The primary amines on the anti-PDGFRα (Ab) were thiolated with 2-Iminothiolane•HCl (IMT) in PBS (Fig. 1). A mixture of Ab and IMT was made using a molar ratio Ab:IMT of 10:1, with a concentration of IMT of 13.7 μg/ml. Ab and IMT were incubated under agitation for 1 h during which the solution was vortexed every 15 min [START_REF] Behzadi | Cellular uptake of nanoparticles: journey inside the cell[END_REF]. Then, 200 μl of a NH 2 -PEG-Maleimide solution (1.25 mg/ml in MilliQ water) were mixed with 100 μl of the Ab: IMT solution and incubated under agitation for 2 h (vortexed every 30 min).

Pegylation of Ab with NH 2 -PEG-DBCO

According to supplier instructions, Ab and anti-IgG2a were azidomodified using the Thermofisher® Site-Click kit (Fig. 2). Briefly, a βgalactosidase enzyme was used to remove the terminal galactose residues of the carbohydrate chains localized on the Fc region of the antibody. Those terminal residues were replaced by an azide-containing sugar (GalNAz) using a β-1,4-galactosyltransferase. Then 200 μl of a NH 2 -PEG-DBCO solution (1,25 mg/ml in MilliQ water) was incubated with 100 µl of a solution containing 280 μg/ml of azido modified antibody diluted in PBS.

C O R R E C T E D P R O O F Y. Labrak et al.
International Journal of Pharmaceutics xxx (xxxx) 121623

OPC primary culture

Cortical mixed glial cultures were generated from Sprague-Dawley rat pups (postnatal day 0-2), according to Directive 2010/63/EU, to guidelines of the Belgian Government following the approval by the ethical committee for animal care of the faculty of medicine of UCLouvain (2017/UCL/MD/030), as described previously by Miron et al [START_REF] Miron | M2 microglia and macrophages drive oligodendrocyte differentiation during CNS remyelination[END_REF]. Briefly, brains were dissected and the cerebellum, olfactory bulbs, and meninges were removed. Brains were then digested using papain (40 μg/ml) and platted in T75 flasks, for 10 days, in DMEM containing 4.5 g l -1 glucose, L-glutamine, pyruvate, 10% fetal calf serum (vol/vol) and 1% penicillin/streptomycin (vol/vol). To remove microglia, flasks were shaken on a rotary shaker at 230 rpm (1 h, 37 °C). After addition of 10 ml of fresh media, OPC were retrieved after further agitation (16 h on a rotary shaker at 37 °C at 220 rpm). OPC were then pelleted (250xg for 5 min) and plated at 1 × 10 4 cells/well in poly-d-Lysine coated (4µg/ml) 96 well plates Tc treated (BD Falcon) or 12 well plates. The medium consisted in DMEM containing 4.5 g/L glucose, L-glutamine, pyruvate, SATO (16 μg/ml putrescine, 400 ng/ml L-thyroxine, 400 ng/ml tri-iodothyroxine, 60 ng/ml progesterone, 5 ng/ml sodium selenite, 100 μg/ml bovine serum albumin fraction V, 10 μg/ml insulin, 5.5 μg/ml halo-transferrin (all from Sigma-Aldrich)), 0.5% fetal calf serum 1% penicillin/streptomycin, 10 ng/ml PDGFAA, and 10 ng/ml FGF. For experiments with depleted PDGFAA media, PDGFAA was removed 18 h prior to LNC treatment.

LNC cytotoxicity on OPC

LNC were diluted at different concentrations (0.63 mg/ml to 0.15 mg/ml) in OPC medium and were incubated for 1 h, 4 h and 24 h with OPC 2 days post-seeding. The media was then removed and replaced with fresh OPC medium containing 10% of PrestoBlue® Cell Viability Reagent. After 18 h of incubation, the fluorescence was read at λex = 530 nm and λem = 580 nm. Untreated OPC were used as positive control (100 % viability).

LNC-Ab association with OPC

Confocal microscopy

Cells were seeded in 96 well plates and were treated 2 days after seeding with LNC (DiD)-Ab for 30 min, at the concentration of 0.42 mg/ml. Then, they were washed once before fixation (15 min, PFA 4%). After fixation, cells were washed 3 times with PBS, blocked and permeabilized using PBS containing 5% normal goat serum and 100 µg/ml digitonin. Cells were then washed gently 3 times with PBS and were incubated 30 min with Phalloidine-488 (1:100) diluted in PBS 1% Normal goat serum for 30 min. Cells were then washed 3 times and kept in PBS. Images were taken using a Cell Observer Spinning Disk Confocal microscope (ZEISS) and a 40x oil objective.

Fluorescence associated cell sorting (FACS)

Cells were seeded and treated in 12-well plates, with either LNC (DiD)-Ab or LNC (DiD)-IgG2a isotype or LNC (DiD). The nanoparticles were diluted at a concentration of 0.15 mg/ml in complete DMEM media and incubated with OPC for 30 min. After incubation, the media was removed, and cells were rinsed with Dulbecco's phosphate-buffered saline. To detach the cells, 500 μl of DMEM 0,05% trypsin-EDTA were added into each well and incubated at 37 °C for 8 min. Cells were then pelleted (300xg for 5 min) and washed in FACS buffer (0.1% BSA and 1 mM EDTA in PBS). Dead cells were excluded from the analysis based on Propidium iodide staining. To differentiate DiD + cells from DiD - ones, cells that were not incubated with LNC were used as control. Samples were analyzed with a BD FACSverse™. Flow cytometry data were treated with the Flowjo® software.

Statistical analysis

T-tests, one-way ANOVA and two-way ANOVA were performed using PRISM version 9 (GraphPad Software, United-States) to determine statistical significance. Results were considered significant if p < 0.05. N indicates the number of independent experiments and n the number of replicates. Detailed information about the number of replicates and the statistical test applied can be found in figure captions.

Results

Characterization of LNC-Ab obtained with the maleimide coupling strategy

LNCs had a size of 58 nm, a PDI of 0.04 and a zeta potential of -3 mV (Fig. 3). The addition of maleimide moieties on LNCs surface with approach 1 significantly increased their size (+9 nm) and decreased their zeta potential (from -3 to -24 mV). The second approach increased LNC size (+13 nm), although it did not significantly impact the zeta potential (-3 to -8 mV). The PDI was < 0.2 for all these formulations. Grafting the Ab on LNC-Maleimide had no impact on their size and PDI, while it impacted LNC zeta potential for approach 2 (-8 mV vs -24 mV).

Impact of PEG-Maleimide insertion method on Ab grafting efficiency

The average number of Ab grafted at LNC surface was quantified using a primary amine quantification assay developed by Schelté et al. (Schelte et al. 2000). Approach 1 resulted in a higher number of antibodies at the nanoparticle's surface, with an estimate of 49 Ab per LNC, than approach 2 where an average of 7 Ab per LNC was detected (Table 1). Since approach 1 provided the highest grafting efficiency, it was selected for the next step.

Impact of grafting on the interaction between anti-PDGFRα and PDGFRα

As grafting could modify Ab interaction with its receptor, the objective of this part was to evaluate if LNC-Ab had the same degree of interaction with its receptor than the unmodified Ab. We also evaluated if LNC would interfere with the ELISA signal by using the same concentration of Ab diluted in LNC (Ab + LNC) but there was no significant change on the biding curve, meaning that LNC did not interfere with the assay (Fig. 4).

While mixing LNC with Ab and Ab thiolation (Ab-SH) did not impact their interaction with the rmPDGFRα, covalently grafting the Ab on LNC surface (with approach 1) impaired its ability to recognize its antigen (Fig. 4). We also wanted to assessthe impact of PEGylation on Ab. It appeared that the addition of PEG-Maleimide on the Ab (Ab-PEG-Maleimide) prevented its interaction with its target.

We reasoned that if the unspecific multi-pegylation of the Ab was responsible for the loss of response of the Ab-PEG-Maleimide, then decreasing the number of thiols on the Ab could overcome its inactivation. The hypothesis was that if less PEG-Maleimide chains were grafted on the Ab, its activity might be less affected. Thus, different concentrations of IMT were used for the Ab thiolation but the interaction between the modified Ab and its target remained poor, regardless of the concentration of IMT used (supplementary data Fig. 2

.S).

While these approaches are primarily used and reported in the literature for other types of nanoparticles [START_REF] Altieri | Influence of Ellagitannins Extracted by Pomegranate Fruit on Disulfide Isomerase PDIA3 Activity[END_REF][START_REF] Khayrani | Targeting Ovarian Cancer Cells Overexpressing CD44 with Immunoliposomes Encapsulating Glycosylated Paclitaxel[END_REF][START_REF] Oh | Preparation of stable maleimide-functionalized au nanoparticles and their use in counting surface ligands[END_REF], our data showed that they were poorly efficient as far as Ab grafting on LNC surface was concerned. An alternative strategy was thus used to graft the Ab at LNC surface using click chemistry.

Impact of the click chemistry method on Ab activity

A third strategy, based on click chemistry, was explored as an alternative to the maleimide-thiol coupling (approach 3) [START_REF] Van Geel | Chemoenzymatic Conjugation of Toxic Payloads to the Globally Conserved N-Glycan of Native mAbs Provides Homogeneous and Highly Efficacious Antibody-Drug Conjugates[END_REF].

The grafting of a PEG-DBCO polymer at LNC surface increased LNC size and decreased its zeta potential, similarly to what was observed following the addition of the maleimide conjugate with Approach 1 (Table 2). Adding the azido-modified Ab did not modify LNC size, but significantly (p < 0,05) increased LNC zeta potential from -28 mV to -19 mV.

When using a 1:100 M ratio of PEG-DBCO: Kolliphor HS®, no Ab was detected using primary amine quantification. As it is selective, click-chemistry offers less linkage sites. Thus, to compensate the lower amount of linking sites, the ratio of PEG-DBCO: Kolliphor HS® was increased to 1:50. Using this molar ratio, an average of 5 ± 3 Ab per LNC was obtained (23 ± 7 % of grafting efficiency).

Ab azido-modification (Ab-N 3 ) and PEGylation using PEG-DBCO (Ab-PEG-DBCO) did not affect Ab interaction with the PDGFRα (Fig. 5A). When the Ab was grafted on LNC surface,using approach 3, the Ab was still able to recognize its target, albeit to a lesser extent than the un- modified Ab (Fig. 5B). This grafting strategy was consequently used for the following experiments.

Impact of Ab grafting at LNC surface on LNC interactions with OPC

This part of the study aimed to characterize the interactions between LNC-Ab obtained with Approach 3 and OPC in vitro.

First, LNC impact on OPC viability was evaluated. The highest nontoxic concentration was 0.31 mg/ml of LNC for 1 and 4 h of incubation (Fig. 6). However, LNC were toxic (no metabolic activity) for OPC after 24 h of incubation whatever the concentration (data not shown).

Then, DiD-loaded LNC-Ab, in conjunction with confocal microscopy and FACS, were used to assess whether LNC-Ab were able to interact with OPC. As illustrated by Fig. 7, LNC (DiD)-Ab were mainly visible in the cytoplasm of OPC, supporting their ability to enter these cells. Additional pictures of OPC treated with LNC (DiD)-Ab and negative control (untreated OPC) can be found in supplementary data (Fig. 3.S). FACS was then used to quantify the amount of LNC associated with OPC and whether the Ab at LNC surface would increase LNC/OPC association compared to unmodified LNC. As shown in Fig. 8, grafting of the PDGFRα Ab at LNC surface allowed to increase by 1.5-fold their association with OPC.Fig. 9.

As modifying the surface of a nanomedicine can strongly influence its interaction with cells [START_REF] Yu | Size-and charge-dependent non-specific uptake of PEGylated nanoparticles by macrophages[END_REF][START_REF] Lorenz | Uptake of functionalized, fluorescent-labeled polymeric particles in different cell lines and stem cells[END_REF], this part aimed to determine whether the increased interaction of LNC-Ab with OPC was specific of the anti-PDGFRα or was linked to LNC surface modification due to an antibody grafting. Thus, OPC association with LNC-Ab was compared with LNC grafted with an isotype control (LNC-IgG2a). It appeared that grafting the isotype control had the same effect than grafting the anti-PDGFRα (Fig. 8). Finally, to determine if LNC-Ab interactions with OPC could be affected by the presence of PDGFAA in the culture medium (PDGFRα endogenous ligand), the same experiment was repeated but without PDGFAA (i.e. the ligand of the receptor targeted by the Ab). However, the results were the same as the ones obtained in the presence of PDGFAA (Fig. 9).

Discussion

Nowadays, the only treatments available for multiple sclerosis are immunomodulatory therapies with mostly a peripheral action. Although they limit the burden of the symptoms, none of them stimulate the remyelination process (McGinley, Goldschmidt, and Rae-Grant 2021). This is why, for the last decades, researchers have developed strategies to promote remyelination, notably by inducing OPC differentiation into myelinating oligodendrocytes. Nevertheless, these therapies need to be efficiently delivered to OPC to be effective, and this aspect remains challenging. Hence, our goal was to improve the efficiency of pro-remyelinating therapies by improving their delivery and selectivity towards OPC. To do so, we selected lipid-based nanocarriers and we grafted an anti-PDGFRα at their surface to specifically target OPC. In the present work, for the first time, we successfully grafted an anti-PDGFRα at LNC surface, comparing two strategies: thiol-maleimide interaction and copper less click-chemistry. We were also able to quantify Ab at LNC surface, and for the first time, to demonstrate that modification of LNC surface by an antibody affected their uptake by OPC.

The thiol-maleimide chemistry is a classic technique widely used to modify nanoparticle surface (Martinez-Jothar et al. 2018). To attach the maleimide moiety, we used two approaches already described in the literature, transacylation (approach 1) and post-insertion (approach 2). The transacylation of NH 2 -PEG-Maleimide has never been used to graft an antibody at LNC surface. However, transacylation itself has been used to functionalize LNC surface with chitosan by Messaouidi et al. [START_REF] Messaoudi | Anti-epidermal growth factor receptor siRNA carried by chitosan-transacylated lipid nanocapsules increases sensitivity of glioblastoma cells to temozolomide[END_REF]. We observed an increase of LNC size and a decrease of zeta potential after post-insertion of DSPE-PEG-Maleimide. Perrier et al. reported similar observations [START_REF] Perrier | Post-insertion into Lipid NanoCapsules (LNCs): From experimental aspects to mechanisms[END_REF] after the post-insertion of DPSE-PEG-OCH 3 . However, in the work of Béduneau et al., after post-insertion of DPSE-PEG-Maleimide, the size of LNC increased to a lesser extent in our case (+24 nm vs. + 7 nm in our study) [START_REF] Béduneau | Design of targeted lipid nanocapsules by conjugation of whole antibodies and antibody Fab' fragments[END_REF]). This might be explained by the smaller amount of maleimide moiety used in our work (50-fold lower).

To compare the different approaches regarding grafting efficiency, a reliable method to quantify the Ab at LNC surface was essential. Unfortunately, LNC interacted with most of the classical used methods for proteic ligand quantification or detection at a nanoparticle surface (i.e., Bradford, RMN, SDS PAGE…) [START_REF] Jahan | Investigation and optimization of formulation parameters on preparation of targeted anti-CD205 tailored PLGA nanoparticles[END_REF][START_REF] Kirpotin | Building and characterizing antibody-targeted lipidic nanotherapeutics[END_REF][START_REF] Perera | Using NMR Spectroscopy To Measure Protein Binding Capacity on Gold Nanoparticles[END_REF], inducing a strong background signal (data not shown). Only the method developed by Schelte et al., based on primary amine quantification, allowed the direct quantification of the Ab at LNC surface without interferences (Schelte et al. 2000). To our knowledge, this is the first time that this methodology has been used to quantify an antibody at LNC surface and represent a real asset for surface modification characterization of LNC with a proteic moiety. We ob- served that transacylation provided the highest grafting efficiency compared to post-insertion. As transacylation linked the maleimide moiety covalently to LNC surface when post-insertion only incorporated it in the LNC shell, we hypothesized that either more maleimide moieties were attached to LNC, as the whole LNC surface was accessible, or/and that the association was more stable in case of transacylation. To our knowledge, no other work has been published concerning the grafting of an antibody on LNC surface using the transacylation of NH 2 -PEG-Maleimide, and no other study directly compared post-insertion and transacylation. Béduneau et al. successfully grafted an antibody at the surface of LNC using post-insertion and calculated that +/-67 antibod-ies were incorporated in LNC, but they used an indirect quantification [START_REF] Béduneau | Design of targeted lipid nanocapsules by conjugation of whole antibodies and antibody Fab' fragments[END_REF]). Chemical modification of antibodies occurring during grafting can hinder their ability to associate with their antigen. We found that thiolation of antibody's lysines with IMT did not decrease Ab response level. However, the subsequent PEGylation of the thiol residues resulted in the loss of Ab activity. Our results suggest that PEGylation very likely occurred at the Fv region of Ab upon thiolation by IMT of the lysines of the Fv region. Hence, the pegylation of the Ab most likely hindered its interaction with PDGFRα resulting in a loss of Ab activity. This could explain why LNC-Ab obtained using approaches 1 were not able to interact with PDGFRα. Of note, Béduneau et al. also demonstrated that a thiolated OX26 antibody could still interact with its target, but no investigation was made after grafting of the antibody on the nanoparticle [START_REF] Béduneau | Design of targeted lipid nanocapsules by conjugation of whole antibodies and antibody Fab' fragments[END_REF]). Kitamura et al. reported that the unspecific coupling of PEG via active ester on an antibody led to a decrease of 90% of the antibody activity [START_REF] Kitamura | Polyethylene glycol modification of the monoclonal antibody A7 enhances its tumor localization[END_REF]). The decrease was linked to the number of PEG on the antibody and their molecular weight, reinforcing the hypothesis of a steric hindrance [START_REF] Kitamura | Polyethylene glycol modification of the monoclonal antibody A7 enhances its tumor localization[END_REF][START_REF] Chapman | PEGylated antibodies and antibody fragments for improved therapy: a review[END_REF]. This is why we finally used a more specific approach involving click-chemistry. While fewer Ab were grafted per LNC, nor its azido modification nor its PEGylation affected the Ab association with PDGFRα. Gai et al. modified an anti-CD11 Ab using the same strategy and observed no impact of the azido modification on the anti-CD11 functional integrity compared to the native antibody [START_REF] Gai | A bio-orthogonal functionalization strategy for site-specific coupling of antibodies on vesicle surfaces after self-assembly[END_REF]. Taken together, our data and those reported by others put forth a site-specific modification strategy for Ab grafting. Nonetheless, we found that once on LNC surface the Ab response level decreased of 40%. We hypothesized that this could be due to a steric hindrance created by the LNC, mainly via the PEG moieties at its surface, as they could prevent the Ab from reaching its target. Interestingly, Botosa et al. observed a similar phenomenon with PEGylated liposomes. They demonstrated, using surface plasmon resonance, that antibody-functionalized liposomes could interact with their antigen, whereas PEGylated antibody functionalized liposomes had a decreased interaction with the antigen. They showed that it was related to PEGylated lipid fraction and PEG molecular weight (Botosoa et al. 2011).

The association of LNC-Ab with primary OPC cultures was higher than LNC but the extent of this increase was more modest than we hoped for. As OPC uptook LNC quite quickly (87% of the cells were DiD positive after 30 min of incubation only) the advantage conferred by the Ab was more difficult to highlight. While the uptake of the lipidbased nanoparticles by OPC is not extensively studied, Osorio-Querejeta et al. found that primary OPC endocytosed liposomes to a greater extent than PLGA nanoparticles and exosomes (96%, 83 %, and 61%, respectively) [START_REF] Osorio-Querejeta | MiR-219a-5p Enriched Extracellular Vesicles Induce OPC Differentiation and EAE Improvement More Efficiently Than Liposomes and Polymeric Nanoparticles[END_REF]. This tropism for lipid-based nanoparticles is likely due to the involvement of several unspecific endocytosis pathways, as reported for other types of cells. For instance, it has been shown that vectorized LNC with the NFL-TBS.40-63 peptide use clathrin-, caveolin-, and micropinocytosismediated pathways to enter oligodendrocytes [START_REF] Fressinaud | Lipid Nanoparticles Vectorized with NFL-TBS.40-63 Peptide Target Oligodendrocytes and Promote Neurotrophin-3 Effects After Demyelination In Vitro[END_REF], whereas for monocytes they use mostly caveolae-mediated endocytosis and pinocytosis [START_REF] Pinton | Targeting of immunosuppressive myeloid cells from glioblastoma patients by modulation of size and surface charge of lipid nanocapsules[END_REF].

For the targeting to be efficient, LNC need to enter OPC primarily by specific receptor-mediated endocytosis rather than by unspecific pathways such as those mentioned above. The antibody addition only induced a slight increase in uptake. Probably because the uptake occurring through receptor-mediated endocytosis is negligible compared to the other pathways. It can be speculated that a nanoparticle with a lower tropism for OPC would have been more suitable to target OPC, as receptor-mediated endocytosis would have been the most significant route to penetrate the cell. As many studies have demonstrated that different types of nanoparticles have different uptake rates for the same cell line [START_REF] Behzadi | Cellular uptake of nanoparticles: journey inside the cell[END_REF], this strategy could be considered for future experiments.

Lastly, we observed that grafting an isotype control produced the same increase in LNC -OPC association as grafting the anti-PDGFRα antibody. While this critical control is lacking in many papers, Walters et al. showed that the grafting of an isotype control on PLGA nanoparticle surface increased their cell association compared to the unmodified nanoparticle [START_REF] Walters | Assessment of the enhancement of PLGA nanoparticle uptake by dendritic cells through the addition of natural receptor ligands and monoclonal antibody[END_REF]. We can hypothesize that this could be due to the interaction of the Fc region with the immunoglobulin Fc receptors (FcR). These receptors are traditionally at the surface of immune cells, such as macrophages and monocytes, but are also present at OPC surface (especially the γ subunit) [START_REF] Nakahara | Signaling via immunoglobulin Fc receptors induces oligodendrocyte precursor cell differentiation[END_REF]. Hence, having an antibody at LNC surface may have unlocked receptormediated endocytosis via the FcR. The question remains on whether increasing the anti-PDGFRα at LNC surface is required to reach a threshold allowing to differentiate between Ab and control isotype as suggested by some studies [START_REF] Bruckner | The conjugation strategy affects antibody orientation and targeting properties of nanocarriers[END_REF].

Conclusion

In summary, we produced anti-PDGFRα functionalized LNC to target OPC to favor remyelination and reduce off-target effects by targeting OPC. To graft the antibody, we used three different approaches (transacylation, post-insertion of maleimide moiety and finally coperless click-chemistry). To evaluate the anti-PDGFRα grafting efficiency on LNC, we used primary amine quantification. This method can be considered as a real asset to quantify the amount of functionalized protein moiety on LNC since these nanoparticles interfere with classical protein quantification techniques. We also developed an in-house ELISA to gauge the anti-PDGFRα activity after grafting on LNC. Our results demonstrated that site-selective antibody grafting on nanoparticles was the best way to maintain its activity. Nevertheless, in vitro uptake by primary OPC was only modestly increased by the Ab grafting and to the same extent as isotype control-grafted LNC. This observation highlights how crucial appropriate control is for uptake studies involving nanoparticle surface modification and how this modification impacts cell-nanoparticle interaction.

Fig. 1 .

 1 Fig. 1. Preparation of LNC-PEG-Maleimide and grafting of Ab (A) The PEG-Maleimide conjugate was added at the surface of the LNC using two different approaches: Approach 1 consisted of the transacylation of NH 2 -PEG-Maleimide, and Approach 2 involved the post-insertion of DSPE-PEG-Maleimide. Both led to the formation of LNC-Maleimide. (B) The Ab (anti-PDGFRα) was thiolated by using IMT (2-iminothiolane•HCl). Then, the thiolated Ab formed a thioether bond with the maleimide moiety present at LNC surface. Unattached Ab were removed by dialysis. (created with Biorender.com)

Fig. 2 .

 2 Fig. 2. Preparation of LNC-PEG-DBCO and grafting of Ab (A) A transacylation reaction was used to add the NH 2 -PEG-DBCO conjugate at LNC surface. (B) The azide moiety was added on Ab using the Thermofisher® Site-Click kit. The modification was made on the carbohydrate chains of the Fc region of the Ab specifically. The DBCO alkyne reacted with the Ab azide to form a triazole bond, linking the Ab covalently to the LNC. (created with Biorender.com)

Fig. 3 .

 3 Fig. 3. Impact of transacylation and post-insertion of PEG-Maleimide on the physicochemical properties of LNC Following transacylation ofNH 2 -PEG-Maleimide (approach 1) or post-insertion of DSPE-PEG-Maleimide (approach 2) of the LNC, the Ab was linked to the LNC-Maleimides. LNC size (A) and Zeta potential (B) were measured, in water, using a Nanosizer. The values were presented as mean ± SD (N = 3, n = 3). Statistical significance was determined by a one-way ANOVA test, *p < 0.05.

Fig. 4 .

 4 Fig.4. Impact of Ab grafting to the surface of the LNC (approach 1) on its interaction with PDGFRα. An ELISA was used to determine the interaction between the Ab and its target protein (PDGFRα). Data are shown as a percentage of 1 nM Ab response to 20 nM of PDGFRα. All percentages were calculated relatively to unmodified anti-PDGFRα. In all conditions, Ab was at 1 nM. The values were presented as mean ± SD (N = 3, with 3 different batches of LNC-Ab, Ab-PEG-Maleimide, and Ab-SH).

FormulationsFig. 5 .

 5 Fig. 5. Impact of Ab grafting with approach 3 on its interaction with PDGFRα. An ELISA was used to determine the interaction between the Ab and its target protein (PDGFRα) for (A) modified Ab and (B) Ab grafted on the LNC. Data are shown as a percentage of 1 nM Ab response to 20 nM of PDGFRα. All percentage were calculated relatively to Ab (unmodified anti-PDGFRα). The values were presented as mean ± SD (N = 3, with 3 different batches of LNC-Ab, Ab-N 3 and Ab-PEG-DBCO).

Fig. 6 .

 6 Fig. 6. Effect of LNC on OPC viability. OPC were incubated in the presence of LNC for 1 and 4 h before assessment of their viability using PrestoBlue® Cell Viability Reagent. The dotted line represents 100% of living cell and corresponds to untreated OPC. The values were presented as mean ± SD (N = 3, n = 4).

Fig. 7 .

 7 Fig. 7. Visualization of LNC-Ab localization in OPC. Representative picture of LNC localization in OPC. LNC-Ab were diluted to 0.42 mg/ml in OPC media and incubated 1 h with the cells. Blue is DAPI for cell nucleus; green is Alexa 488-Phalloidine, for F-actin, cytoskeleton; red is DiD for LNC.(A) Merged image of yz, xz, and zy sections; (B) DiD-labeled LNC image of yz, xz, and zy sections.

Fig. 8 .

 8 Fig. 8. Impact of anti-PDGFRα grafting on LNC OPC-associated fluorescence. DiD-Loaded LNC were incubated for 30 min with OPC at a concentration of 0.15 mg/ml. The fold increase in Mean Fluorescence Intensity per cell (MFI) was calculated relatively to LNC's MFI. Statistical significance was calculated based on an unpaired t-test *p < 0.05. The values were presented as mean ± SD (N = 3, n = 3).

Fig. 9 .

 9 Fig. 9. Impact of LNC-Ab and LNC-IgG2a uptake by OPCs in the presence of PDGFAA in the media. Statistical significance was calculated based on a two-way ANOVA*p < 0.05, **p < 0,01. The values were presented as mean ± SD (N = 3, n = 3).

  et al. International Journal of Pharmaceutics xxx (xxxx) 121623

Table 1 Impact of PEG-Maleimide insertion method on Ab grafting efficiency

 1

	Formulations Molar Ratio of Maleimide / Kolliphor HS®	Quantity of antibody added at the beginning of the reaction (μg)	Grafting efficiency (%)	Number of antibodies per LNC
	LNC-Ab approach 1 LNC-Ab approach 2	1:100 1:100	28 28	66 ± 9 38 ± 7	49 ± 1 7 ± 4

. The values are presented as mean ± SD (N = 3).

Table 2

 2 Impact of Ab grafting using Approach 3 on LNC physicochemical properties.

Acknowledgments

Yasmine Labrak is a F.R.S.-FNRS (Fonds de la recherche scientifique) FRIA grant holder. Anne des Rieux is a F.R.S.-FNRS Senior Research Associate. Anne des Rieux was recipient of a grant from the foundation Charcot. The authors would like to thank Dr. Nicolas Dauguet for his help regarding FACS data analysis and Dr. Leopold Thabault for scientific discussions. In memory of a beloved friend, Françoise Lemoine, who died from MS. Illustrations were created using Biorender.com

Uncited references

 Carradori et al., 2016a.

CRediT authorship contribution statement

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary material

Supplementary data to this article can be found online at https:// doi.org/10.1016/j.ijpharm.2022.121623.