PhD, PharmD a , Anne Marchalot

MSc Catherine Horiot

PhD Jean-Marie Lambert

MSc Claire Carrion

MSc Christelle Oblet

MSc Justine Pollet

MD, PhD Michel Cogné

PhD Jeanne Moreau

PhD Brice Laffleur

PhD Laurent Delpy
email: laurent.delpy@unilim.fr

Targeting IgE polyadenylation signal with antisense oligonucleotides decreases IgE secretion and plasma cell viability

Keywords: Immunoglobulin E, Antisense Oligonucleotide, Polyadenylation, Allergy, B Cells, Plasma Cells, Gene Therapy, Cell Viability

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INTRODUCTION

Immunoglobulin E (IgE) is a well-characterized actor in Type 1 hypersensitivity reactions playing a crucial role in allergy. Upon immunization with an allergen, B cells and plasma cells secrete specific IgE, which binds to the surface of tissue mast cells and basophils through the high-affinity IgE receptor (FcεRI), producing allergic symptoms [START_REF] Macglashan | IgE-dependent signaling as a therapeutic target for allergies[END_REF]. Omalizumab, an anti-IgE monoclonal antibody, reduces allergic inflammation by depleting circulating free-IgE and preventing its interaction with FcRI and the low-affinity receptor CD23/FcεRII. In addition, the absence of IgE binding to FcεRI downregulates its expression on the surface of mast cells and basophils [START_REF] Kawakami | From IgE to Omalizumab[END_REF]. IgE is first produced as a membraneassociated form in B lymphocytes, but those cells expressing surface IgE are extremely rare in humans [START_REF] Wu | The production and regulation of IgE by the immune system[END_REF]. Consistent with the scarcity of IgE+ memory B cells, previous studies have shown that IgE B cell receptor (BCR) expression leads to rapid differentiation into short lived plasma cells and/or apoptosis, preventing IgE memory B cell formation (4-7).

Antisense oligonucleotides (ASO) are short single strands of modified DNA, which can be used to modify RNA maturation processes such as splicing or polyadenylation [START_REF] Bennett | Therapeutic Antisense Oligonucleotides Are Coming of Age[END_REF][START_REF] Smith | Therapeutic Oligonucleotides: State of the Art[END_REF]. Recently, two spliceswitching oligonucleotides obtained marketing authorization: eteplirsen and nusinersen, for the treatment of Duchenne's muscular dystrophy and spinal muscular atrophy respectively, rekindling hope for the implementation of new ASO therapeutic strategies in many diseases [START_REF] Levin | Treating Disease at the RNA Level with Oligonucleotides[END_REF]. ASO can also modulate polyadenylation by targeting polyadenylation signals (PAS) or a donor splice site either to reduce gene expression or to direct alternative polyadenylation (APA) and preferably generate one transcript over the other [START_REF] Vickers | Fully modified 2′ MOE oligonucleotides redirect polyadenylation[END_REF][START_REF] Vorlová | Induction of Antagonistic Soluble Decoy Receptor Tyrosine Kinases by Intronic PolyA Activation[END_REF][START_REF] Elkon | Alternative cleavage and polyadenylation: extent, regulation and function[END_REF]. Thereby, ASO remain a viable solution for RNA polyadenylation modulation avoiding DNA modifications that can trigger off-target effects [START_REF] Fu | High-frequency off-target mutagenesis induced by CRISPR-Cas nucleases in human cells[END_REF][START_REF] Grünewald | Transcriptome-wide off-target RNA editing induced by CRISPR-guided DNA base editors[END_REF].

Here we address a new therapeutic antisense strategy targeting PAS sequences for secreted IgE to decrease IgE secretion while inducing the expression of membrane-associated IgE mRNA isoforms and apoptosis of IgE-secreting plasma cells.

J o u r n a l P r e -p r o o f

RESULTS AND DISCUSSION

To evaluate this strategy, we used a Cre tamoxifen-inducible transgenic mouse model called InEps™ where human IgM and IgE constant genes have been inserted between Eµ and mouse IgM constant genes. This model produces human IgE upon in vitro hydroxytamoxifen treatment of isolated spleen cells (Fig 1,A). We found that IgE targeting ASO treated spleen cells were less likely to secrete IgE and less IgE was detected in supernatants compared to irrelevant control ASO (CTRL) ( To evaluate the feasibility of our antisense approach in vivo, IgE secretion was assessed after treatment with morpholino ASO harboring different cell-penetrating moieties. We compared ASO conjugated to octa-guanidine dendrimer (i.e. compounds used throughout this study) with ASO coupled to Pip6a (18), J o u r n a l P r e -p r o o f as an arginine-rich cell-penetrating peptide. Interestingly, IgE concentrations were decreased to similar extent after treatment with ASO and Pip6a-ASO in U266 cell supernatants (Fig 5,A). For in vivo delivery assessment, Tamoxifen-treated InEps TM mice received 1 intravenous injection (tail vein) of CTRL, ASO and Pip6a-ASO (12.5 mg/kg) and serum IgE concentrations were determined after 24h (Fig 5 ,B).

Interestingly, lower IgE amounts were found in serum of ASO and Pip6a-ASO treated mice, with a significant decrease in the later compared to controls (Fig 5 ,C). Thus, these data provide evidence for a systemic effect of Pip6a-ASO targeting the IgE PAS on antibody-secreting cells.

IgE+ B cells can be generated either by direct class switching from IgM+ B cells or sequential class switching from IgG1+ B cells [START_REF] Wu | The production and regulation of IgE by the immune system[END_REF][START_REF] He | IgG1 memory B cells keep the memory of IgE responses[END_REF], but exhibit a short lifespan and low levels of BCR IgE expression [START_REF] Wade-Vallance | Intrinsic and extrinsic regulation of IgE B cell responses[END_REF][START_REF] Laffleur | B Cell Intrinsic Mechanisms Constraining IgE Memory[END_REF]. Interestingly, modulation of APA after treatment by IgE targeting ASO induced apoptosis in U266 myeloma cells, yet further studies are needed to identify whether toxic effects are caused by the re-expression of IgE BCR or by a more global attenuation of the PC phenotype with less IgE secretion and MZB1 expression. Several studies including ours showing that the BCR IgE tonic signal drives apoptosis support the former hypothesis, but conflicting evidence has been also described [START_REF] Wade-Vallance | Intrinsic and extrinsic regulation of IgE B cell responses[END_REF][START_REF] Laffleur | B Cell Intrinsic Mechanisms Constraining IgE Memory[END_REF]. Since the ER-localized cochaperone MZB1 plays a crucial role in protein folding in plasma cells [START_REF] Andreani | Cochaperone Mzb1 is a key effector of Blimp1 in plasma cell differentiation and β1-integrin function[END_REF][START_REF] Rosenbaum | MZB1 is a GRP94 cochaperone that enables proper immunoglobulin heavy chain biosynthesis upon ER stress[END_REF], its low expression together with disturbed stoichiometric ratio of Ig heavy and light chains induced by ASO treatment could lead to ER stress-associated apoptosis in U266 cells, but this needs further investigation.

The herein described proof-of-principle for systemic delivery of ASO targeting IgE PAS could open new avenues for a broad range of IgE-dependent allergies. Nonetheless, the impact of IgE ASO needs to be confirmed with some formulation adjustments to target long-lved plasma cells in bone marrow niches, and conjugation of ASO to monoclonal anti-CD38 antibody used for the treatment of multiple myeloma should be envisioned. Local delivery of ASO could be also advantageous for food allergy since a recent study identified IgE+ B lineage cells in gastrointestinal tract of peanut allergic patients [START_REF] Hoh | Origins and clonal convergence of gastrointestinal IgE+ B cells in human peanut allergy[END_REF]. Of note, intradermal injections of a splice-switching oligonucleotide targeting FcRIβ have also demonstrated J o u r n a l P r e -p r o o f positive results in a mouse model of allergic dermatitis [START_REF] Cruse | Exon skipping of FcεRIβ eliminates expression of the high-affinity IgE receptor in mast cells with therapeutic potential for allergy[END_REF]. In addition, respirable ASO for aerosol delivery has already been developed [START_REF] Tang | RASONs: a novel antisense oligonucleotide therapeutic approach for asthma[END_REF] and such a formulation should be useful to track local IgE production in various inflammatory conditions.

We show here that targeting the secreted IgE PAS with an ASO is an effective method to reduce IgE secretion which has already proven to be beneficial for IgE-dependent allergic patients (2) while enhancing apoptosis of IgE-expressing plasma cells. This latter effect could be even more favorable for allergic patient prognosis as it could reduce the IgE plasma cell compartment (4) and, in this manner, decrease IgE production to promote allergen tolerance as other Ig isotypes are not affected.

Fig 1 ,

 1 B). In addition, secreted IgE mRNA significantly decreased when membrane IgE mRNA increased with ASO treatment (Fig 1, C), with strongly diminished secreted / membrane IgE mRNA ratios (Fig 1, D). Consistent with this, the frequency of IgE-expressing cells was reduced by ASO treatment (Fig 1, E). We next verified this effect on InEps™ mouse hybridoma cells secreting allergen-specific human IgE and found less IgE in supernatants, decreased secreted IgE mRNA, and increased membrane IgE mRNA in ASO treated cells compared to controls (Fig 1, F,G). To characterize the effect of IgE polyadenylation switching following ASO treatment on a complete human background, human IgE-secreting myeloma U266 cells were also treated in vitro. Similarly to InEps TM transgenic mouse spleen cells, U266 myeloma cells secreted less IgE in supernatants in the presence of IgE ASO compared to cells cultured with control ASO (Fig 2, A). Again, secreted IgE mRNA was strongly reduced whereas the expression of the membrane IgE mRNA isoform was increased (Fig 2, B,C). These results were confirmed by exon coverage analysis of mRNA sequencing reads from which we observed a decrease in CHS reads and an increase in M1 and M2 reads in ASO treated cells compared to control treated cells (Fig 2, D). CHS and M1-M2 exons are only found in secreted IgE mRNA and membrane IgE mRNA respectively. Further analysis of total read counts confirmed the significant modulation of CHS/CH4 and M2/CH4 ratios in ASO conditions compared to controls (Fig 2, E). Next, apoptosis was examined in U266 cells treated 24h and 48h with ASO. Early and late apoptotic cells were increased in ASO treated cells compared to controls (Fig 2, F). Consistent with this increased J o u r n a l P r e -p r o o f apoptosis, higher amounts of cleaved PARP proteins were found in ASO treated U266 cells compared to controls (Fig 2, G). RNA sequencing of ASO compared to CTRL treated U266 cells revealed 202 differentially expressed genes (Fig 3, A and Supplemental Table E1) among which IGHE expression was significantly decreased by 1.7 fold. Pathway analysis performed on this list revealed eight significant pathways related to lymphocyte proliferation and activation along with regulation of immunoglobulin production and interleukin 4 and 13 signalling (Fig 3, B). CD80 and PD-L2 expression, markers of a subtype of memory B cells (16), were increased by almost 2 fold while MZB1, an essential gene for plasma cell differentiation (17), was diminished by 2 fold. This transcriptomic analysis suggests that IgE ASO treatment attenuates the plasma cell phenotype of U266 myeloma cells. To address whether IgE ASO treatment displayed a selective effect on IgE secretion, normal human sorted B cells were cultivated and stimulated for IgG1 and IgE class switching in vitro. Comparable to other models, secreted IgE mRNA was decreased and membrane IgE mRNA was increased but none of total unswitched IgM or switched IgG1 mRNA were affected by ASO treatment (Fig 4, A). IgM and IgG1 membrane and secreted mRNA were also checked to verify that no polyadenylation switching effect occurred on those Ig isotypes, regardless of total mRNA amounts (Fig 4, B). In agreement with the low surface expression of IgE BCR compared to IgG1 BCR (7), activated B cells displayed much higher secreted / membrane Ig mRNA ratios for  heavy chains (HCs) (Fig 4, C) than for 1 (Fig 4, D) and µ HCs (Fig 4, E) in control conditions, albeit the former ratio was strongly diminished by ASO treatment. Our IgE-targeting ASO is therefore specific for the IgE isotype and will not affect synthesis or polyadenylation of other Ig subclasses, thus maintaining a responsive immune system against pathogens.

FIG 1 .

 1 FIG 1. IgE targeting ASO decreased secreted IgE and increased membrane IgE in a human IgE

FIG 2 .FIG 3 .

 23 FIG 2. IgE targeting ASO decreased secreted IgE and promoted apoptosis in a human plasma cell line.

FIG 4 .FIG 5 .

 45 FIG 4. IgE targeting ASO decreased secreted IgE and increased membrane IgE expression in human

ACKNOWLEDGMENTS

We thank ArkAb (a division of B Cell Design) for kindly providing InEps TM mice and IgE-specific hybridoma cells. We thank also the staff of our animal facility (University of Limoges, France) and Michael J Gait (Medical Research Council, Laboratory of Molecular Biology, Cambridge, United Kingdom) for helpful discussions regarding the use of Pip6a-ASO for the targeting of antibody-secreting cells in vivo.

J o u r n a l P r e -p r o o f

This work was supported by grants from Fondation ARC (PJA 20161204724), ANR (2017-CE15-0024-01), INSERM Transfert (MAT-PI-19135-A-02), Ligue Contre le Cancer (CD87, CD19, CD23) and Fondation Française pour la Recherche contre le Myélome et les Gammapathies monoclonales (FFRMG).

AUTHORS CONTRIBUTION

Anne Marchalot designed and performed experiments, analysed data and wrote the manuscript.

Catherine Horiot, Jean-Marie Lambert, Claire Carrion and Christelle Oblet performed experiments and


Ziyad Chaker

Guido Ori

Christine Tugène

Sébastien Le Roux

Mauro Boero

Carlo Massobrio

Evelyne Martin

Assil Bouzid

The role of dispersion forces on the atomic structure of glassy chalcogenides: the case of GeSe 4 and GeS 4

Keywords: Car-Parrinello Molecular Dynamics (CPMD), Atomic structure, di-chalcogenides, van der Waals

. The atomic structures obtained agree well with the ones obtained by Bouzid et al. [3] without considering dispersion forces. Due to the vdW interactions, glassy GeSe 4 features a higher number of Ge fourfold coordinated. The two vdW approaches also agree to a large extent, exceptions occurring for some moderate differences in the intensity of the peaks in the Ge-Ge pair correlation function.

Introduction

The inclusion of dispersion (van der Waals, vdW) forces in first-principles molecular dynamics (FPMD) treatments of disordered systems is of paramount importance to assess and improve the predictive power of these approaches for various kinds of bonding characteristics. In the case of water, for instance, vdW interactions are crucial to obtain realistic properties for such universal solvent [START_REF] Ikeda | Role of van der Waals corrections in first principles simulations of alkali metal ions in aqueous solutions[END_REF]. Turning to chalcogenides network-forming disordered materials, it appears that dispersion forces are more likely to play a role in Ge x Te 1-x than in Ge x Se 1-x ones, as highlighted by a recent set of FPMD results [START_REF] Micoulaut | Towards accurate models for amorphous GeTe: Crucial effect of dispersive van der Waals corrections on the structural properties involved in the phase-change mechanism[END_REF]. This is due to the impact of predominant bonding components (of ionic or iono-covalent origin) screening more effectively dispersion effects in Ge x Se 1-x than in Ge x Te 1-x systems.

In spite of these achievements, the issue of dispersion forces in chalcogenides disordered networks cannot be considered as completely settled and deserves further investigations. This is due to the paucity of the cases examined so far and the availability of several vdW recipes, not necessarily equally performing and of general applicability [START_REF] Bouzid | Role of the van der Waals interactions and impact of the exchange-correlation functional in determining the structure of glassy GeTe 4[END_REF][START_REF] Chaker | First-principles study of the atomic structure of glassy Ga 10 Ge 15 Te 75[END_REF].

These concepts have been exemplified by our recent investigation devoted to liquid GeSe 2 [START_REF] Lampin | Impact of dispersion forces on the atomic structure of a prototypical network-forming disordered system: The case of liquid GeSe 2[END_REF]. In that paper, the authors employed two distinct descriptions for the dispersion forces, namely the Grimme-D2 or the maximally localized Wannier function scheme (detailed later in the section devoted to the methodology).

This second scheme is more profoundly rooted into density functional theory since the electronic structure, obtained within the selected DFT-GGA framework, is used to compute the maximally localized Wannier functions (MLWF) on which the van der Waals scheme is based. In what follows the results corresponding to each one of these two schemes will be referred to as vdW G (Grimme) and vdW W (Wannier) respectively.

We remind that in the case of liquid GeSe 2 , by calculating properties such as partial structure factors, pair correlation functions, bond angle distribution, and number of corner vs edge sharing connections, it was found that the maximally localized Wannier function scheme is more reliable than the Grimme-D2 scheme in reproducing existing first-principles results. In particular, the Grimme-D2 scheme worsens the agreement with experiments in the case of the Ge-Ge pair correlation function. The main message of that study was that the impact of dispersion forces on disordered chalcogenides is not necessarily the same when adopting different theoretical schemes.

Based on the above findings, this paper is intended to address the two following issues: (a) whether there are other disordered chalcogenides liquid or glasses (among those already investigated) for which dispersion forces cannot be neglected and, related to this, (b) to establish the sensitivity to the specific vdW recipe employed, in analogy with the case of liquid GeSe 2 [START_REF] Lampin | Impact of dispersion forces on the atomic structure of a prototypical network-forming disordered system: The case of liquid GeSe 2[END_REF]. To attain these purposes we focus here on glassy g-GeSe 4 and g-GeS 4 by performing a comparative study and by considering three set of results, namely those obtained by Bouzid et al. [START_REF] Bouzid | Origin of structural analogies and differences between the atomic structures of GeSe 4 and GeS 4 glasses: A first principles study[END_REF] with no vdW interactions account (NovdW) and the present new data for which we employed the vdW G and vdW W schemes. In short, our results show that dispersion forces are at the origin of minor changes in the structural properties of both glasses, g-GeSe 4 being the one most affected in terms of Ge tetrahedral coodination. This paper is organized as follows. In section II, we provide the methods and computational details of the calculations performed in this work with a special emphasis on the two schemes of vdW. In section III, the different results obtained for both atomic structures highlighting the specific contributions of the vdW corrections are detailed. For each system and each vdW scheme, we compare the total pair correlation function and the total structure factors S(k) to the experimental data available. Then we move to the partial Faber-Ziman structure factors and to the partial pair correlation functions. Finally, we draw a detailed table of the different coordination numbers obtained for the atomic structures we considered. In section IV, general conclusions are proposed on the role of vdW corrections for this pair of glassy chalcogenide systems.

Computational methods

Our simulations were performed within the Car-Parrinello [START_REF] Car | Unified approach for molecular dynamics and density-functional theory[END_REF] molecular dynamics (CPMD) scheme as implemented in the CPMD code [START_REF] Hutter | Computer code CPMD[END_REF]. We employ the exchange density-functional proposed by Becke [START_REF] Becke | Density-functional exchange-energy approximation with correct asymptotic behavior[END_REF] and the one due to Lee, Yang and Parr for the correlation part [START_REF] Lee | Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density[END_REF] (BLYP). This Generalized Gradient Approximation (GGA) is known to provide an accurate description of the network topology in the case of binary glassy chalcogenide systems [START_REF] Bouzid | Role of the van der Waals interactions and impact of the exchange-correlation functional in determining the structure of glassy GeTe 4[END_REF]. For the treatment of the core-valence interactions, we adopted a norm-conserving pseudo-potential according to the description of Troullier and Martins [START_REF] Troullier | Efficient pseudopotentials for plane-wave calculations. II. operators for fast iterative diagonalization[END_REF]. A plane wave basis set is chosen for the representation of the valence electrons with a corresponding energy cutoff of 30 Ry [START_REF] Bouzid | Role of the van der Waals interactions and impact of the exchange-correlation functional in determining the structure of glassy GeTe 4[END_REF][START_REF] Bouzid | Origin of structural analogies and differences between the atomic structures of GeSe 4 and GeS 4 glasses: A first principles study[END_REF][START_REF] Lampin | Impact of dispersion forces on the atomic structure of a prototypical network-forming disordered system: The case of liquid GeSe 2[END_REF]. The Brillouin zone integration is restricted to the Γ point.

As mentioned in the introduction, we consider two types of implementations of the van der Waals (vdW) corrections. The first is the DFT-D2 formula proposed by Grimme [START_REF] Grimme | Semiempirical GGA-type density functional constructed with a long-range dispersion correction[END_REF] which is a DFT-based formulation in which parameters are self-consistently tuned in conjunction with the specific exchange-correlation functional considered. We recall that, although empirical, the parameters involved in this formulation tuned on different functionals, including the one used in this work, and benchmarked on a wealth of different systems from simple molecules to complex reactive surfaces and chalcogenides. No experimental parameters are considered in the construction of this specific vdW correction. Its inclusion does not affect any stage of the Kohn-Sham equations, thus preserving the first-principle character of all electronic structure calculations. However, the Grimme formalism does not allow for any update of the vdW interactions resulting from the changes in the electronic structure that occur during the dynamical evolution.

The second scheme (vdW W ) considered makes use of the Wannier functions analysis [START_REF] Wannier | The structure of electronic excitation levels in insulating crystals[END_REF] to compute the maximally localized Wannier functions [START_REF] Silvestrelli | Maximally-localized Wannier functions for disordered systems: Application to amorphous silicon[END_REF] (MLWFs) and use these for the ab initio evaluation of the vdW energy. The inclusion of vdW W correction using MLWFs, first introduced in Ref. [START_REF] Silvestrelli | Van der Waals interactions in DFT made easy by Wannier functions[END_REF], is written as [START_REF] Ikeda | Role of van der Waals corrections in first principles simulations of alkali metal ions in aqueous solutions[END_REF]:

E vdW = - n<l f (r nl ) C 6,nl r 6 nl (1)
In this case, the full system is partitioned into fragments on the basis of its connectivity in a given configuration so that r nl is the distance between two MLWF centers on pairs of fragments while f(r nl ) is a damping function. The MLWFs allow to perform unbiased partitioning of the charge density while their computation can be performed on the fly during the CPMD run with a reasonably low computational cost [START_REF] Ikeda | Role of van der Waals corrections in first principles simulations of alkali metal ions in aqueous solutions[END_REF]. The MLWF centers are defined as:

x n = - L 2π m {log ( w n |exp(-2iπ • x/L)|w n )} (2)
for the x-direction but similar expressions can be written for the other two spatial directions. The spreads of the MLWF are used to evaluate the C 6,nl coefficients according to the procedure proposed by Silvestrelli et al. [START_REF] Ambrosetti | van der waals interactions in density functional theory using wannier functions: Improved C 6 and C 3 coefficients by a different approach[END_REF]. Although the analytical form of the vdW energy ( 1) is similar to the one of the DFT-D2 scheme, the C 6 coefficients are calculated directly from the first principles electronic structure calculation at each molecular dynamics step.

During our first-principles molecular dynamics runs, the temperature of the ions was controlled via a Nosé-Hoover thermostat [START_REF] Nosé | A unified formulation of the constant temperature molecular dynamics methods[END_REF][START_REF] Hoover | Canonical dynamics: equilibrium phase-space distributions[END_REF] and a similar method has been applied to control the evolution of the temperature of the fictitious electronic degrees of freedom along the scheme proposed by Blöchl and Parrinello [START_REF] Blöchl | Adiabaticity in first-principles molecular dynamics[END_REF]. An integration step of 7 au (0.168 fs) has been used for the GeS 4 -vdW G case while a slightly lower time-step of 5 au (0.120 fs) is used for the three other cases (GeSe 4 -vdW G , GeS 4 -vdW W , GeSe 4 -vdW W ), ensuring an optimal control of the conserved quantities all along the molecular dynamics trajectories.

Our GeX 4 (X = Se or S) glassy systems are periodic structures with a cubic primitive cell containing 480 atoms (96 Ge and 384 X) and a side equal to 24.82 Å for GeS 4 and 24.87 Å for GeSe 4 . By taking as initial configuration one extracted from the trajectory produced in the NovdW case, extended trajectories were implemented to lose memory of this starting condition [START_REF] Bouzid | Role of the van der Waals interactions and impact of the exchange-correlation functional in determining the structure of glassy GeTe 4[END_REF]. Both systems were constructed and studied within the framework of the CPMD-vdW G or CPMD-vdW W methods applying a specific thermal cycle.

For the vdW G case, the initial systems were brought at a ionic temperature of T= 900 K and equilibrated during about 40 ps, the temperature was then lowered to T = 700 K for 55 ps and finally lowered to room temperature (T = 300 K) to produce the trajectory (10 ps) exploited for the structural analysis. A shorter cycle have been considered for the vdW W calculations including: 1 ps at 300 K, 1.5 ps at 600 K, 10 ps at 900 K, 5 ps at 600 K and finally a trajectory larger than 10 ps at 300 K for both GeX 4 models to produce the data used in this work.

To characterize the atomic structures of the glassy materials studied within our FPMD calculations, the partial pair correlation functions are defined as the ratio between the density ρ αβ (r) in a shell of thickness dr and the total density of the system ρ 0

g αβ (r) = ρ αβ (r) ρ 0 (3)
where α and β denote the chemical species considered (Ge, Se or S). In addition, the position of the first peak of each g αβ (r) can be taken as a measure of the bond length r αβ . By integrating up to the first minimum of the corresponding pair correlation function, one obtains the partial coordination number N αβ .

The total pair correlation function g T (r) is obtained as follows

g T (r) -1 = 2 α=1 2 β=1 c α c β b α b β b 2 [g αβ (r) -1] (4)
The quantities c α and b α are, respectively, the atomic fractions and the coherent neutron scattering lengths of Ge (8.185 fm), Se (7.97 fm) and S (2.847 fm). The mean coherent neutron scattering length b

is defined as b = c Ge b Ge + c X b X (5)
with X = Se or S. The reciprocal space counterpart of the partial pair correlation functions are the Faber-Ziman (FZ) partial structure factors obtained by applying a Fourier transform to g αβ

S F Z αβ (k) -1 = 4πρ 0 k ∞ 0 r[g αβ (r) -1]sin(kr)dr (6)
The total neutron structure factor S T (k) is a weighted sum of these partial quantities

S T (k) -1 = 2 α=1 2 β=1 c α c β b α b β b 2 [S F Z αβ (k) -1] (7)

Results

A -Neutron total structure factor and pair distribution function

.

In figure 1, we report the total structure factors for both g-GeSe 4 and g-GeS 4 . We include the results obtained with no consideration of vdW interactions [START_REF] Bouzid | Origin of structural analogies and differences between the atomic structures of GeSe 4 and GeS 4 glasses: A first principles study[END_REF] as well as the experimental data obtained by Petri [START_REF] Petri | The topology of Ge x -Se 1-x (0 < x < 0.4) glasses[END_REF], Salmon [START_REF] Salmon | Structure of liquids and glasses in the Ge-Se binary system[END_REF] and bychkov [START_REF] Bychkov | Short, intermediate and mesoscopic range order in sulfur-rich binary glasses[END_REF].

We observe that all the methods used succeed in reproducing a signature (more or less intense depending on the system) of the first sharp diffraction peak (FSDP) at about k 1 Å-1 . This means that the vdW forces do not play a major role in the establishment of an intermediate range. The different level of intensity recorded for the FSDP in the total neutron structure factor of g-GeS 4 and g-GeSe 4 can be correlated to the sizes of the rings existing in these glasses, as shown by Bouzid et al. [START_REF] Bouzid | Origin of structural analogies and differences between the atomic structures of GeSe 4 and GeS 4 glasses: A first principles study[END_REF]. Indeed, through the n-atoms rings by Petri [START_REF] Petri | The topology of Ge x -Se 1-x (0 < x < 0.4) glasses[END_REF], Bychkov [START_REF] Bychkov | Short, intermediate and mesoscopic range order in sulfur-rich binary glasses[END_REF] and Salmon [START_REF] Salmon | Structure of liquids and glasses in the Ge-Se binary system[END_REF]. Two different forms of the van der Waals corrections are given: vdW G using the Grimme approach [START_REF] Grimme | Semiempirical GGA-type density functional constructed with a long-range dispersion correction[END_REF] (blues solid lines) and vdW W using the Wannier approach introduced by Silvestrelli et al. [START_REF] Silvestrelli | Van der Waals interactions in DFT made easy by Wannier functions[END_REF] (red solid lines)

analysis, it was demonstrated that the occurrence of six-membered rings is much more frequent in g-GeS 4

than in g-GeSe 4 . In addition, the presence of higher ring sizes in g-GeSe 4 (n = 10, 13, 15) can be associated to ring diameters beyond the first two nearest neighbors (> 5 Å). Thus, such Ge-S motifs are responsible for the differences between the FSDP of g-GeS 4 and g-GeSe 4 (figure 1). Globally, the total neutron structure factors are equally well reproduced by all schemes, with the exception of the second main peak in the GeS 4 system.

However, for this feature, the underestimate persists regardless of the presence or absence of dispersion forces.

Similar considerations can be expressed when focusing on the total pair correlation function (see figure 2). The experiments are due to Petri [START_REF] Petri | The topology of Ge x -Se 1-x (0 < x < 0.4) glasses[END_REF], Bychkov [START_REF] Bychkov | Short, intermediate and mesoscopic range order in sulfur-rich binary glasses[END_REF] and Salmon [START_REF] Salmon | Structure of liquids and glasses in the Ge-Se binary system[END_REF]. We refer to the work of Bouzid et al. [START_REF] Bouzid | Origin of structural analogies and differences between the atomic structures of GeSe 4 and GeS 4 glasses: A first principles study[END_REF] for the FPMD calculations performed with no inclusion of vdW interactions. The experimental data sets referred to were obtained by applying a Fourier transformation to the total neutron structure factors using, in both cases, the upper limits of integration of the experimental finite measurement window function of the diffractometer: k max (g-GeSe 4 ) = 19.95 Å-1 , k max (g-GeS 4 ) = 49.95 Å-1 . As shown in Ref. [START_REF] Bouzid | Origin of structural analogies and differences between the atomic structures of GeSe 4 and GeS 4 glasses: A first principles study[END_REF], this procedure of calculation can lead to spurious oscillations obtained in both cases in the region r < 2 Å (figure 2). Our calculations do not show such artifacts since our calculations were performed directly in real space by applying the definition of the pair correlation function. As a first observation, we note that the first sharp maximum corresponding to the nearest neighbor distance is very well reproduced both by vdW G (blue lines) and vdW W (red curves) calculations for g-GeS 4 (2.19 Å) and g-GeSe 4 (2.37 Å).

As regard to the overestimated intensity of this peak in the g-GeSe 4 case, it should be reminded that such discrepancy stems from the different methodology employed to produce these data, i.e. integration from the Fourier space in the experiments as opposed to direct calculations for the vdW W and vdW G cases.

There is a clear sensitivity to such procedures for the case of the smaller measurement window (g-GeSe 4 , k max (g-GeSe 4 ) = 19.95 Å-1 ), while no effects are observable for a much larger interval of measurement in reciprocal case, (g-GeS 4 ). Overall, at this level of comparison, it is hard to detect any impact of the dispersion forces on the real space properties as expressed by the total pair correlation functions. Even the small differences found in the shape of the second maxima could be ascribed to statistical fluctuations and cannot be taken as pieces of evidence of any real dependence on the scheme used. with no inclusion of vdW interactions (green curves) as reported by Bouzid et al. [START_REF] Bouzid | Origin of structural analogies and differences between the atomic structures of GeSe 4 and GeS 4 glasses: A first principles study[END_REF] and compared to our results including the two different forms of the van der Waals corrections discussed in the text: vdW G (blues solid lines) and the vdW W (red solid lines). The experimental data (yellow symbols) correspond to those reported by Petri [START_REF] Petri | The topology of Ge x -Se 1-x (0 < x < 0.4) glasses[END_REF], Bychkov [START_REF] Bychkov | Short, intermediate and mesoscopic range order in sulfur-rich binary glasses[END_REF] and Salmon [START_REF] Salmon | Structure of liquids and glasses in the Ge-Se binary system[END_REF].

B Partial structure factors

. In order to go further in the analysis of the atomic structure, we analyze the partial Faber-Ziman (FZ) structure factors for each atomic pair. The partial structure factors for both systems are reported in figure 3. Focusing on the FSDP visible for g-GeSe 4 in S F Z GeGe , we observe that the same effect is reproduced by both vdW G and vdW W calculations and by the NovdW approach used in ref. [START_REF] Bouzid | Origin of structural analogies and differences between the atomic structures of GeSe 4 and GeS 4 glasses: A first principles study[END_REF]. The height of the FSDP 135 intensities is reduced in the g-GeS 4 case with a split pattern appearing around k 1 Å-1 , mostly to be ascribed to statistical noise. We observe that the FSDP is obtained in the Ge-S and Ge-Se partial structure factors but not in the Se-Se and S-S case. Therefore, one can draw similar conclusions as the ones obtained in the NovdW case, namely that the peak obtained in the total structure factor at k 1 Å-1 (figure 1) is due to the Ge-Ge and Ge-X (X = Se, S) correlations that are at origin of intermediate range order. . We describe the real space properties of g-GeSe 4 and g-GeS 4 by calculating the partial pair correlation functions of the different atomic pairs. These results are reported in figure 4.

For the Ge-X pair correlation functions, the results obtained by the three methods are practically super- with no inclusion of vdW interactions (green curves) as reported by Bouzid et al. [START_REF] Bouzid | Origin of structural analogies and differences between the atomic structures of GeSe 4 and GeS 4 glasses: A first principles study[END_REF] are compared to those including van der Waals, vdW G (blues solid lines) and the vdW W (red solid lines) imposed for both systems reproducing the same differences between GeS 4 and GeSe 4 materials found in the report by Bouzid et al. [START_REF] Bouzid | Origin of structural analogies and differences between the atomic structures of GeSe 4 and GeS 4 glasses: A first principles study[END_REF].

In the Ge-Ge case, the first small peak observed at r 2.45 Å is obtained with the three calculation methods at the same position for both systems. In terms of its intensity, the three approaches reproduce the same intensity for g-GeSe 4 (g GeSe4 GeGe 0.5) and for g-GeS 4 (g GeS4 GeGe 0.2). This peak is the signature of the presence of homopolar Ge-Ge bonds. Two other peaks are noticeable. The first corresponds to the edge-sharing (ES) tetrahedra and the second to corner-sharing (CS) tetrahedra. These peaks are obtained (figure 4) at values of r 3.0 Å and r 3.6 Å for GeSe 4 , slightly differing from the GeS 4 case in which they are obtained at r 2.9 Å and r 3.6 Å. A close look at the CS-tetrahedra population of g GeGe (peaks at r 3.6 Å) reveals that the vdW W approach tend to match the vdW G results in g-GeSe 4 with a higher intensity of this peak in comparison to the NovdW calculation (green line). However, the opposite situation is obtained for g-GeS 4 system, for which the vdW G scheme overestimates the intensity of Ge-Ge correlations at r 3.6 Å . On the contrary vdW W gives an intensity comparable to the case with no vdW inclusion.

The situation for g XX is again indicative of small differences between the vdW G and vdW W results. The In the case of GeS 4 , there are even less differences among the three set of results, the percentage number of Ge atoms fourfold coordinated to Se atoms being already very close to the unity in the NovdW case. It looks like at this level of description, involving the first shell of coordination of these disordered systems, the dispersion forces can be safely neglected for g-GeS 4 and they bring limited and yet appreciable changes for g-GeSe 4 , by reducing the number of Ge atoms that deviate from the tetrahedral environment.

Conclusion

We revisited the structural properties of glassy GeSe 4 and GeS 4 systems by relying on first-principles 200 molecular dynamics. We undertake such a study since other disordered chalcogenide systems were found sensitive to the inclusion of dispersion forces and, to a lesser extent, also sensitive to the kind of theoretical recipe employed to model such contributions [START_REF] Bouzid | Role of the van der Waals interactions and impact of the exchange-correlation functional in determining the structure of glassy GeTe 4[END_REF]. In this work we presented a detailed comparison between two specific approaches designed for the proper inclusion of vdW forces contributions, namely, the vdW G due to Grimme [START_REF] Grimme | Semiempirical GGA-type density functional constructed with a long-range dispersion correction[END_REF] and relying on a semi-empirical description and a fully first-principles based method (vdW W ) taking advantage of the the Wannier functions formalism [START_REF] Silvestrelli | Maximally-localized Wannier functions for disordered systems: Application to amorphous silicon[END_REF]. Based on the results obtained for the total and partial pair correlation functions, total and partial structure factors, supplemented by an analysis of the neighbor environments (coordination units with the neighbors of each species) we could not detect any sizable effect of the dispersion forces on the main features of the networks. However, there is one effect that is worth pointing out, this being the tendency of both vdW schemes to enhance the fourfold coordination environment in glassy GeSe 4 , by producing an atomic structure that turns out very similar to that of glassy GeS 4 . In conclusion, the body of our results brings new information on the structure of these glasses when compared to what is already available in the literature. The new outcome is twofold: on the one hand, lack of substantial sensitivity to dispersion forces, once again to be contrasted to the case of some Te-based chalcogenides [START_REF] Micoulaut | Towards accurate models for amorphous GeTe: Crucial effect of dispersive van der Waals corrections on the structural properties involved in the phase-change mechanism[END_REF]. On the other hand, the inclusion of dispersion forces attenuates the differences between the network topologies of glassy GeSe 4 and GeS 4 , both of them made by a highly predominant presence of Ge atoms fourfold coordinated with very few Ge-Ge homopolar bonds.

Figure 1 :

 1 Figure 1: Total neutron structure factors for both GeS 4 (top panel shifted upwards by 1.5) and GeSe 4 (bottom panel) evaluated as a Fourier transform of the total pair correlation function. The "NovdW" results correspond to those with no inclusion of vdW interactions (green curves) as reported by Bouzid et al. [3]. The experimental data (circle symbols) are those reported

Figure 2 :

 2 Figure 2: Total pair correlation function for GeS 4 (top panel shifted upwards by 7.5 Å) and GeSe 4 (bottom panel) calculated

Figure 3 :

 3 Figure 3: The Faber-Ziman partial structure factors for both glassy binary chalcogenides: GeSe 4 (left panel) and GeS 4 (right panel), calculated with no inclusion of vdW interactions (green curves) as reported by Bouzid et al. [3]. The calculations including the two different forms of the van der Waals corrections are vdW G (blues solid lines) and the vdW W (red solid lines)

Figure 4 :

 4 Figure 4: The partial pair correlation functions for the atomic pairs of g-GeSe 4 (left panel) and g-GeS 4 (right panel). Results

  [START_REF] Ikeda | Role of van der Waals corrections in first principles simulations of alkali metal ions in aqueous solutions[END_REF] (left part) and GeS 4 (right part) for the specie α (Ge, S or Se). These quantities have been calculated including neighbors separated by a cutoff corresponding to the first minimum in the partial pair correlation functions. The corresponding average atomic pairs and total coordination numbers are given in the bottom part of the table.

Table :

 : Percentage nα(l) of the different coordination units (l) in glassy GeSe

			vdW G	vdW W	Bouzid-JCP2015		vdW G	vdW W	Bouzid-JCP2015
			0.00	0.56	4.8		0.33	0.00	-
			0.34	0.60	3.6		0.63	0.00	0.4
			95.47	94.67	85.0		0.87	1.17	0.7
			4.16	4.17	6.2		96.57	97.80	96.7
			< 0.1	0.00	0.1		1.60	1.03	2.0
			< 0.1	0.00	-
	m = 1	Se	0.28	< 0.1	1.7		0.48	0.15	0.5
		Ge	0.53	0.27	1.5		0.83	0.98	1.3
			27.85	28.71	30.7		32.24	31.77	32.0
		Ge 2	26.57	27.08	26.5		31.76	32.18	31.8
		GeSe	44.07	43.49	38.2		34.60	34.45	33.9
		Se 3	0.25	< 0.1	-		< 0.1	0.00	0.2
		Ge 3	0.25	0.00	0.3	S 3	0.00	0.22	-
		Ge 2 Se	0.19	0.23	0.3		< 0.1	0.24	0.2
		GeSe 2	< 0.1	0.12	0.5
	N GeGe		0.04	0.04	0.36	N GeGe	0.02	0.01	0.03
	N GeSe		3.96	3.94	3.85	N GeS	3.95	3.98	3.98
	N SeGe		0.99	0.99	0.96	N SGe	0.99	1.00	0.99
	N SeSe		1.01	1.02	1.04	N SS	1.00	1.00	0.99
	N Ge		4.00	3.98	4.21	N Ge	3.97	3.99	3.99
	N Se		2.00	2.00	2.00	N S	1.99	1.99	1.98

first peak indicative of nearest neighbor Se-Se distances (r 2.4 Å) and the one corresponding to S-S bonds (r 2.1 Å) are very close in the three models. However, for the second peak located at r 3.8 Å (GeSe 4 ) and r 3.6 Å (GeS 4 ), the vdW W calculation tend to reproduce the NovdW results rather than the vdW G ones. Such a trend is similar to what already observed in the case of liquid GeSe 2 [START_REF] Lampin | Impact of dispersion forces on the atomic structure of a prototypical network-forming disordered system: The case of liquid GeSe 2[END_REF]. It appears that Ge-Ge correlations are the most sensitive to the presence and/or the quality of the dispersion forces considered.

While the three models are broadly consistent and the changes observed of moderate extent, the impact on Ge-Ge correlations of the dispersion forces will be an issue worth pursuing with additional calculations.

D -Local order: coordination numbers

. Despite the trace of some moderate level of sensitivity to the presence of dispersion forces, it appears that the properties examined so far do not provide any evidence on the occurrence of any striking effect in g-GeSe 4 and g-GeS 4 , either when adopting the dispersion forces or when selecting the Wannier scheme instead of the DFT-D2 one. We complete the structural analysis presented above by the investigation of the local coordination obtained through the different calculation schemes considered. These results are reported in the Table. In the bottom part of this table, we provide the detailed coordination numbers N αβ for both g-GeSe 4

(left part) and g-GeS 4 systems as well as the resulting total ones N α (α = Ge, Se or S). These coordination numbers provide information on the number of neighbors for each atom and to the kind of structural unit formed with the given neighbors, by identifying the chemical nature of each interatomic linkage.

Ge atoms are found to be four fold coordinated (N Ge 4) mainly due to the tetrahedral arrangement of Se and S around Ge species in GeSe 4 and GeS 4 . This is confirmed by all N GeX values found to be very close to 4. X (X = Se, S) atoms are two-fold coordinated for both materials with heteropolar (X-Ge) and homopolar X-X bonds having coordination numbers are very close to 1 (N XGe N XX 1).

The three calculations methods give almost identical results indicating that the contribution of vdW interactions inclusion does not affect the characteristic tetrahedral network of these materials. Nevertheless, the NovdW scheme leads to a higher amount of homopolar Ge-Ge bonds in the g-GeSe 4 system. Indeed,

N GeSe4

GeGe values (0.36 for NovdW) differ from the values very close to 0 found in the present work (N GeGe = 0.04).

In this Table (top part), we also report the coordination numbers in terms of the contributions (percentage n α (l)) of each specific environment. In the case of g-GeSe 4 , the deviation from the tetrahedral arrangement is quite limited when dispersion forces are included, values of the percentage of Ge atoms fourfold coordinated to Se atoms approaching closely the unity. No other effects due to the different account of dispersion forces are found, the different amounts of the corresponding coordination units being very close.