Enrico Bodo
email: en-rico.bodo@uniroma1.it

Giulia Bovolenta

Chloe Simha

Riccardo Spezia
email: riccardo.spezia@sorbonne-universite.fr

On the formation of propylene oxide from propylene in space: gas-phase reactions

On the formation of propylene oxide from propylene in space: gas phase reactions.

Enrico Bodo • Giulia Bovolenta • Chloe Simha • Riccardo Spezia the date of receipt and acceptance should be inserted later Abstract In the present article we have investigated the possibility of forming propylene oxide (PO) from propylene (PE) by bi-molecular reactions. Propylene oxide is the first chiral molecule observed in the interstellar medium, and studying the thermodynamics and kinetics of formation can suggest possible synthetic routes. We have focused our attention on gas phase reactions, and the presence of an environment is discussed in particular for the possibility of forming it by association reactions. In particular, we have considered radical and ion-molecule reactions. Results show that the main gas-phase route to PO formation is represented by ion-molecule reactions which turn out to be compatible with astrophysical conditions, notably: PE + O + and PE + HO + 2 . Their final product is not PO, but its ionized variant PO + that can be neutralized by electron capture. The only thermodynamically and kinetically allowed reaction which can directly lead to neutral PO is a collision of PE with a singlet-excited OH + but two competing reactions (leading to PE + and PO + ) are thermodynamically favored and thus more plausible in space.

Introduction

In last years, thanks to the rapid development of radio-telescopes and space missions, the number of complex organic molecules (COMs) detected in space has been an incredible growth. In particular, the interstellar medium (ISM) was found to be populated of different organic molecules, like for example propylene [1], formamide [2], cyanic or isocianic acids [3,4]. Restraining to ISM, seven new molecules were reported in 2017 and six in 2018 and in first months of 2019 already two new COMs (Z-cyanomethanimine [5] and glycolonitrile [6]) have been added to the family of known astromolecules, showing how the complexity of species present in the ISM is not limited to simple and elementary atoms or diatomics. Recently, the propylene oxide (C 3 H 6 O) was detected in Sagittarius B2 [7] and it is a particularly intriguing molecule since it was the first chiral molecule ever detected. Although its enantiomeric composition was not measured, its presence in the ISM can let us surmise that a reservoir of chiral molecules exists and that it is formed outside the earth, being a possible grain for further chiral discrimination in the universe.

While many molecules were detected, much less is known on how they were formed. Generally, two classes of source are discussed and considered: (i) formation by gas phase reactions; (ii) formation in the interstellar grains. While in last years some experimental evidences have shown that some molecules can be formed on icy grains under conditions which mimic reasonable astrophysical ones, [8][9][10][11][12] the possibility of gas-phase reactions as responsible of their origin cannot be excluded even for complex molecules. [13][14][15] The fundamental problem at the basis of the synthesis of such molecules is that the ISM is characterized by very low temperatures (in 10 -70 K range) and densities (10 4 -10 6 molecules per cubic centimeter in densest nebulae). [START_REF] Roueff | Gas-Phase Chemistry in Space[END_REF][START_REF] Ferrière | [END_REF] This is at the origin of two aspects which must be taken into account when proposing synthetic pathways. First, the reactions must be exothermic and without an activation barrier (or a very low one), since temperature strongly limits the kinetic energies required to overcome reaction barriers (10 K and 70 K will correspond to 0.02 and 0.1 kcal/mol, respectively). Secondly, in the case of bi-molecular associations (e.g. reactions like A + B → C) the system must have a way to dissipate its energy before dissociating back to reactants. Two processes can stabilize the associated species: collisional deactivation and/or spontaneous emission of a photon (radiative association). [14,18] These two processes are in competition with the unimolecular fragmentation, which has, by definition, enough energy to occur. Under extreme vacuum conditions the first process is not likely to occur, therefore, only radiative association is possible. The rate of radiative association depends on different factors (number of atoms, dipole moment, density of vibrational states), but for molecules of about 10 atoms in size it turns out very likely to be slower than unimolecular dissociation, [19] as we have estimated recently for urea. [20] In other words, the most efficient route for forming a molecule out of a binary collision, is a reactive scattering processes (such as A + B → C + D) where the excess energy due to the formation of the more stable products can be converted into translational energy. Clearly, if the density of the environment is high enough, the direct association A +B → C becomes a competitive route of formation of the specie C because its internal energy can be dissipated by interacting with nearby atoms/molecules: in this case the process overall rate is characterized by its collisional rate with the environment. [14] Using theoretical chemistry methods represents a powerful approach to understand the various formation/depletion channels of relatively complex molecular species, both in the gas phase and on the grain surfaces. Such approach has been applied to investigate possible reaction pathways for the synthesis of different COMs, [21] like e.g. formamide, [22][23][24][START_REF] Saitta | Proc. Nat. Acad. Sci. USA[END_REF] methanol, [START_REF] Rimola | [END_REF] acetamide, [23] urea, [20] formaldehyde, [27,[START_REF] Rimola | [END_REF] acetone, [27] acetaldehyde [27,28], glycolaldehyde, [29] acetic acid [29], methyl formate [30], hydroxyacetonitrile [31], formic acid [29] or glycine. [11,32,33,28] Here we focus on the possibility of obtaining propylene oxide by gas phase ion-molecule or radical reactions. Note that more recently it was shown that supplementary insights can be obtained by chemical dynamics [34][35][36]: these methods need information obtained from the study of thermodynamics and energy barriers which can be obtained accurately only from highly-correlated quantum chemistry calculations.

By inspecting the astromolecule list one can notice that propylene was also been observed, with a relatively high abundance [1]. This can be reasonably thought as a viable precursor of propylene oxide. We have thus considered the possible reactions between propylene and other simple molecular species with relatively high abundances, such as: O, OH, OH + , HO 2 , HO + 2 . Column densities of the considered species are reported in Table 1 with corresponding references. We have also considered the possibility of reaction with O + which is likely to be formed in the ISM by the simple reaction: [37]

H + + O → H + O +
In particular, we focused on both radical-neutral and ion-neutral reactions, given that the latter reactions generally have a very low activation energy due to the attractive ion-dipole potentials. However, radical-neutral reactions were found recently to be a possible route to synthesize COMs in the gas phase, as for formamide glycolaldehyde, acetic acid and formic acid [24,29]. In the present work, we studied reaction thermodynamics and kinetics in the gas phase by means of quantum chemistry calculations, providing insights of elementary reactions in absence of any environment, so focusing on intrinsic properties.

Computational Details

All calculations have been performed using Gaussian16 [44] and Orca. [45] Isolated ground state molecules partaking to the various reactions have been geometryoptimized using the following methods: B3LYP/cc-pVTZ [46,47], B2PLYP-D3/augcc-pVTZ [48,49], MP2/aug-cc-pVTZ [50] and PBEh-3c [51] where the respective unrestricted schemes were used for open shell species. Singlet, open-shell intermediates have been computed using the unrestricted, broken symmetry formalism. The molecular energy at the CCSD(T)/aug-cc-pVTZ [52] has then been evaluated using the MP2 geometries. B3LYP was used because it is well known to provide reasonable geometries, MP2 and CCSD(T) are somehow the standard in astrochemistry, [22,23,20] and B2PLYP-D3 gives excellent thermodynamics and was used recently by Skouteris et al. in astrochemical related radical reactions. [29] In order to investigate the reaction paths and to evaluate the possible presence of barriers along them, we have also performed many different scans of the internal coordinates. Generally these scans are obtained by imposing a constrain on one coordinate and optimizing all the others (relaxed PES scan). Since the optimizations have to be repeated for very many different geometries and in order to make our computation efficient, we have adopted two different simplified schemes for the relaxed scans. For the radical reactions, we have performed the entire computations with the B3LYP/cc-pVTZ method. For the ionic reactions, where the energy differences are much larger, we have employed the PBEh-3c method for an even more efficient evaluation. The thermodynamic reliability of the PBEh-3c method, for the molecules under study, can be seen by looking at the data reported in Table 2 where it performs almost like the much more expensive B2PLYP-D3 approach.

Results

Thermodynamics

In order to model the formation of the PO molecule, we have taken into considerations reactions that involve its obvious precursor that is PE. As possible reactive partners we have obviously taken into consideration several oxygen containing species that have a sizable abundance in the ISM. Among the possible oxygen bearing molecules we have only considered radicals and ions since neutral closed shell species do present high activation barriers towards the double bond addition. This means that we have not considered reactions with water or CO which are ubiquitous and abundant components of the ISM. For example, a set of preliminar computations has shown that the gas phase addiction of water to the double bond of PE shows a barrier of more than 60 kcal/mol. Our selection of oxygen bearing molecules, thus, includes the O, OH and OOH radicals and their respective positive ions. Ions such as CO + and H 2 O + have also been considered, but preliminary calculations have shown the reaction to be nearly impossible because the former has a very high dissociation energy while the latter presents an unfavorable reaction mechanism given that H + 2 has to be eliminated after oxygen addiction.

Table 2 reports the energy difference with zero-point vibrational energy (ZPE) corrections between products and reactants of the various possible routes we have considered for PO formation. The two reactions 1 and 4 are two exothermic association processes. Actually the first one is the well known reaction of oxygen addiction to an olefin. In the context of astrochemistry, these two routes are likely to occur either within a high density environments where frequent collisions processes can remove the excess energy from the molecular complex or by radiative association. Reaction 2 is an endothermic neutral-radical process which involves Energetic values are obtained at different levels of theory and, assuming that CCSD(T) is the most accurate one, we can provide some method comparison. Mean absolute error (MAE) was used to provide an overall evaluation. We can notice that DFT provides better results than MP2. Interestingly, cheaper methods like B3LYP and PBEh-3c perform very well, with results not far from more expensive B2PLYP-D3. The former methods are thus used to perform specific scans in the following studies of reaction pathways.

Radicalic Reactions

Among the radical reactions, only 1 and 3 have a favorable thermodynamics (∆ E < 0). Nevertheless, we shall discuss in details all three radical-neutral reactions. The fact that the reaction requires an inter-system crossing (generally a slowly occurring process) and that the singlet complex 1 [PE-O] requires an energetic stabilization (either from the environments or by photon emission), makes this reaction a rather unlikely route to PO formation under astrophysical conditions. Furthermore, PA is more stable than PO and following the so-called "minimum energy principle" in astrochemistry [53,54] PA should be obtained.

3.2.2

The PE + OH( 2 Σ) reaction.

This reaction is globally endothermic by at least 19 kcal/mol (see Table 2), therefore almost impossible under astrophysical conditions. At difference with the previous case, the reaction takes place on a single PES of doublet multiplicity without the need to have an inter-system crossing. In addition, the reaction has a barrier along the exit channel due to the high dissociation energy of the OH bond which has to be broken in order to release H. This "late" transition state is characterized by a structure where the incipient formation of the epoxide is apparent as shown by the structure reported in Figure 3. The energy of this transition state is around 30 kcal/mol higher than the entrance channel thereby making the collision energy required to for the desired product even larger than the 20 kcal/mol due to endothermicity.

The PE + HO

2 ( 2 A ) reaction.
The global reaction with hydroperoxide radical (OOH) is exothermic and therefore it appears as a possible realistic formation channel of PO. The ground state of OOH is a doublet and so the reaction to form PO has to proceed on a single PES of doublet multiplicity. Although the reaction seems, in principle, quite straightforward, the ground state of OOH ( 2 A ) is not reactive toward the double bond [55,56]. This is the consequence of a "wrong" symmetry of the singly occupied molecular orbital that, in the ground state, is perpendicular to the radical plane. An electronic rearrangement of the electrons of OOH into its first excited configuration ( 2 A ), where the singly occupied orbital is in the plane, makes the radical reactive toward to the double bond of PE. The energy required for the electronic rearrangement results in a repulsive interaction between the ground state OOH ( 2 A ) and PE and hence, in the emergence of a barrier in the entrance channel of the reaction. The ground state potential due to its repulsive shape, crosses the excited 2 A PES. The crossing point between the 2 A and 2 A 1 PES's (actually a conical intersection, CI) can be localized around 16 kcal/mol above the entrance channel as reported in Figure 4 where the entire PES for the relevant reaction is shown. In addition to the first, a second barrier appears on the ground state PES in the exit channel before the formation of PO. The height of this second barrier is about 10 kcal above the ground state entrance channel, but about 6 kcal lower than the excited state one. As a consequence of the above electronic Fig. 4 PES of the reaction PE + HO 2 → PO + OH as obtained at the UB3LYP/cc-pVTZ level of theory. The excitation energy of the isolated radical on the left has been taken from ref. [57] structure problem, the reaction with the OOH radical does not appear as a viable route to the formation of PO in the ISM. The only possibility for this reaction to occur efficiently at low temperature is an electronic excitation (of about 0.9 eV, due to visible radiation) of the reactants from the 2 A to the 2 A state. For this reason this reaction can be effective only in region of the ISM where a sufficient irradiation occurs.

Ion-molecule Reactions

All the ion-molecule reactions, except reaction 8 are exothermic thereby representing viable routes of formation of PO in the ISM. As it often happens for ion molecule reactions, and as we shall see in below, these reactions are barrierless and the pathways that leads to product formations are straightforward.

The

PE + O + ( 2 P ) reaction.
Reaction 4 proceeds by association from the reactants to the charged product PO + , without any stable intermediate. In analogy to the reaction with atomic neutral oxygen, this is a typical association process which needs the releasing of the excess energy through collisions or photon emission. After association, the cation should combine with an electron and form the neutral PO, so that the overall process is:

PE + O + → PO + + hν PO + + e -→ PO
Radiative association processes are often inefficient, but their rate tends to increase with the stabilization energy of the complex, the dipole of the system and the number of atoms in the final product (the key factors that determine the density of available final vibrational states [58]). Given that the stabilization energy of the PO + complex exceeds 10 eV and that the complex contain 10 atoms we can estimate the reaction rate to be of the order of 10 -9 cm 3 s -1 if not larger. This value is larger than what measured, for example, by Gerlich and co-workers [59] for the formation of C 3 HD + , C 3 HD + 2 and C 3 D + 3 and thus radiative association cannot be disregarded as possible formation mechanism. Note that the most stable electronic configuration of O + is a 4 S (that cannot associate directly with PE) therefore the likelihood of this process depends also on the abundance of 2 P oxygen.

Neutralization of PO + can occur directly by combination with an electron, but also via a charge exchange process with other species present in the ISM. In this case the ionization energy (IE) drives the thermodynamics of the process:

PO + + A → PO + A +
where A must have an IE smaller than that of PO, which is 10.22 eV. [START_REF] Lias | NIST Chemistry WebBook[END_REF] This is a relatively low value, such that most abundant species in the ISM have higher IE. Between the species considered in the reaction studied here, interestingly only PE has a lower IE (9.73 eV). [START_REF] Lias | NIST Chemistry WebBook[END_REF] Radical species observed in the ISM have lower IE, like formyl radical (8.12 eV) [START_REF] Lias | NIST Chemistry WebBook[END_REF] or cyanoethynyl radical (4.3 eV). [START_REF] Lias | NIST Chemistry WebBook[END_REF] Also hydrocarboxyl radical has a lower IE (8.2 eV) [START_REF] Berkowitz | [END_REF] and interestingly only the charged HOCO + species was observed in the ISM. [62]

The PE + OH

+ ( 1 ∆) reaction.
The reaction with OH + ( 1 ∆) is exothermic and produces two possible products depending where the charge is localized in the exit channel. The lowest energy one is the channel PO + + OH which corresponds to a globally singlet state made by two doublet radicals coming from the homolytic dissociation of the O-H bond. The one with higher energy (around 80 kcal/mol asymptotically) corresponds to PO + OH + , requiring an heterolytic dissociation of the O-H bond. A scheme of the energies involved in the four ionic reaction is reported in the left panel of Figure 5. As it is clear from this figure, the (non-reactive) charge exchange process PE + OH + → PE + + OH is a "parasitic" channel with a higher exothermicity, thereby favored by thermodynamics alone. However, the formation of PO + by PE + OH + → PO + + H is energetically competitive and might represent a possible product of the reaction depending on the mutual orientation of the two colliding partners. In order to explore the pathways bringing the collision to form PO + or PO and to ensure that no barriers are present, we have decided to perform a scan of the potential energy surface (PES) in the entrance and in the exit channel. First of all, the complex of PO with OH + has been optimized. Starting from this geometry, a restricted PBEh-3c series of calculation has been performed at different values of the relevant reactive coordinates. At each of the coordinate values the entire geometry of the system has been optimized in order to find the minimum energy path along the PES: to describe the PES in the exit channel we have gradually increased the O-H coordinate. The results are reported in the right panel of Figure 6 in black; to describe the entrance channel we have to gradually increase one of the C-O distances. Since there are two possible C-O distances we have produced two PESs. An additional constrain (apart from the reactive coordinate) that we had to enforce in order to compute the entrance channel PES was to keep the direction of approach of the OH molecule along a straight line. Therefore, for both C-O distance scans we have also kept fixed the C-C-O angle. The two scans along both C-O bonds have produced very similar results and we limit ourselves here to present the results pertaining to the inner carbon atom that are reported in the left panel of Figure 6.

Since a restricted calculation naturally produces an heterolytic bond cleavage, at each of the optimized geometries on the PES, we have performed an additional "broken symmetry" unrestricted calculation to obtain the energy of the homolytic dissociation channel (that is the actual ground state of the system). The two broken symmetry PES for both the entrance and exit channels have been also reported in Figure 6 where the data in red correspond to the homolytic bond cleavage. For short distances the red and black PES are identical and we reported the data only in black color. The reason why the energies do not perfectly match those in Table 2 or in Figure 5 lies in the fact that broken symmetry calculations are only an approximation to the true PESs that should be computed by means of a multiconfigurational scheme and also in the use of angular constraints that alter the true asymptotic energy. Nevertheless these qualitative calculations are sufficient to ensure that there are no barriers along the reaction coordinates. We point out that, although the reaction processes are barrierless, the collision between PE and OH + remains unlikely to provide an efficient route to PO formation because of the presence of a non reactive, low energy charge-exchange product (PE + + OH). In addition, even if PO + is produced, it is necessary a fur-ther electron capture process, since the energetically favored product of a reactive PE + OH + collision is PO + and not neutral PO.

In addition, we have to remark that the ground state electronic configuration of OH + is a 3 Σ (that cannot associate or react directly with PE, unless a very unlikely inter-system crossing takes place) therefore the likelihood of this process depends also on the abundance of 1 ∆ molecule.

The PE + HO

+ 2 ( 1 A) reaction.
The discussion of this reaction is substantially similar to what we have already said for PE+OH + . The main differences can be easily grasped by inspection of the right panel of Figure 5. The exit channel that produces directly neutral PO is highly endothermic. The only useful outcome of this reaction for producing PO is in the possibility of forming its ionized precursor PO + that, then, has to be neutralized by electron capture. From our calculations, and contrarily to what we had found for the reaction with OH + , it turns out that the final energy of the reactive PO + +OH channel is lower than the non-reactive charge exchange one that leads to PE + +OOH. Therefore the collision with OOH + can represent an actual viable route to the formation of PO + .

Conclusions

In the present work, we have investigated by means of quantum chemistry calculations the possibility of forming propylene oxide (PO) from propylene (PE) in the gas phase. In particular, conditions close to the astrophysical ones are discussed: extreme low temperature and density. Bimolecular radical and ionic process have been considered and, as expected, the latter ones are more likely to occurr, in terms of both formation energies and kinetic barriers. Among the bimolecular radical reactions, the collision of PE with HO 2 , might represent a possible route of formation once we assume that there exists sufficient UV irradiation to trigger the reaction that proceeds only on an excited state PES. Radiative association processes have also been considered. They are strongly exothermic and barrierless, thereby representing a possible formation route of PO, but competition with unimolecular fragmentation (dominant at low densities) is an important limiting factor for the viability of such processes. The presence of a sufficiently dense environment which removes the excess energy can promote such reactions.

Ion-molecule reactions represent the most likely formation routes of PO in the ISM (at least in a pure gas-phase chemistry). In particular, we have found that the PE + HO + 2 collision, which leads directly to the formation of PO + represents an important pathway to PO once an ensuing recombination with an electron (electron capture or transfer from another species) occurs. The PE + OH + channel has also been analyzed and turned out to be able to form directly both PO + and PO with barrierless processes, but a competitive charge exchange route leading to PE + and OH turned out to be thermodynamically favored. Furthermore, it is necessary that OH + be in the high energy 1 ∆ electronic configuration instead of the more stable 3 Σ one.

Concluding, from this study we have suggested some bi-molecular reactions which can be at the origin of the observation of propylene oxyde in the interstellar medium. Nicely, computationally cheap methods like B3LYP and PBEh-3c provide a good energetic description and thus they could be used in deeper studies using reaction dynamics and/or considering an environment (like a surface) explicitly.

3. 2 . 1

 21 The PE + O( 3 P ) reaction. This is an associative reaction which needs a spin crossing from the triplet PES involving O( 3 P ) to the final singlet one involving PO. The reaction proceeds by forming a stable compound between the triplet oxygen atom and the PE molecule (we indicate this compound as 3 [PE-O]) as shown in Scheme 1. The formation of the triplet adduct leads to a gain of about 25 kcal/mol.3 [PE-O] is a triplet intermediate from which two (singlet) products can be formed by inter-system crossing:(1) the propylene oxide (PO) by a simple "closure" of the 3-member ring, and (2) the propionaldehyde (propanal, PA) which can be formed by hydrogen migration.

Fig. 1

 1 Fig. 1 Triplet oxygen addiction to PE

Fig. 2

 2 Fig. 2 PES of the reaction PE + ( 3 P) O → PO/PA as obtained at B3LYP/cc-pVTZ level of theory. The structure of the triplet 3 [PE-O] compound is also shown.

Fig. 3

 3 Fig.3PES of the reaction PE + ( 2 Σ) OH → PO as obtained at B3LYP/cc-pVTZ level of theory. The minimum energy path in the exit channel is reported in the inset. The structures of the PE-OH complex and of the transition state in the exit channel are also shown.

Fig. 5

 5 Fig.5Ionic reactions: energies of the entrance and exit channels and of the ionic complexes at the PBEh-3c level. ZPE is not included.

Fig. 6

 6 Fig. 6 PE+OH + reaction scan along the C-O coordinate on the left (entrance channel) and along the O-H coordinate on the right (exit channel). The singlet diradical state energies corresponding to the homolytic cleavage of the bonds are reported in red. The zero has been set to the last point of the entrance channel PES. PBEh-3c calculations are shown.

Fig. 7

 7 Fig. 7 PE+OOH + reaction scan along the C-O coordinate on the left (entrance channel) and along the O-O coordinate on the right (exit channel). The singlet diradical state energies corresponding to the homolytic cleavage of the bonds is reported in red. The zero has been set to the last point of the computed entrance channel PES. PBEh-3c calculations are shown.

Table 1

 1 Column densities of species considered in this study

	Species Column density (cm -2 )	Reference
	PE	4 • 10 13	Marcelino et al. [1]
	O ( 3 P)	> 10 15	Glassgold and Langer [37]
			Hollenbach et al. [38]
	OH	1.7 -3.9 • 10 14	Wiesemeyer et al. [39]
	OH +	2.6 • 10 14	Wyrowski et al. [40]
	HO 2	2.8 • 10 12	Parise et al. [41]
	HO + 2 PO	∼ 10 9 3.0 -6.7 • 10 14	Widicus Weaver et al. [42] Cunningham et al. [43]
	PE = propylene; PO = propylene oxide; HO + 2 was not directly detected, the abundance
	reported is an estimation.

Table 2

 2 Energies of reactions (different methods) including ZPE in kcal/mol. a

			PBEh-3c B3LYP B2PLYP	MP2 CCSD(T) b
		Radicalic reactions
	1	PE + O( 3 P) → PO	-80.8	-79.8	-83.8	-92.3	-82.3
	2	PE + OH( 2 Σ) → PO + H( 1 S)	+13.8	+19.3	+17.3	+7.2	+16.9
	3	PE + HO 2 ( 2 A ) → PO + OH( 2 Σ)	-21.8	-17.0	-19.6	-28.8	-22.1
			Ionic Reactions
	4	PE + O + ( 2 P ) → PO +	-264.4	-264.8	-261.8 -259.0	-240.9
	5	PE + OH + ( 1 ∆) → PO + + H( 1 S)	-124.0	-121.1	-119.6 -118.5	-103.0
	6	PE + OH + ( 1 ∆) → PO + H +	-43.9	-37.0	-39.9	-49.4	-24.2
	7 8	PE + HO + 2 ( 1 A) → PO + + OH( 2 Σ) PE + HO + 2 ( 1 A) → PO + OH + ( 1 ∆)	-67.8 +70.1	-65.8 +77.0	-57.5 +79.5	-45.4 +80.3	-52.7 +66.9
		Mean Absolute Error	10.9	11.0	9.4	13.2	-
	PE = propylene; PO = propylene oxide.
	a Basis sets are: cc-pVTZ (B3LYP), aug-cc-pVTZ (B2PLYP-D3, MP2 and CCSD(T)).

b ZPE and geometry were calculated at MP2 level of theory.

the dissociation of the rather stable OH radical molecule. Reaction 3 requires a collision with the peroxide radical and represents a neutral-radical pathway which is exothermic because it involves the formation of the highly stable OH radical molecule. Reactions 5-6 are two ion-molecule reactions with the same entrance channel and two possible products. The lowest energy one is an ionized PO that can be further neutralized by electron capture. Reactions 7-8 are ion-molecule reactions which require a collision with an ionized peroxide. As for reactions 4-5, the lowest energy outcome is an ionized PO.

Acknowledgements We thank ANR DynBioReact (Grant No. ANR-14-CE06-0029-01) and CNRS program INFINITI (project ASTROCOL) for support. EB thankfully acknowledges CINECA for its support through computational grant IscrC-COMPAA-2 and "La Sapienza" for its financial support through grant RM11715C7C86B2BE.


domain: sdv sde

text:
Stephane Boivin

Marc Lepetit
email: marc.lepetit@inra.fr

Partner preference in the legume-rhizobia symbiosis and impact on legume inoculation strategies

Introduction 324 2. Early partner choice in the legume-rhizobium symbiosis 326 2.1 Legume and rhizobial symbiotic mechanisms controlling the AFN 326 2.1.1 Symbiosis initiation by the perception of legume plant flavonoid spectra 326 2.1.2 Rhizobial AFN is generally determined by the range of secreted NFs 327 2.1.3 The genetic diversity of legume LysM-RLK receptors impacts rhizobial AFN 329 2.1.4 AFN can depend on the secretion of bacterial effectors 330 2.2 Competitiveness to form root nodules (CFN) is a determinant of early partner choice in rhizobial populations 331 3. Post-infection partner preference in the legume-rhizobium symbiosis 332 3.1 Integration of legume-rhizobium interactions at the whole plant level 332 3.2 Control of the symbiosis by local N availability 334 3.3 Control of symbiosis by the whole plant N demand 335 3.4 Differential allocation of C metabolites by the plant to the nodules 337 4. Conclusions

shape partner choice by favoring effective symbiotic N 2 fixing structures to the expense of inefficient ones. Little is known about mechanisms involved in legume-rhizobium partner choices despite the relevance of this trait to design new strategies to improve inoculation of legume crops.

Introduction

Legumes have the unique ability to associate with rhizobia within specific symbiotic root organs, called nodules. The legume-rhizobium symbiosis has the emerging property to use dinitrogen (N 2 ) present in the air as an unlimited nitrogen (N) source and therefore to circumvent a soil mineral N limitation. Atmospheric N 2 fixation takes place within bacteroids where it is transformed into ammonium and translocated to the legume host roots. In return, the plant provides photosynthates to the bacteria [START_REF] Oldroyd | The rules of engagement in the legume-rhizobial symbiosis[END_REF]. Legume-rhizobium interactions are however not ubiquitous as these symbioses happen only between compatible partners.

In soil and rhizosphere, bacteria form complex populations which composition vary depending on environmental conditions [START_REF] Fierer | The diversity and biogeography of soil bacterial communities[END_REF][START_REF] Kaiser | Driving forces of soil bacterial community structure, diversity, and function in temperate grasslands and forests[END_REF][START_REF] Rousk | Soil bacterial and fungal communities across a pH gradient in an arable soil[END_REF]. Rhizobia represent a little part of soil bacteria (<1%) but high local variations in population size and symbiotic performances are often observed [START_REF] Wakelin | High spatial variation in population size and symbiotic performance of Rhizobium leguminosarum bv. Trifolii with white clover in New Zealand pasture soils[END_REF]. Although different protocols were designed to study rhizobia populations from soil samples, their identification and direct quantification remain difficult, mainly because of their low density in soils combined with quality issues of the DNA extracted from soil samples [START_REF] Laguerre | Isolation from soil of symbiotic and nonsymbiotic Rhizobium leguminosarum by DNA hybridization[END_REF][START_REF] Sullivan | Four unnamed species of nonsymbiotic rhizobia isolated from the rhizosphere of Lotus corniculatus[END_REF][START_REF] Zézé | Direct amplification of nodD from community DNA reveals the genetic diversity of Rhizobium leguminosarum in soil[END_REF]. Taking advantage of their capacity to associate with plants within nodules, rhizobia have been mostly collected from root nodules, which were considered to be generally occupied by a dominant rhizobium genotype [START_REF] Bourion | Co-inoculation of a pea core-collection with diverse rhizobial strains shows competitiveness for nodulation and efficiency of nitrogen fixation are distinct traits in the interaction[END_REF][START_REF] Laguerre | Local and systemic N signaling are involved in Medicago truncatula preference for the most efficient Sinorhizobium symbiotic partners[END_REF]. This so-called "trapping" strategy coupled with molecular methods allowed drawing indirect pictures of the rhizobia diversity in soils [START_REF] Kumar | Bacterial genospecies that are not ecologically coherent : Population genomics of Rhizobium leguminosarum[END_REF][START_REF] Laguerre | Rapid identification of rhizobia by restriction fragment length polymorphism analysis of PCR-amplified 16S rRNA genes[END_REF][START_REF] Young | Sym plasmid and chromosomal genotypes are correlated in field populations of Rhizobium leguminosarum[END_REF]. Indeed, legume-rhizobium partner choice mechanisms biased the diversity assessment. Although a large genetic diversity is frequently found at a local scale in soils [START_REF] Bailly | Population genomics of Sinorhizobium medicae based on low-coverage sequencing of sympatric isolates[END_REF][START_REF] Kumar | Bacterial genospecies that are not ecologically coherent : Population genomics of Rhizobium leguminosarum[END_REF], some rhizobia are occasionally absent, and therefore some specific legume hosts cannot be nodulated in these soils. For example, soybean is native from East Asia where its symbionts are naturally found in soils, but the compatible bacteria Bradyrhizobium japonicum are not indigenous in western Europe and inoculation is then required [START_REF] Revellin | Influence of soil properties and soya bean cropping history on the Bradyrhizobium japonicum population in some French soils[END_REF].

The partner choice influences the symbiotic interaction from early steps, i.e. in relation with the infection of the plant by symbiotic bacteria, as well as later steps, i.e. in N 2 fixing nodules. The intrinsic Ability to Form root Nodules (AFN) is generally estimated as the capacity to form nodules with a legume in mono-inoculation experiments. As the host spectrum of some rhizobia is larger than for others, AFN specificities are then observed at various phylogenetic levels, from specific rhizobium genotypes to different rhizobium complex species. However, rhizobia in a given soil potentially share an equivalent AFN, but display a wide range of Competitiveness to Form root Nodules (CFN) with their compatible host plants. This CFN is estimated as the capacity of a specific genotype to form nodules when multiple different compatible partners co-exist. Therefore, not only AFN but also CFN determine the early partner choice [START_REF] Amarger | Competition for nodule formation between effective and ineffective strains of Rhizobium meliloti[END_REF][START_REF] Triplett | Genetics of competition for nodulation of legumes[END_REF]. Once young nodules are formed after the selection of both compatible and competitive rhizobium genotypes, the Symbiotic N 2 Fixation (SNF) begins progressively. The SNF efficiency of individual bacteria strongly varies within rhizobial populations, as well as in function of the legume host and of environmental conditions. Because CFN and SNF efficiency are genetically independent, young nodules with different levels of SNF efficiency are formed on the same host root system [START_REF] Bourion | Co-inoculation of a pea core-collection with diverse rhizobial strains shows competitiveness for nodulation and efficiency of nitrogen fixation are distinct traits in the interaction[END_REF]. Consequently, a mosaic of symbiotic nodule organs, displaying various levels of efficiency, is frequently observed in natural conditions on legume root systems [START_REF] Laguerre | Compatibility of rhizobial genotypes within natural populations of Rhizobium leguminosarum biovar viciae for nodulation of host legumes[END_REF][START_REF] Mutch | Diversity and specificity of Rhizobium leguminosarum biovar viciae on wild and cultivated legumes[END_REF]. At this stage, Post-Infection Partner Preference (PIPP) mechanisms influence both the dynamic of the interaction and nodule development, in order to (1) satisfy the plant N demand and (2) prevent dissipation of carbon (C) metabolites toward inefficient symbiotic structures. Understanding genetic and molecular bases of AFN, CFN and PIPP is therefore highly relevant to select the best symbiotic partners, design inoculation strategies, and predict their benefits for agro-ecological systems.

This chapter reviews our current knowledge on symbiotic partner choices in conditions where multiple symbiotic partners can interact with their host plants. The first part focuses on the early partner choice and describes mechanisms modulating the initiation of the legume-rhizobium symbiotic interaction (i.e. AFN and CFN). The second part focuses on PIPP that occurs later in nodules when legume hosts are associated with multiple partners. Mechanisms related to SNF efficiency and plant N signaling, potentially involved in PIPP, are additionally presented. To conclude, consequences of partner choice for the improvement of inoculation strategies in legume crops is discussed.

Early partner choice in the legume-rhizobium symbiosis

Legume and rhizobial symbiotic mechanisms controlling the AFN

2.1.1 Symbiosis initiation by the perception of legume plant flavonoid spectra Under N deficit, legumes associate with compatible rhizobia, and the Ability to Form root Nodules (AFN) mainly depends on two conditions: the capacity of rhizobia to detect plant signals (i.e. flavonoids) and in return, the capacity of legume plants to recognize Nod Factors (NFs) and bacterial surface polysaccharides (SPs; Fig. 1; [START_REF] Oldroyd | The rules of engagement in the legume-rhizobial symbiosis[END_REF]. Legume roots release a wide range of flavonoids in the rhizosphere. The amount and the chemical structure of secreted flavonoids impact bacterial symbiotic responses, as some chemical species are more effective than others to trigger responses on specific rhizobia [START_REF] Jiménez-Guerrero | Transcriptomic studies of the effect of nod gene-inducing molecules in Rhizobia : Different weapons, one purpose[END_REF][START_REF] Maj | Response to flavonoids as a factor influencing competitiveness and symbiotic activity of Rhizobium leguminosarum[END_REF]. Synergy between the different types of flavonoids exsuded can modulate the symbiotic initiation [START_REF] Begum | Specific flavonoids induced nod gene expression and pre-activated nod genes of Rhizobium leguminosarum increased pea (Pisum sativum L.) and lentil (Lens culinaris L.) nodulation in controlled growth chamber environments[END_REF][START_REF] Firmin | Flavonoid activation of nodulation genes in Rhizobium reversed by other compounds present in plants[END_REF]. Flavonoids interact with the LyR transcriptional activator nodulation D (NodD) protein which binds to specific Nod Boxes (NBs) DNA motifs located upstream of a number of bacterial nodulation genes (nod genes) involved in the production, modification or transport of NFs [START_REF] Hong | Evidence that DNA involved in the expression of nodulation (nod) genes in Rhizobium binds to the product of the regulatory gene nodD[END_REF][START_REF] Peck | Diverse flavonoids stimulate NodD1 binding to nod gene promoters in Sinorhizobium meliloti[END_REF]. The broad host-range Rhizobium sp. NGR234 strain possess two different nodD alleles, called NodD1 and NodD2, which potentially interact with 19 NBs [START_REF] Fellay | nodD2 of Rhizobium sp. NGR234 is involved in the repression of the nodABC operon[END_REF][START_REF] Kobayashi | Flavonoids induce temporal shifts in gene-expression of nod-box controlled loci in Rhizobium sp[END_REF], whereas the Rhizobium leguminosarum symbiovar viciae (Rlv) strain 3841, which forms nodule only with plants of the Fabeae tribe, has only one NodD protein that potentially interact with 6 NBs (4 validated and 2 putatives; [START_REF] Young | The genome of Rhizobium leguminosarum has recognizable core and accessory components[END_REF]. Therefore, plasticity and diversity of flavonoids produced by the plant and their perception by rhizobia influence the AFN. Moreover, the regulation of nod gene expression and nodulation via NodD can be also affected by non-flavonoid compounds secreted by legumes (i.e. jasmonic acid, stachydrine, trigonelline, tetronic and erythronic acids) and non-legume plants (i.e. vanillin and isovanillin), suggesting that a large set of plantsecreted molecules can influence the bacterial NodD function [START_REF] Gagnon | Aldonic Acids : A novel family of nod gene inducers of Mesorhizobium loti, Rhizobium lupini, and Sinorhizobium meliloti[END_REF][START_REF] Strange | The Rhizobium strain NGR234 nodD1 gene product responds to activation by the simple phenolic compounds vanillin and isovanillin present in wheat seedling extracts[END_REF][START_REF] Sun | Crosstalk between jasmonic acid, ethylene and Nod factor signaling allows integration of diverse inputs for regulation of nodulation[END_REF].

2.1.2 Rhizobial AFN is generally determined by the range of secreted NFs The best characterized genes regulated by flavonoids and NodD are nod genes, grouped together in clusters generally located on a symbiotic plasmid or in specific mobile islands of the chromosome [START_REF] Kaneko | Complete genomic sequence of nitrogen-fixing symbiotic Bacterium Bradyrhizobium japonicum USDA110[END_REF][START_REF] Kondorosi | Physical and genetic analysis of a symbiotic region of Rhizobium meliloti : Identification of nodulation genes[END_REF][START_REF] Young | The genome of Rhizobium leguminosarum has recognizable core and accessory components[END_REF]. The typical set of nod genes include conserved core genes and additional genes specific to some rhizobia [START_REF] Mergaert | Molecular mechanisms of Nod factor diversity[END_REF][START_REF] Triplett | Genetics of competition for nodulation of legumes[END_REF]. In Rlv, the nod gene cluster contains the nodD, nodO genes, and the nodABCIJ(X), nodFEL, nodMN(T) operons. These transcriptional units are under the control of 4 NBs [START_REF] Spaink | Promoters in the nodulation region of the Rhizobium leguminosarum Sym plasmid pRL1JI[END_REF]. The nodABC, nodFEL and nodMN operons are responsible of the biosynthesis of lipo-chitooligosaccharidic NF molecules that are composed of four to five N-acetyl glucosamines (forming the NF sugar backbone) and a terminal N-acylated sugar carrying a fatty acid chain of 16e18 C residues [START_REF] Mergaert | Molecular mechanisms of Nod factor diversity[END_REF]. Different species of rhizobia produce different NFs characterized by various chemical substitutions (i.e. acetyl, carbamoyl, sulfate, fucosyl, arabinosyl and methyl residues) on the sugar backbone, and by different unsaturation levels of the acyl chain [START_REF] Cooper | Multiple responses of rhizobia to flavonoids during legume root infection[END_REF]. Specific nod genes are involved in these modifications and hence, depending on strains and species, this allows modulating the rhizobial AFN with compatible legumes. For example, some Rlv strains are able to specifically interact with the Pisum sativum cultivar 'Afghanistan' because they produce a specific NF resulting of the nodX gene function [START_REF] Firmin | Resistance to nodulation of cv. Afghanistan peas is overcome by nodX, which mediates an O-acetylation of the Rhizobium leguminosarum lipo-oligosaccharide nodulation factor[END_REF]. As NFs are important factors in the legume-rhizobium symbiotic initiation, their secretion in the extracellular medium is a key step for legume NF perception and is mediated by the transmembrane proteins NodI and NodJ (Spaink et al., 1995). Some genes are present in the nod gene cluster of certain rhizobia, such as nodT and nodO in R. leguminosarum [START_REF] Rivilla | Rhizobium leguminosarum NodT is related to a family of outer-membrane transport proteins that includes TolC, PrtF, CyaE and AprF[END_REF][START_REF] Surin | Molecular characterization of the nodulation gene, nodT, from two biovars of Rhizobium leguminosarum[END_REF]. These two genes are involved in the secretion of NFs as well as in the modulation of the host-specificity and AFN [START_REF] Djordjevic | Tn5 mutagenesis of Rhizobium trifolii host-specific nodulation genes result in mutants with altered host-range ability[END_REF][START_REF] Lewis-Henderson | NodT, a positively-acting cultivar specificity determinant controlling nodulation of Trifolium subterraneum by Rhizobium leguminosarum biovar trifolii[END_REF].

The AFN with compatible legumes (generally defined as "symbiovars") is generally well-correlated with the nod gene phylogenetic diversity, but very poorly with the whole chromosome genetic variation [START_REF] Kumar | Bacterial genospecies that are not ecologically coherent : Population genomics of Rhizobium leguminosarum[END_REF]. Consequently, closely-related chromosome backgrounds can be found in different "symbiovars". Symbiovars are well discriminated by their nod genes present on plasmids or on mobile islands. Because nod genes are generally located on symbiotic plasmids, horizontal gene transfer (HGT) is one of the main drivers of AFN genetic evolution in populations. One example illustrating the impact of HGTs on AFN has been evidenced in New Zealand where Rhizobium loti is absent in most of uncultivated soils [START_REF] Patrick | Response of Lotus corniculatus to inoculation and pelleting on a range of Otago tussock grassland environments[END_REF]. A strain of R. loti, which is able to nodulate Lotus corniculatus, was introduced in a field and root nodule trapping was performed seven years later at the same place [START_REF] Sullivan | Nodulating strains of Rhizobium loti arise through chromosomal symbiotic gene transfer in the environment[END_REF]. Molecular genotyping revealed the transfer of symbiotic genes from the introduced strain to native non-symbiotic rhizobia already present in the soil. HGTs have been well studied in pure cultures and bioinformatic tools are now available to investigate them across various microbe genomes [START_REF] Li | A novel strategy for detecting recent horizontal gene transfer and its application to Rhizobium strains[END_REF][START_REF] Soucy | Horizontal gene transfer : Building the web of life[END_REF]. However, HGTs can only happen between compatible bacteria, and mechanisms controlling gene exchanges within complex bacterial populations are not well understood [START_REF] Kl€ Umper | Broad host range plasmids can invade an unexpectedly diverse fraction of a soil bacterial community[END_REF]. The Quorum Sensing (QS) is a gene expression regulatory system acting at the level of bacterial populations [START_REF] Papenfort | Quorum sensing signaleresponse systems in Gramnegative bacteria[END_REF]. In R. leguminosarum, the transfer of the symbiotic plasmid carrying nod genes is mediated by LuxR-type QS regulators and therefore, the QS system is predicted to influence the diversity and the abundance of rhizobial genotypes in soil populations [START_REF] Mcanulla | Quorum-sensing-regulated transcriptional initiation of plasmid transfer and replication genes in Rhizobium leguminosarum biovar viciae[END_REF].

The genetic diversity of legume LysM-RLK receptors impacts

rhizobial AFN Perception of NFs is mediated by plant receptors that trigger the first steps of rhizobial infection (Fig. 1). They belong to the large and diverse family of LysM receptor-like kinases (LysM-RLKs) [START_REF] Gough | Evolutionary history of plant LysM receptor proteins related to root endosymbiosis[END_REF], which possess several extracellular LysM domains that are able to bind NFs, a transmembrane domain, and an intracellular kinase domain which transduces the signal. In Medicago truncatula and Lotus japonicus model legumes, two different LysM-RLK co-receptors, likely forming dimers, have been identified (MtLYK3 and MtNFP, and LjNFR1 and LjNFR5 respectively [START_REF] Dénarié | Rhizobium lipo-chitooligosaccharide nodulation factors : Signaling molecules mediating recognition and morphogenesis[END_REF][START_REF] Madsen | Autophosphorylation is essential for the in vivo function of the Lotus japonicus Nod factor receptor 1 and receptor-mediated signalling in cooperation with Nod factor receptor 5[END_REF][START_REF] Radutoiu | LysM domains mediate lipochitineoligosaccharide recognition and Nfr genes extend the symbiotic host range[END_REF]. The MtLYK3/LjNFR1 receptors belong to the "LysM domain-containing RLK" (LYK) family of proteins that have functional kinase domains, whereas MtNFP/LjNFR5 belong to the "LYK-related" (LYR) family of proteins that have lost an activation loop motif, leading to unfunctional kinase domains. Although a role in specific NF perception is yet demonstrated only for few LysM-RLKs, it is likely that polymorphism of these protein families has an important role for the variation and diversity of AFN. The ectopic expression of L. japonicus LjNFR1 and LjNFR5 receptors in transgenic M. truncatula roots indeed Partner preference in the legume-rhizobia symbiosis allowed the formation of nodules by Mesorhizobium loti that is not a natural host of M. truncatula [START_REF] Radutoiu | LysM domains mediate lipochitineoligosaccharide recognition and Nfr genes extend the symbiotic host range[END_REF]. Evidences for a positive selection pressure on residues of the LysM domain of LYK3 have been shown, suggesting a role of LYK3 in controlling host specificity [START_REF] Sulima | Selection signatures in the first exon of paralogous receptor kinase genes from the Sym2 region of the Pisum sativum L. Genome[END_REF]. In the case of the specific interaction between the P. sativum cultivar 'Afghanistan' and the Rlv strain TOM, the pea sym2 allele, encoding a LysM-RLK, prevented the nodulation of European Rlv strains lacking the nodX gene [START_REF] Davis | Identification of nodX, a gene that allows Rhizobium leguminosarum biovar viciae strain TOM to nodulate Afghanistan peas[END_REF][START_REF] Firmin | Resistance to nodulation of cv. Afghanistan peas is overcome by nodX, which mediates an O-acetylation of the Rhizobium leguminosarum lipo-oligosaccharide nodulation factor[END_REF][START_REF] Lie | Host genes in Pisum sativum L. conferring resistance to European Rhizobium leguminosarum strains[END_REF][START_REF] Sulima | Selection signatures in the first exon of paralogous receptor kinase genes from the Sym2 region of the Pisum sativum L. Genome[END_REF]. However, all symbiotic functions of LysM-RLKs may be not exclusively related to NFs and some SPs directly interact with LysM domains [START_REF] Kawaharada | Receptor-mediated exopolysaccharide perception controls bacterial infection[END_REF]. SPs are composed of extracellular polysaccharides (EPS), capsular polysaccharides (KPS) and lipopolysaccharides (LPS), and are implicated at various stages of the legume-rhizobium interaction, from root attachment to nodule colonization (for a review see Janczarek, Rachwa1, Marzec, Grza ˛dziel, & Palusi nska-Szysz, 2015; [START_REF] Kelly | Legume LysM receptors mediate symbiotic and pathogenic signalling[END_REF]. The chemical structure of SPs, mainly composed of a mono or polysaccharide core unit decorated with various substitutions, can be variable and therefore may modulate the partner choice.

AFN can depend on the secretion of bacterial effectors

Bacterial effectors are released by secretion systems in the extracellular medium or directly inside plant root cells, and some of these are proposed to modulate the legume-rhizobium symbiosis [START_REF] Costa | Secretion systems in Gram-negative bacteria : Structural and mechanistic insights[END_REF][START_REF] Miwa | How effectors promote beneficial interactions[END_REF]. Until today, type I, III and VI secretion systems were involved in legume-rhizobium symbioses. The type I secretion system (T1SS), composed of transmembrane proteins such as PrsD and PrsE, can directly translocate proteins into the extracellular environment. This is the case for the Ca 2þ -binding protein NodO, as well as for glycanases and adhesins [START_REF] Economou | The Rhizobium nodulation gene nodO encodes a Ca2(þ)-binding protein that is exported without Nterminal cleavage and is homologous to haemolysin and related proteins[END_REF][START_REF] Russo | Proteins exported via the PrsD-PrsE type I secretion system and the acidic exopolysaccharide are involved in biofilm formation by Rhizobium leguminosarum[END_REF]. The type III secretion system (T3SS) is a complex of about twenty different proteins which form a syringe embedded in both bacterial and plant root host cell membranes [START_REF] Miwa | How effectors promote beneficial interactions[END_REF][START_REF] Staehelin | Nodulation outer proteins : Double-edged swords of symbiotic rhizobia[END_REF]. The T3SS has been initially implicated in the secretion of bacterial effectors during plant pathogenic interactions [START_REF] Miwa | How effectors promote beneficial interactions[END_REF][START_REF] Staehelin | Nodulation outer proteins : Double-edged swords of symbiotic rhizobia[END_REF]. T3SS effectors were identified in several rhizobial species like B. japonicum, B. elkani, S. fredii, but not in R. leguminosarum and Sinorhizobium meliloti. Proteins secreted via the T3SS in host root cells, which are called Nops for Nodulation outer proteins, influence the symbiosis establishment [START_REF] Miwa | How effectors promote beneficial interactions[END_REF]. NodD regulates the type III secretion system 1 (tts1) bacterial transcription factor that drives effector gene expression [START_REF] Okazaki | Hijacking of leguminous nodulation signaling by the rhizobial type III secretion system[END_REF]. Interestingly, in B. japonicum, the two effectors NopE1 and NopE2 stimulate nodulation in soybean but repress it in mungbean [START_REF] Krause | Mutational and transcriptional analysis of the type III secretion system of Bradyrhizobium japonicum[END_REF], illustrating that T3SS can modulate the AFN. Some effectors are released through a type VI secretion system (T6SS), composed of membrane and tail complexes that translocate bacterial effectors into host cells, and which was initially linked to pathogenic bacteria effector secretion (for review see [START_REF] Costa | Secretion systems in Gram-negative bacteria : Structural and mechanistic insights[END_REF]. Despite the T6SS was suspected to inhibit the R. leguminosarum e pea symbiosis [START_REF] Bernal | Type VI secretion systems in plant-associated bacteria[END_REF] the specific contribution of such secreted effectors in Fabeae-rhizobium early partner choice remains to be demonstrated. Some effectors released in legume host cells modulate plant immunity, illustrating that a crosstalk between immunity and early partner choice likely exist during nodulation [START_REF] Gourion | Rhizobiumelegume symbioses : The crucial role of plant immunity[END_REF][START_REF] Miwa | How effectors promote beneficial interactions[END_REF]. A soybean R gene (rj2) was implicated in the decrease of AFN, suggesting that establishment of the root nodule symbiosis requires the evasion of plant immune responses triggered by rhizobial effectors [START_REF] Yang | R gene-controlled host specificity in the legume-rhizobia symbiosis[END_REF]. Several evidences confirmed the role of secretion systems in the regulation of plant immune responses. The NopL and NopM T3SS-secreted proteins of the rhizobium NGR234 strain were indeed shown to suppress defense responses in N. benthamiana [START_REF] Bartsev | NopL, an effector protein of Rhizobium sp. NGR234, thwarts activation of plant defense reactions[END_REF][START_REF] Xin | Functional analysis of NopM, a novel E3 ubiquitin ligase (NEL) domain effector of Rhizobium sp. Strain NGR234[END_REF]. In addition, T3SS-secreted effector proteins of the B. elkanii USDA61 bacterial strain were shown to highjack the NF-dependent pathway by suppressing plant defense responses in the soybean cultivar Clark-rj-1 [START_REF] Okazaki | Hijacking of leguminous nodulation signaling by the rhizobial type III secretion system[END_REF].

Competitiveness to form root nodules (CFN) is a determinant of early partner choice in rhizobial populations

The capacity of a rhizobium to form nodules with a legume in mono-inoculation experiments does not necessarily predict the competitive success of the interaction in a context of multiple compatible partners (Fig. 1). Different rhizobia can share similar AFN but display a wide range of CFN in mixture, depending on the legume host [START_REF] Bourion | Co-inoculation of a pea core-collection with diverse rhizobial strains shows competitiveness for nodulation and efficiency of nitrogen fixation are distinct traits in the interaction[END_REF]. Although Rlv are generally able to form nodules with pea or fababean when monoinoculated, these two plant species exposed to complex soil Rlv populations select preferentially different Rlv genotypes [START_REF] Laguerre | Compatibility of rhizobial genotypes within natural populations of Rhizobium leguminosarum biovar viciae for nodulation of host legumes[END_REF][START_REF] Mutch | Diversity and specificity of Rhizobium leguminosarum biovar viciae on wild and cultivated legumes[END_REF]. Preferential nodulation within compatible partners populations was also evidenced in the soybean-Bradyrhizobium symbiosis [START_REF] Cregan | Soybean genotype restricting nodulation of a previously unrestricted serocluster 123 bradyrhizobia[END_REF][START_REF] Keyser | Nodulation and competition for nodulation of selected soybean genotypes among Bradyrhizobium japonicum serogroup 123 isolates[END_REF]. More recently, a coinoculation of Rlv genotypes in mixture with a panel of pea accessions resulted in preferential symbiotic associations depending on pea genotypes [START_REF] Bourion | Co-inoculation of a pea core-collection with diverse rhizobial strains shows competitiveness for nodulation and efficiency of nitrogen fixation are distinct traits in the interaction[END_REF]. Although the general concept of CFN has been described since several decades, very little is known about mechanisms controlling this process [START_REF] Amarger | Competition for nodule formation between effective and ineffective strains of Rhizobium meliloti[END_REF][START_REF] Triplett | Genetics of competition for nodulation of legumes[END_REF]. The hypothesis of a differential proliferation of competitive bacterial genotypes in the host rhizosphere cannot be ruled out, but received little experimental support [START_REF] Moawad | Rhizosphere response as a factor in competition among three serogroups of indigenous Rhizobium japonicum for nodulation of field-grown soybeans[END_REF]. In most rhizobia, a preferential association between the partner choice and the NF gene diversity supports the hypothesis that signaling pathways associated to early symbiont recognition are the major drivers of CFN [START_REF] Kumar | Bacterial genospecies that are not ecologically coherent : Population genomics of Rhizobium leguminosarum[END_REF][START_REF] Laguerre | Compatibility of rhizobial genotypes within natural populations of Rhizobium leguminosarum biovar viciae for nodulation of host legumes[END_REF][START_REF] Triplett | Genetics of competition for nodulation of legumes[END_REF]. As described above, mechanisms controlling the symbiotic establishment can drastically differ among both host legumes and rhizobia genotypes (i.e. flavonoids, NFs, LysM-RLKs, SPs, TSSs) and may explain some variations in rhizobial CFN in natural populations. For instance, when the Rlv strain TOM is mixed with strains that do not express NodX and inoculated with the P. sativum cultivar 'Afghanistan' (nodulating only with the strain TOM), the NFs produced by the non-nodulating strain compete with NFs produce by TOM and drastically reduce its nodulation capacity [START_REF] Dowling | Competitive nodulation blocking of Afghanistan pea is determined by nodDABC and nodFE alleles in Rhizobium leguminosarum[END_REF][START_REF] Hogg | Competitive nodulation blocking of cv. Afghanistan pea is related to high levels of nodulation factors made by some strains of Rhizobium leguminosarum bv. Viciae[END_REF][START_REF] Winarno | Competition between Rhizobium strains in nodule formation : Interaction between nodulating and non-nodulating strains[END_REF]. In soil bacterial populations, NFs may be provided in trans between individuals, allowing bacteria unable to produce NFs by themselves to form nodules [START_REF] Borthakur | Analysis of pss genes of Rhizobium leguminosarum required for exopolysaccharide synthesis and nodulation of peas : Their primary structure and their interaction with psi and other nodulation genes[END_REF]. Other mechanisms such as antibiosis (antibiotics released in the extracellular medium by rhizobia and nonrhizobia) may also modulate the CFN [START_REF] Triplett | Trifolitoxin production and nodulation are necessary for the expression of superior nodulation competitiveness by Rhizobium leguminosarum bv. Trifolii strain T24 on clover 1[END_REF][START_REF] Robleto | Trifolitoxin production in Rhizobium etli strain CE3 increases competitiveness for rhizosphere colonization and root nodulation of Phaseolus vulgaris in soil[END_REF]; for a review see; Naamala, Jaiswal, & Dakora, 2016).

Post-infection partner preference in the legumerhizobium symbiosis

Integration of legume-rhizobium interactions at the whole plant level

Symbiotic N 2 Fixation (SNF) efficiency of the legume-rhizobium associations varies among bacteria able to infect legume roots and form nodules [START_REF] Laguerre | Local and systemic N signaling are involved in Medicago truncatula preference for the most efficient Sinorhizobium symbiotic partners[END_REF][START_REF] Terpolilli | The model legume Medicago truncatula A17 is poorly matched for N2 fixation with the sequenced microsymbiont Sinorhizobium meliloti 1021[END_REF][START_REF] Triplett | Genetics of competition for nodulation of legumes[END_REF]. Moreover, a single strain may result in different levels of N acquisition when mono-inoculated on different compatible host legumes [START_REF] Bourion | Co-inoculation of a pea core-collection with diverse rhizobial strains shows competitiveness for nodulation and efficiency of nitrogen fixation are distinct traits in the interaction[END_REF][START_REF] Kazmierczak | Specific host-responsive associations between Medicago truncatula accessions and Sinorhizobium strains[END_REF]. These different capacities depend on symbiotic partner couples as, for example, the S. meliloti strain RCR2011 was characterized as a poor N 2 fixer in M. truncatula but as an efficient fixer in M. sativa [START_REF] Terpolilli | The model legume Medicago truncatula A17 is poorly matched for N2 fixation with the sequenced microsymbiont Sinorhizobium meliloti 1021[END_REF]. As bacterial populations in the soil contain multiple competitive rhizobia, it is rather frequent that bacteria with different levels of N 2 fixation efficiency form nodules on roots [START_REF] Laguerre | Compatibility of rhizobial genotypes within natural populations of Rhizobium leguminosarum biovar viciae for nodulation of host legumes[END_REF][START_REF] Mutch | Diversity and specificity of Rhizobium leguminosarum biovar viciae on wild and cultivated legumes[END_REF]. Therefore, symbiotic legume root systems in soils are expected to be a mosaic of nodule organs with various level of SNF efficiency. However, the plant influences the dynamic of the interaction and activates Post-Infection Partner Preference (PIPP) mechanisms that favor the most efficient symbiotic organs to the expenses of the inefficient ones, in order to satisfy the plant N demand (Fig. 1).

Although plant N deficit is required to enable rhizobium-legume symbiosis [START_REF] Streeter | Inhibition of legume nodule formation and N2 fixation by nitrate[END_REF], there is little evidence suggesting its role in early choices between various compatible symbiotic partners [START_REF] Grillo | Nitrogen addition does not influence pre-infection partner choice in the legume-rhizobium symbiosis[END_REF]. Indeed, the capacity of the legume-rhizobium association to fix N 2 has little impact on partner choice until differentiation of the mature N 2 fixing symbiotic organ occurs, and variations in early partner choice depend mainly on the capacities of bacteria to infect and colonize root cells rather than on whole plant CeN trade-offs. Indeed, studies on M. truncatula/Sinorhizobium [START_REF] Amarger | Competition for nodule formation between effective and ineffective strains of Rhizobium meliloti[END_REF][START_REF] Laguerre | Local and systemic N signaling are involved in Medicago truncatula preference for the most efficient Sinorhizobium symbiotic partners[END_REF] or pea/R. leguminosarum [START_REF] Westhoek | Policing the legume-rhizobium symbiosis : A critical test of partner choice[END_REF][START_REF] Bourion | Co-inoculation of a pea core-collection with diverse rhizobial strains shows competitiveness for nodulation and efficiency of nitrogen fixation are distinct traits in the interaction[END_REF] showed that inefficient N fixing bacteria genotypes, either corresponding to artificial mutants or natural isolates, can be as compatible and competitive as efficient N 2 fixing bacteria, indicating that CFN is likely independent of SNF efficiency. Consequently, N 2 fixing inefficient bacteria, so-called "cheaters", are frequently present in a fraction of the nodules of an host plant [START_REF] Fujita | Evolutionary dynamics of nitrogen fixation in the legumeerhizobia symbiosis[END_REF]. In addition, mixtures of M. truncatula compatible rhizobia displaying different levels of SNF efficiency were inoculated on plants under contrasted N regimes [START_REF] Laguerre | Local and systemic N signaling are involved in Medicago truncatula preference for the most efficient Sinorhizobium symbiotic partners[END_REF], revealing an effect of the N status of the plant on nodule numbers but not on CFN. The plant is therefore most probably unable to discriminate between inefficient and efficient bacteria as a function of its N demand before N 2 fixation is indeed operating. However, as the mature symbiotic organs become efficient for N 2 fixation, fluxes of N and C metabolites between the plant and the mature symbiotic organs impact significantly the whole plant growth and consequently its nutritional demand (Fig. 1). This then allows triggering plant N signaling mechanisms that modulate the symbiotic interaction and the partner preference. When a mixture of mature N 2 fixing efficient and inefficient nodules is present within the same root system, the plant develop mechanisms stimulating the development of efficient structures to the expense of inefficient ones, in order to satisfy its N demand [START_REF] Laguerre | Local and systemic N signaling are involved in Medicago truncatula preference for the most efficient Sinorhizobium symbiotic partners[END_REF]. It has been shown that regulation of plant nitrate acquisition is highly integrated at the whole plant level (for reviews see [START_REF] Bouguyon | Nitrate sensing and signaling in plants[END_REF][START_REF] Ruffel | Signal interactions in the regulation of root nitrate uptake[END_REF]. The presence of nitrate induces both local and whole plant responses: nitrate stimulates locally root proliferation, nitrate uptake and nitrate assimilation whereas accumulation of downstream N metabolites by the whole plant triggers a systemic feedback repression of nitrate acquisition and root development when the N demand is satisfied. C metabolites accumulation also contributes to the regulation of nitrate acquisition: the level of photosynthates, translocated from shoots to roots, stimulates the root capacity to acquire nitrate [START_REF] Lejay | Regulation of root ion transporters by photosynthesis : Functional importance and relation with hexokinase[END_REF]. It is well known from early studies that the addition of mineral N or of N metabolites strongly inhibits nodulation [START_REF] Parsons | Nodule growth and activity may be regulated by a feedback mechanism involving phloem nitrogen*[END_REF][START_REF] Streeter | Inhibition of legume nodule formation and N2 fixation by nitrate[END_REF] but mechanisms adjusting symbiotic capacities to the nutritional demand of the legume plant are not well documented. However, several evidences argue that reminiscent mechanisms also exist in the case of SNF.

Control of the symbiosis by local N availability

Evidences for a local regulation of mature symbiotic organs by the efficiency of SNF have been reported. Suppressing N 2 fixation by Ar/O 2 treatments result locally in a rapid inhibition of nodule growth [START_REF] Kiers | Host sanctions and the legume-rhizobium mutualism[END_REF][START_REF] Jeudy | Adaptation of Medicago truncatula to nitrogen limitation is modulated via local and systemic nodule developmental responses[END_REF]. It was proposed that the plant activates nodule autonomous mechanisms to locally restrict the development of nodules formed with ineffective bacteria [START_REF] Kiers | Host sanctions and the legume-rhizobium mutualism[END_REF][START_REF] Oono | Failure to fix nitrogen by non-reproductive symbiotic rhizobia triggers host sanctions that reduce fitness of their reproductive clonemates[END_REF]. Long term Ar/O 2 treatments in determinate legumes resulted in a decrease of bacteroids fitness in nodules, associated with an early senescence [START_REF] Kiers | Host sanctions and the legume-rhizobium mutualism[END_REF][START_REF] Oono | Controlling the reproductive fate of rhizobia : How universal are legume sanctions?[END_REF]. This result was interpreted as a "host sanction" toward the less beneficial partners. Indeed, in an evolutionary point of view, such sanction would tend to limit ineffective rhizobia multiplication and dispersion when they are released in the soil (Fig. 1). The concept has been extended to indeterminate nodules although bacteroids are, in this case, terminally differentiated and that only undifferentiated bacteria are able to multiply [START_REF] Oono | Comparing symbiotic efficiency between swollen versus nonswollen rhizobial Bacteroids1[C][W][OA[END_REF][START_REF] Oono | Failure to fix nitrogen by non-reproductive symbiotic rhizobia triggers host sanctions that reduce fitness of their reproductive clonemates[END_REF]. The general small size and the early developmental arrest of nodules formed by fix À mutant bacteria is globally in agreement with a concept that an absence of N 2 fixation is associated to an inhibition of nodule development. Although reports in soybean/Bradyrhizobium and Medicago/Sinorhizobium symbioses indicate that mutations suppressing N 2 fixation do not necessarily impact the reproductive fitness of rhizobia present in nodules [START_REF] Laguerre | Local and systemic N signaling are involved in Medicago truncatula preference for the most efficient Sinorhizobium symbiotic partners[END_REF][START_REF] Marco | An experimental and modelling exploration of the host-sanction hypothesis in legume-rhizobia mutualism[END_REF], evidences for a long-term stimulation of the reproductive fitness of fix þ Cupriavidus taiwanensis bacteria versus fix À bacteria in coinfected root systems of Mimosa pudica have also been reported [START_REF] Daubech | Spatio-temporal control of mutualism in legumes helps spread symbiotic nitrogen fixation[END_REF]. Overall, these data demonstrate a control of symbiotic organ development by SNF efficiency. Mechanisms related to nodule oxygen permeability or pH have been additionally proposed to be instrumental in the local control of legume-rhizobium symbiotic organs by N signaling [START_REF] Hunt | Gas exchange of legume nodules and the regulation of nitrogenase activity[END_REF][START_REF] Kiers | Host sanctions and the legume-rhizobium mutualism[END_REF] but, up to date, mechanisms involved remain to be precisely elucidated.

Control of symbiosis by the whole plant N demand

Symbiotic organ development is also under the control of systemic signals integrated at the whole plant level. Nodule formation is inhibited by preexisting nodules through the autoregulation of nodulation (AON) pathway (review by [START_REF] Ferguson | Legume nodulation : The host controls the party[END_REF]. A role of the N status of the plant in AON was suggested by the ability of several AON mutants to nodulate in the presence of high concentrations of nitrate that normally systemically inhibits nodulation in wild type plants. Conversely, a plant N deficit releases this repressive mechanism resulting in the stimulation of nodule formation [START_REF] Jeudy | Adaptation of Medicago truncatula to nitrogen limitation is modulated via local and systemic nodule developmental responses[END_REF]. This contributes to the adjustment of nodule number to the N demand of the plant, and may explain the stimulation of nodulation frequently observed in plant mono-inoculated with poorly N 2 fixing rhizobia [START_REF] Bourion | Co-inoculation of a pea core-collection with diverse rhizobial strains shows competitiveness for nodulation and efficiency of nitrogen fixation are distinct traits in the interaction[END_REF]. Systemic regulations of mature symbiotic organs function and development by the whole plant N demand have been evidenced in M. truncatula using split root systems [START_REF] Jeudy | Adaptation of Medicago truncatula to nitrogen limitation is modulated via local and systemic nodule developmental responses[END_REF][START_REF] Laguerre | Local and systemic N signaling are involved in Medicago truncatula preference for the most efficient Sinorhizobium symbiotic partners[END_REF][START_REF] Ruffel | Systemic signaling of the plant nitrogen status triggers specific transcriptome responses depending on the nitrogen source in Medicago truncatula[END_REF]. The whole plant N satiety systemic signaling results in a rapid repression of the N 2 fixation activity as well as in the initiation of nodule senescence. Whether this repression is the consequence of senescence or a direct modulation of the N 2 fixation activity is not known. A change in permeability to oxygen within the nodule (so called the "oxygen barrier") has been also proposed [START_REF] Hunt | Gas exchange of legume nodules and the regulation of nitrogenase activity[END_REF], but whether this change is the consequence or the cause of the reduction of N 2 fixation remains once more a matter of debate. A whole plant N deficit obtained either by Ar/O 2 treatments or by inoculation with fix À mutant bacteria (fix À roots) in a split-root experimental system triggers a compensatory response on the remaining fix þ roots [START_REF] Jeudy | Adaptation of Medicago truncatula to nitrogen limitation is modulated via local and systemic nodule developmental responses[END_REF][START_REF] Laguerre | Local and systemic N signaling are involved in Medicago truncatula preference for the most efficient Sinorhizobium symbiotic partners[END_REF]. It is firstly observed a systemic stimulation of nodule expansion, and secondly the formation of additional symbiotic organs [START_REF] Jeudy | Adaptation of Medicago truncatula to nitrogen limitation is modulated via local and systemic nodule developmental responses[END_REF][START_REF] Laguerre | Local and systemic N signaling are involved in Medicago truncatula preference for the most efficient Sinorhizobium symbiotic partners[END_REF]. Whether this developmental response is associated to the upregulation of the specific N 2 fixation activity (per gram of nodule) remains controversial [START_REF] Laguerre | Local and systemic N signaling are involved in Medicago truncatula preference for the most efficient Sinorhizobium symbiotic partners[END_REF][START_REF] Ruffel | Systemic signaling of the plant nitrogen status triggers specific transcriptome responses depending on the nitrogen source in Medicago truncatula[END_REF]Sulieman & Schulze, 2010). Systemic mechanisms adjusting the N 2 fixation capacity to the symbiotic plant N demand are instrumental for the root nutrient "foraging", which is relevant to optimize plant growth in soil conditions that are intrinsically highly variable in time and space. These systemic regulations enable the plant to compensate a lower N 2 fixation in the inefficient part of its symbiotic root system by stimulating the symbiotic development of the remaining beneficial roots. In contrast to the local regulation described above ("sanction"), this mechanism integrating the N 2 fixation capacity to the plant N demand is likely to operate at the scale of the root bundle rather than at the scale of the individual nodule [START_REF] Laguerre | Local and systemic N signaling are involved in Medicago truncatula preference for the most efficient Sinorhizobium symbiotic partners[END_REF]. A plant facing a uniform reduction of its symbiotic root capacity (e.g. having both fixþ and fix-nodules uniformly distributed on its root system) is unable to triggers this systemic response probably because it is not possible to discriminate between efficient and inefficient root bundles and therefore to allocate resources preferentially to the efficient symbiotic roots [START_REF] Laguerre | Local and systemic N signaling are involved in Medicago truncatula preference for the most efficient Sinorhizobium symbiotic partners[END_REF].

Very little is known about the nature of systemic N signals [START_REF] Parsons | Nodule growth and activity may be regulated by a feedback mechanism involving phloem nitrogen*[END_REF]. As addition of amino acids in plant nutrient media generally rapidly represses N 2 fixation, a pioneer hypothesis was that products of N assimilation, namely amino acid translocated through the phloem from shoots to roots, may act as mobile signals [START_REF] Bacanamwo | The feedback mechanism of nitrate inhibition of nitrogenase activity in soybean may involve asparagine and/or products of its metabolism[END_REF][START_REF] Sulieman | Asparagine as a major factor in the N-feedback regulation of N2 fixation in Medicago truncatula[END_REF]Sulieman & Schulze, 2010). However, this hypothesis was never supported by a clear demonstration, as amino acids are also N sources rapidly assimilated and are able to trigger a repression of N 2 fixation without inducing a direct signaling effect. Mechanisms behind the systemic regulation of symbiosis by N therefore remain mostly not known. AON is suggested to be implicated in the regulation of nodule formation by the N demand (Fig. 1; reviewed by [START_REF] Ferguson | Legume nodulation : The host controls the party[END_REF], as AON hypernodulating mutants are generally able to form nodules independently of the presence of a high level of mineral N, as previously mentioned [START_REF] Krusell | Shoot control of root development and nodulation is mediated by a receptor-like kinase[END_REF][START_REF] Olsson | Lack of systemic suppression of nodulation in split root systems of supernodulating soybean (Glycine max [L.] Merr.) mutants[END_REF]. However (1) N is not the only driver of AON, as the AON pathway is activated far before the nodule becomes N 2 fixing [START_REF] Kosslak | Suppression of nodule development of one side of a split-root system of soybeans caused by prior inoculation of the other side[END_REF][START_REF] Kosslak | Competition of Rhizobium japonicum strains in early stages of soybean nodulation[END_REF]; and (2), the nodule expansion response to plant N deficit remains active in hypernodulating mutants, suggesting that additional AON-independent mechanisms are implicated [START_REF] Jeudy | Adaptation of Medicago truncatula to nitrogen limitation is modulated via local and systemic nodule developmental responses[END_REF][START_REF] Kassaw | Multiple autoregulation of nodulation (AON) signals identified through split root analysis of Medicago truncatula sunn and rdn1 mutants[END_REF]. Interestingly, another systemic mechanism acting in legumes in parallel of the classical AON pathway to positively regulate nodule formation was discovered recently [START_REF] Huault | Local and systemic regulation of plant root system Architecture and symbiotic nodulation by a receptor-like kinase[END_REF][START_REF] Laffont | Independent regulation of symbiotic nodulation by the SUNN negative and CRA2 positive systemic pathways[END_REF], but its function in symbiotic N signaling remain to be fully understood.

Differential allocation of C metabolites by the plant to the nodules

Symbiotic organs require large fluxes of C metabolites (namely sucrose and organic acids) translocated from photosynthetic shoots to nodules through the phloem. The main part of these C fluxes is required to fuel N 2 fixation both as energy, as reducing power sources, and as C acceptors for ammonium assimilation [START_REF] Oldroyd | The rules of engagement in the legume-rhizobial symbiosis[END_REF]. C metabolites are also major resources required for root and nodule development (Fig. 1). Amino acids are products of C and N metabolisms that are tightly adjusted [START_REF] Voisin | Symbiotic N2 fixation activity in relation to C economy of Pisum sativum L. as a function of plant phenology[END_REF]. A high CO 2 level increases photosynthesis and C metabolites production in the shoot, therefore enhancing N 2 fixation in roots and the nodule biomass [START_REF] Rogers | Increased C availability at elevated carbon dioxide concentration improves N assimilation in a legume[END_REF][START_REF] Rogers | Will elevated carbon dioxide concentration amplify the benefits of nitrogen fixation in legumes?[END_REF]. As an elevation of CO 2 is not generally associated to an increase of nitrate uptake from the soil, it was suggested that symbiotic N 2 fixation will become more ecologically competitive compared to nitrate acquisition in a context of climate change associated to a strong increase of atmospheric CO 2 concentrations [START_REF] Rogers | Will elevated carbon dioxide concentration amplify the benefits of nitrogen fixation in legumes?[END_REF]. It is generally assumed that the C provision to the nodule limits N 2 fixation efficiency [START_REF] Rogers | Increased C availability at elevated carbon dioxide concentration improves N assimilation in a legume[END_REF]. Variations of N 2 fixation capacity of symbiotic associations may be associated to differences in the C use efficiency of bacteroids. For example, the activity of so-called the gamma-aminobutyric acid "shunt" of the bacteroid tricarboxylic acid cycle (Sulieman & Schulze, 2010), or plant/bacteroid amino acid exchanges [START_REF] Lodwig | Amino-acid cycling drives nitrogen fixation in the legume-rhizobium symbiosis[END_REF][START_REF] Prell | Legumes regulate Rhizobium bacteroid development and persistence by the supply of branched-chain amino acids[END_REF] have been implicated in these variations. The hypothesis that differential allocations of C metabolites may be a driver to pilot symbiotic organ development and function has been frequently suggested [START_REF] Voisin | Symbiotic N2 fixation activity in relation to C economy of Pisum sativum L. as a function of plant phenology[END_REF] and references therein), but only few studies have directly investigated this hypothesis [START_REF] Jeudy | Adaptation of Medicago truncatula to nitrogen limitation is modulated via local and systemic nodule developmental responses[END_REF]. Indeed, as C metabolites fuel nodule functioning and development, C allocation and N 2 fixation are always correlated and therefore, specific signaling associated to C allocation is difficult to discriminate from N signaling (Fig. 1). Nevertheless, a 13 C labeling experiment has shown that the systemic stimulation of nodule development in response to a local N deficit is correlated to very rapid changes of C metabolite allocation toward symbiotic organs before any measurable response on nodule development can be detected [START_REF] Jeudy | Adaptation of Medicago truncatula to nitrogen limitation is modulated via local and systemic nodule developmental responses[END_REF]. This is in agreement with the hypothesis that plant C metabolites allocation to the bacteroid mediates at least a part of the plant N demand systemic response.

According to this model, C allocation to nodules may be a driver allowing the plant to pilot the whole plant systemic preference toward N 2 fixing efficient structures (i.e. with efficient partners) to the expense of the inefficient ones (i.e. with inefficient partners). However, how the plant perceive individual nodule N 2 fixation efficiency and how the plant controls the differential C metabolite allocation toward N 2 fixing efficient versus inefficient nodules is unknown and will deserve future investigations.

Conclusions

Symbiotic legumes are strategical for sustainable agriculture as well as a source of proteins for both human and animal food. Genetic selection during domestication improved their performances to agriculture needs (i.e. increased grain yields and protein content; [START_REF] Duc | Breeding annual grain legumes for sustainable Agriculture : New methods to approach complex traits and target new cultivar ideotypes[END_REF][START_REF] Zhou | Resequencing 302 wild and cultivated accessions identifies genes related to domestication and improvement in soybean[END_REF], however the symbiotic interaction with rhizobia was rarely considered as a selection trait. Consequently, plant selection was even occasionally associated to a reduction of symbiotic capacities (Pérez-Jaramillo, Mendes, & Raaijmakers, 2016; [START_REF] Weese | Long-term nitrogen addition causes the evolution of less-cooperative mutualists[END_REF]. Inoculation strategies were then designed to bring in field more efficient N-fixing rhizobia for different legume crops [START_REF] Triplett | Genetics of competition for nodulation of legumes[END_REF]. Nevertheless, inoculation strategies frequently failed because highly efficient selected strains were outcompeted by indigenous bacteria, which were highly competitive but poorly N 2 fixing efficient with host plants [START_REF] Triplett | Genetics of competition for nodulation of legumes[END_REF]. Identifying rhizobium genetic determinants controlling AFN and CFN is therefore a key to allow selecting bacteria well adapted to inoculation strategies, i.e. both competitive and efficient. As the effect of biotic and abiotic soil environmental variations on AFN and CFN are almost unknown, a new frontier is to decipher and predict their impacts on early partner choice, in order to improve and stabilize inoculation strategies.

Legume genetic selection seems to have sometime reduced their wild capacities to interact with the rhizobial genetic diversity existing in natural soil populations [START_REF] Bourion | Co-inoculation of a pea core-collection with diverse rhizobial strains shows competitiveness for nodulation and efficiency of nitrogen fixation are distinct traits in the interaction[END_REF][START_REF] Kim | Phylogenetic diversity of Mesorhizobium in chickpea[END_REF][START_REF] Mutch | Diversity and specificity of Rhizobium leguminosarum biovar viciae on wild and cultivated legumes[END_REF], and in laboratory conditions legume productivity can be decreased when associated with a mixture of rhizobium genotypes compared to mono-inoculations [START_REF] Barrett | Partner diversity and identity impacts on plant productivity in Acaciaerhizobial interactions[END_REF]. Some domesticated soybean cultivars have an improved SNF when mono-inoculated with elite bacteria than wild soybeans [START_REF] Muñoz | Data from : Improvement in nitrogen fixation capacity could be part of the domestication process in soybean[END_REF]. However, the gain is lower for the domesticated genotypes than for wild soybeans when a mixture of effective and ineffective rhizobial strains is used as inoculant [START_REF] Kiers | Human selection and the relaxation of legume defences against ineffective rhizobia[END_REF]. As legume genetic selection programs using single-strain inoculation tend to select specific traits associated to a specific bacterial strain, selection of new cultivars able to maintain high symbiotic performances upon multi-inoculation may be a new strategy to improve symbiotic capacities of legumes. The establishment of rhizobial core collections covering geographical, genomic, and symbiotic (i.e. nod genes .) diversities, could be interesting tools to measure legume agronomic traits when challenged with multiple different partners.

Rhizobia are not obligate symbionts and can then be found as free-living bacteria in soils, meaning that their interaction with legumes is therefore only optional for their maintenance, survival and multiplication. Consequently, the dynamic of rhizobial populations cannot be explained only on the basis of their symbiotic interaction traits, and other selection pressures drive genetic population structures in soils. Notably, certain genotypes of rhizobia are able to colonize the endorhizosphere of non-legumes and to act potentially as Plant-Growth Promoting Rhizobacteria (PGPR; [START_REF] Tan | Assessment of plant growth-promoting rhizobacteria (PGPR) and rhizobia as multi-strain biofertilizer on growth and N2 fixation of rice plant[END_REF][START_REF] Adnan | Impact of rhizobial inoculum and inorganic fertilizers on nutrients (NPK) availability and uptake in wheat crop[END_REF][START_REF] Santoyo | Plant growth-promoting bacterial endophytes[END_REF][START_REF] Vargas | Potential of rhizobia as plant growth-promoting rhizobacteria[END_REF]. In this case, the plant endorhizosphere likely plays the role of an ecological niche that favors bacterial proliferation, similarly as legume nodules. Therefore, soils contain a large set of rhizobia having heterogeneous behaviors with various plants, including non-legumes, and their soil symbiotic capacities are then very difficult to predict. New sequencing technologies, such as metagenomics and metabarcoding, have allowed to better describe dynamics of soil bacterial communities [START_REF] Daniel | The metagenomics of soil[END_REF][START_REF] Taberlet | Towards next-generation biodiversity assessment using DNA metabarcoding[END_REF][START_REF] Tringe | Comparative metagenomics of Microbial communities[END_REF], but these methods cannot predict symbiotic functions yet.

Fig. 1

 1 Fig. 1 Early partner choice and post-infection partner preference in the legume-rhizobium symbiosis in a context of multiple partners. The schematized transversal root section represents the main developmental steps of the legume-rhizobium symbiosis, from the root hairs infection to the N 2 fixing nodule. Rhizobia in soils are diverse and display variable Abilities and Competitiveness to Form root Nodules (AFN and CFN), as well as variable capacities to drive efficient Symbiotic N 2 Fixation (SNF). Nod factors, surface polysaccharides, and secretion systems from rhizobia, as well as flavonoids and LysM-RLKs from legume hosts, are the main factors modulating the early partner choice between symbiotic partners. Symbiosis initiation and nodule formation result in young nodules that are non N 2 fixing and differentiate into expanded mature nodules with a large central zone containing N 2 fixing bacteroids. In these nodules, large fluxes of nitrogen (N) from the nodules to the plant roots and carbon (C) phytosynthates from the plant to the nodules are exchanged. Evidences suggest that the local N 2 fixation capacity, the whole plant N demand, and C allocation may pilot the proliferation of efficient N 2 -fixing nodules to the expenses of the inefficient ones, and are therefore potential drivers of Post-Infection Partner Preference (PIPP). Dark green: root hairs and epidermis; pale green: cortex; middle green: division of cortical cells; light blue: endodermis; dark blue: pericycle; pink, stele tissues including vascular bundles; orange: nodule meristem; pink points: nodule infection zone; pink circles: nodule N 2 fixation zone; blue arrow: N flux; orange arrow: C flux. Different rhizobium genotypes are represented with different colors.

Stephane Boivin and Marc Lepetit

Partner preference in the legume-rhizobia symbiosis

However, the use of bacterial genetic markers, associated with symbiotic traits such as AFN, CFN and PIPP, should be a way for improving the prediction of soil symbiotic capacities.