Christopher Thomas

Acirete S Da

Rosa Simões

Claudine Lacroix

José Roberto Iglesias

Bernard Coqblin

Effect of anisotropy in the S = 1 underscreened Kondo lattice

We study the effect of crystal field anisotropy in the underscreened S = 1 Kondo lattice model. Starting from the two orbital Anderson lattice model and including a local anisotropy term, we show, through Schrieffer-Wolff transformation, that local anisotropy is equivalent to an anisotropic Kondo interaction (J = J ⊥ ). The competition and coexistence between ferromagnetism and Kondo effect in this effective model is studied within a generalized mean-field approximation. Several regimes are obtained, depending on the parameters, exhibiting or not coexistence of magnetic order and Kondo effect. Particularly, we show that a re-entrant Kondo phase at low temperature can be obtained. We are also able to describe phases where the Kondo temperature is smaller than the Curie temperature (TK < TC ). We propose that some aspects of uranium and neptunium compounds that present coexistence of Kondo effect and ferromagnetism, can be understood within this model.

Introduction

The properties of many cerium or ytterbium compounds are well accounted for by the S = 1/2 Kondo-lattice model, where a strong competition exists between the Kondo effect and magnetic ordering arising from the RKKY (Ruderman-Kittel-Kasuya-Yosida) interaction between rare-earth atoms at different lattice sites. This situation is well described by the Doniach diagram, [START_REF] Doniach | Phase diagram for the Kondo lattice[END_REF][START_REF] Iglesias | Revisited Doniach diagram: Influence of short-range antiferromagnetic correlations in the Kondo lattice[END_REF] which gives the variation of the Néel temperature and of the Kondo temperature with increasing antiferromagnetic intrasite exchange interaction J K between localized spins and conduction-electron spins. However, uranium and neptunium compounds exhibit a different behavior. The Kondo behavior of rare earth and actinide compounds depends on the number of f electrons. For example, in the case of cerium and ytterbium rare earth systems, the localized S = 1/2 spins of the 4f electrons interact with the spin of the conduction electrons via the s -f exchange, leading to Kondo and magnetic interactions that can be described by the usual S = 1/2 Kondo lattice model. The situation is different for the uranium and neptunium compounds. In this case, the total spin of the 5f electrons is S > 1/2 and screening may be only partial when the number of conduction electrons channels n is smaller than 2S [START_REF] Nozières | Kondo effect in real metals[END_REF]. Many actinide compounds, like UTe [START_REF] Schoenes | Variation of f-electron localization in diluted US and UTe[END_REF], UCu 0.9 Sb 2 [START_REF] Bukowski | Single-crystalline study of the ferromagnetic Kondo[END_REF], NpNiSi 2 [START_REF] Colineau | Magnetic properties of NpNiSi 2[END_REF] and Np 2 PdGa 3 [START_REF] Tran | Magnetic and electronic properties of the ferromagnetic Kondo-lattice system Np 2 PdGa 3[END_REF], have been reported to exhibit an underscreened Kondo effect; all of them also exhibit ferromagnetic order, with a relatively large Curie temperature of the order of 50-100 K. Very recently it was found another neptunium compound, Np 2 PtGa 3 [START_REF] Tran | Ferromagnetic behavior of the Kondo lattice compound Np 2 PtGa 3[END_REF], presenting a similar effect, i.e. coexistence of Kondo effect and ferromagnetism, but with a smaller Curie temperature ∼ 26 K.

Another important point is that the 5f electrons are less localized than the 4f electrons [START_REF] Zwicknagl | Microscopic description of origin of heavy quasiparticles in UPt 3[END_REF][START_REF] Zwicknagl | Fermi surface and heavy masses for UPd 2 Al 3[END_REF][START_REF] Hoshino | Itinerant Versus Localized Heavy-Electron Magnetism[END_REF] and their localized character can be easily changed under pressure. For example, when applying pressure in UTe samples, the Curie temperature, T C initially increases, then reaches a maximum and decreases [START_REF] Schoenes | Transport properties of uranium monochalcogenide and monopnictide single crystals[END_REF]. This can be understood as a decrease of the degree of localization of the 5f electrons under pressure [START_REF] Sheng | Pressure-induced magnetic ordering effects in correlated-electron uranium monochalcogenides[END_REF][START_REF] Thomas | Application of the S=1 underscreened Anderson lattice model to Kondo uranium and neptunium compounds[END_REF].

In previous works [START_REF] Thomas | Application of the S=1 underscreened Anderson lattice model to Kondo uranium and neptunium compounds[END_REF][START_REF] Perkins | The underscreened Kondo lattice model applied to heavy fermion uranium compounds[END_REF][START_REF] Thomas | Application of the underscreened Kondo lattice model to neptunium compounds[END_REF], the possible coexistence of ferromagnetic order and Kondo effect was dis-cussed in detail. Particularly, the Schrieffer-Wolf transformation was applied to a degenerate periodic Anderson Hamiltonian with two f -electrons on a degenerate f -level, resulting in a S = 1 spin in the ground state, and a Kondo interaction between the S = 1 spins and the conduction electrons was obtained, together with an effective 5f bandwidth that corresponds to a delocalization of the f -electrons [START_REF] Thomas | Application of the S=1 underscreened Anderson lattice model to Kondo uranium and neptunium compounds[END_REF]. In this way it was possible to obtain a qualitative phase diagram that agrees with the experimental results for some uranium and neptunium compounds which show coexistence of Kondo effect and ferromagnetism.

Here we are interested in the effect of crystal field anisotropy on the S = 1 Kondo lattice model. The effect of anisotropy has been well studied for the case of S = 1/2 Kondo compounds, particularly cerium compounds [START_REF] Cornut | Influence of Crystalline Field On Kondo Effect of Alloys and Compounds With Cerium Impurities[END_REF][START_REF] Coqblin | Strongly Correlated Electron Behaviors and Heavy Fermions in Anomalous Rare-earth and actinide Systems[END_REF] where the specific heat and transport properties have been well understood by considering anisotropy. In the case of actinide compounds with larger values of the spin, and stronger delocalization of the f -electrons, we also expect that the behavior of the Kondo and Curie temperatures will change when anisotropy is considered. So, in the following we analyze the anisotropic underscreened Kondo lattice (UKL) model, focusing on two different regimes which are peculiar to the S = 1 UKL model : the re-entrant Kondo regime and the ferromagnetic phase with T K < T C .

The UKL Model with anisotropy

Following ref. [START_REF] Thomas | Application of the S=1 underscreened Anderson lattice model to Kondo uranium and neptunium compounds[END_REF] we first describe the 5f electrons system using the periodic Anderson lattice model with two localized orbitals. This allow us to describe local S = 1 magnetic sites. The Hamiltonian is written as follows:

H = H 0 + H hyb , H 0 = H s + H f + H ani , (1)
where

H s = kσ ǫ k c † kσ c kσ , (2)
H f = iασ ǫ f n f iασ + i U (n f i1↑ n f i1↓ + n f i2↑ n f i2↓ ) + U ′ (n f i1↑ n f i2↓ + n f i1↓ n f i2↑ ) + (U ′ -J)(n f i1↑ n f i2↑ + n f i1↓ n f i2↓ ) -J(f † i1↑ f i1↓ f † i2↓ f i2↑ + h.c.) , (3)
H hyb = ikασ V kα e ik•Ri c † kσ f iασ + V * kα e -ik•Ri f † iασ c kσ , (4)
H ani = -D i (S f z ) 2 i . (5)
H s represents the kinetic energy for the conduction electrons, being ǫ k the dispersion relation and c † kσ (c kσ ) the creation (annihilation) operator for conduction electrons.

As usual, no degeneracy of the conduction band is considered. The local energy ǫ f , the Coulomb interaction of two f electrons in the same orbital, U , in different orbitals, U ′ and the Hund coupling, J, are included into H f , with f † iασ (f iασ ) being the creation (annihilation) operator in the site i, orbital α and spin σ. Finally, the term H hyb represents the hybridization between the conduction electrons and the f electrons and H ani is a local magnetic anisotropy, leading to uniaxial (for D > 0) or planar anisotropy (for D < 0). This model has been partially studied in ref. [START_REF] Thomas | Application of the S=1 underscreened Anderson lattice model to Kondo uranium and neptunium compounds[END_REF] but without the last term. Here we study the effect of anisotropy. For this purpose we generalize the Schrieffer-Wolff (SW) transformation [START_REF] Schrieffer | Relation between Anderson and Kondo Hamiltonians[END_REF] for the Hamiltonian described in equation ( 1) (details of the SW transformation are given in Appendix A). The anisotropy term in equation ( 5) removes the degeneracy between the f states S z = | ± 1 and S z = |0 . For positive values of the parameter D, the states with S f z = ±1 have smaller energy than the one with S z = 0.

From the SW transformation of the Hamiltonian (1), the Kondo interaction can be written as:

H K = 1 2 ik J ⊥ (c † k ′ ↑ c k↓ S f - i + c † k ′ ↓ c k↑ S f + i ) +J (c † k ′ ↑ c k↑ -c † k ′ ↓ c k↓ )S f zi , (6)
where the parallel (diagonal) and the perpendicular (nondiagonal) Kondo interactions are

J = -2 |V kF | 2 U ′ -J + ǫ f -µ -3D/4 , J ⊥ = -|V kF | 2 1 U ′ -J + ǫ f -µ -3D/4 + 1 U ′ -J + ǫ f -µ + D/4 , (7)
To stabilize ferromagnetic order, we include in the UKL model a ferromagnetic exchange interaction between neighboring spins

H H = 1 2 J H ij S f i • S f j , with J H < 0.
The presence of the anisotropy is explicitly visible in the expressions of these interaction parameters J and J ⊥ , given by equation [START_REF] Tran | Magnetic and electronic properties of the ferromagnetic Kondo-lattice system Np 2 PdGa 3[END_REF]. Thus, the magnetic anisotropy induces an anisotropic Kondo interaction. It can be checked easily from equation ( 7) that, D > 0 implies that J < J ⊥ . We define new parameters α and J K as follows:

α = J J ⊥ , and
J K = J + J ⊥ 2 . ( 8
)
D > 0 is equivalent to α < 1. The anisotropic S = 1/2 Kondo lattice model has been studied by several authors [START_REF] Zhang | Kondo singlet state coexisting with antiferromagnetic long-range order: A possible ground state for Kondo insulators[END_REF] without any microscopic justification of the anisotropy of the interaction; here we show that for S = 1, the anisotropic Kondo interaction results from the local anisotropy.

Influence of anisotropy on the phase diagram

In the following, we use the same generalized mean field decoupling scheme already utilized in refs. [START_REF] Thomas | Application of the S=1 underscreened Anderson lattice model to Kondo uranium and neptunium compounds[END_REF][START_REF] Perkins | The underscreened Kondo lattice model applied to heavy fermion uranium compounds[END_REF] and calculate self-consistently the order parameters:

M f i = S z i ≡ S z i1 + S z i2
for the magnetization of the f electrons and λ iσ = α f † iασ c iσ for the Kondo hybridization as a function of J K , temperature and α. From the variation of the critical temperature for ferromagnetic order, T C , and Kondo temperature, T K , we can build the phase diagram. As it will be shown in the next paragraph, it is also necessary to introduce two characteristic temperatures T 1 and T ′ 1 , associated with re-entrant phases that appear when the order parameters, λ σ and M f , are zero at T = 0 but different from zero above T 1 and T ′ 1 . In all the following calculations, the half bandwidth W D is taken as the energy unit, and we fix the intersite exchange J H = -0.01, the conduction band filling to n c = 0.8, and the total number of f electrons per site and per orbital to n f = 1.

In the UKL model, the f electrons are not purely localized and a small effective bandwidth was obtained from the SW transformation [START_REF] Thomas | Application of the S=1 underscreened Anderson lattice model to Kondo uranium and neptunium compounds[END_REF]. This effective f bandwidth is defined as

W f = 2A σ ǫ k , (9)
where A σ is proportional to the magnetization of the f electrons M f , the Kondo exchange interactions J's and a numerical parameter P (see equation [START_REF] Troć | Dualism of the 5f electrons of the ferromagnetic superconductor UGe 2 as seen in magnetic, transport, and specific-heat data[END_REF] in Appendix B and ref. [START_REF] Thomas | Application of the S=1 underscreened Anderson lattice model to Kondo uranium and neptunium compounds[END_REF]) that measures the width of the f -band compared to the width of the conduction band. Here, we consider P as a free parameter, and we describe the results for two values of P : P = 0.20 and for P = 0.30. The phase diagram as a function of J K is shown on figure 1(a) for P = 0.20, and in the absence of anisotropy (α = 1). When the Kondo coupling J K is not strong enough (J K 0.51), Kondo effect is not stable for T → 0, but it is stable in a narrow temperature region for J K very close to 0.50. In this region, the Kondo effect can occur between two characteristic temperatures: T 1 and T K . Figure 3 shows the behavior of the mean field parameters as a function of temperature. Such re-entrant behavior corresponds to the case presented in figure 3(b) for J K = 0.50. Also, figure 1(b) shows the phase diagram for a value of J K = 0.50, and as a function of α. The re-entrance is found in a large range of α. The width of the re-entrance region is maximum for α ∼ 1 and decreases when α increases. On the other hand, the Kondo effect is enhanced when α decreases to values smaller than 1. Thus, it seems clear that the anisotropy plays against the Kondo effect while the Curie temperature is almost insensitive to changes in the anisotropy.

Figure 2(a) shows the phase diagram for a larger f -bandwidth, (P = 0.30) and no anisotropy (α = 1). In this case, there is a region where T K < T C , i.e. Kondo effect start to occur within the ferromagnetic phase. Such a behavior corresponds to some experiments in actinide compounds [START_REF] Colineau | Magnetic properties of NpNiSi 2[END_REF][START_REF] Tran | Magnetic and electronic properties of the ferromagnetic Kondo-lattice system Np 2 PdGa 3[END_REF]. It can be seen on figure 3(e), close to the critical J K value below which Kondo effect disappears, that the transition is abrupt between a ferromagnetic state and mixed phase Kondo+ferromagnetic with a discontinuous jump of the magnetization. The variation of the critical temperatures for fixed J K = 0.43, as a function of anisotropy, is presented in figure 2(b). In this case, there is also a re-entrant phase, but for the ferromagnetic phase: the ferromagnetic state is stable only between two temperatures T ′ 1 and T C , but below T ′ 1 , Kondo effect dominates and ferromagnetism disappears. This behavior can be clearly seen on figure 3(d), where it is evident that ferromagnetism disappears at low temperature. Summarizing, for both values of P , T C has a similar behavior. It increases with increasing J K and has a maximum when T C is of the same order than T K . This variation of T C corresponds to what was observed in experiments [START_REF] Schoenes | Variation of f-electron localization in diluted US and UTe[END_REF][START_REF] Link | High-pressure resistance study of UTe[END_REF][START_REF] Cornelius | High-pressure susceptibility studies on the ferromagnetic uranium monochalcogenides US, USe and UTe[END_REF] and it was already discussed from a theoretical point of view in [START_REF] Cooper | f -Electron delocalization/localization and the abrupt disappearance of uranium magnetic ordering with dilution alloying[END_REF], where it was proposed that this maximum is due to delocalization of the 5f electrons. Here, as in our previous papers, [START_REF] Perkins | The underscreened Kondo lattice model applied to heavy fermion uranium compounds[END_REF][START_REF] Thomas | Application of the S=1 underscreened Anderson lattice model to Kondo uranium and neptunium compounds[END_REF], we propose that this maximum is related to the competition with Kondo effect.

Figure 3 presents the variation of the order parameters M f and λ ↑ as a function of temperature, for different values of α for P = 0.20, (figures 3(a-c)), and J K = 0.50, and for P = 0.30 and J K = 0.43, (figures 3(df)). The values of α in figure 3 were chosen to emphasize the difference between the possible scenarios present for this model.

For P = 0.20, the coexistence of FM and Kondo effect is clearly observed for α = 0.90, where T K > T C (figure 3(a)). Close to the case without anisotropy (α ≈ 1), the behavior is very interesting, as already pointed out: at low T , the system presents a purely FM phase, while a coexistence FM + Kondo is observed above a temperature T 1 (figure 3(b)). Increasing α, ferromagnetism dominates, and Kondo effect is observed only in a small temperature-region (figure 3(c)). On the other hand, the results for P = 0.30 are very different. For α 0.96, Kondo effect is strong enough to destroy completely the FM state at low temperature (figure 3(d)). A coexistence of FM + Kondo is observed at low T when α ≈ 1 (figure 3(e)). With decreasing temperature, there is first a ferromagnetic state between T C and T K and then a mixed Kondo-ferromagnetic state below T K with a clear decrease of the ferromagnetic magnetization. In the Kondo-ferromagnetic phase, the f -moments are partially screened, and the f -moments are reduced to a value close to 1/2. This is in agreement with the description given by Nozières and Blandin [START_REF] Nozières | Kondo effect in real metals[END_REF] of the underscreened Kondo effect: the conduction electrons cannot completely screen a S = 1 localized spin, and the system is described below T K by an effective S = 1/2 spin, which can order due to the intersite exchange. For bigger values of α the FM is predominant and no Kondo effect is observed (figure 3(f)).

Summary and conclusions

We have shown that the anisotropic UKL Hamiltonian can be derived from the S = 1 Kondo lattice model, if a local anisotropy term is included. A large variety of possible phase diagrams has been obtained, exhibiting interesting behaviors, as the possibility of abrupt transitions in the order parameters or re-entrant Kondo and FM phases at finite temperatures. The results have been shown for two different values of the parameter P , which measures the delocalization of the 5f electrons. The changes when the calculations are performed with other possible values of P are only qualitative.

Finally, the results shown in this paper present some similarities with experimental results on two groups of compounds. For P = 0.20, the variation of anisotropy can describe the variation of the Kondo and Curie temperatures as a function of pressure or magnetic field in UGe 2 [START_REF] Saxena | Superconductivity on the border of itinerant-electron ferromagnetism in UGe 2[END_REF][START_REF] Hardy | Two magnetic Grüneisen parameters in the ferromagnetic superconductor UGe 2[END_REF][START_REF] Taufour | Tricritical Point and Wing Structure in the Itinerant Ferromagnet UGe 2[END_REF][START_REF] Troć | Dualism of the 5f electrons of the ferromagnetic superconductor UGe 2 as seen in magnetic, transport, and specific-heat data[END_REF]. In some regions of the phase diagram, a transition between two different ferromagnetic orders is observed, with a higher magnetic moment for T → 0. In our curves this can be observed in figure 3(b), where the transition occurs from FM to FM+Kondo phases. For P = 0.30, the kink found in 3(e) is also observed in some neptunium compounds (NpNiSi 2 , Np 2 PdGa 3 and Np 2 PtGa 3 ) [START_REF] Colineau | Magnetic properties of NpNiSi 2[END_REF][START_REF] Tran | Magnetic and electronic properties of the ferromagnetic Kondo-lattice system Np 2 PdGa 3[END_REF][START_REF] Tran | Ferromagnetic behavior of the Kondo lattice compound Np 2 PtGa 3[END_REF]. In these compounds, the magnetization at small applied magnetic field collapses at low temperatures, while the magnetization grows to a finite value and goes trough a second order transition for higher temperature. So, the UKL model, and the idea of a possible coexistence of Kondo effect and ferromagnetic order, first suggested by B. Coqblin [START_REF] Le Hur | Underscreened Kondo effect: A two S = 1 impurity model[END_REF][START_REF] Coqblin | Narrow-band effects in rareearths and actinides: Interaction between the Kondo effect and magnetism[END_REF][START_REF] Núñez Regueiro | The underscreened Kondo lattice model: application to uranium compounds[END_REF], is very promising for the description of actinide compounds that present Kondo effect and ferromagnetism.

c † kσ f † i1σ f † i2σ |0 ; E = U ′ -J + ǫ k + 2ǫ f -D , (11) c
† kσ 1 √ 2 f † i1↑ f † i2↓ + f † i1↓ f † i2↑ |0 ; E = U ′ -J + ǫ k + 2ǫ f , (12)
c † kσ c † k ′ σ ′ f † iασ ′′ |0 ; E = ǫ k + ǫ k ′ + ǫ f -D/4 . (13)
For the second process we have

f † jβσ ′ f † i1σ f † i2σ |0 ; E = U ′ -J + 3ǫ f -5D/4 , (14)
f † jβσ 1 √ 2 f † i1↑ f † i2↓ + f † i1↓ f † i2↑ |0 ; (15)
E = U ′ -J + 3ǫ f -D/4 , (16)
c † kσ f † jβσ ′ f † iασ ′′ |0 ; E = 2ǫ f + ǫ k -D/2 . ( 17
)
The first scattering process gives origin to the Kondo interaction. The inclusion of anisotropy in the model, equation 1, modifies the diagonal and the non-diagonal part of the Kondo interaction as shown below

H K = 1 2 ikk ′ J k,k ′ ⊥ (c † k ′ ↑ c k↓ S f - i + c † k ′ ↓ c k↑ S f + i ) +J k,k ′ (c † k ′ ↑ c k↑ -c † k ′ ↓ c k↓ )S f zi , (18)
where the perpendicular and parallel part of

J k,k ′ are J k,k ′ ⊥ = -V k ′ α V * k α e i(k-k ′ )•Ri × 1 U ′ -J + ǫ f -ǫ k ′ -3D/4 + 1 U ′ -J + ǫ f -ǫ k + D/4 , (19)
J k,k ′ = -V k ′ α V * k α e i(k-k ′ )•Ri × 1 U ′ -J + ǫ f -ǫ k ′ -3D/4 + 1 U ′ -J + ǫ f -ǫ k -3D/4 . (20)

B Mean field approach

Taking into account all terms from the Schrieffer-Wolff transformation and the terms from H 0 and H H , a new Hamiltonian can be written as

H ≡ H 0 + H H + H . (21)
After a mean-field approximation an effective Hamiltonian is obtained and it reads

H = iασ E f σ n f iασ + kσ ǫ kσ n c kσ + kασ Λ σ λ kασ + λ † kασ + kασ A σ ǫ k f † kασ f kασ + C , (22)
where

E f σ = ǫ f + U ′ n f σ + (U ′ -J) n f σ + J σ m c - J 8 λ ↑ 2 + λ ↓ 2 - J ⊥ 4 λ ↑ λ ↓ + J H zσ M f + B σ , (23)
B σ = -P n f σ ǫ J 2 (1 + 2σ M f ) + J ⊥ 8 (1 -2σ M f ) + P n f σǫ J 8 (1 + 2σ M f ) - J ⊥ 8 (3 + 2σ M f ) , (24)
ǫ kσ = ǫ k + J σ M f , σ = ± 1 2 , (25)
Λ σ = - 1 4 J λ σ + J ⊥ λ σ , (26)
A σ = - P 32 3J + 4J ⊥ + 4σ M f 5J -2J ⊥ +3J M f 2 , (27)
C = -2U ′ N n f ↑ n f ↓ -(U ′ -J)N n f ↑ 2 + n f ↓ 2 + J 2 N λ ↑ 2 + λ ↓ 2 + J ⊥ N λ ↑ λ ↓ - J H 2 zN M f 2 -J N m c M f -4A σ n f σ ǫ , (28)
The value of zJ H is renormalized by zJ H → zJ H + D (z is the number of first neighbor and is taking equal to 6 in a cubic lattice). We consider the mean field parameters in the uniform solution, and we assume that both orbitals remain equivalent. We also define the average occupation number of conduction electrons, n c , where the magnetization is m c = 1 2 ( n c ↑ -n c ↓ ), and the average occupation number of f electrons per orbital, n f . The mean field parameters are obtained by calculating the Green's functions. Considering that the conduction electrons have a constant density of state ρ 0 = 1/2W D , the self-consistent equations are written as:

n c σ = ρ 0 WD -WD dǫ F 1σ (ǫ) -(A σ ǫ + E f σ )F 2σ (ǫ) , (29)
n f σ = ρ 0 2 WD -WD dǫ f (E f σ + A σ ǫ) + F 1σ (ǫ) -ǫ -µ + σJ M f F 2σ , (30)
λ σ = 2ρ 0 WD -WD F 2σ (ǫ)Λ σ , (31)
n f σ ǫ = ρ 0 2 WD -WD ǫdǫ f (E f σ + A σ ǫ) + F 1σ (ǫ) -ǫ -µ + σJ M f F 2σ , ( 32
)
where µ is the chemical potential, f (ω) = (1 + e ω/T ) -1 is the Fermi-Dirac distribution and

F 1σ (ǫ) = f [Ω + σ (ǫ)] -f [Ω - σ (ǫ)] (33) F 2σ (ǫ) = f [Ω + σ (ǫ)] -f [Ω - σ (ǫ)] ∆Ω σ (ǫ) , (34)
with

Ω ± σ (ǫ) = 1 2 ǫ(1 + A σ ) -µ + E f σ + σJ M f ± ∆Ω σ (ǫ) , (35)
∆Ω σ (ǫ) = ǫ(1 -A σ ) -µ -E f σ + σJ M f 2 + 8(Λ σ ) 2 .
(36)

Figure 1 :Figure 2 :

 12 Figure 1: (color online) Phase diagrams for P = 0.20. (a) T versus J K for α = 1 and (b) T versus α for J K = 0.50. The red color region represents the ferromagnetic order and the blue color region represents the Kondo phase. A region of coexistence can be observed in both phase diagrams.

Figure 3 :

 3 Figure 3: Variation of M f and λ ↑ as a function of temperature for different values of α in the two cases studied here, P = 0.20 and P = 0.30.

  This equation represents the scattering process from an initial state |a , through a intermediate state |c , to a final state |b where E a , E c and E b are the respective eigenenergies. The states |a , |b and |c should be eigenstates of H 0 . We basically consider two scattering process: the first one is the process where the initial and final states have one conduction electron and two f -electrons; the second scattering process have three f -electrons in both initial and final states.

								are defined as
	b| H|a =	1 2	c	b|H hyb |c c|H hyb |a	1 Ea -Ec	+	1 E b -Ec	.
							(10)
	The eigenstates and eigenenergies for the first process

Acknowledgments

CT acknowledge the financial support of Capes-Cofecub Ph 743-12. This research was also supported in part by the Brazilian Ministry of Science, Technology and Innovation (MCTI) and the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq). Research carried out with the aid of the Computer System of High Performance of the International Institute of Physics-UFRN, Natal, Brazil.

Appendix A Schrieffer-Wolff transformation

The Schrieffer-Wolff transformation [START_REF] Schrieffer | Relation between Anderson and Kondo Hamiltonians[END_REF] relates the Anderson and Kondo Hamiltonians. In this work we use the same method described in Ref. [START_REF] Schrieffer | Kondo effect -link between magnetic and nonmagnetic impurities in metals[END_REF], where the canonical transformation permit us to obtain from the hybridization term H hyb , a new term H, give by


Sandro Alves
email: sandropfalves@gmail.com

Guillaume Churlaud

Mickael Audrain

Kristin Michaelsen-Preusse

Romain Fol

Benoit Souchet

Jérôme Braudeau

Martin Korte

David Klatzmann
email: david.klatzmann@upmc.fr

Nathalie Cartier
email: nathalie.cartier@inserm.fr

Interleukin-2 improves amyloid pathology, synaptic failure and memory in Alzheimer's disease mice

Keywords: Neurological diseases, Immunomodulation, Immunosuppression, Therapy, Astrocytes, Neurons, AAV, Gene therapy

INTRODUCTION

There are many interactions between the central nervous and immune systems. The immune privileged nature of the brain has been revisited and it is clear that cells from the adaptive as well as innate immune system circulate in the brain [START_REF] Louveau | Revisiting the Mechanisms of CNS Immune Privilege[END_REF]. This has led to a renewed interest for investigating the role of the immune system in neurological diseases, beyond clearly immune-mediated pathologies such as multiple sclerosis. In this line, accumulating evidence suggests that inflammation plays an important role in the pathophysiology of neurodegenerative disorders, including Alzheimer's disease (AD) [START_REF] Heneka | Innate immunity in Alzheimer's disease[END_REF][START_REF] Heppner | Immune attack: the role of inflammation in Alzheimer disease[END_REF][START_REF] Skaper | The brain as a target for inflammatory processes and neuroprotective strategies[END_REF]. In Alzheimer's disease, amyloid-β peptide (Aβ) processed from the β-amyloid precursor protein (APP), accumulates and aggregates in senile plaques [START_REF] Hardy | Alzheimer's disease: the amyloid cascade hypothesis[END_REF]. Reactive astrocytes are observed in close association with senile plaques in Alzheimer's disease brains [START_REF] Shao | Astrocyte-apolipoprotein E associations in senile plaques in Alzheimer disease and vascular lesions: a regional immunohistochemical study[END_REF], contain intracellular Aβ deposits [START_REF] Pihlaja | Transplanted astrocytes internalize deposited beta-amyloid peptides in a transgenic mouse model of Alzheimer's disease[END_REF] and degrade Aβ contributing to Aβ clearance [START_REF] Nicoll | A new role for astrocytes: beta-amyloid homeostasis and degradation[END_REF]. Activated microglia also accumulates around senile plaques in Alzheimer's disease patients [START_REF] Mcgeer | Reactive microglia in patients with senile dementia of the Alzheimer type are positive for the histocompatibility glycoprotein HLA-DR[END_REF] and may restrict amyloid plaque formation by phagocytosing Aβ [START_REF] Simard | Bone marrow-derived microglia play a critical role in restricting senile plaque formation in Alzheimer's disease[END_REF]. Early stages of the neurodegenerative process are associated with glial dysfunction that may result in reduced Aβ clearance and cause disruptions in synaptic connectivity [START_REF] Heneka | Innate immunity in Alzheimer's disease[END_REF].

Cytokines, molecules involved in the cross-talk between cells of the immune and neuroendocrine systems, are secreted by microglia and astrocytes and regulate the intensity of the brain immune response [START_REF] Serpente | Innate immune system and inflammation in Alzheimer's disease: from pathogenesis to treatment[END_REF]. Hence, administration of Interleukin-4 (IL-4) and Interleukin-10 (IL-10), cytokines stimulating anti-inflammatory cascades, has been reported to improve symptoms in Alzheimer's disease mice [START_REF] Kiyota | CNS expression of anti-inflammatory cytokine interleukin-4 attenuates Alzheimer's disease-like pathogenesis in APP+PS1 bigenic mice[END_REF][START_REF] Kiyota | AAV serotype 2/1-mediated gene delivery of anti-inflammatory interleukin-10 enhances neurogenesis and cognitive function in APP+PS1 mice[END_REF].

Strikingly, the role of Interleukin-2 (IL-2) has not been much investigated in neurodegenerative diseases although numerous works highlighted the role of Interleukin-2 in the central nervous system (CNS) and immune systems. It has been described that Interleukin-2 can contact the CNS through the blood-brain-barrier (BBB) [START_REF] Waguespack | Interleukin-2 does not cross the bloodbrain barrier by a saturable transport system[END_REF].

Despite this, it has also been reported that Interleukin-2 access into the brain is limited given the absence of a transporter to the brain and further slowed by circulating elements [START_REF] Banks | Permeability of the mouse blood-brain barrier to murine interleukin-2: predominance of a saturable efflux system[END_REF]. It has numerous effects on hippocampal neurons, where its receptors are enriched, thus improving cognitive performances in rodents [START_REF] Dansokho | Regulatory T cells delay disease progression in Alzheimer-like pathology[END_REF][START_REF] Hanisch | Neurotoxic consequences of central long-term administration of interleukin-2 in rats[END_REF][START_REF] Lacosta | Influence of acute and repeated interleukin-2 administration on spatial learning, locomotor activity, exploratory behaviors, and anxiety[END_REF]. Furthermore, Interleukin-2 can afford trophic support to neurons and glia [START_REF] Awatsuji | Interleukin-2 as a neurotrophic factor for supporting the survival of neurons cultured from various regions of fetal rat brain[END_REF], enhancing neurite branching [START_REF] Sarder | Comparative effect of IL-2 and IL-6 on morphology of cultured hippocampal neurons from fetal rat brain[END_REF], dendritic development and spinogenesis [START_REF] Shen | Interleukin-2 enhances dendritic development and spinogenesis in cultured hippocampal neurons[END_REF], thus playing a role in neuronal development [START_REF] Sarder | Interleukin-2 promotes survival and neurite extension of cultured neurons from fetal rat brain[END_REF]. In line with these observations, Interleukin-2 knockout (KO) mice display cytoarchitectural modifications in the dentate gyrus of the hippocampus and have impaired learning and memory ability [START_REF] Beck | IL-2 deficiency results in altered septal and hippocampal cytoarchitecture: relation to development and neurotrophins[END_REF][START_REF] Petitto | Impaired learning and memory and altered hippocampal neurodevelopment resulting from interleukin-2 gene deletion[END_REF].

Recently, it has been suggested that impact on learning and memory in IL-2 KO mice mainly rely on indirect immune-related effects [START_REF] Petitto | Effects of Brain-Derived IL-2 Deficiency and the Development of Autoimmunity on Spatial Learning and Fear Conditioning[END_REF]. Besides these direct roles on brain cells and function, Interleukin-2 has pleiotropic immune function [START_REF] Klatzmann | The promise of low-dose interleukin-2 therapy for autoimmune and inflammatory diseases[END_REF]. However, low dose Interleukin-2 supports survival and function of regulatory T cells (Tregs), that control inflammation and autoimmunity [START_REF] Klatzmann | The promise of low-dose interleukin-2 therapy for autoimmune and inflammatory diseases[END_REF].

The anti-inflammatory effects of Tregs have been observed in various models of inflammatory diseases in mice [START_REF] Sakaguchi | Regulatory T cells and immune tolerance[END_REF][START_REF] Wing | Regulatory T cells exert checks and balances on self tolerance and autoimmunity[END_REF] and in humans. The role of Tregs in neuroinflammation is controversial but Tregs are considered as inflammation-resolving immune cells, as well as monocytes-derived macrophages [START_REF] Baruch | Breaking immune tolerance by targeting Foxp3(+) regulatory T cells mitigates Alzheimer's disease pathology[END_REF]. Peripheral blood Tregs numbers have been described as the best outcome predictor in Amyotrophic Lateral Sclerosis (ALS), with fewer peripheral Tregs correlating with worse clinical outcome [START_REF] Henkel | Regulatory T-lymphocytes mediate amyotrophic lateral sclerosis progression and survival[END_REF]. Importantly, recent clinical trials showed that low-dose Interleukin-2 is safe, selectively activates Tregs without activating effector T cells and improves autoimmune and alloimmune inflammatory conditions in humans [START_REF] Klatzmann | The promise of low-dose interleukin-2 therapy for autoimmune and inflammatory diseases[END_REF]. These trials also revealed the Interleukin-2 anti-inflammatory effects [START_REF] Saadoun | Regulatory T-cell responses to low-dose interleukin-2 in HCVinduced vasculitis[END_REF]. Interleukin-2 has thus dual properties, improving memory formation and controlling inflammation, which warrants its investigation in Alzheimer's disease. Here, we report that sustained Interleukin-2 expression using single administration of an AAV induces brain tissue remodeling and recovery of memory deficits in APP/PS1ΔE9 mice.

MATERIALS AND METHODS

Human AD brain samples

Post-mortem samples were obtained from brains collected as part of the Brain Donation Program of the GIE-Neuro-CEB Brain Bank, Pitié-Salpêtrière Hospital (Paris). Autopsies were carried out by accredited pathologists, after informed consent had been obtained from the relatives, in accordance with French Bioethics laws. Five hippocampal samples from five patients with sporadic forms of Alzheimer's disease (male and female; Braak 6 Thal 5; aged between 69 and 89 years, with a post-mortem interval (PMI) of 30 to 59 h) and five hippocampal samples from five age-matched control subjects (male and female, aged between 69 and 92 years, PMI of 6 to 63 h) were used in this study.

Animals

Eight-month old APPswe/PS1ΔE9 male mice (n=31) (hereafter referred as APP/PS1ΔE9) and the wild-type littermates (n=32) (Jackson Laboratories, Bar Harbor, Maine, USA) were used in this study. APP/PS1ΔE9 mice overexpress the mutated human APP (Swedish mutation, K595N/M596L) gene as well as the Human PS1 gene deleted from its exon 9 [START_REF] Jankowsky | Mutant presenilins specifically elevate the levels of the 42 residue beta-amyloid peptide in vivo: evidence for augmentation of a 42-specific gamma secretase[END_REF]. APP/PS1ΔE9 mice and wild-type littermates were bred and maintained in our animal facility under specific pathogen-free conditions. Mice were housed in a temperaturecontrolled room and maintained on a 12 h light/dark cycle. Food and water were available ad libitum. The experiments were carried out in accordance with the European Community Council directive (86/609/EEC) for the care and use of laboratory animals. All procedures were approved by the Regional Ethics Committee in Animal Experiment No. 5 of the Ile-de-France region (Ce5/2012/031).

rAAV generation and in vivo administration of AAVs

Recombinant AAV8 vectors were generated by triple transfection of human embryonic kidney 293T cells, as described previously [START_REF] Churlaud | Sustained stimulation and expansion of Tregs by IL2 control autoimmunity without impairing immune responses to infection, vaccination and cancer[END_REF]. Transgenes used were luciferase (LUC) and murine Interleukin-2 (IL-2) driven by the hybrid cytomegalovirus enhancer/chicken beta-actin constitutive promoter (CAG). Mice were injected once intraperitoneally with 10 10 viral genomes (vg) of rAAVs (AAV8-CAG-IL2 or AAV8-CAG-LUC) diluted in 100 µL of 0.1M phosphate-buffered saline (PBS) (APP/PS1ΔE9 AAV8-CAG-IL2, n=16; APP/PS1ΔE9 AAV8-CAG-LUC, n=15; wild-type littermates AAV8-CAG-IL2, n=16; wild-type littermates AAV8-CAG-LUC, n=16.

Detection of Interleukin-2 in the serum

Sera were collected, frozen and kept at -80 °C until use. Levels of Interleukin-2 were measured using a mouse Interleukin-2 ELISA (eBioscience) according to the manufacturer's recommendations.

Analysis of cell surface markers and Foxp3 expression

Direct ex vivo immunostaining was performed on 150 µL of heparinized fresh whole blood from mice after red blood cells lysis, as described [START_REF] Churlaud | Sustained stimulation and expansion of Tregs by IL2 control autoimmunity without impairing immune responses to infection, vaccination and cancer[END_REF]. Briefly, blood was stained with the following monoclonal antibodies for 20 min at 4 °C: CD3-PE, CD8-Alexa700, CD4-HorizonV500, CD25-PeCy7, NKp46-APC and B220-FITC (eBioscience).

Intracellular detection of Foxp3 (Foxp3-E450, eBioscience) was performed on fixed and permeabilized cells using appropriate buffer (eBioscience). Cells were acquired on an LSR II (Becton Dickinson) and analyzed with FlowJo (Tree Star, Inc.) software. Dead cells were excluded by forward/side scatter gating. Tregs were defined as CD25 + Foxp3 + cells among CD4 + cells, and activated effector T cells as CD25 + cells among CD4 + Foxp3 -cells. For the fluorescence-activated cell sorting (FACS) analysis of Tregs, CD25 Mean Fluorescence Intensity (MFI) in Tregs and Foxp3 MFI in Tregs were assessed.

Brain samples

APP/PS1ΔE9 mice and wild-type littermates were sacrificed 5 months post-injection (13 months old). The animals, given an overdose of sodium pentobarbital, were perfused transcardially with ice-cold PBS 0,1M before brain extraction. For flow cytometry analysis, freshly perfused brain was dissociated and digested in collagenase/DNase solution in RPMI medium [START_REF] Churlaud | Sustained stimulation and expansion of Tregs by IL2 control autoimmunity without impairing immune responses to infection, vaccination and cancer[END_REF]. A Percoll (Sigma-Aldrich) gradient was used to isolate braininfiltrating lymphocytes. Cells were then stained as described earlier for blood.

For histological processing, the left cerebral hemisphere was dissected and post-fixed in 4% paraformaldehyde (PFA) in 0.1M PBS for 1 week. Brains were cryoprotected by incubation in a 30% sucrose/0.1 M PBS solution. Coronal brain sections (40 µm) were cut on a freezing microtome (Leica, Wetzlar, Germany), collected serially, and stored at -20°C until additional analysis. The right hemisphere was dissected to extract the hippocampus, used biochemistry analysis. Samples were then homogenized in a lysis buffer (TBS, NaCl 150mM and Triton 1%) containing phosphatase (Pierce) and protease (Roche) inhibitors. After centrifugation (20min, 13 000 rpm, 4°c), the supernatant was collected and the protein concentration was quantified (BCA Protein Assay, Thermo Fisher Scientific, Waltham, USA). Lysate aliquots (3mg of protein/ml) were stored at -80°C until use. The same procedure was conducted for human samples (GIE NeuroCEB Brain Bank).

Western Blot

Total protein concentrations were determined using the BCA kit (Pierce). Equal amounts of total protein extract (30 µg) were electrophoretically separated using SDS-PAGE in 4-12% Bis-Tris gels (NuPAGE ® Novex Bis-tris midi gel 15 or 26 wells, Life Technologies, Carlsbad, USA) and transferred to nitrocellulose membranes. Blocked membranes (5% nonfat dry milk in TBS-0.1% Tween-20) were incubated with primary antibodies overnight at 4°C, and washed three times with TBS-0.1% Tween-20 (T-BST) for 10 min. Membranes were then labeled with secondary IgG-HRP antibodies raised against each corresponding primary antibody. After three washes with T-BST, the membranes were incubated with ECL chemiluminescent reagent (Clarity Western ECL substrate; GE Healthcare, Little Chalfont, UK) according to the instructions of the supplier. Peroxydase activity was detected with camera system Fusion TX7 (Fisher Scientific). Normalization was done by densitometry analysis with the Quantity One 1D image analysis software (version 4.4; Biorad, Hercules, CA, USA). The optical densities were normalized with respect to a "standard protein" (GAPDH). A partition ratio was calculated and normalized with respect to the sample with the highest value defined as 1.

Primary antibodies

Antibodies used in western-blot (WB) and immunohistochemical (IHC) analyses:

Primary antibodies

ELISA assay

Aβ-38, Aβ-40 and Aβ-42 were measured using the MSD Human Aβ42 V-PLEX Kit and the triplex Aβ Peptide Panel 1 (6E10) V-PLEX Kit (Mesoscale Discovery, Rockville, MD, USA).

β-CTF was measured using the Human APP β-CTF Assay Kit (IBL, Hamburg, Germany).

Interleukin-2 was measured using the MSD proinflammatory panel 1 (Mesoscale Discovery, Rockville, MD, USA). ELISA assays were performed following supplier instructions.

Immunostaining

The immunohistochemical procedure was initiated, by incubating slices in 88% formic acid solution for 15 min (antigen retrieval) and then by quenching endogenous peroxidase by incubating free-floating sections in hydrogen peroxide for 30 min at room temperature (RT).

After three washes, slices were blocked in PBS/0.1% Triton X-100 containing 10% Normal Goat Serum (NGS, Gibco) for 1h at RT. The sections were then incubated with the primary antibody (4G8), overnight at 4°C. After three washings, the sections were incubated with the corresponding biotinylated secondary antibody (1:250; Vector Laboratories Inc., CA, USA) diluted in PBS/0.1% Triton X-100 and 10% NGS for 2 h at RT. After three washes, bound antibodies were visualized by the ABC amplification system (Vectastain ABC kit, Vector Laboratories, West Grove, USA) and 3,3′-diaminobenzidine tetrahydrochloride (peroxidase substrate kit, DAB, Vector Laboratories, CA, USA) as the substrate. The sections were mounted, dehydrated by passing twice through ethanol and toluol solutions, and coverslipped with Eukitt ® (O. Kindler GmbH & CO, Freiburg, Germany).

For immunofluorescence, slices were washed with PBS 0.1 M, permeabilized in PBS-Triton 0.1% before blocking in PBS-Triton 0.1% containing 5% normal goat serum (NGS) for 1 hour. Sections were then incubated with the respective primary antibodies, overnight at 4°C.

After three successive washes, brain slices were incubated for 2 hours at room temperature with fluorescent secondary Alexa Fluor-conjugated antibodies (Invitrogen). Slices were stained with DAPI (1:5000; Sigma), mounted in Vectashield fluorescent mounting media (Vector laboratories) and conserved at 4°C.

Quantification of the microglia and astrocytes around plaques

Plaques, GFAP and Iba1 immunoreactivity were quantified using Image J (NIH, Bethesda, Analysis of data was blind with respect to treatments and genotypes.

Image acquisition

Images of immunostained sections were acquired with a Z6 APO macroscope (Leica) and LAS V3.8 (Leica) software, at room temperature, with a brightfield Leica DM 5000B microscope equipped with a Leica DFC310FX digital camera. Confocal images were acquired with a Leica SP8 confocal microscope. Photographs for comparison were taken under identical conditions of image acquisition, and all adjustments of brightness and contrast were applied uniformly to all images.

Behavioral assessment-Morris Water Maze

Experiments were performed in a 120-cm diameter, 50 cm deep tank filled with opacified water kept at 21°C and equipped with a 10 cm diameter platform submerged 1 cm under the

Dendrite and spine analysis in Golgi-Cox stained slices

Golgi-Cox staining

Golgi staining was performed using the Golgi Staining Kit (FD NeuroTechnologies, Columbia, USA) according to the manufacturer's instructions. All procedures were performed under dark conditions. Brains hemispheres used for Golgi cox staining were immersed in 2 ml mixtures of equal parts of kit solutions A and B and stored at RT for 2 weeks. Then, brain tissues were stored in solution C at 4ºC for at least 48h and up to 7 days before sectioning.

Solutions A, B and C were renewed within the first 24h. Coronal sections of 200 µm were cut with a vibrating microtome (Leica, VT1200S) while embedded in 2% Agar in 0.1M PBS.

Each section was mounted with Solution C on an adhesive microscope slide pre-coated with 1% gelatin/0.1% chromalaun on both slides and stained according to the manufacturer's protocol with the exception that AppliClear (AppliChem) was used instead of xylene. Finally, slices were coverslipped with Permount (Thermo Fisher Scientific).

Imaging and analysis of spine density in Golgi-Cox stained slices

Imaging of dendritic branches of hippocampal pyramidal neurons was done with an Axioplan 2 imaging microscope (Zeiss) using a 63x oil objective (NA 1.3) and a z-stack thickness of 0.5 µm under reflected light. The number of spines was determined per micrometer of dendritic length (in total 100 µm) at apical compartments using ImageJ (1.48v, National

Instruments of Health, USA). Three animals per genotype and 8-10 neurons per animal were analyzed blinded to genotype and injected AAV. Data were analyzed using Graphpad Prism (Version 5.01) software. Spine density is expressed as mean ± SEM. Differences between genotypes were detected with one-way ANOVA followed by Bonferroni's post hoc test using IBM SPSS Statistics 21.

Statistical analysis

Statistical analyses were defined regarding the experimental design used. All data are presented as the mean ± SEM. In most cases, data were analyzed using Student's T test, the Mann-Whitney test or one-way ANOVA with experimental group as factor. One-way ANOVA with repeated measures were carried out when required by the experimental plan to assess statistical effects. Correlations were generated using non-parametric Spearman rank correlation coefficient. For all analysis statistical significance was set to a p-value<0.05. All analyses were performed using Statistica (StatSoft Inc., Tulsa, USA) or GraphPad Prism (GraphPad Software, La Jolla, USA).

RESULTS

Interleukin-2 expression is decreased in the hippocampus of AD patients

We first analyzed Interleukin-2 protein levels in frozen hippocampal biopsies from five severely affected Alzheimer's disease patients (Braak 6/Thal5) and five age-matched healthy controls. We observed a 2-fold decrease in Interleukin-2 levels (p<0.05) (Fig. 1A andB)

paralleled by a ≈ 80% reduction in APP levels (p=0.001) and synaptic protein PSD-95 levels (p=0.004) (Fig. 1A,C & D) in the hippocampus of AD patients relatively to controls. The Aβ42/Aβ40 ratio, an outcome measure for Alzheimer's disease severity [START_REF] Ferrari | Frontotemporal dementia and its subtypes: a genome-wide association study[END_REF], was found increased in Alzheimer's disease patients (p=0.07) (Fig. 1E). Remarkably, there is a significant positive Spearman correlation between Interleukin-2 and APP levels (correlation coefficient 0.72, p = 0.0017) and between Interleukin-2 and PSD-95 levels (correlation coefficient 0.68, p = 0.003) (Fig. 1F andG).

Peripheral Interleukin-2 delivery induces increased Interleukin-2 and Tregs levels in the brain of APP/PS1ΔE9 mice

As Alzheimer's disease is a slow developing disease, we anticipated that long term Tregs stimulation could be necessary for obtaining therapeutic benefit. As Interleukin-2 has a short half-life in mice, maintaining an effect on Tregs would require frequent sub-cutaneous (sc)

injections that could have an effect on mice behavior. We thus delivered Interleukin-2 by intraperitoneal (ip) injection of a recombinant adeno-associated virus (AAV) coding for murine Interleukin-2, which allows sustained and stable release of Interleukin-2 for at least 20 weeks [START_REF] Churlaud | Sustained stimulation and expansion of Tregs by IL2 control autoimmunity without impairing immune responses to infection, vaccination and cancer[END_REF][START_REF] Wang | Adeno-associated virus serotype 8 efficiently delivers genes to muscle and heart[END_REF]. Eight-month old APP/PS1ΔE9 mice and littermates was injected with rAAV8-IL2 or luciferase-expressing control vectors (rAAV8-LUC). Four months after rAAV8 injections, serum Interleukin-2 was undetectable in mice receiving rAAV8-LUC, and was of 25.2 ± 5.3 or 29.5 ± 4.8 pg/mL (mean ± SEM) in Interleukin-2 treated littermates and APP/PS1ΔE9, respectively (Fig. 2A). These serum Interleukin-2 levels are those necessary for expanding and activating Tregs without effects on effector T cells, as previously described [START_REF] Churlaud | Sustained stimulation and expansion of Tregs by IL2 control autoimmunity without impairing immune responses to infection, vaccination and cancer[END_REF]. Indeed, peripheral

Interleukin-2 production expanded blood Tregs, significantly more in the APP/PS1ΔE9 mice than wild type littermates (Fig 2C). Tregs from Interleukin-2 treated mice were also more activated as assessed by increased CD25 cell surface expression [START_REF] Rosenzwajg | Low-dose interleukin-2 fosters a dose-dependent regulatory T cell tuned milieu in T1D patients[END_REF] (Fig 2E). Mice were sacrificed at 5.5 months post-injection (13.5 months of age). In hippocampal biopsies, there was a significant increase of Interleukin-2 levels only in Interleukin-2 treated APP/PS1ΔE9 mice (Figure 2B). These levels were approximately doubled compare to Interleukin-2 treated wild-type littermates and rAAV8-LUC controls, as detected both by western blot (Supplementary Figure 1) and ELISA (Figure 2B). There was a concomitant 3-fold increase of brain Tregs in Interleukin-2 treated normal and APP/PS1ΔE9 mice (Fig 2D). These Tregs also showed a higher activation status as attested by an increased CD25 expression (Fig 2F). In order to evaluate whether the increased Interleukin-2 levels observed in APP/PS1ΔE9 transgenic mice could be due to the transduction of brain cells by AAV vectors, we analyzed the biodistribution of AAV after injection of rAAV8-LUC in normal and in APP/PS1ΔE9 transgenic mice. We assessed luciferase bioluminescence in peripheral organs including the brain. As negative control, we used non-injected age-matched APP/PS1ΔE9 mice. Two weeks post-injection, luciferase expression could be detected in most of peripheral organs (liver, heart, kidney and spleen). In accordance with the known tropism of AAV8, most of the expression was detected in the liver. In contrast, no expression could be detected in the brain (Supplementary Figure 2A andB). To further substantiate these data, we also used a sensitive qPCR targeting the inverted terminal repeat (ITR2) sequence from the AAV8 vector genome to probe its biodistribution. ITR2 sequences were readily detected in the liver, while no expression could be detected in the brain of APP/PS1ΔE9 mice (Supplementary Figure 2C). Thus, the increased brain Interleukin-2 levels in APP/PS1ΔE9 mice results from passage from the periphery and not from local production by rAAV8 transduced brain cells.

Interleukin-2 treatment rescues memory impairment in APP/PS1ΔE9 mice

To evaluate the therapeutic effects of increasing brain Interleukin-2 on spatial learning and memory, mice were tested in the Morris water-maze place navigation task (Fig. 3). Treated APP/PS1ΔE9 mice or wild-type littermates were tested 5 months post-injection. All mice learned platform position across time during learning session, as demonstrated by decreased latency (Fig. 3A) or path length (Fig. 3B) to reach the platform over the 5 days of training.

Noteworthy, an overall significantly improved learning was detected in rAAV-IL-2 treated littermates (p<0.05). Average swimming speed was comparable in all groups ruling out potential motor abilities differences (Fig. 3C). The 4 hours probe trial that evaluates spatial reference memory (short-term memory) after the last training trial, revealed strong memory impairment in APP/PS1ΔE9 mice injected with rAAV-LUC compared to rAAV-LUC littermates (p=0.0002 and p=0.0002 using % of time and % of distance as readouts; Fig. 3D,

Interleukin-2 rescues impaired synaptic plasticity and restores decreased spine density in APP/PS1ΔE9 mice

Aβ-induced damage of synaptic transmission is one probable mechanism inducing memory impairments in APPP/S1 mice [START_REF] Snyder | Regulation of NMDA receptor trafficking by amyloid-beta[END_REF]. We evaluated whether Interleukin-2based memory restoration in APP/PS1ΔE9 mice was reflected at the functional neuronal network level. We investigated synaptic plasticity at 13.5 months of age, which is considered to represent the basis of newly shaped declarative memory. Long-term potentiation (LTP) was induced at the Schaffer collateral to hippocampal CA1 pathway by theta-burst stimulation after baseline recording (Fig. 4A). As expected, slices from transgenic APP/PS1ΔE9 mice exhibited significantly lower induction and maintenance of LTP compared with littermates after rAAV8-LUC administration (1.15 ± 0.001 (n; number of slices=12, p<0.05, F value 6.01, ANOVA) compared with 1.51 ± 0.003 (n=9)). Interleukin-2 treated APP/PS1ΔE9

showed significantly improved LTP as evidenced by statistically significant increase of average potentiation (1.23 ± 0.01, n=10, p<0.05, F value 5.92, ANOVA) compared with APP/PS1ΔE9 mice receiving rAAV8-LUC. However, LTP magnitude was lower relatively to Interleukin-2 treated littermates (1.45 ± 0.001, n=8, p<0.05, F value 6.01) (Fig. 4A andB).

The fEPSP slope was not different between different groups (Fig. 4C), suggesting that basal synaptic transmission in all groups was not affected. In addition, we analyzed paired-pulse facilitation (PPF) of fEPSP to afferent stimulation, a form of short-term synaptic plasticity.

Analysis of the EPSP2/EPSP1 ratio revealed significant (p<0.05, ANOVA) facilitation of second response in all interpulse intervals in APP/PS1ΔE9 mice administered with rAAV-IL-2 compared with their littermates. Paired-pulse facilitation in APP/PS1ΔE9 mice administered with rAAV-LUC was also significantly (p<0.05, ANOVA) higher compared with littermates.

Paired-pulse facilitation was not different between APP/PS1ΔE9 mice administered with rAAV-IL-2 or rAAV-LUC (Fig. 4D). Spine density was analyzed as a correlate of excitatory synapses in the same animals used for electrophysiological recordings. Spine density of midapical dendritic segments (between 100 and 400 µm form soma) of the hippocampal CA1 pyramidal layer was analyzed by the Golgi cox method (Fig. 4E). We found an overall decrease in spine density in APP/PS1ΔE9 mice treated with control rAAV-LUC at the CA1 apical dendritic compartment relatively to littermates injected with either rAAV-LUC or rAAV-IL-2 (p<0.001, 1-way ANOVA followed by Bonferroni's post-hoc test). Importantly, rAAV-IL-2-treated APP/PS1ΔE9 mice revealed a complete restoration of the spine deficit in apical dendrites of the CA1 layer (p>0.1) (Fig. 4F). Altogether, these data indicate that Interleukin-2 strikingly ameliorates both structural and functional synaptic impairments in Alzheimer's disease mice.

Interleukin-2 peripheral administration alleviates hippocampal amyloid pathology in

APP/PS1ΔE9 mice APP/PS1∆E9 mice show highly abundant plaques from 6 months [START_REF] Jankowsky | Mutant presenilins specifically elevate the levels of the 42 residue beta-amyloid peptide in vivo: evidence for augmentation of a 42-specific gamma secretase[END_REF].

Interleukin-2 treatment was started at 8 months of age, a time at which we already evidence increased levels of Aβ peptides (Aβ38, Aβ40 and Aβ42) and β-CTF in hippocampus from APP/PS1∆E9 mice (Supplementary Figure 3). Mice were sacrificed at 13.5 months of age.

Hippocampal APP levels were slightly increased in mice receiving rAAV8-IL-2 compared to rAAV8-LUC injected mice (Fig. 5A-C). The production of Aβ peptides and β-CTF, known to induce hippocampal neurophysiological impairments, was quantified in the hippocampus of injected mice by ELISA. No differences in β-CTF levels were detectable (Fig. 5D). There was a trend towards increased amounts of Aβ38 and Aβ40 (Fig. 5E-F) and a trend to decrease in soluble Aβ42 levels (Fig. 5G). This translated into a significant reduction in the Aβ42/Aβ40 ratio (p=0.0013) (Fig. 5H). This correlated with a decrease in the surface covered by plaques in APP/PS1∆E9 mice (p=0.023) (Fig. 5I,J). Altogether, these data indicate that Interleukin-2 reduces amyloid load and plaque deposition in the hippocampus of APP/PS1∆E9 mice with established pathology.

Interleukin-2 administration induces widespread recruitment of astrocytes in the vicinity of amyloid plaques

Amyloid plaques in APP/PS1∆E9 mice were surrounded by microglia and astrocytes at the time of the treatment (8 months) (Supplementary Figure 4).

The protein levels of microglial Iba1 were not statistically different in the hippocampus of IL-2 treated APP/PS1∆E9 mice compared to APP/PS1∆E9 mice receiving rAAV8-LUC (Fig. 6A and B); no differences were detected in littermates receiving rAAV8-LUC or rAAV8-IL-2.

No differences were observed in the expression of microglia markers, cytokine transforming growth factor-beta (TGF-β), Arginase-1 and Triggering Receptor Expressed on Myeloid cells (TREM2) or insulin-degrading enzyme (IDE), which contributes to Aβ clearance [START_REF] Leissring | Enhanced proteolysis of beta-amyloid in APP transgenic mice prevents plaque formation, secondary pathology, and premature death[END_REF] (Supplementary Figure 5). No major difference in Iba1 immunoreactivity around hippocampal amyloid plaques was observed (Fig. 6D andE).

Astrocytic markers analysis demonstrated a 3 to 4-fold increase of GFAP expression (p<0.0001) in APP/PS1∆E9 mice injected with rAAV8-IL-2 compared to APP/PS1∆E9 mice treated with rAAV8-LUC (Fig. 6A andC). Immunostaining clearly showed that these GFAP immunoreactive astrocytes were hypertrophic, indicating their activation (Fig. 6F). Moreover, a statistically significant increase of GFAP immunoreactivity around amyloid plaques was found in rAAV8-IL-2 treated APP/PS1∆E9 mice (Fig. 6G). In addition, in regions surrounding plaques, astrocytes were hypertrophic with thick proximal processes overlapping with the plaque, suggesting process invasion within plaques in AAV-IL2-treated APP/PS1∆E9 mice. In contrast, astrocytes from APP/PS1∆E9 mice treated with the control vector exhibited lower hypertrophic processes (Fig. 6F). Littermates treated with Interleukin-2 or Luciferase vectors did not exhibit hypertrophic process.

Interleukin-2 administration activates the JAK/STAT3 pathway in the hippocampus of APP/PS1ΔE9 mice

We next assessed whether this Interleukin-2 mediated astrocytic activation was correlated with stimulation of the JAK/STAT3 pathway. STAT3 is an important signaling molecule for many cytokines and growth factor receptors that prompts astrocyte reactivity [START_REF] Chiba | Amyloid-beta causes memory impairment by disturbing the JAK2/STAT3 axis in hippocampal neurons[END_REF][START_REF] Heim | The Jak-STAT pathway: cytokine signalling from the receptor to the nucleus[END_REF]. Western-blot analysis demonstrated a 2-fold increase in the levels of Stat3-α in APP/PS1∆E9 mice receiving rAAV8-IL-2 compared to APP/PS1∆E9 mice treated with the control vector (Fig. 6H and I) (p<0.0001). The phosphorylated form of STAT3

[Phospho-STAT3 (Tyr705)] was increased in APP/PS1∆E9 mice treated with the control rAAV8-LUC, relatively to littermates treated with rAAV8-IL-2 or rAAV8-LUC (Fig. 6H andJ). Remarkably, we found a 2.2-fold increase of phospho-STAT3 in Interleukin-2 treated APP/PS1∆E9 mice as compared to APP/PS1∆E9 mice that received the control vector (Luciferase) (Fig. 6H and J) (p<0.0001). Taken together, these results reveal an increased recruitment of astrocytes around amyloid plaques and the activation of the JAK/STAT3 pathway in APP/PS1∆E9 mice treated with Interleukin-2.

DISCUSSION

Gliosis and inflammation are hallmarks of Alzheimer's disease [START_REF] Schwab | Inflammatory aspects of Alzheimer disease and other neurodegenerative disorders[END_REF].

It is still not clear whether inflammation has a direct or indirect influence on the build-up of Aβ pathology. It has long been considered that the increase of pro-inflammatory mediators would contribute to Alzheimer's disease progression, thereby implying potential benefit of anti-inflammatory immunotherapies [START_REF] Birch | Modulation of inflammation in transgenic models of Alzheimer's disease[END_REF]. Likewise, inhibiting the signaling of the pro-inflammatory cytokines IL-12/IL-23 in APPPS1 mice decreased glial activation, amyloid load and cognitive decline [START_REF] Vom Berg | Inhibition of IL-12/IL-23 signaling reduces Alzheimer's diseaselike pathology and cognitive decline[END_REF]. The hippocampal AAV-mediated overexpression of the anti-inflammatory cytokines Interleukin-10 or Interleukin-4 in AD mice enhanced neurogenesis and improved spatial learning and Aβ deposition in APP/PS1 mice [START_REF] Kiyota | CNS expression of anti-inflammatory cytokine interleukin-4 attenuates Alzheimer's disease-like pathogenesis in APP+PS1 bigenic mice[END_REF][START_REF] Kiyota | AAV serotype 2/1-mediated gene delivery of anti-inflammatory interleukin-10 enhances neurogenesis and cognitive function in APP+PS1 mice[END_REF][START_REF] Latta | Determining the role of IL-4 induced neuroinflammation in microglial activity and amyloid-beta using BV2 microglial cells and APP/PS1 transgenic mice[END_REF]. Despite this, two recent studies support a detrimental impact of Interleukin-10 in Alzheimer's disease pathology [START_REF] Chakrabarty | IL-10 alters immunoproteostasis in APP mice, increasing plaque burden and worsening cognitive behavior[END_REF][START_REF] Guillot-Sestier | Il10 deficiency rebalances innate immunity to mitigate Alzheimer-like pathology[END_REF]. Interestingly, hippocampal expression of IL-1β in Alzheimer's disease mice did not result in the expected exacerbation of the amyloid plaque deposition, but instead in plaque improvement [START_REF] Shaftel | Chronic interleukin-1beta expression in mouse brain leads to leukocyte infiltration and neutrophil-independent blood brain barrier permeability without overt neurodegeneration[END_REF]. AAV-mediated expression of Interleukin-6 [START_REF] Chakrabarty | Massive gliosis induced by interleukin-6 suppresses Abeta deposition in vivo: evidence against inflammation as a driving force for amyloid deposition[END_REF] and TNF-α [START_REF] Chakrabarty | Hippocampal expression of murine TNFalpha results in attenuation of amyloid deposition in vivo[END_REF] induced massive gliosis that suppressed Aβ deposition. Recently, immune checkpoint blockade directed against the programmed death-1 (PD-1) pathway evoked an interferon (IFN)-γ-dependent systemic immune response leading to clearance of plaques and improved cognitive performance [START_REF] Baruch | PD-1 immune checkpoint blockade reduces pathology and improves memory in mouse models of Alzheimer's disease[END_REF]. Thus, and surprisingly, it appears that modulation of the immune system towards both effector and regulatory functions may counteract Alzheimer's disease.

In this context, there is a strong rationale to investigate the therapeutic effects of Interleukin-2 in Alzheimer's disease in vivo: (i) Interleukin-2 KO mice exhibit impaired learning and memory formation and altered hippocampal development [START_REF] Petitto | Impaired learning and memory and altered hippocampal neurodevelopment resulting from interleukin-2 gene deletion[END_REF]; (ii) serum

Interleukin-2 levels are low in Alzheimer's disease patients, compared with both elderly and middle-aged subjects [START_REF] Beloosesky | Cytokine levels and phagocytic activity in patients with Alzheimer's disease[END_REF]; (iii) Interleukin-2, at low dose, has an antiinflammatory effect [START_REF] Saadoun | Regulatory T-cell responses to low-dose interleukin-2 in HCVinduced vasculitis[END_REF]. In this report, we show that Interleukin-2 prompts

Treg expansion and activation in the brain of APP/PS1∆E9 mice and improves Alzheimer's disease pathology. Increased Interleukin-2 concentrations were observed in the hippocampus of Interleukin-2 treated APP/PS1∆E9 mice but not in Interleukin-2 treated littermates. Since AAV vectors do not transduce brain cells and Interleukin-2 is produced in the periphery, we may speculate that CNS penetration of peripherally produced Interleukin-2 could be favored in APP/PS1∆E9 mice due to BBB leakage. Indeed, the BBB is relatively impermeable in healthy subjects, however compromised in Alzheimer's disease given disruption of the tightly packed endothelial cells that support brain vasculature. Importantly, BBB permeability has been reported in Alzheimer's disease mouse models [START_REF] Tanifum | Cerebral vascular leak in a mouse model of amyloid neuropathology[END_REF] and was shown to increase before plaque formation in Alzheimer's disease mice [START_REF] Ujiie | Blood-brain barrier permeability precedes senile plaque formation in an Alzheimer disease model[END_REF]. This has important implications for the route of administration of therapeutic molecules such as Interleukin-2 [START_REF] Waguespack | Interleukin-2 does not cross the bloodbrain barrier by a saturable transport system[END_REF].

Tregs have a controversial role in controlling or worsening Alzheimer's disease. Treg depletion was reported to improve Alzheimer's disease in 5XFAD mice [START_REF] Baruch | Breaking immune tolerance by targeting Foxp3(+) regulatory T cells mitigates Alzheimer's disease pathology[END_REF] or to accelerate the onset of cognitive deficits in APPPS1 mice [START_REF] Dansokho | Regulatory T cells delay disease progression in Alzheimer-like pathology[END_REF]. In any case, how transient Treg ablation (observed in the periphery but not asserted in the brain) can impact a disease that develops along months is unexplained. Actually, the brief and transient Tregs depletion reported as improving Alzheimer's disease [START_REF] Baruch | Breaking immune tolerance by targeting Foxp3(+) regulatory T cells mitigates Alzheimer's disease pathology[END_REF] resulted in a marked enrichment of Tregs in the brain three weeks after the last Treg depletion modality (53.4% vs 18.1%) [START_REF] Baruch | Breaking immune tolerance by targeting Foxp3(+) regulatory T cells mitigates Alzheimer's disease pathology[END_REF]. The authors concluded that Tregs recruitment to cerebral sites of Alzheimer's disease pathology may have led to reduction of gliosis and Aβ plaque, with improvement of cognitive functions [START_REF] Baruch | Breaking immune tolerance by targeting Foxp3(+) regulatory T cells mitigates Alzheimer's disease pathology[END_REF]. As efficient Treg depletion in mice leads to rapid (3 to 6 weeks) catastrophic autoimmunity, inflammation and death [START_REF] Fontenot | Foxp3 programs the development and function of CD4+CD25+ regulatory T cells[END_REF], this precludes the evaluation of the effects of long-term Treg ablation that might be important for slow-developing diseases. Thus, Treg depletion might not be an optimal method to assess Treg role in Alzheimer's disease. Other investigators [START_REF] Dansokho | Regulatory T cells delay disease progression in Alzheimer-like pathology[END_REF] used an anti-CD25 monoclonal antibody to deplete

Tregs in vivo in APPPS1 mice. We considered that this strategy was not suitable in our study, as Treg depletion is only transient and CD25 is also expressed by other immune cells such as NK cells, activated B cells, activated effector T cells, myeloid cells, which could induce non expected effects by depleting these populations [START_REF] Baeyens | Limitations of IL-2 and rapamycin in immunotherapy of type 1 diabetes[END_REF]. In this study, we used the reverse setting and evaluated whether Treg activation and expansion could improve Alzheimer's disease. We administered Interleukin-2 over 5 months and observed increased

Treg numbers and activation in the brain, correlating with histological and clinical Alzheimer's disease improvement. Similar observations were also recently reported, although the authors did not assess Tregs in the brain [START_REF] Dansokho | Regulatory T cells delay disease progression in Alzheimer-like pathology[END_REF]. Thus, altogether, indirect evidences suggest a beneficial role of activated Tregs in Alzheimer's disease. We show that Interleukin-2 -induced Alzheimer's disease improvement is linked to an astrocytic activation.

We observed a marked astrocytic activation that is considered as reflecting an attempt to recover from CNS injury [START_REF] Wegiel | The role of microglial cells and astrocytes in fibrillar plaque evolution in transgenic APP(SW) mice[END_REF]. Indeed, astrocytes were proposed to protect neurons by forming a physical barrier around plaques [START_REF] Wegiel | The role of microglial cells and astrocytes in fibrillar plaque evolution in transgenic APP(SW) mice[END_REF]. Interestingly, the astrocytic phenotypic activation was correlated with stimulation of the JAK/STAT3 pathway that was shown to activate astrocytes in models of acute brain injury and is involved in cell growth, neuronal survival and differentiation [START_REF] Bareyre | In vivo imaging reveals a phase-specific role of STAT3 during central and peripheral nervous system axon regeneration[END_REF][START_REF] Lang | STAT3 promotes corticospinal remodelling and functional recovery after spinal cord injury[END_REF].

Astrocytes have been described as a potential source of brain Interleukin-2 [START_REF] Eizenberg | Interleukin-2 transcripts in human and rodent brains: possible expression by astrocytes[END_REF]. Astrocytes make part of the BBB and may well be the primary brain parenchymal cell type encountered by peripheral Tregs. Indeed, previous reports have described astrocyte/T cells interactions [START_REF] Barcia | Imaging the microanatomy of astrocyte-T-cell interactions in immune-mediated inflammation[END_REF]. More recently, a close interaction between Tregs and astrocytes has been reported, in which the activation of an Interleukin-2/STAT5 signaling pathway is implicated in an astrocyte-mediated maintenance of Tregs [START_REF] Xie | Cerebral regulatory T cells restrain microglia/macrophage-mediated inflammatory responses via IL-10[END_REF].

Further studies are still needed to better understand the sequential cross-talk between astrocytes and Tregs during Interleukin-2-based therapy.

Increased astrocytic reactivity around amyloid plaques suggests that astrocytes may influence Alzheimer's disease-like pathogenesis through invasion of plaques as an attempt to clear Aβ and limit its extracellular deposition. In line with this finding, mouse astrocytes were reported to degrade amyloid-beta in vitro and in situ [START_REF] Wyss-Coray | Adult mouse astrocytes degrade amyloid-beta in vitro and in situ[END_REF], and exogenous astrocytes transplanted into the brain of plaque-bearing Alzheimer's disease mice, were shown to migrate towards Aβ deposits, internalizing them [START_REF] Pihlaja | Transplanted astrocytes internalize deposited beta-amyloid peptides in a transgenic mouse model of Alzheimer's disease[END_REF]. Furthermore, it was shown that attenuating astrocyte activation accelerates plaque deposition in Alzheimer's disease mice [START_REF] Kraft | Attenuating astrocyte activation accelerates plaque pathogenesis in APP/PS1 mice[END_REF].

Consistent with these properties of astrocytes, Interleukin-2 treatment and consequent astrocytic activation were accompanied by a reduction of amyloid plaques and a decrease in the Aβ42/Aβ40 ratio [START_REF] Murray | beta-Amyloid 42/40 ratio and kalirin expression in Alzheimer disease with psychosis[END_REF]. The strong Aβ40 increase in Interleukin-2 treated APP/PS1∆E9 mice is in line with in vitro and in vivo data showing that Aβ40 protects neurons from Aβ42 induced damage in culture and in rat brain [START_REF] Zou | Amyloid beta-protein (Abeta)1-40 protects neurons from damage induced by Abeta1-42 in culture and in rat brain[END_REF] and inhibits amyloid deposition in Alzheimer's disease mice, protecting them from premature death [START_REF] Kim | Abeta40 inhibits amyloid deposition in vivo[END_REF]. In a different mouse model of Alzheimer's disease (APPPS1 mice), Interleukin-2 was proposed to work by a microglial activation [START_REF] Dansokho | Regulatory T cells delay disease progression in Alzheimer-like pathology[END_REF]. In our APP/PS1∆E9 mice we did not observe such activation. Iba1, arginase-1, TGF-ß, IDE and Trem2B detection by western blot were unchanged in the hippocampus. There was no increase of Iba1-positive cells by immunofluorescence around plaques.

We further report that the recovery of memory deficits observed in APP/PS1∆E9 mice was supported by a remarkable Interleukin-2-mediated tissue remodeling in the brain characterized by increased synaptic plasticity and restoration of spine density. To our knowledge, this is the first demonstration that in vivo immunomodulatory treatment can actually induce such brain tissue remodeling. These findings are in accordance with previous reports showing that Interleukin-2 promotes survival and neurite extension of cultured neurons as well as enhances dendritic development and spinogenesis [START_REF] Awatsuji | Interleukin-2 as a neurotrophic factor for supporting the survival of neurons cultured from various regions of fetal rat brain[END_REF][START_REF] Sarder | Interleukin-2 promotes survival and neurite extension of cultured neurons from fetal rat brain[END_REF][START_REF] Shen | Interleukin-2 enhances dendritic development and spinogenesis in cultured hippocampal neurons[END_REF].

Interleukin-2 is an approved drug used for the stimulation of effector cells for the treatment of metastatic melanoma and renal cell carcinoma. In these indications it is given at very high doses (up to 160 MIU per day) and actually poorly used because of severe side effects [START_REF] Klatzmann | The promise of low-dose interleukin-2 therapy for autoimmune and inflammatory diseases[END_REF]. The demonstration that low-dose Interleukin-2 is safe and selectively activates and expands Tregs without activating effector T cells in humans has changed the paradigm for Interleukin-2 therapeutic use. Interleukin-2 is now intensively developed as a stimulant of Tregs at daily dose around 1 to 3 MIU. At these low doses, Interleukin-2 is well tolerated in humans with autoimmune diseases [START_REF] Castela | Effects of low-dose recombinant interleukin 2 to promote Tregulatory cells in alopecia areata[END_REF][START_REF] Hartemann | Low-dose interleukin 2 in patients with type 1 diabetes: a phase 1/2 randomised, double-blind, placebo-controlled trial[END_REF][START_REF] He | Low-dose interleukin-2 treatment selectively modulates CD4(+) T cell subsets in patients with systemic lupus erythematosus[END_REF][START_REF] Saadoun | Regulatory T-cell responses to low-dose interleukin-2 in HCVinduced vasculitis[END_REF]. Noteworthy, these doses lead to increased serum concentration of Interleukin-2 that are in the range of the long-term elevated concentrations observed during pregnancy [START_REF] Curry | Maternal plasma cytokines in early-and mid-gestation of normal human pregnancy and their association with maternal factors[END_REF]. Finally, a pre-clinical study of the long-term effects of Interleukin-2 in mice showed that a yearlong treatment is well tolerated [START_REF] Churlaud | Sustained stimulation and expansion of Tregs by IL2 control autoimmunity without impairing immune responses to infection, vaccination and cancer[END_REF]. Thus, long-term treatment with low-dose Interleukin-2 of Alzheimer's disease patients can be envisioned. In summary, our results demonstrate the therapeutic effects of Interleukin-2 in AD mice with established pathology. Although it remains to elucidate the direct and Treg-mediated contribution of Interleukin-2 to Alzheimer's disease improvements, these results warrant investigating the low dose Interleukin-2 for neuroinflammatory diseases.

  USA) or Icy(Institut Pasteur, Paris, France). Laserpower, numeric gain and magnification were kept constant between animals to avoid potential technical artefacts. Images were first converted to 8-bit gray scale and binary thresholded to highlight a positive staining. At least 3 sections per mouse (between -1.7 mm to -2.3 mm caudal to bregma) were quantified. The average value per structure was calculated for each mouse. For quantification of Iba1 and GFAP immunoreactivity around plaques, a region of interest (ROI) was drawn around the center of the plaque. The diameter of the circular ROI was set as 3 times the diameter of the plaque. Mean fluorescence intensity values were measured for either Iba1 or GFAP immunoreactivity and were processed via Icy software (Institut Pasteur, Paris, France).

  water surface. Visual clues were disposed around the pool as spatial landmarks for the mouse and luminosity was kept at 430 lux. Training consisted of daily sessions (three trials per session) during 5 consecutive days. Start positions varied pseudo-randomly among the four cardinal points. Mean inter-trial interval was 15 min. Each trial ended when the animal reached the platform. A 60-second cut-off was used, after which mice were gently guided to the platform. Once on the platform, animals were given a 30-second rest before being returned to their cage. Four hours (short-term memory) and 72 hours after the last training trial (day 8), retention was assessed during probe trial in which the platform was no longer present. Animals were video tracked using Ethovision software (Noldus, Wageningen, Netherlands) and behavioral parameters (swim speed, travelled distance, latency, percentage of time in each quadrant) were automatically calculated. Experiments and statistical evaluation of data were performed by an experimenter blind to genotype and treatment group.ElectrophysiologyFemale 13.5 months-old APP/PS1dE9 mice injected with the rAAV-IL-2 (n=5) or rAAV8-LUC (n=5) and their littermates administered with rAAV-IL-2 (n=4) or rAAV8-LUC (n=4) were used for electrophysiological examination of synaptic plasticity in hippocampus. Mice, deeply anesthetized by inhalation of high concentration of CO 2 , were decapitated and brain was removed and divided into two parts. One hemisphere was transferred into the Golgi staining solution and processed accordingly to allow investigation of neuronal morphology of regions of interest. The second hemisphere was transferred into cold (4 ºC) artificial cerebrospinal fluid (ACSF), containing the following (in mM): 124 NaCl, 4.9 KCl, 1.2 KH 2 PO 4 , 2.0 MgSO 4 , 2.0 CaCl 2 , 24.6 NaHCO 3 , 10 D-glucose, equilibrated with 95% O 2 and 5% CO 2 . The hippocampus was dissected from the second hemisphere and transverse hippocampal slices of 400 µm were cut using tissue chopper. Hippocampal slices were incubated at 32 °C in an interface chamber with the constant flow of carbogenated (95% O 2 and 5% CO 2 ) ACSF for 2 hours prior recording. Field excitatory postsynaptic potentials (fEPSPs) were recorded in stratum radiatum of the CA1 region of hippocampus. Synaptic responses were evoked by stimulation of the Schaffer collaterals. An input/output curve (dependence of fEPSP slope on stimulation intensity) was plotted prior to each experiment. Data of electrophysiological recordings were collected, stored and analyzed with LABVIEW software (National Instruments, Austin, USA). The initial slope of fEPSPs elicited by stimulation of the Schaffer collaterals was measured over time, normalized to baseline and plotted as average ± SEM. Analysis of the Paired-pulse facilitation (PPF) data was performed by calculating the ratio of the slope of the second fEPSP divided by the slope of the first one and multiplied by 100.

  F and H); wild-type littermates treated with either rAAV-LUC or rAAV-IL-2, showed similar preference. Strikingly, by contrast to APP/PS1ΔE9 mice injected with rAAV-LUC, Interleukin-2 -treated APP/PS1ΔE9 mice showed a clear preference for the target quadrant (rAAV-LUC-treated vs Interleukin-2 -treated APP/PS1ΔE9 mice: % of time in TQ; p=0.0034 and % of distance in TQ; p<0.0001), and were statistically indistinguishable from control littermates. These results were confirmed at 72 hours (long-term memory; rAAV-LUC-treated vs IL-2-treated APP/PS1ΔE9 mice: % of time in TQ; p=0.0199 and % of distance in TQ: p=0.0092) (Fig.3E, G and I) suggesting a beneficial effect of Interleukin-2 during memory consolidation phase. These data clearly demonstrate that Interleukin-2 rescued impairments in memory retention observed in APP/PS1ΔE9 mice.

ACKNOWLEDGEMENTS

We thank Françoise Fouquet, Gaëlle Dufayet-Chaffaud and Gwladys Fourcade for excellent technical assistance. Human post-mortem samples were kindly provided by the GIE-Neuro-CEB brain bank (Pitié-Sâlpétrière Hospital, Paris, France), which is run by a consortium of patients' associations. We thank Fatima Bosch for providing the initial generation of the AAV vectors.

Funding

This work was supported by The "Fondation pour La Recherche Médicale" (grant DBS20140930765) to NC and by French state funds within the Investissement d'Avenir programme (ANR-11-IDEX-0004-02).