Sébastien Brodeur

M.D. M.Sc Hugo Terrisse

Arnaud Pouchon

M.D. M.Sc Ophelia Godin

PhD Bruno Aouizerate

Valerie Aubin

Frank Bellivier

Raoul Belzeaux

Thierry Bougerol

M D Phd

Philippe Courtet

Caroline Dubertret

Sebastien Gard

Emmanuel Haffen

Chantal Henry

Marion Leboyer

Emilie Olié

Paul Roux

Ludovic Samalin

Raymund Schwan

The Fondamental

Disorders (FACE-BD Bruno Etain

Jean-Luc Bosson

Mircea Polosan
email: mpolosan@chu-grenoble.fr

P M Llorca

V Barteau

S Bensalem

H Laouamri

K Souryis

S Hotier

A Pelletier

N Drancourt

J P Sanchez

E Saliou

C Hebbache

J Petrucci

L Willaume

E Bourdin

G H Ap-Hp

Saint

M Carminati

E Marlinge

M Meyrel

C Hôpital

Centre Perrens

B Antoniol

A Desage

A Jutant

K Mbailara

I Minois

L Zanouy

C Abettan

L Bardin

A Cazals

B Deffinis

D Ducasse

M Gachet

A Henrion

E Martinerie

F Molière

B Noisette

G Tarquini

N Correard

F Groppi

A Lefrere

L Lescalier

E Moreau

J Pastol

M Rebattu

B Roux

N Viglianese

Nancy ; R Cohen

Raymond Schwan

J P Kahn

M Milazzo

O Wajsbrot-Elgrabli

A M Galliot

I Grévin

A S Cannavo

N Kayser

C Passerieux

M A Dupont

J Loftus

I Medecin

C Mazer

Portalier

C Moreau

D Lacelle

S Pires

C Doriat

O Blanc

R Cohen

B Fredembach

A Suisse

I Cussac

N Mazer

C Portalier

Bruno Godin

Valerie Aouizerate

Frank Aubin

Raoul Bellivier

Thierry Belzeaux

Philippe Bougerol

Caroline Courtet

Sebastien Dubertret

Emmanuel Gard

Chantal Haffen

Marion Henry

Emilie Leboyer

Christine Olié

Ludovic Passerieux

Raymund Samalin

Schwan

Pharmacological treatment profiles in the FACE-BD cohort: An unsupervised machine learning study, applied to a nationwide bipolar cohort

Keywords: Bipolar disorder, maintenance treatment, mood stabilizers, unsupervised machine learning, functioning

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Bipolar disorders (BD) are classified according to a clinical spectrum predominantly represented by bipolar 1 disorder (BD1) and bipolar 2 disorder (BD2). Fluctuations in energy and mood state are core features of this chronic disease [START_REF] Grande | Bipolar disorder[END_REF][START_REF] Vieta | Bipolar disorders[END_REF]. BD affect daily functioning and quality of life of people who suffer from it, mainly because of their early onset, the severity of the disease and the recurrence of episodes.

Acute treatment of mood relapses is essential, but because of the chronic nature of bipolar disorder, attention should also be emphasized on maintenance treatment [START_REF] Carvalho | Bipolar Disorder[END_REF]. Most patients with BD will require mood stabilizers as the basis of the maintenance treatment [START_REF] Yatham | Canadian Network for Mood and Anxiety Treatments (CANMAT) and International Society for Bipolar Disorders (ISBD) 2018 guidelines for the management of patients with bipolar disorder[END_REF]. Despite the emergence and development of new mood stabilizers since the 1960s, lithium remains the treatment of choice for maintenance therapy because of its efficacy in reducing the risk of relapses and recurrences (especially manic episodes) and its ability in maintaining sustained periods of remission [START_REF] Bauer | Lithium: about discrepancies between efficacy and clinical use[END_REF][START_REF] Hayes | Lithium vs. valproate vs. olanzapine vs. quetiapine as maintenance monotherapy for bipolar disorder: a population-based UK cohort study using electronic health records[END_REF][START_REF] Post | The New News about Lithium: An Underutilized Treatment in the United States[END_REF][START_REF] Tondo | Clinical use of lithium salts: guide for users and prescribers[END_REF]. However, the use of second generation antipsychotics, as mood stabilizers, remains very common in clinical practice [START_REF] Rhee | 20-Year Trends in the Pharmacologic Treatment of Bipolar Disorder by Psychiatrists in Outpatient Care Settings[END_REF].

Usually, the clinician will choose among several maintenance treatments proposed in the 1st and 2nd line options according to practice guidelines [START_REF] Yatham | Canadian Network for Mood and Anxiety Treatments (CANMAT) and International Society for Bipolar Disorders (ISBD) 2018 guidelines for the management of patients with bipolar disorder[END_REF]. Even when the clinician knows the bipolar subtypes accurately, they will proceed by a trial-and-error approach until they find a treatment that is effective and well tolerated by the patient [START_REF] Alda | Personalized management of bipolar disorder[END_REF]. This period can be very long and may bring consequences for the patient and substantial costs for the society [START_REF] Grande | Bipolar disorder[END_REF]. Also, it is surprising that, despite established treatment guidelines and known epidemiological factors predisposing to a good clinical response, it remains very difficult to individualize treatment. In this regard, there is great heterogeneity (López-Villarreal et al., 2019; [START_REF] Sarrazin | Neurodevelopmental subtypes of bipolar disorder are related to cortical folding patterns: An international multicenter study[END_REF][START_REF] Wolfers | Mapping the Heterogeneous Phenotype of Schizophrenia and Bipolar Disorder Using Normative Models[END_REF] among patients in terms of their clinical evolution, beyond the subtypes of bipolarity, but also in terms of their treatments [START_REF] Bauer | Areas of uncertainties and unmet needs in bipolar disorders: clinical and research perspectives[END_REF][START_REF] Bauer | Drug treatment patterns in bipolar disorder: analysis of longterm self-reported data[END_REF]. Usually, for one given patient, different treatments are tried and more often, in combination [START_REF] Bauer | Drug treatment patterns in bipolar disorder: analysis of longterm self-reported data[END_REF][START_REF] Fornaro | Prevalence and clinical features associated with bipolar disorder polypharmacy: a systematic review[END_REF]. In this context, it is mandatory to understand the treatment choices made by clinicians, in real clinical practice, and to figure out the rationale behind these choices. To date, few studies have succeeded in determining the prescribing patterns of clinicians treating bipolar patients.

In order to further understand the patient's treatment heterogeneity, some statistical methods are better suited to explore this variability (Passos et al., 2019a). More precisely, data mining methods render possible understanding of complex data from large datasets, through computer and statistical methods [START_REF] Iniesta | Machine learning, statistical learning and the future of biological research in psychiatry[END_REF]. Rather than proposing a hypothesis and verifying it with traditional statistical tests, data mining let the data speak by themselves (Passos et al., 2019b). Conventional methods are hypothesis-based and not designed to manage different variables from diverse modalities simultaneously (Menke, 2018). Machine learning has been used, in the last decade, for almost all psychiatric disorders. However, to date no study has attempted to find, in bipolar disorder, the different patterns of treatments, in a naturalistic way.

By using a large cohort of patients suffering from bipolar disorder in France, we tried to determine if groups of patients' profiles could be formed based on their treatments or combination of treatments, within a one-year period. Following this, the objective was to compare this new classification with the current bipolar subtypes classification.

MATERIAL AND METHODS

Study design

This multicentre longitudinal study was based on the patient database from FondaMental Advanced Centres of Expertise for Bipolar Disorders (FACE-BD) cohort. This cohort has been fully described elsewhere [START_REF] Godin | Trajectories of functioning in bipolar disorders: A longitudinal study in the FondaMental Advanced Centers of Expertise in Bipolar Disorders cohort[END_REF][START_REF] Henry | Bipolar patients referred to specialized services of care: Not resistant but impaired by sub-syndromal symptoms. Results from the FACE-BD cohort[END_REF][START_REF] Henry | A French network of bipolar expert centres: a model to close the gap between evidence-based medicine and routine practice[END_REF][START_REF] Henry | Outcomes for bipolar patients assessed in the French expert center network: A 2-year follow-up observational study (FondaMental Advanced Centers of Expertise for Bipolar Disorder[END_REF]. We searched for clusters of individuals based on their treatments during the first year following inclusion. We then compared the patient's baseline characteristics and one-year follow-up according to these clusters. We similarly compared the patients according to the usual bipolar subtypes.

Setting

The FACE-BD cohort recruited patients from a national network of 12 expert centres in France, set up by the French FondaMental Foundation (www.fondation-fondamental.org). General practitioners and psychiatrists referred outpatients with bipolar disorders to these Expert Centres. Recruitment started in June 2008. We extracted the data on 02/04/2019. The FACE-BD cohort includes a follow-up at 12, 24 and 36 months (respectively V12, V24 and V36).

The assessment protocol, including a letter of information for patients, was approved by the institutional review board (CPP-Ile de France IX, January 18th, 2010), in accordance with French laws for non-interventional studies. Anonymized data are stored in a national database that was approved by the French body overseeing the safety of computerized databases (Commission Nationale de l'Informatique et des Libertés, DR-2011-069).

Participants

Inclusion criteria for our study included an evaluation in one of the Expert center at baseline and at least one follow-up visit, a diagnosis of bipolar disorder and ambulatory patients between 18 and 65 years old. The criteria for non-inclusion were having a schizophrenia spectrum and other psychotic disorder diagnosis.

Variables

The structured clinical interview for DSM-IV Axis I disorders (SCID) [START_REF] First | Structured clinical interview for DSM-IV axis I disorders, clinician version (SCID-CV)[END_REF] was used for the diagnosis of bipolar disorders, as well as bipolar subtypes. We calculated days on treatment during the first year for each active ingredient. Hence, each patient can have up to 365 days on treatment for each active ingredient. Evaluation of patients at inclusion and V12 used clinical evaluation and biological measurements. Clinical evaluation at inclusion and V12 included characterisation of mood episodes within last year and questionnaires. Clinical evaluation at inclusion also included characterisation of mood episodes within lifetime. We evaluated the mood using the Montgomery and Asberg Depression Rating Scale (MADRS) (Montgomery and Asberg, 1979), the Young Mania Rating Scale (YMRS) [START_REF] Young | A rating scale for mania: reliability, validity and sensitivity[END_REF], the Quick Inventory of Depressive Symptoms 16 items (QIDS-SR16) [START_REF] Rush | The 16-Item Quick Inventory of Depressive Symptomatology (QIDS), clinician rating (QIDS-C), and self-report (QIDS-SR): a psychometric evaluation in patients with chronic major depression[END_REF] and the Altman Mania Rating Scale (AMRS) [START_REF] Altman | The Altman Self-Rating Mania Scale[END_REF]. We evaluated the global functioning using the Global Assessment of Functioning (GAF) [START_REF] Endicott | The global assessment scale. A procedure for measuring overall severity of psychiatric disturbance[END_REF] and the Functioning Assessment Short Test (FAST) [START_REF] Rosa | Validity and reliability of the Functioning Assessment Short Test (FAST) in bipolar disorder[END_REF]. We assessed the severity of the disease using the Clinical Global Impression-Severity scale (CGI-S) [START_REF] Guy | ECDEU assessment manual for psychopharmacology[END_REF]. We assessed the quality of sleep using the Pittsburgh Sleep Quality Index (PSQI) [START_REF] Buysse | The Pittsburgh Sleep Quality Index: a new instrument for psychiatric practice and research[END_REF]. At inclusion, we evaluated childhood trauma using the Childhood Trauma Questionnaire (CTQ) [START_REF] Bernstein | Childhood trauma Questionnaire, A retrospective Self-Report[END_REF] and childhood symptomatology of ADHD using the Wender Utah Rating Scale (WURS) [START_REF] Ward | The Wender Utah Rating Scale: an aid in the retrospective diagnosis of childhood attention deficit hyperactivity disorder[END_REF]. We evaluated adherence to pharmacological treatment using the Medication Adherence Rating Scale (MARS) [START_REF] Misdrahi | Therapeutic adherence and schizophrenia: the interest of the validation of the French translation of Medication Adherence Rating Scale (MARS)][END_REF] and side effects of treatments using the Patient Rated Inventory of Side Effects inventory (PRISE-M) [START_REF] Rush | Patient Rated Inventory of Side Effects (PRISE): unpublished rating scale[END_REF]. Biological measurements at inclusion and V12 were creatinine, HDL, LDL, total cholesterol, triglycerides, ASAT, ALAT, fasting blood sugar, platelets, TSH, T3 and T4.

Data sources/measurement

Expert Centres filled up the data through a web application, e-bipolar©. Clinicians reported all treatments received. We then computed the days on treatment for each active ingredient during the first year following inclusion. The QIDS-SR16, AMRS, PSQI, PRISE-M, MARS, WURS and CTQ were self-administered. The clinician administered the MADRS, YMRS, FAST, CGI-S and GAF.

Statistical methods

The available data determined the sample size. We analysed the quantitative variables without modification. We performed hierarchical agglomerative clustering to understand patterns of treatments for bipolar patients. The features we used to classify the patients were the days on treatment for each active ingredient present in the dataset during the first year following the inclusion. The distance metric was the squared Euclidean distance. We used Ward's agglomerative methods. We chose the number of clusters using the visual analysis of the dendrogram associated to the hierarchical agglomerative clustering and the interpretability of the groups. We then compared the clinical outcomes between the identified clusters. We used Chi-squared tests for categorical outcomes if all expected frequencies of the contingency table were higher than 5, else we used Fisher's exact test. We used ANOVA for continuous outcomes. For continuous outcomes at one-year follow-up, if the value at inclusion was available, we used ANCOVA instead of the ANOVA, to account for the inclusion value. We performed the same analysis for bipolar subtypes comparisons. All tests were bilateral, with a first-type error level of 0.05. As the purpose of this paper is to describe patient profiles, we did not correct for multiple testing. However, we provide all calculated p-values for transparency. We did not impute missing data and performed the analysis for complete cases only. We performed all analysis using R software version 3.6.3. As a post-hoc analysis, we compared the ANCOVA for the FAST scale using either the bipolar subtypes or the clusters using Akaike Information criterion (AIC). The lowest the AIC, the better the model explains the data.

RESULTS

3302 patients have been included in the FACE-BD cohort since the implementation of expert centers in France. 1494 patients were lost to follow-up after one year. 1808 patients were retained. Thirteen patients were excluded because they had inconsistent treatment dates. A total of 1795 patients were analyzed.

Patients within the study population had a median age of 41 years and consisted of 60.5% females and 39.5% males. Diagnosis of bipolar 1 was found in 865 patients, bipolar 2 in 764 patients and bipolar NOS in 166 patients. A proportion of 81.7% of the patients were referred to expert centers by a psychiatrist. Median age at first psychotropic treatment was 25-year-old and 21 at first mood episode. At baseline visit, 29.7% of patients had a current episode. In the last year before inclusion, 39% had been hospitalized at least once. At baseline, 69.9% of patients declared having complete remission between episodes. At inclusion, 39.5% of patients had attempted suicide in their lives. Results for the total included population can be found in Table 1 and supplementary material.

We found 117 different treatments in the database. Among these, 107 treatments were used by less than 5% of the study cohort during the first-year follow-up. The 10 others were: lithium (36.2%), valproate (30.1%), lamotrigine (20.7%), quetiapine (15.1%), aripiprazole (13.5%), venlafaxine (11.5%), escitalopram (7.9%), olanzapine (6.2%), alprazolam (6.2%), cyamemazine (6%). When these treatments were used, this was for more than 300 days throughout the study period (see complete data of treatment in supplementary material) for more information). Information regarding the other treatments can be found in supplementary material.

Main results

Hierarchical ascendant clustering

Hierarchical ascendant clustering (HAC) was performed with 117 treatments. The resulting dendrogram is represented in Figure 1.

At the dendrogram level, a cluster stood out from the classification immediately. This group had a significantly different treatment profile compared with the other groups established, even after several divisions in the number of patients. This is followed by other divisions in the dataset. Overall, four groups were selected for their size and clinical relevance and by using the Calinski function on RStudio. That method initially suggested that we should choose between 2 clusters. However, this choice of cluster was purely statistical and had no clinical relevance as we would end up with a group of 1530 patients and 265 patients. Subsequently, in order to be as comprehensive as possible but also keeping in mind the clinical perspective, Calinski function suggested that the optimal division choice was 4 clusters. This division in four groups is represented by the red line on the Dendrogram Cluster (Fig 1).

The first group in the classification represented 1099 out of 1795 included patients. The treatments received during one year in this group were mainly: lithium (27.8%), valproate (24.3%), quetiapine (18.1%) and aripiprazole (15.7%). Group 2 was the one that stood out to the right during the first division of the dendrogram and consisted of 265 patients. The treatments received during one year in this group were mainly: lithium (99.2%), lamotrigine (23.4%) and venlafaxine (17%). Group 3 consisted of 268 patients and the main treatments were mainly valproate (88.4%), venlafaxine (33.2%) and lithium (18.3%). Group 4 consisted of 163 patients. The treatments received during one year in this group were mainly: lamotrigine (93.9%), quetiapine (27.6%) lithium (19.6%) and aripiprazole (17.2%) (see Figure 2). In the rest of the paper, we will refer to group 1 as "heterogeneous", group 2 as "lithium", group 3 as "valproate" and group 4 as "lamotrigine". (Figure 2 andTable 2.1) Clinical description according to clusters (Tables 2.2 and 2.4) Group "heterogeneous" had a higher proportion of BD1 (48.2%) versus BD2 (41.8%). Group "lithium" was formed by a higher proportion of BD1 (57.0%) while there was a higher proportion of BD2 (57.1%) in the group "lamotrigine" compared with the other groups. The median age was higher (43 [34.8; 53]) in group "valproate". There was no statistically significant difference in the type of referring doctors, as well as in the occupational status of the different patients from the individualized groups. The first three groups had received a similar number of treatments in the year of follow-up (median =2). Group 4 had used more treatments during the year of follow-up (median=3). Duration of disease prior to inclusion was comparable in the first three groups (median=15 years) except in the "lamotrigine" group with a median of 14 years.

Groups "heterogeneous" and "lithium" started psychotropic treatment at a younger age than other groups. At first episode, patients were older in group "valproate" (23 [18; 31]). At the lifetime assessment level, patients in all groups had at least one MDE in greater proportion compared to other types of mood episodes. Group "lithium" had a higher proportion of patients who had at least one-lifetime manic episodes (53.1%) as well as manic episodes with psychotic characteristics (39.8%). There was a higher proportion of rapid cycles in the group "lamotrigine" (28.5%). There was no statistically significant difference between groups in the number of patients hospitalized at V12. At the initial visit, patients had mainly MDE in the past year compared with other types of episodes. Also, the group "lithium" had more manic episodes with (15.2%) and without (22.1%) psychotic characteristics in the last year, at the initial visit. There was no statistically significant difference in patients who already attempted suicide between the different clusters established at the initial visit and at V12. The proportion of patients with a current episode, at V12, decreased in all groups compared to the initial visit.

Self-administered questionnaire (Table 2.3)

On the QIDS-SR16 questionnaire at the initial visit, group "lamotrigine" had a higher score (11 [6; 16]) and was in the moderate depression category (11)(12)(13)(14)(15). The decrease in depressive symptoms was greater in this same group at V12 (6 [4; 12]). On the ALTMAN scale, the four clusters had a score of less than 5 and indicated a low probability of a manic or hypomanic episode, at both initial and follow-up visits. On the PSQI scale, the scores of each cluster at the initial visit exceeded the threshold of more than 5 indicating sleep problems for most patients. On the WURS scale, the median score of patients in all subtypes was less than 46, suggesting the absence of ADHD in childhood. Side effects were assessed using the PRISE-M scale on a range of 0 to 62 (62 corresponding to a maximum of side effects). Groups "heterogeneous" (12 [6; 19]) and "lamotrigine" (13 [6; 19.8]) had more side effects from their treatment than groups "lithium" and "valproate". Adherence to treatment was similar across all clusters according to MARS scale.

Clinician administered scale (Table 2.3)

On the MADRS scale, patients in groups "lithium" and "valproate" had a lower score, while patients in groups "heterogeneous" and "lamotrigine" had greater depressive symptoms, both at baseline and V12. All groups showed an improvement between baseline and V12. Based on YMRS scale, patients had no hypomanic/manic symptoms at either V0 or V12.

All groups had functional impairment on the FAST scale at baseline. A score of 12 or more indicated problems with functioning in daily life. Group "lamotrigine" had a higher median score (22 [12.8; 29]) than other clusters. At V12, group "lithium" had the lowest scores on the FAST scale (10 [3; 22]), and more than 50% of them did not have functioning impairment. As well, group "valproate" had a median score of (12 [3; 23]) in the lower portion of the diagnostic threshold for functional problems on this scale. For the treatment profiles classification, the AIC was 9253 for the ANOVA at V0 and 6957 for the ANCOVA at V12. For bipolar subtypes classification, the AIC was 9258 for the ANOVA at V0 and 6960 for the ANCOVA at V12. This indicates that treatment profiles better explain the FAST at baseline and its evolution at V12 than bipolar subtypes.

On the CGI scale, most patients were in the mildly-ill category, both at baseline and V12, in all clusters. At V12 only group "lithium" had changed category with a median score of 2 [1; 4] indicating the category "borderline mentally ill". On the Global Assessment of Functioning Scale [GAF] at V0, there were more patients in the 100-71 category [absent or transient symptoms] and 70-51 [mild symptoms of moderate intensity] with no statistically significant difference between groups established. At V12, Group "lithium" patients had a higher proportion in category 71-100 GAF [59.2%], and a lower proportion in the category 50-0.

Psychiatric and somatic comorbidities (Table 2.5)

There was a higher proportion of comorbid anxiety disorders in cluster "lamotrigine" (51.6%), as well as feeding and eating disorders [30.7%]. At the somatic level, there was a higher proportion of hypertension (11.6%) and hair loss (20.8%) in group "valproate". However, there was a higher proportion of thyroid disease (17.4%) in the group "lamotrigine". There was no clinically relevant difference between clusters according to the BMI level.

Biological parameters

There was no clinically relevant difference in blood parameters between the different groups.

DISCUSSION

Key results

Our study demonstrated that hierarchical ascending classification categorized patients according to different pharmacological treatment profile. In fact, four groups were identified, from the treatments they received, over a period of one year: group "heterogeneous", group "lithium", group "valproate" and group "lamotrigine". Groups "heterogeneous" and "lamotrigine" had a more pronounced depressive symptomatology and greater functional impact, at baseline, compared with groups "lithium" and "valproate". Despite this difference already existing at baseline between the 4 groups, group "lithium" and group "valproate" had a more favourable evolution based on different clinical scales, especially the ones measuring functioning (GAF, FAST). Moreover, these findings do not seem to be influenced by the duration of disease prior to inclusion and neither by the number of treatments used during the follow-up period.

This new classification seems to demonstrate clinical relevance. In fact, patients in group "lithium" were functioning better. Furthermore, these treatment clusters were formed beyond classical bipolarity subtypes. Treatments received during the one-year period, either in mono or polytherapy, seemed to further explain the functional evolution of the patients during this one-year follow-up.

Strengths

We obtained data from all patients (1795 patients) followed in FondaMental Academic Centres of Expertise for Bipolar Disorders, in France. This brings us results, with an interesting scope, since they reflect a population of specialized clinics, across a whole country. This is even more relevant, since randomized controlled clinical trials sometimes struggle to include population that reflects the clinical reality (Vieta et al., 2018). Moreover, data obtained for each patient were exhaustive (self-administered scales, clinicianadministered scales, blood tests, etc.). Also, the methods used (data mining) made possible the exploitation of a large data set and allowed to find relevant links between these same data.

Finally, using individualized drugs instead of drug classes permitted to exploit the data set without any boundary.

Interpretation

Based on results obtained, treatment used over one-year period seems to better predict functional prognosis than bipolar subtypes. Previous literature highlighted the differences in terms of functional evolution for bipolar disorder subtypes 1 and 2 (Yatham et al., 2018). Beyond bipolarity subtypes, patients predominantly treated with lithium in our cohort during one-year follow-up, were doing better than all other patients in other clusters. Beyond clinical scores, which were all improved in all clusters, functioning in group "lithium" was improved in a clinically relevant way and also in a statistically significant manner. This finding is consistent with what is stated by some authors about the place that lithium should deserve in BD1 and BD2 patients (Tondo et al., 2019); this adding up to lithium's potential neuroprotective effects (Hozer et al., 2020). This is even more important since functioning is a therapeutic target which has been lately studied, even in euthymic patients with BD (Léda-

Rêgo et al., 2020; Sole et al., 2018).

Treatment of bipolar disorders is heterogenous in clinical practice (Bauer et al., 2013) as shown by the use of several mood-stabilizing treatments. In the same way, for more than half of the patients it was difficult, according to our methodology, to group them solely based on treatment. These patients were clustered in group "heterogeneous" (n=1099). This strong heterogeneity is in itself a reality, but could it be a different phenotype of the disease or a sign of the non-systematic use of first-line drugs by clinicians? Side effects associated with lithium and valproic acid intake are often a hindrance for clinicians in their daily practice. However, our study shows fewer side effects in groups that had many patients treated with these drugs (groups "lithium" and "valproate"), compared with groups "heterogeneous" and "lamotrigine". In addition, renal, metabolic and thyroid blood tests were comparable in all four groups. Given our current results, concerns about side effects associated with lithium do not seem to be that justified compared to other treatments although based on the short maintenance period.

Limitations

One of the major limitations of the study remains the duration of the analysis. Indeed, the oneyear period under mood stabilization remains short in the course of bipolar disease. In addition, drug dosage was not taken into account in our study in order to form different clusters. Previous treatment section prior to inclusion had a high rate of missing data potentially due to recall bias, which limited this data analysis. Also, patients could be recruited at any stage of the illness in our study. Nevertheless, the duration of illness prior to inclusion didn't have an impact on our results. In fact, the duration of illness prior to inclusion in our new clusters was very similar. Also, non-pharmacological treatment section of the database was not thoroughly documented, such as psychotherapy. Moreover, combination of pharmacological and non-pharmacological treatments would have been very useful to better understand the impact of combining these two approaches. In addition, due to missing data regarding the total number of thymic episodes, patient polarity index was not calculated. Based on the chosen methodology and our database, all the reasons behind clinician's choice for maintenance treatment were not exhaustively available for analysis. Unsupervised machine learning does not have the same aim as a randomized controlled trial (RCT). In fact, it can help revealing new findings among clinical data from patients we encounter in daily practice. Moreover, it can generate a hypothesis which can be further explored through RCTs. In that sense, these results remain exploratory and should therefore be interpreted with caution. Despite these limitations, observational studies are well known for their nonrestrictive inclusion criteria and to be more representative of real-life patients followed up in specialized clinics.

In conclusion, treatment profiles were associated with functional evolution of patients and were not clearly determined by bipolar subtypes. These findings do not seem to be influenced by the duration of disease prior to inclusion and neither by the number of treatments used during the follow-up period. This sheds light on future research to better understand these specific phenotypes beyond bipolar subtypes defined by the DSM-5. An additional question would be to determine what factors predict accurately the odds to be part of one group or another at baseline visit. Our findings encourage the use of supervised machine learning approaches to better predict the clinical response, functional evolution and side effects to different treatments.

DISCLOSURE

Dr. Brodeur, H. Terrisse, Dr. Pouchon, O. Godin, Dr. Aubin, Dr. Bellivier, Dr. Belzeaux, Dr. Bougerol, Dr. Courtet, Dr. Dubertret, Dr. Gard, Dr. Henry, Dr. Leboyer, Dr. Roux, Dr. Schwan, Dr. Bosson have nothing to disclose. Dr. Aouizerate reports personal fees from Janssen-Cilag, personal fees from Lilly, personal fees from Sanofi, during the conduct of the study. Dr. Haffen reports personal fees and non-financial support from Janssen, personal fees and non-financial support from Lundbeck, personal fees and non-financial support from Otsuka, outside the submitted work. Dr. Olié reports personal fees from Janssen-Cilag, outside the submitted work. Dr. Samalin reports personal fees and non-financial support from Janssen, personal fees and non-financial support from Lundbeck, personal fees and nonfinancial support from Otsuka, outside the submitted work.. Dr. Etain reports grants from INSERM, grants from Assistance Publique des Hôpitaux de Paris, grants from Agence Nationale pour la Recherche, grants from Fondation de France, grants from Research Council of Norway, personal fees from SANOFI, outside the submitted work. Dr. Polosan reports personal fees from Lundbeck, personal fees from Janssen-Cilag, outside the submitted work.

The FondaMental Advanced Centers of Expertise in Bipolar Disorders (FACE-BD) Collaborators have no conflicts of interest to disclose except PM Llorca. PM Llorca has received grants, honoraria, or consulting fees from ESAI, Gedeon Richeter, Janssen, Lundbeck, Otsuka and Sanofi.

FUNDING

This work was supported (in part) by the Fondation FondaMental, Créteil, France and by the Investissements d'Avenir programs managed by the ANR under references ANR-11-IDEX-0004-02 and ANR-10-COHO-10-01. This funding source had no role in the study design, data collection, analysis, preparation of the manuscript, or decision to submit the manuscript for publication. M Polosan had full access to all the data in the study and takes responsibility for the integrity of the data and the accuracy of the data analysis. Figure 1 :

Treatment received during one-year follow-up period (bipolar disorder subtypes): The treatments received during one year in bipolar disorder 1 were mainly: lithium (44 %), valproate (32.9%), lamotrigine (15.4), quetiapine (15.3%) and aripiprazole (17.3%). As for bipolar disorder 2, they received lithium (30.8%), valproate (28.4%), lamotrigine (25.4), quetiapine (15.8%) and aripiprazole (9.8%). Finally regarding, bipolar disorder NOS, patients received mainly lithium (19.9 %), valproate (23.5%), lamotrigine (26.5), quetiapine (10.8%) and aripiprazole (10.2%).

Treatment received during one-year follow-up period (treatment clusters): The treatments received during one year in group 1 were mainly: lithium (27.8%), valproate (24.3%), quetiapine (18.1%) and aripiprazole (15.7%). The treatments received during one year in group 2 were mainly: lithium (99.2%), lamotrigine (23.4%) and venlafaxine (17%). The main treatments in group 3 were mainly valproate (88.4%), venlafaxine (33.2%) and lithium (18.3%). The treatments received during one year in group 4 were mainly: lamotrigine (93.9%), quetiapine (27.6%) lithium (19.6%) and aripiprazole (17.2%).

  The profiles formed according to the treatments seem to group together common patient phenotypes. Could this additional classification explain common pathophysiological mechanisms? This way of conceptualizing bipolar disorders, which is different from the current classification is being studied by other groups (Fuente-Tomas et al., 2019; Tamminga et al., 2017).

Figure 1 :

 1 Figure 1: Days on treatment for each active ingredient present in the dataset, during the first year following the inclusion, were used to classify patient. The division in four groups was suggested by Calinski function on RStudio and is represented by the red line on the dendrogram cluster.

Figure 1 :Figure 1 :

 11 Figure 1 : cluster dendrogram :

Figure 2 :

 2 Figure 2: Treatment received during one-year follow-up period:

Table 1 : Subtypes of bipolar disorder

 1

	Name of variable	Type 1	Type 2	NOS	Total population	p value
			n (%) or median [Q1; Q3]
	N	865	764	166	1795
	Age	39 [31; 48]	43 [33; 52]	44.5 [33.2; 54]	41 [32; 50]	8.6 x 10 -7
	Gender					8.9 x 10 -3
	Woman	492 (56.9)	490 (64.4)	102 (61.4)	1084 (60.5)
	Men	372 (43.1)	271 (35.6)	64 (38.6)	707 (39.5)
	Referring doctor					2.5 x 10 -4
	Psychiatrist	676 (86.1)	551 (77.8)	119 (76.8)	1346 (81.7)
	General practionner	70 (8.9)	113 (16.0)	25 (16.1)	208 (12.6)
	Other	39 (5.0)	44 (6.2)	11 (7.1)	94 (5.7)
	Education level (years)	15 [12; 17]	14 [12; 16]	14 [11; 16]	14 [12; 17]	1.1 x 10 -3
	Occupational status					4.7 x 10 -1
	Active	429 (57.3)	413 (60.7)	88 (62.0)	930 (59.2)
	Unemployed	152 (20.3)	124 (18.2)	21 (14.8)	344 (21.9)
	Other	168 (22.4)	143 (21.0)	33 (23.2)	297 (18.9)
	Age at first psychotropic treatment V0	24 [19; 31]	27 [20; 37]	25.5 [20; 35.8]	25 [20; 34]	6.5 x 10 -10
	Age at first episode	21 [17; 27]	22 [17; 30]	22 [17; 31.5]	21 [17; 29]	1.1 x 10 -3
	Duration of illness before V0	15 [8; 23]	15 [9; 25]	16 [8; 27]	15 [8; 24]	3.37 x 10 -2
	Number of treatments received during one-year follow-up	2 [1; 3]	2 [1; 3]	2 [1; 3]	2 [1; 3]	1.27 x 10 -1
	Actual mood episode
	V0	216 (25.6)	249 (33.5)	53 (33.3)	518 (29.7)	1.5 x 10 -3
	At least one hospitalization
	V0	303 (50.1)	157 (28.4)	36 (31.6)	496 (39.0)	9.2 x 10 -14
	Complete remission between episodes V0	532 (73.1)	429 (66.2)	91 (70.0)	1052 (69.9)	2.1 x 10 -2
	Number of patient who already attempts suicide
	Lifetime V0	303 (36.4)	305 (40.9)	79 (48.8)	687 (39.5)	7.1 x 10 -3
	V0 = baseline visit
	V12= one-year follow-up visit

Table 2 : Clusters 2.1: Treatment received for clusters

 2

	Name of variable	Group 1	Group 2	Group 3	Group 4	p value
		"heterogeneous"	"lithium"	"valproate"	"lamotrigine"
			n (%) or median [Q1; Q3]
	N	1099	265	268	163
	Number of treatments received during one year follow-up	2 [1; 3]	2 [1; 3]	2 [1; 3]	3 [2; 4]	1.41 x 10 -5
	Treatment received, n (%)
	lithium	305 (27.8)	263 (99.2)	49 (18.3)	32 (19.6)
	valproate	267 (24.3)	22 (8.3)	237 (88.4)	15 (9.2)
	lamotrigine	142 (12.9)	62 (23.4)	14 (5.2)	153 (93.9)
	quetiapine	199 (18.1)	11 (4.2)	16 (6)	45 (27.6)
	aripiprazole	173 (15.7)	13 (4.9)	28 (10.4)	28 (17.2)
		55 (5)	45 (17)	89 (33.2)	18 (11)
	escitalopram	115 (10,5)	10 (3,8)	7 (2,6)	9 (5,5)
	olanzapine	76 (6.9)	13 (4.9)	13 (4.9)	10 (6.1)
	alprazolam	95 (8.6)	6 (2.3)	6 (2.2)	4 (2.5)
	cyamemazine	75 (6.8)	16 (6)	10 (3.7)	6 (3.7)

At least one mixed episode with psychotic features

	Last year V12 ‡		22 (2.5)	2 (0.9)	4 (1.7)	5 (3.8)	3.1 x 10 -1
	V0 = baseline visit, V12= one-year follow-up visit
	†= adjusted for V0
	‡,=Fisher test
	2.5: Comorbidities for clusters
	Name of variable		Group 1	Group 2	Group 3	Group 4	p value
			"heterogeneous"	"lithium"	"valproate"	"lamotrigine"
			n (%) or
			median [Q1;
			Q3]
	N		1099	265	268	163
	Psychiatric comorbidities V0
	Current smoking		473 (44.6)	107 (42.1)	111 (42.7)	62 (39.0)	5.5 x 10 -1
	Anxiety disorders		459 (45.8)	85 (35.4)	109 (44.5)	81 (51.6)	7.8 x 10 -3
	Substance use disorders:	349 (34.5)	72 (30.0)	74 (29.7)	49 (31.6)	3.5 x 10 -1
	Alcool use disorder	243 (24.0)	42 (17.5)	52 (20.9)	40 (25.8)	1.1 x 10 -1
	Cannabis use disorder	186 (18.4)	46 (19.2)	36 (14.5)	17 (11.0)	6.7 x 10 -2
	Feeding and Eating Disorder	189 (18.7)	32 (13.2)	41 (16.6)	47 (30.7)	1.7 x 10 -4
	Somatic Symptom and Related Disorder	39 (3.9)	5 (2.1)	13 (5.2)	8 (5.2)	2.8 x 10 -1
	Somatic comorbidities V0
	Neurologic disease:
	Migraine		208 (20.0)	50 (19.7)	51 (20.3)	40 (25.8)	4.0 x 10 -1
	Epilepsy ‡		17 (1.6)	6 (2.4)	3 (1.2)	2 (1.3)	8.0 x 10 -1
	Head trauma		132 (12.8)	38 (15.2)	33 (13.3)	23 (15.0)	7.1 x 10 -1
	Cardiovascular disease:
	Arrythmia		33 (3.2)	10 (4.0)	9 (3.6)	8 (5.3)	6.2 x 10 -1
	Hypertension		62 (6.0)	23 (9.1)	29 (11.6)	14 (9.2)	1.2 x 10 -2
	Metabolic and endocrine disorders:
	Diabetes ‡		29 (2.8)	4 (1.6)	12 (4.9)	5 (3.2)	1.8 x 10 -1
	Thyroid disease		99 (9.6)	36 (14.3)	33 (13.2)	27 (17.4)	9.6 x 10 -3
	Dyslipidemia		185 (18.0)	30 (12.0)	43 (17.3)	21 (13.6)	9.1 x 10 -2
	Skin disease:
	Acne		134 (13.0)	35 (13.9)	36 (14.4)	28 (18.2)	3.8 x 10 -1
	Cutaneous adverse drug reactions	86 (8.3)	16 (6.4)	11 (4.4)	13 (8.4)	1.6 x 10 -1
	Hair loss		148 (14.3)	29 (11.5)	52 (20.8)	20 (13.0)	1.9 x 10 -2
	Urinary tract disorder:
	Nephropathy ‡		33 (3.2)	3 (1.2)	4 (1.6)	1 (0.6)	9.3 x 10 -2
	Gastro-intestinal disorder:
	V0 ‡ Drug-induced hepatitis ‡	15 (1.5) 14 (1.4)	5 (2.1) 3 (1.2)	4 (1.8) 3 (1.2)	2 (1.4) 2 (1.3)	8.8 x 10 -1 1.0
	V12 ‡ BMI		8 (1,0)	0 (0,0)	3 (1,4)	0 (0,0)	3.5 x 10 -1
	V0		25.2 [22.5; 28.7]	24.9 [22.2; 27.9]	24.5 [22.4; 28.4]	24.7 [22.4; 29.0]	4.8 x 10 -1
	At least one hospitalization V12	25.4 [22,6 ; 29,1]	24.5 [21,9 ; 28,2]	24.8 [22,6 ; 28,4]	24.7 [22,1 ; 28,5]	4.1 x 10 -5
	V0		305 (38.7)	89 (47.1)	61 (35.1)	41 (34.2)	5.6 x 10 -2
	V12	V0 = baseline visit, V12= one-year follow-up visit	109 (14,4)	21 (11,6)	18 (9,4)	18 (15,9)	2.2 x 10 -1
		†= adjusted for V0
	Lifetime V0	‡,=Fisher test
	At least one MDE		863 (95.9)	210 (94.6)	208 (96.7)	131 (99.2)	1.6 x 10 -1
	At least one MDE with psychotic features	97 (9.7)	24 (9.9)	25 (10.4)	5 (3.4)	7.9 x 10 -2
	At least one hypomanic episode	609 (76.3)	149 (78.8)	136 (75.1)	98 (83.1)	3.4 x 10 -1
	At least one manic episode	460 (46.0)	128 (53.1)	104 (43.3)	41 (26.5)	2.7 x 10 -6
	At least one manic episode with psychotic features	322 (31.6)	97 (39.8)	58 (23.7)	18 (11.7)	4.7 x 10 -9
	At least one mixed episode	177 (19.2)	45 (19.8)	43 (20.0)	23 (16.8)	8.8 x 10 -1
	At least one mixed episode with psychotic features	66 (6.5)	16 (6.7)	15 (6.3)	4 (2.7)	3.2 x 10 -1
	Rapid cycling V0		130 (13.6)	38 (16.8)	29 (12.8)	41 (28.5)	4.1 x 10 -5
	Complete remission between episodes V0	638 (69.3)	164 (71.9)	162 (73.6)	88 (64.2)	2.4 x 10 -1
	Seasonal pattern V0	314 (32.8)	77 (33.3)	80 (35.4)	50 (36.0)	9.5 x 10 -1
	Number of patient who already attempts suicide
	Lifetime V0		439 (41.4)	93 (36.6)	89 (33.5)	66 (41.2)	7.9 x 10 -2


Frédéric Moynier

Yan Hu

Kun Wang

Ye Zhao

Yvan Gérard

Zhengbin Deng

Julien Moureau

Weiqiang Li

Fang-Zhen Justin I Simon

Fang-Zhen Teng

Potassium isotopic composition of various samples using a dual-path collision cell-capable multiple-collector inductively coupled plasma mass spectrometer, Nu instruments Sapphire

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Introduction

Potassium is a major or an important minor element in most geological and biological environments. Potassium is the 20 th most abundant element in the Sun, and the 17 th on Earth [START_REF] Palme | Solar System Abundances of the Elements[END_REF]. Due to its incompatible behavior during magmatic processes, K is highly enriched in the continental crust, which is a major terrestrial reservoir that contains ≈24% of the total K [START_REF] Rudnick | Composition of the Continental Crust[END_REF]. It is also a highly water-soluble element and a major cation in seawater [START_REF] Bruland | The control of trace metals in seawater[END_REF]. In biological systems, K is fundamental in cell biochemical reactions, energy metabolism, and is essential to cellular osmotic regulation and the propagation of the nerve impulses through cell membranes (e.g. [START_REF] Carver | Essential Metals in Medicine: Therapeutic Use and Toxicity of Metal Ions in the Clinic[END_REF]. It is inferred to be one of the light elements in the terrestrial [START_REF] Gessmann | Potassium in the Earth's core?[END_REF] and lunar [START_REF] Steenstra | Depletion of potassium and sodium in mantles of Mars, Moon and Vesta by core formation[END_REF] cores due to its siderophile behavior under high-pressure conditions. Moreover, K is a moderately volatile lithophile element (temperature of 50 % condensation = 1006 K, [START_REF] Lodders | Solar System abundances and condensation temperatures of the elements[END_REF], with an abundance that varies greatly between planetary bodies and understanding the origin of these variations may hold clues to the mechanisms of planetary formation (e.g. [START_REF] Humayun | Potassium isotope cosmochemistry: Genetic implications of volatile element depletion[END_REF].

Potassium has 2 stable isotopes: 39 K (93.258 %) and 41 K (6.730 %) and a longlived radioactive isotope ( 40 K, T1/2=1.248×10 9 years, 0.0117 %). In this work, the isotope composition of K refers to the mass-dependent fractionation of stable isotopes 39 K and 41 K. The difference in the ratio of 41 K/ 39 K can be used to decipher the different processes governing the origin of its abundance variations (e.g. evaporation/condensation, core formation, magmatic processes, weathering, disease affecting it imbalance in the organism). For example, [START_REF] Wang | Potassium isotopic evidence for a high-energy giant impact origin of the Moon[END_REF] found that the Moon is isotopically heavier in K isotopes compared to the Earth, and suggested that this reflected volatile events during Moon formation.

While potassium is one of the elements with the lowest first ionization potential, ≈4.34 eV (https://physics.nist.gov/PhysRefData/ASD/ionEnergy.html), there have been relatively limited high precision isotopic studies because of major drawbacks on both multi-collector thermo-ionization (TIMS) and inductively-coupled plasma (MC-ICP-MS) mass spectrometers and in-situ measurements by secondary ion mass spectrometers (SIMS) returned precision of ≈ 0.5 ‰ [START_REF] Humayun | Potassium isotope cosmochemistry: Genetic implications of volatile element depletion[END_REF]. Because K has only 3 natural occurring isotopes, it is not possible to correct for instrumental mass bias by double spike addition which therefore limits the precision that can be obtained for stable isotope ratios by TIMS to ≈1 ‰ at best (e.g. [START_REF] Verbeek | Variations in 39K: 41K ratio and movement of potassium in a granite-amphibolite contact region[END_REF]. On the other hand, MC-ICP-MS has become the instrument of choice to analyze elements with 2 or 3 stable isotopes mostly because of its rapid sample throughput and compatibility with sample-standard bracketing method for mass bias correction (e.g. Lu, [START_REF] Blichert-Toft | Separation of Hf and Lu for highprecision isotope analysis of rock samples by magnetic sector-multiple collector ICP-MS[END_REF], Cu [START_REF] Maréchal | Precise analysis of copper and zinc isotopic compositions by plasma-source mass spectrometry[END_REF]). However, ionization is obtained in an Ar plasma for conventional MC-ICP-MS, which generates major isobaric interferences as 38 ArH + , 40 Ar + and 40 ArH + on 39 K, 40 K and 41 K, respectively, which makes high-precision K isotopic measurements more cumbersome than for most elements. One approach to circumvent these problems has been to limit argides generation at a decreased Ar plasma temperature and to resolve the interferences at an increased mass resolution (e.g. [START_REF] Chen | High-precision potassium isotopic analysis by MC-ICP-MS: an inter-laboratory comparison and refined K atomic weight[END_REF][START_REF] Hu | High-precision analysis of potassium isotopes by HR-MC-ICPMS[END_REF][START_REF] Morgan | High-precision 41K/39K measurements by MC-ICP-MS indicate terrestrial variability of δ41K[END_REF][START_REF] Tuller-Ross | Potassium isotope systematics of oceanic basalts[END_REF][START_REF] Xu | Potassium isotopic compositions of international geological reference materials[END_REF].

Using this technique, 41 K/ 39 K reproducibility as precise as ≈50 ppm (2SE) can be obtained but it necessitates the use of over 5 µg of K [START_REF] Chen | High-precision potassium isotopic analysis by MC-ICP-MS: an inter-laboratory comparison and refined K atomic weight[END_REF][START_REF] Hu | High-precision analysis of potassium isotopes by HR-MC-ICPMS[END_REF][START_REF] Xu | Potassium isotopic compositions of international geological reference materials[END_REF]. Recently [START_REF] Chen | Potassium isotope fractionation during chemical weathering of basalts[END_REF] also achieved a similar precision with a dry plasma method where an Apex Omega desolvating nebulizer system was used to suppress the formation of argon hydrides without lowering the RF power. Alternatively, collision cell MC-ICP-MS, theoretically allows the reduction of the amount of charged argides via collision and reaction with a neutral or reactive gas. Until recently [START_REF] Ku | Potassium isotope anomalies in meteorites inherited from the protosolar molecular cloud[END_REF], only the Micromass Isoprobe, which is an older generation single-focusing MC-ICP-MS had been equipped with such collision cell. For example, [START_REF] Li | Precise measurement of stable potassium isotope ratios using a single focusing collision cell multi-collector ICP-MS[END_REF] performed isotopic measurements on a Micromass Isoprobe using D2 as the collision gas, and obtained a precision of ≈200 ppm (2SD) for 41 K/ 39 K with a couple of µg of K samples being analyzed. A new generation of dual-path MC-ICP-MS with collision cell capability has been released by Nu Instruments in 2018, known as the Sapphire. It is promising to obtain high-precision K isotopic data on small samples with this novel instrument because it is the first MC-ICP-MS to combine stat-of-the-art interface, doublefocusing ion optics, and a collision cell, to allow testing the accuracy of the data obtained using pseudo-high resolution and the older generation collision cell instrument. So far only one paper reported K isotopic data measured on this instrument [START_REF] Ku | Potassium isotope anomalies in meteorites inherited from the protosolar molecular cloud[END_REF]; their analyses use ≈1 µg of K and yield an internal precision (2SE) of 30 ppm and an external reproducibility (2SD) of 27 ppm over a 9-day period. However, this paper focused on the potassium isotopic composition of meteorites and report only 5 data for terrestrial rock geostandards (including seawater). Here we report new data obtained on 23 samples, including a large variety of international geostandards on which data had been previously acquired by pseudo-high resolution on a Neptune Plus or on a Nu Plasma II. Furthermore, we report the limitation on the accuracy of the data obtained from various analytical effects such as the effect of Ca (that would produce CaH + interference on 41 K) and on the intensity mismatch between samples and standard.

Samples and Methods

Samples

The samples analyzed here comprise W-1 (diabase, United States Geological Survey, USGS), JB-1 (basalt, Geological society of Japan, GSJ), SGR-1 (shale, USGS), GSP-1 (granodiorite, USGS), AGV-1 and AGV-2 (andesite, USGS), BHVO-2 (basalt, USGS), BCR-2 (basalt, USGS), G-2 (granite, USGS), SY-1 and SY-2 (Syenite, Canadian Certified Reference Materials Project, CCRMP), MAG-1 (marine mud, USGS), Hawaiian seawater (internal standard, University of Washington), GH (granite, Centre de Recherches Pétrographiques et Géochimiques, CRPG), GA (granite, CRPG), GBW07111 (granite, National Research Center for Geoanalyses of China, NRCG), GBW07103 (granite, NRCG), FK-N (Feldspar potassium, ANRT), SDC-1 (Mica shist, USGS), QLO-1 (quartz latite, USGS), DRN (diorite, ANRT), RGM-1 (rhyolite, USGS) and LAP 02224 (lunar meteorite). The Hawaiian seawater is an internal standard from the University of Washington, but as demonstrated before (Hill et al. 2019, Wang et al. 2020), seawater is homogeneous regardless of location, depth, or K concentration, and therefore it can be taken as representative of global seawater. The selected samples cover a range of chemical compositions and most of them have previously been analyzed for their K isotopic compositions in multiple laboratories. Therefore, they are well suited to test the accuracy of the Nu Sapphire measurements, as well as to confirm previous results obtained on standard MC-ICP-MS. Furthermore, BHVO-2 has been used to evaluate the long-term reproducibility of the method and has been analyzed 11 times over a 6-month period from three separate dissolutions and chemical purifications (Table S1).

To evaluate the effect of the intensity mismatch between sample and standard we performed tests on a pure K concentration standard (NIST SRM 3141a) as well as on one geological material (DR-N) running them both with 0 to 10 % intensity mismatch, as compared to the bracketing standard (NIST SRM3141a). The effect of 40 CaH + interference on 41 K has also been tested on both the pure K standard and on one geological material (GH) by adding Ca up to 4%. Finally, we tested the effect of K concentration on the accuracy of the data from 150 ppb down to 25 ppb of K (which for 5 replicates would represent ≈750 and ≈125 ng of K, respectively).

Dissolution and chemical purification

The chemical purification has been conducted at either the Institut de Physique du Globe de Paris (IPGP), and University of Washington as described here [START_REF] Xu | Potassium isotopic compositions of international geological reference materials[END_REF] or at Washington University in St Louis as described in [START_REF] Chen | High-precision potassium isotopic analysis by MC-ICP-MS: an inter-laboratory comparison and refined K atomic weight[END_REF]. At Washington University, all samples were grounded in an agate mortar. 50-100 mg of powders were dissolved in concentrated HF-HNO3 following by a second dissolution in HCl-HNO3 using Parr sample digestion vessels for both steps. Then samples were dried down and re-dissolved in 0.7 N HNO3. Potassium is purified using a two-step ion exchange chromatography. The first separation is done on a "big" column (Bio-Rad Econo-Pac; I.D.=1.5cm) filled with 17 mL of AG50-X8 100-200 mesh cation-exchange resin. A second purification is done on a "small" column (Bio-Rad glass Econo-column; I.D.=0.5cm) filled with 2.4 mL of the same resin. Both columns were first cleaned with 6 N HCl. Samples in 1 mL of 0.7 N HNO3 were loaded on the "big" columns. First 87 mL of 0.7 N of HNO3 are passed to clean up the matrix. The K fractions were collected by adding 107 mL of 0.7 N HNO3. On the second column, the samples are loaded in 1 mL of 0.5 N HNO3. Matrix were eluted using 16 mL 0.5 N HNO3. 18 mL of 0.5 N HNO3 are then added to collect the K.

At IPGP and University of Washington, 20-25 mg pulverized rock standards were digested sequentially using Optima-grade concentrated HF-HNO3, HCl-HNO3, and HNO3. The closed beakers were heated on a hotplate at 120°C, periodically vibrated in an ultrasonic bath, and opened and dried at 100°C. The dried samples were redissolved in 0.5 N HNO3 in preparation for the cation-exchange chromatography. Potassium was purified by two passes of 2mL pre-cleaned Bio-Rad AG50W-X8 resin (200-400 mesh) that was filled in Bio-Rad Poly-Prep polyethylene columns and conditioned by 10 mL 0.5 N HNO3. Sample solutions were then loaded on the resin and eluted by 0.5 N HNO3.

Matrix elements were eluted with 13 mL of 0.5 N HNO3, and K was collected from the subsequent 22 mL fraction. The resin was cleaned with 10 mL of 6 N HCl afterward.

To minimize procedure blank, acid-washed teflon beakers and double-distilled acids were used exclusively in this study, which were prepared in house at either Washington University in St Louis, University of Washington, USA, or at IPGP.

K isotopic measurements on Sapphire

Collision cells have been in use with quadrupole ICP-MS for nearly 20 years and have proven effective to remove Ar based species and other molecular interferences. But it is also known to create complications for isotope systems due to the mass discrimination effects of the multipole and inherent instrumental isotopic bias.

The Nu Sapphire features by a dual-path design (Figure 1), including both a conventional MC-ICP-MS (High Energy, 6 kv acceleration) pathway and a collision cell (Low Energy, 4 kv acceleration) pathway. This design allows for selecting either classic or novel applications without compromising the analysis. For K isotope measurements, we used the collision cell pathway.

The Nu Sapphire installed at IPGP is a double-focusing magnetic sector MC-ICP-MS instrument equipped with 16 fixed Faraday collectors that are fitted with selectable resistors ranging from 10 10 to 10 13 ohm. For the low energy pathway, at the plasma source, the ions are accelerated at 4kV. The ions are deflected off-axis and decelerated to a few 10eV's of energy to enter the radio frequency (RF) multipole collision/reaction cell. The RF hexapole reduces mass bias effects compared to quadrupole-based cells due to the larger mass transmission window. This is because quadrupoles have the steepest confining potential, i.e., the potential rises quickly from the center of the device to the rods, thus permitting operation within a narrow bandwidth as well as operation in other modes that are highly selective with respect to the mass-to-charge ratio [START_REF] Amr | The collision/reaction cell and its application in inductively coupled plasma mass spectrometry for the determination of radioisotopes: A literature review[END_REF].

Hexapoles, on the contrary, are much less selective with respect to the mass-to-charge ratio, but can provide higher ion transmission and reduced scattering losses.

Within the gas filled cell the ions are collisionally thermalized by colliding with the buffer background gas, and charge exchange takes place with hydrogen, removing the Ar based species. After the cell, the ions are re-accelerated to 4 kV and focused back onto the mass spectrometer source slit in the same manner as on a conventional MC-ICP-MS (or as if it were following the high energy path on the Nu Sapphire).

The charge exchange with H2 gas in the collision/reaction cell reduces the Ar + signal by greater than 9 orders of magnitude, to almost completely remove any Ar based species, for example:

Ar + + H2 → Ar + H2 + Eq. 1

ArH + + H2 → ArH + H2 + Eq. 2

In addition to the hydrogen gas required for the reaction, He gas is introduced in the cell as a buffer gas and contributes to the collisional thermalisation of the ions within the cell in order to maximise transmission through the hexapole ion guide. The relative amount of He and H2 introduced in the cell is optimised to minimise the Ar + , ArH + and CaH + backgrounds (see Table 1 for the parameters used here).

In this study, the K isotope data were acquired on the Sapphire instrument in its Low Energy mode. A 150 ng/g (ppb) NIST SRM3141a K standard solution and various samples were introduced into the mass spectrometer using an Apex Omega desolvating system fitted with a 100 μL/min PFA nebulizer (MicroFlow nebuliser, Elemental Scientific, Omaha, NE, USA) and with standard Ni dry cones ("dry plasma"). We also performed comparative test using a cyclonic spray chamber ("wet plasma"). Zoom optics were used to optimize focusing and peak coincidence.

Data was collected in static mode (no peak jump), with 39 K + measured in a Faraday cup (L5) connected to a pre-amplifier fitted with a 10 10 ohm resistor and 41 K + using a 10 11 ohm resistor (L1). The intensity of the mass 40 was monitored on the faraday cup L3 using a 10 11 ohm resistor. Each analysis consists of a 60-second zero measurement in 3% HNO3, followed by 1 block of 50 cycles with 5 second integrations (Table 1). A 90-120 second wash was performed in 3 % HNO3 between each standard and sample analysis and a transfer time of 60 or 90 seconds was applied. Each sample was measured between 6 and 12 times, bracketed by the NIST-SRM 3141a standard. No tuning was made once the sequence had begun. The operating parameters of the instrument are listed in Table 1.

In these conditions, the background on the masses 39 and 41 were approximatively 150 mV and 2 V respectively in dry plasma mode and 39 mV and 450 mV in wet plasma mode. The signal on the mass 40 were approximatively between 20 and 100 mV in dry plasma mode and 24 and 62 mV in wet plasma mode. For comparison, the signal for 150 ppb of K returned over 300 V in dry plasma mode and 20

V in wet plasma mode.

All the samples and tests have been performed in dry plasma mode. The wet plasma mode has only been run to compare the precision and intensity of the SRM3141a K standard solution to previous studies [START_REF] Chen | High-precision potassium isotopic analysis by MC-ICP-MS: an inter-laboratory comparison and refined K atomic weight[END_REF][START_REF] Li | Precise measurement of stable potassium isotope ratios using a single focusing collision cell multi-collector ICP-MS[END_REF][START_REF] Li | An optimal separation method for highprecision K isotope analysis by using MC-ICP-MS with a dummy bucke[END_REF][START_REF] Morgan | High-precision 41K/39K measurements by MC-ICP-MS indicate terrestrial variability of δ41K[END_REF][START_REF] Xu | Potassium isotopic compositions of international geological reference materials[END_REF]. The mass bias was corrected by measuring the samples alternatively with the NIST SRM3141a K standard solution (standard-sample bracketing).

Results and discussion

The K isotopic data for the samples are reported in Table 2. All the data for the analytical tests and long-term reproducibility are reported in supplementary tables.

All the data are reported using the δ 41 K notation as:

δ K (‰) = -1 × 1000 (3)
The errors are reported as the 2 standard-deviation of the replicated measurements as well as the 95% confidence interval (see [START_REF] Hu | High-precision analysis of potassium isotopes by HR-MC-ICPMS[END_REF] for details).

Accuracy and long-term reproducibility

The accuracy of our analytical protocol is confirmed by 1) self-bracketing pure K standards that had expected δ 41 K of zero (Fig. 2), 2) measuring 19 well-characterized geostandards that were previously analyzed at UW (Table 2) and replicating the chemical purification of FK-N geostandard and the seawater at IPGP. The δ 41 K values of these geostandards obtained on the Nu Sapphire at IPGP are consistent with those measured on a Nu Plasma II at UW (Table 2). We also fully processed BHVO-2, BCR-2, and AGV-2 at IPGP; their δ 41 K values agree well literature data (Table 2).

The long-term reproducibility of the K isotopic measurement was evaluated by repeated measurements of BHVO-2 during 11 analytical sessions (where in each session BHVO-2 was analyzed between 6 and 10 times) over 6 months, on three separate dissolution and chemical purification (see Table S1). We obtained an average δ 41 K of -0.434±0.040 ‰ (2SD, n=11), which is consistent with literature values (δ 41 K= -0.411±0.012 ‰, Xu et al. 2020). Our results reveal a long-term reproducibility of 0.040 ‰ (2SD).

Comparison of Sapphire with previous methods

Figure 2 illustrates the sensitivity of the double-focusing, dual-path collision cellcapable Sapphire instrument for K isotopic measurement compared to previous methods using either older generation, single-focusing collision cell MC-ICPMS [START_REF] Li | Precise measurement of stable potassium isotope ratios using a single focusing collision cell multi-collector ICP-MS[END_REF] or no collision cell, double-focusing MC-ICPMS in high energy and cold or hot plasma [START_REF] Chen | High-precision potassium isotopic analysis by MC-ICP-MS: an inter-laboratory comparison and refined K atomic weight[END_REF][START_REF] Hu | High-precision analysis of potassium isotopes by HR-MC-ICPMS[END_REF][START_REF] Morgan | High-precision 41K/39K measurements by MC-ICP-MS indicate terrestrial variability of δ41K[END_REF][START_REF] Tuller-Ross | Potassium isotope systematics of oceanic basalts[END_REF][START_REF] Xu | Potassium isotopic compositions of international geological reference materials[END_REF]. The sensitivity is reported to reflect a standard at 150 ppb K for each method.

The Sapphire provides the highest reproducibility both in wet and dry plasma mode compared to any previous method, as well as the highest sensitivity even when only using the wet plasma compared to high resolution/dry plasma on conventional MC-ICP-MS.

Given the gain in sensitivity by over a factor of 30 when coupled to the Apex Omega we have decided to perform most of the tests presented below, as well as the measurement of the natural samples, in these conditions.

Effect of K concentration on accuracy

While all the samples have been analyzed using 150 ppb K (≈750 ng of K for 5 replicates), we have performed tests to evaluate the accuracy of the measurements down to 25 ppb K (≈125 ng of K for 5 replicates) (Figure 3). For both the pure K standard (Figure 3a) and for a rock sample (DR-N, Figure 3b), the accuracy is maintained down to 25 ppb K. For DR-N the value obtained when running 25ppb of K (δ 41 K = -0.555±0.028 ‰) is consistent with the value obtained at 150 ppb (δ 41 K = -0.566±0.034 ‰) as well as with literature data (shown as the grey bar on Figure 3b, δ 41 K = -0.562±0.025 ‰, [START_REF] Xu | Potassium isotopic compositions of international geological reference materials[END_REF]). This method is therefore very promising for analyzing samples with low K content. For example, the solution at 25 ppb of K of DR-N was run 8 times (i.e. 200 ng of K) for a precision of 0.028 ‰ and analyzing it only 5 times (125 ng of K) would provide similar precision. This is a major gain compared to previous methods that would require several micrograms of K for similar quality of data.

Effect of K concentration mismatch

The effect of intensity mismatch tests was tested by maintaining the NIST-SRM 3141a bracketing standard at 150 ppb of K while varying the concentration of both the NIST-SRM 3141a K standard measured as a sample (Figure 4a) or the rock sample (granite GA) from 10 % lower to 10 % higher concentrations. In Figure 4, the variation of δ 41 K values is plotted as a function of the ratio between the K concentration of the sample analyzed (at various concentrations) and of NIST-SRM 3141a analyzed at 150 ppb. Both the pure K standard and granite GA sample show consistent correlation between measured offset in δ 41 K and intensity mismatch. The correlation returns a relationship of δ 41 K≈2-2×Ksample/Kstandard for the pure standard and δ 41 K≈2.169-2.656×Ksample/Kstandard for granite GA. Therefore, a 1% mismatch creates a ≈0.02 ‰ isotopic bias, which is presently a clear limitation in the K isotopic measurements using the Sapphire. It is therefore paramount to analyze the samples with an intensity match within 1% of the bracketing standard to obtain accurate data on the Sapphire, which is the protocol used in this study. As shown below, when the intensities match well, the data obtained on the Sapphire are accurate and precise (<50 ppm). This sensitivity of the δ 41 K values to the intensity is most likely due to a combination of the hexapole setup and of the high K background observed on our APEX Omega, over 2 V of K compared to a signal of > 300 V of K for a 150 ppb solution. The K background therefore represents ≈1 ppb of K. It should be noted that the effect reported above is relevant to the instrumental parameters utilized in our study and this may be different for different instrumental parameters.

Effect of matrix elements

The application of standard-sample bracketing method requires column chemistry to isolate K from the matrix elements; therefore, the instrumental mass bias on pure K standards can be assumed to represent that on the bracketed samples. Here we tested the presence of Ca, Na, Rb, Ti, and Cr on the accuracy of K isotopic measurements. The elution interval of K overlaps significantly with that of Rb and Cr on common cation exchange resin (e.g., [START_REF] Chen | High-precision potassium isotopic analysis by MC-ICP-MS: an inter-laboratory comparison and refined K atomic weight[END_REF][START_REF] Xu | Potassium isotopic compositions of international geological reference materials[END_REF], and residual Ti is identified when using large columns to process low-K samples [START_REF] Wang | Potassium isotopic evidence for a high-energy giant impact origin of the Moon[END_REF]. While

Na and Ca can be completely separated from K, they are common contaminants in the environment, and Na potentially forms molecular interference of 23 Na 16 O + at mass 39.

Plastic containers made of polyethylene, polyethylene terephthalate, or polypropylene typically have high Ca blanks even after repeated acid cleaning. The presence of Ca is particularly problematic for analysis using the H2-fed collision cell, whereby a fraction of Ca combines with H to produce CaH + and create an isobaric interference on 41 K.

For Ca-doping test, we added various amounts of Sigma-Aldrich Ca (up to 5 % Ca) to pure NIST-SRM 3141a K solutions and then measured them against paired pure NIST-SRM 3141a K solutions at the same K concentration (Figure 5a). All the tests were performed with 150 ppb of K, i.e. that 1 % Ca corresponds to 1.5 ppb of Ca, which on a Faraday cup equipped with a 10 11 ohm resistor returned ≈2V of 40 Ca. A similar approach has been followed to test the effect on a rock sample (granite GH, Figure 5b). The effect is similar on both the pure K standard and on the sample, where the δ 41 K correlates with the Ca/K ratio (%) of the solution analyzed with a slope of 0.069. In other words, a Ca/K ratio of 1% (≈2V of 40 Ca in our cases for 1.5 ppb of Ca) would affect the δ 41 K value by + 0.069 ‰. We therefore suggest that the Ca content in the solution analyzed should always be kept under 0.3 ppb (400mV on 40 Ca in our case). It should be noted that all the samples reported here (except one) had a 40 Ca intensity similar to the pure NIST-SRM 3141a solution at 150ppb analyzed as bracketing standard (≈100mV) and therefore did not cause any isobaric interferences. The exception is lunar meteorite LAP 02224, for which 40 Ca has an intensity of ≈1V. This sample is prepared at Washington University in St Louis using a large column and hence more acids that likely contribute to the high Ca contents in the purified sample. Giving the relation defined in Figure 5, the presence of Ca in this sample would cause a potential increase its δ 41 K by ≈ 0.034 ‰. To minimize Ca contamination, we used Teflon beakers for instrumental analysis.

The other elements (Na, Rb, Cr and Ti) are doped with 1%, 2.5%, 5%, and 10% concentration ratios to that of K (see supplementary tables). These elements produce smaller matrix effects than Ca. Sodium creates the smallest effect of these four elements with ~0.1 ‰ for 10 %, while Na, Rb, and Ti have similar effect ~0.2 ‰ for 10%. In any case, the influence of these elements is negligible if the matrix element concentration is less than 2.5% of that of K. When presented at higher concentrations, Na, Rb, Cr and Ti all cause a shift of δ 41 K to lower values (see supplementary table ).

Effect of K concentration mismatch

We evaluated the effect of the HNO3 concentration mismatch between the samples and the standard on the accuracy of the δ 41 K as variations in the acid molarity of the analyzed solution had been shown to affect the mass bias for Fe isotopes (Malinovsky et al. 2003). Pure NIST-SRM 3141a K solution were dissolved in HNO3 at various concentrations (from 1 % to 5 %) and were analyzed against a NIST-SRM 3141a solution dissolved in 3 % HNO3 (Figure 6). There is a clear correlation (R 2 =0.95) between the δ 41 K and the mismatch in HNO3 concentration. It is therefore important for the accuracy of the measurements to dilute all the samples and standards with the same acid concentrations (Malinovsky et al. 2003;[START_REF] Dauphas | Routine isotopic analysis of iron by HR-MC-ICPMS: How precise and how accurate?[END_REF]. For all the samples analyzed here, samples and standards were prepared from the same bottle of 3 % HNO3.

Potassium isotopic variations in terrestrial geostandards and a lunar meteorite

The various samples analyzed here covers a δ 41 K range of ≈0.6 ‰, with the granite GH being the lightest (δ 41 K=-0.590±0.018 ‰) and the Hawaiian seawater standard being the heaviest (δ 41 K=+0.139±0.022 ‰) samples.

The data obtained on the Sapphire compare well with previously published data (see Table 2 andS1 andFigure 7). All samples fall on a slope of 1 line in Figure 7, Furthermore, our data are consistent with the values previously obtained on the Sapphire at Harvard University (see Table S2), for AGV-1 (-0.473±0.043 ‰ vs -0.440±0.012 ‰) and G-2 (-0.470±0.021 ‰ vs -0.420±0.017 ‰).

The lunar meteorite analyzed here was the only sample that had a 40 Ca signal higher than the pure K standard (by about 1V, i.e. ≈0.7 ppb of Ca in the measured solution). The data obtained on the Sapphire without correcting for the Ca interference (-0.021 ± 0.034 ‰) as well as after Ca correction using the relation define above (-0.055 ± 0.034 ‰) are fairly consistent with the literature value (-0.01±0.03 ‰, [START_REF] Tian | Potassium isotopic composition of the Moon[END_REF].

Therefore, although the Ca content of the lunar sample is resolvable, the data appears to confirm the δ 41 K≈ -0.02 ‰ of lunar rocks discovered by [START_REF] Wang | Potassium isotopic evidence for a high-energy giant impact origin of the Moon[END_REF] and later confirmed by [START_REF] Tian | Potassium isotopic composition of the Moon[END_REF]. Terrestrial igneous rocks analyzed here and in the literature are systematically lighter by ≈0.4 ‰ (see Figure 8). The heavy isotope enrichment of the lunar basalts for K as well as for other volatile elements such as Zn (e.g., [START_REF] Paniello | Zinc isotopic evidence for the origin of the Moon[END_REF][START_REF] Kato | Extensive volatile loss during formation and differentiation of the Moon[END_REF], Cl (e.g. [START_REF] Gargano | Proceedings of the national academy of sciences. The Cl isotope composition and halogen contents of Apollo-return samples[END_REF], Ga [START_REF] Kato | Gallium isotopic evidence for extensive volatile loss from the Moon during its formation[END_REF], and Rb (Pringle and Moynier 2017) is a strong case of an evaporative loss of the volatiles from the Moon and of the presence of a transient lunar atmosphere (Van Kooten et al. 2020).

The excellent agreement between the δ 41 K values obtained on the Sapphire in IPGP, Paris on a wide range of previously analyzed samples on different instruments as well as with the two common samples analyzed on the Harvard Sapphire, confirms the accuracy of the high precision K data for the meteorites reported in [START_REF] Ku | Potassium isotope anomalies in meteorites inherited from the protosolar molecular cloud[END_REF] and the remarkable systematic isotopic variation between chondritic samples.

Given a factor of 10 improvement in the sensitivity of K isotopic measurements using a Nu Sapphire, this instrument opens up new applications in cosmochemistry such as the analyses of K-poor samples (e.g. angrite meteorites), meteorite fractions (e.g. chondrules, CAIs) or very precious samples such as future sample returned mission from asteroids, the Moon, and Mars.

Conclusions

We report K isotopic data acquired with a Nu Sapphire dual-path collision cellcapable MC-ICP-MS connected to an Apex Omega for 23 samples, including seawater, terrestrial and lunar rocks that all had been previously analyzed for K isotopes by older generations of mass-spectrometers. We show that K isotopic data acquired using the collision-cell on the Nu Sapphire are both accurate (by comparing our data to published values) and precise (2SD of replicated measurements typically around 0.05 ‰). A major advantage is the high sensitivity of the instrument as the samples can be analyzed in lowresolution mode (≈2000V/ppm of K) and accurate data can be obtained at running concentrations as low as 25 ppb (which for 5 replicates correspond to ≈125 ng of K). This represents a remarkable improvement compared to other methods to analyze small or Kpoor samples and will certainly open up new applications. In order to obtain these results, care needs to be taken to 1) avoid the presence of Ca in the K solution (a Ca/K ratio of 1% create a 0.069 ‰ offset), 2) match the concentration of the sample and of the standard (a 1% mismatch create a 0.02 ‰ offset, using our instrumental parameters) as well as the acid molarity of the sample, and 3) well-characterize the instrument behavior and apply correction functions for K and Ca signals. Controlling these factors, the data reported here for 23 geostandards are in good agreement with previous studies using Neptune plus or Nu Plasma II instruments. This consistency therefore confirms the accuracy of the data that can be obtained on the Sapphire in the future.

Acknowledgements: We thank the two anonymous reviewers for their constructive reviews that greatly improved the quality of the work. We also thank editor Balz Kamber for his comments and efficient handling of our manuscript. Figure 3: δ 41 K as a function of the K concentration (ppb) for the pure K standard SRM3141a (Figure 3a) and for the geostandard DR-N (Figure 3b). Measurements are accurate down to 25ppb. Figure 4: Effect of the intensity mismatch on the accuracy of the K isotopic composition. The x-axis represents the ratio of the total intensity of the sample and of the standard. The standard was measured at 150ppb. Figure 4a: Effects on the pure K standard. Figure 4b: Effects on the GA rock standard.

Figure 5: Effect of the Ca content of the solution analyzed on the accuracy of the K isotopic composition. The x-axis represents the Ca content of the solution with regards to the K concentration (150ppb for all samples) in %. Figure 5a corresponds to the pure NIST SRM3141a standard and Figure 5b corresponds to the GH rock standard. The slope is similar in both cases (0.069) and therefore 1% Ca/K ratio biased the δ 41 K by +0.069 ‰.

Figure 6: Effect of HNO3 concentration mismatch between sample and standard on the δ 41 K values. The "sample" here represents the pure NIST SRM3141a standard dissolved in acid at various molarity from 1% to 5% HNO3. The bracketing standard is a pure NIST SRM3141a solution in 3% HNO3. There is a clear effect of the mismatch of acid molarity on the accuracy of the δ 41 K.

  indicating the consistency in the absolute values obtained on the Sapphire with both a Nu Plasma II and a Neptune plus. This consistency also demonstrates the accuracy of the high-precision data acquired using other instruments from[START_REF] Ku | Potassium isotope anomalies in meteorites inherited from the protosolar molecular cloud[END_REF][START_REF] Chen | High-precision potassium isotopic analysis by MC-ICP-MS: an inter-laboratory comparison and refined K atomic weight[END_REF]), Tuller-Ross et al. (2019), and[START_REF] Tian | Potassium isotopic compositions of howardite-eucrite-diogenite meteorites[END_REF]. For example, the sample that was analyzed the most here and in various literatures, the seawater, returns a δ 41 K=+0.139±0.022 ‰ (n=12), which is in excellent agreement with the most recent value suggested by[START_REF] Ku | Potassium isotope anomalies in meteorites inherited from the protosolar molecular cloud[END_REF] (δ 41 K=+0.168±0.014 ‰, n=64), as well as with previously acquired values with lower precisions : δ 41 K=+0.100±0.305 ‰,[START_REF] Wang | Potassium isotopic evidence for a high-energy giant impact origin of the Moon[END_REF], +0.02±0.40 ‰, +0.05±0.70 ‰, +0.12±0.13 ‰[START_REF] Li | Precise measurement of stable potassium isotope ratios using a single focusing collision cell multi-collector ICP-MS[END_REF], 0.03±0.70 ‰[START_REF] Morgan | High-precision 41K/39K measurements by MC-ICP-MS indicate terrestrial variability of δ41K[END_REF], +0.12±0.07 ‰[START_REF] Wang | Global average potassium isotope composition of modern seawater[END_REF] and +0.14 ± 0.02 ‰[START_REF] Hille | Homogeneous and heavy potassium isotopic composition of global oceans[END_REF].

  F. M. thanks the DIM ACAV+ (Domaine d'Interet Majeur, Astrophysique et Condition d'Apparition de la Vie) of the region Ile de France for providing part of the funding for the Nu Sapphire. F.M. acknowledges funding from the European Research Council under the H2020 framework program/ERC Starting Grant Agreement (#637503-PRISTINE) and financial support of the UnivEarthS Labex program at Sorbonne Paris Cité (#ANR-10-LABX-0023 and #ANR-11-IDEX-0005-02). Parts of this work were supported by IPGP multidisciplinary program PARI.

FigureFigure 1 .

 1 Figure and TableCaptions:

Figure 2 :

 2 Figure 2: Comparison of the sensitivity of various instruments and techniques used to analyze the K isotopic composition of a pure K standard at 150ppb. The error bar represents the 2SD.Figure 3: δ 41 K as a function of the K concentration (ppb) for the pure K standard SRM3141a (Figure3a) and for the geostandard DR-N (Figure3b). Measurements are accurate down to 25ppb. Figure4: Effect of the intensity mismatch on the accuracy of the K isotopic composition. The x-axis represents the ratio of the total intensity of the sample and of the standard. The

Figure 7 :

 7 δ 41 K values from the literature (see

Table 1 .

 1 Table2) reported against δ 41 K values obtained here on the Nu Sapphire. The dotted line represents a straight line with a slope 1. Most samples fall on the slope 1 line and confirms that the data obtained on the Sapphire are consistent with literature values. Figure8: δ 41 K values of the different samples reported here. The lunar basaltic meteorite (LAP 02224) is isotopically heavier than all terrestrial rocks. Operating parameters of the Sapphire instrument and the Apex Omega introduction system.

Table 2 :

 2 Potassium isotopic data of the various rock samples analyzed here. The literature data are all from[START_REF] Xu | Potassium isotopic compositions of international geological reference materials[END_REF] except for FK-N[START_REF] Chen | High-precision potassium isotopic analysis by MC-ICP-MS: an inter-laboratory comparison and refined K atomic weight[END_REF] and LAP 02224[START_REF] Tian | Potassium isotopic composition of the Moon[END_REF].

Nu Sapphire Instrument Setting utilized in this study

	RF Power Sample		Type	δ 41 K (‰)	1300 W 2SD 95%c.i. N	δ 41 K (‰) literature	95%c.i.	95%c.i. std	Chemical preparation
	Coolant gas flow rate W-1 Diabase	-0.402	13 L/min 0.058 0.031		6	-0.391	0.024	0.038	UW
	Auxiliary gas flow JB-1 Basalt BCR-2 Basalt	-0.387 -0.428	0.053 0.75-0.9 L/min 0.028 0.028 0.013		6 7	-0.416 -0.417	0.036 0.030	0.038 0.036	UW IPGP
	Sampler/skimmer cone material BHVO-2* Basalt -0.434	Ni 0.04		11	-0.411	0.011	0.017	IPGP
	He collision gas flow AGV-1 Andesite	-0.451	2-3 sccm 0.035 0.016		7	-0.447	0.017	0.027	UW
	H2 reaction gas flow AGV-2 Andesite QLO-1 Quartz Latite	-0.450 -0.398	0.034 5 sccm 0.049	0.016 0.026		7 6	-0.410 -0.391	0.020 0.042	0.033 0.038	IPGP UW
	Quad 1 DR-N		Diorite	-0.566	18.4 0.066	0.034		6	-0.562	0.025	0.042	UW
	Quad 2 GSP-1	Granodiorite	-0.509	-43.0 0.035	0.016		7	-0.494	0.016	0.036	UW
		duplicate	-0.495	0.058	0.030		6			0.041	UW
	GBW07111 Granodiorite	-0.396	0.059	0.031		6	-0.379	0.023	0.044	UW
	Apex parameters G-2 Granite	-0.470	0.039	0.021		6	-0.462	0.014	0.040	UW
	Argon Sweep Gas Flow GH Granite GA Granite	-0.560 -0.454	0.050 2.18-3.42 L/min 0.026 0.034 0.018	6 6	-0.522 -0.425	0.035 0.023	0.039 0.043	UW UW
	Nebulizer pressure GBW07103 Granite	-0.509	27.4-29.0 psi 0.056 0.026		7	-0.478	0.023	0.038	UW
	Peripump Speed RGM-1	Rhyolite	-0.386	17.0 (rpm) 0.051 0.027		6	-0.376	0.031	0.044	UW
	Peripump Flow SY-1 Nebulizer uptake rate Syenite SY-2 Syenite SGR-1 Shale	-0.298 -0.273 -0.270	0.046 600.0 (µL/min) 0.019 0.069 0.032 50 or 100 µL/min 8 7 0.061 0.028 7	-0.253 -0.270 -0.264	0.059 0.023 0.015	0.032 0.038 0.036	UW UW UW
	Peltier Cooler temperature MAG-1 Marine Mud	-0.460	3.0 o C 0.037	0.019		6	-0.385	0.025	0.024	UW
	Desolvator temperature SDC-1 Mica Shist	-0.468	155.0 o C 0.048 0.022		7	-0.461	0.017	0.033	UW
	Spray chamber temperature FK-N K-Felspar FK-N IPGP	-0.281 -0.303	0.031 140 o C 0.054	0.016 0.025		6 7	-0.26	0.09	0.024 0.033	UW IPGP
	Seawater		Water	0.139	0.075	0.024	12	0.146	0.018	0.019	UW
			replicate	0.130	0.070	0.032		7			0.033	UW
	LAP 02224		Lunar	-0.021	0.034	0.018		6	-0.01	0.03	0.024	WU
	*

BHVO-2 has been used to estimate the long-term reproducibility evaluated over the course of 11 sessions and three separate chemical procedures (see Table S1 for the details of the measurements).