N Wang

D Delahaye

A Gondran

M Mongeau

Automatic dependent surveillance and broadcast ground-station optimal deployment problem

ADS-B (Automatic Dependent Surveillance and Broadcast) is a new surveillance technology that allows an aircraft to broadcast its own position periodically to ground stations. It has better precision, higher refresh rate, and lower cost than traditional secondary radar. Therefore, it is envisaged as a potential solution for air traffic surveillance in the context of nowadays growing traffic. In this study, we focus on a location problem that aims to deploy a network of ADS-B ground stations, in order to cover a given traffic space at minimum cost. We propose three mathematical optimization models based on a 2D discretized airspace under the form of discrete-optimization problems. Results obtained with the Mixed-Integer Linear Programming (MILP) solver Gurobi tested on a real-life size problem (8,476 daily flights over France) shows that our approach is viable in an operational context. The performances of the three proposed formulations are analyzed and compared. I. Introduction Automatic dependent surveillance-broadcast (ADS-B) is a new aeronautic surveillance technology that has been applied broadly around the world in recent years. ADS-B system consists of ground infrastructures and on-board transponders. This system provides two different services: ADS-B OUT and ADS-B IN.

the aircraft position as well as other important flight information periodically down to the ground, or to other interested receivers such as communication satellites and other aircraft. The ADS-B IN service allows aircraft to receive ADS-B messages from nearby aircraft, and therefore to benefit from a clear understanding of the surrounding traffic situation. ADS-B OUT service has been well developed in practical applications, as installation of qualified transponders has been mandatory in several countries, while ADS-B IN service remains an operational choice for airline operators.

As an essential part of this system, ADS-B ground stations receive ADS-B OUT messages, process them, and then send these messages to Air Traffic Control (ATC) facilities, as showed in Fig. 1. Aircraft positions transferred by ADS-B are calculated based on a Global Navigation Satellite System (GNSS), which is more accurate and has much shorter refresh rate than traditional radar surveillance systems. ADS-B enables air traffic management systems to apply more efficient traffic routing procedures, empowers an increased capacity, and improves aviation safety. Additionally, an ADS-B ground infrastructure has lower installation and maintenance costs compared to radar systems. With these benefits, ADS-B technology has become a critical part of next-generation air traffic surveillance systems.

Fig. 1 ADS-B system

Up to now, several leading countries have started, or already finished the installation of ADS-B ground infrastructures. Australia started its ADS-B project in 2004. In 2009, it became the worldfirst for nationwide ADS-B coverage, with 28 sites throughout the country. In the United States, 634 sets of ADS-B ground facilities have been installed; a national-wide network was completed in 2014. This network provides ADS-B OUT services across the country for terminal and en-route service volumes, and it continues to grow to improve the service. In Europe, ADS-B deployment is progressing, combining with the Wide Area Multilateration (WAM) technology. About 70 ADS-B stations are currently deployed for operational use, and more than 700 WAM/ADS-B stations are committed at various sites. In China, several ADS-B ground infrastructures have been deployed to cover separate west air routes, and more trial implementations are expected to continue the adaptation phase. Other ADS-B implementation related work is also being undertaken in all continents worldwide.

To deliver a stable and solid air traffic surveillance service, ADS-B ground stations have to be deployed across whole continents, including the old radar service areas and non-radar airspace. The layout of an ADS-B ground station network needs to be optimized to ensure a seamless coverage, and to meet air traffic safety requirements, while staying within a reasonable cost range. The present study contributes to the research in optimizing ADS-B ground station deployment by introducing three different mathematical formulations for the problem, and comparing their performances by solving the problem using a MILP solver, Gurobi [START_REF]Gurobi optimizer reference manual[END_REF].

A. Previous related work

To our knowledge, there is no exhaustive literature survey on nation-wide ADS-B deployment methodologies: no systematic approach for site selection has been yet proposed, and operational and geographical constraints are rarely taken into consideration in the ADS-B optimal deployment processes. E. Boci [START_REF] Boci | RF coverage analysis methodology as applied to ADS-B design[END_REF][START_REF] Boci | A systems approach for designing a radio station layout for the U.S. national airspace[END_REF][START_REF] Boci | ADS-B service volume engineering: Designing an efficient radio station layout while meeting stringent radar interference levels[END_REF] uses an integrated radio-frequency software for ADS-B coverage prediction. In his work, the siting solutions are proposed according to the maximum radar interference with the existing radar sites; and for the non-radar areas, the cone-of-silence problem due to the vertical pattern of ADS-B antenna is addressed in order to determine the distance between two sites. These siting principles allow the author to implement a computer algorithm for searching some initial solutions to cover the entire US territory.

A more recent work, by W. Langhans et al. [START_REF] Langhans | Implementation of a nationwide wide-area multilateration system for Austrian airspace[END_REF], presents a national-wide WAM system for Austria, which consists of one central processing station and 61 remote units. Apart from taking in account a multiple-coverage requirement, this network must also be synchronized to perform multilateration. A site-scoring system is presented in this work to perform the site selection. Performance requirements such as position accuracy, air-route coverage, and data capacity are used as metrics for guiding the optimization process. W. Zhang [START_REF] Zhang | The research of ADS-B ground stations arrangement based on GIS[END_REF] gives a detailed analysis of ADS-B ground-station range calculation and visual field calculation based on Geographical Information System (GIS) data in order to realize seamless coverage of few air routes in western China. Similar research work on radar or sensor networks can also provide useful guidelines for research on this subject, see for instance [START_REF] Guan | SSR surveillance network covering problem with obstacle effect consideration[END_REF][START_REF] Minciardi | Optimal planning of a weather radar network[END_REF].

B. Overview

The present study focuses on large-scale ADS-B ground-station optimal deployment, concentrating more precisely on a nation-wide integrated ADS-B ground station network. To ensure an efficient and robust ADS-B function service, we concentrate particularly on the mathematical formulation of the problem. The results are expected to provide reasonable initial deployment plans to decision makers.

The remainder of this article is organized as follows: Section 2 analyses ADS-B ground station performance to define the coverage range. Section 3 introduces three mathematical optimization models based on a 2D discretized airspace. Numerical tests based on real traffic data are performed, and results obtained by Gurobi are presented in Section 4. Finally, Section 5 presents a conclusion on this study and draws perspectives.

II. ADS-B ground-station performance

The antenna of an ADS-B ground-station can receive messages sent from the on-board transponder within a certain distance, called the station coverage range, noted R. This range depends on many factors: the transmitted-signal frequency and strength, the sensibility of the receiving antenna, the propagation loss during the transmission path, etc. ADS-B data link uses Very High Frequency (VHF) electromagnetic waves. The wave follows the Line Of Sight (LOS) propagation rule, which means that in perfect vacuum, it travels following straight line. When signals transfer from aircraft to the ground or the opposite, the curvature of Earth affects the sight propagation line (radio horizon effect). Remark that the coverage range R is smaller than the maximum LOS range, d LOS , the farthest propagation distance of the sight line, as showed in Fig. 2, where R E denotes the mean radius of the Earth. Suppose that Earth is a perfect sphere and that there is no atmosphere, then an approximate LOS range can be calculated by a simple formula. Given the mean radius of Earth R E = 6, 371 km, and the height of the aircraft in flight h, if the height of the station is neglected, the LOS range is expressed as:

d LOS = (R E + h) 2 -(R E ) 2
In the usual case, since h R E , the above formula can reasonably be approximated by:

d LOS = 2R E h
With the height h given in meters, and d LOS in kilometers, we get:

d LOS [km] ≈ 3.57 h[m]
The geodetical distance d GEO is the distance measured along the surface of the Earth:

d GEO = R E arccos R E R E + h
For the range of our data, the maximum geodesic distance and the maximum LOS range are approximately equal: d GEO ≈ d LOS . Then, in first approximation, the coverage range R is equal to d LOS . However, in reality, under the refractive effect of atmosphere, VHF radio waves actually travel as a curve. Meanwhile, the atmosphere absorbs partially the wave energy during the propagation.

Other environment aspects, like multi-path effect, can also decrease the effective propagation distance. Taking the above factors into account, a list of maximum coverage R ≈ 0.872 × d LOS for representative Flight Levels (FL) is presented in Table 1. Besides the electromagnetic wave attenuation, terrain blockage is another important factor to take into account when analyzing the effective coverage field of an antenna. volves obtaining an ECF database. This database comes normally from a pre-calculation performed by specialized software [START_REF] Boci | RF coverage analysis methodology as applied to ADS-B design[END_REF][START_REF] Boci | A systems approach for designing a radio station layout for the U.S. national airspace[END_REF][START_REF] Zhang | The research of ADS-B ground stations arrangement based on GIS[END_REF]. The challenge here is to design a dynamic algorithm that can deal with real-time ECF computations integrated within the optimization process. This requires much memory space and a powerful processor. Such an approach has the advantage of allowing the decision maker to consider a continuum of candidate site positions, instead of a finite set of given discrete positions. In this article, we do not take into account of ECF and discrete candidate site positions is considered.

III. Mathematical formulations of the problem

In this section, we first introduce the airspace discretization model to process the real traffic data. Then, we formulate our ADS-B ground-station deployment problem under the form of a classical Set Covering Problem (SCP). According to the different considerations of the decision maker, two other formulations are also proposed for this problem: the second formulation accepts a flexible trade-off between full-coverage and the cost associated to a high number of selected stations, while the third formulation maximizes the coverage with a fixed number of selected stations.

A. 2D airspace discretization

Here we consider the airspace as the 2D projection of a given 3D flight zone; all civil aviation trajectories inside this zone are also projected in 2D. Consider a rectangle large enough to include this airspace; this rectangle is then discretized as a grid (G a ) consisting of small squares, called grid elements, of size a s × a s , where a s is the airspace step size.

In this preliminary study, we assume that the coverage range of all station are identical, noted as R. Hence, the coverage field of any station is a R-radius disk when terrain blockage is not taken into account. A grid element i is considered to be covered by a station if the distance between the central point of this grid element and the station position is less than or equal to R, as illustrated in Fig. 4. In further works, we integrate ECF in order to take into account the terrain blockage as shown in Fig. 3-b. We consider that a set of candidate ADS-B station sites is provided as input to the problem. For this study, we shall generate artificially a set of candidate stations by using some other discretization grid of the airspace (G c with candidate-station step size c s ) and assuming that there is a candidate station site at the center of each grid element generated thereby. In order to generate a realistic instance of the ADS-B ground station optimal deployment problem, we use real-traffic data to create a traffic density map based on our discrete airspace.

The traffic data consists of 4D trajectory sample points (latitude, longitude, altitude, time). These points are then projected on the 2D grid of our discretized airspace G a . Each grid element i has a density index d i , defined as the total number of trajectory sample points lying in the grid element i. Grid elements with higher density index can thereby be given higher priority during the optimization phase. Fig. 5 shows an example of 50 simulated direct flights in France. Fig. 6 displays the correspondent density map; grid elements featuring darker colors correspond to higher density indices. This sub-section presents three optimization formulations for the ADS-B ground station optimal deployment problem. Recall that in this study, we assume that candidate stations have identical coverage ranges and identical installation costs. These hypotheses imply that minimizing the cost of an ADS-B network is equivalent to minimizing the number of selected ground stations.

With the 2D airspace discretization, instead of constructing an ADS-B ground station network to cover every sample point of each flight trajectory, we aim at covering all the non-empty grid elements (whose density index is not zero). We first consider a basic, single-layer coverage problem, where each grid element must be covered at least once. Under the special context of air-traffic surveillance, additional coverage performance requirements can be added. More precisely, in the robust version of the problem, which aims at delivering a service that is robust to material failures, station redundancy is required. This means that each grid element needs to be covered by at least two stations, so that in the occurrence of one station out of mission, there is another one to complete the service. Another practical motivation for considering the multi-layer coverage problem is the multilateration application, for which each grid element needs to be covered by at least three stations for allowing 2D position calculations, and four stations for 3D position calculations to ensure the proper implementation of this cooperative aircraft surveillance technology. These extra coverage requirements can easily be translated into inequality constraints in the optimization formulations we are about to present.

The first optimization formulation we present here aims at selecting a minimal number of stations, while ensuring that every grid element is covered by at least K stations. This optimization problem can be modeled as a Set Covering Problem (SCP), which is the most-common optimization model in facility location problems [START_REF] Daskin | Introduction to Location Theory and Models, chapter 1[END_REF].

Let us define the following notation:

• Given input data:

-E = {1, 2, . . . , n} is the set of non-empty grid elements; i ∈ E will designate a specific grid element -S = {1, 2, . . . , m} is the complete set of candidate stations; j ∈ S will designate a specific candidate station -K ∈ N + is the required coverage level: K = 1 in the single-layer coverage version of the problem, K = 2 in the robust variant, and K = 4 in the multilateration application -S i , denotes the set of candidate stations that can cover grid element i, i ∈ E

• Optimization variables:

x j is a binary decision variable whose value is 1 if the candidate station j is selected, 0 otherwise, j ∈ S

The first formulation of our problem (SCP), is the following Integer Linear Program (ILP):

minimize x m j=1 x j (1) subject to j∈Si x j ≥ K, i = 1, 2, . . . , n (2)
x j ∈ {0, 1}, j = 1, 2, . . . , m

where x is the vector whose j th component is the binary decision variable x j .

The SCP is a well-known combinatorial optimization problem. It is NP-hard in the general sense, but with the fast development of commercial solvers, even large instances can be solved to optimality with exact methods. One may consider for instance, the commercial optimization solver

Gurobi [START_REF]Gurobi optimizer reference manual[END_REF]. It relies on a branch and cut method to solve ILP problems, while using heuristic approaches to generate efficient cutting planes and admissible solutions.

Heuristic algorithms can also be considered to tackle large instances of the SCP, in which the

f (X) = n i=1 (1 + )y i - m j=1 x j (4)
subject to

y i = min   j∈Si x j , K   , i = 1, 2, . . . , n (5)
x j ∈ {0, 1}, j = 1, 2, . . . , m

y i ∈ {0, 1, . . . , K}, i = 1, 2, . . . , n (6)
• y i is an auxiliary integer-valued decision variable that is related to the violation level of the specific constraint in (2) that corresponds to the grid element i, i ∈ E

• X denotes the vector of optimization variables: (x, y), where y is the vector whose i th component is y i , i ∈ E

• is a user-defined parameter Constraints [START_REF] Boci | ADS-B service volume engineering: Designing an efficient radio station layout while meeting stringent radar interference levels[END_REF] define the link between the vectors of decision variables x and y: since we only need to reach the given target coverage level K, when a grid element i ∈ E is more covered than this required level, the extra service provided is considered useless, therefore it is not taken into account in y i . In other words, once a grid element reaches a coverage level higher than required, it does not contribute further to the total-coverage objective-function value.

The sign of the user-defined parameter plays an important role in this reformulation. From the decision maker's point of view, if the full-coverage is a hard constraint (that must be satisfied), then should be given a strict positive value. In this case, the coverage constraints (2) are enforced and the above penalized reformulation is equivalent to the SCP formulation. Indeed, by generalizing the results of [START_REF] Bilal | A new formulation of the set covering problem for metaheuristic approaches[END_REF], we have:

Proposition 1 Assuming that there exists a feasible solution for the SCP formulation, the SCP formulation and the penalized formulation are equivalent optimization problems in the case where > 0. More precisely: an optimal solution of one problem can straightforwardly yield an optimal solution for the other problem.

Proofs: see Appendix A.

When -1 < ≤ 0, the penalized formulation is a relaxation of the original SCP formulation.

If full-coverage can be compromised, one should choose a value in ]-1,0]. In this case, the penalized reformulation boils down to optimizing the weighted sum of two criteria: maximizing the sum of coverage for each grid element, while minimizing the number of selected stations. For example, when K = 1 and = -0.9, any extra grid elements covered yields an increase of 1 + = 0.1 in the first criterion (coverage), and an increase of 1 in the other criterion (number of stations). As a result, the objective-function value is changed by 0.1 -1 = -0.9. One can then easily see that one extra station must cover at least 10 grid elements that are not covered yet to obtain an increase in the objective-function value.

In order to allow the possibility of presenting a pool of good alternate solutions to the decider, we propose a third optimization formulation: the maximum covering SCP (MSCP) formulation.

In this formulation, we fix the number of stations to some pre-defined value N and we look for the N stations that cover as many grid elements as possible:

maximize

X=(x,y) n i=1 y i (8)
subject to

y i = min   j∈Si x j , K   , i = 1, 2, . . . , n (9)
m j=1

x j = N (10)

x j ∈ {0, 1}, j = 1, 2, . . . , m (11)
y i ∈ {0, 1, . . . , K}, i = 1, 2, . . . , n (12)
IV. Numerical tests

In this section, we first present the traffic data used for the numerical tests in Subsection 4.1.

The next two subsections present and compare the results obtained with the original SCP formulation and the penalized formulation with > 0 (Subsection 4.2), and with the MSCP formulation and the penalized formulation with < 0 (Subsection 4.3). All tests are carried out with the MILP solver Gurobi version 7.2 on an Intel i7-4700 2.4GHz processor with 8 cores.

A. Traffic data

We test our problem on a large realistic instance constructed from data of flight plans corresponding to a period of 24 hours over the France airspace; it involves 8,476 flights, displayed on Fig. 7. The data is provided under the form of a table of 1,874,741 trajectory sample points, resulting from a time discretization with a time step of 15 seconds. A square of 2,000 km × 2,000 km that includes the French territory is taken as the 2D airspace. This 2D airspace is discretized into a grid G a with step size of a s = 20 km. After projecting the trajectory sample points in this 2D grid, we obtain an instance involving 10,000 square grid elements. To generate the set S of candidate stations, we use the discretization step size of c s = 10 km, that yields 40,000 candidate stations. We then use a pre-processing algorithm to eliminate the empty grid elements (those not intersecting any trajectory) and the candidate stations that do not cover any grid element. As a result, the instance has n = 2, 700 non-empty grid elements and m = 6, 687 candidate stations.

In this preliminary study, we suppose that all candidate station radius are identical and taken to be R = 200 km (which corresponds to consider all flights at FL 110), and they feature identical installation costs. First, we study the case of exact covering that we modeled with the SCP formulation and the penalized formulation with > 0 and that requires all the grid elements to be covered by at least

K ADS-B antenna.
Results obtained by Gurobi are presented in Table 2, where N * is the minimal number of selected stations obtained for different K values; t SCP and t >0 are respectively the CPU run time in seconds for the original SCP and the penalized formulations. The SCP formulation clearly dominates the penalized formulation with > 0.

The SCP formulation always yields an optimal solution (but with very large CPU times when

K = 4 et K = 5
). The penalized formulation with > 0 yields faster convergence than the SCP formulation only when K = 1, but it does not succeed to find an optimal solution within 48 hours of CPU time when K = 4 et K = 5. The optimal number of stations displays almost perfect linear increase with K values, as showed in Fig. 8. This reveals that for each K coverage, there are only a limited number of grid elements exceeded the requirement coverage level. For example, 17 stations are required for K = 1, if each grid element is covered only once, then 17 more stations are required for K = 2; but in reality, the coverage area of the 17 stations overlapped for a number of grid elements so that only 16 more stations are required for K = 2. The optimal solution obtained from the single-covering (K=1) instance is displayed in Fig. 9, where the points represents the non-empty grid elements while each green circle represents the coverage disk of one selected station. All grid elements are covered by these N * = 17 selected stations. In this Subsection, we study ADS-B deployment when one allows some grid elements not to be covered at the required level. This corresponds to the MSCP formulation and the penalized formulation with < 0.

Given a set of selected stations, let us define the overage deficit of the grid element i, i ∈ E to be dc Results obtained by the MSCP formulation for various input values for the desired number N of selected stations are presented in Table 3. To solve these instances, we use Gurobi with a time limit of 2 hours (7200 seconds). Global optima proved by Gurobi are noted in bold in the table, otherwise only the suboptimal solution (upper bound) and the lower bound found are provided. In this table, N denotes the fixed number of stations, "best dc" denotes the best value of dc found by Gurobi at the end of two hours, "LB dc" denotes the lower bound of dc found by Gurobi at the end of two hours. Remark that for each value of K, the first value of N is the optimal numbers of selected stations found previously by the SCP formulation (for which full coverage is thereby same number of selected stations: it takes longer computation time than the MSCP formulation to find the same results; or it ends up with more grid elements not covered by the selected stations at the end of two hours of CPU time. There is only one exception: for K = 4 and N = 56 the penalized formulation with < 0 finds a solution with dc = 161, while the MSCP formulation ends up with dc = 165. initially proposed for the single-coverage (K = 1) case that we extended to the multi-coverage case.

i := K -y i = K -min   j∈Si x j , K 
The last model we proposed, the maximum set covering problem formulation, allows the user to impose the number of stations to be deployed in his search for compromised solutions.

In order to test and compare the above models, we build a real-life size problem instance involving 8,476 flights, from real traffic data in the France airspace. We presented results obtained with the state-of-the-art MILP solver Gurobi. Optimal solutions were found for a series of different coverage requirements. These results show that our approach is viable in an operational context and the MSCP formulation contributes a lot to build the solution pool for decision makers in the end. While the performance of penalized formulation is not as good as the other two formulations in the simplified context of this preliminary study, but it may be more effective than the other two formulations when more realistic features will be considered. Among such features that can be interested in the penalized model, let us mention using a 3D model taking into account the elevation of station position and the terrain blockage around the position (caused by obstacles such as mountains) that will replace the 2D discretized airspace model. This will require the integration of geographical information into the current model.

Covering problems have basically two criteria to optimize: on one hand, the cost of the solution, evaluated by the number of installed stations and our models can easily account for installation costs that differ from one station to another. On the second hand, the quality of service (QoS) of the solution, evaluated by the number of clients here, the trajectory points obtained by discretization (sufficiently) covered. In our specific case, the QoS is not only the number of ADS-B antenna that cover each point of the airspace, like in this study, but rather a more complex evaluation of the QoS based on the possibility to localize one aircraft in the airspace by trilateration. For example, if some of the four antenna covering a given airspace point are localized close from each other, then the trilateration is subject to large error. This leads to interesting perspectives in the continuation of our work:

• A combination of wide-area mulilateration technology and ADS-B service is promising in the future: in this case, each trajectory point has to be covered by at least four stations and distances and angles between these four stations need to be carefully restricted via constrained optimization models in order to ensure accuracy of the calculation of the aircraft position.

• In the context of more complex QoS measurement, non-linear optimization should be taken into account. As a consequence, specific heuristics methods based on the penalized formulation should be considered, instead of the exact linear Gurobi solver, in order to address the resulting difficult optimization problems. which contradicts the fact that X * is an optimal solution for the penalized formulation. Therefore,

x * is a feasible solution for the SCP formulation. In a second step, we prove that this truncated solution x * is optimal for the SCP formulation. We show this again by contradiction: suppose that x * were not an optimal solution for the SCP formulation; then, there exists x feasible for SCP that is better than x * for SCP, i.e. such that This means that X is strictly better than X * in terms of the penalized objective function, and since moreover X is feasible for the penalized formulation, we obtain a contradiction with the fact that X * is an optimal solution for the penalized formulation. Therefore, x * is an optimal solution for the SCP formulation.

To show the converse, let us consider a solution x * that is optimal for the SCP formulation. We shall show that the extended solution: X * := (x * , y * ), where y * i := min( j∈Si x * j , K) = K is optimal for the penalized formulation. This solution x * is clearly feasible for the penalized formulation.

Consider now any solution X = (x, y) satisfying ( 5) and [START_REF] Daskin | Introduction to Location Theory and Models, chapter 1[END_REF]. We have:

f (X * ) -f (X) = ( x * j ≥ 0 since x * is optimal for the SCP formulation Therefore, X * is optimal for the penalized formulation.

Fig. 2 LOS

 2 Fig. 2 LOS range from an antenna site S to an aircraft A at height h; O and RE denote respectively the center and the mean radius of the Earth.

Fig. 3 Fig. 3

 33 Fig. 3 Terrain blockage: vertical (a) and plan (b) views. The shadowing angle of the obstacle is given by: tanθs = ho-ha do

Fig. 4

 4 Fig. 4 2D airspace discretization and coverage field of one ADS-B station

Fig. 5

 5 Fig. 5 50 direct flights Fig. 6 Corresponding density map

  constraint of full coverage usually raises difficulties. Indeed, our empirical tests with basic heuristic approaches involving local-improvement steps exhibit premature convergence towards local optima that are not satisfactory. A natural idea consists in allowing the search to proceed temporarily outside the feasible domain. This, in return, involves addressing the very difficult task of projecting the current infeasible iterate back into the feasible domain without losing too much quality in terms of the objective-function value. Therefore, we propose a reformulation of the problem that penalizes constraints (2) by adding a term in the objective function. Inspired by the reformulation proposed by Bilal et al. [2], our original SCP formulation becomes what we call the penalized formulation: maximize X=(x,y)

Fig. 7

 7 Fig. 7 One day of air traffic in France: 8,476 flights

Fig. 8

 8 Fig. 8 Minimal number of stations needed for different K coverages

Fig. 9

 9 Fig. 9 Deployment of the N * = 17 stations with covering (K = 1) the 8,476 flights over France. The points represent the 2,700 grid elements, each green circle represents the coverage disk of one of the 17 selected stations.



  , and let dc be the total coverage deficit: dc := n i=1 dc i .

Fig. 10

 10 Fig. 10 Comparison of the MSCP and the penalized ( < 0) for K = 1 and K = 4.

Fig. 11 (

 11 Fig. 11 (respectively Fig. 12) represents an example of partial covering found with the MSCP

Fig. 11

 11 Fig. 11 Deployment of 16 stations with 3 grid elements not covered.

Fig. 12

 12 Fig. 12 Deployment of 15 stations with 17 grid elements not covered.

Fig. 13

 13 Fig. 13 Number of stations (N ) vs total coverage deficit (dc) for different K coverages.

y- 1 = 1 =

 11 i = y * i for all i = I). Its objective-function value is f (X) = f (X * ) + (1 + )(y I -y * I ) f (X * ) + (1 + )f (X * ) + > f (X * )

> 0

 0 i . Consider now the following solution X for the penalized formulation: X := (x, ŷ), where ŷi := min( j∈Si xj , K). We have: f ( X) -f (X * ) = ( both x and x * satisfy (2) and thereforeŷ i = y * i since x is better than x * for the SCP formulation.

  since for all i : y * i = K while y i ≤ K

Table 1

 1 Maximum coverage range for different flight levels

	FL (100 feet)	30	120	240	330	400
	Corresponding altitude h (m)	914	3657	7315	10058	12192
	dLOS ≈ dGEO (km)	108	216	305	358	394
	Maximum coverage R (km)	94	188	266	312	344

Table 2

 2 Optimal number of stations and CPU times (in seconds) obtained from the SCP formulation and the penalized formulation with > 0 for different K coverages (" -" means over 48 hours of CPU time).

	K	1	2	3	4	5	6	7
	N *	17	33	49	64	80	96	112
	t SCP	103	547	6,042	42,511	25,722	4039	4282
	t >0	90	2,746	13,716	-	-	7146	5801

Acknowledgements

This work has been supported by the Civil Aviation University of China (Tianjin) and the China Scholarships Council program.

possible). In the case where K = 1, 2 and 3, MSCP formulation proves the optimality faster than SCP formulation. For K = 4 and N = 64, the MSCP do not prove the optimality in 2 hours. In fact, the number of stations N and the total coverage deficit dc are two contrary objectives for our problem (that have both to be minimized). The problem is fundamentally bi-objective. Fig. 10 displays two graph that show two Pareto front (best trade-offs) corresponding to the solutions found by the MSCP formulation (in blue) and the penalized formulation with < 0 (in red) for K = 1

(left) and K = 4 (right). The solutions obtained for the MSCP formulation results from providing various values for the input parameter N (imposed number of stations to be selected). On the other hand, the solutions of the penalized formulation (with < 0 correspond to different settings of the input penalty parameter , according to the emphasis the decider wishes to place on minimizing the number of stations (cost) rather than minimizing the lack of coverage. The two populations of solutions are close but, the penalized formulation with < 0 finds less interesting results with the Appendix: Proof of equivalence for the first two formulations Proposition 1 Assuming that there exists a feasible solution for the SCP formulation, the SCP formulation and the penalized formulation are equivalent optimization problems in the case where > 0. More precisely: an optimal solution of one problem can straightforwardly yield an optimal solution for the other problem.

Proofs: First, remark that an optimal solution X * = (x * , y * ) of the penalized formulation can be truncated into a solution x * that is an optimal solution for the SCP formulation. Indeed, in a first step, we prove that this solution x * is feasible for the SCP formulation. Suppose by contradiction that x * were not feasible for the SCP formulation. This means that there exists at least one grid element I ∈ E that does not reach its target coverage level K. Since the SCP formulation is feasible, there exists at least one non-selected station J ∈ S that covers the element I. Consider the following solution X for the penalized formulation so that it is identical to X * except that it includes moreover the station J (more precisely, x J := x * J + 1, x j := x * j for all j = J; y I := min( j∈S I

x j , K),


Eric Nguema-Ona
email: eric.nguema-ona@univ-rouen.fr

Maite Vicre-Gibouin

Maxime Gotté

Barbara Plancot

Patrice Lerouge

Muriel Bardor

Azeddine A Driouich

Maïté Vicré-Gibouin

Elisabeth Jamet

Ian S Wallace

Richard Strasser

Cell wall O-glycoproteins and N-glycoproteins: aspects of biosynthesis and function

Keywords: arabinogalactan protein, cell wall, endoplasmic reticulum, extensin, glycan, glycosyltransferase, Golgi apparatus, plants

INTRODUCTION

Plants synthesize glycoconjugates that are structurally diverse and complex reflecting the diversity of plant physiological functions. The glycomolecules are usually assembled and modified within the plant endomembrane system, including the endoplasmic reticulum (ER), the Golgi apparatus and secretory vesicles responsible for their transport to different cell compartments/organelles including the cell wall. Their synthesis involves a number of steps, beginning with the formation of activated nucleotide sugars such as NDP-sugars or NMP-sugars (Bar-Peled and O'Neill, 2011). After their synthesis in the cytosol, the nucleotide sugars are then actively transported into the ER and Golgi stacks where they serve as donor substrates during glycan synthesis. Glycosyltransferases (GTs) transfer specific sugars from activated nucleotide sugars to a specific glycan acceptor leading to the extension of the glycomolecule involved. This occurs through a stepwise and sequential process which involves a number of different GTs of the secretory system. It is worth noting that 1.8% of Arabidopsis thaliana's genome currently encode GT genes representing more than 462 GTs in total [START_REF] Ulvskov | Classification, naming and evolutionary history of glycosyltransferases from sequenced green and red algal genomes[END_REF].

Among the different plant organelles, the plant cell wall is a polysaccharide-rich extracellular compartment [START_REF] Albersheim | Plant Cell Walls: from Chemistry to Biology[END_REF]. In addition to polysaccharides, the plant cell wall also contains a significant percentage (∼10-15%) of N -and O-glycosylated proteins that are relatively less studied with regards to their biosynthesis and function. Both the N -and the Oglycosylation of proteins has a significant impact on both their structural properties and biological activities [START_REF] Varki | Biological roles of oligosaccharides: all of the theories are correct[END_REF]. Glycosylation and glycan processing are major post-translational modifications (PTMs) that cell wall proteins undergo inside the cell, and are considered important for their proper function. Indeed, in general, glycans are involved in the control of protein folding, cellular targeting and mobility, as well as signaling for regulation of plant growth, defense and different interactions with the surrounding environment [START_REF] Varki | Biological roles of glycans[END_REF][START_REF] Larkin | The expanding horizons of asparagine-linked glycosylation[END_REF][START_REF] Cannesan | Effect of arabinogalactan proteins from the root caps of pea and Brassica napus on Aphanomyces euteiches zoospore chemotaxis and germination[END_REF][START_REF] Nguema-Ona | Arabinoga-lactan-proteins in root microbe interactions[END_REF][START_REF] Chen | Nglycosylation of effector proteins by an α-1,3-mannosyltransferase is required for the rice blast fungus to evade host innate immunity[END_REF].

The N-/O-glycosylation of cell wall proteins is critical for plant development and responses to stress. Understanding and controlling O-and N-glycosylation of secreted proteins is also important in plant biotechnological applications.

N-GLYCOSYLATED PROTEINS: SYNTHESIS AND FUNCTION

The N-glycosylation of proteins starts in the ER. ER-synthesizing events for N-glycans are highly conserved in all eukaryotes studied so far since they are instrumental for efficient protein folding [START_REF] Aebi | N -linked protein glycosylation in the ER[END_REF]. The N-glycosylation pathway starts by the transfer en bloc of a lipid linked preassembled precursor (Glc 3 Man 9 GlcNAc 2 ) by the oligosaccharyltransferase (OST) onto the N-glycosylation sites (Asn-X-Ser/Thr and/or Asn-X-Cys) of the nascent proteins [START_REF] Burda | The dolichol pathway of N -linked glycosylation[END_REF][START_REF] Gil | N -glycosylation microheterogeneity and site occupancy of an Asn-X-Cys sequon in plasma-derived and recombinant Protein C[END_REF][START_REF] Zielinska | Precision mapping of an in vivo N -glycoproteome reveals rigid topological and sequence constraints[END_REF][START_REF] Matsui | N -glycosylation at noncanonical Asn-X-Cys sequences in plant cells[END_REF]. The α-glucosidases I and II then remove two glucose residues from the N-glycan resulting in the presence of only one terminal glucose on the glycoprotein. This allows its entry into the ER control quality cycle [START_REF] Aebi | N -linked protein glycosylation in the ER[END_REF]. Once the glycoprotein is correctly folded, the last glucose residue is removed by the α-glucosidase II prior to its transport into the Golgi apparatus where further modifications occur including removal of mannose residues and sequential addition of specific sugars through the action of GTs resulting in the formation of complextype N-glycans. In plants, many genes encoding for Golgi GTs have already been identified (Table 1). These include, for example, N-acetylglucosaminyltransferase I (GnT I; [START_REF] Bakker | An Arabidopsis thaliana cDNA complements the N -acetylglucosaminyltransferase I deficiency of CHO Lec1 cells[END_REF]Strasser et al., 1999a;[START_REF] Wenderoth | Isolation and characterization of plant N-acetyl glucosaminyltransferase I (GntI) cDNA sequences. Functional analyses in the Arabidopsis cgl mutant and in antisense plants[END_REF], Nacetylglucosaminyltransferase II (GnT II; Strasser et al., 1999b), core α-1,3-fucosyltransferase (α1,3-FuT; [START_REF] Leiter | Purification, cDNA cloning, and expression of GDP-L-Fuc:Asn-linked GlcNAc α-1,3-fucosyltransferase from mung beans[END_REF]Wilson et al., 2001a), β-1,2-xylosyltransferase (β1,2-XylT; Strasser et al., 2000;[START_REF] Pagny | Structural requirements for Arabidopsis β-1,2-xylosyltransferase activity and targeting to the Golgi[END_REF], Lewis-type α-1,4-fucosyltransferase (α1,4-FuT [START_REF] Bakker | Plant members of the α-1-3/4-fucosyltransferase gene family encode an α-1-4-fucosyltransferase, potentially involved in Lewis(a) biosynthesis, and two Frontiers in Plant Science | Plant Physiology core α-1-3-fucosyltransferases[END_REF][START_REF] Wilson | Analysis of Asn-linked glycans from vegetable foodstuffs: widespread occurrence of Lewis a, core α-1,3-linked fucose and xylose substitutions[END_REF][START_REF] Léonard | The presence of Lewis a epitopes in Arabidopsis thaliana glycoconjugates depends on an active α-4-fucosyltransferase gene[END_REF], and β-1,3-galactosyltransferase (β1,3-GalT; [START_REF] Strasser | A unique 1,3-galactosyltransferase is indispensable for the biosynthesis of N-glycans containing Lewis a structures in Arabidopsis thaliana[END_REF]. In contrast to the ER steps, evolutionary adaptation of N-glycan processing in the Golgi apparatus has given rise to a variety of organism-specific complex structures [START_REF] Varki | Evolutionary forces shaping the Golgi glycosylation machinery: why cell surface glycans are universal to living cells[END_REF]. Therefore, more complex plant N-glycans consist of specific glycoepitopes such as core β-1, 2-xylose, core α-1,3-fucose residues, and Lewis a substitutions on the terminal position of the antenna (Figure 1A; [START_REF] Lerouge | N-glycoprotein biosynthesis in plants: recent developments and future trends[END_REF][START_REF] Bardor | Immunoreactivity in mammals of two typical plant glycoepitopes, core α-(1,3)fucose and core xylose[END_REF]Bardor et al., , 2011;; Strasser This N-glycan results from the action of a plant-specific repertoire of glycosyltransferases that lead to the formation of a glycan bearing plant-specific glyco-epitopes such as a core β-1,2-xylose; a core α-1,3-fucose and a Lewis a antennae [START_REF] Lerouge | N-glycoprotein biosynthesis in plants: recent developments and future trends[END_REF][START_REF] Wilson | Analysis of Asn-linked glycans from vegetable foodstuffs: widespread occurrence of Lewis a, core α-1,3-linked fucose and xylose substitutions[END_REF][START_REF] Bardor | Immunoreactivity in mammals of two typical plant glycoepitopes, core α-(1,3)fucose and core xylose[END_REF]Bardor et al., , 2011)). The N-glycan structures presented here are drawn according to the symbolic nomenclature adopted by the Consortium for Functional Glycomics (Varki et al., 2009). , 2004).When abnormally processed, N-glycosylated proteins cause major developmental disorders and are usually associated to diseases in mammals [START_REF] Ioffe | Mice lacking N -acetylglucosaminyltransferase I activity die at mid-gestation, revealing an essential role for complex or hybrid N -linked carbohydrates[END_REF][START_REF] Metzler | Complex asparagine-linked oligosaccharides are required for morphogenic events during post-implantation development[END_REF][START_REF] Lowe | A genetic approach to mammalian glycan function[END_REF][START_REF] Hennet | Diseases of glycosylation beyond classical congenital disorders of glycosylation[END_REF]. In plants, abnormal N-glycosylated proteins rarely present developmental disorders under normal growth conditions [START_REF] Von Schaewen | Isolation of a mutant Arabidopsis plant that lacks N -acetyl glucosaminyl transferase I and is unable to synthesize Golgi-modified complex N -linked glycans[END_REF][START_REF] Strasser | Generation of Arabidopsis thaliana plants with complex N -glycans lacking β-1,2-linked xylose and core α-1,3-linked fucose[END_REF]. However, the cellulose-deficient Arabidopsis mutant rsw3 which is defective in the catalytic subunit of the α-glucosidase II presents radially swollen roots and a deficiency in cellulose content [START_REF] Burn | The cellulose-deficient Arabidopsis mutant rsw3 is defective in a gene encoding a putative glucosidase II, an enzyme processing N -glycans during ER quality control[END_REF]. Moreover, under stress conditions (e.g., salt), modified phenotypes such as abnormal plant growth [START_REF] Strasser | A unique 1,3-galactosyltransferase is indispensable for the biosynthesis of N-glycans containing Lewis a structures in Arabidopsis thaliana[END_REF] or altered root growth in the Arabidopsis cgl mutants [START_REF] Kang | Salt tolerance of Arabidopsis thaliana requires maturation of N -glycosylated proteins in the Golgi apparatus[END_REF][START_REF] Von Schaewen | Role of complex N -glycans in plant stress tolerance[END_REF], have been observed. Indeed, in these studies, reduced root growth and abnormal root morphology were observed for Arabidopsis plants cultivated on media containing high NaCl concentration. In contrast to Arabidopsis, a severe phenotype with arrested seedling development and premature death before reaching the reproductive stage has been reported recently for rice gntI mutant [START_REF] Fanata | N -glycan maturation is crucial for cytokinin-mediated development and cellulose synthesis in Oryza sativa[END_REF]. Such plants also present defects in cell wall composition, especially reduced cell wall thickness, and decreased in cellulose content as well as reduced sensitivity to cytokinin. Plant complex-type N-glycans are ascribed to many biological functions in relation with plant development that have been recently reviewed by [START_REF] Strasser | Biological significance of complex N -glycans in plants and their impact on plant physiology[END_REF]this issue). These include effects on plant innate immunity, tolerance to abiotic stress and root development. Therefore these functional aspects will not be further described in this review.

O-GLYCOSYLATED CELL WALL PROTEINS, ARABINOGALACTAN PROTEINS, AND EXTENSINS

Plant O-glycosylated cell wall proteins belong to the superfamily of hydroxyproline-rich glycoproteins (HRGPs). This superfamily of plant cell wall proteins which account for nearly 10% of the dry weight of the wall, is characterized by a high proline (Pro) content. Furthermore many of these Pro residues become hydroxylated (hydroxyproline, Hyp) during synthesis and consequently become glycosylated in various ways. Pro residues are distributed at different sites within the sequence and these patterns have suggested different classifications of HRGP members into different groups. EXTs and arabinogalactan proteins (AGPs) are two O-glycosylated HRGP subfamilies which have gained much attention [START_REF] Kieliszewski | Synthetic genes for the elucidation of glycosylation codes for arabinogalactan-proteins and other hydroxyprolinerich glycoproteins[END_REF][START_REF] Showalter | Arabinogalactan proteins: structure, expression and function[END_REF][START_REF] Schultz | Using genomic resources to guide research directions. the arabinogalactan protein gene family as a test case[END_REF][START_REF] Showalter | A bioinformatics approach to the identification, classification, and analysis of hydroxyproline-rich glycoproteins[END_REF][START_REF] Kieliszewski | Hydroxyprolinerich glycoproteins: form and function[END_REF][START_REF] Lamport | Role of the extensin superfamily in primary cell wall architecture[END_REF][START_REF] Nguema-Ona | Arabinogalactan-proteins in root and pollen tube cells: distribution and functional properties[END_REF][START_REF] Aebi | N -linked protein glycosylation in the ER[END_REF][START_REF] Tan | Arabinogalactan-proteins and the research challenges for these enigmatic plant cell surface proteoglycans[END_REF][START_REF] Velasquez | Recent advances on the posttranslational modifications of EXTs and their roles in plant cell walls[END_REF]. The nature of sugars being incorporated and the level of glycosylation vary between these two families, but also within the members of these subfamilies. For example, [START_REF] Kieliszewski | Hydroxyprolinerich glycoproteins: form and function[END_REF] have shown that occurrence of contigs of 3-5 Hyp, preceded by a serine residue (Ser-Hyp 4 ) led to the synthesis of a short arabinoside of 3-5 residues. Serine residue in the Ser-Hyp 4 contig is often O-glycosylated with a single galactose [START_REF] Velasquez | Recent advances on the posttranslational modifications of EXTs and their roles in plant cell walls[END_REF][START_REF] Saito | Identification of novel peptidyl serine α-galactosyltransferase alactosyltransferase gene family in plants[END_REF]. This action is performed by serine-O-galactosyltransferases (Ser-O-Gal-T), specific to plants [START_REF] Saito | Identification of novel peptidyl serine α-galactosyltransferase alactosyltransferase gene family in plants[END_REF]. Non-contiguous Hyp residues rather lead to the synthesis of a large arabino-galactosylated glyco-epitope on the protein [START_REF] Kieliszewski | Extensins: repetitive motifs, functional sites, post-translational codes, and phylogeny[END_REF][START_REF] Shpak | Synthetic genes for glycoprotein design and the elucidation of hydroxyproline-O-glycosylation codes[END_REF][START_REF] Kieliszewski | Hydroxyprolinerich glycoproteins: form and function[END_REF]. Arabinogalactan proteins and EXTs have been studied for decades, and shown to fulfill many functions related to development, and responses to biotic and abiotic stresses in plants [START_REF] Hall | The cell wall hydroxyproline-rich glycoprotein RSH is essential for normal embryo development in Arabidopsis[END_REF][START_REF] Motose | A proteoglycan mediates inductive interaction during plant vascular development[END_REF][START_REF] Lee | Arabinogalactan proteins are required for apical cell extension in the moss Physcomitrella patens[END_REF][START_REF] Nguema-Ona | Disruption of arabinogalactan proteins disorganizes cortical microtubules in the root of Arabidopsis thaliana[END_REF][START_REF] Aebi | N -linked protein glycosylation in the ER[END_REF][START_REF] Seifert | The biology of arabinogalactan proteins[END_REF][START_REF] Cannon | Self-assembly of the plant cell wall requires an extensin scaffold[END_REF][START_REF] Ellis | Arabinogalactan protein: key regulators at the cell surface[END_REF][START_REF] Lamport | Role of the extensin superfamily in primary cell wall architecture[END_REF][START_REF] Velasquez | O-glycosylated cell wall proteins are essential in root hair growth[END_REF][START_REF] Cannesan | Effect of arabinogalactan proteins from the root caps of pea and Brassica napus on Aphanomyces euteiches zoospore chemotaxis and germination[END_REF]Moore et al., 2014a,b). These studies have emphasized the importance of their O-glycan structures. Indeed, AGPs and EXTs are decorated with complex to simple carbohydrate-chains (Figures 1B,C) that are required for functionality of these glycomolecules. Until recently, the enzymes, as well as the molecular mechanisms controlling the synthesis of HRGP O-glycans, were poorly understood. A recent effort in the identification of the genes involved in the biosynthesis of HRGP O-glycans has considerably improved our understanding of the molecular events controlling the addition of sugars on these Hyprich proteins. The aim of this section is to bring together recent advances in the biosynthesis of HRGP O-glycans, with a focus on AGPs and EXTs. Structural and biological functions are also discussed.

AGPs AND EXTs: THE SYNTHESIS OF O-GLYCANS

PRO HYDROXYLATION OF HRGPs

Pro hydroxylation of plant cell wall HRGPs occurs predominantly on Hyp that are formed in the secretory pathway through the action of proline hydroxylases (P4Hs). In Arabidopsis, 13 P4Hs have been identified [START_REF] Hieta | Cloning and characterization of a low molecular weight prolyly 4-hydroxylase from Arabidopsis thaliana[END_REF][START_REF] Vlad | Arabidopsis prolyl-4 hydroxylases are differentially expressed in response to hypoxia, anoxia and mechanical wounding[END_REF][START_REF] Velasquez | O-glycosylated cell wall proteins are essential in root hair growth[END_REF]. P4Hs are membrane-anchored enzymes [START_REF] Yuasa | Membrane-anchored prolyl hydroxylase with an export signal from the endoplasmic reticulum[END_REF]. It is likely that Pro hydroxylation begins in the ER and continues in the Golgi apparatus. Detailed investigations of substrate affinity of two Arabidopsis P4-Hs, AtP4H1 and AtP4H2, showed that both AtP4H1 and AtP4H2 hydroxylate AGP-like and EXT-like synthetic peptides [START_REF] Hieta | Cloning and characterization of a low molecular weight prolyly 4-hydroxylase from Arabidopsis thaliana[END_REF][START_REF] Tiainen | Characterization of a second Arabidopsis thaliana prolyl-4-hydroxylase with distinct substrate specificity[END_REF]. However, the substrate specificity of the enzymes towards the two classes of synthetic peptides differed. Additional data showed that AtP4H2 poorly hydroxylated animal collagen, but did not hydroxylate animal hypoxia-inducible transcription factor (HIF); while AtP4H1 hydroxylates both animal Hyp-containing proteins collagen and HIF [START_REF] Hieta | Cloning and characterization of a low molecular weight prolyly 4-hydroxylase from Arabidopsis thaliana[END_REF]. Similarly, [START_REF] Velasquez | O-glycosylated cell wall proteins are essential in root hair growth[END_REF] showed that some root hair-specific P4Hs are able to hydroxylate EXTs, and displayed almost no activity toward AGP-like peptides. Root hair morphology of Arabidopsis p4h mutants was dramatically altered. Complementation of these mutants with wild type genes restored the phenotype. In addition to being substrate-specific, [START_REF] Velasquez | O-glycosylated cell wall proteins are essential in root hair growth[END_REF] also showed that some P4Hs were also cell typespecific: P4H2 and P4H5 being confined to trichoblast cells, while P4H13 being present in both trichoblast and atrichoblast cells. Recently, it has also been shown that different tomato P4Hs played a role in plant growth, and exhibited substrate-and tissue-specific activities [START_REF] Fragkostefanakis | Virus induced gene silencing of three putative prolyl 4-hydroxylases enhances plant growth in tomato (Solanum lycopersicum)[END_REF]. The authors have shown that silencing individual P4Hs result on an increased expansion of root and leaf cells in tomato. This increase correlated with a reduction in the amount of AGPs and possibly EXTs. Plants are therefore likely to regulate the secretion of various classes of

Frontiers in Plant Science | Plant Physiology

HRGPs at different stages of development and/or responses to stress to perform specific functions in a given cell type or organ. After their synthesis and secretion, HRGPs may be modified and/or re-arranged in the cell wall, but this aspect has received little attention so far, particularly in the case of AGPs. [START_REF] Liang | Identification and characterization of in vitro galactosyltransferase activities involved in the arabinogalactan protein glycosylation in tobacco and Arabidopsis[END_REF] has suggested that ∼15 GTs are involved in AGP glycan biosynthesis. Initiation of the biosynthesis requires the action of specific AGP O-Hyp Gal-T, able to initiate the galactosylation of hydroxylated residues on AGP backbone. Recently, an Arabidopsis Gal-T (AtGalT2), belonging to CAZy GT family 31 and containing a pfam 01762 domain encoding a Gal-T catalytic domain, able to add one galactosyl residue to Hyp residues of synthetic AGP-like peptides, has been identified [START_REF] Basu | Functional identification of a hydroxyproline-O-galactosyltransferase specific for arabinogalactan protein biosynthesis in Arabidopsis[END_REF]. The authors showed that AtGalT2 was able to add one galactose residue to synthetic AGP-like peptide, and not to synthetic EXTlike peptides. AtGalT2 was also harboring a GAL-LECTIN binding domain pfam 00337. This domain, previously identified as a Nacetylgalactosaminyl GT (CAZy GT family 27), was involved in catalyzing the first steps of the glycosylation of mammalian mucins [START_REF] Hassan | The Lectin domain of UDP-N -acetyl-D-galactosamine: polypeptide N -acetylgalacto-saminyltransferase-T4 directs its glycopeptide specificities[END_REF][START_REF] Wandall | The lectin domains of polypeptide GalNaC-transferases exhibit carbohydrate binding specificity for GalNaC. Lectin bind to GalNaC-glycopeptide substrates is required for high density GalNaC O-glycosylation[END_REF]. AtGAlT2 was found to be located in the ER and in the Golgi apparatus, a pattern similar to the one displayed by P4Hs [START_REF] Yuasa | Membrane-anchored prolyl hydroxylase with an export signal from the endoplasmic reticulum[END_REF][START_REF] Velasquez | O-glycosylated cell wall proteins are essential in root hair growth[END_REF]. It is possible that these two enzymes co-operate in plants to hydroxylate Pro residues and add the first galactosyl residue of the newly synthesized β-1,3galactan chain. In addition to AtGalT2, [START_REF] Qu | Identification of a novel group of putative Arabidopsis thaliana β-(1,3)-galactosyltransferases[END_REF], using a combination of bioinformatic approaches, identified several additional Gal-Ts belonging to the GT family 31, and showed their putative involvement in the elongation of the β-1,3galactan backbone of AGPs. For instance, the protein encoded by the gene At1g77810 was demonstrated to exhibit a specific β-1,3-Gal-T activity. An additional Gal-T activity that adds the second galactose to the Gal-Hyp nascent chains has also been partially characterized [START_REF] Liang | Identification and characterization of in vitro galactosyltransferase activities involved in the arabinogalactan protein glycosylation in tobacco and Arabidopsis[END_REF].

GLYCOSYLTRANSFERASES INVOLVED IN AGP O-GLYCAN BIOSYNTHESIS

In addition to β-1,3-Gal-T, AGP glycan synthesis also requires the action of different other β-1,6-Gal-T, α-1,3and α-1,5arabinosyltransferase (Ara-T), β-glucuronosyltransferase (GlcA-T), and α-1,2-fucosyltransferase (FuT; [START_REF] Wu | Functional identification of two non-redundant Arabidopsis α-(1,2)fucosyltransferases specific to arabinogalactan proteins[END_REF]. Recently, two Arabidopsis Gal-Ts showing a β-1,6-Gal-T activity have been identified: AtGalT31A, a β-1,6-Gal-T which is classified into the CAZy GT family 31, is required for the addition of Gal residues to existing β-1,6galactan chains [START_REF] Geshi | A galactosyltranferase acting on arabinogalactan protein glycans is essential for embryo development in Arabidopsis[END_REF] while AtGalT29A (CAZy GT family 29) is required for the addition of galactose residues to β-1,3and β-1,6galactan chains [START_REF] Dilokpimol | Galactosyltransferases from Arabidopsis thaliana in the biosynthesis of type II arabinogalactan: molecular interaction enhances enzyme activity[END_REF]. Both AtGalT31A and AtGalT29A are type II transmembrane proteins located in the Golgi apparatus. Traces of ER-localization previously observed with P4Hs and AtGalT2 were not found, suggesting that addition of β-1,6galactose residues to the side chains of AGPs occurs later during the transit of nascent HRGPs into Golgi stacks. Using subcellular co-localization approaches, FRET acceptor photo-bleaching techniques as well as immuno-precipitation techniques, the authors showed that (i) AtGalt31A and AtGal29A were organized into heterodimer complexes, and (ii) this heterodimer had an enhanced enzymatic activity than the homodimer AtGalT31A/AtGalT31A, or AtGalT29A/AtGalT29A. AGP arabinogalactan chains are also modified with glucuronic acid (GlcA) residues. [START_REF] Knoch | A β-glucuronosyltransferase from Arabidopsis thaliana involved in biosynthesis of type II arabinogalactan has a role in cell elongation during seedling growth[END_REF] have identified an Arabidopsis transferase belonging to the CAZy GT family 14, named AtGlcAT14A, exhibiting an AGP-specific GlcA-T activity, able to transfer GlcA residues both onto β-1,3and β-1,6-galactan chains (see also [START_REF] Zhou | BC10, a DUF266-containing and Golgi-located type II membrane protein, is required for cell wall biosynthesis in rice (Oriza sativa L.)[END_REF][START_REF] Ye | Comparative analysis of GT14/GT14-like gene family in Arabidopsis, Oryza, Populus, Sorghum and Vitus[END_REF]. Interestingly, AtGlcAT14A was localized to the Golgi apparatus. AtGlcAT14A is co-expressed with AtGalT31A and co-localize in the Golgi apparatus. However, the FRET photo-bleaching acceptor technique showed that both enzymes did not physically interact. These findings suggest that all the enzymes involved in AGP glycan synthesis, although probably co-regulated, are not necessarily part of a unique multi-protein complex. Arabidopsis AGP glycans were also shown to contain fucose residues [START_REF] Tryfona | Structural characterization of Arabidopsis leaf arabinogalactan polysaccharides[END_REF]. Two Arabidopsis FuT AtFUT4 and AtFUT6, belonging to the CAZy GT family 37, were shown to specifically add fucose residues to tobacco arabinogalactosylated AGP glycan chains [START_REF] Wu | Functional identification of two non-redundant Arabidopsis α-(1,2)fucosyltransferases specific to arabinogalactan proteins[END_REF]. Interestingly, de-arabinosylation of tobacco AGP glycans (using arabinofuranosidase) prevented the addition of fucose residue to the glycan, suggesting that arabinosylation was required for further addition of fucose by AtFUT4 and AtFUT6, supporting the arguments for sequential synthesis of AGP glycans along the Golgi cisternae. Biochemical data showed that both FuTs fucosylate AGP glycan in a different manner, most likely on different arabinose residues [START_REF] Wu | Functional identification of two non-redundant Arabidopsis α-(1,2)fucosyltransferases specific to arabinogalactan proteins[END_REF]. Finally, arabinose, along with galactose, is the more abundant sugar found in AGP glycans. Recently, [START_REF] Gille | Arabinosylation of a Yariv-precipitable cell wall polymer impacts plant growth as exemplified by the Arabidopsis glycosyltransferase mutant ray1[END_REF] have identified an AGP-altered mutant of Arabidopsis named reduced arabinose yariv1 (ray1-1). Monosaccharide composition of a root AGP fraction precipitated with β-glucosyl Yariv, showed a significant decrease in arabinose content in the ray1-1 mutant, as compared to the wild type. In addition, the ray1-1 mutant showed a reduction in the length of its primary roots. RAY1-1 gene was found to encode for a CAZy GT family 77 Ara-T, localized in the Golgi apparatus [START_REF] Gille | Arabinosylation of a Yariv-precipitable cell wall polymer impacts plant growth as exemplified by the Arabidopsis glycosyltransferase mutant ray1[END_REF]. It is however, unknown if RAY1 is able to add arabinosyl residues to short oligo-arabinosides also found on AGPs.

EXT O-GLYCAN BIOSYNTHESIS

Extensin O-glycans consists of short arabinoside chains with single galactose residues, linked respectively to Hyp residues, and serine residues of the Ser-Hyp 4 motifs. In contrast to the length and the molecular weight of arabinogalactan chains found in AGPs; EXT arabinoside chains are limited to 4-5 arabinosyl residues, predominantly β-1,2-linked. The number of enzymes required for their biosynthesis is also reduced to Ara-T initiating and elongating the arabinoside chains, and to the Ser-O-Gal-T, adding the single galactose residue to serine [START_REF] Velasquez | Recent advances on the posttranslational modifications of EXTs and their roles in plant cell walls[END_REF][START_REF] Saito | Identification of novel peptidyl serine α-galactosyltransferase alactosyltransferase gene family in plants[END_REF]. Ser-O-Gal-T are type I transmembrane proteins, located in the ER and possibly in the cis-Golgi cisternae [START_REF] Saito | Identification of novel peptidyl serine α-galactosyltransferase alactosyltransferase gene family in plants[END_REF], and prior hydroxylation of Pro residues is required for galactosylation of serine residues on EXTs. It is unknown if this initial galactosylation is required for further EXT arabinosylation.

While the enzyme adding the first galactose residue to AGPs is now identified, the enzyme transferring the first arabinosylresidue to O-Hyp EXT (and maybe on Ser-Hyp 3 domains of certain AGPs; [START_REF] Qi | Gum arabic glycoprotein is a twisted hairy rope: new model based on O-galactosylhydroxyproline as a polysaccharide attachment site[END_REF], remains unidentified. However, Ara-Ts adding the second, the third, and then the fourth arabinose residue to O-Hyp EXTs have been identified. Indeed, Arabidopsis RRA1-3, XEG113, and ExAD were shown (or proposed for ExAD; [START_REF] Velasquez | Recent advances on the posttranslational modifications of EXTs and their roles in plant cell walls[END_REF] to transfer respectively, the second, the third and the fourth arabinose residue β-1,2-linked to EXT [START_REF] Egelund | Molecular characterization of two Arabidopsis thaliana glycosyltransferase mutants, rra1 and rra2, which have a reduced residual arabinose content in a polymer tightly associated with the cellulosic wall residue[END_REF][START_REF] Gille | Identification of plant cell wall mutants by means of a forward chemical genetic approach using hydrolases[END_REF][START_REF] Velasquez | O-glycosylated cell wall proteins are essential in root hair growth[END_REF][START_REF] Velasquez | Recent advances on the posttranslational modifications of EXTs and their roles in plant cell walls[END_REF]. XEG113 belongs to the CAZy GT family 77 and xeg113 mutants exhibited abnormally elongated hypocotyls under stress conditions. XEG113 was found to be associated with Golgi membranes [START_REF] Gille | Identification of plant cell wall mutants by means of a forward chemical genetic approach using hydrolases[END_REF]. RRA3 is also a type II transmembrane protein, member of the CAZy GT family 77, localized in the Golgi apparatus, and shown to reduce root hair growth. Rra3 Arabidopsis mutants exhibited impaired root hairs. Using a base-mediated hydrolysis of the peptide backbone, followed by mass spectrometry analyses, the authors elegantly showed that XEG113 was responsible for the addition of the second arabinose residue to an elongating β-1,2arabinan chain, while RRA3 was responsible for the addition of the third residue. RRA3, XEG113, P4H2, and P4H5 were co-expressed, also indicating that EXT glycan synthesis must be tightly regulated within the endomembrane system. Moreover, different cell wall related proteins including AtRSH1 (a classical EXT HRGP), AtLRX1 (a hybrid EXT HRGP), AtPRP1 (a prolinerich protein), and several peroxidase genes were also co-expressed with Ara-T and P4Hs, in Arabidopsis root hairs [START_REF] Velasquez | O-glycosylated cell wall proteins are essential in root hair growth[END_REF].

Together, these studies suggest that AGP and EXT glycan synthesis is initiated in the ER and continues in the Golgi apparatus, similarly to the N-glycosylation pathway. P4Hs and AtGalT2 may co-operate during hydroxylation and galactosylation of AGP in the ER and in the Golgi apparatus. Elongation and ramification of the AGP glycans would probably take place in different Golgi subcompartments before their export to the cell surface. But specific compartmentalization of the enzymes involved in HRGPs synthesis within specific Golgi cisternae is not yet established and requires further investigations. Such an arrangement has already been described for enzymes involved in the N-glycosylation of secreted proteins [START_REF] Saint-Jore-Dupas | Plant N -glycan processing enzymes employ different targeting mechanisms for their spatial arrangement along the secretory pathway[END_REF] and for the synthesis of the hemicellulosic polysaccharide xyloglucan [START_REF] Chevalier | Subcompartment localization of the side chain xyloglucan-synthesizing enzymes within Golgi stacks of tobacco suspension-cultured cells[END_REF][START_REF] Driouich | Golgi-mediated synthesis and secretion of matrix polysaccharides of the primary cell wall of higher plants[END_REF].

AGPs AND EXTs: ROLE IN MORPHOLOGY AND DEVELOPMENT

Cell wall components are organized into networks of polysaccharides and glycoproteins which, apart from operating individually, are strongly interconnected [START_REF] Carpita | Structural models of primary cell walls in flowering plants: consistency of molecular structure with the physical properties of the walls during growth[END_REF][START_REF] Burton | Heterogeneity in the chemistry, structure and function of plant cell walls[END_REF][START_REF] Albersheim | Plant Cell Walls: from Chemistry to Biology[END_REF]. Indeed, it is widely acknowledged that cellulose microfibrils and hemicellulose constitute a primary network of polysaccharides, embedded into a second network made of pectic polysaccharides. Less often referred as such, O-Hyp cell wall proteins constitute the third network of the wall component. Bridges between these three networks do also exist and structural alteration occurring on a single cell wall component often affects overall cell wall architecture and integrity. Thus, structurally altered AGPs/EXTs weaken cell wall architecture (both covalently and non-covalently), and affect biological processes controlled by the cell wall compartment.

Indeed, most of the Arabidopsis mutants defective in one or more enzymes described above presented various developmental and morphological alterations. [START_REF] Van Hengel | Fucosylated arabinogalactan-proteins are required for full root cell elongation in Arabidopsis[END_REF] showed that the lack of fucose residue in the Arabidopsis mur1 mutant caused their roots to be shortened. This growth defect was due to structural modification of root AGPs [START_REF] Van Hengel | Fucosylated arabinogalactan-proteins are required for full root cell elongation in Arabidopsis[END_REF], as well as a result of altered rhamnogalacturonan-II synthesis, since the disorder was partially rescued by exogenous application of boric acid [START_REF] O'neill | Requirement of borate cross-linking of cell wall rhamnogalacturonan II for Arabidopsis growth[END_REF]. [START_REF] Liang | Biochemical and physiological characterization of fut4 and fut6 mutants defective in arabinogalactan-protein fucosylation in Arabidopsis[END_REF] showed that a deficiency in the genes AtFUT4 and AtFUT6 caused a reduction of root growth under saline stress conditions (see also [START_REF] Tryfona | Characterization of FUT4 and FUT6 α-(1-2)-Fucosyltransferases reveals that absence of root arabinogalactan fucosylation increases Arabidopsis root growth salt sensitivity[END_REF]. The lack of fucose residue was proposed to affect intramolecular interactions between AGPs and other wall components. Similarly reduced galactosylation of AGPs in reb1-1 mutant of Arabidopsis caused strong swelling of trichoblast cells as well as reduced root growth [START_REF] Andème-Onzighi | The reb1-1 mutation of Arabidopsis alters the morphology of trichoblasts, the expression of arabinogalactan-proteins and the organization of cortical microtubules[END_REF][START_REF] Nguema-Ona | The reb1-1 mutation of Arabidopsis. Effect on the structure and localization of galactose-containing cell wall polysaccharides[END_REF]. The Arabidopsis mutant atglcat14a, deficient in an AGP-specific GlcA GT, showed an abnormal increase in root and hypocotyl length, when compared to the wild type [START_REF] Knoch | A β-glucuronosyltransferase from Arabidopsis thaliana involved in biosynthesis of type II arabinogalactan has a role in cell elongation during seedling growth[END_REF]. Biochemical analysis in this mutant showed an alteration in the AGP composition and associated glycosidic linkages as compared to the wild type, suggesting that biochemical phenotype indirectly impacts cell elongation via an overall change in cell wall architecture and integrity. The mutation in AtGalT31A caused the arrest of the embryo development at the globular stage, while complementation of the mutant with AtGALT31A restored the wild type phenotype, thus linking the requirement of correctly glycosylated AGPs with the progression of embryogenesis beyond the globular stage [START_REF] Geshi | A galactosyltranferase acting on arabinogalactan protein glycans is essential for embryo development in Arabidopsis[END_REF]. However, a study of atgalt2 deficient Arabidopsis mutants showed that allelic mutant lines contained less Gal-T activity when compared to the wild type without displaying any significant alteration of the phenotype. [START_REF] Basu | Functional identification of a hydroxyproline-O-galactosyltransferase specific for arabinogalactan protein biosynthesis in Arabidopsis[END_REF] suggested that other Hyp-O Gal-Ts may compensate for the loss of AtGalT2, and that examination of these mutants under non-physiological conditions, or the production of multigene mutants within this gene family may reveal novel phenotypes. Recently, an unusual AGP (named APAP1) was found to be covalently linked to pectin rhamnogalacturonan-I and to arabinoxylans [START_REF] Tan | An Arabidopsis cell wall proteoglycan consists of pectin and arabinoxylan covalently linked to an arabinogalactan protein[END_REF]. Absence of APAP1 in the corresponding mutant led to an increased extractability of pectins and xylans, thus suggesting the alteration of its overall wall architecture. Apap1 mutants exhibited a significant increase in the height inflorescence stem, although the overall morphology was comparable to that of the wild type.

Arabidopsis EXT-deficient or EXT-altered mutants also presented various developmental and morphological alterations, due to an alteration in their overall wall architecture. [START_REF] Velasquez | O-glycosylated cell wall proteins are essential in root hair growth[END_REF] showed that disrupting the Pro hydroxylation and/or improper O-glycosylation impacted EXT ability to form covalent intra and inter-molecular network in the wall. Indeed, secondary helix conformation found in EXTs, required for normal catalysis of the di-isodityrosine bondages by wall peroxidases [START_REF] Held | Di-isodityrosine is the intermolecular cross-link of isodityrosine-rich extensin analogs cross-linked in vitro[END_REF], was altered in P4H-deficient and Ara-T-defective Arabidopsis mutants. The authors concluded that the absence, or the alteration of their Hyp-O-arabinosides, destabilized the EXT helical secondary structure, altering their ability to interact in the wall with other cell wall components, thus altering their structural function in muro. Interestingly, unlike in plants, the hydroxylated Pro residues of animal proteins are not glycosylated. Pro hydroxylation itself is sufficient for the conformational stability of animal Hyp-rich proteins such as collagen. This PTM is generally sufficient for proper functioning of such proteins. Indeed, Hyp stabilizes their triple helical structure at body temperature [START_REF] Kivirikko | Collagen hydroxylases and the protein disulfide isomerase subunit of prolyl 4-hydroxylases[END_REF][START_REF] Myllyharju | Prolyl 4-hydroxylases, the key enzymes of collagen biosynthesis[END_REF], and to date, no animal Hyp-containing proteins have been found to be glycosylated. O-glycosylation of Hyp is a rather plant-specific PTM, required for the proper functioning of plant Hyp-containing proteins including HRGPs. While the enzymes hydroxylating Pro residues on AGPs and EXTs are similar to mammalian systems, the ones that initiate and elongate the glycan chains of these HRGPs are unique to plants.

Furthermore, the study of the Arabidopsis rsh mutant, deficient in an EXT (RSH/EXT3) has also shown the importance of EXTs for normal plant cell wall architecture and function in development. RSH/EXT3 is an Arabidopsis EXT which was shown to play a key role during cytokinesis, by controlling cell plate formation [START_REF] Hall | The cell wall hydroxyproline-rich glycoprotein RSH is essential for normal embryo development in Arabidopsis[END_REF][START_REF] Cannon | Self-assembly of the plant cell wall requires an extensin scaffold[END_REF]. RSH/EXT3 positively charged was proposed to interact with negatively charged pectins to create a template for newly synthesized cell walls.

AGPs AND EXTs: ROLE IN BIOTIC STRESS

In addition to their role in morphology and growth, and EXTs were shown to play key roles in plant responses to biotic stress. [START_REF] Esquerré-Tugayé | Cell surfaces in plant-microorganism interactions: I. A structural investigation of cell wall hydroxyproline-rich glycoproteins which accumulate in fungus-infected plants[END_REF] and [START_REF] Esquerré-Tugayé | Cell surfaces in plant-microorganism interactions: II. Evidence for the accumulation of hydroxyproline-rich glycoproteins in the cell wall of diseased plants as a defense mechanism[END_REF] have shown that plants respond to fungal infection by an increased secretion of HRGPs. Both AGPs (reviewed in [START_REF] Nguema-Ona | Arabinoga-lactan-proteins in root microbe interactions[END_REF] and EXTs were later on shown to play various roles in this response to pathogens. More specifically root apices and exudates were found to be enriched in AGPs (Figure 2), their chemical composition being different depending on both root tissues and plant species [START_REF] Dolan | An AGP epitope distinguishes a central metaxylem initial from other vascular initials in the Arabidopsis root[END_REF][START_REF] Durand | The organization pattern of root border-like cells of Arabidopsis is dependent on cell wall homogalacturonan[END_REF][START_REF] Cannesan | Effect of arabinogalactan proteins from the root caps of pea and Brassica napus on Aphanomyces euteiches zoospore chemotaxis and germination[END_REF]. AGPs have long been suspected to be involved in root-microorganisms interaction including symbiotic associations [START_REF] Scheres | Sequential induction of nodulin gene expression in the developing pea nodule[END_REF][START_REF] Balestrini | Differential localization of carbohydrate epitopes in plant cell walls in the presence and absence of arbuscular mycorrhizal fungi[END_REF][START_REF] Berry | Arabinogalactan proteins are expressed at the symbiotic interface in root nodules of Alnus spp[END_REF]. For instance, alteration of AGP synthesis or secretion was shown to inhibit Rhizobium sp. YAS34 attachment to the root surface of Arabidopsis thaliana [START_REF] Vicré | Root border-like cells of Arabidopsis. microscopical characterization and role in the interaction with rhizobacteria[END_REF]; Figure 2). [START_REF] Xie | A plant arabinogalactanlike glycoprotein promotes a novel type of polar surface attachment by Rhizobium leguminosarum[END_REF] further demonstrated that AGPs from pea root exudates promote polar orientation and adhesion of Rhizobium leguminosarum. However, AGP functioning in root defense remained speculative until recently, as demonstrated by the study of Cannesan et al. ( 2012) on pea roots. The authors have shown that AGPs isolated from root cap (RC) and border cells are strong attractants of zoospores of the pathogenic oomycete Aphanomyces euteiches in vitro [START_REF] Cannesan | Effect of arabinogalactan proteins from the root caps of pea and Brassica napus on Aphanomyces euteiches zoospore chemotaxis and germination[END_REF]. The AGPs also inhibited in vitro cyst germination and the subsequent mycelium growth and propagation. These findings highlight the important contribution of AGPs in Aphanomyces euteiches root infection and show for the first time that AGPs are involved in controlling root-pathogenic oomycete interaction (see also [START_REF] Nguema-Ona | Arabinoga-lactan-proteins in root microbe interactions[END_REF].

Extensins have also been shown to play a significant role in plant defense and protection against bioagressors. Immunolocalization studies using the mAbs JIM 20 and JIM 11 revealed the abundant presence of EXT epitopes in cell walls of the resistant wax gourd cultivar to Fusarium oxysporum as compared to susceptible cultivar [START_REF] Xie | Immunohistochemical analysis of cell wall hydroxyproline-rich glycoproteins in the roots of resistant and susceptible wax gourd cultivars in response to Fusarium oxysporum f. sp. Benincasae infection and fusaric acid treatment[END_REF]. In addition, elicitation with fusaric acid

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or infection with F. oxysporum caused important decrease of the immunofluorescence in both resistant and susceptible cultivars. Also, elicitation of grapevine callus cultures resulted in both the insolubilization of a specific 89.9 kD EXT and the induction of the catalytic activity of an EXT peroxidase [START_REF] Jackson | Rapid deposition of extension during the elicitation of grapevine callus cultures is specifically catalyzed by a 40-kilodalton peroxidase[END_REF]. Furthermore, EXTs have been shown to accumulate in response to the pathogenic oomycete Sclerospora graminicola in resistant pearl millet cultivar [START_REF] Deepak | Role of hydroxyproline-rich glycoproteins in resistance of pearl millet against downy mildew pathogen Sclerospora graminicola[END_REF]. The high content of EXTs was tightly correlated with an increase in the levels of isodityrosine and H 2 O 2 suggesting cell wall strengthening in the resistant cultivar presumably to limit Sclerospora graminicola penetration and tissue infection.

More recently, the implication of EXTs as part of the innate immune response of root border-like cells (BLCs) of Arabidopsis thaliana and Linum usitatissimum has been by [START_REF] Plancot | Deciphering the responses of root border-like cells of Arabidopsis thaliana and Linum usitatissimum to pathogen derived elicitors[END_REF]. Root border cells from plants such as pea, soybean, or cotton are highly specialized in root protection and production of various anti-microbial compounds [START_REF] Hawes | The role of root border cells in plant defense[END_REF][START_REF] Hawes | Root caps and rhizosphere[END_REF]. Although such a function still needs to be clearly established for BLCs, a class of border cells that is relatively less studied. Recent work suggests a role for these BLCs in root defense [START_REF] Driouich | Root border cells and secretions as critical elements in plant host defense[END_REF]. [START_REF] Plancot | Deciphering the responses of root border-like cells of Arabidopsis thaliana and Linum usitatissimum to pathogen derived elicitors[END_REF] have also demonstrated that, in response to elicitors (e.g., flagellin 22), a significant increase in the production of H 2 O 2 was detected in root BLCs together with a strong activation of genes involved in EXT biosynthesis and crosslinking. This is consistent with the finding of [START_REF] Velasquez | O-glycosylated cell wall proteins are essential in root hair growth[END_REF] which showed that EXTs biosynthesis genes were co-expressed with peroxidase genes. Interestingly, treatment with elicitors also caused modifications in the distribution of EXT epitopes within cell walls of root BLCs (Figure 2). The effect of elicitation on the pattern of labeling with the mAb LM1 was shown to depend on both the nature of elicitors and plant species. Elicitation with flagellin 22 almost abolished immunostaining of LM1-recognized epitopes reflecting reorganization of the EXT network within the cell wall due to extensive cross-linking. Such an oxidative crosslinking of EXTs may result in a reinforced glyco-network that enhances physical properties of the cell wall in both Arabidopsis thaliana and L. usitatissimum [START_REF] Plancot | Deciphering the responses of root border-like cells of Arabidopsis thaliana and Linum usitatissimum to pathogen derived elicitors[END_REF]. This reinforcement of the cell wall would in turn limit/prevent penetration and progression of pathogens within root tissues.

Together these findings strongly suggest that AGPs and EXTs are key components of root protection, and more specifically of root border cells. However, further investigations where root border cells are directly challenged with specific pathogens are needed to provide a biological context for these observations. So far, the immune response in roots remains poorly understood and appears to be highly complex and cell-type specific [START_REF] Millet | Innate immune responses activated in Arabidopsis roots by microbe-associated molecular patterns[END_REF][START_REF] Cannesan | Effect of arabinogalactan proteins from the root caps of pea and Brassica napus on Aphanomyces euteiches zoospore chemotaxis and germination[END_REF][START_REF] Balmer | More beneath the surface? Root versus shoot antifungal plant defenses[END_REF]. To our knowledge, the only study that clearly demonstrated the relationship between the production of EXT and plant resistance to pathogens was performed in leaf tissues [START_REF] Wei | Extensin over-expression in Arabidopsis limits pathogen invasiveness[END_REF]. In this study, over-expression of the EXT1 gene in leaves of Arabidopsis thaliana clearly limits the spreading of the pathogenic bacteria Pseudomonas syringae DC3000 within the tissues. Subsequently, the infection symptoms are significantly reduced. It is clear that the implication of EXT and AGP populations in root protection is far from being fully understood and more studies are needed to elucidate the role of individual HRGPs/or their glycans in resistance to biotic stress.

CONCLUSION AND OUTLOOK

Like N-glycoproteins, cell wall O-glycoproteins, AGPs and EXTs, are synthesized, assembled and modified within the secretory system. Their glycans, although structurally different and diverse, play a major role in their stability, activity and function. Both types of glycoproteins were shown to be involved in the control of many biological activities and physiological processes in various plant species. However, the specific role of each glycan type and the associated oligosaccharides in biological processes is not known. One of the important challenges for the future is to elucidate the contribution of each of these glycans (and associated sugars) in regulating cell growth, development and adaptation of plants to environmental stresses, either biotic or abiotic. Even more challenging is the search for potential relationships between a given glycan/oligosaccharide structure and a given function in a given tissue. For instance, how specific O-glycan structures regulate morphology, growth or biotic interactions of certain root cell types with microbes is a major issue that deserves further attention.

Recently, a number of the carbohydrate active enzymes involved in N-and O-glycan metabolism have been identified and have advanced our understanding of the biosynthetic machineries of these glycoproteins. How these enzymes are spatially organized and assembled within different compartments of the endomembrane system (i.e., specifically within Golgi subcompartments and Golgi-derived secretory vesicles) and how these are regulated during development is not fully understood and remains an exciting research opportunity for the future.

FIGURE 1 |

 1 FIGURE 1 | Typical structure of plant N -and O-glycans from cell wall proteins. (A) Specific complex-type N-glycans attached to plant glycoproteins.This N-glycan results from the action of a plant-specific repertoire of glycosyltransferases that lead to the formation of a glycan bearing plant-specific glyco-epitopes such as a core β-1,2-xylose; a core α-1,3-fucose and a Lewis a antennae[START_REF] Lerouge | N-glycoprotein biosynthesis in plants: recent developments and future trends[END_REF][START_REF] Wilson | Analysis of Asn-linked glycans from vegetable foodstuffs: widespread occurrence of Lewis a, core α-1,3-linked fucose and xylose substitutions[END_REF][START_REF] Bardor | Immunoreactivity in mammals of two typical plant glycoepitopes, core α-(1,3)fucose and core xylose[END_REF] Bardor et al., , 2011)). The N-glycan structures presented here are drawn according to the symbolic nomenclature adopted by the Consortium for Functional Glycomics(Varki et al., 2009). (B) Schematic representation of O-glycans (type II arabinogalactan) attached to AGPs. These glycans predominantly consist of arabinose and galactose. Minor

  FIGURE 1 | Typical structure of plant N -and O-glycans from cell wall proteins. (A) Specific complex-type N-glycans attached to plant glycoproteins.This N-glycan results from the action of a plant-specific repertoire of glycosyltransferases that lead to the formation of a glycan bearing plant-specific glyco-epitopes such as a core β-1,2-xylose; a core α-1,3-fucose and a Lewis a antennae[START_REF] Lerouge | N-glycoprotein biosynthesis in plants: recent developments and future trends[END_REF][START_REF] Wilson | Analysis of Asn-linked glycans from vegetable foodstuffs: widespread occurrence of Lewis a, core α-1,3-linked fucose and xylose substitutions[END_REF][START_REF] Bardor | Immunoreactivity in mammals of two typical plant glycoepitopes, core α-(1,3)fucose and core xylose[END_REF] Bardor et al., , 2011)). The N-glycan structures presented here are drawn according to the symbolic nomenclature adopted by the Consortium for Functional Glycomics(Varki et al., 2009). (B) Schematic representation of O-glycans (type II arabinogalactan) attached to AGPs. These glycans predominantly consist of arabinose and galactose. Minor

FIGURE 2 |

 2 FIGURE 2 | Root cap (RC) and border cells are both enriched in AGP and EXT epitopes. (A) Immunostaining of AGP epitopes at the surface of RC and border-like cells of Brassica napus with the mAb JIM8 (from Cannesan et al., 2012 with permission). Root border-like cells are produced and released from the RC. (B) Micrographs showing the association between root border-like cells from Arabidopsis thaliana and Rhizobium sp. YAS34-GFP. The GFP-expressing bacteria appear green at the root surface (from Vicré et al., 2005 with permission). This association is AGP-dependant as demonstrated in Vicré et al. (2005). (C) Fluorescent micrographs of root border-like cells from flax (Linum usitatissimum) immunostained with the monoclonal antibody LM1 specific for EXT epitopes (from Plancot et al., 2013 with permission). Bars = 20 μm (A), 50 μm (B), and 8 μm (C). BLCs, border-like cells; M, mucilage; RC, root cap.

Table 1 | Known enzymes involved in plant N -glycans and O-cell wall glycan biosynthesis. AGP glycan biosynthetic enzymes CAZy family Protein name Origin Reference

 1

	Hydroxyproline	GT31	At GALT2	Arabidopsis thaliana	Basu et al. (2013)
	O-galactosyltransferase
	β-1,3-galactosyltransferase	GT31	At 1g77810	Arabidopsis thaliana	Qu et al. (2008)
	β-1,6-galactosyltransferase	GT31	At GalT31A	Arabidopsis thaliana	Geshi et al. (2013)
	-	GT29	At GalT29A	Arabidopsis thaliana	Dilokpimol et al. (2014)
	Arabinofuranosyltransferase	GT77	RAY1	Arabidopsis thaliana	Gille et al. (2013)
	β-glucuronosyltransferase	GT14	At GlcAT14A	Arabidopsis thaliana	Knoch et al. (2013)
	α-1,2-fucosyltransferase	GT37	At FUT4	Arabidopsis thaliana	Wu et al. (2010)
	-	GT37	At FUT6	Arabidopsis thaliana	Wu et al. (2010)
	Extensin glycan biosynthetic	CAZy family	Protein name	Origin	Reference
	enzymes
	Serine O-galactosyltransferase	unknown	SGT1	Chlamydomonas reinhardtii;	Saito et al. (2014)
				Arabidopsis thaliana
	Arabinosyltransferase	GT77	RRA3	Arabidopsis thaliana	Velasquez et al. (2011)
	-	GT77	XEG113	Arabidopsis thaliana	Gille et al. (2009)

N -glycan biosynthetic enzymes CAZy family Protein name Origin Reference

	Oligosaccharyltransferase		OST	Arabidopsis thaliana; Oryza	Farid et al. (2013), Qin et al. (2013)
				sativa
	α-glucosidase I		GCS I	Arabidopsis thaliana	Boisson et al. (2001)
	α-glucosidase II		GCS II	Solanum tuberosum	Taylor et al. (2000)
	α-mannosidase I		MNS 1-3	Arabidopsis thaliana	Liebminger et al. (2009)
	N-acetylglucosaminyltransferase I	GT13	GnT I	Arabidopsis thaliana;	Bakker et al. (1999), Strasser et al. (1999a),
				Nicotiana tabacum; Solanum	Wenderoth and von Schaewen (2000)
				tuberosum
	α-mannosidase II		GM II	Arabidopsis thaliana	Strasser et al. (2006)
	N-acetylglucosaminyltransferase II	GT16	GnT II	Arabidopsis thaliana	Strasser et al. (1999b)
	α-1,3 fucosyltransferase	GT10	α-1,3-FuT	Vigna radiata; Arabidopsis	Leiter et al. (1999), Wilson et al. (2001a),
				thaliana; Medicago sativa	Sourrouille et al. (2008)

β-1,2-xylosyltransferase GT61 β-1,2-XylT Arabidopsis thaliana

[START_REF] Strasser | Molecular cloning and functional expression of β-1, 2-xylosyltransferase cDNA from Arabidopsis thaliana[END_REF]

,

[START_REF] Pagny | Structural requirements for Arabidopsis β-1,2-xylosyltransferase activity and targeting to the Golgi[END_REF]

,

[START_REF] Bencúr | Arabidopsis thaliana β-1,2-xylosyltransferase: an unusual glycosyltransferase with the potential to act at multiple stages of the plant N -glycosylation pathway[END_REF]

β-1,3-galactosyltransferase GT31 β-1,3-GalT Arabidopsis thaliana

[START_REF] Strasser | A unique 1,3-galactosyltransferase is indispensable for the biosynthesis of N-glycans containing Lewis a structures in Arabidopsis thaliana[END_REF]

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ACKNOWLEDGMENTS

Part of the work described in this review was supported by the University of Rouen, and the GRR-Végétal-Agronomie-Sol-Innovation of Haute Normandie, Le Fonds Européen de Développement Regional (FEDER), and the ANR. We are grateful to our lab members for their active implication in various "Plant Glycobiology" projects and to Dr. C. Santaella (CNRS Cadarache-Université de Marseille) for her stimulating discussions during the course of our root-microbe interaction studies. The authors are thankful to Dr. J. P. Moore (University of Stellenbosch-Republic of South Africa) for careful reading of the manuscript.

Conflict of Interest Statement:

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.