Mihael Vucur
email: mvucur@ukaachen.de

Anne T Schneider

Jérémie Gautheron

Tom Luedde

The enigma of RIPK1 in the liver: More than just a kinase

Keywords: RIP1, TRAF2, Hepatocarcinogenesis, HCC, Acetaminophen, APAP, Concanavalin A, ConA

Receptor interacting protein kinase 1 (RIPK1) represents a key molecule in cell death.

Here, we discuss our recent data on RIPK1 in liver injury and hepatocellular carcinoma development and put these into relation to previous experimental findings to underpin that it exerts opposing kinase-dependent and -independent functions in liver cells.

various pathogenic factors, triggering a sequence of inflammation, compensatory regeneration and oxidative stress that ultimately drive malignant transformation of hepatocytes. [START_REF] Villanueva | The transition from inflammation to cancer in the liver[END_REF] Clinical data and animal models suggest that hepatocyte death is the key trigger of liver disease progression [START_REF] Luedde | Cell Death and Cell Death Responses in Liver Disease: Mechanisms and Clinical Relevance[END_REF] , and different modes of cell death such as apoptosis, necrosis, and necroptosis trigger specific cell death responses and promote progression of liver disease through distinct mechanisms.

Receptor interacting protein kinase 1 (RIPK1) is a multifunctional regulator of cell death triggered by tumor necrosis factor and other death ligands. [START_REF] Luedde | Cell Death and Cell Death Responses in Liver Disease: Mechanisms and Clinical Relevance[END_REF] RIPK1 is regulated by posttranscriptional modifications (phosphorylation and ubiquitination) and is part of distinct cell-death related complexes, such as complex IIb (mediating apoptosis) or the necrosome (mediating necroptosis). [START_REF] Luedde | Cell Death and Cell Death Responses in Liver Disease: Mechanisms and Clinical Relevance[END_REF] Based on its central position in cell death regulation, RIPK1 is currently one of the most intensively studied but also most controversially discussed molecules in liver research. Initial evidence for a role of RIPK1 in experimental models of acute liver failure came from studies that relied on usage of a chemical inhibitor of RIPK1's kinase function, necrostatin-1 (Nec-1), suggesting e.g. a role in the mediation of acetaminophen (APAP) toxicity. [START_REF] Takemoto | Necrostatin-1 protects against reactive oxygen species (ROS)-induced hepatotoxicity in acetaminophen-induced acute liver failure[END_REF] However, Nec-1 is neither specific for RIPK1, nor is it stable in vivo or specific for hepatocytes, and experiments with conditional cre-loxP-based RIPK1 knockout mice in liver parenchymal cells (RIPK1 LPC-KO ) could not confirm this putative function in the APAP model (Fig. 1). [START_REF] Schneider | Receptor interacting protein kinase 1 (RIPK1) in hepatocytes does not mediate murine acetaminophen toxicity[END_REF] More recently, comparative experimental approaches studying the different functional and biological effects of conditional knockout mice versus mice harboring a kinase-inactive form of RIPK1 (RIPK1 K45A ) could provide important new insights into the opposing functional traits of RIPK1 in liver disease. As such, Filliol and colleagues recently published an interesting study in which they examined the role of RIPK1 in the Concanavalin A (ConA) model of liver injury, which is primarily driven by the activation and recruitment of T cells to the liver. [START_REF] Filliol | RIPK1 protects from TNF-alpha-mediated liver damage during hepatitis[END_REF] Using the more specific RIPK1 kinase inhibitor Nec-1s as well as RIPK1 K45A kinase-dead mice, the authors saw protection upon inhibition of RIPK1. In contrast, ConA treated RIPK1 LPC-KO mice showed more severe liver damage compared to littermate controls, suggesting that kinase-dependent and -independent functions of RIPK1 differentially regulate the outcome of liver injury. [START_REF] Filliol | RIPK1 protects from TNF-alpha-mediated liver damage during hepatitis[END_REF] Mice lacking the IB-Kinase subunit Nemo in LPC (NEMO LPC-KO ) fail to activate NF-B, which drives the spontaneous development of hepatocyte apoptosis, chronic inflammation and liver cancer, a similar sequence as seen in human hepatocarcinogenesis. [START_REF] Kondylis | NEMO Prevents Steatohepatitis and Hepatocellular Carcinoma by Inhibiting RIPK1 Kinase Activity-Mediated Hepatocyte Apoptosis[END_REF] Recently, Kondylis and colleagues showed that additional ablation of Ripk1 in NEMO LPC-KO mice had no significant effect on cell-death activation and hepatocarcinogenesis. [START_REF] Kondylis | NEMO Prevents Steatohepatitis and Hepatocellular Carcinoma by Inhibiting RIPK1 Kinase Activity-Mediated Hepatocyte Apoptosis[END_REF] In contrast, subcrossing of NEMO LPC-KO animals with RIPK1 D138N kinase-dead mice prevented apoptosis and cancer development. [START_REF] Kondylis | NEMO Prevents Steatohepatitis and Hepatocellular Carcinoma by Inhibiting RIPK1 Kinase Activity-Mediated Hepatocyte Apoptosis[END_REF] This important finding showed that apoptosis in Nemo-deficient hepatocytes is primarily mediated through RIPK1-containing complexes (IIb), and that RIPK1 kinase inactivation keeps inactive Caspase-8 bound to this putative complex. Only when RIPK1 is absent, apoptosis in a Nemo-deficient hepatocyte occurs independently of RIPK1, putatively through complex IIa (Fig. 1).

We could recently add an additional piece to the puzzle in terms of RIPK1's functions in HCC development. In our study, we examined the phenotype of LPC-specific conditional RIPK1 mice and showed that RIPK1 is dispensable for normal liver homeostasis but withholds an additional TNF-dependent pro-survival function in liver cells. [START_REF] Schneider | RIPK1 Suppresses a TRAF2-Dependent Pathway to Liver Cancer[END_REF] As such, RIPK1 acts as a scaffold to prevent the proteasomal degradation of the E3-ligase TNF receptorassociated factor 2 (TRAF2) in a kinase-independent manner, thereby inhibiting Caspase-8 dependent apoptosis. Interestingly, ablation of Ripk1 did not affect NF-B activation in hepatocytes. [START_REF] Schneider | RIPK1 Suppresses a TRAF2-Dependent Pathway to Liver Cancer[END_REF] Moreover, we detected a basal turnover of TRAF2 that was increased in the absence of RIPK1. At present, it remained unclear which specific E3 ligase is targeting TRAF2 for proteasomal degradation and how exactly this process is influenced by RIPK1 in liver cells. One possibility is that loss of RIPK1 detracts c-IAPs from their proper substrate which is RIPK1 and in turn leads to the conjugation of Ub onto TRAF2, leading to its degradation. Of note, Dupoux and colleagues observed that c-IAP1-mediated TRAF2 degradation is possible in monocytes undergoing macrophage differentiation, but in contrast to our findings in hepatocytes, it did not sensitize those cells to TNF-induced apoptosis. [START_REF] Dupoux | cIAP1-dependent TRAF2 degradation regulates the differentiation of monocytes into macrophages and their response to CD40 ligand[END_REF] TRAF2 was suggested to support K48-linked ubiquitination and proteasomal degradation of Caspase-8 in vitro, thereby tagging Caspase-8 with an "ubiquitin shut-off timer" and curbing apoptosis. [START_REF] Gonzalvez | TRAF2 Sets a threshold for extrinsic apoptosis by tagging caspase-8 with a ubiquitin shutoff timer[END_REF] This respective scenario is one possible explanation for the observed apoptosis activation in the presence of NF-B activation in RIPK1 LPC-KO mice.

To confirm the functional relationship between RIPK1 and TRAF2, we finally generated mice with combined ablation of Ripk1 and Traf2 in LPC, which led to a dramatic phenotype: RIPK1/TRAF2 LPC-KO mice developed spontaneous LPC apoptosis, which was not only caused by direct activation of Caspase-8 but also defective NF-B activation, showing that RIPK1 and TRAF2 have redundant functions in NF-B activation. This spontaneous apoptosis initiated a sequence of regeneration and inflammation that resulted in the spontaneous development of aggressive hepatocellular carcinoma (HCC) development in older mice. Interestingly, histological examination of human HCCs with different etiologies revealed a significant survival benefit for those patients that expressed both, RIPK1 and TRAF2, in their tumors. In contrast, low or undetectable tumor expression of both molecules showed the worst prognosis, which suggested that the new anti-carcinogenic checkpoint controlled by RIPK1 and TRAF2 in mouse livers might be of great relevance in human hepatocarcinogenesis.

Together with the previously published data in various experimental setups, our present data underlined that beyond the previously known functions in NF-B-, apoptosis-, and necroptosis-activation, RIPK1 harbors an additional, kinase-independent scaffold function that transmits a survival signal via TRAF2 and is important in preventing cancer (Fig. 1). While loss of RIPK1 expression obviously represents a risk factor for cancer development, the present data from several groups and distinct experimental models provide more solid evidence that inhibition of its kinase activityideally by more specific and effective new molecular inhibitorsmight be a promising strategy not only in the treatment of acute liver injury but also in the chemoprevention of cancer. Moreover, the available experimental data on RIPK1 in liver disease models nicely illustrate the power of combining genetic knockout studies with specific genetic point mutations, not only on a functional level but also in terms of their translation into human disease. Based on the fact that new phosphorylation sites have recently been identified in RIPK1 [START_REF] Koppe | IkappaB kinasealpha/beta control biliary homeostasis and hepatocarcinogenesis in mice by phosphorylating the cell-death mediator receptor-interacting protein kinase 1[END_REF] , it is more than likely that the story of RIPK1 in liver disease is not over yet but that new genetic tools will reveal more yet unrecognized functions and translational opportunities.

Disclosure of potential conflicts of interest

No potential conflicts of interest were disclosed.

Figure legend Figure 1 .

 legend1 Figure legend

Funding

This work was supported by the Start-Program of the faculty of Medicine, RWTH Aachen to M.V.. T.L. was supported by the German Cancer Aid (Deutsche Krebshilfe 110043 and a Mildred-Scheel-Professorship), the German-Research-Foundation (LU 1360/3-1 and SFB-TRR57/P06), an ERC Starting Grant (ERC-2007-Stg/208237-Luedde-Med3-Aachen), the EMBO Young Investigator Program, the Ernst-Jung-Foundation Hamburg and a grant from the medical faculty of the RWTH Aachen.


Lucile Marion-Poll
email: polllucile.marion-poll@curie.fr

Antoine Besnard

Sophie Longueville

Emmanuel Valjent

Olivia Engmann

Jocelyne Caboche

Denis Hervé

Jean-Antoine Girault
email: antoine.girault@inserm.fr

Cocaine conditioned place preference: unexpected suppression of preference due to testing combined with strong conditioning

Keywords: cocaine, conditioned place preference, reconsolidation

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

INTRODUCTION

The discovery that memory can return to a labile state after memory recall revealed that memory is in fact malleable (Nader et al., 2000b;[START_REF] Przybyslawski | Reconsolidation of memory after its reactivation[END_REF]. If not destabilized during a period of time after retrieval termed "reconsolidation window", the memory can be consolidated again and strengthened, a phenomenon referred to as reconsolidation [START_REF] Lee | Memory reconsolidation mediates the strengthening of memories by additional learning[END_REF]. During the reconsolidation window the memory can also be modified to allow incorporation of new information [START_REF] Choi | Protein synthesis and degradation are required for the incorporation of modified information into the pre-existing object-location memory[END_REF][START_REF] Lee | Reconsolidation: maintaining memory relevance[END_REF]. The occurrence of memory erasure following recall has been supported by a growing amount of studies, using different paradigms and pro-amnestic procedures, including electroconvulsive shock [START_REF] Misanin | Retrograde amnesia produced by electroconvulsive shock after reactivation of a consolidated memory trace[END_REF], protein synthesis inhibitors (Nader et al., 2000a), extracellular signal-regulated kinase (ERK) pathway inhibitors [START_REF] Cestari | The MAP(K) of fear: from memory consolidation to memory extinction[END_REF][START_REF] Miller | Molecular substrates for retrieval and reconsolidation of cocaineassociated contextual memory[END_REF][START_REF] Valjent | Inhibition of ERK pathway or protein synthesis during reexposure to drugs of abuse erases previously learned place preference[END_REF], or other types of manipulations [START_REF] Mactutus | Retrograde amnesia for old (reactivated) memory: some anomalous characteristics[END_REF][START_REF] Reichelt | Memory reconsolidation in aversive and appetitive settings[END_REF].

Most studies on memory reconsolidation have focused on aversive memories and less is known about appetitive conditioning and reward-associated memories. The latter can be implicated in pathological learning associations as in the case of drug abuse [START_REF] Torregrossa | Aberrant learning and memory in addiction[END_REF]. Long-lasting associations between a drug and a specific context can trigger relapse after withdrawal [START_REF] Milton | The persistence of maladaptive memory: addiction, drug memories and anti-relapse treatments[END_REF]. Therefore, the manipulation of drug-associated memories could have potential therapeutic implications in the context of addiction. The most widely used paradigm in studies of appetitive memory is conditioned place preference (CPP), which can be performed in various animal species [START_REF] Bardo | Conditioned place preference: what does it add to our preclinical understanding of drug reward?[END_REF]. The CPP paradigm has been used to show memory disruption by various procedures [START_REF] Milekic | Persistent disruption of an established morphine conditioned place preference[END_REF][START_REF] Miller | Molecular substrates for retrieval and reconsolidation of cocaineassociated contextual memory[END_REF][START_REF] Valjent | Inhibition of ERK pathway or protein synthesis during reexposure to drugs of abuse erases previously learned place preference[END_REF][START_REF] Xue | A memory retrieval-extinction procedure to prevent drug craving and relapse[END_REF].

Cocaine is the most frequently illegal drug reported to the Drug Abuse Warning Network by emergency departments in the United States (Substance Abuse and Mental Health Services Administration, 2016) and is also the second most commonly used illegal drug in Europe, according to the European Monitoring Center on Drugs and Drug Addiction (EMCDDA, 2016). A wide variety of studies have shown the importance of ERK in memory formation across several species and brain areas [START_REF] Peng | ERK in learning and memory: a review of recent research[END_REF]. Our group and others have shown that a cocaineassociated memory can be apparently erased by inhibiting the ERK pathway during recall [START_REF] Miller | Molecular substrates for retrieval and reconsolidation of cocaineassociated contextual memory[END_REF][START_REF] Valjent | Inhibition of ERK pathway or protein synthesis during reexposure to drugs of abuse erases previously learned place preference[END_REF]. However, as ERK is a ubiquitous pathway, identification of more specific targets and a better understanding of the apparent erasure are required before considering any potential therapeutic application. Therefore, in the present study we aimed at finding a more specific target and defining the conditions that allow cocaine CPP erasure. This series of experiments unexpectedly led us to discover that testing the mice once, specifically after conditioning with a high dose of cocaine, can cause by itself a complete loss of preference. To our knowledge, this effect has never been reported before and can have important implications in the interpretation of studies which use CPP as a model and for deciphering the underlying mechanisms.

MATERIALS AND METHODS

Animals

All the experiments were conducted with 8-12 week old male C57Bl/6J mice (Janvier, France), except for immunofluorescence experiments in which we used mutant adult male mice aged 2-6 months: drd1::EGFP and drd2::EGFP BAC transgenic mice (expressing EGFP under the control of dopamine D1 and D2 receptor promoter, respectively) generated by GENSAT (Gene Expression Nervous System Atlas; [START_REF] Gong | A gene expression atlas of the central nervous system based on bacterial artificial chromosomes[END_REF]). The animals were housed 4 per cage, in a 12-h light-dark cycle, in stable conditions of temperature, with food and water ad libitum. They were acclimatized at least one week, before being handled for 3 days prior to behavioral conditioning. The procedures were always performed during the light phase of the diurnal cycle.

Behavioral experiment setup

Conditioned place preference (CPP) was performed in two compartments of a Y-shaped apparatus (Imetronic, Pessac, France) with different wall textures and different visual cues (Fig. 1a &b), in a low luminosity environment (10 lux). The two types of cues were used simultaneously, unless otherwise indicated. The two different textures and visual cues (Fig. 1c) were chosen so that naïve C57Bl/6J mice did not show any preference on average for either compartment. The floor was kept completely smooth because we observed a strong interaction between floor texture and increase in place preference after cocaine conditioning (data not shown), similarly to [START_REF] Rakover-Atar | The influence of natural preference for tactile stimuli on appetitive learning in rat pups[END_REF]. After each mouse the different parts were cleaned with demineralized water and H2O2 2% (vol/vol), before being carefully dried. Hydrogen peroxide is a strong oxidizer and therefore degrades odorant molecules.

Behavioral procedure

The typical procedure was as follows (Fig. 1d). (i) Pretest: on the first day, mice were placed in the center of the apparatus (Fig. 1a) and allowed to explore freely both compartments for 15 min. The time spent in each compartment was automatically recorded. Then mice were assigned to one or the other compartment in an unbiased counterbalanced way for each group, to avoid any initial bias in preference prior to conditioning. (ii) Conditioning: the second day mice were injected with cocaine and placed immediately in the assigned closed compartment (Fig. 1b) for 20 min. The next day they were placed in the other closed compartment after saline injection (10 mL/kg). This was repeated twice (3 cocaine-pairings, 3 saline, in total) unless otherwise specified. (iii) Test 1: CPP was tested the following day during 15 min to assess the efficiency of conditioning. (iv) Re-exposure: the mice treated or not with various inhibitors at the indicated times (see below for each experiment) were injected with cocaine and placed in the cocaine-paired compartment as during the initial conditioning phase. (v) Test 2: the disappearance or not of the preference was tested on day 10. (vi) Drug priming: in some experiments, a priming dose of 10 mg/kg of cocaine was injected just before CPP testing, in order to evaluate if it could restore the place preference.

During testing sessions, the experimenter was unaware of which treatment and which compartment had been previously assigned to the mice.

Drugs

Cocaine hydrochloride (Cooper, Melun, France) was dissolved in 9 g/L NaCl solution (saline) and injected i.p. (10 mL/kg). Solutions were made fresh every day as cocaine can undergo spontaneous hydrolysis [START_REF] Isenschmid | A comprehensive study of the stability of cocaine and its metabolites[END_REF]. SCH23390 hydrochloride (Tocris Bioscience, Bristol, United Kingdom) was dissolved in saline and injected i.p. 0.25 mg/kg [START_REF] Pascoli | cAMP and extracellular signal-regulated kinase signaling in response to d-amphetamine and methylphenidate in the prefrontal cortex in vivo: role of beta 1-adrenoceptors[END_REF], 10 minutes before the animal was placed in the apparatus. SCH58261 (Tocris Bioscience, Bristol, United Kingdom) was dissolved in DMSO (final dose 2.5 mL/kg) and injected i.p. 10 mg/kg [START_REF] Beeler | A role for dopamine-mediated learning in the pathophysiology and treatment of Parkinson's disease[END_REF] 30 minutes before the animal was placed in the apparatus. Raclopride (Tocris Bioscience, Bristol, United Kingdom) was dissolved in saline and injected i.p. 0.3 mg/kg (6.67 mL/kg), 15 minutes before the animal was placed in the apparatus [START_REF] Valjent | Involvement of the extracellular signal-regulated kinase cascade for cocaine-rewarding properties[END_REF].

Statistical analysis

After each test, the percentage of "preference for the cocaine-paired compartment" for each mouse was calculated as follows:

𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑠𝑠𝑠𝑠𝑡𝑡𝑠𝑠𝑡𝑡 𝑡𝑡𝑠𝑠 𝑡𝑡ℎ𝑡𝑡 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑡𝑡𝑠𝑠𝑡𝑡 𝑠𝑠𝑐𝑐𝑡𝑡𝑝𝑝𝑡𝑡𝑝𝑝 𝑐𝑐𝑐𝑐𝑡𝑡𝑠𝑠𝑐𝑐𝑝𝑝𝑡𝑡𝑡𝑡𝑡𝑡𝑠𝑠𝑡𝑡 (𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑠𝑠𝑠𝑠𝑡𝑡𝑠𝑠𝑡𝑡 𝑡𝑡𝑠𝑠 𝑡𝑡ℎ𝑡𝑡 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑡𝑡𝑠𝑠𝑡𝑡 𝑠𝑠𝑐𝑐𝑡𝑡𝑝𝑝𝑡𝑡𝑝𝑝 𝑐𝑐𝑐𝑐𝑡𝑡𝑠𝑠𝑐𝑐𝑝𝑝𝑡𝑡𝑡𝑡𝑡𝑡𝑠𝑠𝑡𝑡) + (𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡 𝑠𝑠𝑠𝑠𝑡𝑡𝑠𝑠𝑡𝑡 𝑡𝑡𝑠𝑠 𝑡𝑡ℎ𝑡𝑡 𝑠𝑠𝑐𝑐𝑠𝑠𝑡𝑡𝑠𝑠𝑡𝑡 𝑠𝑠𝑐𝑐𝑡𝑡𝑝𝑝𝑡𝑡𝑝𝑝 𝑐𝑐𝑐𝑐𝑡𝑡𝑠𝑠𝑐𝑐𝑝𝑝𝑡𝑡𝑡𝑡𝑡𝑡𝑠𝑠𝑡𝑡)

The time spent in the small central zone was negligible and not taken into account in the calculation. Results were expressed as mean ± SEM. Results were analyzed by two-way repeated measures ANOVA with matching between consecutive tests within mice, followed by Bonferroni post hoc tests, using the GraphPad Prism program. The "matching" F value evaluates whether the matching was effective, i.e. the chance of randomly observing an effect this big (or bigger) in an experiment of this size with unmatched samples.

Tissue preparation and immunofluorescence

Drd1a::EGFP and drd2::EGFP mice were quickly and deeply anesthetized with pentobarbital (500 mg/kg, i.p.) and transcardially perfused with 40 g/L formaldehyde in PBS for 5 min. Brains were post-fixed overnight at 4°C before being cut in 30 µm sections using a vibratome (Leica, France). Sections were stored at -20°C in a cryoprotective solution containing glycerol: ethylene glycol: PBS 30:30:40 (vol/vol). Selected free-floating sections were processed for immunolabeling in 48well plates. They were rinsed with Tris-buffered saline (TBS) pH 7.5 containing 50 mM NaF (as phosphatase inhibitor). Sections were first permeabilized with 10% (vol/vol) methanol in TBS containing 50 mM NaF, for 5 min. After being rinsed three times, they underwent a second permeabilization with 0.2% (vol/vol) Triton X-100 in the same buffer, for 20 min. They were then rinsed again 3 times before being incubated overnight at 4°C with the anti-phospho-ERK1/2 (pERK) mouse IgG (Cell Signaling; ref 5726, 150 ng/mL final). After 3 10-min rinses in TBS, sections were incubated with a Cy3-coupled goat anti-mouse secondary antibody (Jackson Laboratory, 1/400) for 45 min at room temperature. Finally, they were rinsed twice in TBS, twice in 50 mM Tris pH 7.5 and mounted in Vectashield with 4,6-diamidino-2-phenylindole (DAPI), (Vector Laboratories, USA).

Confocal microscopy

A laser scanning confocal microscope (TCS SP2, Leica) with a 40X objective was used for image acquisition. It was carried out at the Institut du Fer à Moulin Cell and Tissue Imaging Facility.

RESULTS

ERK is selectively activated in D1 striatal neurons during cocaine CPP re-exposure session

Previous studies have shown that MEK (MAP-kinase/ERK-kinase) inhibition during re-exposure of mice to the environment in which they were initially conditioned [START_REF] Miller | Molecular substrates for retrieval and reconsolidation of cocaineassociated contextual memory[END_REF], or during a reconditioning session [START_REF] Valjent | Inhibition of ERK pathway or protein synthesis during reexposure to drugs of abuse erases previously learned place preference[END_REF] was sufficient to trigger an apparent erasure of the previously learned cocaine CPP. Local infusion of MEK inhibitors in the nucleus accumbens triggered this erasure [START_REF] Miller | Molecular substrates for retrieval and reconsolidation of cocaineassociated contextual memory[END_REF], suggesting that target cells of the inhibitors are located in this brain region. With the experimental settings that we had established in our laboratory, both the conditioned stimulus (the context) and the unconditioned stimulus (cocaine) were necessary to trigger a reconsolidation window sensitive to MEK inhibitor [START_REF] Valjent | Inhibition of ERK pathway or protein synthesis during reexposure to drugs of abuse erases previously learned place preference[END_REF]. To determine in which neurons the ERK pathway is activated at the time of action of MEK inhibitors, we immuno-labeled for pERK (activated form of ERK) brain sections of mice which were formaldehyde-fixed just after a reconditioning session (Fig. 2a). Since the striatal projection neurons (SPNs) are mainly divided in two approximately equal populations, expressing either D1 or D2 dopamine receptors (D1-and D2-SPNs, respectively) [START_REF] Gagnon | Striatal Neurons Expressing D1 and D2 Receptors are Morphologically Distinct and Differently Affected by Dopamine Denervation in Mice[END_REF], we used drd1a::EGFP and drd2::EGFP reporter mouse lines to identify in which neurons ERK was activated. Study of sections in both lines of mice showed that virtually all pERK immunoreactive cells were D1-SPNs in both the dorsal striatum (DS) and nucleus accumbens (NAc) when mice were reconditioned to cocaine (DS 99 ± 1%, NAc core 91 ± 6%, NAc shell 97 ± 3%, n = 6 mice) (Fig. 2a). These results show that activation of the ERK pathway is restricted to D1-SPNs during cocaine re-exposure in the associated context, at a time when CPP memory is sensitive to MEK inhibitors.

A D1R antagonist during re-exposure erases previously learned CPP

We then explored if the D1R antagonist SCH23390, which can prevent cocaine-induced ERK activation in the striatum [START_REF] Valjent | Involvement of the extracellular signal-regulated kinase cascade for cocaine-rewarding properties[END_REF], could recapitulate the effects of MEK inhibition during re-exposure (cocaine + context). We first verified that in our experimental conditions SCH23390 (0.25 mg/kg) completely prevented ERK phosphorylation (in the DS and the NAc) when injected before the re-exposure session with cocaine (Fig. 2b). To evaluate the effects of SCH23390 on previously acquired CPP we used the same procedure as previously described for MEK inhibitors [START_REF] Valjent | Inhibition of ERK pathway or protein synthesis during reexposure to drugs of abuse erases previously learned place preference[END_REF]. We conditioned mice with cocaine (20 mg/kg, 3 cocaine pairings in one compartment, alternated with 3 saline pairings in the other; in this experiment the two compartments differed by tactile cues only) and tested them subsequently to assess their preference for the cocaine-paired compartment (Test 1, Fig. 2c). The next day, these mice received an injection of either SCH23390 (0.25 mg/kg) or vehicle 10 min before being reconditioned with an injection of 20 mg/kg cocaine in the previously cocaine-paired compartment. The following day they were subjected to a second test (Test 2) (Fig. 2c). Re-exposure to both cocaine and context in the presence of SCH23390 completely abolished CPP (Fig. 2c). Thus, the specific blockade of D1R was sufficient to inhibit the ERK pathway in the striatum during the reexposure and to mimic the erasure of the cocaine-place preference obtained with MEK inhibition. Although we did not previously observe it [START_REF] Valjent | Inhibition of ERK pathway or protein synthesis during reexposure to drugs of abuse erases previously learned place preference[END_REF], in a new series of experiments we noticed that the mice undergoing re-exposure without SCH23390 (equivalent to "reconditioning") displayed a significantly decreased CPP when tested again (Test 2, Fig. 2c). Although behavioral results are known to be quantitatively variable across experimenters [START_REF] Lewejohann | Environmental bias? Effects of housing conditions, laboratory environment and experimenter on behavioral tests[END_REF], we were intrigued by this difference and we investigated it further.

Loss of CPP following simple reconditioning is restricted to high doses of cocaine and is resistant to priming

We explored the parameters which might explain the existence of a variable decrease in CPP following a reconditioning session. First, we hypothesized that the conditioning was not robust enough, so we added visual cues to the walls and floors of compartments, in addition to the tactile cues (Fig. 1c), and repeated the procedure. In contrast to our anticipations, the mice lost their place preference between Test 1 and Test 2 (Fig. 3a) with all experimenters. So, reinforcing the conditioning cues did not prevent the loss of CPP between Test 1 and Test 2, but rather facilitated it.

It is known that repeated testing without reward can extinguish a previously learned place preference [START_REF] Mueller | Cocaine-induced conditioned place preference: reinstatement by priming injections of cocaine after extinction[END_REF], but not as rapidly as we observed in our experiments. After extinction, further conditioning [START_REF] Brown | The NMDA antagonist MK-801 disrupts reconsolidation of a cocaine-associated memory for conditioned place preference but not for selfadministration in rats[END_REF] or cocaine priming (i.e. injecting a low dose of cocaine just before testing) [START_REF] Mueller | Cocaine-induced conditioned place preference: reinstatement by priming injections of cocaine after extinction[END_REF] have been shown to reinstate the place preference. However, in our experimental conditions, an additional cocaine conditioning session between the two tests did not prevent the loss of CPP. Moreover, cocaine priming (10 mg/kg just before the test) did not restore the place preference (Fig. 3a). This indicates that the loss of CPP between the two tests cannot be considered as a classical extinction.

We next investigated whether the dose of cocaine would influence the loss of CPP observed in our experimental conditions. We repeated the experiment as in Figure 2c (without SCH23390 during reconditioning) with 10, 15, and 20 mg/kg of cocaine. Within this dose range, the mice developed a comparable place preference, spending about two thirds of their time in the cocainepaired compartment during the first testing (Test 1) indicating the existence of a dose ceiling effect (Fig. 3b). However, when mice were tested after reconditioning (Test 2) a difference appeared between the 3 groups. The mice conditioned with 20 mg/kg consistently and significantly lost their place preference at Test 2, whereas the mice receiving only 10 mg/kg kept the same level of preference between Test 1 and Test 2 (Fig. 3b). Mice receiving 15 mg/kg had an intermediate response (Fig. 3b). Thus, the loss of cocaine CPP was grossly dose-dependent, being clearly apparent with a high dose.

Testing once CPP learned with a high dose of cocaine and 3 pairings is sufficient to trigger a complete loss of place preference

Since the disappearance of place preference occurred when the dose of cocaine was high and since such doses can mediate aversion [START_REF] Riley | The paradox of drug taking: the role of the aversive effects of drugs[END_REF], we reasoned that it was perhaps the repeated exposure to a high dose of cocaine, which was responsible for the erasure of CPP. To test this hypothesis we assessed the respective contributions of Test 1 and of the subsequent 4 th cocaine injection paired with the conditioned context (reconditioning), using 20 mg/kg of cocaine. To our surprise the mice which underwent Test 1 but no reconditioning consistently lost their preference for the cocaine-paired compartment at Test 2 (Fig. 4a). In contrast, the mice for which Test 1 was omitted had a normal preference at the time of Test 2, whether or not they had received the 4 th cocaine-pairing (Fig. 4a). This result clearly demonstrated that Test 1 was the main step responsible for the subsequent loss of CPP.

We then explored whether the apparent erasure due to Test 1 would also occur with a weaker conditioning, i.e. a reduced number of pairings. We therefore performed conditioning with the same experimental setup, but using only one injection of cocaine 20 mg/kg and one saline injection in the other compartment. With 16 mice per group, this single pairing was sufficient to induce a highly significant place preference, although the increased time spent in the cocainepaired compartment was less pronounced than after 3 repeated cocaine pairings (Fig. 4b). When we carried out a second test (Test 2) the mice still showed a significant preference for the cocainepaired compartment (Fig. 4b). So the loss of place preference after Test 1 did not occur when the conditioning was done with only one pairing. This latter result was in line with the previous findings and indicates that, somehow paradoxically, testing the mice once (Test 1) is responsible by itself for the complete loss of place preference observed after strong conditioning (i.e. increased visual cues, high dose of cocaine, high number of pairings).

Test-induced loss of place preference following strong conditioning is transient and CPP is spontaneously restored after 1 month

To complete the characterization of the test-induced loss of place preference, we investigated whether the CPP induced by repeated pairings with 20 mg/kg cocaine and apparently erased by Test 1 could spontaneously be re-expressed at a later time. After conditioning with 3 pairings of cocaine 20 mg/kg and a first post-conditioning test (Test 1), we re-tested the mice (Test 2) either the next day or 4 weeks later (Fig. 5). Whereas the animals tested the next day consistently showed a lack of preference for the cocaine-paired compartment, the group tested after a month interval still displayed a strong place preference (Fig. 5). So, even if the loss of preference was not reinstated in the short term by further conditioning or cocaine priming, the mice spontaneously and completely re-expressed their conditioned place preference in the longer term.

A high dose of cocaine and the existence of a first test are necessary for D1R-antagonistinduced apparent erasure of CPP

After having identified this unexpected effect of Test 1 observed with a conditioning cocaine dose of 20 mg/kg but not 10 mg/kg, we examined the role of these parameters in the D1R antagonistmediated erasure of place preference. First we used a dose of 10 mg/kg instead of 20 mg/kg with the same procedure as above (Pretest/Conditioning/Test 1/Re-exposure/Test 2) with SCH23390 (0.25 mg/kg) or vehicle injected 10 min before re-exposure (cocaine + context) (similarly to Figure 2c). In this experiment, D1R antagonist-mediated erasure of the place preference did not occur (Fig. 6a). This experiment indicated that the apparent erasure of CPP by SCH23390 was only observed following conditioning with a high dose of cocaine, not a lower one.

We then evaluated if Test 1 (just after the initial conditioning) was necessary. Initially, this intermediate test was implemented only to make sure that the animals were correctly conditioned and it is widely used in "erasure" procedures. The mice were conditioned with 3 pairings of cocaine 20 mg/kg and subsequently underwent the re-exposure (cocaine + context) in the presence or absence of SCH23390, before finally being tested for their preference, without any intermediate test. The injection of SCH23390 just before re-exposure did not have any effect on the final preference (Fig. 6b). Our results show that the D1-antagonist SCH23390 does not mediate the disappearance of the place preference when the intermediate test is omitted. Both the intermediate test and the dose of cocaine are necessary conditions required for the D1Rantagonist place preference-mediated erasure to occur (see Fig. 2c).

D1R-antagonist-induced CPP erasure is prevented by an A2aR antagonist, indicating a role of D2 SPNs

The transient character of the disappearance of CPP following Test 1 with a reappearance when Test 2 was carried out a month later, suggested that conditioning was not fully reversed or "erased" but rather masked by another process. Since D1R-and D2R-expressing striatal neurons have opposite effects on the induction of CPP [START_REF] Kravitz | Regulation of parkinsonian motor behaviours by optogenetic control of basal ganglia circuitry[END_REF], we hypothesized that the D2 neurons might play a role in the loss of CPP we observed in our experimental conditions. Dopamine receptors 2 (D2R) and adenosine 2A receptors (A2aR) are mostly localized in D2 SPNs [START_REF] Schiffmann | Striatal restricted adenosine A2 receptor (RDC8) is expressed by enkephalin but not by substance P neurons: an in situ hybridization histochemistry study[END_REF], have an opposite effect on adenylyl cyclase [START_REF] Kull | Reciprocal interactions between adenosine A2A and dopamine D2 receptors in Chinese hamster ovary cells co-transfected with the two receptors[END_REF], and can potentially form heteromers [START_REF] Fuxe | Adenosine A2A and dopamine D2 heteromeric receptor complexes and their function[END_REF]. We used raclopride and SCH58261, antagonists of D2R and A2aR, respectively, to determine whether these drugs could modify the loss of CPP induced by reconditioning in the presence of the D1R antagonist. We investigated the effects of these compounds on the D1R-antagonist place preference mediated-erasure, within the conditions in which it does occur (i.e. as in Figure 2c). We conditioned mice with 3 pairings of cocaine (20 mg/kg), tested them just after conditioning (Test 1), before performing the re-exposure session with the D1R antagonist injection (exactly as in Figure 2c). The mice injected with the D1R antagonist before re-exposure (cocaine + context) did not show any preference the next day in Test 2 (Fig. 7), as reported above. The mice which were injected with the D2R antagonist also lost the previous CPP (Fig. 7). In contrast, the mice which received the A2aR antagonist during reconditioning in the presence of D1R antagonist, displayed a strong preference for the cocainepaired compartment (Fig. 7). These results revealed that following blockade of A2aR during the reconditioning step the erasing effects of the D1R antagonist combined with the intermediate Test1 were not observed. In contrast, the D2R antagonist appeared to increase these effects, possibly in relation with the opposing actions of D2R and A2aR on signaling in D2 neurons. These experiments strongly suggest that in addition to D1 neurons, the D2 neurons play a key role in the place preference disappearance.

DISCUSSION

In the present study we show that a D1R antagonist can contribute to the apparent loss of cocaineinduced CPP, using similar experimental settings as in a previous study showing that a MEK inhibitor could erase cocaine-induced CPP [START_REF] Valjent | Inhibition of ERK pathway or protein synthesis during reexposure to drugs of abuse erases previously learned place preference[END_REF]. However, our study revealed a regulation of CPP expression, which was more complex than anticipated and highly dependent on the overall experimental conditions. Further investigation revealed the existence of a transient blockade of CPP that can follow its simple evaluation and paradoxically appears only following strong conditioning.

The loss of CPP after a strong conditioning (strong cues, high dose, repeated pairings) is surprising and may reveal important features of this cocaine-induced behavioral modification. It is known that letting the animal freely access the previously cocaine-paired environment in the absence of cocaine, as done during the test sessions, results in a small extinction [START_REF] Mueller | Cocaine-induced conditioned place preference: reinstatement by priming injections of cocaine after extinction[END_REF]. To completely extinguish CPP expression, this exposure has to be repeated several times [START_REF] Mueller | Cocaine-induced conditioned place preference: reinstatement by priming injections of cocaine after extinction[END_REF]. In our conditions the loss of CPP was complete after only one session of "test" and strikingly occurred specifically in "strong conditioning conditions", whereas this effect was absent if the conditioning was weaker (3 pairings 10 mg/kg, or only one pairing 20 mg/kg). This suggests that such CPP loss may result from mechanisms at least partially different from those of standard extinction or that our experimental conditions triggered a particularly strong extinction mechanism. Indeed, in contrast to extinction, the loss of CPP we observed was not prevented by cocaine reconditioning and was also not rescued by cocaine priming before Test 2. However, the loss of CPP we observed was transient since place preference was fully restored when Test 2 was carried out a month after initial conditioning, suggesting that the initial learning was preserved.

How can only one test trigger a complete but transient loss of preference behavior? And why does it appear only when the conditioning has been strong? Several levels of explanation can be envisioned. Dopamine response encodes a reward prediction error rather than the reward itself [START_REF] Schultz | Responses of midbrain dopamine neurons to behavioral trigger stimuli in the monkey[END_REF]. Recent data indicate that it may also signal reward value through regulation of different aspects of dopamine neurons firing and dopamine release [START_REF] Hamid | Mesolimbic dopamine signals the value of work[END_REF]. Formal models of learning used to predict behavior derived from [START_REF] Rescorla | A theory of Pavlovian conditioning: Variations in the effectiveness of reinforcement and nonreinforcement[END_REF], propose that there is a predictive value associated to a given action. This value depends on the history of previous rewards and is updated after each trial depending on the prediction error. In our experimental conditions, we could hypothesize that the stronger the conditioning, the higher the expectation during the test, possibly leading to a strong negative prediction error. This negative error would be less pronounced when the conditioning was weaker. Another aspect of the experimental conditions that could contribute to the loss of CPP in this paradigm is the difference between the testing conditions and the conditioning conditions. During the test, mice have free access to both compartments, whereas during conditioning they are confined in one compartment. It is possible that mice discriminate the two situations and that the more they trained in the first situation (conditioning), the better they make the difference with the second situation (testing). In this case, the animal would finally expect a reward in the conditioning situation but not in the testing situation, and thus would not show place preference anymore. This would be consistent with the fact that an extra conditioning session after the test would not improve the performance of the mice. Nevertheless, these two lines of explanation do not account for the reappearance of CPP when Test 2 was carried out 4 weeks after conditioning (see Fig. 5). This suggests that, as in the case of extinction, disappearance of the behavior involves the recruitment of separate inhibitory pathway(s).

Even though our study is phenomenological and does not allow to precisely identify the underlying mechanisms at the molecular and cellular levels, the effects of pharmacological agents provide some interesting clues. Apparent erasure of CPP is triggered or enhanced by the blockade of the ERK pathway or of D1R, which triggers the activation of this pathway. ERK activation in the striatum following cocaine injection is restricted to D1 SPNs and depends on D1R stimulation ( [START_REF] Valjent | Involvement of the extracellular signal-regulated kinase cascade for cocaine-rewarding properties[END_REF], and this study). Although the precise site of action of the D1R antagonist SCH23390 was not investigated in this study, striatal neurons are good candidates, although involvement of other brain regions including amygdala, hippocampus and prefrontal cortex is also possible, as suggested in distinct but related paradigms [START_REF] Alleweireldt | Effects of SCH-23390 infused into the amygdala or adjacent cortex and basal ganglia on cocaine seeking and selfadministration in rats[END_REF][START_REF] Cosme | D1, but not D2, receptor blockade within the infralimbic and medial orbitofrontal cortex impairs cocaine seeking in a region-specific manner[END_REF] . In addition, we found evidence for an opposite role of D2 SPNs. The blockade of A2aR by an antagonist counteracted the loss of CPP, whereas the blockade of D2R if anything further decreased the preference. Further work will be needed to address the precise cellular bases of these effects. Synaptic plasticity in the form of long term potentiation of corticostriatal synapses is known to depend on cAMP and ERK stimulation by D1R in D1 SPNs and on cAMP stimulated by A2aR and inhibited by D2R in D2 SPNs [START_REF] Pascoli | Reversal of cocaine-evoked synaptic potentiation resets drug-induced adaptive behaviour[END_REF][START_REF] Shen | Dichotomous dopaminergic control of striatal synaptic plasticity[END_REF]. The effects of antagonists of these various receptors in our experimental conditions are compatible with a positive contribution of cAMP/ERK-dependent plasticity in D1 SPNs to the CPP expression, as previously shown for its induction. Conversely A2aR-mediated cAMP-dependent plasticity in D2 SPNs might reinforce an opposite behavioral regulation, which may lead to an apparently decreased preference or even an avoidance, as suggested by the effects of D2R blockade during reconditioning. Thus, a hypothesis that could account for our observations is that apparent erasure of CPP could result from its masking through increased cAMP-dependent plasticity and gain of function of D2 SPNs. The recruitment of this putative negative mechanism might be facilitated by strong dose and/or cues. A variable balance between striatal circuits comprising D1 and D2 SPNs may thus regulate the behavioral output of preference for a particular place. The modifications in the behavioral choices observed after the initial conditioning suggest that this balance is not definitely blocked but remains dynamic. In rat it was shown that blockade of D1 receptors with SCH23390 12 h after the test session delayed extinction, suggesting that a D1 dependent mechanism might also be operating [START_REF] Fricks-Gleason | Dopamine D1 receptor antagonism impairs extinction of cocaine-cue memories[END_REF]. In that study as in ours the antagonist was administered systematically and it may have exerted its effects at various levels, including the dorsal hippocampus, in which stimulation of D1-like receptors has been reported to enhance extinction [START_REF] Abraham | Activation of D1/5 Dopamine Receptors: A Common Mechanism for Enhancing Extinction of Fear and Reward-Seeking Behaviors[END_REF]. Such an effect is unlikely to account for our results which rather correspond to an enhancement of an extinction-like response.

In the erasure protocols, intermediate tests are usually performed to check the preference of the animals, but their effects are neglected. Here we show that an apparent erasure of place preference with D1R antagonist during a recall does not occur in the absence of the intermediate test, meaning that these tests should be more globally taken into consideration in the design of "erasure" protocols and their interpretations. The erasure phenomena are probably highly complex and their understanding is far from being complete. Many inconsistencies are apparent in the published reports and subtle boundary conditions are suspected to be at stake [START_REF] Nader | Memory reconsolidation: an update[END_REF]. Even with fear conditioning which is the most widely used paradigm, boundary conditions are being discussed to elucidate discrepancies and sometimes opposite results using similar protocols [START_REF] Auber | Post-retrieval extinction as reconsolidation interference: methodological issues or boundary conditions?[END_REF]. Conflicting results are difficult to decipher [START_REF] Lee | D-cycloserine potentiates the reconsolidation of cocaine-associated memories[END_REF][START_REF] Pineyro | Memory destabilization is critical for the success of the reactivation-extinction procedure[END_REF] and boundary conditions are still not clearly defined. Besides, some studies suggest that memory erasure is not as long lasting as previously thought [START_REF] Alberini | The role of protein synthesis during the labile phases of memory: revisiting the skepticism[END_REF][START_REF] Eisenberg | Reconsolidation of fresh, remote, and extinguished fear memory in Medaka: old fears don't die[END_REF][START_REF] Rudy | Anisomycin and the reconsolidation hypothesis[END_REF]. Erasure is considered as an absence of recovery of the behavior but different parameters and different reinstatement procedures can be used, and they are rarely all tested. Therefore, it is never to exclude that an apparently erased memory could be reinstated by another appropriate procedure. The frontier between extinction (formation a new memory which hides the expression of the initial learning) and reconsolidation is narrow [START_REF] Monfils | Extinction-reconsolidation boundaries: key to persistent attenuation of fear memories[END_REF].

In summary the present results suggest the existence of a balance between D1R-and A2aR -regulated mechanisms that control the compartment preference in the CPP paradigm, which can be shifted depending on the details of the experimental conditions. The present work points out some potential caveats in "erasure" studies, and resulting difficulties to interpret and compare different studies. It also raises the question of the vocabulary used, which influences the way we comprehend these phenomena. We hope the present findings will facilitate the design and interpretation of future studies aiming at understanding the mechanisms of memory erasure, which could have many therapeutic implications, including for drug addiction.

Figure 1 :

 1 Figure 1: Experimental setup and outline. (a) Testing configuration and the corresponding simplified scheme. (b) Conditioning configuration and simplified schemes. (c) The two different combinations of tactile and visual cues on the compartment walls. (d) Typical experimental outline.

Figure 2 :

 2 Figure 2: Role of D1 striatal neurons in CPP re-consolidation. (a) Confocal sections showing phospho-ERK (pERK) immunofluorescence in the dorsal striatum were generated from drd1a::EGFP and drd2::EGFP mice. Animals were sacrificed and perfused at the end of the 20 min reconditioning session. (b) Mice were treated as in A except that they received SCH23390 (0.25 mg/kg i.p.) 10 min before cocaine and re-exposure session. Confocal section showing phospho-ERK immunofluorescence in the striatum. (A and B), scale bar 50 µm. (c) The day after Test 1, the mice were subjected to a "reexposure" (cocaine and paired-context) session. Ten min before cocaine injection and placement in the apparatus, mice received a D1R antagonist SCH23390 (0.25 mg/kg i.p.) or vehicle. Mice were subjected to a new test the following day (Test 2). Data are means ± SEM (n= 22-24 WT mice per group). Two-way repeated-measures ANOVA: tests effect, F(2,88)=52.2, P<0.0001; treatment effect F(1,44)=4.09, P=0.049; interaction, F(2,88)=4.02, P = 0.021; matching, F(44,88)=2.56, P<0.0001. Bonferoni post hoc test: ○○ P<0.01, ○○○ P<0.001 (Test 1 vs. Pretest);  P<0.01,  P<0.001 (Test 2 vs. Test 1); **P<0.01.

Figure 3 :

 3 Figure 3: Disappearance of CPP: lack of effect of priming and dependence on cocaine doses. Mice were subjected to a cocaine CPP protocol, similarly to Fig. 2, but with additional visual cues on the compartment walls (see Methods and Results). (a) In these conditions, the CPP response observed in Test 1 was no longer detected in Test 2. The day after Test 2 they received a priming cocaine injection (10 mg/kg, i.p.) and were tested for preference. (b) Mice were conditioned with the indicated doses of cocaine. Note that the CPP was similar in Tests 1 and 2 when the dose of 10 mg/kg cocaine was used for conditioning. (a) Data are means ± SEM (n= 20 mice per group). One-way repeated-measures ANOVA: tests effect, F(3,57)=6.0, P=0.0013; matching, F(19,57)=1.36, P=0.19. Bonferoni post hoc test: ○ P<0.05, ○○ P<0.01, ○○○ P<0.001 (Test 1 vs. Pretest);  P<0.05,  P<0.01 (Test 2 vs. Test 1). (b) Data are means ± SEM (n= 16-20 mice per group). Two-way repeated-measures ANOVA: tests effect, F(2,98)=16.3, P<0.0001; treatment effect F(2,98)=0.60, P=0.51; interaction, F(4,98)=0.90, P=0.47; matching, F(49,98)=3.90, P<0.0001. Bonferoni post hoc test: ○ P<0.05, ○○ P<0.01, ○○○ P<0.001 (Test 1 vs. Pretest);  P<0.05,  P<0.01 (Test 2 vs. Test 1).

Figure 4 :

 4 Figure 4: A first CPP test (Test 1) can be necessary and sufficient to trigger the disappearance of CPP to 20 mg/kg cocaine in subsequent test. Mice were subjected to a cocaine CPP protocol, similar to that in Fig. 3. When Test 1 or cocaine re-exposure were omitted, mice simply stayed in their home cage on that day. The actual day number of each manipulation is indicated below the bars. (a) Data are means ± SEM (n = 12 mice per group). One-way ANOVA: F(9,110)=6.62, P<0.0001. Bonferoni's multiple comparison post hoc test: ○ P<0.05, ○○○ P<0.001 (Test 1 vs. Pretest);  P<0.05,  P<0.001 (Test 2 vs. Test 1). (b) Data are means ± SEM (nsaline= 8, ncocaine= 16). Two-way repeated-measures ANOVA: tests effect, F(2,44)=2.85, P=0.068; treatment effect F(1,22)=3.99, P=0.058; interaction, F(2,44)=4.113, P=0.023; matching, F(22,44)=2.87, P=0.0014. Bonferoni post hoc test: n.s. non-significant, ○ P<0.05, ○○○ P<0.001 compared to Pretest.

Figure 5 :

 5 Figure 5: Spontaneous CPP recovery when Test 2 is delayed. Mice were conditioned to 20 mg/kg cocaine similarly to Fig. 3, except that Test 2 was carried out 1 day or 1 month later. Data are means + SEM (n= 12 mice per group). Two-way repeated-measures ANOVA: tests effect, F(2,44)=29.2, P<0.0001; treatment effect F(1,44)=2.60, P=0.12; interaction, F(2,44)=5.18, P=0.0096; matching, F(22,44)=4.71, P<0.0001. Bonferoni post hoc test: ○○○ P<0.001 (Test 1 vs. Pretest),  P<0.001 (Test 2 vs. Test 1).

Figure 6 :

 6 Figure 6: SCH23390-mediated erasure depends on experimental conditions. (a) SCH23390 was ineffective to change CPP response between Test 1 and Test 2 when animals were conditioned with 10 mg/kg cocaine, in contrast to what observed after conditioning with 20 mg/kg cocaine (see Fig. 3a). Data are means + SEM (n= 12 mice per group). Two-way repeatedmeasures ANOVA: test effect, F(2,44)=10.33, P=0.0002; effect F(1,44)=0.06, P=0.80, interaction, F(2,44)=0.11, P=0.90; matching, F(22,44)=3.20, P=0.0005. Bonferoni post hoc test: ○ P<0.05, ○○ P<0.01, ○○○ P<0.001 compared to Pretest (b) SCH23390-induced disappearance of CPP requires Test 1.Data are means ± SEM (n= 12 mice per group). Two-way repeated-measures ANOVA: tests effect, F(1,22)=45.86, P<0.0001; treatment effect F(1,22)=0.03, P=0.86; interaction, F(1,22)=0.02, P = 0.89; matching, F(22,22)=1.95, P=0.063. Bonferoni post hoc test: ○○○ P<0.001 compared to Pretest.

Figure 7 :

 7 Figure 7: SCH23390-induced disappearance of CPP is prevented by an A2aR antagonist and increased by a D2R antagonist. Mice were treated as in Fig. 2B, SCH23390 was administered 10 min before the reconditiong session without or with raclopride (0.3 mg/kg, D2R antagonist -20 min before SCH23390-) or SCH58261 (10 mg/kg, A2aR antagonist -5 min before SCH23390-). Data are means ± SEM (n= 8 mice per group). Two-way repeated-measures ANOVA: tests effect, F(2,42)=8.02, P=0.011; treatment effect F(2,21)=0.86, P=0.44; interaction, F(4,42)=3.11, P =0.02 ; matching, F(21,42)=2.99, P=0.012. Bonferoni post hoc test: ○ P<0.05 (Test 1 vs. Pretest),  P<0.05 (Test 2 vs. Test 1), *P<0.05.

  All the experiments were in accordance with the European Community Council Directive 2010/63/EU and approved (Ce5/2012/095) by the Comité d'éthique pour l'expérimentation animale Charles Darwin (Paris, France) #05.

Acknowledgments

We thank Yohann Bertelle and Annie Rousseau for animal care, Julie Chaumeil for help with the figures, and members of the Girault & Hervé's lab for stimulating discussions. We are grateful to Paul Greengard (The Rockefeller University, New York) for initially providing the drd1a::EGFP and drd2::EGFP mice. The authors declare no competing interest. Microscopy and image analysis were carried out at the Institut du Fer à Moulin Cell and Tissue Imaging Facility. This work as supported by Inserm and Sorbonne-Universités/Université Pierre et Marie Curie, and by grants from ERC AIG-250349 and Fondation pour la Recherche Médicale (FRM) to JAG.

Author Contributions

JAG and DH conceived and supervised the project. JAG, DH and LMP designed the experiments. LMP, EV, AB and SL performed experiments and analyzed data. OE provided experimental support and conceptual advice. JAG, DH, LMP, JC, and AB interpreted and discussed the data. LMP and JAG wrote the manuscript, with critical revision of the article from AB, DH, EV, JC, and OE. All the authors approved the final version of the manuscript.


Saloua Peatier
email: salouapeatier@cerfacs.fr

M Sanderson

L Terray

R Roehrig

B M Sanderson

Investigating Parametric Dependence of Climate Feedbacks in the Atmospheric Component of CNRM-CM6-1

come

Introduction

The Equilibrium Climate Sensitivity (ECS) refers to the steady state change in the annual global mean surface temperature following a doubling of the atmospheric equivalent CO 2 concentration [START_REF] Pachauri | Annex ii: Glossary [mach[END_REF].The ECS depends on the climate feedback strength, defined as the change in radiative forcing at the Top of Atmosphere (TOA) following a unit change in the annual global mean surface temperature. The recent study of [START_REF] Sherwood | An assessment of earth's climate sensitivity using multiple lines of evidence[END_REF], combine three lines of evidence including feedback process understanding, historical climate record and paleoclimate record and find a stronger constraint on ECS than previously assessed with a 66% probability range of 2.3 < ECS < 4.5K.In contrast, in the sixth phase of the Coupled Model Intercomparison Project (CMIP), 10 General Circulation Models (GCMs) out of 27 have values of ECS exceeding 4.5K [START_REF] Zelinka | Causes of higher climate sensitivity in cmip6 models[END_REF], including CNRM-CM6-1, which shows an ECS of 4.9K [START_REF] Voldoire | Evaluation of cmip6 deck experiments with cnrm-cm6-1[END_REF].

The unconstrained parameters introduced in the climate model representation of subgridscale processes (i.e. in so-called parameterizations) strongly impact climate sensitivity [START_REF] Murphy | Quantification of modelling uncertainties in a large ensemble of climate change simulations[END_REF][START_REF] Stainforth | Uncertainty in predictions of the climate response to rising levels of greenhouse gases[END_REF]. One way to explore this parametric uncertainty is to create Perturbed Parameter Ensembles (PPE), in which parameters are varied within expert-defined ranges. PPEs can be used to better calibrate climate models [START_REF] Williamson | Identifying and removing structural biases in climate models with history matching[END_REF][START_REF] Bellprat | Objective calibration of regional climate models[END_REF][START_REF] Hauser | Artificial neural network assisted bayesian calibration of climate models[END_REF] or to explore uncertainty associated with climate change [START_REF] Piani | Constraints on climate change from a multi-thousand member ensemble of simulations[END_REF][START_REF] Sanderson | Constraints on model response to greenhouse gas forcing and the role of subgrid-scale processes[END_REF][START_REF] Shiogama | Multiparameter multi-physics ensemble (mpmpe): A new approach exploring the uncertainties of climate sensitivity[END_REF]. In 2005, PPE of the HadAM3 GCM found versions with a 2 -11K ECS range [START_REF] Stainforth | Uncertainty in predictions of the climate response to rising levels of greenhouse gases[END_REF][START_REF] Murphy | Quantification of modelling uncertainties in a large ensemble of climate change simulations[END_REF], albeit with varying present-day climatological skill [START_REF] Sanderson | Constraints on model response to greenhouse gas forcing and the role of subgrid-scale processes[END_REF]. This wide ECS range could not be reproduced with a similar PPE constructed with the Community Atmosphere Model [START_REF] Sanderson | A multimodel study of parametric uncertainty in predictions of climate response to rising greenhouse gas concentrations[END_REF], which produced a range of 2.2 -3.2K, highlighting that two models can respond very differently to similar parameter perturbations. Recently, a PPE of HadGEM3 atmosphere-only simulations showed a larger range of climate feedbacks, from -1.80 to -0.93 W.m -2 .K -1 (D. [START_REF] Sexton | Finding plausible and diverse variants of a climate model. part 1: Establishing the relationship between errors at weather and climate time scales[END_REF][START_REF] Karmalkar | Finding plausible and diverse variants of a climate model. part ii: development and validation of methodology[END_REF]. However, the performance filtering applied to this atmosphere-only PPE limited the diversity of sensitivity in the HadGEM3 coupled perturbed simulations, especially in the low-end of the distribution [START_REF] Rostron | The impact of performance filtering on climate feedbacks in a perturbed parameter ensemble[END_REF].

The primary purpose of this study is to propose a tractable, semi-autonomous approach for producing model candidates which span a range of responses. We explore the diversity of climate feedbacks in a PPE based on the CNRM-CM6-1 atmospheric component and assess feedback likelihood through the use of statistical emulators and observational datasets. We discuss how model performance evaluated on different fields constrains the model climate feedbacks. Finally, we propose an approach for determining an optimal subset of calibrations maximising performance across a range of feedback values.

Model and Methods

This work presents a PPE using ARPEGE-Climat 6.3 [START_REF] Roehrig | The cnrm global atmosphere model arpege-climat 6.3: Description and evaluation[END_REF], the CNRM-CM6-1 atmospheric component [START_REF] Voldoire | Evaluation of cmip6 deck experiments with cnrm-cm6-1[END_REF]. ARPEGE-Climat 6.3 as used here has a spatial resolution of about 150 km, with 91 vertical levels from near 6 m to 82 km (or 0.01 hP a). The released version of this model will be referred to as the reference model version and thereafter named CNRM-CM6-1. Alternative versions of this model will be referred to as CNRM-CM. Two experiments are considered: (1) an AMIP [START_REF] Eyring | Overview of the coupled model intercomparison project phase 6 (cmip6) experimental design and organisation[END_REF] simulation, where the model is forced by observed Sea Surface Temperatures (SSTs) and Sea Ice Concentrations (SICs); (2) the AMIP-future4K experiment following the Cloud-Feedback Model Inter-comparison Project (CFMIP) [START_REF] Webb | The cloud feedback model intercomparison project (cfmip) contribution to cmip6[END_REF] protocol, where a composite SST warming pattern derived from the CMIP3 coupled models is added to the AMIP SSTs and scaled such that the global mean SST increase averaged over the ice-free oceans is +4K. Both simulations use observed CO 2 concentrations from 1979 to 1981. They are three-years long, (1979)(1980)(1981), which is a reasonable length to achieve the stabilization on the net radiative feedback in different CFMIP models (Figure S1). A total of 30 parameters are selected and their uncertainty limits are determined by expert solicitation with model developers (Table S1). The parameter values simultaneously vary and are sampled with a Latin Hypercube (LH) design where the minimum distance between points is maximized in order to have a uniform sampling of the parameter space [START_REF] Urban | A comparison of latin hypercube and grid ensemble designs for the multivariate emulation of an earth system model[END_REF]. After the crash of 68 simulations, the PPE considered here has 102 members.

Model performance

In order to assess the present-day climatological performance of the PPE members, we take a subset of atmospheric variables from the AMIP simulation and compare them with observational datasets (Table S2, [START_REF] Loeb | Clouds and the earth's radiant energy system (ceres) energy balanced and filled (ebaf) top-of-atmosphere (toa) edition-4.0 data product[END_REF][START_REF] Rohde | The berkeley earth land/ocean temperature record[END_REF][START_REF] Adler | Global precipitation climatology project (gpcp) climate data record (cdr), version 2.3 (monthly)[END_REF]. Rather than using a full Root Mean Square Error (RMSE), we chose to use a metric that focuses on the part of the error related to parameter changes.

For each variable, we consider the model annual mean climatology and calculate EOFs.

In contrast to conventional EOFs, the temporal dimension is replaced by the ensemble member dimension (as in [START_REF] Higdon | Computer model calibration using high-dimensional output[END_REF][START_REF] Biegler | Large-scale inverse problems and quantification of uncertainty[END_REF][START_REF] Sexton | Multivariate probabilistic projections using imperfect climate models part i: outline of methodology[END_REF][START_REF] Sanderson | Constraints on model response to greenhouse gas forcing and the role of subgrid-scale processes[END_REF]. This analysis provides compact description of the spatial variability of the ensemble variance control climate. The resulting EOFs are spatial patterns, while their principal components (PCs) are the expansion coefficients showing the projection of each ensemble member onto the respective EOF. We then project the annual mean climatology of the observations of a given variable s on the EOF basis and reconstruct the 3-dimensional fields of both the models and the observations, using only the first five modes of the EOFs. The error score is then represented by the area weighted RMSE of these reconstructed fields.

The truncation of the EOF after 5 modes is a subjective choice that allows a skillfull emulation while applying the same truncation to all the climatic fields. This truncation explains 63% (for the precipitation) to 85-90% (for the other variables) of the PPE variance. This metric is , by construction, strongly correlated to a standard RMSE (Figure S2) but has the benefit of assessing the model performance within the space defined by the chosen parameter range. For each PPE member, the error associated with each variable E s can be standardized by the error of the CNRM-CM6-1 AMIP simulation E CM6,s , allowing the combination of errors associated with the different variables and the estimation of a total error E tot :

E tot = 1 P P s=1 E s E CM6,s (1)
where P is the number of variables considered. As described in Table S2, we use four climatological fields to calculate the total error (thus P = 4). The aggregated metric E tot represents a standardized distance between observations and model, considering the four variables described in Table S2. In this framework, when E tot < 1, the given member is considered better than the reference model version.

Statistical predictions of model results

The 102-member PPE is a sparse sample of a 30 dimensional parameter space, with ensemble size limited by finite computational resources. We therefore consider statistical tended to produce an over-fitted result (Figure S3).

The LASSO model is a regression method that performs both variable selection and regularization in order to enhance the prediction accuracy. The LASSO and the MLR models show comparable overall performance, with lower out-of-sample errors for the LASSO model. However, both models, and especially the LASSO, have difficulty predicting extreme feedback values (Figure S4). The MLR model is used in the rest of the study, in order to better predict the extreme values of feedback (Figure S5). The control mean state emulator is built and trained to predict the five first PCs of the EOF analysis described in the previous section, expressed as follows:

Y = K j=1 a j x j + R (2)
with Y = PC i , the i-th PC of the EOF analysis (from a total N = 5), .

Optimization with constraint and relative likelihood function

The objective here is to use the statistical emulator to find optimal model versions spanning the whole range of net feedback. For this purpose, we optimize the emulated response described above in order to obtain a subset of the best calibrations given a specified feedback value. In other words, we aim to find the calibrations which minimize the error E tot given by the mean state emulator, while conditioning the predicted global net feedback value to lie within a chosen bin. We use a constrained linear minimization optimizer [START_REF] Virtanen | Scipy 1.0: fundamental algorithms for scientific computing in python[END_REF] based on sequential least squares programming.

The optimization process is iterative and carried out as follows :

•

Step 1 -The emulators are used to produce a 100,000-member ensemble. A vector of discrete global feedback values is created, of length n λ , such that λ i spans for all values of i the range of feedbacks seen in the ensemble in increments of 0.01 W.m -2 .K -1 .

•

Step 2 -For each bin of feedback parameter, we select, within the 100,000 Latin Hypercube sample, the calibration which shows the lowest E tot when used in the mean state emulator while lying within a given bin (i.e. λ i -0.005

W.m -2 .K -1 < λ < λ i + 0.005 W.m -2 .K -1
). These parameter values are used to initialize the optimizer.

•

Step 3 -The optimizer is used to produce P 1 -a 30 by n λ matrix with initial optimal parameter estimates for each discrete bin of λ i .

•

Step 4 -P 1 seems like a good guess of optimal parameter values but is very noisy.

We make the hypothesis that a smooth parameter pathway exists along the feedback range (as suggested by [START_REF] Neelin | Considerations for parameter optimization and sensitivity in climate models[END_REF]) and repeatedly apply a three-point moving average along this axis to each parameter value individually.

•

Step 5 -These smoothed values of parameter are then used to reinitialize the optimizer, which produces a smoothed final estimate of optimal calibrations P 2 , validating our previous hypothesis.

•

Step 6 -Finally, we sample 24 calibrations from P 2 , along the feedback range, and use it to perform a new set of simulations with the CNRM-CM atmospheric component.

After the optimization process, the total error associated with the optimal calibration depends on λ i , which allows us to estimate the relative likelihood of the feedback parameters, within the range of λ we can simulate. The likelihood function is usually expressed as [START_REF] Friedman | The elements of statistical learning[END_REF], considering the parametric model θ = (µ, σ 2 ) with µ the mean and σ the standard deviation in the case of a normal distribution.

L(θ, x i ) ∼ exp -(xi-µ) 2 2σ 2 (
Here, the error associated with the optimal calibration E i (λ i ) is considered drawn from a Gaussian distribution of width σ. The parametric model of λ is then written as θ = (E i (λ i ), σ 2 ) and the likelihood becomes :

L(θ, λ i ) ∼ exp - E i (λ i ) 2 2 × σ 2 (3)
The error E i (λ i ) and the Gaussian width σ remains to be defined. In this study, two estimates of feedback likelihood are proposed. The first one is based on the emulated total errors associated with the optimal calibrations. In this case, the emulated error E tot,i (λ i ) is scaled by the sum of the out-of-sample error of the emulator (representing the emulator error)

and the standard deviation of E tot within the CFMIP multi-model ensemble (representing the diversity of acceptable errors in climate models) :

E(λ i ) = E tot,i (λ i ) and σ = (OSE + σ Etot,CF M IP ).
A revised estimate of feedback likelihood is then proposed, based on the total errors associated with actual CNRM-CM runs of the optimal calibrations (as described in Step 6 of the optimization). A cubid spline under tension is used to interpolate between the errors of sampled optimal candidates along the feedback range, and this interpolation Êtot,i (λ i ) is used in the likelihood estimate. In this other case, the out-of-sample error of the emulator can be removed from the likelihood equation : E(λ i ) = Êtot,i (λ i ) and σ = σ Etot,CF M IP .

3 Results

Feedback distribution

The most accurate method to estimate of the feedback parameter λ from the CMIP6 simulations is based on the increase of the atmospheric CO 2 concentration in fully coupled atmosphere-ocean models. However, the high computational cost of coupled simulations and the need of running them for hundreds of years to get an equilibrated control simulations renders the production of fully-coupled PPE practically impossible. A cheaper way of estimating the total feedback parameter is to raise the sea surface temperatures (SSTs) in atmosphere-only models [START_REF] Cess | Intercomparison and interpretation of climate feedback processes in 19 atmospheric general circulation models[END_REF], even though it has been shown that this estimate of the total net feedback parameter can differ from the coupled-derived estimate due to differences in the clear-sky feedbacks [START_REF] Ringer | Global-mean radiative feedbacks and forcing in atmosphere-only and coupled atmosphere-ocean climate change experiments[END_REF]. In the PPE context of this study and given the limits of our computational resources, the total net feedback parameter

λ (W.m -2 .K -1
) is based on the difference (∆ operator) between the forced AMIP-future4K and the control AMIP experiments. In both experiments, the net radiative budget N , in W.m -2 , is the difference between the downward and the upward radiative fluxes at the top of atmosphere and T , in K, is the annual global mean surface temperature.

λ = ∆N ∆T (4)
Assuming the CNRM-CM6-1 forcing of F 2x ≈ 6.5 W.m -2 [START_REF] Voldoire | Evaluation of cmip6 deck experiments with cnrm-cm6-1[END_REF], we can estimate the climate sensitivity S (in K) [START_REF] Andrews | Accounting for changing temperature patterns increases historical estimates of climate sensitivity[END_REF] :

S = -F 2x λ (5)
The PPE provides a large diversity of climate feedback parameters (figure 1), which range from -0.7 to -1.8 W.m -2 .K -1 . The CNRM-CM6-1 feedback value (-1.33 W.m -2 .K -1 ) falls near the center of the distribution. The PPE feedback parameter range is notably wider than the one simulated by the multi-model CFMIP ensemble (from -1.7 to -1.1 W.m -2 .K -1 ) [START_REF] Webb | The cloud feedback model intercomparison project (cfmip) contribution to cmip6[END_REF]. For comparison, the feedback distribution obtained in the HadGEM3 atmosphere-only PPE [START_REF] Karmalkar | Finding plausible and diverse variants of a climate model. part ii: development and validation of methodology[END_REF] ranges from -1.7 to -0.9 W.m -2 .K -1 , which is comparable to the results obtained with our current PPE. We note that both PPEs could not reach the lower end of the CFMIP feedback distribution, corresponding to the lowest climate sensitivities.

Model performance and constraints on the feedback range

The PPE members indicate that some CNRM-CM versions simulate mean surface temperature, precipitation and radiative fluxes with comparable or better skill than the reference model version (figure 2). However, none of the CNRM-CM models show better results than CNRM-CM6-1 in the aggregated metric (Figures 2e andS7e).

We now consider potential optimal performance and its relationship to ECS in a larger emulated ensemble. The emulation of 100,000 new members predicts model versions performing as well as or better than the reference version, spanning a wide range of feedback values. The total error E tot described in equation ( 1) is presented on figure 2e. It is notable that CNRM-CM6-1 has the lowest E tot of all the PPE members, and only 1% of the emulated members show a better performance -indicating a rather successful expert calibration of the model when a multi-variate metric is considered.

The PPE results are also compared with those of the six CFMIP climate models. The global annual means of the four climatic fields of the CFMIP models are projected onto the PPE-derived EOF basis. Then, the RMSE between these projections and the observations are computed. In the aggregated metric as well as in the individual metrics, the other CFMIP models mostly show better performance than CNRM-CM6-1 and than most of the emulated CNRM-CM versions.

In Figure 2, and following Equation ( 5), lower feedback parameters |λ| correspond to higher estimated ECS values. The emulated CNRM-CM versions with lower-than-reference errors span a reduced range of ECS compared to the full emulated ensemble (Figure S6).

This range is rather centered around the CNRM-CM6-1 value for the individual metrics, but is slightly shifted to the high ECS for the aggregated metric (Figure S6e). The slope in the optimization line of Figure 2e seems to indicate that the best performing calibration correspond to model version with ECS higher than the reference (Figure 2e).

Selection of optimal calibrations along feedback range

This section now confirms the previous results with a subset of twenty-three calibrations selected among ones with the lowest E tot along the feedback values λ i . This subset is used to produce CNRM-CM candidate versions, discretely sampling the feedback range.

This selection is presented in Figure 3, in which colored disks show the emulations of the selected calibrations and the colored triangles are the corresponding CNRM-CM simulations.

The disks and triangles of the same color correspond to the same calibrations. There is a shift toward the lowest |λ| between the emulations and the simulations in the lowest values of feedback. This result is consistent with the emulator's overestimate of small feedback magnitudes noted in the emulator evaluation phase (Figure S1).By the end of the optimisation process, none of the selected calibrations perform better than the reference model, highlighting the success of the CNRM-CM6-1 calibration, which achieve the best possible performance, given this metric. However, we observe fifteen model versions showing errors within the standard deviation of the multi-model ensemble CFMIP associated with a diversity of feedback.

The selection of calibrations along the E tot optimization line results in candidates with relatively low total error, but unequal performance in each of the climate fields considered (Figure S8). This implies trade-offs between performance in this different fields. Different choices could be made depending on the variable of interest. We could imagine choosing a weighted metric that favors a good performance in some of the fields over others. However, in terms of SW fluxes and surface temperature, most members in our selection perform better than the default model. The LW fluxes and precipitation errors are rather high for our selection compared to the reference model. Nevertheless, these errors are comparable with other PPE members (Figure S8d). Additionally, our metric does not require a nearzero top-of-atmosphere radiative budget. Therefore, most of the candidates presenting high ECS are not balanced at the top-of-atmosphere (Figure S9). We note in Figure S9 To conclude, fifteen of the optimal CNRM-CM versions exhibit good performance in the individual metrics, with errors comparable to or better than CNRM-CM6-1 for the shortwave fluxes and surface temperature. In terms of the aggregated metric, none of the model versions show better performance than CNRM-CM6-1, highlighting the difficulty of finding a better model version than the reference. However, fifteen of the optimised CNRM-CM versions have an aggregate errors within the standard deviation of the CFMIP models errors, with feedback values ranging form -1.6 to -0.9 W.m -2 .K -1 . This range corresponds to estimated ECS from 4.14 to 7.22 K.

In this paper, we propose a novel approach for optimizing model performance condi- The metric considered here suggests the existence of model variants with comparable climatological performance to CNRM-CM6-1, with both lower and higher net feedback strengths. However, the model with higher climate sensitivities tend to exhibit strong radiative unbalanced at the top-of-atmosphere. To further understand this result, future studies should consider a broader range of metrics, ideally with a range of CMIP6 atmospheric models.

In conclusion, the method proposed here succeeded in producing model candidates spanning a range of climate responses. Our work sets out to understand the inconsistency between observational evidence which finds high values of ECS to be increasingly less likely [START_REF] Sherwood | An assessment of earth's climate sensitivity using multiple lines of evidence[END_REF]

  emulators to predict, based on the perturbed parameter values, the model's outputs. The emulators are used to predict both the climatological mean state and the global net feedback in response to an idealised warming signal. Different emulators were tested, including non-linear models as Neural Networks and linear models as multi-linear regressions (MLR) and LASSO (Least Absolute Shrinkage and Selection Operator[START_REF] Ranstam | Lasso regression[END_REF]) models. Because of the reduced size of the PPE, the neural network (multilayer perceptron)

  x j the parameter value, a j the regression coefficient estimated based on the training of the model, R the intercept and K = 30 the number of perturbed parameters. The feedback emulator is trained to predict directly the global net feedback values (in W.m -2 .K -1 , calculated as for equation (2) with Y = λ). During the evaluation process, both emulators are trained on 80 members of the PPE, the 22 other members being used to estimate the out-of-sample emulator error: OSE = 22 i=1 (predi-truei) 2 22

Figure 1 .

 1 Figure 1. Feedback parameter λ [W.m -2 .K -1 ] distribution in the ARPEGE-Climat PPE (blue histogram), the CFMIP models (red histogram) and the HadGEM3 ensemble (green line). The black dashed line shows the feedback associated with CNRM-CM6-1.

Figure 2 .

 2 Figure 2. Errors Es as measured between the simulations and the observations (y axis) as a function of the feedback parameter λ (x axis) in the CNRM-CM PPE (black dots), the emulated ensemble (gray dots) and the CFMIP models (colored squares). The solid lines are the results of the optimization with constraints on feedback values for the individual metrics (gray lines) and the aggregated metric (black line). The errors are estimated for (a) the short wave fluxes (SW) and (b) the long-wave fluxes (LW) at the top of the atmosphere, (c) the air surface temperature (tas) and (d) the total precipitation (pr). These 4 errors Es are standardized and averaged to estimate the aggregated metric Etot presented in plot (e). The black dashed lines show the errors and the feedback associated with CNRM-CM6-1.

  that the balanced runs are all showing estimated ECS lower than the reference and that a relationship is present between the top-of-atmosphere radiative budget and the net feedback for most candidates, except the four with the highest ECS. The presence of this clear linear constraint suggests that a single process could drive and constrain the net feedback variation in a big region of the CNRM-CM PPE. Further study is needed to identify this process and to understand what differs between model versions with low and high estimated ECS. The last four candidates showing large errors and very unbalanced top-of-atmosphere radiative budget suggest that such high ECS values are associated with an unrealistic mean climate and are therefore ruled out from the interpolation and likelihood function estimate.The estimated likelihood profiles for λ differ depending on the use of emulated value (where the profile peaks for ECS higher than reference) or actual CNRM-CM runs (where the profile peaks for ECS lower than reference) in the equation (3). Even though the 80% ranges and quite similar, the use of actual climate simulations in the estimate of the final likelihood allows to obtain a more realistic constraint on feedback range. The median of the final likelihood profile is very close to the reference feedback, with an estimated ECS of 4.86K. The estimated 10 th -90 th percentile range of ECS is [4.26K -6.15K]. Some of the perturbed atmospheric parameters correlate with the net feedback in the optimized emulations (FigureS10). Among these parameters, the ones with the highest coefficient of linear regressions are the minimum drag for the convective updraft vertical velocity (RKDN), the liquid cloud heterogeneity coefficient in the shortwave spectrum (RSWINHF LIQ) and the critical ice content for ice auto-conversion at high negative temperatures (RQICRMAX). These results confirm that the calibration of convection and cloud optical properties strongly affect the ECS.[START_REF] Saint-Martin | Tracking changes in climate sensitivity in cnrm climate models[END_REF] identified the cloud radiative response as the main driver of the ECS increase between the current and the previous version of the CNRM-CM climate model, with a predominant contribution of the

Figure 3 .

 3 Figure 3. CNRM-CM simulations with optimized calibrations conditional on target values of feedback parameters λ. The plot shows the multi-variate error Etot (y axis) as a function of the feedback parameter λ (bottom x axis) for the emulated optimal candidates (blue line). Twentythree calibrations have been selected along the feedback range (colored disks) and used in ARPEGE-Climat to produce actual climate runs (colored triangles) : one run crashed (gray thick line) and fifteen others have associated errors within the standard deviation of the CFMIP models errors (green area). Disks and triangles of the same color correspond to the same calibration. The climate sensitivity is estimated from λ, assuming the default model forcing (equation (5)). The two relative likelihoods of the feedback parameter, estimated with the equation (3), are represented by the shaded distributions, with the 10 th -90 th percentiles range (80% range) and the median in bright colors. The blue distribution is the initial likelihood function, estimated from the emulated optimal candidates (blue line). The red distribution is an adjusted likelihood function based on a smooth fit (using a cubic spline under tension interpolation) of CNRM-CM optimal candidates error metric along the feedback range (red line).

  tional on a target value of net climate feedback, based on a 102-member perturbed physics ensemble (PPE) of the atmospheric component of CNRM-CM6-1. Our method allows the determination of potentially plausible model configurations which span a wide range of net climate response. This optimization with feedback constraint allows us to predict twentythree conditionally optimized calibrations spanning a wide range of net feedbacks, which we subsequently tested through realized additional simulations. None of these twenty-three CNRM-CM versions exhibit better performance than CNRM-CM6-1, but fifteen of them have error scores within the standard deviation of CFMIP models errors. These fifteen CNRM-CM versions span an ECS range of [4.14K -7.22K] and the likelihood profile of their ECS suggests an 80% range of [4.26K -6.15K].In all of the individual metrics as well as in the aggregated metric, the other CFMIP models seem to perform better than the CNRM-CM emulated versions. This specificity could be the result of the basis choice. By projecting the different global means of the CFMIP models onto the CNRM-CM PPE-derived EOF basis, we do not consider any parts of the model errors orthogonal to this chosen basis. This projection might give CFMIP models an unfair advantage by hiding an important part of their error. This point will be investigate in future study.The present work does not seek to recommend calibrations suitable for operational use, given optimal candidates are conditional on a subjective and non extensive multi-variate metric used here to demonstrate the technique. Further study will consider how constraints result in trade-offs between performance in different variables. For optimization purposes, we have made defensible but subjective choices in terms of the variables chosen, the EOF truncation length, the nature of the feedback constraints for the optimization and the error metric. Moreover, the top-of-atmosphere radiative balance is not yet constrained by the method, which results in imbalanced model versions in the final candidate selection. These are all elements which an operational tuning procedure may wish to expand on, but are out of the scope of the present study.

  , and a new generation of models in which many members exhibited ECS values outside of the previously assessed range. Our model optimization exercise suggests that, for the simulation of mean climatological performance, optimal model configurations may exhibit lower or higher values of ECS. Understanding how these findings integrate into a general assessment of ECS is thus a priority for future research.simulations. CMIP6 data are available through a distributed data archive developed and operated by the Earth System Grid Federation (ESGF) : https://esgf-node.ipsl.upmc .fr/search/cmip6-ipsl/. Data files and code for reproducing the plots are available here : https://doi.org/10.5281/zenodo.6077885.

Acknowledgments

This work is partly funded by the French National Research Agency, project no. ANR-17-MPGA-0016. Benjamin Sanderson is an affiliate scientist with the National Center for Atmospheric Research, sponsored by the National Science Foundation. The authors thank the CNRM-CERFACS modeling group for developing and supporting the CNRM-CM6-1 model. In particular Marie-Pierre Moine, for the technical support provided for the


domain: spi math math.math-oc

text:
Laboratoire Plasma et Conversion d'Energie

Conclusion

• We have introduced a major optimization algorithm known as trust region reflective method. This algorithm was able to provide a good correlation between 4 different Simulation/Experiment with 4 different applied field. • Two different cost functions have been optimized considering charge and current data's individually.

• Charge density data are more sensitive than current density data with respect to the parameters. • To improve our approach, parameters sensitivity will be analyzed in order to quantify the impact of insensitive parameters on the charge and current for different experimental conditions

Objective

Recently, a numerical model has been developed for describing bipolar charge transport with two levels of traps in Low Density Polyethylene (LDPE). This paper presents an optimization method which is based on trust region algorithm (TRA). This algorithm will be utilized to minimize the sum of the squares of the deviations between the experimental data and simulated data.

Principle of optimization technique

• 𝑪 𝟏 is the difference between experimental and simulated current densities • 𝑪 𝟐 is the difference between experimental and simulated charge densities C(𝑃)

𝑄 𝑘 𝑠 = C 𝑃 𝑘 + 𝐶 ′ 𝑃 𝑘 𝑠 + 1 2 𝐶 ′′ 𝑃 𝑘 𝑠 2 Solve 𝑪 ′′ 𝑷 𝒌 𝒔 𝒌 = -𝑪′(𝑷 𝒌 ) 𝑃 𝑘+1 = 𝑃 𝑘 + 𝑠 𝑘

  of Toulouse, CNRS, INPT, UPS, France.

  Experimental data that have been used are net density charge measured by the pulsed electro acoustic method (PEA) along with what is infamous by external charging current measurements. Simulated data are computed by the bipolar charge transport model which is developed for low density polyethylene. Our targeted aim is to find a set of physical parameters for the model, in such a way that these parameters should provide simulation outputs that are directly correlated to the experimental measurements. • Injection barriers for electrons and holes. (𝑒𝑉) 𝑤 𝑒 , 𝑤 ℎ • The depth of a single trapping level for electrons and holes. (𝑒𝑉) 𝑤 𝑚𝑜𝑒 , 𝑤 𝑚𝑜ℎ • Detrapping barrier for electrons and holes. (𝑠 -1 ) 𝐷 𝑒 , 𝐷 ℎ • Trapping coefficients for electrons and holes (𝑠 -1 ) 𝐵 𝑒 , 𝐵 ℎ • Recombination coefficients(𝑚 3 . 𝑠 -1 ) 𝑅 0 , 𝑅 1 , 𝑅 2 • Standard deviation for guassian filter 𝜎 𝑗 𝑒,ℎ 𝑥, 𝑡 𝑞 = 𝜇 𝑒,ℎ (𝑥, 𝑡). 𝐸 𝑥, 𝑡 . 𝑛 𝑒,ℎ 𝑥, = 𝑗 𝑒𝑥𝑝 -𝑗 𝑠𝑖𝑚 • 𝐶 2 𝑃 = 𝑛 𝑒𝑥𝑝 -𝑛 𝑠𝑖𝑚

mm 40°C 200µm -30kV/mm Set of parameters(𝑷)

		Taylor
	𝑷 𝒌+𝟏	development
	𝒔 𝒌	𝒅𝑸 𝒌 𝒔 𝒅𝒔	= 𝟎
			40°C 200µm				ZOOM			ZOOM
			-30kV/𝑤 𝑒	𝑤 ℎ	𝑤 𝑚𝑜𝑒	𝑤 𝑚𝑜ℎ	𝐷 𝑒	ZOOM 𝐷 ℎ	𝐵 𝑒	𝐵 ℎ	ZOOM 𝑅 0	𝑅 1	𝑅 2	𝝈
		𝑋 0	1.1 1.05 0.62	0.62	0.95	0.97	0.05	0.15	0	0	0	1
		𝑃 𝑢𝑠𝑖𝑛𝑔 𝐶 2

1.2 1.1 0.71 0.6 0.0014 4.2 0.003 0.001 𝟏𝟎

  -𝟏𝟐 𝟏𝟎 -𝟏𝟐 𝟏𝟎 -𝟏𝟐 2.6

		𝑤 𝑒	𝑤 ℎ	𝑤 𝑚𝑜𝑒	𝑤 𝑚𝑜ℎ	𝐷 𝑒	𝐷 ℎ	𝐵 𝑒	𝐵 ℎ	𝑅 0	𝑅 1	𝑅 2	𝝈
	𝑋 0	1.1 1.05 0.62	0.62	0.95	0.97 0

.05 0.15 0 0 0 1 𝑃 𝑢𝑠𝑖𝑛𝑔 𝐶 1 1.09 1.26 0.71 0.6 0.0009 0.0082 1.12 0.22 1 1 0.9 1 • Sample: LDPE • Permittivity: 2.3 • Thickness: 200 µm • Electric Field: -30 kV/mm • Temperature: 40 °C • Polarization: 7000 s Optimization using one experimental current and charge density measurments

		𝑤 𝑒	𝑤 ℎ	𝑤 𝑚𝑜𝑒	𝑤 𝑚𝑜ℎ	𝐷 𝑒	𝐷 ℎ	𝐵 𝑒	𝐵 ℎ	𝑅 0	𝑅 1	𝑅 2	𝝈
	𝑿 𝟎	1.2	1.1	0.71	0.6	0.0014	4.2	0.003	0.001	𝟏𝟎 -𝟏𝟐	𝟏𝟎 -𝟏𝟐	𝟏𝟎 -𝟏𝟐	2.6
	𝑃 𝑢𝑠𝑖𝑛𝑔 𝐶 2 1.22	1.21	0.58	0.59	0.0001	0.0001	0.064	0.9	𝟏𝟎 -𝟏𝟐	1	𝟏𝟎 -𝟏𝟐	1.

85 Optimization using 4 Different experimental charge density measurments with different applied voltages