Thanayut Kaewmaraya

Laetitia Vincent

Michele Amato

Accurate Estimation of Band Offsets in Group IV Polytype Junctions: A First-Principles Study

Recent advances in the fabrication of group IV homojunctions made by cubic-diamond (3C) and hexagonal-diamond (2H) phases call for a detailed understanding of the physics underlying their electronic structure. In this work, we employ hybrid density functional theory (hybrid-DFT) calculations to study the structural and electronic properties of Si and Ge polytype junctions. Starting from high-resolution transmission electron microscopy (HRTEM) micrographs of 2H/3C Si nanowires, we build a computational model that takes into account both crystal-phase effects and the length of the junction. We obtain accurate estimations of the magnitudes of the band offsets: In particular, we show that 2H/3C Si interfaces induce a type-II band alignment, whereas the Ge structures exhibit a type-I band offset. Furthermore, both Si and Ge homojunctions have direct gaps that are smaller than those of the bulk 3C phase. Finally, we demonstrate that, in all of the considered systems, varying the thickness of the hexagonal phase preserves the nature of the band alignment. Because of the high degree of novelty and the accuracy of the method employed, these results could represent a robust starting point for further experimental investigations in this field.

■ INTRODUCTION

The crystal structure of Si and Ge nanowires (NWs) at standard conditions usually takes a well-defined cubic-diamond phase, as in the case of their bulk counterparts. [1][START_REF] Amato | Surface Physics of Semiconducting Nanowires[END_REF][START_REF] Amato | Silicon-Germanium Nanowires: Chemistry and Physics in Play, from Basic Principles to Advanced Applications[END_REF][START_REF] Rurali | Colloquium: Structural, Electronic, and Transport Properties of Silicon Nanowires[END_REF] Nevertheless, the possibility of synthesizing NWs exhibiting other phases, namely, the hexagonal-diamond phase, was recently demonstrated. For example, Hauge et al. obtained pure and stable hexagonal-diamond Si NWs using hexagonal GaP NWs as a template. [START_REF] Hauge | Hexagonal Silicon Realized[END_REF] Other studies have instead succeeded in growing Si and Ge NWs containing both the cubic-diamond and hexagonal-diamond phases, opening the way to the fabrication of well-ordered group IV polytype homojunctions. [START_REF] Jeon | Origin of Polytype Formation in VLS-Grown Ge Nanowires through Defect Generation and Nanowire Kinking[END_REF][START_REF] Biswas | Diameter-Controlled Germanium Nanowires with Lamellar Twinning and Polytypes[END_REF][START_REF] Vincent | Novel Heterostructured Ge Nanowires Based on Polytype Transformation[END_REF][START_REF] Qiu | Epitaxial Diamond-Hexagonal Silicon Nano-Ribbon Growth on (001[END_REF] In these materials, the hexagonal-diamond phase appears both as a structural crystal imperfection (i.e., stacking fault) [START_REF] Jeon | Origin of Polytype Formation in VLS-Grown Ge Nanowires through Defect Generation and Nanowire Kinking[END_REF][START_REF] Shin | Rational Defect Introduction in Silicon Nanowires[END_REF][START_REF] Lopez | Silicon Nanowire Polytypes: Identification by Raman Spectroscopy, Generation Mechanism, and Misfit Strain in Homostructures[END_REF][START_REF] Shin | Sidewall Morphology-Dependent Formation of Multiple Twins in Si Nanowires[END_REF] and in more extended domains. [START_REF] Vincent | Novel Heterostructured Ge Nanowires Based on Polytype Transformation[END_REF][START_REF] Qiu | Epitaxial Diamond-Hexagonal Silicon Nano-Ribbon Growth on (001[END_REF] The latter was recently realized by Vincent et al., who proposed a strain-induced phase transformation for the synthesis of Ge NW polytype homojunctions. [START_REF] Vincent | Novel Heterostructured Ge Nanowires Based on Polytype Transformation[END_REF] The possibility of synthesizing novel phases for Si and Ge might allow for the achievement of a sophisticated control of the materials' properties, as has already been demonstrated in the cases of light emission efficiency, [START_REF] Fabbri | Visible and Infra-red Light Emission in Boron-Doped Wurtzite Silicon Nanowires[END_REF][START_REF] Li | Broadband Infrared Photoluminescence in Silicon Nanowires with High Density Stacking Faults[END_REF] band-gap engineering, [START_REF] Rodl | Wurtzite Silicon as a Potential Absorber in Photovoltaics: Tailoring the Optical Absorption by Applying Strain[END_REF][START_REF] De | Electronic Structure and Optical Properties of Si, Ge and Diamond in the Lonsdaleite Phase[END_REF] optical absorption, [START_REF] Rodl | Wurtzite Silicon as a Potential Absorber in Photovoltaics: Tailoring the Optical Absorption by Applying Strain[END_REF][START_REF] Haberl | Pathways to Exotic Metastable Silicon Allotropes[END_REF][START_REF] Beekman | Clathrates and Beyond: Low-Density Allotropy in Crystalline Silicon[END_REF][START_REF] Amato | Crystal Phase Effects in Si Nanowire Polytypes and Their Homojunctions[END_REF] and thermal transport. [START_REF] Majumdar | Probing Thermal Flux in Twinned Ge Nanowires through Raman Spectroscopy[END_REF][START_REF] Porter | Intrinsic Nanotwin Effect on Thermal Boundary Conductance in Bulk and Single-Nanowire Twinning Superlattices[END_REF][START_REF] Zhan | Thermal Conductivity of Si Nanowires with Faulted Stacking Layers[END_REF] Indeed, it is well-known that advanced device functionalities, such as modulation doping, electrical insulation, internal field generation, and charge separation, can be induced by bringing together different materials, that is, forming a heterojunc-tion, [START_REF] Alferov | The History and Future of Semiconductor Heterostructures[END_REF][START_REF] Lauhon | Semiconductor Nanowire Heterostructures[END_REF] and taking advantage of how the electronic bands of the two materials align. In this context, the study of group IV polytype homojunctions is particularly appealing. One can intuitively expect that hexagonal-diamond/cubic-diamond junctions in NWs will provide novel properties with respect to the single-phase systems because of the intrinsic band offsets developing at the interface. From this point of view, it is worth noting that an accurate knowledge of band alignment plays a crucial role in the engineering of advanced optical and electronic devices (see, for example, refs 26-29) because of the importance of band alignment for electrical transport across the interface and for optical transitions.

A proper description of band offsets in semiconductors requires the correct prediction of band gaps and band positions. Several theoretical studies on group IV hexagonal-diamond/ cubic-diamond polytype homojunctions have been conducted, with misleading results sometimes being reported. [START_REF] Murayama | Chemical Trend of Band offsets at Wurtzite/zinc-blende Heterocrystalline Semiconductor Interfaces[END_REF][START_REF] Raffy | Properties of Hexagonal Polytypes of Group-IV Elements from First-principles Calculations[END_REF][START_REF] Raffy | Ab initio Study of Structural and Electronic Properties of Planar Defects in Si and SiC[END_REF] For example, the conclusions in the case of Si still remain contradictory: It was first reported that hexagonal-diamond/ cubic-diamond Si superlattices have a type-I band offset, [START_REF] Murayama | Chemical Trend of Band offsets at Wurtzite/zinc-blende Heterocrystalline Semiconductor Interfaces[END_REF][START_REF] Raffy | Properties of Hexagonal Polytypes of Group-IV Elements from First-principles Calculations[END_REF] whereas it was later argued that the band alignment was of type II. [START_REF] Amato | Crystal Phase Effects in Si Nanowire Polytypes and Their Homojunctions[END_REF][START_REF] Raffy | Ab initio Study of Structural and Electronic Properties of Planar Defects in Si and SiC[END_REF] exchange-correlation (XC) functionals are derived according to either the local density approximation (LDA) or its gradientcorrected extensions (generalized gradient approximation, GGA)], which severely underestimates band gaps in semiconductors. [START_REF] Hummer | Heyd-Scuseria-Ernzerhof Hybrid Functional for Calculating the Lattice Dynamics of Semiconductors[END_REF] This limitation is even more pronounced in the case of Ge, for which previous works employing the LDA predicted a metal for both the hexagonal-diamond and cubicdiamond phases, thus making the correct evaluation of valenceand conduction-band discontinuities difficult (see, for example, ref 31).

On the other hand, hybrid density functional theory (hybrid-DFT), which combines Hartree-Fock exchange with conventional DFT, has been demonstrated to be capable of providing precise estimations of band gaps, in particular, in the case of group IV semiconductors. [START_REF] Garza | Predicting Band Gaps with Hybrid Density Functionals[END_REF][START_REF] Heyd | Hybrid Functionals based on a Screened Coulomb Potential[END_REF][START_REF] Paier | Screened Hybrid Density Functionals Applied to Solids[END_REF] Moreover, this method has been successfully employed for the evaluations of band discontinuities of InGaN alloys, [START_REF] Moses | Bowing and Band Alignment in InGaN Alloys[END_REF] two-dimensional semiconducting heterostructures, [START_REF] Kang | Band Offsets and Heterostructures of Two-dimensional Semiconductors[END_REF] and polytype rutile-anatase TiO 2 . [START_REF] Pfeifer | Energy Band Alignment between Anatase and Rutile TiO 2[END_REF][START_REF] Scanlon | Band Alignment of Rutile and Anatase TiO 2[END_REF] Wadehra et al. highlighted the major success of this approach in evaluating the band alignments of numerous technologically important heterostructures. [START_REF] Wadehra | Band Offsets of Semiconductor Heterostructures: A hybrid Density Functional Study[END_REF] This success is mainly attributed to the inclusion of the Hartree-Fock exact exchange energy in the XC functional, which consequently reduces the self-interaction error.

In this work, we employ hybrid-DFT methods to investigate the structural and electronic properties of group IV hexagonal-diamond/cubic-diamond junctions. Starting from high-resolution transmission electron microscopy (HRTEM) images of 2H/3C Si NWs, we build a computational model that takes into account both crystal-phase effects and the length of the junction. By providing a precise and accurate estimation of band discontinuities, we show that Si junctions induce a type-II band alignment, with the valence-band edge localized on the hexagonal-diamond phase and the conduction-band edge on the cubic-diamond phase. On the other hand, Ge junctions exhibit a type-I band offset, where the valence-and conductionband edges are both located at the center of the Brillouin zone in the hexagonal-diamond region. Moreover, both Si and Ge homojunctions have direct gaps that are smaller than those of the corresponding bulk cubic-diamond junctions. This might, in principle, be associated with enhanced direct optical transitions. Finally, we demonstrate that, for both Si and Ge junctions, varying the thickness of the hexagonal-diamond phase preserves the nature of the band alignment, as the changes in band discontinuities are negligible.

■ COMPUTATIONAL DETAILS

Structural optimizations and electronic structure calculations were carried out using the VASP code [START_REF] Hafner | Ab-initio Simulations of Materials using VASP: Density-functional Theory and beyond[END_REF] within the framework of DFT. The core-valence interactions were described by a projector-augmented wave (PAW) approach, [START_REF] Blochl | Projector Augmented-wave Method[END_REF] and four electrons (Si, 3s 2 3p 2 ; Ge, 4s 2 4p 2 ) were treated as the valence states. The exchange-correlation functional was approximated using a hybrid Heyd-Scuseria-Ernzerhof (HSE06) functional. [START_REF] Heyd | Hybrid Functionals based on a Screened Coulomb Potential[END_REF] This approach incorporates the error function to screen the slowly decaying Coulomb potential to reduce the computational cost in calculating the Hartree-Fock exact exchange (E x HF ). In more detail, the HSE06 exchangecorrelation can be written as

α μ α μ μ = + - + + E E E E E ( ) (1 ) ( ) ( ) xc HSE x HF,SR x PBE,SR x PBE,LR c PBE (1)
where E c PBE denotes the Perdew-Burke-Ernzerhof (PBE) correlation functional, [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF] α is an empirical mixing value, and μ is an adjustable parameter that decouples the short-range (SR) Coulomb potential from the long-range (LR) counterpart. The standard values of α = 0.25 and μ = 0.2 are typically referred to HSE06. [START_REF] Heyd | Hybrid Functionals based on a Screened Coulomb Potential[END_REF] This hybrid functional yields good results (such as lattice parameters and band gaps), especially for small-to medium-gap semiconductors (such as Si and Ge) because adding 25% of the HF exchange is the suitable amount for weak dielectric screening. [START_REF] Paier | Screened Hybrid Density Functionals Applied to Solids[END_REF] The energy cutoff for representing the plane-wave basis was set to 500 eV. A k-point mesh of 8 × 8 × 1 was used for Brillouin zone sampling of the junctions. Structural optimizations were satisfactorily terminated when the residual Hellmann-Feynman forces exerted on each atom became less than 0.02 eV/Å. Spin-orbit coupling (SOC) effects were considered only in the case of Ge bulk crystals.

We first considered Si and Ge bulk crystal structures. The cubic-diamond phase exhibits the ABC stacking sequence along the ⟨111⟩ direction and, in the Ramsden nomenclature, corresponds to a 3C structure. The same phase can be obtained by considering a hexagonal cell containing six atoms. On the other hand, an ABAB packing pattern along the c direction characterizes the hexagonal-diamond polytype (hence denoted as 2H), which has four atoms in the unit cell. This 2H structure belongs to the space group P6 3 /mmc (D 6h [START_REF] Rurali | Colloquium: Structural, Electronic, and Transport Properties of Silicon Nanowires[END_REF] ) and exhibits lower symmetry than the cubic-diamond phase, which instead belongs to the space group Fd3̅ m (O h 7 ). Despite this dissimilarity, the tetrahedral coordination is preserved in both the 3C and 2H phases.

We also considered 2H-[0001]//3C-⟨111⟩ junctions represented by the 72-atom unit cell constructed from the HSE06relaxed unit cells of 3C and 2H (as shown in Figure 3 below). The lateral lattice constant of the junctions was fixed to that of the 3C phase, meaning that a small amount of intrinsic stress was imposed on the 2H phase. Band structures were determined along the M → Γ → K path according to the hexagonal symmetry. The length of the 72-atom unit cell along the c-axis was large enough (∼12 nm) to make the first Brillouin zone a hexagon. [START_REF] Iwata | Effective Masses of Two-Dimensional Electron Gases around Cubic Inclusions in Hexagonal Silicon Carbide[END_REF] The proposed structural models were built on the basis of high-resolution transmission electron microscopy (HRTEM) characterization that we performed on 2H/3C-⟨111⟩ Si NW junctions synthesized following the procedure presented in ref 8. In particular, we report in Figure 1 an example of how the sizes of the 2H domains in Si NWs can be tuned by adjusting the temperature of the phase transformation process. At 500 °C (Figure 1a), the 2H Si domains are 7-8 nm in width, whereas at 900 °C (Figure 1b), the width increases to 20 nm. Figure 1c shows an enlarged view of the resulting homojunction at 900 °C. More details about the synthesis and HRTEM characterization are given in ref 46.

Driven by these experimental observations, we decided to study how the variation of the thickness of the hexagonal region influences the electronic properties of the junction. Indeed, as shown in previous studies, 47 the variation of the width of the 2H region in such systems can affect the magnitude of the band offsets. Because of the high computational cost of hybrid-DFT, we could not handle systems with the same size as the experimental samples. Consequently, we restricted our analysis to smaller 2H domains, aiming to elucidate how the properties of the junction can depend on the length of 2H region. We modeled this aspect by considering different junctions obtained by varying the thickness of the 2H phase (denoted by L 2H in Figure 3) from three to nine 2H unit cells, but keeping the total length of the junction constant. The considered structures were periodic in all directions of space. This means that our findings are valid for large-diameter NWs (far from the quantum confinement regime) and layered systems.

The structural optimizations of the junctions were performed using the PBE functional, whereas the electronic properties were then evaluated using HSE06. The band offsets in such systems are usually determined by utilizing the average potential method, [START_REF] Baldereschi | Band Offsets in Lattice-Matched Heterojunctions: A Model and First-Principles Calculations for GaAs/AlAs[END_REF][START_REF] Colombo | Valence-band Offsets at Strained Si/Ge Interfaces[END_REF] in which the valence-and conductionband offsets (ΔE v 3C-2H and ΔE c 3C-2H , respectively) are estimated by the expressions

Δ = Δ + Δ - - - E E V v 3C 2H VBM 3C 2H dis 3C 2H (2)
Δ = Δ + Δ - - - E E E c 3C 2H g 3C 2H v 3C 2H (3)
where ΔE g 3C-2H represents the difference between the band gaps of the 3C and 2H phases and ΔE VBM 3C-2H is the difference between the valence-band maxima (VBM) of the 3C and 2H bulk phases. The positions of the bulk valence-band edges were measured with respect to the average of the electrostatic potential in each bulk material. On the other hand, ΔV dis 3C-2H represents the discontinuity of the average electrostatic potential between the 3C and 2H phases across the interface of the junction. Although this method is very accurate for the determination of band offsets in the limit of an isolated interface, it is not appropriate for the calculation of the band lineups for very thin superlattices or confined systems, as is the case of the junctions in Figure 3a,b. This is mainly due to the rapidly oscillating nature of the electrostatic potential and its small discontinuities in the case of homojunctions that make the determination of an energy reference level difficult. To resolve this issue, in this work, we evaluated the band offset by employing an extensive analysis of the spatial localization of wave functions, as was successfully done in other works. [START_REF] Nduwimana | Spatial Carrier Confinement in Core-shell and Multishell Nanowire Heterostructures[END_REF][START_REF] Amato | Band-offset Driven Efficiency of the Doping of SiGe Core-Shell nanowires[END_REF] This semiquantitative method is based on a careful examination of the spatial distributions of single-particle wave functions in the proximity of valence-and conduction-band edges. Band offsets are then calculated as energy differences between the eigenvalues corresponding to the electronic state of a band edge, which can be localized in a 3C or 2H segment, and the first electronic state, which is completely delocalized (i.e., not confined in a specific region of the junction). The method of the average reference potential was instead used only to further check the results obtained for the junction with L 2H = 5.94 nm (Figure 3c). 1 show very good agreement with the results of previous studies. [START_REF] Raffy | Ab initio Study of Structural and Electronic Properties of Planar Defects in Si and SiC[END_REF][START_REF] Joannopoulos | Electronic Properties of Complex Crystalline and Amorphous Phases of Ge and Si. II. Band Structure and Optical Properties[END_REF] The c/a ratios evaluated for both 2H Si and 2H Ge are larger than those for the ideal 2H polytype. This discrepancy is related to the tendency of Si and Ge to normally crystallize in the 3C phase. [START_REF] Raffy | Ab initio Study of Structural and Electronic Properties of Planar Defects in Si and SiC[END_REF][START_REF] Yeh | Zinc-blende-Wurtzite Polytypism in Semiconductors[END_REF] It is worth noting that the difference in the growth-direction lattice constants of these allotropes is less than 0.5%, indicating that the 2H-[0001]//3C-⟨111⟩ interface is ideally latticematched.

Regarding total energies, the 2H phases of both Si and Ge present higher values than the corresponding 3C phases, as already shown in previous LDA studies. [START_REF] Raffy | Ab initio Study of Structural and Electronic Properties of Planar Defects in Si and SiC[END_REF][START_REF] Yeh | Zinc-blende-Wurtzite Polytypism in Semiconductors[END_REF] In particular, the differences in total energy between the 2H and 3C bulk phases amount to 17.3 meV/atom for Si and 14.2 meV/atom for Ge.

The calculated band structures of bulk Si and Ge are presented in Figure 2, and the corresponding band gaps are summarized in Table 2. For the 3C phases, the values obtained by the HSE06 functional are in close agreement with experimental findings. [START_REF] Kittel | Introduction to Solid State Physics[END_REF] Interestingly, it is possible to directly compare the electronic band structures of cubic-diamond and hexagonal-diamond crystals by mapping their high-symmetry points in the Brillouin zone (BZ) (for a detailed discussion of the correspondence of the k-point groups between the BZs of the 3C and 2H phases, see refs 30 and 58). The cubic-diamond phase contains two basis atoms in the unit cell, whereas there are four atoms in the unit cell of the hexagonal-diamond phase. The later has twice as many bands as the former. Hence, there is a two-to-one correspondence of the high-symmetry points in the irreducible BZ passing from the cubic-diamond phase to the hexagonaldiamond phase. The Γ and L points in the cubic BZ are mapped onto the Γ point in the hexagonal BZ. Both X and L correspond to a point on the line U of the hexagonal-diamond BZ. This is why, for both Si and Ge, the band edges of the 3C and 2H phases occur at different points.

This band-mapping approach can be easily evidenced by examining the band structures of the 3C phase represented in both cubic and hexagonal symmetries, as illustrated in Figure 2a,b for Si and in Figure 2d,e for Ge. The fundamental gaps of the cubic-diamond phase are identical regardless of the symmetrical representation (i.e., 1.14 eV for Si and 0.73 eV for Ge). The valence-band maxima are all located at the Γpoint. In the hexagonal symmetry, the conduction-band edge of Si appears at the point near M located on the line U of the hexagonal BZ, whereas that of Ge occurs at Γ according to the folding from L to Γ. For the 2H phase, in both Si and Ge, the valence-and conduction-band edges occur at the same point as those of the cubic-diamond phases represented in hexagonal symmetry. A reduction of the band gap is also observed for the two semiconductors. Interestingly, 2H Ge is characterized by a direct gap whose value is in fair agreement with recent GW calculations. [START_REF] Chen | Calculation of Lonsdaleite Ge[END_REF] As demonstrated in previous theoretical works (see, for example, ref 59), in the case of Ge, the inclusion of spin-orbit coupling (SOC) is responsible for a reduction of the fundamental band gap that, in our case, amounts to nearly 0.1 eV for both phases (see the fourth column of Table 2).

The universal reduction of the gap of the group IV 2H allotrope with respect to the 3C allotrope is associated with the distinct stacking sequence where structures with higher hexagonality exhibit larger gaps. [START_REF] Raffy | Properties of Hexagonal Polytypes of Group-IV Elements from First-principles Calculations[END_REF][START_REF] Kiefer | Structure, and Electronic Properties of 4H-germanium[END_REF] In addition, there is a visible split-off band right below the valence-band maximum (VBM) in the 2H phase. This band originates from the 3-folddegenerate VBM in the cubic-diamond crystal that splits into a 2-fold Γ 6v (p x and p y ) band and a lower one-fold Γ 1v (p z ) band. The splitting energy (E cr ) determines the variation of the interactions caused by the change in symmetry. [START_REF] Raffy | Properties of Hexagonal Polytypes of Group-IV Elements from First-principles Calculations[END_REF] The calculated values of E cr amount to 0.44 eV for Si (in agreement with a recent study employing many-body GW methods [START_REF] Rodl | Wurtzite Silicon as a Potential Absorber in Photovoltaics: Tailoring the Optical Absorption by Applying Strain[END_REF] ) and 0.29 eV for Ge. It is worth mentioning that the gap at Γ of 2H Si is 1.70 eV, remarkably less than that of 3C Si. Polytype Junctions. After having acquired basic information concerning the bulk phases, we proceeded to a study of the 2H-[0001]//3C-⟨111⟩ polytype junctions. As expected, the geometry relaxation of the junctions (whose atomic structures are shown in Figure 3) revealed that the structural discontinuity and stress at the interface cause only minor atomic rearrangements. This was confirmed by the deviations of the Si-Si and Ge-Ge bond distances and bond angles by less than 0.5% with respect to the corresponding values for the bulk phase.

In terms of the total energies, the junction with three 2H unit cells (L 2H = 1.93 nm) is the most stable, and the stability decreases with increasing 2H thickness. For Si, the junctions with six and nine 2H unit cells, corresponding to L 2H = 3.92 nm and L 2H = 5.94 nm, respectively, exhibit higher energies than that with three 2H unit cells by 0.12 and 0.24 eV/interface, respectively. The same is trus for Ge, with corresponding values of 0.24 and 0.48 eV/interface, respectively. These findings are related to the fact that, for both Si and Ge, the bulk 2H phase is less stable than the bulk 3C phase [START_REF] Mujica | High-pressure Phases of Group-IV, III ̆V, and II ̆VI Compounds[END_REF] and, hence, increasing the number of 2H atomic layers induces instability. A related point to consider is that the distance between the periodic images of the 2H regions is at least 60 Å. Thus, the physics of our model does not contain any fictitious interactions between the hexagonal-diamond segments. The modeled junctions correspond to a set of independent quantum wells, and there is no penetration of wave functions between the nearby wells that could yield mini-bands. [START_REF] Miller | Optical Physics of Quantum Wells[END_REF][START_REF] Weisbuch | Fundamental Properties of III-V Semiconductor Two-Dimensional Quantized Structures: The Basis for Optical and Electronic Device Applications[END_REF] However, a brief word of caution is in order here: The analysis of the stability through total energy arguments does not take into account the effect of the temperature, and it is thus quite far from the complex growth dynamics of such types of systems.

To obtain information regarding band offsets, we calculated the projected density of states (PDOS), as shown in Figure 4a. The Si junction containing nine 2H unit cells (L 2H = 5.94 nm) induces a staggered band lineup (also known as a type-II band offset). This is clear if one examines the plots of the localization of wave functions corresponding to the band edges (Figure 4b). The wave function of the valence-band edge is completely localized in the 2H region, whereas that of the conduction-band edge appears only in the 3C phase region of space. This behavior is a general characteristic of 2H/3C Si junctions, already observed in 2H-[0001]//3C-⟨111⟩ Si superlattices [START_REF] Raffy | Ab initio Study of Structural and Electronic Properties of Planar Defects in Si and SiC[END_REF] and, more recently, in thin 2H-[0001]//3C-⟨111⟩ polytype Si nanowires. [START_REF] Amato | Crystal Phase Effects in Si Nanowire Polytypes and Their Homojunctions[END_REF] On the other hand, the Ge junction with L 2H = 5.94 nm exhibits a straddling band lineup (type-I band offset), as one can deduce from the PDOS (Figure 4c) and the spatial localization of the wave functions corresponding to the band edges (Figure 4d).

Remarkably, in spite of having different types of band offsets, for both the Si and Ge junctions, the band gap changes only slightly when the length of the 2H region is reduced from nine to three unit cells (see the insets of Figure 4a,c). This means that the nature and values of the band discontinuities are almost independent of the length of the 2H region. We computed the values of the band offsets by analyzing the localization of the wave functions following the method already presented in refs 51 and 65. In the case of the junction with nine 2H unit cells (L 2H = 5.94 nm), we further checked our results by also calculating the band lineup with the average potential technique described previously, and we found very good agreement.

Figure 5 shows the band structures of Si junctions (top panel) projected onto the 3C bulk band structure (shaded regions) together with the calculated magnitudes of the band offsets (bottom panel). For the Si junction with L 2H = 5.94 nm (right graph), the discontinuities of the valence and conduction bands are 0.123 and 0.094 eV, respectively. These band offsets lead to a finite quantum well. Holes are trapped in the hexagonal region with a relatively deeper well, whereas electrons are confined in cubic region with a shallow barrier. The band gap of the junction is indirect at the point near M because the conduction-band edges of both the 3C and 2H bulk polytypes are located near this point. This staggered band lineup could induce several interesting properties, such as an enhanced photocatalytic activity due to the natural separation of photoexcited charge carriers (as for the case of polytype anatase-rutile TiO 2 [START_REF] Pfeifer | Energy Band Alignment between Anatase and Rutile TiO 2[END_REF][START_REF] Scanlon | Band Alignment of Rutile and Anatase TiO 2[END_REF] and mixed-phase TiO 2 particles [START_REF] Bickley | A Structural Investigation of Titanium Dioxide Photocatalysts[END_REF][START_REF] Hurum | Explaining the Enhanced Photocatalytic Activity of Degussa P25 Mixed-Phase TiO2 Using EPR[END_REF][START_REF] Ohno | Morphology of a TiO2 Photocatalyst (Degussa, P-25) Consisting of Anatase and Rutile Crystalline Phases[END_REF][START_REF] Kho | Photocatalytic H2 Evolution over TiO2 Nanoparticles. The Synergistic Effect of Anatase and Rutile[END_REF] ). Varying the 2H thickness (i.e., modifying the length of the 2H region embedded in the 3C phase) preserves the type-II feature as the changes in energy offsets are very small (see the bottom panel of Figure 5). Interestingly, this behavior differs from that observed in our recent work on Si NW polytypes, in which we demonstrated that the band offsets are diameterdependent, namely, type I at smaller diameter and type II at larger diameters. [START_REF] Amato | Crystal Phase Effects in Si Nanowire Polytypes and Their Homojunctions[END_REF] The dissimilarity is due to the enhanced quantum confinement in thin NWs with respect to the systems considered in this study. We argue that the behavior we report here should be observed in large-diameter NWs.

The difference in the magnitudes of the conduction-band offsets for Si junctions with L 2H = 1.93 nm and L 2H = 3.92 nm is quite small. This can lead to some difficulty and ambiguity in identifying the band offsets of 2H/3C Si interfaces unless the position of the conduction-band edge in k-space is precisely determined. [START_REF] Raffy | Ab initio Study of Structural and Electronic Properties of Planar Defects in Si and SiC[END_REF] The tiny band offsets in the Si junctions can be ascribed to the fact that the difference in the fundamental gaps of the bulk 2H and 3C phases is nearly 0.2 eV. In addition, increasing the value of L 2H gives rise to more discretized bound states of the 2-fold Γ 6v band (p x and p y ) of 2H phase near the valence-band edge. The energy spacings between them are large for L 2H = 1.93 nm (i.e., the narrow well), and they gradually become narrower as this parameter is increased. This is basically a consequence of the particle-in-a-box model, where the increase in the number of discretized states for thicker 2H regions comes from the increasing number of particles (i.e., holes) being confined in the quantum well. The 2-fold Γ 6v feature remains unaltered, indicating that the degeneracy of the holes is not influenced by the quantum confinement. The numbers of bound states in the valence bands of 2H inclusions with L 2H = 3.92 nm and L 2H = 5.94 nm are similar. On the other hand, this behavior is not observed for the conductionband offsets where electrons are trapped. This is because the offset is so small that electrons are not strongly confined.

Unlike Si junctions, Ge junctions composed of nine 2H unit cells are characterized by a type-I band lineup with a direct band gap of 0.32 eV as depicted in Figure 6 (right graph). The top of the valence band and the bottom of the conduction band are located at the Γ-point of the 2H region, meaning that the band-gap transition is direct not only in k-space but also in real space. The valence-and conduction-band offsets amount to 0.127 and 0.280 eV, respectively. Therefore, both electrons and holes are confined in 2H Ge regions, but electrons are trapped more strongly than holes. Notably, the magnitudes of the conduction-band discontinuities in Ge junctions are relatively greater than those in Si junctions. This is probably due to the fact that the fundamental band gap of bulk 3C Ge (0.72 eV) differs considerably from that of 2H Ge (0.32 eV) and that quantum confinement in Ge is more pronounced than that in Si.

As in the case of Si, variation of the thickness of the 2H region in Ge junctions does not create a significant change in the band gap, type, or magnitude of the band offsets, as shown in Figure 6 (bottom panel). The junctions with L 2H = 1.93 nm and L 2H = 3.92 nm maintain a semiconducting character, with band gaps of 0.41 and 0.38 eV, respectively. The band lineup remains of type I for all of the cases, and the magnitude of the energy offsets deviates slightly from that of the junction containing nine 2H unit cells. Even here, we observed the presence of discretized bound states at the valence-and conduction-band edges as a consequence of quantum confine-ment. The energy spacings decreases with increasing thickness of the hexagonal phase. Notably, the degeneracy of the 2-fold Γ 6v (p x and p y ) feature of the 2H phase in the valence band was further shifted when L 2H was reduced to 1.93 nm. On the other hand, this circumstance does not occur in junctions with thicker hexagonal segments where such degeneracy is still maintained.

■ CONCLUSIONS

We employed hybrid density functional theory (hybrid-DFT) calculations to investigate the structural and electronic properties of 2H/3C group IV homojunctions. We found that Si junctions are characterized by a type-II band alignment, with the valence-band edge localized on the hexagonal-diamond phase and the conduction-band edge localized on the cubicdiamond phase. As already demonstrated in the case of Si NWs, this band lineup could be of some benefit for photovoltaics as well as other advanced technological applications.

On the other hand, Ge junctions exhibit a type-I band lineup where the valence-and the conduction-band edges are both located in the 2H region. This type of band alignment could in principle offer an enhancement in optical transitions as already proposed in the case of Ge superlattices. [START_REF] Ikonic | Direct Optical Transitions in Indirect Semiconductors: The case of Ge Twinning Superlattices[END_REF] Yet, our findings indicate that Ge polytype homojunctions present a direct band gap whose value is smaller if compared with the bulk 3C phase one. This property could be related to enhanced direct optical transitions that may be exploited in infrared optoelectronics.

Finally, we have also demonstrated that, for both Si and Ge homojunctions, varying the thickness of the 2H region leaves the nature of the band alignment, the band-gap values, and the offset magnitudes almost unaltered. This indicates that the presence of even short hexagonal segments can give rise to major changes in the properties of the entire crystal (as in the case of 2H regions locally induced by crystal defects).

In view of the recent successful achievements in fabricating Si and Ge polytype NWs, [START_REF] Hauge | Hexagonal Silicon Realized[END_REF][START_REF] Vincent | Novel Heterostructured Ge Nanowires Based on Polytype Transformation[END_REF] all of these findings could guide and help further experimental investigations in this field.

■ AUTHOR INFORMATION

Corresponding Author *E-mail: michele.amato@u-psud.fr.

ORCID

Michele Amato: 0000-0002-3690-3194 Notes

  This is mainly due to the well-known limitation of conventional density functional theory (DFT) [in which the r e a t e

Figure 1 .

 1 Figure 1. HRTEM micrographs showing the effect of the temperature on the 2H domain size in ⟨111⟩ Si NWs obtained by phase transformation: (a) enlargement of the 2H domain formed at 500 °C, (b) enlargement of the 2H domain formed at 900 °C, and (c) overview of the 2H/3C homojunction obtained at 900 °C. The width of the 2H region and the types of phases are indicated.

■

  RESULTS AND DISCUSSION Bulk Structures. As an initial step, we performed calculations on bulk crystal structures. The optimized lattice The Journal of Physical Chemistry C Article r e a t e

Figure 2 .

 2 Figure 2. Band structures of bulk (a) cubic-diamond Si, (b) cubicdiamond Si in hexagonal symmetry, (c) hexagonal-diamond Si, (d) cubic-diamond Ge, (e) cubic-diamond Ge in hexagonal symmetry, and (f) hexagonal-diamond Ge. The valence-band maximum (VBM) has been shifted to zero for the sake of visualization.

Figure 3 .

 3 Figure 3. View in the plane (yz) of the atomic structures of the 2H-[0001]//3C-⟨111⟩ Si and Ge junctions with 2H regions of different thicknesses: (a) three 2H unit cells (L 2H = 1.93 nm), (b) six 2H unit cells (L 2H = 3.92 nm), and (c) nine 2H unit cells (L 2H = 5.94 nm). All of the junctions contain 72 atoms. The structure are periodic in all of the directions. Blue spheres represent Si or Ge atoms.

Figure 4 .

 4 Figure 4. (a,c) Projected densities of states (PDOS) of the 2H-[0001]/3C-⟨111⟩ junctions of (a) Si and (c) Ge containing nine 2H unit cells (L 2H = 5.94 nm), indicating that (a) the Si junction induces a staggered band lineup whereas (c) the Ge junction is characterized by a type-I band lineup. (b,d) These findings are also supported by the spatial localization of the wave functions corresponding to band edges for (b) Si and (d) Ge. The total DOS shown in the insets of panels a and c indicate that the variation of L 2H from three to nine 2H unit cells yields only a minor change in the band gap. In all of the plots, the valence-band maximum (VBM) has been shifted to zero for the sake of visualization.

Figure 5 .

 5 Figure 5. Band structures of Si junctions as a function of the thickness of the hexagonal-diamond region, denoted by L 2H for three different cases: L 2H = 1.93 nm (left), L 2H = 3.92 nm (center), and L 2H = 5.94 nm (right). The band structures of the junctions are projected onto the 3C bulk band structure (shaded regions). The valence-band maximum (VBM) has been shifted to zero for the sake of visualization. The schematic band lineup (not to scale) is illustrated below each band structure.

Figure 6 .

 6 Figure 6. Band structures of Ge junctions as a function of the thickness of the hexagonal-diamond region, denoted by L 2H for three different cases: L 2H = 1.93 nm (left), L 2H = 3.92 nm (center), and L 2H = 5.94 nm (right). The band structures of the junctions are projected onto the 3C bulk band structure (shaded regions). The valence-band maximum (VBM) has been shifted to zero for the sake of visualization. The schematic band lineup (not to scale) is illustrated below each band structure.

Table 1 .

 1 Calculated Lattice Constants of Si and Ge

	crystal structure	a (Å)	c (Å)	c/a (Å)	u (Å)	notes
			Si
	cubic-diamond (3C)	5.435				this work (HSE06)
		5.435				calc 33
		5.431				expt 54
	hexagonal-diamond (2H)	3.830	6.321	1.650	0.373	this work (HSE06)
		3.828	6.325	1.652	0.374	calc 16
		3.800	6.269	1.650	0.374	calc 53
		3.837	6.317	1.646		expt 55
			Ge
	cubic-diamond (3C)	5.680				this work (HSE06)
		5.682				calc 33
		5.657				expt 54
	hexagonal-diamond (2H)	4.010	6.590	1.643	0.378	this work (HSE06)
		3.960	6.450	1.629		calc 56
		3.960	6.570			expt 57

Table 2 .

 2 Calculated Band Gaps of Si and Ge

	crystal structure	E g at Γ (eV)	E g (eV)	E g (SOC) (eV)	band edge	notes
			Si
	cubic-diamond (3C)	3.29	1.14		Γ-X	this work (HSE06)
		3.20	1.14		Γ-X	calc 16
		3.33	1.15		Γ-X	calc 33
		3.40	1.17		Γ-X	expt 61
	hexagonal-diamond (2H)	1.70	0.95		Γ-M	this work (HSE06)
		1.63	0.95		Γ-M	calc 16
			Ge
	cubic-diamond (3C)	0.84	0.72	0.61	Γ-L	this work (HSE06)
		0.94	0.85	0.71	Γ-L	calc 33
		0.81	0.66		Γ-L	expt 54
	hexagonal-diamond (2H)	0.32		0.23		this work (HSE06)
		0.23				calc 56
		0.31				calc 17

The authors declare no competing financial interest.

■ ACKNOWLEDGMENTS

We acknowledge support from the Nanodesign project Nanoharvesting funded by the IDEX Paris-Saclay (ANR-11-IDEX-0003-02). The high-performance computing (HPC) resources for this project were granted by the Institut du developpement et des ressources en informatique scientifique (IDRIS) under allocations i2015097422 and i2016097531 through GENCI (Grand Equipement National de Calcul Intensif).


Maria Manfredi-Lozano

Valerie Leysen

Michela Adamo

Isabel Paiva

Renaud Rovera

Jean-Michel Pignat

Fatima Ezzahra Timzoura

Michael Candlish

Sabiha Eddarkaoui

Samuel A Malone

Mauro S B Silva

Sara Trova

Monica Imbernon

Laurine Decoster

Ludovica Cotellessa

Manuel Tena-Sempere

Marc Claret

Ariane Paoloni-Giacobino

Damien Plassard

Emmanuelle Paccou

Nathalie Vionnet

James Acierno

Aleksandra Maleska Maceski

Antoine Lutti

Frank Pfrieger

S Rasika

Federico Santoni

Ulrich Boehm

Philippe Ciofi

Luc Buée

Nasser Haddjeri

Anne- Laurence Boutillier

Jens Kuhle

Andrea Messina

Bogdan Draganski

Paolo Giacobini

Nelly Pitteloud
email: nelly.pitteloud@chuv.ch

Vincent Prevot
email: vincent.prevot@inserm.fr

GnRH replacement rescues cognition in Down Syndrome

Keywords: Trisomy, dementia, intellectual disability, cognitive decline, preoptic area, hypothalamic-pituitarygonadal axis, anosmia, infertility, microRNA, Otx2

Currently, no viable treatment exists for cognitive and olfactory deficits in Down syndrome (DS). We show in a DS model (Ts65Dn mice) that these progressive non-reproductive neurological symptoms closely parallel a post-pubertal decrease in hypothalamic as well as extra-hypothalamic expression of a master molecule controlling reproduction -gonadotropin-releasing hormone (GnRH), and appear related to an imbalance in a microRNA-gene network known to regulate GnRH neuron maturation together with altered hippocampal synaptic transmission. Epigenetic, cellular, chemogenetic and pharmacological interventions that restore physiological GnRH levels abolish olfactory and cognitive defects in Ts65Dn mice, while pulsatile GnRH therapy improves cognition and brain connectivity in adult DS patients. GnRH thus plays a crucial role in olfaction and cognition, and pulsatile GnRH therapy holds promise to improve cognitive deficits in DS.

Introduction

Down syndrome (DS) or Trisomy 21 is the most common genetic cause of intellectual disability, for which treatment options are few and of doubtful efficacy [START_REF] Antonarakis | Down syndrome[END_REF][START_REF] De La Torre | Safety and efficacy of cognitive training plus epigallocatechin-3-gallate in young adults with Down's syndrome (TESDAD): a double-blind, randomised, placebo-controlled, phase 2 trial[END_REF]. The extra chromosome 21 is associated with increased gene dosage and global alterations of gene expression, disrupting biological homeostasis and contributing to its various clinical and neurological manifestations (3) (4). Among these, adult DS patients present with cognitive decline due to an early-onset Alzheimer disease (AD)-like pathology [START_REF] Bull | Down Syndrome[END_REF][START_REF] Fortea | Clinical and biomarker changes of Alzheimer's disease in adults with Down syndrome: a cross-sectional study[END_REF][START_REF] Bayen | Prevalence of Aging, Dementia, and Multimorbidity in Older Adults With Down Syndrome[END_REF][START_REF] Antonarakis | Down syndrome and the complexity of genome dosage imbalance[END_REF][START_REF] Dierssen | Down syndrome: the brain in trisomic mode[END_REF][START_REF] Editorial | Strengthening connections between Down syndrome and AD[END_REF][START_REF] Lott | Dementia in Down syndrome: unique insights for Alzheimer disease research[END_REF], and have also revealed white matter pathology and hypomyelination [START_REF]Down Syndrome Developmental Brain Transcriptome Reveals Defective Oligodendrocyte Differentiation and Myelination[END_REF]. A progressive loss of olfaction, typical of neurodegenerative diseases, is also prevalent [START_REF] Doty | Olfactory dysfunction in Parkinson disease[END_REF], starting during the prepubertal period [START_REF] Nijjar | Olfactory impairment increases as a function of age in persons with Down syndrome[END_REF], and men with DS may display deficits in sexual maturation [START_REF] Hsiang | Gonadal function in patients with Down syndrome[END_REF].

The inability to perceive odors, together with infertility, is also characteristic of gonadotropinreleasing hormone (GnRH) deficiency in patients with Kallmann syndrome [START_REF] Boehm | Expert consensus document: European Consensus Statement on congenital hypogonadotropic hypogonadism--pathogenesis, diagnosis and treatment[END_REF]. GnRH, essential for reproduction in all mammals [START_REF] Knobil | The GnRH pulse generator[END_REF], is secreted by specialized neurons in the hypothalamus and activates the hypothalamic-pituitary-gonadal (HPG) axis to produce sex steroids [START_REF] Boehm | Expert consensus document: European Consensus Statement on congenital hypogonadotropic hypogonadism--pathogenesis, diagnosis and treatment[END_REF]. However, the first centrally driven gonad-independent activation of the HPG axis occurs well before puberty, during the infantile period in both humans and mice [START_REF] Messina | A microRNA switch regulates the rise in hypothalamic GnRH production before puberty[END_REF][START_REF] Pellegrino | GnRH neurons recruit astrocytes in infancy to facilitate network integration and sexual maturation[END_REF], a phenomenon known as "minipuberty" that sets in motion the entire process of reproductive maturation [START_REF] Lanciotti | Up-To-Date Review About Minipuberty and Overview on Hypothalamic-Pituitary-Gonadal Axis Activation in Fetal and Neonatal Life[END_REF]. Additionally, the expression of GnRH and its cognate receptor GnRHR in extrahypothalamic areas not directly involved in reproduction suggests a role for GnRH in higher brain functions [START_REF] Casoni | Development of the neurons controlling fertility in humans: new insights from 3D imaging and transparent fetal brains[END_REF][START_REF] Skrapits | The cryptic gonadotropin-releasing hormone neuronal system of human basal ganglia[END_REF][START_REF] Schang | GnRH receptor gene expression in the developing rat hippocampus: transcriptional regulation and potential roles in neuronal plasticity[END_REF]. In light of these phenotypic and temporal correlations, we used Ts65Dn mice, which overexpress the mouse genomic region orthologous to chromosome 21 (chromosome 16) [START_REF] Reeves | A mouse model for Down syndrome exhibits learning and behaviour deficits[END_REF] and recapitulate many of the anatomical, neurobiological, and behavioral phenotypes of human DS [START_REF] Kola | Down syndrome and mouse models[END_REF][START_REF] Epstein | Protocols to establish genotype-phenotype correlations in Down syndrome[END_REF][START_REF] Bianchi | Age-related impairment of olfactory bulb neurogenesis in the Ts65Dn mouse model of Down syndrome[END_REF], to examine whether olfactory and cognitive deficits in DS could stem from GnRH abnormalities, and could be reversed by its replacement in mice and DS patients.

Results

Ts65Dn mice show Down-like olfactory, cognitive deficits

To explore whether olfactory and cognitive deficits, observed in DS patients, also occurred in Ts65Dn mice and determine their temporality, we performed habituation/dishabituation tests to assess odor discrimination [START_REF] Breton-Provencher | Interneurons produced in adulthood are required for the normal functioning of the olfactory bulb network and for the execution of selected olfactory behaviors[END_REF], and a novel object recognition test (also used in DS patients [START_REF] Nelson | Learning and memory as a function of age in Down syndrome: a study using animal-based tasks[END_REF]) to assess recognition memory, a hippocampus-dependent task [START_REF] Cohen | The rodent hippocampus is essential for nonspatial object memory[END_REF], in prepubertal (P35) and young adult (P90) mice (Fig. 1A). While olfactory performance in Ts65Dn mice was normal at birth (as assessed by milk intake, an olfaction-dependent behavior in newborns) and the infantile period (assessed using the homing test) (Fig. S1), olfactory deficits appeared between the second week of life and the juvenile period. While male and female prepubertal (P35) Ts65Dn mice showed normal habituation (i.e. reduced sniffing time when an odor was reintroduced), once habituated, they were unable to distinguish novel from known odors (Fig. 1B), a deficit that persisted in adulthood (Fig. 1C), phenocopying the prepubertal onset of olfactory deficits in DS patients [START_REF] Nijjar | Olfactory impairment increases as a function of age in persons with Down syndrome[END_REF]. In contrast, novel object recognition in prepubertal Ts65Dn mice was comparable to wild-type (WT) littermates (Fig. 1D) but impaired in young adults (Fig. 1E), revealing an age-dependent cognitive decline reminiscent of DS. Two alternative explanations for age-related cognitive deterioration -neuroinflammation [START_REF] Zhang | Hypothalamic programming of systemic ageing involving IKK-beta, NF-kappaB and GnRH[END_REF] and triplication of the amyloid precursor protein (App) gene in both DS patients and Ts65Dn mice (24) -were eliminated, as inflammatory markers were comparable between the two genotypes (Fig. S2), and any changes in the expression of AD-related proteins occurred in middle-aged (P360) but not young adult (P90) Ts65Dn animals (Fig. S3), i.e. well after the onset of olfactory and cognitive changes.

With regard to sexual development and reproductive maturation, Ts65Dn mice are known to show abnormalities [START_REF] Reeves | A mouse model for Down syndrome exhibits learning and behaviour deficits[END_REF], with males being infertile and females subfertile [START_REF] Moore | Increased male reproductive success in Ts65Dn "Down syndrome" mice[END_REF]. We found, additionally, that males displayed severe hypogonadism in adulthood (Fig. S4), whereas females showed normal puberty timing and regular estrous cyclicity as young adults, but became anovulatory at 12 months of age (Fig. S5). These sexually dimorphic phenotypes also resemble those reported in DS patients [START_REF] Hsiang | Gonadal function in patients with Down syndrome[END_REF]. To understand whether these changes stemmed from alterations to the HPG axis, we measured serum gonadotropin levels. Adult male (Fig. 2A-C) and female (Fig. S5I-K) Ts65Dn mice showed normal luteinizing hormone (LH) pulse frequency but decreased LH pulse amplitude. However, at P12, during the peak of minipuberty, levels of the gonadotropins LH and follicle stimulating hormone (FSH) were not markedly altered in female Ts65Dn mice (Fig. S5L). In male Ts65Dn mice at P12, LH but not FSH levels were higher than in WT mice, while both gonadotropins were elevated in adulthood (Fig. 2D), a phenomenon also seen in DS men [START_REF] Hsiang | Gonadal function in patients with Down syndrome[END_REF][START_REF] Grinspon | Early onset of primary hypogonadism revealed by serum anti-Mullerian hormone determination during infancy and childhood in trisomy 21[END_REF]. Despite this, adult male Ts65Dn mice displayed unaltered testosterone levels (Fig. 2D), similar to DS men [START_REF] Hsiang | Gonadal function in patients with Down syndrome[END_REF]. However, serum LH levels before, and 14 and 30 days after bilateral orchidectomy were comparably increased in both groups (Fig. 2E), indicating intact gonadal steroid communication between the testes and the hypothalamus. Similarly, orchidectomy did not affect olfactory or cognitive performance (Fig. 1F,G), suggesting that any deficits were not due to gonadal steroid deficiency or altered gonad-brain communication.

Together, these results confirm that trisomic Ts65Dn mice also reproduce the olfactory, cognitive and sexually dimorphic reproductive phenotype of DS patients, and implicate HPG axis dysregulation as a putative cause of these deficits.

GnRH is progressively lost in Ts65Dn mice

In keeping with our studies in human fetuses [START_REF] Casoni | Development of the neurons controlling fertility in humans: new insights from 3D imaging and transparent fetal brains[END_REF], three-dimensional (3D) imaging and analyses of solvent-cleared tissue (iDISCO) from adult WT mice revealed numerous extrahypothalamic GnRH projections (Fig. 2F), often in close apposition to the walls of the lateral ventricles (Movie S1-2). Unilateral stereotaxic injections of adeno-associated viral vectors encoding Yellow Fluorescent Protein (AAV9.EF1a.DIO.eYFP.WPRE.hGH) into the dorsolateral median eminence, where GnRH neuroendocrine terminals are located, in adult WT Gnrh::Cre mice (Fig. S6A) led to YFP labeling not only of GnRH neuronal cell bodies and processes in the preoptic area (POA) (Fig. S6B,C), but also of processes in the cortex (Fig. S6D,E), hippocampus (Fig. S6D,F) and paraventricular thalamus (Fig. S6D,F). Thus, at least some extra-hypothalamic GnRH projections in brain areas controlling cognitive and social behaviors actually came from hypophysiotropic GnRH neurons in the hypothalamus (Fig. 2F,S6A). iDISCO analyses of Gnrhr::Cre;Tau-GFP loxp/+ mice also identified GFPlabeled neurons expressing the GnRH receptor (GnRHR) promoter in the mouse cerebral cortex and hippocampus (Fig. 2G, S7A-F), supporting a non-reproductive role for GnRH.

Using conventional immunohistofluorescence and iDISCO, which provide comparable and accurate counts of GnRH neurons [START_REF] Casoni | Development of the neurons controlling fertility in humans: new insights from 3D imaging and transparent fetal brains[END_REF][START_REF] Belle | Tridimensional Visualization and Analysis of Early Human Development[END_REF], we found no difference in either the distribution or the number of GnRH somata at birth (P0) between Ts65Dn and WT mice regardless of sex, but a profound loss of both hypothalamic and extra-hypothalamic GnRHimmunoreactive somata and fibers starting after puberty onset in Ts65Dn mice (Fig. 2H, Fig. S8). In adult (P90) Ts65Dn mice, although GnRH fibers were visible in the median eminence (Fig. 2I), extensive extra-hypothalamic GnRH projections were absent (Fig. 2F,I), mirroring the age-related deterioration of cognitive performance observed in these mice (Fig. 1D,E).

microRNA-transcription factor imbalances underlie olfactory, cognitive impairments

HPG axis activation through GnRH expression at minipuberty (P12) is regulated by a complex switch consisting of several microRNAs-in particular miR-155 and the miR-200 family, as well as their target transcriptional repressor/activator genes, in particular Zeb1 and Cebpb (Fig. 3A) [START_REF] Messina | A microRNA switch regulates the rise in hypothalamic GnRH production before puberty[END_REF]. Human chromosome 21 and murine chromosome 16 code for at least five of these microRNAs (miR-99a, let-7c, miR-125b-2, miR-802 and miR-155), of which all except miR-802 are selectively enriched in GnRH neurons in WT mice around minipuberty [START_REF] Messina | A microRNA switch regulates the rise in hypothalamic GnRH production before puberty[END_REF]. Given the peripubertal loss of GnRH-immunoreactivity in Ts65Dn mice, we analyzed global microRNA and gene expression in the POA in adult mice and found a downregulation of miR99a, as well as smaller decreases in let-7c, miR-125b-2, miR-802 and miR-155 (Fig. 3B). Despite not being located on chromosome 16, miR-200 family members were reduced by 50% or more (Fig. 3C), accompanied by an upregulation of Zeb1 mRNA and a consequent marked decrease in Gnrh1 expression (Fig. 3D). Real-time PCR analyses of cell-sorted GnRH neurons from Gnrh::gfp;Ts65Dn mice (Fig. S9; Fig. 3E) confirmed that this increase in Zeb1, a Gnrh1 promoter repressor, and a concomitant downregulation of the Gnrh1 promoter activators Otx2 and Kiss1r already occurred during the infantile period, i.e. minipuberty (Fig. 3F), initiating decreased Gnrh1 expression (Fig. 3D). Accordingly, the selective overexpression of miR-200b in the POA of adult (P90) Ts65Dn males using stereotaxic injections of AAV9-EF1a-mmu-mir200b-eGFP but not a control vector (Fig. 3G,H; Fig. S10A,B), which rescued the capacity to differentiate odors (Fig. 3L) and recognize novel objects (Fig. 3M), also increased the number of neurons expressing Gnrh1 (Fig. 3I-K, Fig. S10D) and the Gnrh1 promoter regulator Otx2 (Fig. S10C,D, Fig. 3I) in the POA. Conversely, male Gnrh::Cre;Dicer loxP/loxP mice, in which miRNA processing (and thus GnRH expression) is selectively knocked out in GnRH neurons, phenocopied Ts65Dn mice, displaying impaired olfactory discrimination and cognition (Fig. 3N,O).

Hypothalamic miR-200b overexpression rectifies hippocampal gene expression

To further analyze how miR-200 expression in the POA could influence cognitive function, we performed RNA-seq and differential gene expression analyses of the POA and hippocampus dissected from 6-8 month-old WT and Ts65Dn littermates injected in the POA with control AAV, and from Ts65Dn mice infected with the vector overexpressing miR-200b (Fig. S11A). While 8 genes were differentially expressed in the POA of Ts65Dn vs. WT littermates (Fig. S11B), 91 were differentially expressed in the hippocampus (Fig. 4A-B), many involved in axon ensheathment, myelination and oligodendrocyte differentiation, as well as in potassium ion transport (Fig. 4C), in agreement with previous transcriptomic studies of the hippocampus of autopsied DS patients and mouse models [START_REF] Pinto | Rescuing Over-activated Microglia Restores Cognitive Performance in Juvenile Animals of the Dp(16) Mouse Model of Down Syndrome[END_REF] [START_REF]Down Syndrome Developmental Brain Transcriptome Reveals Defective Oligodendrocyte Differentiation and Myelination[END_REF]. Downregulated genes were involved in G-protein-coupled receptor signaling, amino acid transport and neurotransmission (Fig. S11C-D).miR-200b overexpression for 3 months in the POA of adult Ts65Dn mice reversed the upregulation of 53 of 72 genes in the hippocampus (Fig. 4D), in particular those involved in the aforementioned biological processes (Fig. S11E), and the downregulation of 6 of 19 genes (Fig. S11D). This phenomenon was confirmed by qRT-PCR analyses for key genes involved in axon ensheathment, myelination and oligodendrocyte differentiation, including myelin basic protein (Mbp) and inhibitor of DNA binding 4 (Id4), and potassium ion transport, such as the potassium channel Kcnj13 and aquaporin 1 (Aqp1) (Fig. 4E, Fig. S11F,G). Additionally, 7 genes upregulated in the Ts65Dn hippocampus are known to be similarly altered in DS patients (Fig. S12A) [START_REF] Pinto | Rescuing Over-activated Microglia Restores Cognitive Performance in Juvenile Animals of the Dp(16) Mouse Model of Down Syndrome[END_REF], and include 4 that are involved in myelination, of which the upregulation of 3 is reversed by miR-200b overexpression in the POA of Ts65Dn mice (Fig. S12B). However, while protein levels of two of these, Kcnj13 and Mbp, in the contralateral hippocampus of the same animals showed an effect of miR-200b, there were discrepancies in the direction of change between the two analyses, as might be expected given the complex control mechanisms involved, and the concomitant up-or downregulation of other transcriptional regulators, such as the known Mbp transcriptional stabilizer Quaking (Qk) (36) (Fig S11F ,G), which can also act as translational repressor depending on the molecular context [START_REF] Schafer | Translational regulation shapes the molecular landscape of complex disease phenotypes[END_REF][START_REF] Chothani | Widespread Translational Control of Fibrosis in the Human Heart by RNA-Binding Proteins[END_REF]. Similarly, transcripts for the multifunctional homeoprotein Otx2 (39) were upregulated in the hippocampal Cornu Ammonis area 1 (CA1) in Ts65Dn mice, in contrast to the POA (Fig. S10C,B), but normalized by preoptic miR-200b overexpression (Fig. S12C-E). Regardless of the direction of these changes, they provide a putative molecular basis for anomalies of brain structure and composition in DS patients [START_REF]Down Syndrome Developmental Brain Transcriptome Reveals Defective Oligodendrocyte Differentiation and Myelination[END_REF], and their reversal by miR-200b infusion in the POA is of both mechanistic and therapeutic interest.

Hypothalamic miR-200b overexpression rectifies hippocampal synaptic transmission

Next, to explore whether the functional basis of recognition memory was altered in Ts65Dn mice, we assessed basal hippocampal synaptic transmission in vivo by stimulating commissural fibers from the left hippocampus in anesthetized mice, and for each stimulation site, recording both population spikes and field excitatory post-synaptic potentials (fEPSPs) from CA1 stratum radiatum of the contralateral hippocampus (Fig. 4F). Paired-pulse stimulation (Fig. S13A) revealed similar facilitation of fEPSPs in the CA1 pyramidal cell layer of WT and Ts65Dn mice (Fig. S13B). However, the stimulus-response curve obtained by recording both fEPSPs and population spikes in the CA1 (Fig. 4G, Fig. S13C) as well as the area under the curve (Fig. 4H), were significantly lowered in Ts65Dn compared to WT mice, suggesting lower dendritic excitability. These changes were diminished by miR-200b overexpression in the POA (Fig. 4G,H, Fig. S13D). To further examine the relationship between synaptic input strength and the amplitude and latency to firing of CA1 pyramidal cells, we analyzed population spike-fEPSP coupling at different stimulation intensities (Fig. 4I). The highest and lowest values on the Boltzmann-fitted population spike-fEPSP curve were lower in Ts65Dn mice than in WT animals, reflecting a lower maximal-minimal spike amplitude in Ts65Dn mice that was rescued by miR-200b overexpression (Fig. 4J). While latency did not significantly change (Fig. 4K, Fig. S13 E,F), cellular excitability was lowered in Ts65Dn mice and partially reversed by miR-200 overexpression (Fig. 4L).

Together, these results suggest that miR-200 family expression in the POA alters electrical signal propagation in the hippocampus, and that these deficits can be remotely rescued by overexpressing miR-200b in the hypothalamus.

Hypothalamic GnRH compensation reverses olfactory and cognitive deficits

We next attempted to rescue olfactory and cognitive function in adult Ts65Dn mice by GnRH replacement. Stereotactic injection of dissociated cells [START_REF] Messina | A microRNA switch regulates the rise in hypothalamic GnRH production before puberty[END_REF] from the POA of neonatal WT Gnrh::gfp pups (WT-POA) into the third ventricle (3V) of adult male and female Ts65Dn mice (Fig. 5A, Fig. S14) [START_REF] Krieger | Brain grafts reverse hypogonadism of gonadotropin releasing hormone deficiency[END_REF] completely reversed both olfactory and cognitive impairments in Ts65Dn males (Fig. 5B) as well as short-term visuospatial memory assessed in a Y-maze test (Fig. 5C-E). Graft of WT-POA also rescued cognition in adult Ts65Dn females, but only partly restored olfactory capacity (Fig. 5F). However, unlike adult hypogonadal mice [START_REF] Krieger | Brain grafts reverse hypogonadism of gonadotropin releasing hormone deficiency[END_REF], WT-POA transplantation did not restore fertility in either Ts65Dn females (Fig. S15) or males (see methods). We next generated Gnrh::Cre; BoNTB loxP-STOP-loxP mice in which vesicular GnRH release is selectively silenced by the GnRH-neuron-specific expression of botulinum neurotoxin B (BoNTB Gnrh ). When neonatal POA cells from these animals were grafted into adult Ts65Dn males (Fig. 5G), no olfactory or cognitive rescue was observed (Fig. 5H,I). However, intraperitoneal GnRH injection 6 months post-graft rescued olfactory and cognitive performance in both sham (Fig. 5B) and BoNTB Gnrh POA-grafted Ts65Dn mice (Fig. 5H,I), indicating that the effects of the graft were specifically due to GnRH release.

To determine whether activating endogenous GnRH neuronal activity in Ts65Dn mice could rescue olfactory and cognitive function, we bilaterally injected adult Gnrh::Cre and Ts65Dn;Gnrh::Cre mice with a Cre-dependent neuron-activating hM3Dq-DREADD (Designer Receptor Exclusively Activated by Designer Drugs) vector into the POA (Fig. 5J). Unlike vehicle injection (Fig. 5K,M), intraperitoneal clozapine N-oxide (CNO) injections elicited increased LH levels in both Gnrh::Cre and Ts65Dn;Gnrh::Cre males (Fig. 5L,N), indicating GnRH release. Additionally, they acutely restored olfactory discrimination (Fig. 5O) and cognitive performance (Fig. 5P) in Ts65Dn mice. Conversely, when neurons expressing GnRHR in the hippocampus of WT Gnrhr::Cre mice were infected with an inhibitory DREADD vector (AAV8-hSYN-DIO-hM4D(Gi)-mCherry) (Fig. 5Q), acute CNO injection (3 mg/kg) dramatically reduced both cognitive and olfactory performance (Fig. 5R,S).

These data together highlight the possibility that normal cognitive and olfactory function depends on extra-hypothalamic GnRH neuronal projections and action, which are lost in Ts65Dn mice during postnatal development, leading to their DS-like phenotype.

GnRH pulsatility is essential for deficit reversal

Finally, we tested whether restoring physiological (i.e. pulsatile) GnRH release in Ts65Dn mice could reverse cognitive performance using Lutrelef -the native GnRH used to treat hypogonadotropic infertility [START_REF] Hoffman | Induction of puberty in men by long-term pulsatile administration of low-dose gonadotropin-releasing hormone[END_REF][START_REF] Hurley | Induction of ovulation and fertility in amenorrheic women by pulsatile low-dose gonadotropin-releasing hormone[END_REF]. Adult Ts65Dn males were implanted with a subcutaneous programmable mini-pump that delivered either pulsatile Lutrelef (0.25 μg of GnRH per pulse over 10 min given every 3h), leading to activation of the GnRH receptor and the reproductive axis, or continuous Lutrelef infusion (0.25 μg per 3h), which downregulates the GnRH receptor and blocks the reproductive axis [START_REF] Belchetz | Hypophysial responses to continuous and intermittent delivery of hypopthalamic gonadotropin-releasing hormone[END_REF], for 15 days (Fig. 6A). Continuous infusion did not improve olfactory or cognitive performance in male Ts65Dn mice, and had a significant deleterious effect in WT mice (Fig. 6B,C), in addition to blunting LH pulsatility (Fig. 6D-I). In contrast, pulsatile Lutrelef, which rescued both olfactory discrimination (Fig. 6B) and cognitive function (Fig. 6C), increased LH pulse amplitude to WT levels in Ts65Dn males (Fig. 6D). Neither Lutrelef treatment nor miR-200b overexpression in the POA rescued testicular weight in Ts65Dn mice (Fig. S16). Bilateral orchidectomy did not affect the rescue of olfaction (Fig. 6J) or recognition memory (Fig. 6K) by pulsatile Lutrelef, suggesting that the functional improvements observed were independent of the gonadotropic effects of GnRH, and could instead be due to the mobilization of cognitive reserves in Ts65Dn mice.

Pulsatile GnRH improves cognition in Down Syndrome patients

Based on compelling results in Ts65Dn mice, we conducted an open-label pilot study to assess the effects of pulsatile GnRH therapy on cognition in DS patients. Seven DS men (26.4±2.3 years) who had completed puberty and presented with olfactory defects were enrolled (Table S1). Despite normal testosterone and inhibin B levels, patients exhibited mildly elevated LH and FSH levels, and a mild increase in estradiol levels as compared to controls (Fig. 7A-D, Fig. S17C), yet normal pituitary sensitivity to a GnRH challenge (Fig. S17A-B). LH pulsatility was not assessed in this vulnerable population. DS patients displayed normal BMI and no major alteration in biochemical profile except for increased hsCRP, i.e., systemic inflammation (Fig. 7F, Table S1). Serum neurofilament light chain, a marker of neuronal damage [START_REF] Benkert | Serum neurofilament light chain for individual prognostication of disease activity in people with multiple sclerosis: a retrospective modelling and validation study[END_REF], was within the normal range for age (Fig. S17S). The Montreal Cognitive Assessment (MoCA) score was used to assess cognition in DS patients for whom long cognitive battery tests are challenging, given their intellectual disability, attention deficit and fatigue. The seven DS patients had impaired cognition (Fig. 7G-K), while 4 had altered verbal comprehension (Token test) (Fig. 7L). Using quantitative relaxometry-based MRI, we observed DS-related loss of myelin along the corticospinal tract and thalamus, increased iron in the pallidum, and volume loss in the cingulate gyrus, cerebellum and thalamus, compared to healthy age-matched controls (Fig. 7N, Fig. S17R, Table S2-3) [START_REF] Lee | Hypoplasia of cerebellar afferent networks in Down syndrome revealed by DTIdriven tensor based morphometry[END_REF]. Resting-state functional magnetic resonance imaging (rs-fMRI) showed altered default mode network (DMN) in our DS cohort (Fig. 7O), as previously reported [START_REF] Figueroa-Jimenez | Resting-state default mode network connectivity in young individuals with Down syndrome[END_REF][START_REF] Figueroa-Jimenez | Complexity Analysis of the Default Mode Network Using Resting-State fMRI in Down Syndrome: Relationships Highlighted by a Neuropsychological Assessment[END_REF].

Pulsatile GnRH therapy using a LutrePulse pump was given for 6 months at a dose of 75ng/kg/pulse every two hours to mimic the LH pulse frequency observed in healthy men [START_REF] Hoffman | Induction of puberty in men by long-term pulsatile administration of low-dose gonadotropin-releasing hormone[END_REF], and was well tolerated (Fig. S17L-M). The reproductive hormonal profile did not change on GnRH therapy (Fig. 7A-C, S17A, Table S1) except for a slight decrease in serum FSH (Fig. 7D). Most metabolic parameters showed a trend towards improvement or no change (Fig. S17D-K,S, Table S1). Cognitive performance, as assessed by total MoCA score, increased in 6 out of 7 patients (Fig. 7G), driven by sub-scores for visuospatial function (Fig. 7H,M), executive function (Fig. 7I), attention (Fig. 7J) and a trend for episodic memory (Fig. 7K). GnRH therapy also enhanced verbal comprehension (Fig. 7L). Olfactory performances (Fig. S17N-Q) and brain anatomical features did not change (Tables S2-S3, Fig. S18A-D). However, functional connectivity as assessed by rs-fMRI increased mainly within a broad network encompassing visual and sensorimotor DMN regions, while connectivity within the hippocampal regions (ventral DMN) linked to the amygdala decreased (Fig. 7O), approaching control values [START_REF] Figueroa-Jimenez | Resting-state default mode network connectivity in young individuals with Down syndrome[END_REF][START_REF] Huang | Age-related changes in resting-state networks of a large sample size of healthy elderly[END_REF][START_REF] Pujol | Anomalous brain functional connectivity contributing to poor adaptive behavior in Down syndrome[END_REF].

Discussion

Our study demonstrates an unexpected role for GnRH in olfactory and cognitive performance, consistent with the expression of GnRH and its cognate receptor GnRHR in extra-hypothalamic areas [START_REF] Casoni | Development of the neurons controlling fertility in humans: new insights from 3D imaging and transparent fetal brains[END_REF][START_REF] Skrapits | The cryptic gonadotropin-releasing hormone neuronal system of human basal ganglia[END_REF][START_REF] Schang | GnRH receptor gene expression in the developing rat hippocampus: transcriptional regulation and potential roles in neuronal plasticity[END_REF]. The progressive loss of GnRH expression during postnatal development precedes the onset of cognitive and olfactory impairments in a mouse model of DS, which can be reversed by replacing GnRH. Furthermore, in our pilot study of DS patients pulsatile GnRH therapy improved cognition, consistent with improved connectivity in the relevant brain regions. This is particularly important given that translational studies in DS have fallen short, and no pharmacological therapy to date has significantly improved cognition [START_REF] Antonarakis | Down syndrome[END_REF][START_REF] Goeldner | A randomized, double-blind, placebo-controlled phase II trial to explore the effects of a GABAA-alpha5 NAM (basmisanil) on intellectual disability associated with Down syndrome[END_REF][START_REF] Hanney | Memantine for dementia in adults older than 40 years with Down's syndrome (MEADOWS): a randomised, double-blind, placebo-controlled trial[END_REF][START_REF] Mcshane | Memantine for dementia[END_REF][START_REF] Boada | Antagonism of NMDA receptors as a potential treatment for Down syndrome: a pilot randomized controlled trial[END_REF].

In DS patients, a deviation from neurotypical developmental trajectories leads to reduced cognitive abilities [START_REF] Carr | Stability and change in cognitive ability over the life span: a comparison of populations with and without Down's syndrome[END_REF] and AD-like neurodegenerative changes in their forties after a long preclinical phase [START_REF] Bull | Down Syndrome[END_REF][START_REF] Fortea | Clinical and biomarker changes of Alzheimer's disease in adults with Down syndrome: a cross-sectional study[END_REF][START_REF] Lott | Dementia in Down syndrome: unique insights for Alzheimer disease research[END_REF][START_REF] Ballard | Dementia in Down's syndrome[END_REF]. Olfactory deficits of prepubertal onset worsen in adulthood concomitant with the acceleration of cognitive decline [START_REF] Nijjar | Olfactory impairment increases as a function of age in persons with Down syndrome[END_REF]. In our trisomic model, which faithfully phenocopies several clinical aspects of DS, cognitive and olfactory deficits parallel a gradual loss in GnRH expression beginning in childhood and culminating in adulthood, well before any AD-like changes. The loss of GnRH itself can be traced even further back, to the perturbation of the minipubertal microRNA-transcription factor switch in Gnrh1 promoter activity during the infantile period, which integrates multiple feedback loops [START_REF] Messina | A microRNA switch regulates the rise in hypothalamic GnRH production before puberty[END_REF], and is partially localized on the triplicated region of both the human and mouse chromosome. Overexpressing miR-200b, one of the effectors of this switch, in the hypothalamic POA, where most GnRH neuronal cell bodies reside, not only rescues other genes of the GnRH transcriptional regulation network but remotely normalizes olfaction and hippocampal synaptic transmission. miR-200 members have multiple targets, but while an action through other pathways cannot be ruled out, similar effects can be obtained by directly replacing physiologically relevant GnRH levels. The improvement in cognitive function induced by pulsatile GnRH infusion is independent of changes in the sex steroid milieu in both DS patients and Ts65Dn mice. Similarly, in patients with congenital GnRH deficiency, who show a marked impairment of spatial ability while verbal abilities remain unchanged, these deficits are not rescued by exogenous androgen therapy [START_REF] Hier | Spatial ability in androgen-deficient men[END_REF]. Conversely, inhibiting GnRHR-expressing cells in extra-hypothalamic target regions, to which hypothalamic GnRH neurons also project, leads to DS-like changes, indicating that GnRH neurons have two or more sites of action, for reproductive and non-reproductive functions, respectively.

While gonadotropin-induced gonadal function is not necessary for the cognitive or olfactory functions of GnRH, its pulsatility, necessary to regulate gonadotropin release, does appear necessary for these other functions also, and may even regulate age-related cognitive decline [START_REF] Wang | GnRH pulse frequency and irregularity play a role in male aging[END_REF]. Thus LH serum concentration and pulsatility, while not measurable in our study, may still be a useful marker for DS-like changes [START_REF] Moenter | Gonadotropin-releasing hormone (GnRH) measurements in pituitary portal blood: A history[END_REF]. Similarly, in a mouse model of AD, FSH, which is elevated in DS patients and reduced by pulsatile GnRH treatment, acts directly on hippocampal neurons to mediate the AD phenotype, supporting a similar mechanism in DS [START_REF] Xiong | FSH blockade improves cognition in mice with Alzheimer's disease[END_REF]. In that study, the effects of reducing FSH were mediated by inhibiting C/EBPβ, the product of the Cebpb gene, a part of the minipubertal GnRH switch that both directly and indirectly, through Zeb1, controls GnRH expression (18) (Fig. 3A), and whose expression was also increased in our adult trisomic mice.

Other than those genes involved in Gnrh expression, several genes involved in oligodendrocyte differentiation or myelination, including some that show age-related dysregulation in human DS brains, were also differentially expressed in Ts65Dn mice [START_REF]Down Syndrome Developmental Brain Transcriptome Reveals Defective Oligodendrocyte Differentiation and Myelination[END_REF]. This may explain the myelin loss observed, even though decreased brain volume and hypocellularity in DS are often attributed to a neurogenesis deficit [START_REF] Guidi | Widespread proliferation impairment and hypocellularity in the cerebellum of fetuses with down syndrome[END_REF]. During human brain development, myelin content increases during adolescence in the cortical grey matter and to some extent in white matter [START_REF] Corrigan | Myelin development in cerebral gray and white matter during adolescence and late childhood[END_REF], concomitant with improved cognition [START_REF] Kwon | Regional growth trajectories of cortical myelination in adolescents and young adults: longitudinal validation and functional correlates[END_REF]. Given that miR-200 in the POA normalizes the expression of myelination-related genes in the Ts65Dn mouse hippocampus, it is tempting to suggest that pulsatile GnRH secretion at puberty, a crucial hypothalamic event, could also be a signal for overall brain maturation. Some animal models of dementia, including AD, also show an upregulation of myelination genes (63) that overlap with those found in Ts65Dn mice (Fig. S19A), while genes involved in GnRH signaling are among the most downregulated in discrete cortical areas of post-mortem AD patient brains [START_REF] Wang | Integrative network analysis of nineteen brain regions identifies molecular signatures and networks underlying selective regional vulnerability to Alzheimer's disease[END_REF], as well as being dysregulated in the hippocampus of the THY::TAU22 mouse AD model [START_REF] Chatterjee | Reinstating plasticity and memory in a tauopathy mouse model with an acetyltransferase activator[END_REF], which progressively develop a hippocampal Tau pathology in parallel with cognitive deficits [START_REF] Schindowski | Alzheimer's disease-like tau neuropathology leads to memory deficits and loss of functional synapses in a novel mutated tau transgenic mouse without any motor deficits[END_REF][START_REF] Van Der Jeugd | Progressive age-related cognitive decline in tau mice[END_REF]. Like adult Ts65Dn mice (Fig. 2A-C), 12-month-old male THY::TAU22 mice showed normal LH pulse frequency (Fig. S19B) but decreased LH pulse amplitudes (Fig. S12C). Pulsatile Lutrelef infusion rescued odor discrimination (Fig. S12D,E) and object recognition memory (Fig. S12F) in these mice, confirming that olfactory and cognitive deficits in other neurodegenerative disorders could also be caused by the loss of GnRH and reversed by its replacement, perhaps through the same molecular pathways. Strengthening the parallels between DS and AD, Afg3l2, a mitochondrial gene downregulated in the Ts65Dn hippocampus, prevents both demyelination and Tau hyperphosphorylation, linking it to the AD-like phenotype observed in DS [START_REF] Kondadi | Loss of the m-AAA protease subunit AFG(3)L(2) causes mitochondrial transport defects and tau hyperphosphorylation[END_REF][START_REF] Wang | The Mitochondrial m-AAA Protease Prevents Demyelination and Hair Greying[END_REF]. Additionally, mutations in DUSP6 have been identified in patients with hypogonadotropic hypogonadism [START_REF] Miraoui | Mutations in FGF17, IL17RD, DUSP6, SPRY4, and FLRT3 are identified in individuals with congenital hypogonadotropic hypogonadism[END_REF], but it is also hypermethylated in AD and prevents Tau hyperphosphorylation [START_REF] Liu | Promoter DNA hypermethylation -Implications for Alzheimer's disease[END_REF][START_REF] Banzhaf-Strathmann | MicroRNA-125b induces tau hyperphosphorylation and cognitive deficits in Alzheimer's disease[END_REF]. The differentially modulated genes identified in Ts65Dn mice thus lie at the interface between reproductive dysfunction, AD-like cognitive and neurodegenerative alterations much like the phenotype of DS patients themselves, making these mice a valuable DS model.

In terms of neuronal activity, cognitive deficits in Ts65Dn mice could result from alterations of synaptic plasticity and neurotransmission [START_REF] Cramer | From abnormal hippocampal synaptic plasticity in down syndrome mouse models to cognitive disability in down syndrome[END_REF]. Aberrant GABAergic signaling has been previously observed in Ts65Dn mice [START_REF] Deidda | Reversing excitatory GABAAR signaling restores synaptic plasticity and memory in a mouse model of Down syndrome[END_REF], as has altered long-term potentiation associated with increased hippocampal GABA release [START_REF] Begenisic | Fluoxetine in adulthood normalizes GABA release and rescues hippocampal synaptic plasticity and spatial memory in a mouse model of Down syndrome[END_REF] and GABAergic inhibition [START_REF] Schulz | Enhanced Dendritic Inhibition and Impaired NMDAR Activation in a Mouse Model of Down Syndrome[END_REF][START_REF] Freeburn | Signalling pathways contributing to learning and memory deficits in the Ts65Dn mouse model of Down syndrome[END_REF]. Synaptic transmission in the hippocampus of our Ts65Dn mice was partly normalized by miR-200b overexpression in the septal POA, with which it is reciprocally connected [START_REF] Swanson | The connections of the septal region in the rat[END_REF] and which is a source of hippocampal GABAergic neurons during embryogenesis [START_REF] Gelman | The embryonic preoptic area is a novel source of cortical GABAergic interneurons[END_REF].

GABA is known to activate CA1 pyramidal cells in adult Ts65Dn mice, accompanied by a positive shift in the reversal potential of GABAA receptor-driven Cl -currents and increased hippocampal expression of the cation-Cl -cotransporter NKCC1 in both Ts65Dn mice and DS individuals (80). This suggests that the excitation-inhibition balance of hippocampal or other neuronal circuits may be perturbed in DS, resulting in impaired cognition, and that restoring physiological GnRH signaling somehow reestablishes this balance, even after the end of the developmental period. One possible molecular player underlying this mechanism is the homeoprotein Otx2, which acts as a microRNA-regulated Gnrh1 promoter activator in the POA [START_REF] Messina | A microRNA switch regulates the rise in hypothalamic GnRH production before puberty[END_REF], and where it has long been suspected to play a role in maintaining GnRH expression in the adult hypothalamus as well [START_REF] Kelley | The Otx2 homeoprotein regulates expression from the gonadotropin-releasing hormone proximal promoter[END_REF]. Otx2 has also been described to modulate the opening and closure of critical developmental windows for cortical GABAergic neurons at the end of the infantile period [START_REF] Spatazza | Homeoprotein signaling in development, health, and disease: a shaking of dogmas offers challenges and promises from bench to bed[END_REF], raising the possibility that POA-derived Otx2 during the minipubertal GnRH switch could influence neocortical development and function. To summarize, our results provide the rationale to launch a randomized multicentric study to confirm the efficacy of pulsatile GnRH therapy in correcting the neurodevelopmental trajectory and age-related cognitive decline seen in DS and other conditions, such as AD, that share similar molecular or functional underpinnings. Ts65Dn mouse phenotyping-Sexual maturation and postnatal acquisition of reproductive, olfactory and cognitive impairments were assessed throughout life using external signs of puberty, hormonal profiling, olfactory discrimination, novel object recognition and visuospatial memory tests etc.

Methods Summary

Animals

Imaging-The distribution of GnRH-immunoreactive neuronal cell bodies and projections in the brain, as well as the neocortical distribution of cells expressing the GnRH receptor promoter were assessed using both classical neuroanatomical approaches (immunofluorescence and multiplex fluorescent in situ hybridization) and advanced threedimensional imaging and analysis of solvent-cleared tissue (iDISCO) methods.

Functional studies-Pharmacological (intraperitoneal administration of GnRH or CNO), viral (stereotaxic infection of the preoptic region or the hippocampus with adeno-associated viral vectors expressing Cre-dependent activatory or inhibitory DREADDs, or untargeted miR-200b) and cellular approaches (grafting dissociated newborn preoptic region cells into the hypothalamus of adult mice) were used to characterize the role of GnRH neurons and secretion in the postnatal acquisition of olfactory and cognitive deficits in Ts65Dn mice. RNAseq, quantitative RT-PCR, fluorescent in situ hybridization, western blotting and in vivo CA1 field recordings in anesthetized mice were used to further investigate the molecular and cellular mechanisms underlying these processes.

Pulsatile GnRH treatment-Ts65Dn mice were subjected to LH pulsatile release evaluation, olfactory habituation/dishabituation and object recognition tests 1 month before and following 2 weeks of pulsatile GnRH therapy (Lutrelef®, Ferring SA, Switzerland) via a programmable subcutaneous micro-infusion pump, at a rate of 0.25 μg at 3-hr intervals to mimic the LH pulse frequency seen in male WT mice (SMP-300, iPRECIO, Japan).

Patients

Seven French-speaking men with Down syndrome (20-50 years of age) were enrolled in an open-label pilot study at Lausanne University Hospital (CHUV, Switzerland) to assess the effect of 6-month pulsatile GnRH therapy on cognitive and olfactory function (clinicaltrials.gov, NCT04390646). Written informed consent was obtained from all participants and their legal representatives prior to inclusion (Ethics Committee of Vaud, 2020-00270). Patients were subjected to baseline clinical evaluation (detailed history, physical examination, hormonal and cognitive profiling, MRI analyses) before and after 6-month pulsatile GnRH therapy via a subcutaneous pump at a rate of 75 ng/kg/pulse at 2-hr intervals (LutrePulse® manager and LutrePod®, Ferrring SA, Switzerland) to mimic LH pulse frequency in normal men. Six age-matched healthy male controls were also recruited to compare baseline parameters.

Imaging studies comprised structural MRI and resting-state functional MRI using a 3T wholebody MRI system using a 64-channel radiofrequency head and body coil for transmission (Magneton Prisma, Siemens Medical Systems, Germany).

Statistics-Data were assessed for normality and statistical differences evaluated using appropriate parametric or non-parametric tests for two or more groups. (A) Experimental design to evaluate olfactory and visual discrimination during postnatal development. (B-E) Habituation/dishabituation test to assess the ability of P35 and adult Ts65Dn mice and WT littermates to differentiate between two distinct odors (P35: B: WT male dishabituation vs. Ts65Dn male dishabituation, t (45) = 3.67, P = 0.003, n=6,5; WT female dishabituation vs. Ts65Dn female dishabituation, t (105) = 6.10, P < 0.0001, n=6,5. Adult: C: WT male dishabituation vs. Ts65Dn male dishabituation, t (45) = 4.19, P = 0.0006, n=6,5; WT female dishabituation vs. Ts65Dn female dishabituation, t (16) = 5.42, P = 0.0002, n=5,5); or recognize new objects in their environment (P35: D: WT male vs. Ts65Dn male, t (9) = 1.02, P = 0.33, n=6,5; WT female vs. Ts65Dn female, t (16) = 1.278, P = 0.22, n=9,9. E: WT male vs. Ts65Dn male, t (10) = 4.8, P = 0.0007, n=6,6; WT female vs. Ts65Dn female, t (10) = 4.93, P = 0.0006, n=6,6). Values represent means ± SEM. Unpaired Student's t-test to compare 2 conditions; two-way repeated-measures ANOVA followed by Sidak's post hoc test for ≥ 3 conditions. **P<0.01; ***P<0.001. subject (S1-S7). S2, S3, S5 and S7 improved at 6M. (N) Statistical parametric maps of brain anatomy differences between DS patients (n=8) and age-matched male controls (n=44) after p FWE <0.05 correction for multiple comparisons at the whole-brain level. Voxelbased quantification of magnetization transfer (MT) saturation maps reveal volume loss in the cerebellum, anterior cingulate cortex, supplementary motor cortex, substantia nigra, thalamus, insula and primary motor cortex M1, and loss of myelin content in the thalamus, primary sensorimotor cortex S1/M1, angular gyrus, insula, and superior frontal and temporal gyri bilaterally. (O) Resting-state functional MRI comparison of functional connectivity in DS (n=7) at BL and after 6MGnRH therapy in the visual (including all occipital regions, the lingual gyrus and the cuneus) and sensorimotor (pre-and post-central gyri, middle frontal gyrus) default-mode network (DMN), connected to the superior parietal lobule, the superior temporal gyrus, some prefrontal areas and part of the anterior DMN (increased; FDR-corrected p<0.0005); as well as within the hippocampal regions of the ventral DMN linked to the amygdala (reduced; FDR-corrected p<0.0005). *p<0.05, **p<0.01. MoCA: Montreal cognitive assessment; FDR: false discovery rate; FWE: family-wise error; GM: grey matter; WM: white matter.

  Male and female Ts65Dn mice (P9-P360) and their wild-type (WT) littermates were housed under specific pathogen-free conditions in a temperature-controlled room (20-21°C) with 12h light/dark cycle and ad libitum standard chow and water. Several additional transgenic mouse lines were used in this study. Animals studies were approved by the Institutional Ethics Committees for the Care and Use of Experimental animals of the Universities of Lille and Lyon 1, and the French Ministry of National Education, Higher Education and Research (APAFIS# 29172-2020121811279767 v5 and APAFIS#10164-2017060710541958 v4).

Fig. 1 .

 1 Fig. 1. Ts65Dn mice show age-dependent olfactory, cognitive loss.

Fig. 2 .

 2 Fig. 2. Ts65Dn mice progressively lose GnRH expression, function. (A) LH pulsatility assessment by serial blood sampling. (B) LH pulse frequency (n=8,8 mice). (C) LH pulse amplitude (n=5,6 mice). (D) Circulating levels of LH, FSH (at P12 and in adults) and testosterone (in adults) (WT n=8,12,8,13,15 mice; Ts65Dn n=5,12,9,14,20 mice). (E) Effect of orchidectomy on LH levels 14 days (14D) and 30 days (30D) after surgery (WT: n=8,4,4,4,4 mice; Ts65Dn: n=9,4,4,5,5 mice). (F) GnRH-immunoreactive neuronal fiber tracing, pseudocolored projection pathways. Green: GnRH neurons and projections to median eminence (ME); magenta: neuronal projections to the anterodorsal

Fig. 3 .

 3 Fig. 3. GnRH transcriptional machinery disequilibrium underlies cognitive impairments. (A) Putative microRNA-transcription-factor network regulating hypothalamic GnRH promoter activation during postnatal development (adapted from (18)). (B-D) RT-PCR analysis of expression levels of microRNAs located on chromosome 16 (B) and miR-200 family members (C), as well as hypothalamic GnRH promoter modulators (D) in the preoptic region (POA) of adult WT and Ts65Dn littermates (B: n=11,10,10,11,10 WT mice; n=9,8,8,9,8 Ts65Dn mice; C: n=8,9,7,9,9 WT mice; n=6,6,6,6,6 Ts65Dn mice; D: n=11,11,9,10,11,11,7,11,11,8 WT mice; n=9,9,9,9,9,9,6,9,9,6 Ts65Dn mice). (E)

Fig. 4 .

 4 Fig. 4. Hypothalamic miR-200b overexpression rescues hippocampal transcriptome, connectivity. (A)MA plot of gene expression changes (estimated log 2 fold changes as a function of the mean of normalized counts; P Adj <0.05) in the hippocampus of adult male (P180) Ts65Dn (n=3) vs. WT mice (n=4). (B) Pie chart of the number of differentially regulated genes between Ts65Dn and WT littermates in the hippocampus (P adj <0.05). (C) STRING protein network analysis of upregulated genes. (D) UpSet plot showing the intersection between differentially up-regulated genes in the Ts65Dn hippocampus and genes rescued by miR-200b. (E) Quantitative RT-PCR confirmation of RNA-seq data. (F) Schematic

Fig. 5 .

 5 Fig. 5. Restoring GnRH neurons/function reverses olfactory, cognitive deficits. (A) Cell therapy by grafting enzymatically dissociated cells from the POA of WT neonatal mice (P0-P2) into the third ventricle of adult Ts65Dn mice. (B-F) Effect of WT-POA grafts in Ts65Dn males on olfactory and cognitive performance (B: n=10,9,5 male mice; F: n=7,5,5 female mice) and short-term visuospatial memory assessed by the Y-maze test (C-E) 3 months after surgery (D: n=5,6,7,5,7 male mice; E: n=5,6,7,5,6 male mice). (G) Experimental design to graft POA cells from neonatal mice with exocytotis-incompetent GnRH neurons (Gnrh::Cre; BoNTB loxP-STOP-loxP ). (H,I) After a 3-month recovery period,

Fig. 6 .

 6 Fig. 6. Olfactory, cognitive deficit reversal requires GnRH pulsatility. (A) Schematic of pharmacotherapy with Lutrelef, a clinically-used GnRH peptide, in adult Ts65Dn mice. Mice were implanted with osmotic pumps to receive a continuous infusion of vehicle or Lutrelef (0.25 μg/3h over 2 weeks), or with a programmable mini-pump (iPRECIO), to receive pulsatile Lutrelef infusion (0.25 μg/10 min every 3 hours over 2 weeks). (B-I) Effect of treatments on odor discrimination (B; n=4,8,3,5,6 mice), object recognition (C; n=4,9,4,4,8 mice) and LH pulsatility (D-I) (D: n=4,9,3,4,8 mice; each dot represents one subject). (J-K) Effects of Lutrelef in orchidectomized (ORX) mice (n=4). Values represent means ± SEM. * P<0.05,** P<0. 01,***P<0.001; paired Student's t-test or Wilcoxon matched-pair test (B,C), unpaired Student's t-test or Mann-Whitney U-test (D) or a two-way repeated-measures ANOVA followed by Sidak's post hoc test (J,K).

Fig. 7 .

 7 Fig. 7. Pulsatile GnRH improves patient brain connectivity, cognition. (A-F) Biochemical profile at baseline (BL, blue dots, n=7) and after 6-month pulsatile GnRH therapy (6M, blue triangles, n=7), compared to healthy age-and sex-matched controls (C, open circles, n=5 for inhibin-B and n=6 for all the other parameters). (G-L) Results of cognitive tests in male Down syndrome patients (n=7) at BL (blue dots) and after 6M of GnRH therapy (blue triangles): MoCA total score, visuo-spatial index, executive index, attention index, memory index and Token test score. (M) 3D-drawings representing a cube and a bed, part of visuospatial index score of the MoCA at BL and 6M for each

Science. Author manuscript; available in PMC 2023 March 02.

Acknowledgments

The authors would like to thank PLBS UAR 2014 -US41 (https://ums-plbs.univ-lille.fr/ ) with its different platforms and staff for expert technical assistance: Charlotte Laloux (behavioral exploration platform for rodents), Nathalie Jouy (cell sorting Facility, BICeL), Meryem Tardivel and Antonino Bongiovanni (microscopy core facility, BICeL) and Julien Devassine (Animal house) of the UMS2014-US41 for expert technical assistance. For the technical expertise during the clinical study, the authors would also like to thank Prof. Basile Landis (Olfactology Unit, HUG), Anne-Sophie Boulin and Peggy Cazin D'Honincthun (neuropsychological tests, Neurorehabilitation Unit, CHUV), Giulia Di Domenicantonio (Dept. of Neuroclinical sciences, LREN -CHUV), Argnesa Stojkai (Dept. of Endocrinology, CHUV), and Pascal Benkert (Dept. Neuroimmunology and Neuroscience, Basel). GnRH therapy was kindly provided by Ferring SA, Switzerland.

Funding This work has been supported by the European Research Council COST action BM1105 for the study of GnRH deficiency (to U.B., P.C., P.G., N.P., V.P., M.T.-S.), Agence Nationale de la Recherche grants ANR-17-CE16-0015 (to V.P., P.C. and L.B.), DistAlz (ANR-11-LABEX-0009 to V.P. and L.B.), I-SITE ULNE (ANR-16-IDEX-0004), the Région Rhône-Alpes-SCUSI 2018-#R18119CC and Swiss National Fund 310030B_201275 (to N.P.). M.M.-L received a postdoctoral fellowship from the European commission (H2020-MSCA-IF-2014, No 656730) and V.L. a doctoral fellowship from Inserm and the Region Hauts de France. PG is supported by the European Union's Horizon 2020 Research and Innovation Programme under grant Agreement No 874741. BD is supported by the Swiss National Science Foundation (project grant numbers 32003B_135679, 32003B_159780, 324730_192755 and CRSK-3_190185), ERA-NET iSEE project, UNIL-EPFL CLIMACT programme and the SPHN-SACR project. AL is supported by the Swiss National Science Foundation (project grant number 320030_184784) and the ROGER DE SPOELBERCH foundation. LREN is very grateful to the ROGER DE SPOELBERCH and Partridge Foundations for their generous financial support.

Supplementary Material

Refer to Web version on PubMed Central for supplementary material.

Data and code availability

The accession number for the RNA-seq data reported in this paper is GEO: GSE199974. All the other data supporting the findings of this study are available within the article and its supplementary information files.