PhD Aditi Verma

PhD Ajit Ray

MSc Deepti Bapat

PhD Latha Diwakar

Peera Reddy

Bernard L Kommaddi

Etienne C Schneider

Vijayalakshmi Hirsch

Ravindranath

; Reddy

PhD Peera Kommaddi

PhD Bernard L Schneider

PhD Etienne C Hirsch

PhD Vijayalakshmi Ravindranath

Glutaredoxin 1 downregulation in the substantia nigra leads to dopaminergic degeneration in mice

Keywords: Parkinson's disease, dopaminergic neurons, glutaredoxin 1, shRNA, tyrosine hydroxylase

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INTRODUCTION

Cardinal histopathological feature of Parkinson's disease (PD) is the severe loss of dopaminergic (DA) neurons in the substantia nigra pars compacta (SNpc) and the loss of dopaminergic axonal projections to the striatum. This results in reduced DA signaling in the basal ganglia circuit leading to movement deficits, in particular hypokinesia, bradykinesia and rigidity. Selective vulnerability of SNpc DA neurons has been attributed to several putative mechanisms such as mitochondrial dysfunction [START_REF] Schapira | Mitochondrial Complex I Deficiency in Parkinson's Disease[END_REF][START_REF] Lin | Mitochondrial dysfunction and oxidative stress in neurodegenerative diseases[END_REF][START_REF] Büeler | Impaired mitochondrial dynamics and function in the pathogenesis of Parkinson's disease[END_REF][START_REF] Bose | Mitochondrial dysfunction in Parkinson's disease[END_REF], dopamine metabolism [START_REF] Zucca | Interactions of iron, dopamine and neuromelanin pathways in brain aging and Parkinson's disease[END_REF], iron accumulation [START_REF] Sofic | Increased iron (III) and total iron content in post mortem substantia nigra of parkinsonian brain[END_REF][START_REF] Mochizuki | Iron accumulation in Parkinson's disease[END_REF], dysregulation of the ubiquitin proteasome system [START_REF] Olanow | Ubiquitin-proteasome system and Parkinson's disease[END_REF][START_REF] Zheng | Dysregulation of Ubiquitin-Proteasome System in Neurodegenerative Diseases[END_REF] and increased oxidative stress [START_REF] Jenner | Oxidative stress as a cause of nigral cell death in Parkinson's disease and incidental lewy body disease[END_REF][START_REF] Hirsch | Does Oxidative Stress Participate in Nerve Cell Death in Parkinson's Disease?[END_REF][START_REF] Jenner | Oxidative stress in Parkinson's disease[END_REF]. While different mechanisms have been implicated in the pathogenesis of PD, most of them converge on increased oxidative damage to proteins and other cellular constituents.

Perturbation of protein thiol redox homeostasis as a result of increased oxidative stress mediates cell death signaling that could drive neurodegeneration in PD [START_REF] Garcia-Garcia | Thiolredox signaling, dopaminergic cell death, and Parkinson's disease[END_REF][START_REF] Johnson | The roles of redox enzymes in Parkinson's disease: Focus on glutaredoxin[END_REF]. In its reduced state, thioredoxin (Trx1) binds to apoptosis signalregulating kinase 1 (ASK1), which inhibits ASK1 activity. In the 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP) mouse model of PD, selective thiol oxidation of thioredoxin (Trx1) releases its inhibitory association with ASK1 leading to its activation [START_REF] Ray | MPTP activates ASK1-p38 MAPK signaling pathway through TNF-dependent Trx1 oxidation in parkinsonism mouse model[END_REF]. Activated ASK1 further activates p38 and c-Jun N-terminal kinase (JNK) through phosphorylation of mitogen activated protein kinase kinase 3/6 (MKK3/6) and mitogen activated protein kinase kinase 4/7 (MKK4/7), respectively that results in cell death. Thiol oxidation of critical cysteines in protein kinase B (Akt) leading to its increased dephosphorylation through enhanced association with protein phosphatase 2A (PP2A) has also been reported to cause downregulation of Akt mediated cell survival in MPTP mouse model [START_REF] Durgadoss | Redox modification of Akt mediated by the dopaminergic neurotoxin MPTP, in mouse midbrain, leads to down-regulation of pAkt[END_REF].

Glutaredoxin 1 (Grx1), a protein thiol/disulfide oxidoreductase, is important for regulating cellular protein thiol redox homeostasis [START_REF] Allen | Protein-thiol oxidation and cell death: regulatory role of glutaredoxins[END_REF]. Glutathione (GSH) is a cellular antioxidant defense mechanism that protects proteins from irreversible oxidative damage through reversible glutathionylation. Grx1 acts as a deglutathionylating enzyme that revives the active protein thiols and restores protein thiol redox homeostasis [START_REF] Garcia-Garcia | Thiolredox signaling, dopaminergic cell death, and Parkinson's disease[END_REF] by catalyzing the reversible deglutathionylation of proteinglutathione mixed disulfide (PrSSG) in an NADPH dependent manner thereby restoring the steady-state function of the protein as depicted in supplementary figure S1 [START_REF] Johnson | The roles of redox enzymes in Parkinson's disease: Focus on glutaredoxin[END_REF][START_REF] Allen | Protein-thiol oxidation and cell death: regulatory role of glutaredoxins[END_REF][START_REF] Gravina | Thioltransferase is a specific glutathionyl mixeddisulfide oxidoreductase[END_REF]. Grx1 downregulation could thus, potentially result in diverse alterations within the cell caused by the resulting disequilibrium in protein thiol homeostasis. In the Caenorhabditis elegans model of familial PD wherein human pathogenic LRRK2 mutants were overexpressed, downregulation of Grx1 homologue led to exacerbation of neurodegeneration [START_REF] Johnson | Glutaredoxin deficiency exacerbates neurodegeneration in C. elegans models of Parkinson's disease[END_REF]. We, therefore, set out to determine whether Grx1 downregulation would lead to development of dopaminergic degeneration in mouse. To this end, a viral vector coding for a short hairpin RNA (shRNA) against Grx1 was injected unilaterally into mouse SNpc.

MATERIALS AND METHODS

Animals:

All experiments were performed with 3-5 months old C57BL/6 male mice (25-30 grams) or post natal day 0-1 pups (p0-1) from C57BL/6 mice obtained from Indian Institute of Science. Detailed description of animal experiments is provided in the supplementary material.

Adeno-Associated Virus (AAV) 6-sh/scRNA-Grx1 vector production: For knocking down Grx1, the downregulation cassettes containing the mU6 promoter and the Grx1 short hairpin RNA (shRNA) or scrambled RNA (scRNA) sequences were subcloned from earlier constructs [START_REF] Saeed | DJ-1 loss by glutaredoxin but not glutathione depletion triggers Daxx translocation and cell death[END_REF] The downregulation and scrambled pAAV constructs were then packaged as rAAV serotype 6 (AAV6) particles by co-transfecting them individually with pDF6 into AAV-293 cells (Stratagene, La Jolla, CA) [START_REF] Grimm | Helper virus-free, optically controllable, and two-plasmid-based production of adeno-associated virus vectors of serotypes 1 to 6[END_REF] using calcium phosphate [START_REF] Towne | Lentiviral and Adeno-Associated Vector-Based Therapy for Motor Neuron Disease Through RNAi[END_REF]. At 48 hours after transfection, vector particles were then extracted by cell lysis using repeated freeze-thawing rounds. The lysates were purified and concentrated using fast protein liquid chromatography through a heparin affinity column as described earlier [START_REF] Towne | Systemic AAV6 Delivery Mediating RNA Interference Against SOD1: Neuromuscular Transduction Does Not Alter Disease Progression in fALS Mice[END_REF]. Detailed description of estimation of viral titer has been provided in the supplementary material.

Animals were unilaterally injected with AAV-shRNA-Grx1 or AAV-scRNA-Grx1 at a dilution of ~5×10 10 TU/mL as control. The original titers of the AAV-shRNA-Grx1 and AAV-scRNA-Grx1 vectors were ~2.54×10 11 TU/mL and ~1.33×10 11 TU/mL, respectively. These vectors, when used undiluted resulted in high mortality and focalized cell death, as estimated in pilot experiments. Therefore, the AAV-shRNA-Grx1 vector was diluted five times to give an effective titer of ~5×10 10 TU/mL. The effect of the two dilutions was tested for 14 days and 28 days post-surgery. The scrambled control (scrRNA) was used at a titer equivalent to that of the five-times diluted shRNA-Grx1 vector.

Human PD autopsy samples: All experiments on human autopsy brain tissue were carried out following approval from Institutional Human Ethics Committee (IHEC) and all guidelines were followed (IHEC approval# 4/2010). One half of the brain was fixed and used for neuropathological examination. The other hemi-brain was dissected and flash frozen using dry ice. Sections from the mesencephalon were cut on a cryostat on glass slides kept frozen on dry ice. The SNpc and the VTA were scraped out from the frozen sections and stored at -80°C until use. The whole dissection procedure was performed using RNAse free material. Tissue was prepared from human autopsy midbrain from PD patients and age-matched controls that were obtained from the ICM Brain Bank and the Neuroceb Pitié-Salpêtrière hospital, Paris. A description of the cases studied is provided in the supplementary table S1.

Quantitative real time PCR: A thorough description of RNA isolation and cDNA synthesis is provided in the supplementary text. The nucleotide sequences for primers used for human and mouse gene expression analysis and the PCR conditions are provided in supplementary tables S2, S3 and S4, respectively. Statistical Analyses: All statistical analyses were performed using Prism version 7.0a for Mac OS X (GraphPad Software, La Jolla, CA). For comparison of multiple experimental groups, two-way ANOVA with Tukey's multiple comparison tests was performed. Comparison of two groups was performed with unpaired Student's t-test.

Median absolute deviation (MAD) [START_REF] Leys | Detecting outliers: Do not use standard deviation around the mean, use absolute deviation around the median[END_REF] was the method used for removal of outliers in the qRT-PCR experiments.

RESULTS

Experimental design and Grx1 downregulation using AAV-shRNA-Grx1

The scr/shRNA to Grx1 was cloned under mU6 promoter alongside -globin-GFP under CMV promoter in the AAV6 backbone (Fig. 1A). Mouse primary cortical neurons were transduced with shRNA to Grx1 and quantification of mRNA levels using qRT-PCR revealed that there was 79% downregulation (Fig. 1B). Grx1 was downregulated by unilateral stereotaxic transduction of AAV-shRNA-Grx1 into mouse SNpc (Fig. 1C). Contralateral bias of elevated body swing (E) as well as latency to fall off rotarod (R) were evaluated prior to surgery and were subsequently monitored over 28 days after virus injection as described in figure 1D.

Locomotor deficits observed post unilateral Grx1 downregulation

In order to quantify asymmetric, motor deficits following unilateral viral injection of SNpc, elevated body swing test (EBST) was performed [START_REF] Borlongan | Elevated body swing test: a new behavioral parameter for rats with 6-hydroxydopamine-induced hemiparkinsonism[END_REF]. Increased bias to turn to the contralateral side of viral injection as measured through EBST (contralateral bias) emerged by the 14 th day and persisted until at least the 26 th day post-surgery, implying decreased striatal dopaminergic tone and/or degeneration of SNpc dopaminergic neurons following Grx1 downregulation. Contralateral bias was not observed in animals injected with AAV-scrRNA-Grx1 (Fig. 1E). Further, motor deficits were evaluated by measuring the performance of the mice on rotarod under increased speed of rotation. Latency for falling off rotarod was measured before surgery to rule out inherent animal biases. The AAV-shRNA-Grx1 injected animals showed a significant drop in latency to stay on the rotarod towards 25 th day post injection, which was not observed in animals injected with AAV-scrRNA-Grx1 (Fig. 1F).

Loss of SNpc TH positive neurons post Grx1 downregulation

Stereological analysis was performed at 14 days and 28 days post transduction to assess the loss of TH positive neurons in SNpc and VTA. While significant decrease in total number of TH positive neurons in the ipsilateral SNpc was observed at both 14 days (~74%) and 28 days (~72%) post injection, TH positive neurons on the contralateral side and in both hemispheres in scrambled controls were preserved (Fig. 2A). TH positive neurons were also conserved in the SNpc of mice injected with PBS showing that the procedure of stereotaxic injection per se did not lead to neurodegeneration (Fig. 2A).

To verify that the loss of TH in SNpc following Grx1 downregulation was indeed due to cell loss and not due to reduced expression of TH protein, stereological analysis of Nissl positive neurons was performed. Indeed, loss of total number of Nissl positive neurons was observed in the ipsilateral hemisphere injected with AAV-shRNA-Grx1 at both 14 days (~51%) and 28 days (~51%) (Fig. 2B). Mice transduced with AAV-shRNA-Grx1 did not show robust loss of TH positive neurons in ipsilateral VTA (Fig. 2C). The number of TH positive neurons also did not change significantly in both ipsilateral and contralateral hemispheres of the AAV-scrRNA-Grx1 and PBS injected mice in the VTA (Fig. 2C). Representative micrographs showing dopaminergic degeneration following Grx1 downregulation are shown in figure 2D.

Protein thiol levels following Grx1 downregulation

In order to determine if the protein thiol levels were altered, we estimated the levels of GSH and PrSH after dissecting out SNpc from the ipsilateral and contralateral sides 14 days after unilateral injection of AAV with shRNA to Grx1 or a scrambled sequence. We found no difference in GSH levels between the ipsilateral SNpc and contralateral SNpc, where no virus was injected indicating that the total glutathione levels were unaffected following viral injection of shRNA to Grx1 (Fig. 3A). In further validation of this observation, no difference was found in PrSH levels in SNpc between the animals that received shRNA or the scrambled sequence through AAV injection after 14 days (Fig. 3B).

We also stained brain sections from mice treated with AAV-scr/shRNA-Grx1, 14 days post-surgery, for glial fibrillary acidic protein (GFAP) and Iba1. This was done in order to determine if there was reactive astrogliosis and presence of activated microglia, which could contribute to raise in GSH and protein thiol levels in SNpc.

Previous studies have reported increased levels of GSH in astrocytes and microglia as compared to neurons [START_REF] Hirrlinger | Microglial Cells in Culture Express a Prominent Glutathione System for the Defense against Reactive Oxygen Species[END_REF][START_REF] Dringen | Metabolism and functions of glutathione in brain[END_REF]. It has also been shown that the levels of GSH further increase in microglia upon activation [START_REF] Persson | Lipopolysaccharide increases microglial GLT-1 expression and glutamate uptake capacity in vitro by a mechanism dependent on TNF-α[END_REF][START_REF] Dopp | Expression of the p75 TNF receptor is linked to TNF-induced NFkappaB translocation and oxyradical neutralization in glial cells[END_REF]. The presence of reactive astrogliosis is evident from the GFAP staining along with the presence of hypertrophic morphology and shorter and thicker processes of the astrocytes on the ipsilateral SNpc (Fig. 3C).

The presence of activated microglia with large cell body and thick processes on the ipsilateral SNpc in contrast to the resting microglia with long thin processes on the contralateral SNpc is also evident after Iba1 immunohistochemistry [START_REF] Breidert | Protective action of the peroxisome proliferator-activated receptor-γ agonist pioglitazone in a mouse model of Parkinson's disease[END_REF] (Fig. 3D).

Reactive astrogliosis and activated microglia were, therefore, observed in the ipsilateral but not in the contralateral SNpc in mice that were injected with shRNA to Grx1 (Fig. 3C andD, respectively). These observations indicate that the reactive astrogliosis and activated microglia in SNpc could have contributed to the GSH and PrSH levels seen in SNpc (Fig. 3A andB, respectively). Therefore, any loss of GSH or PrSH caused by Grx1 downregulation would have been compensated by the reactive astrogliosis and activated microglia.

Loss of TH positive fibers in striatum post Grx1 downregulation

Analysis of fluorescence intensity following immunohistochemistry for TH on serial sections containing striatum was performed to quantify the loss of TH positive axon terminals in the striatum. A loss of TH positive fibers was observed in ipsilateral striatum in the AAV-shRNA-Grx1 injected mice at both 14 days (~80%) and 28 (~64%) days, while TH fibers in mice injected with AAV-scrRNA-Grx1 were preserved (Fig. 4A andB).

Reduced expression of Grx1 mRNA in human PD autopsy tissue

Evaluation of Grx1 mRNA levels in SNpc from human PD autopsy tissue using qRT-PCR showed reduced Grx1 mRNA expression in PD tissue as compared to agematched controls (~56%) (Fig. 5A). Detailed information on the cases studied is provided in supplementary table 1. Further, as a confirmation that the decrease in the mRNA levels of Grx1 in PD was not a consequence of cell loss, we showed that the mRNA levels of -actin and GAPDH were not altered in SNpc from PD tissue as compared to controls (Fig. 5B andC, respectively). Further, to ensure that the loss of Grx1 mRNA expression in human autopsy SNpc was not a result of prolonged treatment with dopamine replacement drugs such as carbidopa and levodopa, we evaluated the mRNA expression of Grx1 after per oral treatment of C57BL/6 mice with a combination of carbidopa-levodopa (30mg-10mg per kg body weight in 10% w/v sucrose) every day for 14 days. Surprisingly, carbidopa and levodopa treatment upregulated Grx1 (~40%; Fig. 5D).

DISCUSSION

Grx1 is a protein thiol/disulfide oxidoreductase that is critical for maintaining the thiol status in cells. As summarized in supplementary figure S1, in this study we observed that downregulation of Grx1 in SNpc through unilateral stereotaxic injection of AAV-shRNA-Grx1 led to the development of motor deficits. This was accompanied by loss of TH positive neurons in ipsilateral SNpc and their fiber terminals in ipsilateral striatum, while VTA was unaffected. Further, decrease in the number of Nissl positive neurons in SNpc confirmed that there was indeed neuronal degeneration. Finally, we observed significant downregulation of Grx1 mRNA in SNpc from human PD autopsy tissue as compared to controls indicating that Grx1 is potentially important for DA neuron maintenance and survival in SNpc.

Grx1 is expressed in neuronal and glial cells as shown by us and others

previously [START_REF] Balijepalli | Rat brain thioltransferase: regional distribution, immunological characterization, and localization by fluorescent in situ hybridization[END_REF]. The functional activity of Grx1 is highly dependent on availability of GSH and NADPH [START_REF] Deponte | Glutathione catalysis and the reaction mechanisms of glutathionedependent enzymes[END_REF]. GSH is present in higher levels in glial cells as compared to neurons [START_REF] Hirrlinger | Microglial Cells in Culture Express a Prominent Glutathione System for the Defense against Reactive Oxygen Species[END_REF][START_REF] Dringen | Metabolism and functions of glutathione in brain[END_REF][START_REF] Rice | Differential compartmentalization of brain ascorbate and glutathione between neurons and glia[END_REF] and there is a constant cross talk between neurons and glia [START_REF] Dringen | Synthesis of the antioxidant glutathione in neurons: Supply by astrocytes of CysGly as precursor for neuronal glutathione[END_REF].

In co-culture of neurons with astrocytes, the latter helped alleviate thiol mediated stress response in a manner similar to that seen with GSH [START_REF] Gutbier | Prevention of neuronal apoptosis by astrocytes through thiol-mediated stress response modulation and accelerated recovery from proteotoxic stress[END_REF]. Furthermore, astrocytes release GSH constantly into the medium, which impacts the neuron through xCT (cysteine glutamate transporter) [START_REF] Yang | Mn inhibits GSH synthesis via downregulation of neuronal EAAC1 and astrocytic xCT to cause oxidative damage in the striatum of mice[END_REF]. Thus, a global knock-down of Grx1 would better represent the situation that might be seen in PD patients rather than knocking it down selectively only in the neurons. Thus, the viral transduction of shRNA-Grx1 would result in Grx1 downregulation in all cell types in SNpc, presumably not at similar levels [START_REF] Aschauer | Analysis of transduction efficiency, tropism and axonal transport of AAV serotypes 1, 2, 5, 6, 8 and 9 in the mouse brain[END_REF]. The neurodegeneration of TH positive neurons in SNpc could, therefore, have been influenced by the altered redox homeostasis caused by global Grx1 downregulation across cell types including glia. Downregulation of Grx1 is expected to lead to an increase in proteinglutathione mixed disulfide (PrSSG) resulting in the loss of PrSH and GSH. However, we did not find significant difference in the levels of total GSH or protein thiols in the ipsilateral SNpc wherein Grx1 was downregulated as compared to the contralateral SNpc or scrambled control. This is surprising since downregulation of Grx1 has been shown to alter the status of cysteine thiols in a variety of proteins including those involved in glycolysis [START_REF] López-Grueso | Thioredoxin and glutaredoxin regulate metabolism through different multiplex thiol switches[END_REF]. However, we did see reactive astrogliosis and activated microglia (Fig. 3C andD, respectively) in the ipsilateral SNpc 14 days after the viral injection. Since the tissue is homogenized for the measurement of GSH and PrSH levels, the levels assayed would represent the contribution from all cell types including the above. The lack of reliable histological methods for measuring GSH or PrSH in specific cell types precludes the estimation of these thiols in individual cells. Therefore, while it is well acknowledged that Grx1 downregulation leads to alteration in thiol redox homeostasis, we are unable to demonstrate it specifically in the TH positive neurons. Nevertheless, our observations clearly show the loss of TH neurons and increased reactive astrogliosis and activated microglia in the ipsilateral SNpc when Grx1 is downregulated. It could be argued that the estimation of GSH and PrSH could have been done at an earlier time point after the viral injection. However, any measurement done before TH cell loss can be presumed to be transient. It was for this reason that we chose to measure GSH and PrSH levels 14 days after the viral transduction when we saw loss of ~70% TH positive cells.

In contrast to our study, it has been reported that TH loss (assessed by immunoblotting) was not seen in 10 months old Grx1 knock-out mice [START_REF] Miller | Upregulation of Glutaredoxin-1 Activates Microglia and Promotes Neurodegeneration: Implications for Parkinson's Disease[END_REF]. However, it is noteworthy that in this study the quantification of TH was done using whole brain homogenate. Since TH expression in the brain is restricted to monoaminergic neurons, assessment of TH expression using whole brain homogenate would result in averaging of signals and any differences that may exist in selective cell populations, such as SNpc, would not be detected. Therefore, the impact of the knock out of Grx1 in dopaminergic neurons of SNpc needs to be ascertained by careful stereology of SNpc neurons carried out after TH staining. Thus, in the present study we clearly demonstrate that viral mediated knock-down of Grx1 results in loss of TH positive neurons in SNpc specifically since dopaminergic neurons in VTA are unaffected (Fig. 2C).

Change in Grx1 activity is particularly relevant in PD since it affects several cellular processes related to DA neurodegeneration in SNpc. For example, downregulation of Grx1 in Neuro-2A cells leads to loss of mitochondrial membrane potential [START_REF] Saeed | Knockdown of cytosolic glutaredoxin 1 leads to loss of mitochondrial membrane potential: implication in neurodegenerative diseases[END_REF] and restoration of its activity reverses the mitochondrial complex I loss seen after MPTP exposure in mice [START_REF] Kenchappa | Glutaredoxin is essential for maintenance of brain mitochondrial complex I: studies with MPTP[END_REF][START_REF] Diwakar | Downregulation of glutaredoxin but not glutathione loss leads to mitochondrial dysfunction in female mice CNS: Implications in excitotoxicity[END_REF]. Further, Grx1 downregulation leads to loss of DJ-1, which is a multifunctional protein whose mutations are linked to familial PD [START_REF] Klein | Genetics of Parkinson's disease[END_REF][START_REF] Taipa | DJ-1 linked parkinsonism (PARK7) is associated with Lewy body pathology[END_REF], facilitating cytosolic translocation of the death associated protein (Daxx) thus triggering apoptosis [START_REF] Saeed | DJ-1 loss by glutaredoxin but not glutathione depletion triggers Daxx translocation and cell death[END_REF]. Grx1 downregulation also exacerbates neurodegeneration in C. elegans model of PD that carries LRRK2 mutations [START_REF] Johnson | Glutaredoxin deficiency exacerbates neurodegeneration in C. elegans models of Parkinson's disease[END_REF].

Thiol anti-oxidants such as -lipoic acid (ALA) when co-administered with MPTP affords protection against loss of TH neurons in substantia nigra and also reverses the loss of complex I activity seen in animals treated with MPTP for 8 days [START_REF] Karunakaran | Activation of apoptosis signal regulating kinase 1 (ASK1) and translocation of death-associated protein, Daxx, in substantia nigra pars compacta in a mouse model of Parkinson's disease: protection by alpha-lipoic acid[END_REF]. Further, using human primary neurons we have shown that over-expression of Grx1 reverses 1-methyl-4-phenylpyridinium (MPP + ) mediated loss of phosphorylated Akt (pAkt). In the same study we have also demonstrated that the loss of pAkt is due to the oxidation of the cysteine sulfhydryl groups in Akt which is also reversed by overexpression of Grx1 [START_REF] Durgadoss | Redox modification of Akt mediated by the dopaminergic neurotoxin MPTP, in mouse midbrain, leads to down-regulation of pAkt[END_REF]. These studies clearly demonstrate that Grx1 overexpression can afford protection and reverse the pathogenic processes that lead to degeneration of SNpc neurons in model systems of PD even under conditions in which Grx1 is not the primary target of the toxic compound used to kill dopaminergic neurons. Grx1, therefore, plays a critical role in maintaining protein thiol homeostasis and prevents irreversible oxidation of protein thiols, which could potentially initiate the death signaling cascade [START_REF] Saeed | DJ-1 loss by glutaredoxin but not glutathione depletion triggers Daxx translocation and cell death[END_REF][START_REF] Ahmad | Critical cysteines in Akt1 regulate its activity and proteasomal degradation: implications for neurodegenerative diseases, Free Radic[END_REF] as seen in PD mouse models treated with MPTP. Thus, there are multiple consequences of Grx1 downregulation and these effects acting alone or in concert may be responsible for the neurodegeneration seen in the current study.

Interestingly, the extent of cell death did not increase between the 14 days and 28 days post viral injection in our study (Fig. 2A). This suggests that TH neurons infected initially with AAV-shRNA-Grx1 die within 14 days of transduction, and cell death does not progress beyond this time-point. Further, we did not observe significant loss of DA neurons in VTA. This selectivity is reminiscent of human PD and the MPTP-induced neurodegeneration in mouse and non-human primate models [START_REF] Brichta | Molecular determinants of selective dopaminergic vulnerability in Parkinson's disease: an update[END_REF] and suggests that VTA dopaminergic neurons may be protected from Grx1 downregulation through cell-intrinsic and/or extrinsic mechanisms. Several other factors that make VTA DA neurons relatively less vulnerable have also been reported [START_REF] Brichta | Molecular determinants of selective dopaminergic vulnerability in Parkinson's disease: an update[END_REF][START_REF] Kostuk | Subregional differences in astrocytes underlie selective neurodegeneration or protection in Parkinson's disease models in culture[END_REF][START_REF] Lieberman | α-Synuclein-Dependent Calcium Entry Underlies Differential Sensitivity of Cultured SN and VTA Dopaminergic Neurons to a Parkinsonian Neurotoxin[END_REF]. For example, DA neurons in the VTA are more protected against oxidative stress than nigral neurons because they are in an environment with more astrocytes expressing the anti-oxidant enzyme glutathione peroxidase [START_REF] Damier | Glutathione peroxidase, glial cells and Parkinson's disease[END_REF].

An important observation was the downregulation of Grx1 mRNA in SNpc from PD patients (Fig. 5A). In order to determine if the downregulation of Grx1 in human PD could have been caused by the dopaminergic treatment taken by all the subjects, we performed a parallel experiment in mice. We fed mice with carbidopalevodopa (30 mg-10 mg/ kg body weight) for 14 days orally and measured Grx1 in SNpc using qRT-PCR (Fig. 5D). We observed that there was, in fact, an upregulation of Grx1 in mice treated with carbidopa-levodopa as compared to the vehicle controls. Thus, it is unlikely that the decrease in Grx1 seen in human PD patients as reported in the current study is caused by dopaminergic treatment.

The fundamental conclusion of this paper is that knock-down of Grx1 is adequate to cause degeneration of SNpc DA neurons very selectively while preserving them in VTA.

We postulate that the pro-oxidant environment of SNpc coupled with the low levels of GSH in SNpc (which are further lowered in PD) [START_REF] Perry | Parkinson's disease: A disorder due to nigral glutathione deficiency?[END_REF] could result in dysregulation of protein thiol homeostasis. The inability to restore the equilibrium could potentially lead to downregulation of glutaredoxin further exacerbating the degeneration process. In a complex disorder such as Parkinson's disease, it would not be right to attribute Grx1 as a primary mediator of neurodegeneration seen in SNpc. Nevertheless, our study shows that Grx1 is important for maintenance of dopaminergic neurons in SNpc and any perturbation of Grx1 expression can lead to neurodegeneration of DA neurons in SNpc.

  into the pAAV-Cytomegalovirus (CMV)-β-globin intron-Green Fluorescent Protein (GFP) construct (Stratagene, La Jolla, CA). The shRNA and scRNA sequences are: 5'-TTT GCG GAT GCA GTG ATC TAA TAA GTT CTC TAT TAG ATC ACT GCA TCC GCT TTT T-3' and 5'-CTA GAA AAA GCG GAT GCA CTG ATC TAA TAG AGA ACT TAT TAG ATC ACT GCA TCC G-3' for shRNA, and for scrambled: 5' -TTT GTT GGT TAC GGG GTA TCG ATT CAA GAG ATC GAT ACC CCG TAA CCA ACT TTT T-3' and 5'-CTA GAA AAA GTT GGT TAC GGG GTA TCG ATC TCT TGA ATC GAT ACC CCG TAA CCA A-3'. Briefly, the entire cassette was PCR amplified, and MluI restriction sites were introduced on either end using the following primer sequences: Forward: 5'-AAG ATC ACGCGT GGC CAA GCT TAT CCG ACG C-3'; Reverse: 5'-AAG ATT ACGCGT CC GCG GCC GCA AGA A-3'. These PCR products, along with the pAAV-CMV-β-globin intron-GFP, were then digested with MluI and ligated to yield a hybrid Pol II/Pol III construct expressing CMV-β-globin intron-GFP and upstream mU6-Grx1 shRNA/mU6-Grx1 scRNA in opposite orientation, named AAV-shRNA-Grx1 shRNA and AAV-scRNA-Grx1 respectively. The constructs were tested for efficacy in HEK293T cells (ATCC, Manassas, VA) showing robust Grx1 downregulation within 48 hr.

Figure 1 :

 1 Figure 1: Locomotor deficits following unilateral AAV mediated downregulation of

Figure 2 :

 2 Figure 2: Loss of TH positive neurons in SNpc but not in VTA post Grx1

Figure 3 :

 3 Figure 3: Glutathione and protein thiol levels after Grx1 downregulation

Figure 4 :

 4 Figure 4: Loss of TH positive fibers in striatum post AAV-shRNA-Grx1 injection in

Figure 5 :

 5 Figure 5: Downregulation of Grx1 mRNA in human PD autopsy tissue

Acknowledgements

The authors are grateful to Prof. Patrick Aebischer (Ecole Polytechnique Fédérale de Lausanne, Switzerland) for providing lab resources and Indo-Swiss Bilateral Research Initiative for providing funding support to AR for carrying out AAV production and titration. We thank Ms. Rehab Hussain for assistance with immunohistochemistry. We would also like to thank Pr Charles Duyckaerts for the neuropathological examination and Annick Prigent and Sabrina Leclere-Turbant for preparing the human post-mortem samples.

Authors' Contributions


Etienne Balan

Laura Créon

Chrystèle Sanloup

Jérôme Aléon

Marc Blanchard

Lorenzo Paulatto

Chrystele Sanloup

Hélène Bureau

First-principles modeling of chlorine isotope fractionation

Keywords: Cl isotopes, first-principles modeling, brines, Cl-bearing minerals, solar nebula

published or not. The documents may come

Introduction

The 37 Cl/ 35 Cl isotopic composition of chlorine in major Earth's reservoirs (seawater, evaporites, mantle) exhibits a limited range of values, with most of them falling between -0.5 ‰ and +0.5 ‰ from the seawater composition [START_REF] Eggenkamp | Stable isotope fractionation of chlorine during the precipitation of single chloride minerals[END_REF]; [START_REF] Barnes | Chlorine isotope geochemistry[END_REF]. Strong departures from these values are most often ascribed to non-equilibrium kinetic processes affecting the Cl isotopic composition, which include Cl loss during degassing processes (Sharp et al., 2010a,b) as well as diffusion and ion filtration in porous media explaining negative values of sedimentary pore fluids (e.g. [START_REF] Godon | Origin and evolution of fluids from mud volcanos in the Barbados accretionary complex[END_REF]. At a larger scale, degassing processes are expected to explain the heavier isotopic composition of planetary reservoirs, such as the Moon or the crust of Mars, because of the preferential loss of light chlorine isotope (Sharp et al., 2010a; [START_REF] Barnes | Chlorine isotope geochemistry[END_REF][START_REF] Wang | An extremely heavy chlorine reservoir in the Moon: Insights from the apatite in lunar meteorites[END_REF]. Equilibrium isotopic fractionation of chlorine in nature is generally expected to be of smaller magnitude because chlorine mostly occurs under a single redox state, the reduced chloride ions, and the relative mass difference between the isotopes is small. In addition, and although equilibrium isotopic fractionation involving oxidized forms of chlorine such as perchlorates can be large [START_REF] Schauble | Theoretical estimates of equilibrium chlorine-isotope fractionations[END_REF], the photochemical formation of these unstable species is not expected to fractionate the chlorine isotopes [START_REF] Barnes | Chlorine isotope geochemistry[END_REF].

Few equilibrium fractionation factors of Cl isotopes have been experimentally determined. They include the HCl-Cl -(aq), (Sharp et al., 2010b) and the Cl2-Cl -(aq) [START_REF] Giunta | Chlorine isotope fractionation between chloride (Cl -) and dichlorine (Cl2)[END_REF]) fractionation coefficients at near-ambient conditions; as well as fractionation between chloride salts and saturated solutions [START_REF] Eggenkamp | Chloride stable isotope fractionation in evaporites[END_REF][START_REF] Eggenkamp | Experimental determination of stable chlorine and bromine isotope fractionation during precipitation of salt from a saturated solution[END_REF]. At high temperature, [START_REF] Sharp | Chlorine isotope homogeneity of the mantle, crust and carbonaceous chondrites[END_REF] reported a -0.3 ‰ fractionation factor between sodalite and NaCl(l) at 825 °C and Cisneros (2013) documented a +0.1 ‰ fractionation factor between amphibole and NaCl-bearing solution at 700°C and 0.2 GPa. Observations made on seafloor serpentinite and altered oceanic crust also point to a small positive serpentine-Cl -(aq) and amphibole-Cl -(aq) fractionation.

Theoretical isotopic fractionation factors between molecular species and crystalline chlorides have been predicted by combining experimentally observed vibrational frequencies and theoretically predicted frequency shifts due to the isotopic substitution [START_REF] Schauble | Theoretical estimates of equilibrium chlorine-isotope fractionations[END_REF]. For molecules, theoretical predictions were based on ab-initio quantum-mechanical calculations, whereas those for crystalline solids made use of empirical force-fields. This set of theoretical fractionation coefficients revealed significant equilibrium enrichment in 37 Cl in oxidized chlorine species as well as in Clbearing organic molecules. The fractionation between more reduced Cl2 and HCl molecules was found to be consistent with experimental data and the role of the local environment of chloride ions in minerals was underlined, suggesting enrichment of silicates in 37 Cl with respect to simple Na, K or Rb chlorides [START_REF] Schauble | Theoretical estimates of equilibrium chlorine-isotope fractionations[END_REF]. More recently, [START_REF] Schauble | Modeling isotopic signatures of nebular chlorine condensation[END_REF] reported a -0.7 ‰ fractionation between sodalite and HCl at 950 K and a -0.02 ‰ fractionation between sodalite and NaCl(c) at 1098 K.

They also predicted a +3 to +6 ‰ fractionation between crystalline HCl hydrate and HCl(g) at 140-160 K, a fractionation potentially explaining the variability of Cl isotopic composition observed in chondrites [START_REF] Sharp | The chlorine isotopic composition of chondrites and Earth[END_REF]Gargano et al., 2017).

Previous studies have shown that theoretical fractionation factors computed from first-principles within density functional theory (DFT) provide useful information on isotopic systems that are difficult to address on a purely experimental basis because they involve, e.g., uncommon isotopic effects [START_REF] Schauble | Preferential formation of 13 C-18 O bonds in carbonate minerals, estimated using first-principles lattice dynamics[END_REF], slow chemical reactions [START_REF] Méheut | Equilibrium isotopic fractionation between kaolinite, quartz and water: prediction from first-principles densityfunctional theory[END_REF], weakly fractionating isotopes [START_REF] Blanchard | Iron isotope fractionation between pyrite (FeS2), hematite (Fe2O3) and siderite (FeCO3): a first-principles density-functional theory study[END_REF][START_REF] Moynier | Isotopic evidence of Cr partitioning into Earth's core[END_REF][START_REF] Blanchard | Equilibrium fractionation of non-traditional isotopes: A molecular modeling perspective[END_REF], incorporation of minor or trace elements in minerals [START_REF] Rustad | Calculation of site-specific carbon-isotope fractionation in pedogenic oxide minerals[END_REF][START_REF] Balan | Theoretical isotopic fractionation between structural boron in carbonates and aqueous boric acid and borate ion[END_REF] or high-temperature reactions between solids and dilute gas [START_REF] Javoy | First-principles investigation of equilibrium isotopic fractionation of O-and Si-isotopes between refractory solids and gases in the solar nebula[END_REF]. In the present work, we apply this approach to chlorine isotopes by providing a set of theoretical fractionation factors between selected molecules (Table 1) and crystalline solids (Table 2) in which chlorine occurs as a major or a trace element, all systems being treated at the same theoretical level. This study mostly focuses on chloride, the lowest redox state of chlorine, which corresponds to the most frequently observed in natural systems. The investigated phases include cosmochemically important molecules, (HCl(g), NaCl(g) and KCl(g)), Clbearing minerals (chlorapatite, sodalite, chloromagnesite and Cl salts precipitating from aqueous solutions), as well as rock-forming silicates displaying Cl as a trace element (lizardite, anthophyllite, forsterite).

Methods

Expression of isotopic fractionation factors

Assuming a system with two stable isotopes, the equilibrium isotopic fractionation coefficient of an element Y between two phases a and b, referred to as α(a,b,Y), is defined by the isotopic ratios:

α(a,b,Y)=(Y*/Y')a/(Y*/Y')b (1)
where Y* and Y' are the abundances of the two different isotopes. Accordingly, it can be related to the equivalent coefficients, referred to as β-factors, obtained for each phase and a reference system corresponding to an ideal gas of Y atoms:

10 3 ln α(a,b,Y) = 10 3 ln β(a,Y) -10 3 ln β(b,Y) (2)
The β(a,Y) factor is related to the reduced partition function ratio of the isotopomers and harmonic expressions have been derived for molecular systems by [START_REF] Bigeleisen | Calculation of equilibrium constants for isotopic exchange reactions[END_REF]. Using the high-temperature product (Redlich-Teller) rule, the harmonic β-factor of a diatomic molecule is given by:

€ β(a,Y ) = ν * ν e -hν * (2kT ) 1 -e -hν * ( kT ) 1 -e -hν ( kT ) e -hν (2kT ) (3)
were ν and ν* are the harmonic stretching frequencies of molecules differing by a single isotopic substitution, k the Boltzmann constant, h the Planck constant, and T the temperature. This expression is valid for molecules containing more than a single Y atom provided that the isotopic mixing is ideal, a verified assumption in the case of chlorine isotopes [START_REF] Schauble | Theoretical estimates of equilibrium chlorine-isotope fractionations[END_REF].

For a crystal, harmonic β-factors can be calculated in a similar way using the following expression:

€ β(a,Y ) = ν q,i 1 -e -hν q,i ( kT ) e -hν q,i (2kT ) q { } ∏ i=1 3N at ∏ ⎡ ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ 1/(NqN ) (4)
where νq,i are the frequencies of the phonon with wavevector q and branch index i = 1,3Nat. Nat is the number of atoms in the unit cell, νq,i and ν * q,i are the vibrational frequencies in two isotopically different materials, N is the number of sites for the Y atom in the unit cell (e.g., [START_REF] Méheut | Equilibrium isotopic fractionation between kaolinite, quartz and water: prediction from first-principles densityfunctional theory[END_REF]. In the product over the Nq q-vectors of Eq.

(4), the three translational modes at the center of the Brillouin zone with ν0,i = 0 are not considered. The β-factors can thus be calculated for molecules and crystalline solids using Eq. ( 3) and ( 4) and vibrational frequencies calculated from first-principles.

The calculation of the whole vibrational spectrum is sometimes prevented by the too large size of the considered system. In this case, a useful approximation can be used to obtain the β-factor from the restoring force constants Fi corresponding to the displacement of the isotopic atom in three mutually perpendicular directions [START_REF] Bigeleisen | Calculation of equilibrium constants for isotopic exchange reactions[END_REF][START_REF] Moynier | Isotopic evidence of Cr partitioning into Earth's core[END_REF]Ducher et al., 2017):

€ β ≈ 1+ ʹ M -M ʹ M M h 2 96π 2 k 2 T 2 F i i=1 3 ∑ (5)
where M and M' are the masses of the two isotopes.

Computational details

Relevant vibrational properties, i.e. phonon frequencies (Eq. 3 and 4) or restoring force constants (Eq. 5), were obtained within the density functional theory (DFT) framework, using the generalized gradient approximation (GGA) to the exchangecorrelation functional as proposed by Perdew, Burke and Ernzerhof (PBE;[START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF] and a plane-wave / pseudopotential scheme, as implemented in the PWscf and PHonon codes from the Quantum-Espresso package [START_REF] Baroni | Phonons and related crystal properties from density-functional perturbation theory[END_REF][START_REF] Giannozzi | Quantum ESPRESSO: a modular and opensource software project for quantum simulations of materials[END_REF]; http://www.quantum-espresso.org). The ionic cores were described using optimized norm-conserving Vanderbilt (ONCV) pseudopotentials [START_REF] Hamann | Optimized norm-conserving Vanderbilt pseudopotentials[END_REF]Schlipf and Gigy, 2015) with 80 and 480 Ry cut-offs on the electronic wave functions and charge density, respectively, ensuring that total energies are converged within 1 mRy/atom. Before the computation of vibrational properties, the relaxation of atomic internal coordinates was performed until the residual forces were less than 10 -4 Ry/au. Initial guess of mineral structures were built using the experimental data (Table 2) obtained from the American Mineralogist Crystal Structure Database [START_REF] Downs | The American Mineralogist Crystal Structure Database[END_REF]. To compute the properties of isolated molecules (Table 1), a single molecule was inserted in a cubic box with cell parameter a = 15.87 Å, a size large enough to marginalize the interactions between periodic images of the molecule. In this case, the electronic integration was performed by restricting the Brillouin-zone sampling to a single k-point. For minerals, k-point grids are reported in Table 2 and both the cellparameters and atomic positions were relaxed under zero pressure. Depending on the system size a finite grid of q-points (Eq. 4) or the force-constant approximation (Eq. 5)

were used to compute the β-factors (Table 2). In the finite grids of q-vectors (Eq. 4), the center of the Brillouin zone (Γ point) was not included.

Structural models of Cl incorporation in silicates at trace or minor concentration level

Chlorine usually occurs in rock-forming minerals as a trace or minor element.

Hydrous phyllosilicates and amphiboles are able to incorporate chlorine up to the wt. % level. These significant concentrations are explained by the possibility to substitute chloride ions for structural OH groups in these hydrous minerals [START_REF] Volfinger | Structural control of the chlorine content of OH-bearing silicates (micas and amphiboles)[END_REF].

Oceanic serpentines can contain up to 6200 ppm Cl (e.g. Scambeluri et al., 2004) and are considered as key actors of Cl recycling in the mantle [START_REF] Kendrick | High abundances of noble gas and chlorine delivered to the mantle by serpentinite subduction[END_REF].

Accordingly, periodic models of Cl-bearing lizardite (Mg3Si2O5(OH)4) and anthophyllite (Mg7Si8O22(OH)2) have been considered for their relative chemical simplicity. In order to minimize, as much as possible, spurious interactions between the periodic images of the substituted chloride ions, the unit-cell of the periodic Cl-bearing lizardite model has been built from a 2x2x2 supercell containing 112 atoms. Two different lizardite models were considered, referred to as Cl1 and Cl2, corresponding to Cl substitution for an inner-OH or an inter-layer OH group, respectively. The anthophyllite cell also contains two non-equivalent OH-groups leading to two different models, referred to as Cl1 and Cl2. The local environment around the two OH-groups is however more similar than in lizardite. In anthophyllite, the primitive cell contains 164 atoms and it was not possible to handle a larger supercell. The distance between Cl in neighboring cells is 5.27 Å along the c direction. As the structure is constrained along this direction by the silicate chains, we expect that the local structure around chlorine ions, and therefore their isotopic fractionation properties, is weakly affected by the presence of the chlorine ions in neighboring cells.

The incorporation mechanisms of halogens in olivine are still debated, despite its potentially important role in the storage of halogens in the upper mantle [START_REF] Beyer | Fluorine in nominally fluorine-free mantle minerals: experimental partitioning of F between olivine, orthopyroxene and silicate melts with implications for magmatic processes[END_REF][START_REF] Dalou | Experimental determination of F and Cl partitioning between lherzolite and basaltic melt[END_REF][START_REF] Joachim | Experimental partitioning of F and Cl between olivine, orthopyroxene and silicate melt at Earth's mantle conditions[END_REF]2017). Several studies have pointed out the key role of hydroxylated defects in the incorporation of fluorine in forsterite, the Mg olivine end-member [START_REF] Crépisson | Clumped fluoride-hydroxyl defects in forsterite: Implications for the upper mantle[END_REF][START_REF] Joachim | Experimental partitioning of F and Cl between olivine, orthopyroxene and silicate melt at Earth's mantle conditions[END_REF]. Compared with fluorine, partition coefficients of chlorine between olivine and melt are smaller, with a lower dependence on the olivine water content [START_REF] Joachim | Effect of water on the fluorine and chlorine partitioning behavior between olivine and silicate melt[END_REF]. Nonetheless, in absence of definite conclusions concerning the incorporation mechanism of chlorine in olivine, we considered that the Cl for OH substitution in hydroxylated defects of olivine still is a viable incorporation mechanism. Other mechanisms involving, e.g. the charge compensation of cationic vacancies by the association of several chloride ions in a single defect, does not seem to be more favorable because of the low Cl concentration.

Accordingly, two types of models of hydroxylated defects, related to Si or Mg vacancies in forsterite, were considered as potential candidates for the structural incorporation of chloride ions. These models have been built from a 2x1x2 forsterite supercell and previously validated by comparison with infrared spectroscopic observations (Balan et al., 2011;2017). In these models, only one Cl atom has been substituted for one of the OH groups. In the case of the hydroxylated Si vacancy, three non-equivalent OH groups can be substituted, leading to three Cl-bearing forsterite models referred to as Si_Cl1, Si_Cl2 and Si_Cl3 (Table 3), where the number corresponds to the substituted hydroxyl and the configuration is identical to that of the fluorinated models investigated by [START_REF] Crépisson | Clumped fluoride-hydroxyl defects in forsterite: Implications for the upper mantle[END_REF]. An additional model (Si_Cl1b) was considered, corresponding to a configuration in which the O2-H group points toward the neighbouring vacant site as in the hydroxylated Si vacancy model described in [START_REF] Balan | Theoretical Raman spectrum and anharmonicity of tetrahedral OH defects in hydrous forsterite[END_REF]. Five models preserving the electrostatic charge neutrality can be built for the hydroxylated Mg vacancy (Table 3).

The equilibrium geometry of Cl-poor silicates was obtained by displacing all atoms up to a minimum energy state, characterized by the fact that the forces experienced by the atoms vanish. During this relaxation, the cell geometry was kept fixed to that of the pure phase, as previously done in e.g. [START_REF] Balan | First-principles modeling of sulfate incorporation and 34 S/ 32 S isotopic fractionation in different calcium carbonates[END_REF] or [START_REF] Crépisson | New constraints on Xe incorporation mechanisms in olivine from first-principles calculations[END_REF].

Results

Benchmarking the modeling approach

The first-principles calculation of isotopic fractionation factors relies on a number of approximations which can introduce systematic bias in the computed values of β-factors. The stronger approximations rely on the use of the harmonic approximation and in the choice of the exchange-correlation functional, here the PBE functional. As observed in previous studies, the PBE calculations tend to overestimate bond lengths and crystal cell-parameters by typically 1 to 2 % (Table 1 &2). The agreement is slightly poorer for chlorapatite, with a stronger overestimation of the a cell-parameter and a slight contraction of the c cell-parameter (Table 1). Similar distortion of the cell geometry was observed in previous modeling of the properties of Fand OH-apatite at the GGA level [START_REF] Corno | Periodic ab initio study of structural and vibrational features of hexagonal hydroxyapatite Ca10(PO4)6(OH)2[END_REF]Balan et al., 2011b;Aufort et al., 2018). An overestimation of the c cell-parameter of chloromagnesite is also observed. It is likely related to the dominant Van der Waals contribution to the cohesion energy of the layered chloromagnesite structure, a contribution which is not accounted for by the PBE functional. Similar overestimation is observed in other layered minerals displaying non hydrogen-bonded neutral layers, such as talc. It is however not expected to strongly affect the vibrational properties of the structure as the layer geometry is preserved [START_REF] Blanchard | Infrared spectroscopic study of the synthetic Mg-Ni talc series[END_REF]). Significant differences between theory and experiment are also observed in the cell geometry of the hydrated salts bischofite (MgCl2.6(H20)) and BaCl2.2(H20) (Table 2). The structure of bischofite displays Mg(OH2)6 2+ polyhedra sharing H-bonds with neighboring Cl -ions or H2O molecules; whereas the hydrated barium dichloride displays layers of edge sharing Ba(OH2)4Cl4 polyhedra. In such type of molecular edifices, the neglect of Van der Waals interactions and thermal effects related to the anharmonicity of weak H-bonds could be stronger than in crystals whose cohesion is ensured by iono-covalent bonding.

The properties of small molecules (HCl, Cl2) and simple chloride salts (Table 1 & 2) can be compared to their experimental counterparts and to previous calculations by [START_REF] Richet | A review of hydrogen, carbon, nitrogen, oxygen, and chlorine stable isotope fractionation among gaseous molecules[END_REF] and [START_REF] Schauble | Theoretical estimates of equilibrium chlorine-isotope fractionations[END_REF] (Fig. 1). As expected, the systematic overestimation of bond distances and cell parameters due to the GGA, leads to an underestimation of vibrational frequencies by ~5% (Fig. 2). The difference is however larger for CsCl(c) than for the other halides, reaching 25% despite similar agreement between theoretical and experimental cubic cell parameters (Table 2). A modeling of CsCl using a different exchange-correlation functional (PBEsol; [START_REF] Perdew | Restoring the density-gradient expansion for exchange in solids and surfaces[END_REF] provided a smaller a cell-parameter (4.06 Å), increasing the zone-center TO frequency to 93.5 cm -1 and the β-factor at 22°C by 0.43 ‰. For the molecules, a systematic ~0.5 ‰ decrease of β-factor at 0°C with respect to the previously calculated values is observed (Fig. 1). The equilibrium fractionation factor between Cl2 and halite at 0°C is 4.6 ‰, very close to the 4.75 ‰ value computed by [START_REF] Schauble | Theoretical estimates of equilibrium chlorine-isotope fractionations[END_REF]. Similarly the halitesylvite fractionation at 0°C is 0.9 ‰ both in the present study and that of [START_REF] Schauble | Theoretical estimates of equilibrium chlorine-isotope fractionations[END_REF], confirming that systematic bias tend to compensate when combining β-factors computed at the same theoretical level.

As mentioned in the Method section, the whole vibrational spectrum is hardly obtained for systems having a large number of atoms in their unit-cell. In this case, it can be useful to use an approximate expression that relates the β-factor to the restoring force constant when the relevant atom is displaced from its equilibrium position (Eq. 5). This approximation of the harmonic expression of the reduced partition function ratio assumes that the force-constants are isotope-independent. It is valid when the ratio of the relevant vibrational frequencies to the temperature and the relative mass difference between the isotopes are sufficiently small [START_REF] Blanchard | Equilibrium fractionation of non-traditional isotopes: A molecular modeling perspective[END_REF]. Accordingly, the use of the force-constant approximation was tested on the forsterite_Si_ Cl1 model. This model displays a relatively high β-factor indicating that the relevant vibrational frequencies are among the highest observed among the investigated systems. The comparison between the β-factor obtained using the full expression (Eq. 4) and the approximate one (Eq. 5) indicate that for a temperature above 450 K, the difference is smaller than 0.1 ‰. As the force constant approximation is obtained from a finite expansion of the full harmonic expression of the β-factor, the quality of the approximation is better for systems displaying smaller vibrational frequencies and related smaller β-factor. For example, the difference between the force constant approximation and the full calculation for the NaCl and KCl molecules is smaller than 0.1 ‰ at 298 K.

Local environment and isotopic β-factor of chloride in condensed phases

The isotopic fractionation properties of chlorine reflect its local bonding environment. For all the investigated solid phases, the temperature dependence of the reduced partition function ratios is mostly linear and the corresponding slope coefficients are given in Table 4. In monochloride salts, chlorine displays a coordination varying from 8 in CsCl to 6 in the other chlorides with halite structure. The corresponding reduced partition function ratio at 22°C (Table 5) display a systematic variation as a function of the cation ionic radius, the larger cations leading to smaller βfactors (Fig. 3). In the hydrated Mg, Ca and Sr dichloride salts, the chloride ion is bonded to water molecules belonging to the coordination sphere of the cations (Table 3).

Consistently, these phases display similar β-factors, not correlated with the cation radius (Fig. 3). In the peculiar HCl tri-hydrate structure, the HCl molecule is dissociated and the chloride ions are surrounded by Zündel ions (H5O2 + ) [START_REF] Lundgren | Hydrogen bond studies. XV. The crystal structure of hydrogen chloride dihydrate[END_REF]. The corresponding β-factor is larger than that observed in the hydrated dichloride salts in which chloride ions are surrounded by water molecules (Table 4).

When solely bound to divalent cations, chlorine displays a three-fold coordination. This environment is observed in chloromagnesite and chlorapatite, as well as in the silicates anthophyllite and lizardite. The β-factor of chloromagnesite (6.2 ‰ at 0°C) is consistent with the values reported for the isostructural compounds FeCl2 and MnCl2 (6.7 and 6.2 ‰ at 0°C, respectively) by [START_REF] Schauble | Theoretical estimates of equilibrium chlorine-isotope fractionations[END_REF]. Despite an apparently similar environment and Mg-Cl distances close to 2.5 Å, the β-factor of Clsites in lizardite and anthophyllite are significantly higher than that of chloromagnesite (Table 4, Fig. 4). This suggests that the environment of Cl atoms is more constrained when Cl is incorporated as a substituting element in silicates than when it occurs as a major constituent of the mineral. As a matter of fact, the Mg-Cl-Mg angle decreases from 93 ° in chloromagnesite to about 80° in lizardite and anthophyllite. The effect of the host structure on the vibrational and isotopic fractionation properties of Cl is even stronger when considering the Cl sites in forsterite. In the case of the defects related to Si vacancies, the Mg-Cl distances are smaller than in the chloride minerals (Table 3).

Neighboring OH groups can also point toward the Cl ion, suggesting a weak additional bonding to H atoms. For the defects related to Mg vacancies, Cl ions are bound to Si atoms and the largest β-factors are observed. Although it is not possible to directly compare the energy of chemically different incorporation mechanisms, it can be noticed that the less stable configurations of a given defect are observed for the environments leading to the shortest Cl-cation distances (Table 3).

Finally, chloride ions in sodalite display a lower 4-fold coordination states with bonding to Na atoms. Compared with halite, the lowering of the coordination state is balanced by a shortening of the Cl-Na bond leading to a very similar β-factor for both minerals. The calculated fractionation factor between HCl and sodalite (0.7 ‰ at 950 K) is in excellent agreement with the value proposed by [START_REF] Schauble | Modeling isotopic signatures of nebular chlorine condensation[END_REF].

Discussion

Chlorine isotope fractionation during precipitation from saturated solutions

The precipitation of chloride salts from concentrated aqueous solutions is an important natural process leading to the formation of evaporitic rocks. The equilibrium isotopic fractionation factors of chlorine between aqueous solutions and precipitating NaCl, KCl and hydrated MgCl2 has been experimentally determined by [START_REF] Eggenkamp | Chloride stable isotope fractionation in evaporites[END_REF]. The moderate values, varying between +0.26 ‰ and -0.08 ‰ for NaCl(c) and KCl(c), respectively, were found to be roughly consistent with the theoretical values provided by [START_REF] Schauble | Theoretical estimates of equilibrium chlorine-isotope fractionations[END_REF]. Although debated [START_REF] Luo | Stable isotope fractionation of chloride during the precipitation of single chloride minerals[END_REF][START_REF] Luo | Reply to the comment on the paper "Stable isotope fractionation of chlorine during the precipitation of single chloride minerals[END_REF][START_REF] Eggenkamp | Stable isotope fractionation of chlorine during the precipitation of single chloride minerals[END_REF], the initially proposed experimental values have been more recently confirmed by [START_REF] Eggenkamp | Experimental determination of stable chlorine and bromine isotope fractionation during precipitation of salt from a saturated solution[END_REF]. This series was also complemented by the experimental determination of fractionation factors between aqueous solutions and Li, Cs, Rb, Ca and Sr salts [START_REF] Eggenkamp | Experimental determination of stable chlorine and bromine isotope fractionation during precipitation of salt from a saturated solution[END_REF].

The comparison of theoretical results with experimental fractionation factors is not straightforward because theory only provides β-factors within a given level of approximation. Although fractionation factors and β-factors are simply related by Eq. ( 2), the theoretical prediction of equilibrium isotopic fractionation between solids and solutions is hampered by computational constraints which make it difficult to treat the liquid and solid phases at the same approximation level [START_REF] Blanchard | Equilibrium fractionation of non-traditional isotopes: A molecular modeling perspective[END_REF]. Using an empirical electrostatic [START_REF] Eggenkamp | Experimental determination of stable chlorine and bromine isotope fractionation during precipitation of salt from a saturated solution[END_REF]. Assuming that the experiments correspond to isotopic equilibrium conditions, this suggests that the observed departure between empirical and theoretical β-factors for these salts does not solely arise from theoretical or experimental inaccuracies but rather reflects a variation in the β-factor of Cl -ions in concentrated aqueous solutions. The weak experimental fractionation observed between brines and crystalline salts, compared to the theoretical variation of the βfactor of solid phases (Fig. 3), suggests that the β-factor of Cl -ions in concentrated solutions follows the trend observed in the solids. According to the present results, the β-factor of Cl -ions in saturated solutions could be smaller than that observed in dilute solutions. The observed difference is larger than 0.5 ‰ and could reach 1 ‰ for CsCl (Fig. 6), taking into account the ~0.43 ‰ difference related to the lower accuracy of the PBE functional to model CsCl(c). Potential role of ion pairing in solution was previously suggested by [START_REF] Schauble | Theoretical estimates of equilibrium chlorine-isotope fractionations[END_REF] and [START_REF] Eggenkamp | Experimental determination of stable chlorine and bromine isotope fractionation during precipitation of salt from a saturated solution[END_REF]. Significant contact ionpairing in concentrated CsCl and RbCl solutions has been recently observed by X-ray absorption fine structure (XAFS) spectroscopy and X-ray diffraction (XRD) [START_REF] Pham | High-resolution measurement of contact ion-pair structures in aqueous RbCl solutions from the simultaneous corefinement of their Rb and Cl K-edge XAFS and XRD spectra[END_REF]2018). In contrast, CaCl2 solutions are dominated by solvent-separated ion pairs [START_REF] Pham | Ion-pairing in aqueous CaCl2 and RbBr solutions: Simultaneous structural refinement of XAFS and XRD data[END_REF][START_REF] Friesen | Cation hydration and ion pairing in aqueous solutions of MgCl2 and CaCl2[END_REF]. Although deserving further investigation, these observations consistently point to a stronger modification of the local environment of chloride ions in concentrated aqueous solutions for the larger alkaline cations with a smaller ionic potential.

Chlorine isotope fractionation in rock-forming silicates

Equilibrium fractionation of chlorine isotopes among silicate minerals is constrained by few experimental measurements. [START_REF] Sharp | Chlorine isotope homogeneity of the mantle, crust and carbonaceous chondrites[END_REF] reported a -0.3 ‰ fractionation factor between sodalite and NaCl(l) at 825 °C and Cisneros (2013) determined a +0.1 ‰ fractionation factor between amphibole and NaCl-bearing solution at 700°C and 0.2 GPa.

A fractionation of +0.33 ‰ between structurally bound and water-soluble Cl in seafloor serpentinites is documented by [START_REF] Sharp | Water soluble chlorides in massive seafloor serpentinites: a source of chloride in subduction zones[END_REF]. A positive amphibole-Cl -(aq) fractionation is also consistent with observations made on altered oceanic crust [START_REF] Barnes | Mineralogical control on the chlorine isotope composition of altered oceanic crust[END_REF] and metasomatised meta-gabbro [START_REF] Kusebauch | Apatite as probe for the halogen composition of metamorphic fluids (Bamble Sector, SE Norway)[END_REF]. Based on the similarity between the local environment of chlorine in serpentine and amphiboles and that observed in dichloride salts, a 37 Cl enrichment with respect to parent fluids is consistent with the theoretical constraints [START_REF] Schauble | Theoretical estimates of equilibrium chlorine-isotope fractionations[END_REF]. The present results

provide twice as large β-factors of chlorine occurring as a trace or minor element in silicates as those of dichloride salts. Assuming that the Cl β-factor in high temperature fluids does not exceed the theoretical predictions for aqueous Cl [START_REF] Czarnacki | Isotope fractionation in aqua-gas systems: Cl2-HCl-Cl -, Br2-HBr-Brand H2S-S 2[END_REF], they confirm the 37 Cl enrichment of chloride bearing silicates with respect to the parent fluids. The equilibrium isotopic fractionation between silicates and fluids remains however weak, not exceeding 2 ‰ at 400 °C.

Concerning trace chlorine occurring as defects in forsterite, the usually high formation temperature of olivine leads to very small isotopic fractionation. The fractionation factor between forsterite and halite is smaller than 0.3 ‰ at 1300 °C.

Although very weak, measurement of differences in the isotopic composition of experimentally grown samples of forsterite in presence of NaCl might help to discriminate between inclusion of small halite particles and structural incorporation of chlorine. We note however that lower formation temperature (<610 °C) of Fe-rich olivine has been reported in some chondrites [START_REF] Ganino | Reduced and unstratified crust in CV chondrite parent body[END_REF] potentially leading to larger Cl isotope fractionation.

Overall, the weakness of equilibrium isotopic fractionation factors of chlorine at high temperature cannot explain the variations observed in Middle Ocean Ridge basalts [START_REF] Bonifacie | Chlorine isotopic composition in seafloor serpentinites and high-pressure metaperidotites. Insights into oceanic serpentinization and subduction processes[END_REF] or olivine-hosted melt inclusions from island arcs basalts [START_REF] Bouvier | Tracing of Cl input into the sub-arc mantle through the combined analysis of B, O and Cl isotopes in melt inclusions[END_REF]. It sustains the use of Cl isotopes to identify mixing processes involving more fractionated and shallow Cl reservoirs such as seawater, altered oceanic crust serpentinites or sediments.

Isotopic fractionation during Cl condensation in the solar nebula

The behavior of Cl and related isotopic fractionation during the formation of the solar system is still an open question. It was initially thought that the homogeneity of isotopic composition between bulk Earth, chondritic meteorites and lightest values of Moon samples reflected a nebular composition close to 0 ‰ [START_REF] Sharp | Chlorine isotope homogeneity of the mantle, crust and carbonaceous chondrites[END_REF]. The lack of isotopic fractionation between Earth and chondrites is explained by the hydrous character of silicate melts, leading to a compensation between the positive fractionation between HCl and Cl dissolved in melts and the preferential loss of light isotopes during HCl degassing (Sharp et al., 2010a). In contrast, the elevated 37 Cl/ 35 Cl ratio measured on Moon samples is explained by NaCl(g) loss from anhydrous melts.

However, the Cl isotopic composition of several ordinary chondrites [START_REF] Sharp | The chlorine isotopic composition of chondrites and Earth[END_REF], some shergottites having preserved the Mars mantle composition [START_REF] Sharp | The chlorine isotope composition of Martian meteorites 2. Implications for the early solar system and the formation of Mars[END_REF] and several iron meteorites (Gargano et al., 2017), suggests a lighter isotopic composition of the nebular gas, between -3 and -5 ‰ [START_REF] Sharp | The chlorine isotope composition of Martian meteorites 2. Implications for the early solar system and the formation of Mars[END_REF]. Starting from this composition, the high-temperature condensation of chlorine, corresponding to the formation of sodalite at 950 K [START_REF] Fegley | Volatile element chemistry in the solar nebula: Na, K, F, CI[END_REF][START_REF] Lodders | Solar system abundances and condensation temperatures of the elements[END_REF], is not expected to strongly fractionate the Cl isotopes. At this temperature NaCl molecules are the dominant speciation of chlorine in the nebular gas [START_REF] Fegley | Volatile element chemistry in the solar nebula: Na, K, F, CI[END_REF]. Based on the present calculations, NaCl(g) displays almost no fractionation with sodalite, whereas HCl(g) in equilibrium with NaCl(g) is only 0.7 ‰ heavier. Accordingly, the significantly heavier composition observed on various chondrites, as well as in bulk Earth, cannot be explained by high-temperature fractionation mechanisms. For this reason, [START_REF] Sharp | The chlorine isotope composition of Martian meteorites 2. Implications for the early solar system and the formation of Mars[END_REF] proposed that these heavy compositions could reflect the low-temperature (< 140K) addition of Cl as HCl hydrates formed beyond the snow line. Theoretical fractionation factors proposed by [START_REF] Schauble | Modeling isotopic signatures of nebular chlorine condensation[END_REF], confirmed by the present results, indicate that HCl hydrates could be enriched in 37 Cl by up to 3-4 ‰ at these temperatures (Fig. 7). This interpretation is consistent with the suggestion of Zolotov and Miromenko (2007) that aqueous alteration of chondrites at low-pH could reflect the incorporation of HCl hydrates at temperatures as low as 160 to 140 K. However, the postulated enrichment in 37 Cl of HCl hydrates would only correspond to a minor fraction of hydrates in equilibrium with a dominant fraction of HCl gas having escaped from high-temperature condensation processes and still not fully condensed at low temperature. Otherwise, mass balance implies that the isotopic composition of HCl hydrates should tend to that of the nebular gas as their low-temperature condensation proceeds. Such a low fraction of HCl condensed as hydrates is at odd with observations of protostars [START_REF] Kama | Depletion of chlorine into HCl ice in a protostellar core: The CHESS spectral survey of OMC-2 FIR 4[END_REF] and comet 67P/Churyumov-Gerasimenko [START_REF] Dhooghe | Halogens as tracers of protosolar nebula material in comet 67P/Churyumov-Gerasimenko[END_REF], indicating that up to 90% of HCl, the major Cl-bearing species in the interstellar medium is frozen as ice onto the surfaces of dust grains.

The above described scenario is strongly dependent on the assumptions made on the high-temperature condensation of chlorine. Considering the condensation model proposed by [START_REF] Schaefer | Cosmochemistry[END_REF], a different scenario of the evolution of the Cl isotopic composition in the solar nebula could be proposed. According to the thermodynamical modeling of [START_REF] Schaefer | Cosmochemistry[END_REF] and more recently of [START_REF] Wood | The condensation temperatures of the elements: a reappraisal[END_REF], chlorine condensates at a lower temperature, starting by forming chlorapatite at 470K by reaction of previously formed whitlockite or fluorapatite with HCl(g) up to about 40% of total chlorine, and ending by the condensation of halite directly from HCl gas at temperatures below 420K. Such lower condensation temperature of chlorine is also consistent with the recent reevaluation of chlorine during Earth accretion by [START_REF] Clay | Halogens in chondritic meteorites and terrestrial accretion[END_REF]. New measurements of Cl concentration in carbonaceous, enstatite and primitive ordinary chondrites reveals that a lower condensation temperature of chlorine, close to 500 K, would be consistent with the general trend observed for the other volatile elements. Based on the present results, HCl(g), which is the dominant Cl-bearing constituent of the nebular gas at these temperatures [START_REF] Schaefer | Cosmochemistry[END_REF], is enriched by 0.7 ‰ with respect to chlorapatite at 470K and 1.7 ‰ with respect to halite at 420K (Fig. 8). At these temperatures, it is reasonable to assume that the solid grains were isolated from the gas and do not re-equilibrate with the gas, sustaining a Rayleigh fractionation model in the absence of volatilization. In its simplest expression, this model describes the evolution of the 37 Cl/ 35 Cl ratio R of the remaining HCl(g) as a function of the condensed fraction of mineral phase f:

€ R R°= f (α -1) (6)
where R° is the initial ratio of the nebular gas and α the fractionation factor between the gas and the condensed phase. While a significant degree of supercooling or HCl(g) supersaturation during condensation would request the use of kinetic fractionation factors, equilibrium fractionation factors can be used in the theoretical framework of condensation at thermodynamical equilibrium. Using the calculated fractionation factors, it appears that the condensation of halite can lead to a significant enrichment in 37 Cl of the residual HCl(g), which is fractionated by more than +3 ‰ with respect to the starting nebular composition for a condensed fraction above 90 % (Fig. 9). At this point 40% of nebular chlorine is locked in chlorapatite and 50% in halite, while 10% is still present as HCl(g). The fractionation reaches more than +5.5 ‰ for a condensed fraction above 98 % (in this case halite now accounts for 58% of total nebular chlorine and only less than 2% are still present as HCl(g)). Later interaction of chondrites with heavier HCl at lower temperature, still under gas state or condensed as hydrates, could lead to both their acidic alteration (Zolotov and Miromenko, 2007) and isotopic enrichment in 37 Cl as proposed by [START_REF] Sharp | The chlorine isotope composition of Martian meteorites 2. Implications for the early solar system and the formation of Mars[END_REF].

The present scenario relies on an efficient condensation of halite as the source of isotopic fractionation between nebular gas and chondrites and is only based on equilibrium fractionation processes. However, the origin of halite in chondrites remains unclear and more complex processes are likely involved. As for chlorapatite and sodalite, halite probably formed during brine circulations on the parent bodies [START_REF] Zolensky | Asteroidal water within fluid inclusion-bearing halite in an H5 chondrite, Monahans[END_REF][START_REF] Whitby | Extinct 129 I in halite from a primitive meteorite: evidence for evaporite formation in the early solar system[END_REF][START_REF] Bridges | Halite and stable chlorine isotopes in the Zag H3-6 breccia[END_REF] but some halite crystals and their fluid inclusions have H and O isotopic systematics indicating preservation of pristine nebular volatiles [START_REF] Yurimoto | Isotopic compositions of asteroidal liquid water trapped in fluid inclusions of chondrites[END_REF]. While the low Cl abundance in chondrites (less than 10% of the solar Cl based on [START_REF] Clay | Halogens in chondritic meteorites and terrestrial accretion[END_REF] does not favor efficient condensation of halite, we note that the Cl isotopic compositions of halite in the Zag ordinary chondrite (-2.8‰ ≤ δ 37 Cl ≤ -1.4‰, [START_REF] Bridges | Halite and stable chlorine isotopes in the Zag H3-6 breccia[END_REF] and sodalite in carbonaceous chondrites inclusions (-2.1‰ ≤ δ 37 Cl ≤ -0.4‰, [START_REF] Sharp | Chlorine isotope homogeneity of the mantle, crust and carbonaceous chondrites[END_REF] are well in line with the composition expected in our Rayleigh distillation model.

5-Conclusion

In the present work, a consistent set of theoretical 37 Cl/ 35 Cl β-factors has been computed for selected minerals and molecules at the density functional theory level. The β-factor is an intrinsic property of the phases, defined with respect to an ideal system.

They are not directly accessible from experiment but their computation makes it possible to relate the isotopic fractionation properties to local chemical bonding and to disentangle the contribution of individual phases in equilibrium isotopic fractionation processes.

The present results reveal the important role of solution chemistry on the isotopic fractionation of chlorine during the precipitation of chloride salts from aqueous solutions. They also suggest that the variability of chlorine isotopic composition observed in objects of the solar system could be inherited from Rayleigh fractionation processes during the nebula condensation.

Accordingly, further works should aim at developing efficient modeling methods able to treat large systems such as chemically complex aqueous solutions and their interfaces with solids at the best approximation level. The present results could also motivate experimental works on isotopic fractionation processes during the hightemperature condensation of solids and further measurements of Cl isotopic composition in mineral paragenesis of primitive meteorites. and condensates from the nebular environment. Depending on the condensation models, formation of sodalite at 950 K [START_REF] Lodders | Solar system abundances and condensation temperatures of the elements[END_REF][START_REF] Fegley | Volatile element chemistry in the solar nebula: Na, K, F, CI[END_REF] only leads to a weak isotopic fractionation of HCl(g) with other phases; whereas a later chlorine condensation as chlorapatite and halite [START_REF] Schaefer | Cosmochemistry[END_REF]) can lead to a more significant 37 Cl enrichment of HCl(g) at temperatures between 400 and 500K.

Figure captions:

Note that the Cl speciation in the nebular gas is dominated by NaCl at 950 K and by HCl at temperatures below 800 K.

Figure 9: Isotopic composition of remaining HCl(g) in a simple scenario of Rayleigh fractionation during chlorine condensation between 500 and 400 K. The chlorapatite accounts for 40% of chlorine condensation. For condensed fraction above 90 %, the remaining HCl(g) is fractionated by more than +3 ‰ with respect to a starting nebular composition of δ 37 Cl= -3 ‰. [START_REF] Schauble | Modeling isotopic signatures of nebular chlorine condensation[END_REF]. Figure 8: Isotopic fractionation factors between HCl(g) and other Cl-bearing molecules and condensates from the nebular environment. Depending on the condensation models, formation of sodalite at 950 K [START_REF] Lodders | Solar system abundances and condensation temperatures of the elements[END_REF][START_REF] Fegley | Volatile element chemistry in the solar nebula: Na, K, F, CI[END_REF] only leads to a weak isotopic fractionation of HCl(g) with other phases; whereas a later chlorine condensation as chlorapatite and halite [START_REF] Schaefer | Cosmochemistry[END_REF]) can lead to a more significant 37 Cl enrichment of HCl(g) at temperatures between 400 and 500K.

Note that the Cl speciation in the nebular gas is dominated by NaCl at 950 K and by HCl at temperatures below 800 K.

  model of ion solvation by water molecules,[START_REF] Czarnacki | Isotope fractionation in aqua-gas systems: Cl2-HCl-Cl -, Br2-HBr-Brand H2S-S 2[END_REF] have computed the β-factor of the aqueous chloride ion. Combined with the β-factor of the Cl2 molecule computed by[START_REF] Schauble | Theoretical estimates of equilibrium chlorine-isotope fractionations[END_REF], a good agreement was observed between the theoretical values and the experimental fractionation factor between Cl2 vapor and aqueous chloride ions determined by[START_REF] Giunta | Chlorine isotope fractionation between chloride (Cl -) and dichlorine (Cl2)[END_REF]. This suggests that the β-factor determined by[START_REF] Czarnacki | Isotope fractionation in aqua-gas systems: Cl2-HCl-Cl -, Br2-HBr-Brand H2S-S 2[END_REF] can account for equilibrium fractionation properties of chloride in real aqueous solutions. Thus, the β-factor of the salts can be empirically assessed from Eq. (2), assuming that the reduced partition function ratio of aqueous chloride calculated by[START_REF] Czarnacki | Isotope fractionation in aqua-gas systems: Cl2-HCl-Cl -, Br2-HBr-Brand H2S-S 2[END_REF] (1000ln(β)=3.13 ‰ at 22 °C) matches that of saturated solutions and using the fractionation factors determined by[START_REF] Eggenkamp | Experimental determination of stable chlorine and bromine isotope fractionation during precipitation of salt from a saturated solution[END_REF]. Similarly, the β-factor of the Cl2 molecule can be obtained using the experimental data of[START_REF] Giunta | Chlorine isotope fractionation between chloride (Cl -) and dichlorine (Cl2)[END_REF]. The comparison of these empirical βfactors with the present theoretical ones reveal a high level of consistency for the Cl2 molecule and the hydrated Li, Mg, Ca and Sr salts, with a minor theoretical underestimation of the β-factors most likely due to the systematic bias related to the PBE functional (Fig.5). A more pronounced departure is observed for cubic salts (NaCl, KCl, RbCl, CsCl) and hydrated BaCl2, with the empirical values being systematically larger than the theoretical ones. The observed difference is always above 0.5 ‰ and can reach 1.5 ‰ for CsCl. In comparison, the difference between empirical and theoretical β-factors for Cl2 molecules is only 0.14 ‰, supporting the combination of the aqueous chloride β-factor computed byCzarnacki and Hallas (2012) with experimental fractionation factors to infer empirical β-factors of solids and molecules. Experimental measurements also provide isotopic composition values with typical errors smaller than ±0.1 ‰

Figure 1 :

 1 Figure 1: Reduced partition function ratio of HCl(g), Cl2(g), halite (NaCl(c)), sylvite (KCl(c))

Figure 2 :

 2 Figure 2: Comparison of theoretical and experimental vibrational frequencies in Cl2

Figure 3 :

 3 Figure 3: Theoretical β-factors at 22°C of anhydrous (full circles) and hydrated (empty

Figure 4 :

 4 Figure 4: Theoretical β-factors of minerals for temperatures above 450 K. Note the

Figure 5 :

 5 Figure 5: Comparison of empirical and theoretical β-factors at 22°C. Full and empty

Figure 6 :

 6 Figure 6: Estimated theoretical β-factor of aqueous chloride ions, obtained by combining

Figure 7 :

 7 Figure 7: Reduced partition function ratio of HCl(g) and HCl trihydrate. Note the cross-

Figure 8 :

 8 Figure 8: Isotopic fractionation factors between HCl(g) and other Cl-bearing molecules

Figure 1 :

 1 Figure 1: Reduced partition function ratio of HCl(g), Cl2(g), halite (NaCl(c)), sylvite (KCl(c)) and RbCl(c). Continuous lines: this study; dotted lines: Schauble et al. 2003; dashed lines: Richet al. 1977. Inset: comparison of β-factors at 0°C.

Figure 2 :

 2 Figure 2: Comparison of theoretical and experimental vibrational frequencies in Cl2

Figure 3 :Figure 4 :

 34 Figure 3: Theoretical β-factors at 22°C of anhydrous (full circles) and hydrated (empty

Figure 6 :

 6 Figure 6: Estimated theoretical β-factor of aqueous chloride ions, obtained by combining

Figure 7 :

 7 Figure 7: Reduced partition function ratio of HCl(g) and HCl trihydrate. Note the cross-

Figure 9 :

 9 Figure 9: Isotopic composition of remaining HCl(g) in a simple scenario of Rayleigh

Table 1 :

 1 Structure and vibrational stretching frequencies of diatomic molecules. Experimental harmonic frequencies[START_REF] Richet | A review of hydrogen, carbon, nitrogen, oxygen, and chlorine stable isotope fractionation among gaseous molecules[END_REF] are indicated in parenthesis.

		d (Å)	theo. -exp.	ω	35 Cl (cm	-1 )	theo. -exp.	ω	37 Cl (cm	-1 )	theo. -exp.
			(%)				(%)				(%)
	Cl2(g)	2.01 (1.98)	+1.5	538.4 (559.7)	-3.8	523.7 (544.4)	-3.8
	HCl(g)	1.29 (1.27)	+1.6	2888.2(2990.9)	-3.4	2886.0 (2988.7)	-3.4
	NaCl(g)	2.38		352.7			348.9
	KCl(g)	2.67		268.7			264.8

Table 2 :

 2 Structural and modeling parameters of the investigated crystalline phases. (c), (h), (m) and (o) stand for cubic, hexagonal, monoclinic and orthorhombic crystal systems, respectively.

	model		crystal	k-point	atoms/	cell parameters			theo. -exp.	ω TO (cm	-1 )	q-point
			syst.	grid	cell	(Å)				(%)		grid
	halite sylvite	NaCl KCl	(c) (c)	4x4x4 4x4x4	8 8	a = 5.69 (5.64) a = 6.38 (6.29)	a a		+0.9 +1.4	154 (164) 129 (142)	a a	4x4x4 4x4x4
	chloromagnesite	RbCl CsCl MgCl2	(c) (c) (h)	4x4x4 6x6x6 4x4x2	8 2 9	a= 6.70 (6.59) a= 4.21 (4.12) a = 3.68 (3.60)	a a b		+1.6 +2.1 +2.2	102 (116.5) 74 (99.5) a a	4x4x4 6x6x6 4x4x2
	bischofite	MgCl2.6(H2O)	(m)	2x2x2	42	c = 19.62 (17.59) a = 9.08 (9.86) c		+11.5 -7.9		1x1x1
						b = 7.39 (7.11)				+3.9
						c = 6.62 (6.07)				+9.0
		LiCl.H2O	(o)	2x2x2	40	β = 100.6° (93.7 °) a = 7.69 (7.58) d	+1.4		1x1x1
						b = 7.77 (7.68)			+1.2
		BaCl2.2(H2O)	(m)	2x2x2	36	c = 7.64 (7.62) a = 6.85 (6.72) e			+0.3 +1.9		1x1x1
						b = 11.76 (10.91)		+7.8
						c = 6.99 (7.13)				-1.9
		CaCl2.6(H2O)	(h)	3x3x3	21	β =90.06° (91.1°) a= 7.88 (7.88) f		+0.0		2x2x2
		SrCl2.6(H2O)	(h)	3x3x3	21	c= 4.04 (3.95) a= 7.97 (7.96)	f		+2.2 +0.0		2x2x2
	HCl tri-hydrate	HCl.3(H2O)	(m)	3x2x2	32	c= 4.21 (4.12) a = 4.07 (3.99) g		+2.2 +2.0		3x2x2
						b = 12.25 (12.05)		+1.7
						c = 6.75 (6.70)			+0.7
	chlorapatite	Ca5(PO4)3Cl	(h)	2x2x2	42	β = 101.1° (100.6 °) a = 9.86 (9.52) h	+3.6		fca
						c = 6.73 (6.85)			-1.7
	sodalite anthophyllite	Na8Al6Si6O24Cl2 Mg7Si8O22(OH)2	(c) (o)	2x2x2 1x1x2	46 164	a = 8.96 (8.89) a = 18.78 (18.50) j	i	+0.8 +1.5		fca fca
						b = 18.14 (17.90)		+1.3
	lizardite	Mg3Si2O5(OH)4	(h)	3x3x3	18	c = 5.33 (5.27) a = 5.37 (5.33)	j		+1.1 +0.8		fca
						c = 7.35 (7.25)			+1.4
	forsterite	Mg2SiO4	(o)	1x1x1		a = 9.60 (9.5)	k			+1.1		fca
				(2x1x2	112	b = 10.30 (10.19)		+1.1
				supercell)		c = 12.07 (11.96)		+0.9
	References: a Sirdeshmukh et al. (2001), b Wyckoff (1963), c Agron and Busing (1985),
	d Hönnerscheid et al. (2003), e Padmanabhan et al. (1978), f Agron and Busing (1986), g Lundgren
	and Olovsson (1967), h Hendricks et al. (1932), i Hassan et al. (2004), j Gregorkiewitz et al. (1996),
	k Fujino et al. (1981)

Table 3 :

 3 Cl coordination in crystals and relative energy of substitutional Cl-defects. 887 888 For each type of defect, the energy is computed with respect to that of the most stable configuration.

	model		Energy *	Coord.	distances (Å)	model	Coord.	distances (Å)
			kJ/mol
	forsterite	Si_Cl1	9.7	3 Mg, 3H	Mg: 2.44, 2 x 2.40 H: 2 x 1.98, 2.0	halite	6 Na	2.84
		Si_Cl1b	4.0	3 Mg, 2H	Mg: 2 x 2.39, 2.48 H: 2 x 1.95	sylvite	6 K	3.19
		Si_Cl2	44.3	3 Mg, 1H	Mg: 2.29, 2 x 2.31 H: 2.08	RbCl	6 Rb	3.35
		Si_Cl3	0	3 Mg, 1H	Mg: 2.33, 2.39, 2.42 H: 2.0	CsCl	8 Cs	3.65
		Mg_Cl1	0	2 Mg, 1Si	Mg: 2.39, 2.40 Si: 2.17	chloromagnesite	3 Mg	2.53
		Mg_Cl2	83.5	2 Mg, 1Si	Mg: 2.43, 2.47 Si: 2.04	bischofite	4 H	2.13, 2.17, 2.21, 2.23
		Mg_Cl3	94.9	2 Mg, 1Si	Mg: 2.41, 2.50 Si: 2.05	HCl tri-hydrate	4 H	2.03, 2.08, 2.11, 2.15
		Mg_Cl4	56.4	2 Mg, 1Si	Mg: 2.40, 2.51 Si: 2.08	chlorapatite	3 Ca	2.79
		Mg_Cl5	2.1	2 Mg, 1Si	Mg: 2.37, 2.51 Si: 2.14	sodalite	4 Na	2.74
	lizardite	Cl1	0	3 Mg	2.53	LiCl. H2O	4 Li, 2H	Li: 2.56, 2x2.67, 2.93 H: 2x2.20
		Cl2	47.4	3 Mg	2 x 2.42, 2.46	BaCl2.2(H2O)	2 H	2.11, 2.18
							2 H	2.12, 2.19
	anthophyllite Cl1	10	3 Mg	2.47, 2 x 2.48	CaCl2.6(H2O)	6 H	3x2.19, 3x2.28
		Cl2	0	3 Mg	2.45, 2 x 2.5
						SrCl2.6(H2O)	6 H	3x2.21, 3x2.26
	889
	890
	891

*

Table 4 :

 4 Polynomial fits of β-factor of crystals and molecules. The coefficients are defined by the relation: 10 3 ln(β)=ax+bx 2 +cx 3 +dx 4 where x=10 6 /T 2 and T is the temperature in Kelvin. Note that quadratic, cubic and quartic coefficients have no physical meaning and simply aim at reproducing the curvature of 10 3 ln(β) as a function of 10 6 /T 2 for Cl2, HCl molecule and HCl trihydrate.

	model		a *	10	6 /T	2	model	a *	b *		c*		d*	10	6 /T	2
				range								range
	forsterite	Si_Cl1	0.985	0-5		halite	0.253						0-13.4
		Si_Cl1b	0.944	0-5		sylvite	0.185						0-13.4
		Si_Cl2	1.124	0-5		RbCl	0.162						0-13.4
		Si_Cl3	0.988	0-5		CsCl	0.130						0-13.4
		Mg_Cl1	1.080	0-5		bischofite	0.243						0-13.4
		Mg_Cl2	1.295	0-5		LiCl.H2O	0.272						0-13.4
		Mg_Cl3	1.293	0-5		BaCl2.2(H2O)	0.263						0-13.4
		Mg_Cl4	1.173	0-5		CaCl2.6(H2O)	0.263						0-13.4
		Mg_Cl5	1.071	0-5		SrCl2.6(H2O)	0.254						0-13.4
	lizardite	Cl1	0.645	0-5		chloromagnesite	0.471						0-5
		Cl2	0.740	0-5		HCl tri-hydrate	0.319	-1.993 10	-3	3.951 10	-5	-3.629 10	-7	0-45
	anthophyllite Cl1	0.740	0-5		NaCl(g)	0.226						0-5
		Cl2	0.725	0-5		KCl(g)	0.175						0-5
	sodalite chlorapatite		0.234 0.418	0-5 0-5		Cl2(g) HCl(g)	0.6756 -6.557 10 0.9415 -0.1164	-3	8.684 10 9.165 10	-5 -3	-8.648 10 -2.728 10	-7 -4	0-13.4 0-13.4

*

Table 5 :

 5 Theoretical β-factor of chloride salts and Cl2 molecule at 22 °C.

	model	1000 ln(β) at 22°C
	halite	2.9
	sylvite	2.1
	RbCl	1.9
	CsCl	1.5
	bischofite	2.8
	LiCl.H2O	3.1
	BaCl2.2(H2O)	3.0
	CaCl2.6(H2O)	3.0
	SrCl2.6(H2O)	2.9
	Cl2(g)	7.0


Catherine Langlais

Laëtitia Marty

Olivier Sandre

Robert Whitney

Les Journées de la Matière Condensée 2018

Les Journées de la Matière Condensée 2018

La division de physique de la Matière Condensée de la Société Française de Physique (SFP) assure le lien entre toutes les communautés étudiant les propriétés physiques des liquides et des solides, qu'ils soient cristallins ou amorphes, aux échelles allant du nanomètre à celles du monde qui nous entoure. Elle regroupe des domaines aussi divers que la physique quantique, l'étude des surfaces, la structure et la dynamique des liquides et des verres, les transitions de phase, la nanotechnologie, l'interaction rayonnement-matière, les polymères, les cristaux liquides... Les interfaces thématiques y sont nombreuses, par exemple avec la physico-chimie, la mécanique, la biophysique... Cette division organise depuis trente ans les Journées de la Matière Condensée (JMC). Ces journées ont lieu les années paires, en alternance avec le Congrès général de la SFP qui se tient les années impaires. La qualité des intervenants, la pertinence des sujets abordés, en particulier à travers les minicolloques, et l'interdisciplinarité, font des JMC l'un des plus grands congrès de physique en France et l'une des plus grandes rencontres de la physique de la matière condensée. Ces journées constituent un moment essentiel dans la vie scientifique de cette communauté et rencontrent toujours un grand succès, succès confirmé lors de sa 16 e édition qui a rassemblé du 27 au 31 août 2018, sur le campus de l'Université Grenoble Alpes, environ 700 participants venus de toute la France et du monde francophone. L'origine de cette réussite réside dans un programme très riche, avec un panel de 25 orateurs pléniers ou semi-pléniers de tout premier plan, 33 minicolloques proposés et organisés par la communauté. Tous mettent en lumière les sujets phares en matière condensée et contribuent à l'interdisciplinarité au travers d'interventions orales et de posters (150). Cette année, l'accent a également été mis sur la place des femmes en science. Une table ronde plénière « Égalité des chances : un enjeu pour tous, hommes et femmes » organisée par la commission Femmes et Physique de la SFP et l'association Parité Sciences à Grenoble, a permis de débattre autour de deux thèmes : visibilité et harcèlement. Deux autres tables rondes semiplénières, ayant pour thèmes « Recherche et innovation en entreprise et emploi des docteurs » et le « Peer-review au 21 e siècle », ont aussi été très suivies. Il faut souligner ici l'effort particulier de l'équipe organisatrice pour attirer des femmes et des jeunes venant d'horizons géographiques divers. En prenant le parti de discuter d'abord des femmes qu'ils aimeraient inviter, puis de choisir des hommes permettant d'obtenir un bon équilibre thématique, 40% des présentations plénières et semi-plénières ont été données par des femmes. Par ailleurs, des instructions précises envoyées aux organisateurs des minicolloques, rappelant notamment que les JMC étaient une occasion pour les jeunes de présenter leur travail, ont permis d'atteindre un peu plus de 50% de jeunes intervenants dans ces minicolloques et près de 70% pour les posters. Mentionnons, pour terminer ce tour d'horizon, qu'en marge de ces journées le prix Charpak-Ritz, conjoint entre la SFP et la SPS (Société Suisse de Physique), et le prix Holweck, conjoint entre la SFP et l'IOP (Institute of Physics britannique), ont été remis respectivement à Roland Horisberger et Marina Galand. Ces grands prix de la SFP sont une excellente occasion de discuter avec les représentant.e.s de nos sociétés soeurs et d'examiner les actions communes possibles. Les prix Ancel 2016 et 2017 de la division Matière Condensée ont également été remis, avec pour lauréats Sara Ducci et Éric Collet. Au final, les échanges, le brassage d'idées, la convivialité ont été possibles grâce au soutien de nos partenaires, conférenciers, exposants, bénévoles, et aux congressistes que nous remercions ici très chaleureusement. Le rendez-vous est d'ores et déjà pris dans deux ans, à Rennes, pour une nouvelle édition des JMC ! Catherine Langlais (1) , Laëtitia Marty (2) , Olivier Sandre (3) et Robert Whitney (4) (1) Présidente de la SFP. (2) Présidente de la section Alpes de la SFP.

(3) Président de la division Matière Condensée de la SFP. (4) Président du comité local d'organisation.

Reflets de la Physique n° 59