Didier Surdez

Magdalena Benetkiewicz

Virginie Perrin

Zhi-Yan Han

Gaëlle Pierron

Stelly Ballet

François Lamoureux

Françoise Rédini

Estelle Daudigeos-Dubus

Birgit Geoerger

Estelle Daudigeos- Dubus

Olivier Delattre

Franck Tirode
email: franck.tirode@curie.fr

Targeting the EWSR1-FLI1 Oncogene-Induced Protein Kinase PKC-Abolishes Ewing Sarcoma Growth in vivo

Keywords: Ewing sarcoma, EWSR1-FLI1, Protein Kinase

Introduction

Ewing sarcoma (ES) is the second most frequent childhood bone tumor. Clinically, ES is a highly metastatic tumor with around 25% of patients presenting metastasis at the time of diagnosis. Although great advances have been made in the treatment of local disease, therapies used for advanced stages of the disease are still disappointing, the five year overall survival still being critically low. Thus the discovery of novel druggable targets allowing targeted therapies is mandatory.

Since the discovery and characterization of the causal translocation event (1; 2), researches were driven by the quest for targets of the chimeric EWSR1-FLI1 transcription factor, the main oncogenic event in more than 85% of ES. Most of the studies aiming at identifying important molecules involved in ES oncogenesis were based either on EWSR1-FLI1 inhibition in Ewing sarcoma cells or EWSR1-FLI1 expression in non-Ewing cell lines. Thus, many different studies, including ours, identified genes involved in EWSR1-FLI1-dependent cell survival, such as IGF-1R (3) and IGFBP (4; 5), PPP1R1A [START_REF] Wai | Expression analysis of pediatric solid tumor cell lines using oligonucleotide microarrays[END_REF], MK-STYX/STYXL1 (7), NR0B1 (8; 9), NKX2-2 [START_REF] Smith | Expression profiling of EWS/FLI identifies NKX2.2 as a critical target gene in Ewing's sarcoma[END_REF], GSTM4 [START_REF] Luo | GSTM4 is a microsatellite-containing EWS/FLI target involved in Ewing's sarcoma oncogenesis and therapeutic resistance[END_REF] and SOX2 molecules [START_REF] Riggi | EWS-FLI-1 modulates miRNA145 and SOX2 expression to initiate mesenchymal stem cell reprogramming toward Ewing sarcoma cancer stem cells[END_REF]. Proposed as a promising targeted therapy, IGF signaling inhibition has been extensively investigated in the context of Ewing sarcoma and several clinical trials have been conducted. Although well tolerated, several reports of phase II studies suggested that only about one patient out of four would benefit from IGF-1R monoclonal antibodies as single therapy [START_REF] Olmos | Targeting the Insulin-Like Growth Factor 1 Receptor in Ewing's Sarcoma: Reality and Expectations[END_REF]. On the other hand, some studies analyzed primary tumors to find specific gene signature of Ewing sarcoma (6; 14-16).

Aiming at finding genes that are specifically found in primary Ewing tumors compared to other tumors types and modulated by EWSR1-FLI1, we identified the protein kinase C beta (PRKCB). In the context of ES, we demonstrate here that PRKCB is crucial for cell survival in vitro and tumor development in vivo. We demonstrate that inhibition of PRKCB induces apoptosis and stimulates TNF and NF-kB signaling and that concomitant inhibition of both PRKCA and PRKCB, by pharmacological inhibition or RNA silencing is required to decrease histone H3 lysine 4 methylation levels.

Materials and Methods

Microarrays and statistical analysis. Ewing tumors samples (GSE34620) together with samples of other pediatric or bone tumors including 32 small round cell desmoplastic tumors, 52 medulloblastomas (GSE12992), 64 neuroblastomas (GSE12460), 122 rhabdomyosarcoma [START_REF] Williamson | Fusion gene-negative alveolar rhabdomyosarcoma is clinically and molecularly indistinguishable from embryonal rhabdomyosarcoma[END_REF], 27 osteosarcomas (GSE14827) and 34 synovial sarcomas (GSE20196) were used for this analysis. All microarray data were simultaneously normalized using the gcrma package version 2.18.1 in R 2.10.1 environment [START_REF]R: A language and environment for statistical computing[END_REF]. BGA analyses were completed using made4 R package [START_REF] Culhane | MADE4: an R package for multivariate analysis of gene expression data[END_REF]. For siRNA inhibition microarrays, A673 cells were transfected by the indicated siRNA and harvested 72hours post transfection. gene's TSS. H3K4 trimethylated regions were selected according to their profile in the ENCODE Promoter-Associated Histone Mark (H3K4Me3) on 9 Cell Lines dataset [START_REF] Birney | Identification and analysis of functional elements in 1% of the human genome by the ENCODE pilot project[END_REF].

Additional experimental details are available in the SOM .

Results

PRKCB is strongly over-expressed in Ewing tumors

To find specific genes expressed in Ewing sarcoma, a supervised Between Group Analysis [START_REF] Culhane | Between-group analysis of microarray data[END_REF] was performed comparing expression profiles of 39 Ewing tumors samples with those of other pediatric tumors including 32 small round cell desmoplastic tumours, 52 medulloblastomas [START_REF] Fattet | Beta-catenin status in paediatric medulloblastomas: correlation of immunohistochemical expression with mutational status, genetic profiles, and clinical characteristics[END_REF], 64 neuroblastomas [START_REF] Janoueix-Lerosey | Somatic and germline activating mutations of the ALK kinase receptor in neuroblastoma[END_REF] and 122 rhabdomyosarcoma (20) (Figure 1A). Among the top 100 probesets found to be specific for ES (see supplemental table S1) several represented genes that were previously identified as important for Ewing tumors like NKX2-2 (10), NR0B1 (8; 9), LIPI [START_REF] Foell | Membraneassociated phospholipase A1 beta (LIPI) Is an Ewing tumour-associated cancer/testis antigen[END_REF], DKK2 [START_REF] Miyagawa | EWS/ETS regulates the expression of the Dickkopf family in Ewing family tumor cells[END_REF] or XG [START_REF] Meynet | Xg expression in Ewing's sarcoma is of prognostic value and contributes to tumor invasiveness[END_REF] and most of them were previously identified as EWSR1-FLI1-dependent genes (4; 15; 24). Among these genes we focused our attention on the protein kinase C beta (PRKCB) for which five probesets (Figure 1A) were significantly overexpressed in Ewing tumors as compared to other pediatric or bone tumors (Figure 1B). Indeed, mean value of PRKCB expression in Ewing tumors is 13 fold superior to mean value of the closest group (neuroblastomas). Although two isoforms of PRKCB (PRKCB1 and PRKCB2) distinguished by their differentially spliced last exon have been described (hereafter we will indicate PRKCB when referring to both isoforms), PRKCB2

is the predominant isoform in ES as compared to other non-Ewing cancer cell lines (Figure 1C). Strong PRKCB overexpression thus appears to be highly specific of Ewing tumors.

PRKCB expression is directly dependent on EWSR1-FLI1

Inhibition of EWSR1-FLI1 using siRNA in A673, EW24 and SK-N-MC Ewing cell lines dramatically reduced PRKCB expression levels at both RNA and protein levels (Figure 2A and 2B), indicating that PRKCB expression in ES cells is EWSR1-FLI1 dependent. To assess the direct role of EWSR1-FLI1 in PRKCB expression, luciferase reporter experiments with PRKCB promoter (from -1147 to +22 according to transcription start site) were conducted. As shown on figure 2C, ectopic expression of EWSR1-FLI1 in HeLa cell line strongly increased luciferase activity. In addition, in shA673-1C cell line, which allows a doxycycline-mediated inhibition of EWSR1-FLI1 [START_REF] Tirode | Mesenchymal stem cell features of ewing tumors[END_REF], PRKCB promoter activity was significantly decreased upon EWSR1-FLI1 inhibition (Figure 2D). Finally, chromatin immunoprecipitation by two different EWSR1-FLI1 antibodies conducted in A673 cells indicated the presence of EWSR1-FLI1 within the PRKCB promoter in vivo (Figure 2E).

These different results clearly indicate that EWSR1-FLI1 is directly responsible for the high expression of PRKCB in Ewing cell lines.

PRKCB is an active kinase in ES and is responsible for histone H3T6 phosphorylation

In a recent publication on prostate cancer cells [START_REF] Metzger | Phosphorylation of histone H3T6 by PKCbeta(I) controls demethylation at histone H3K4[END_REF], PRKCB was shown to phosphorylate histone H3 on its threonine 6 (H3T6ph) leading to a decreased ability for the cell to remove di/tri-methyl tags on lysine 4 of H3 (H3K4me2/me3). We therefore investigated in Ewing sarcoma if PRKCB overexpression correlated with high H3T6 phosphorylation -and consequently H3K4 methylation-levels and if his effect was related to EWSR1-FLI1 direct DNA binding. Promoter regions of thirteen known EWSR1-FLI1 modulated genes (7 induced:

AURKB, CAV1, CCND1, EZH2, NKX2.2, NR0B1, TERT and 6 repressed: DKK1, IGFBP3, IGFBP5, RUNX2, TGFBI, TGFBR2) and 6 unmodulated genes (CREBBP, ENSA, MAST2, PDPK1, ROCK1, SNF8) were selected according to their profile in the ENCODE Promoter-Associated Histone Mark (H3K4Me3) on a 9 cell lines dataset [START_REF] Birney | Identification and analysis of functional elements in 1% of the human genome by the ENCODE pilot project[END_REF]. In order to study the effect of PRKCB inhibition on H3T6 phosphorylation, we treated A673 cells for 72 hours with

PRKCB is crucial for Ewing cell survival in vitro

Knowing that PRKCB was active in ES cells, we next investigated whether PRKCB expression was necessary for cell survival. For this purpose A673, SK-N-MC and TC71 cell lines were infected with lentiviral particles containing shRNAs against PRKCB (sh463 and sh847 are located 463nt and 847nt downstream of transcription start site according to NM_002738.3, respectively) that elicited strong PRKCB inhibition (supplemental Figure S2A). Five days after infection, inhibition of PRKCB induced a dramatic decrease in proliferation rate in all three Ewing cell lines (Figure 4A). To exclude shRNA off-target effect hypothesis, phenotypical rescue experiments were conducted by re-expressing PRKCB1 or PRKCB2 carrying synonymous mutations within their shRNA-targeted sequence (PRKCB 463m and PRKCB 847m , supplemental Figure S2B-C). In PRKCB-silenced cells, restoration of PRKCB expression completely rescued their growth capacities (Figure 4B), thus excluding off-target effects and confirming the specificity of the shRNA-induced phenotypes. To unravel mechanisms of growth inhibition observed upon PRKCB inhibition, we investigated cell cycle phases and apoptosis pathways. Cell cycle analysis using BrdU incorporation did not show any significant differences in G1, S or G2/M phases between control and PRKCB knockdown condition. In contrast, a strong increase of the subG1 fraction was observed (Figure 4C). Investigation of caspase 3 cleavage and annexin V presentation confirmed that PRKCB inhibition in three different cell lines significantly increased apoptosis (Figure 4C). As several compounds have been previously reported to specifically inhibit protein kinase C beta activity, we investigated whether pharmacological PRKCB inhibition was also effective in ES.

We choose to investigate Enzastaurin [START_REF] Graff | The protein kinase Cbeta-selective inhibitor, Enzastaurin (LY317615.HCl), suppresses signaling through the AKT pathway, induces apoptosis, and suppresses growth of human colon cancer and glioblastoma xenografts[END_REF] as this molecule has been fostered to phase II/III clinical trials for several diseases. Growing Ewing sarcoma A673, SK-N-MC and TC71 cell lines with increasing amount of Enzastaurin led to a dramatic reduction of cell viability with an IC50 around 5 µM. (Figure 4D). Altogether, these results indicate that in vitro inhibition of PRKCB strongly induces cell death via apoptotic pathways.

PRKCB inhibition induces tumor regression in vivo

We next wondered whether we could recapitulate in vivo the tremendous apoptotic effect of PRKCB inhibition observed in vitro. For this purpose, we generated the shA673-B5M3 Ewing cell line that expresses the shRNA463 directed against PRKCB under the control of a doxycycline inducible promoter (supplemental Figure S3). Xenograft tumors were then raised into SCID mice by subcutaneously implanting shA673-B5M3 cells or control cells (shA673-pTER). Remarkably, shA673-B5M3 xenograft tumor growth was completely abolished when mice were treated with doxycycline as soon as four days after cells inoculation (Figure 5A).

Moreover, shRNA-mediated PRKCB inhibition reduced tumor size very significantly when mice were doxycycline-treated once tumors were detectable (Figure 5B). Finally, A673 cells were injected at the bone periphery, into mouse tibial muscle, to mimic the human disease.

In these mice, treatment with Enzastaurin led to a significant reduction of tumor growth (Figure 5C). Overall, these three in vivo experiments clearly demonstrated that blocking PRKCB prevents Ewing sarcoma tumor engraftment, reduces tumor growth and promotes tumor reduction.

Roles of PRKC in Ewing sarcoma

We showed that pharmacological inhibition of PRKC led to a decreased histone phosphorylation and that PRKB inhibition led to apoptosis but it is unlikely that these two mechanisms are related since PRKCB inhibition had no effect on histone modification. Thus, to trying to decipher the molecular roles of PRKCB in Ewing sarcoma we performed expression profiling on A673 Ewing cell lines treated by specific siRNA against either PRKCB or EWSR1-FLI1 and with a non-targeting siRNA as control. Supervised differential analyses between samples treated by either specific siRNAs and samples treated with the control siRNA were performed and the lists of genes modulated in the different conditions were compared to each other (Figure 6A and supplemental table S2). As expected, we found down-regulation of many histones/chromatin/chromosome organization gene categories reinforcing the possible link between EWSR1-FLI1 and chromatin remodeling through PRKCB (supplemental table S3). More striking, we observed an extremely significant overlap while comparing EWSR1-FLI1 and PRKCB modulated genes. Indeed, more than half of the genes modulated upon PRKCB inhibition were also modulated during EWSR1-FLI1 inhibition (Figure 6A). Looking at the gene ontology or pathways modulated by either siRNA inhibition (see supplemental table S3), cell death was significantly up-regulated, which was consistent with the observed phenotype. Indeed, during PRKCB inhibition, caspase 3, caspase 8 and TNFRSF12A (Tweak-receptor) were strongly up regulated and are known to induce apoptosis in some tumors [START_REF] Ikner | TWEAK induces apoptosis through a death-signaling complex comprising receptor-interacting protein 1 (RIP1), Fas-associated death domain (FADD), and caspase-8[END_REF]. Furthermore, gene set enrichment analyses demonstrated that PRKCB inhibition led to a significant increase of TNF and NF-kB pathways, also possibly leading to apoptosis (Figure 6B). Altogether, our results demonstrate that PRKCB possesses

Discussion

We identified PRKCB as a major Ewing specific protein, which overexpression is directly linked to EWSR1-FLI1. Indeed, bioinformatics approaches led to the identification of PRKCB among the most overexpressed gene in Ewing sarcomas, which could be confirmed using Expression profiling experiments showed a strong overlap between genes modulated upon EWSR1-FLI1 knock-down and those modulated by PRKCB inhibition. To account for this result, two hypotheses could be made: i) PRKCB may directly phosphorylate EWSR1-FLI1 therefore affecting its activity or stability. However, preliminary experiments did not allow us to detect PRKCB driven EWSR1-FLI1 phosphorylation but more sophisticated experiments are required. ii) PRKCB may induce chromatin modification of many EWS-FLI1 target genes.

However, we show that both PRKCA and PRKCB are expressed in ES and that they share redundant functions on H3T6 phosphorylation, leading to a more complex regulation of chromatin status as originally thought.

We also demonstrate here that PRKCB is a major therapeutic target in Ewing sarcoma.

Indeed, inhibition of PRKCB either by small molecules inhibitors or by siRNA induces apoptosis. Therefore, PRKCB inhibition in Ewing cell lines has rather a cytotoxic than a cytostatic effect that is of strong interest for therapeutic use. Furthermore, specific shRNA inhibition of PRKCB is sufficient to impair tumorigenesis of Ewing cells in vivo. To our knowledge and apart from EWSR1-FLI1 inhibition [START_REF] Hu-Lieskovan | Sequence-specific knockdown of EWS-FLI1 by targeted, nonviral delivery of small interfering RNA inhibits tumor growth in a murine model of metastatic Ewing's sarcoma[END_REF], this is the first demonstration of a single gene knockdown leading tumor shrinkage in Ewing xenograft models, opening interesting therapeutic opportunities based on PRKCB extinction. Usage of specific drugs such as Enzastaurin also proved its efficacy for inhibiting tumor growth in vivo but to a lesser extent than with RNA inhibition. Accounting for this result, Enzastaurin accumulation in mice adipose tissue was observed in these experiments (data not shown) leading to its reduced bioavailability at tumor sites.

In this study, we clearly demonstrated the anti-apoptotic properties of PRKCB in the context of ES, as its inhibition is sufficient to robustly trigger apoptosis. To account for this effect, microarray data indicate a significant increase of TNF superfamily death receptor upon PRKCB silencing. Indeed, TNFRSF12A (TWEAK receptor), TNFRSF10A and TNFRSF10B

(TRAIL receptor DR4 and DR5, respectively) are of particular interest due to their up regulation upon PRKCB inhibition. Previous report on Jurkat or HL-60 human leukemia cell demonstrated that inhibition of PRKCB sensitized tumor cells to TNF-alpha related apoptosis via ligand-induced death receptor [START_REF] Meng | Protein kinase Cbeta modulates ligandinduced cell surface death receptor accumulation: a mechanistic basis for enzastaurindeath ligand synergy[END_REF]. Similar mechanisms may occur in Ewing sarcoma and further experiments by both impairing PRKCB and targeting TNF-alpha or NFKB pathways may be required to get deeper insights of PRKCB involvement in these processes.

PRKCB, as a kinase, possesses an enzymatic activity that can be directly targeted and we show here that blocking PRKCB in Ewing sarcoma is a new promising therapeutic approach.

Enzastaurin (an inhibitor

  Figure S1). Altogether we demonstrate here that PRKCB is responsible, together with PRKCA, for maintaining steady state H3T6ph and H3K4me3 levels, at least on most of tested promoters.

Figure 1 .

 1 Figure 1. Protein kinase C Beta expression in Ewing tumors

Figure 2 .

 2 Figure 2. Direct EWSR1FLI1 dependency of PRKCB expression

Figure 3 .

 3 Figure 3. Synergistic effect of PRKCA and PRKCB for the prevention of histone demethylation in Ewing sarcomas assessed by chromatin immunoprecipitation. Quantitative PCR targeting trimethylated promoter/enhancer regions of known EWSR1FLI1 modulated genes (7 induced and 6 repressed) as well as 6 EWSR1FLI1 unmodulated genes are shown. QPCR values for each gene/CHIP conditions were normalized to their respective input. Means and standard deviations of 2 replicates are shown.

Figure 4 . 22 B

 422 Figure 4. Crucial importance of PRKCB for in vitro Ewing cell survival

Figure 5 .

 5 Figure 5. Crucial importance of PRKCB for in vivo Ewing cell survival

  Time from treatment (days)Surdez et al. Figure5

Figure 6

 6

  Tumor volume was measured three times a week (length × width × depth × 0.5432). The mice were sacrificed by CO2 inhalation when the tumor volume exceeded 3,000 mm 3 . Experiments were performed in accordance with recommendations of the European Community (86/609/EEC), the French Competent Authority and with the institutional guidelines of the French Ethical Committee (CEEA.PdL.06).

	Chromatin immunoprecipitation. For PRKCB promoter CHIP, experiments were carried
	out as previously described (39) using either C19 or 7.3 FLI1 antibodies except that one
	microliter of CHIP DNA was amplified for 30 cycles by PCR amplification (Applied
	Biosystems) using PRKCB promoter-specific primers (-428/-270 region before TSS). For
	Histone ChIP, experiments were conducted using the MAGnify Chromatin
	Immunoprecipitation system (Invitrogen) using 3 µg of DNA and 2 µg of antibody per ChIP,
	and following manufacturer's recommandations. CHIP DNA was amplified using quantitative
	PCR (Applied Biosystems) using primers specific for H3K4 trimethylated regions around 19
	every 2-3 days until volume reached 1500mm 3 . For the A673 xenograft Ewing sarcoma
	model in nude mice, twenty millions cells were injected next to the tibia of four-week-old male
	athymic mice (Janvier, L'Arbresles, France) under anesthesia [inhalation of a combination of
	isoflurane/ air (1.5%, 1 L/min) and buprenorphine (0.05 mg/kg; Temgésic, Schering-Plough)].

Total RNAs were extracted using Trizol Reagent and processed on Affymetrix HuGene1.1STv1 GeneChip microarrays. RMA normalization was performed using Brainarray Entrez gene CDF v14.1

[START_REF] Dai | Evolving gene/transcript definitions significantly alter the interpretation of GeneChip data[END_REF]

in R environment. Group comparisons were done using Welch Two Sample t-test statistic and DAVID gene ontology analyses

[START_REF] Huang | Bioinformatics enrichment tools: paths toward the comprehensive functional analysis of large gene lists[END_REF]

were performed online (http://david.abcc.ncifcrf.gov/home.jsp). Gene set enrichment analysis

[START_REF] Subramanian | Gene set enrichment analysis: a knowledge-based approach for interpreting genome-wide expression profiles[END_REF]

was done by comparing siPRKCB and siControl samples using a log ratio of classes metric.

In vivo mice experiments. For A673-shPRKCB463_B5M3 xenograft tumors in SCID mice, twenty millions cells resuspended in 200 µl of PBS were injected subcutaneously in the flank of five-weeks-old severe combined immunodeficient (SCID) female mice (Charles River laboratories, Les Arbresles, France). Doxycycline was added to the drinking water at 2 mg/mL together with 5% sucrose. Tumor volume was determined by caliper measurements Once tumors were measurable, mice were randomly assigned into treatment groups receiving either oral gavage with enzastaurin suspended in olive oil (100mg/kg, twice daily; n = 6) or oral vehicle alone (n = 7).

at least two different functions in Ewing sarcoma, the first being its involvement in crucial signaling pathways leading to rapid cell death when impaired, the second being its responsibility for histone H3T6 phosphorylation, leading to long term impact on transcriptional activity.

Acknowledgments

We thank Hans Clevers for the generous gift of the pTER and the Tet repressor expression plasmid (pTet-R), Carlo Lucchessi, Karine Laud and David Gentien for their help.

Grant Support

This work was supported by grants from the Institut National de la Santé et de la Recherche Médicale (FL,FR,OD,FT), the Centre National de la Recherche Scientifique (EDD,BG), the Institut Curie (DS,MB,VP,ZHY,GP,SB), the Institut National du Cancer (DS :SYBEwing project: 2009-1-PLBIO-04 and FT,VP :BORTES project : 2008-PLBIO-06), the Ligue Nationale contre le Cancer (Equipe labellisée and CIT program), the Réseau National des Génopoles, Agence National de la Recherche, the European Union (MB : KCK and EET pipeline programs), the société Française des Cancers de l'Enfant, and the following associations: Courir pour Mathieu, Dans les pas du Géant, Olivier Chape, Les Bagouzamanon and les Amis de Claire.

For each panel, average tumor volume and standard deviation are shown B. GSEA on genes ranked differentially between siPRKCB and siControl identified signature of TNF, NF-kB and death pathways in PRKCB inhibited samples.

Supplementary Online Material Targeting EWSR1-FLI1 oncogene induced protein kinase C beta abolishes Ewing sarcoma growth in vivo

Didier Surdez 1,2 , Magdalena Benetkiewicz 1,2 , Virginie Perrin 1,2 , Zhi-Yan Han 1,2 , Gaëlle Pierron 1,3 , Stelly Ballet 1,3 , François Lamoureux 4,5 , Françoise Rédini 4,5 , Estelle Daudigeos-Dubus 6,7 , Birgit Geoerger 6,7 , Olivier Delattre 1,2,3 and Franck Tirode

Materials and Methods

Antibodies. FLI1 (C-19), PKCb1 (C-16) and PKCb2 (C-18) antibodies were purchased from Santa Cruz Biotechnology (Santa Cruz, CA, USA). Histone H3 (Ab1791), Histone H3 trimethyl K4 (ab1012) and Histone H3 phospho T6 (ab14102) antibodies were purchased from abcam (Cambridge, UK) and b-actin antibody (A-5316) from Sigma-Aldrich (Saint-Quentin Fallavier, France). Anti-FLI-1 antibody (7.3) was described previously (1).

Quantitative RT-PCR. cDNAs were synthesized from 1µg of RNA using the GeneAmp RNA PCR core Kit (Applied Biosystem, Courtaboeuf, France). Quantitative PCR analyses were performed using TaqMan Assays-on-demand Gene expression reagents (Applied Biosystem) with qPCR Mastermix Plus without UNG (Eurogentec, Belgium) or performed using SYBR green (Applied Biosystem). For TaqMan® quantitative RT-PCR, Gene Expression Assays Hs00176998_m1 for PRKCB and Hs9999902_m1 for RPLP0 as control were purchased from Applied Biosystem (Courtaboeuf, France). For SYBR green quantitative PCR used primers are listed in supplemental Table S4. Reactions were run on an ABI/PRISM 7500 (Applied Biosystem) and analyzed using the 7500 system SDS software.

Luciferase assay. The -1147/+22 region (corresponding to chr16:23,846,175-23,847,343 of human genome version GRCh37/hg19) around PRKCB transcription start site was amplified by PCR from A673 genomic DNA. This fragment was cloned into the XhoI site of the pREP4luc vector (kindly provided by Keji Zhao). HeLa cells, untreated or doxycycline treated shA673-1C cells for 10 days (2) were plated into twenty-four well plates and grown in DMEM (Invitrogen, Cergy Pontoise, France) supplemented with 10% fetal calf serum. Cells were transfected 24 hours later using lipofectamine and Reagent plus (Invitrogen) with 400 ng of either pREP4-luc or pREP4-(-1147/+22)pPRKCB-luc and 10 ng of pREP7-Rluc, (kindly provided by Keji Zhao) and respectively 0, 50, 100 ng of either pCDH1-MCS1-puro (System Biosciences, CA) or pCDH1-EWS-FLI1 plasmids (3). Twenty four hours post-transfection, cells were lysed and assayed for luciferase activity using the dual luciferase reporter assay system (Promega, Charbonnieres-les-bain, France) according to the manufacturer's instructions. Firefly activity was normalized to Renilla luciferase activity to adjust differences in transfection efficiency.

Plasmids and cloning.

All primers used in this paper are listed in supplemental Table S4. Proliferation and apoptosis assays. Cell-cycle analyses were performed by BrdU incorporation as previously described (5). Annexin V/PI staining was performed according to the manufacturer's protocol (Apoptosis detection kit I; BD Biosciences, San Diego, USA).

Cleaved caspase3 staining (Ab#C8487, Sigma) was performed according to the manufacturer's protocol. Cells were infected either with shCTRL or shPRKCB lentiviruses, selected with puromycin for one week and then subjected to FACS analysis (FACScalibur, BD Biosciences). The data were processed using FlowJo software (Tree Star, Inc.). Supplemental Figure S1. Single inhibition of PRKCA does not reduce the global level of histone H3K4 tri-methylation (H3K4me3). A673 Ewing sarcoma cell were transfected with siRNA targeting PRKCA or non-targeting negative siRNA control. 3 days after transfection, cells were fixed and processed for CHIP using antibodies y , p g against histone H3K4 tri-methylation (H3K4me3). Quantitative PCR targeting trimethylated promoter/enhencer regions of known EWSR1FLI1 modulated genes (7 induced and 6 repressed) as well as 6 EWSR1FLI1 unmodulated genes. QPCR values for each gene/CHIP conditions were normalized to their respective input.

Cell


Anuradha Chauhan

Stephan Lorenzen

Hanspeter Herzel

Samuel Bernard
email: bernard@math.univ-lyon1.fr

Regulation of cell cycle progression by Cdh1: Insight from an integrated mammalian cell cycle model

Keywords: Liver regeneration, mitosis, G1-S transition, G2 delay, Cdh1, Cyclin

The process of cell division in mammalian cells is orchestrated by cell-cycle-dependent oscillations of the cyclin protein levels. Cyclin levels are controlled by redundant transcriptional, post-translational and degradation feedback loops. How each of these separate loops contributes to the regulation of the key cell cycle events and to the connection between the G1-S transition and the subsequent mitotic events is under investigation. Cdc20 homologue 1 (Cdh1), well-known for controlling G1 phase progression, is emerging as an important regulator of DNA synthesis and mitosis. Here, we present an integrated computational model of the mammalian cell cycle based on the sequential activation of cyclins. We dissect the emergent role of Cdh1 as a universal regulator of the cell cycle. We validate the model against experimental data on liver cells (hepatocytes) during liver regeneration, which undergo one or two rounds of synchronous circadian-clock gated cell divisions. Our model is coherent with the notion that the mitotic exit in mammalian cells is bistable and suggests Cdh1 as a key regulator of mitosis. We suggest that Cdh1 plays an important role in controlling cell cycle events during G2 and mitosis phases.

Introduction

The cell division cycle is a highly organized and structured mechanism in mammals. Because of its dynamical nature, it has been subject to several computational models. First computational models pertained to the cell cycle in amphibian embryos and yeast (Tyson, 1991;Goldbeter, 1991;Novak and Tyson, 1993;Sha et al., 2003;Pomerening et al., 2003;Chen et al., 2004). More recently, computational models were proposed for specific parts of the mammalian cell cycle, particularly the G1/S phase transition and the restriction point (Aguda and Tang, 1999;Qu et al., 2003a,b;Swat et al., 2004;Novak and Tyson, 2004). A generic model for the eukaryotic cell cycle has also been presented (Csikasz-Nagy et al., 2006).

Few detailed, integrative models coupling the main events of the cell cycle, DNA synthesis and mitosis have been proposed. Models of this sort have been proposed for yeast, in which growth of cell mass is playing a key role in regulating mitosis (Chen et al., 2004), and more recently for mammals (Gerard and Goldbeter, 2009). In mammals, however, cell mass is not a major determining factor for the control of cell cycle. Rather, mammalian cells possess multiple control mechanisms that prevent them from proliferating outside specific conditions. Mammalian cells vary in type and degree of differentiation, each one having different proliferative potential and mechanism. This makes the task of modelling mammalian cells challenging, as there is no universal experimental model. In vitro systems of dividing cells provide a way to study synchronized cell populations, which are suitable for modelling cell cycle events. However, cell cycle specific events are obtained under variable experimental conditions and different cell cycle synchronization procedures, which are difficult to reproduce on models. During liver regeneration, liver cells (hepatocytes) divide in a highly synchronized manner. We have taken advantage of the wealth of experimental data on the cell cycle during liver regeneration to construct the first integrative model of the mammalian cell cycle in the regenerating livers.

Liver regeneration is a process by which the liver can recover its normal mass and function following injury. After the surgical removal of two-third of the liver (partial hepatectomy), 90 % of the hepatocytes re-enter the cell cycle synchronously to complete 1 or 2 divisions and restore the liver mass. Partial hepatectomy (PH) triggers the release of pro-inflammatory cytokines (PIC). In the presence of PIC, hepatocytes leave a quiescent state, denoted G0, to enter a primed state, a process denoted priming. Primed cells, which are in the early G1 phase, are then driven by growth factors (GFs) to cross the restriction point, a point of no return beyond which they are irreversibly engaged in the cell cycle and do not require growth factors any more to complete mitosis (Taub, 2004). Progression within the cell cycle is controlled by the sequential activation of a family of cyclin dependent kinases (cdks) that allow an ordered succession of the cell cycle phases: G1, S, G2, and M [START_REF] Morgan | The cell cycle: principles of control[END_REF]. The cdk proteins are only active when they form a complex with their corresponding cyclin proteins. Cyclin D/Cdk4-6, Cyclin E/Cdk2, Cyclin A/Cdk2, and Cyclin B/Cdk1 complexes promote, respectively, progression in G1 phase, the transition from G1 to S phase, progression in S and G2 phase, and finally the G2/M phase transition, allowing entry into mitosis [START_REF] Morgan | The cell cycle: principles of control[END_REF]. Cyclin/cdk complexes are the workhorses of the cell cycle machinery, and as such, they need regulators. Cyclin/cdk regulation, which we henceforth mention as cyclin regulation for simplicity, is achieved through a variety of mechanisms. These include transcriptional regulation [E2F transcription factor 1 (E2F)], association with protein inhibitors [cyclin dependent kinase inhibitor (CKI)], phosphorylation/dephosphorylation [Wee1 and cell division cycle 25 (Cdc25)] and cyclin degradation [complexes formed with anaphase promoting complex (APC) and Cdc20 homologue 1 (Cdh1) or Cell division cycle 20 (Cdc20) (APC Cdh1 , APC Cdc20 ), Skp1/cullin/F-box protein related complexes (SCF)] (Morgan, 2007)(Fig. 1).

2 The model DNA synthesis and mitosis. After both PH and CCl 4 treatment, liver regeneration exhibits well-synchronized DNA synthesis and mitosis (Deguchi et al., 2002). The temporal proliferation pattern of the cells in regenerating rodent livers consists of two waves of mitosis (Fabrikant, 1968). During the first round, hepatocytes synchronously undergo DNA replication and mitosis. It is then followed by a second round of division of less synchrony (Faktor, 1971). In mice, the first peak of DNA synthesis occurs 36 hours after PH and the mitotic peak, 4-12 hours after the peak of DNA synthesis (Matsuo et al., 2003).

E2Fs regulating sequential activation of cyclins. E2F activity is tightly controlled by binding to the retinoblastoma protein (Rb). Rb sequesters E2F and inhibits its transcriptional activity. Cyclins sequentially phosphorylate Rb and activate E2F in a positive feedback loop manner. Only hyperphosphorylated forms of Rb-E2F transactivates Cyclin A and Cyclin B (Lundberg and Weinberg, 1998) (see Appendix A.2 for the derivation of the Rb/E2F equations).

CKI at the interphase of S phase and mitosis. CKI stoichiometrically inhibits Cyclin D, Cyclin E and Cyclin A by forming complexes with their cdk partners (Harper et al., 1995). CKIs are predominantly transcriptionally regulated by cytokine-dependent signaling (Gartel and Tyner, 1999;Coller et al., 2000). For further details on modelling CKI activation refer to (Chauhan et al., 2008). Degradation of CKI is mediated by SCF and APC-Cdc20 (Bashir et al., 2004;Amador et al., 2007). For simplicity, we do not model SCF and/or APC-Cdc20 dependent degradation of CKI, but use a general degradation term for CKI.

Cyclins. The whole process of cell division is orchestrated by the sequential activation of cyclins. Cyclin D and Cyclin E are the G1-S cyclins that trigger DNA synthesis. G1-S cyclins are induced by cytokine-and growth factordependent pathways and their degradation is controlled by SCF. For further details on Cyclin D and Cyclin E modelling refer to (Chauhan et al., 2008). The rise of G1-S cyclins is accompanied by the appearance of Cyclin A during S phase. In the late G2 phase, a transient activation of Cyclin B is observed enabling swift G2-M transition. This transient activation is enabled by regulatory feedbacks imposed on Cyclin B by Cdc25 and Wee1. At metaphase, sufficiently high levels of active Cyclin B phosphorylates Cdc20 to form an active complex with APC, which in turn, degrades Cyclin B. Inactivation of Cyclin B allows mitotic exit and return to the G1 phase [START_REF] Morgan | The cell cycle: principles of control[END_REF]. Inactivation of Cyclin B also leads to dephosphorylated Cdh1 which then forms an active complex with APC to degrade Cyclin B and Cyclin A during G1 phase.

APC and SCF: the degradators controlling the cell cycle APC is a proteasomal degradation machinery that needs to form complexes with subunits to be activated. During the cell cycle, APC is successively activated by two of its subunits, Cdc20 and Cdh1, which have separate windows of activity, each regulated by feedback loops. Cdc20 is activated by Cyclin B during mitosis through a negative feedback loop. Cdh1 becomes active at the end of mitosis through a positive feedback loop, when Cyclin B is degraded, and assembles with APC to further degrade Cyclin A, Cyclin B, Cdc20 and SCF (Wasch et al., 2010). Cdh1 also acts as a G1 regulator by destroying mitotic cyclins during G1 phase and maintaining the cell in G1 by the destruction of SCF (Bashir et al., 2004;Wei et al., 2004). Cdh1 controls Cyclin A and B at two levels: first by a direct cyclin-Cdh1 double feedback loop and second by a CyclinB-Cdc20 negative feedback. Cdh1 controls G1 cyclins, Cyclin D and E by degrading their degradator SCF. SCF can degrade G1-S cyclins, Cyclin D and Cyclin E (Yu et al., 1998;[START_REF] Nakayama | [END_REF]. SCF is down-regulated during M and G1 phases and is induced by Cyclin E near the S phase when its degradator Cdh1 is degraded (Bashir et al., 2004). Cdh1 connects the SCF-driven G1-S proteolytic machinery with the APC-dependent mitotic and G1 proteolysis. Therefore, at the core of the cell cycle lies Cdh1-driven degradation that results in a proteolytic oscillator setting the pace of the cell cycle progression.

Using the existing knowledge about cyclin control mechanisms and their temporal organization during liver regeneration, we designed the network controlling the cyclin-dependent kinase activity at all stages of the cell cycle (Fig. 1). The model is a system of ordinary differential and algebraic equations describing the concentration of key players of the cell cycle (See Appendix A for a description of the model variables). To make the model as tractable as possible, the variables were sorted according to the time scale on which they evolve. The time-scale of reference is the duration of one cell cycle (in hours). Variables that change on a shorter time-scale were approximated by their steady state (quasi-steady state assumption). For instance, concentrations of phosphorylated proteins were approximated by their steady states. To limit the number of variables in the model, we considered explicitly protein concentrations but not their corresponding mRNA concentrations. The kinetic parameters (see Appendix B) were adjusted so that the model could represent the experimentally observed temporal dynamics of respective model species. The induction of gene expression by pro-inflammatory cytokines, growth factors and by Rb-E2F (here called E2F) was incorporated directly by time-dependent input functions modulating the synthesis of cyclins (see (Chauhan et al., 2008) and Appendix A.2). Post-translational regulation through phosphorylationdephosphorylation or through complex formation is explicitly included in the model. For simplicity, we do not distinguish between the nuclear and cytosolic compartments of the cell. The model describes the dynamics of the intracellular cyclin/cdk network and represents an average hepatocyte during liver regeneration. Our aim is to address one cycle of division during liver regeneration triggered by a decaying damage (Hayashi et al., 2003;Blindenbacher et al., 2003). All concentrations in the model are expressed in arbitrary units (a.u.) since for most of the regulatory proteins, the actual concentrations are not known.

Numerical simulations of the full model were performed with Matlab. Bistability analysis of the model was done with the numerical bifurcation continuation process of XPPAUT.

Results

Sequential activation of cyclins and proteolytic degradators

The computational model is able to reproduce the sequential activation of cyclins and proteolytic degradators along the cell cycle (Fig. 2). Damage ac-tivates cytokine-and growth factor-induced pathways which lead to the activation of Cyclin D during late G1 and the subsequent activation of Cyclin E, indicating entry into S phase (Chauhan et al., 2008).

Step-wise activation of E2F via Cyclin D and Cyclin E leads to the sequential transcription of Cyclin A in the S phase and Cyclin B during mitosis [START_REF] Morgan | The cell cycle: principles of control[END_REF] (for equations see Appendix A.2). CKI is activated in early G1 and is maximally elevated at late S phase (Behrens et al., 2002). E2F activity peaks at S phase (Chen et al., 2009). APC Cdh1 is active during late mitosis and early G1 phase, degrading Cyclin A and Cyclin B. APC Cdc20 , which is a degradator of mitotic substrates, is activated during late mitosis, once Cyclin B is sufficiently activated. Degradator of G1-S cyclins, SCF, becomes active at the end of S phase, leading to the degradation of Cyclin D and Cyclin E . Also, mitotic regulators Cyclin B active, Wee1, Cdc25 and APC Cdc20 exhibit a delayed switch-like activation [START_REF] Morgan | The cell cycle: principles of control[END_REF] (Fig. 2).

A switch in Cyclin B activity drives M phase progression

A switch-like increase in the activity of Cyclin B enables entry into mitosis, whereas subsequent Cyclin B proteolysis promotes exit from mitosis [START_REF] Morgan | The cell cycle: principles of control[END_REF]. This switch-like behavior is made possible by the presence of controls on Cyclin B activation, which conserves the total amount of Cyclin B, and on total Cyclin B concentration.

Two feedback loops control Cyclin B activity: a double negative feedback loop from the inhibitory kinase Wee1, which is itself inhibited by Cyclin B, and a positive feedback loop from the activating phosphatase Cdc25, which is further activated by Cyclin B (Tyson et al., 2003). Recently, Potapova et al. (2009) have shown that the exit from mitosis was also a switch phenomenon, due to the Wee1 and Cdc25-dependent positive feedback loops acting during G1 phase.

Total Cyclin B concentration is controlled through synthesis, by E2F, and degradation, by APC Cdh1 and APC Cdc20 . E2F promotes Cyclin B synthesis. At low E2F activity, there is not enough Cyclin B for any of it to be activated. If E2F reaches a threshold value, Cyclin B gets activated. This threshold activation is achieved through a transcritical bifurcation (Fig. 3 (a)) [START_REF] Guckenheimer | Nonlinear oscillations, dynamical systems, and bifurcations of vector fields[END_REF]. At any E2F values, two steady states for Cyclin B exist, one zero and one either negative (below the threshold) or positive (above the threshold). The zero steady state is stable below the threshold and the positive steady state is stable above it. This transcritical bifurcation is possible because of the Cdc25 loop. When this loop is switched off by setting Cdc25 to a low constant level (set at 0.01), the transcritical bifurcation disappears. No effect was observed when Wee1 loop was removed (results not shown). APC Cdh1 is responsible for the activation of Cyclin B by a double negative feedback loop regulation, while APC Cdc20 is mainly responsible for its degradation at the exit of mitosis. Varying the strength of the degradation rate d Cdh1 CB revealed a bistable switch that allows rapid activation and inactivation of Cyclin B (Fig. 3 (b)). At high degradation rate, there is a small total amount of Cyclin B, and no active Cyclin B. When the degradation rate is reduced, a second stable steady state appears through a saddle-node bifurcation. These two stable steady states co-exist until the low level steady state becomes unstable, through a reverse pitchfork bifurcation [START_REF] Guckenheimer | Nonlinear oscillations, dynamical systems, and bifurcations of vector fields[END_REF]). For degradation rates below that level, there is only high Cyclin B activity. This combination of bifurcations form a bistable switch whereby low and high levels of Cyclin B are possible. Thus, our model includes two mechanisms for controlling Cyclin B activity: a transcritical activation by E2F and a bistable switch induced by APC Cdh1mediated Cyclin B degradation. The transcritical activation ensures active Cyclin B levels remain to zero whenever total Cyclin B level are low, therefore preventing accidental entry into mitosis. The bistable switch is responsible for the rapid activation of Cyclin B at the entry to mitosis, and its rapid elimination at the end of mitosis.

Liver regeneration and cell cycle progression are robust processes

Liver regeneration is a robust process. After PH, the liver grows back to its normal mass even in the absence of important cell cycle players. Therefore we expect Cyclin E and Cyclin B activity, as a measure of total DNA synthesis and mitosis respectively, to be robustly activated. We analysed the sensitivity of Cyclin E and Cyclin B activity with respect to changes in biochemical parameters. Both Cyclin E and Cyclin B were robust to parameter change except when parameters immediately downstream of the damage, such as degradation of PIC, were varied. In case of these sensitive parameters, Cyclin E and Cyclin B peaks showed a bell-shaped response to systematic variation in these sensitive parameters (results now shown).

We further went on to study the response of the model to systematic changes in the damage. We varied the damage from strong-transient to weak-sustained input keeping the the total amount of damage, i.e. the integral under the curve, constant. Both DNA synthesis (Cyclin E) and mitosis (Cyclin B) responded as a bandpass filter to such a systematic variation in damage (Fig. 4a-b, upper panels). Weak-sustained and strong-transient damages were rejected and the cells did not progress through both DNA synthesis and mitosis in both cases. The timing of cell cycle events was robust to varying nature of damage (Fig. 4ab, lower panels).

Bandpass filtering properties have been studied previously in a G1/S model (Chauhan et al., 2008). The damage was transmitted through two pathways: 1) direct ultrasensitive induction of Cyclin E, which filtered out the weaksustained damages; and 2) Cytokine mediated delayed pathway, which consisted of nested feedforward loops. Incoherent feedforward loops via CKI and HGF filtered out sharp-transient damages. In the present model, changing the strength of feedback loops during G2/M/G1 phases did not change bandpass filtering behaviour of the model. However, the range of the bandpass filter was affected. Decreasing the positive feedback loop strength of the Cdh1-Cyclin A loop by reducing the two Cyclin A and Cdh1 mutual negative regulation parameters to one-half, one-fourth and zero respectively, had two distinct filtering effects: it decreased the range of the filter in case of Cyclin B, while for Cyclin E, it increased the range of filter (Fig. 5). This opposing control of cell cycle events: DNA synthesis (Cyclin E) and mitosis (Cyclin B) with respect to varying damage, has not been systematically studied to our knowledge.

The circadian clock gates mitosis but not DNA synthesis

Cell division in many mammalian tissues is associated with the circadian clock, a ∼24 h rhythm regulating physiology and behaviour (Reppert and Weaver, 2002). In hepatocytes, Wee1 is the gatekeeper of this circadian control of cell cycle (Matsuo et al., 2003). Wee1 is a clock-controlled gene (its expression is modulated over 24 h), and regulates the timing and efficiency of the cell cycle. In mice hepatocytes, Wee1 synthesis peaks around ZT12 (ZT0 represents lights on and ZT12, lights off, in a 24 h light-dark cycle) (Matsuo et al., 2003). To simulate the circadian expression of Wee1, we used a sinusoidalshaped synthesis rate of Wee1, with a maximal synthesis rate at ZT12 (See Appendix A.6). We simulated PHs performed on mice at ZT8 or ZT0, and used peak of activity in Cyclin B and E as markers of mitosis and S phase. We found that mitotic activity induced by Cyclin B at ZT8 or ZT0 changes from 44.5 to 51.5 hours (Fig. 6). These results reproduce well the gating properties of Wee1 observed experimentally (Matsuo et al., 2003).

In our model, DNA synthesis is directly coupled to mitosis via a Cdh1-SCF loop. Nevertheless, Cyclin E activity, which is representative of DNA replication, was independent from Zeitgeber time PH (Fig. 6). Imposition of circadian control on Wee1 maintains DNA synthesis as an independently controlled property of hepatocytes (Matsuo et al., 2003).

HGF treatment at S phase causes G2 delay

Growth factors are well known to promote the transition from G1 to S phase in cell cycle progression. Beyond G1-S transition, however, growth factors have been considered non-essential for the progression of the cell cycle (Jones and Kazlauskas, 2001). Yet, when injected at S phase, hepatocyte growth factor induces a G2 delay (Park et al., 2007). This delay is marked by a delayed degradation of Cyclin A and Cyclin B, resulting in a delayed mitotic entry. It is not very intuitive how HGF induction at S phase might lead to delayed degradation of Cyclin A and Cyclin B. CKI up-regulation has been implicated in this delay (Park et al., 2007). We simulated growth factor induction at S phase by giving an extra HGF pulse during S phase between 36 and 40 hours (See Appendix A.7). Our model was able to reproduce the observed delay in the degradation of Cyclin A and Cyclin B representing a G2 delay (Fig. 7 (e-f)). Our simulations suggest that HGF treatment at S phase delays APC Cdh1 up-regulation and prolongs E2F activation. Thus, HGF induction at S phase might also prolong E2F mediated mitotic transcription and hence Cyclin A activation. As long as Cyclin A is active at G2, APC Cdh1 can not be activated due to its antagonistic control by Cyclin A. This leads to delayed Cdh1 activation. Delayed Cdh1 activation leads to delayed degradation of Cyclin A and Cyclin B (Fig. 7 (b-d)).

Discussion

Computational Model for Mammalian Cell Cycle

We have developed a computational model for the cell cycle of hepatocytes during liver regeneration that couples different cyclins and proteolytic degradators in a sequential manner. We introduced Cdh1 as a universal controller of the cell cycle. Recent experimental data have identified Cdh1 as a major controller of cell cycle progression.

The model recapitulates the temporal profile of dividing hepatocytes following partial hepatectomy: the sequential activation of cyclins and proteolytic degradators; the effect of the circadian clock on the timing of mitosis; the G2 phase delay caused by HGF treatment during S phase and the effect of Cdh1 on cell cycle progression. Gerard and Goldbeter (2009) recently presented a mammalian cell cycle model describing the sequential cyclin-cdk activation. The model demonstrates repetitive cell cycling in the presence of suprathreshold amounts of growth factors. The emphasis was on the Rb-E2F network during G1 phase and Cyclin A-dependent activation of Cyclin B during mitotic entry. Our model is also structurally able to generate sustained oscillations like many other cell cycle models (Csikasz-Nagy et al., 2006;Gerard and Goldbeter, 2009). However, the focus of the model presented here is to simulate one or two cycles of cell division observed during injury induced liver regeneration, and on the emerging role of Cdh1 in regulating the cell cycle.

Threshold activation of Cyclin B

Entry to and exit from M phase display a switch-like behaviour in Cyclin B levels. It is rapidly switched on at the G2-M phase transition and rapidly switched off at the end of mitosis. Threshold activation provides a robust mechanism for switch. We have shown that total Cyclin B concentration and activity is regulated by two threshold processes: a transcritical bifurcation, mediated by E2F and a bistable loop, mediated by APC Cdh1 . Both the transcritical bifurcation and the bistable loop allowed active Cyclin B to be kept at zero levels outside the specific time window of activity during G2/M phases. Although transcritical activation is qualitatively different from a bistable switch, it also provides a sharp activation threshold.

Bandpass Filter of Damage Input

The model exhibits bandpass filter properties which allows the system to ignore strong-transient and weak-sustained damages, as already discussed (Chauhan et al., 2008). Thus, if the damage is too strong and transient or too weak, cells will not enter the cell cycle events of DNA synthesis and mitosis. This is in agreement with observations that liver regeneration is proportional to the amount of PH but does not occur if the PH is too small or too large (Lambotte et al., 1997). Also, varying the feedback strength of Cdh1-Cyclin A positive feedback loop in the model tunes the range of filtering for Cyclin E and Cyclin B in an opposing manner. Such an opposite control of DNA synthesis and mitosis with varying feedback strength of Cdh1-Cyclin A positive feedback has not been systematically studied to our knowledge. Opposite control of filtering range for Cyclin E and Cyclin B can have some interesting physiological implications. Certain environmental conditions promote DNA synthesis while suppress mitosis during endoreplication and polyploidization (Nevzorova et al., 2009). Cdh1-mediated control of cyclins during endoreplication has been widely reported in mammals, Drosophila and plants (Garcia-Higuera et al., 2008;Sigrist and Lehner, 1997;Sorensen et al., 2000;Kasili et al., 2010). It would be interesting to study Cdh1-mediated feedback loop control of cell cycle with respect to endoreplication and polyploidisation, which are common forms of cell cycle progression during liver regeneration (Duncan et al., 2010).

Circadian control of Wee1

Our model is consistent with a circadian control of Wee1 synthesis, affecting the timing of mitosis but not of DNA synthesis. When the entrainment to light-dark cycle is simulated by varying Wee1 synthesis with a 24 h period, the time at which PH is performed has a impact on the timing of mitosis. In agreement with Matsuo et al (2003) results, we found that in PH performed at ZT0 and ZT8 (at lights on and 8 hours later respectively), cells enter mitosis roughly at the same time (around 60 h after ZT0). This shows that circadian regulation of Wee1 induces a gating process by which cells cannot divide at any time of the day. The timing of DNA synthesis was independent from the timing of PH, and occurred 36 hours after PH, coherent with experimental results. In hepatocytes, Wee1 is a major link between the circadian clock and the cell cycle and S phase is largely a circadian clock-independent process, despite the presence of a feedback loop linking G1/S and G2/M phases via Cdh1 and SCF. In continuously dividing cells this independence might not be preserved as gating mitosis might affect subsequent phases.

HGF treatments during S phase causes G2 delay

HGF accelerates cell cycle progression but has been mostly assumed to be nonessential beyond G1-S transition. However, HGF injection at S phase leads to a G2 delay resulting in delayed degradation of cyclins during G2-M phase. The model was able to reproduce a G2 phase delay caused by growth factor treatment during S phase marked with delayed degradation of Cyclin A and Cyclin B. Erk signaling is known to mediate this G2 delay via CKI (Han et al., 2005;Dangi et al., 2006;Park et al., 2007). Our simulations suggest that CKI, APC Cdh1 and E2F contribute in delaying the degradation of Cyclin A and Cyclin B. This leads us to the conclusion that induction of growth factors during S phase might lead to prolonged transcriptional activity of E2F resulting in increased Cyclin A activity. Since the antagonistic Cyclin A and APC Cdh1 can not coexist, APC Cdh1 is delayed. Thus the APC Cdh1 -dependent degradation machinery might be responsible for the delayed Cyclin A and Cyclin B degradation during G2 phase delay. Therefore, our model shows that APC Cdh1 might have a crucial role to play during G2 delay.

Conclusion

Mounting evidences demonstrate that Cdh1 plays a central role in the control of proliferation, differentiation and maintenance of genomic integrity by timely and coordinated degradation of several substrates (Wasch et al., 2010). Cdh1 maintains the stability of G1 phase by degrading the degradator of G1-S cyclins and SCF. Cdh1 is also required for G2 DNA-damage checkpoint by controlling the degradation of Cyclin A and Cyclin B (Wasch et al., 2010). Cdh1 is also being implicated in genomic instability and cancers and is under investigation as a therapeutic target. Recent developments call for a better characterization of the role of Cdh1 in the control of G2 phase. It will be interesting to dissect a Cdh1 based cell cycle model in order to understand the G2 delay and might help in better understanding of the fate of mitosis. Also, owing to the role of Cdh1 in specialised cell division cycles of endoreplication and polyploidy, widely observed during liver regeneration, a Cdh1 centered cell cycle model would be suitable to understand underlying mechanisms controlling the causes and consequences of such specialised cell cycle events.

B Parameters

Rb T 1 p1 3 p 2 4 k 1 25 k 2 1 k 3 0.1 APC AP C T 1 k Cdh1 AP C 0.5 k Cdc20 AP C 0.1 Mitosis v E2F CA 1.75 d Cdh1 CA 1 d CA 0.1 v CKI CA 0.01 d CKI CA 0.1 k 1 0.03 k 2 5 k a1 60 v E2F CB 1.2 d CB 0.01 d Cdh1 CB 0.8 d Cdc20 CB 0.2 P W ee1
SCF G1 S G2 M G1 S G2 M G1 S G2 M G1 S G2 M G1 S G2 M G1 S G2 M G1 S G2 M G1 S G2 M G1 S G2 M G1 S G2 M G1 S G2 M G1 S G2 M G1 S G2 M G1 S G2 M G1 S G2 M G1 S G2 M G1 S G2 M G1 S G2 M G1 S G2 M G1 S G2 M G1 S G2 M G1 S G2 M G1 S G2 M G1 S G2 M

Fig. 1 .

 1 Fig. 1. Damage induced model of the cell cycle during liver regeneration based on sequential cyclin activation and degradation. The PH-induced damage primes quiescent cells via cytokine signaling. Primed cells then activate growth factor-induced signaling cascades. Cytokine-and growth factor-induced pathways act in concert to provide mitogenic signals for Cyclin D activation in early G1 phase. Cyclin D initiates a chain of sequential phosphorylation of Rb/E2F which leads to sequential transcription of further G1-S (Cyclin E), S (Cyclin A) and M (Cyclin B) phase cyclins. As early as G1 phase, stoichiometric inhibitors of cyclins, CKI, are also activated by cytokines. The G1-S proteolytic degradation machinery, SCF, is activated by Cyclin E. Entry to mitosis is initiated by the abrupt activation of Cyclin B by Cdc25 and Wee1 in a positive feedback loop fashion at G2-M transition. Cdc25and Wee1-mediated positive feedback loops also regulate the rapid exit from mitosis by swiftly inactivating Cyclin B at M-G1 in coordination with a positive feedback loop from the M-G1 degradator APC Cdh1 . Mitotic degradator APC Cdc20 exerts a negative feedback loop. All cyclin-cdk complexes are depicted by their respective activating cyclin partner for simplicity. E2F in the scheme represents all three forms of E2F, viz, unphosphorylated, hypophosphorylated and hyperphosphorylated .

Fig. 2 .Fig. 3 .Fig. 4 .

 234 Fig. 2. Sequential activation and degradation of cyclins and their key regulators. Cyclin D appears at the late G1, Cyclin E at the G1-S transition, Cyclin A in the S phase and Cyclin B in the late S phase and mitosis. At the G2-M interface, transient activation of Cyclin B active, Cdc25 and inactivation of Wee1, leads to abrupt mitotic entry. At the M-G1 interface, Cdc25 and Wee1 are respectively rapidly inactivated and activated, leading to swift exit from mitosis. APC Cdc20 is also transiently activated once enough Cyclin B has accumulated at mitosis. APC Cdh1 is active from late mitosis to G1 phase keeping Cyclin A and Cyclin B degraded in a positive feedback loop fashion during late mitosis and G1. SCF is activated by Cyclin E during G1-S phase leading to degradation of G1-S cyclins. All concentrations are normalized by their maximum concentrations.

Fig. 5 .Fig. 6 .Fig. 7 .

 567 Fig. 5. Opposite bandpass filtering effect on DNA synthesis (a) and mitosis (b) with respect to changing feedback strength of Cdh1-Cyclin A loop.

Acknowledgements

AC was supported by the German Ministry Federal Ministry of Education and Research (BMBF, Hepatosys, 0313078A) and by SFB 618 grant of the Deutsche Forschungsgesellschaft (DFG). SL was supported by the German Ministry Federal Ministry of Education and Research (BMBF, Hepatosys, 0313078A). SB was supported by the Project-Team INRIA Dracula (France), the French National Research Agency (ProCell, ANR-09-JCJC-0100-01), and acknowledges support from Rhône-Alpes Complex Systems Institute (IXXI, France). We thank two anonymous reviewers for their useful suggestions.

Appendix

A Model equations

The model contains 25 dynamical variables and 84 parameters. The 25 variables are the concentrations of the following players involved in the cell cycle control: Damage (D) induced pro-inflammatory cytokine pathways (PIC and PGE); proinflammatory cytokine induced growth factor pathways (PAI, HGF, HB-EGF); Cyclins D, E, A, and B; the inhibitor CKI and its complexes with the active cyclin-cdk complexes; the active and inactive forms of phosphatase Cdc25 and of kinase Wee1; the SCF proteasomal ligases involved in the degradation of cyclin D, Cyclin E and CKI; and the active and inactive forms of the proteins Cdh1 and Cdc20 involved in the degradation of cyclins A and B

A.1 G1-S model

A.2 E2F steady state

Rb phosphorylation is initiated by Cyclin D, releasing E2F in sufficient quantity for Cyclin E activation. Cyclin E further phosphorylates Rb (Rb P ) resulting in hyperphosphorylated Rb pp , releasing higher amounts of E2F required for transcriptional activation of further Cyclins. Phosphorylation/dephsophorylation reactions of Rb and association/dissociation of its three phosphorylated forms with E2F are fast enough to be in the steady state equilibrium.

Substituting the steady state values, we solve the equation for E2F as

Substituting the steady state values, we solve the equation for APC as (2005) with the simplification that the phosphorylation/dephosphorylation of the three inactive forms of Cyclin B viz transcribed Cyclin B (CycB), Tyrosine phosphorylated (CycB Y ), and Tyrosine and Threonine phosphorylated (CycB Y T ) is fast enough to be always in equilibrium; so that equation for CycB Y T can be algebraically solved.

[


Keywords: Dual-Process Theory, Reasoning, Decision-Making, Bias

Studies on human reasoning have long established that intuitions can bias inference and lead to violations of logical norms. Popular dual-process models, which characterize thinking as an interaction between intuitive ("System 1") and deliberate ("System 2") thought processes, have presented an appealing explanation for this observation. According to this account, logical reasoning is traditionally considered as a prototypical example of a task that requires effortful deliberate thinking. In recent years, however, a number of findings obtained with new experimental paradigms have questioned the traditional dual-process characterization. A key observation is that people can process logical principles in classic reasoning tasks intuitively and without deliberation. We review the paradigms and sketch how this work is leading to the development of revised dual-process models.

INTRODUCTION: BIAS AND DUAL-PROCESS MODELS 1.0

Sometimes a solution to a problem pops in to mind instantly and effortlessly whereas at other times arriving at a decision takes time and effort. This simple dichotomy between a more intuitive ("System 1") and more deliberate ("System 2") type of thinking lies at the heart of the dual-process theories that have been prominent in the reasoning and decision-making field since the 1970s. More recently, dual-process theory has gained a broader popularity, having been featured in best-selling books (e.g., [START_REF] Kahneman | Thinking, Fast and Slow[END_REF] and applied to a wide range of fields [START_REF] Evans | Dual-processing accounts of reasoning, judgment, and social cognition[END_REF]-from moral philosophy [START_REF] Greene | The rise of moral cognition[END_REF] to prosocial cooperation [START_REF] Rand | Spontaneous Giving and Calculated[END_REF].

The rise and development of dual-process theory in research on human thinking can be linked to an attempt to explain the phenomenon of "bias" in reasoning and decision-making research [START_REF] Evans | Reasoning, biases and dual processes: The lasting impact of Wason (1960)[END_REF][START_REF] Kahneman | Thinking, Fast and Slow[END_REF]. Decades of research have shown that people readily violate the most elementary logical, mathematical, or probabilistic rules when a task cues an intuitive response that conflicts with these principles (see Table 1 for illustrations). Hence, reasoners often appear to be biased by their intuitions. The broad dual-process framework represents a simple and elegant explanation for the tendency for humans to be biased: Logical and probabilistic principles, unlike simple intuitive tasks like making stereotypical judgments or executing stimulus-response pairings, require demanding deliberate processing (e.g., [START_REF] Evans | Dual-processing accounts of reasoning, judgment, and social cognition[END_REF][START_REF] Stanovich | Individual differences in reasoning: Implications for the rationality debate[END_REF]. Because human reasoners have a strong tendency to minimize demanding computations, they will often refrain from engaging or completing the slow deliberate processing when mere intuitive processing has already cued a response [START_REF] Evans | Dual-process theories of higher cognition advancing the debate[END_REF][START_REF] Kahneman | Thinking, Fast and Slow[END_REF]. Consequently, most reasoners will simply stick to the intuitive response that quickly came to mind and fail to consider the logical implications. Hence, people will typically be biased because they do not detect that their intuitive hunch conflicts with logical considerations. The few reasoners who manage to give the logical response will be those who have sufficient motivation and resources to complete the deliberate computations and override the initially generated intuitive response [START_REF] Stanovich | Individual differences in reasoning: Implications for the rationality debate[END_REF].

INTUITIVE LOGIC

The idea that logical reasoning requires deliberate processing fits nicely with the common belief that following logical or mathematical rules is hard [START_REF] Kahneman | Thinking, Fast and Slow[END_REF]. However, in the last decade numerous findings have questioned this key assumption and indicate that people have intuitive access to logical principles in classic reasoning tasks. That is, logic does not necessarily require System 2. Here we review the experimental paradigms that led to this discovery.

Conflict Detection Paradigm

The conflict detection paradigm was developed to test whether reasoners who are "biased"-that is, they opt for an intuitively cued response instead of the logical responsedetect that their answer violates logical considerations [START_REF] De Neys | Conflict monitoring in dual process theories of thinking[END_REF]. Put differently, the question is whether biased reasoners show some sensitivity to their errors. To assess this, the conflict detection paradigm presents participants with standard "conflict" versions of classic reasoning problems and newly constructed "no-conflict" control versions (as illustrated in Table 1). In the classic conflict versions, an intuitive association cues a response that conflicts with the logical response. In the no-conflict versions, this conflict is removed and both the intuitive association and logical considerations point to the same conclusion. Bias and conflict sensitivity are then reflected in differences in how people process both versions. If biased reasoners do not take logical principles into account, then conflict should be irrelevant and have no impact on reasoning.

Results indicate that biased reasoners often do show conflict sensitivity. For example, biased reasoners display increased response doubt-as reflected in lower confidence and longer decision latencies-when they give a biased answer on the conflict problems [START_REF] De Neys | Bias and conflict a case for logical intuitions[END_REF]. This conflict sensitivity is also observed under time-pressure and cognitive load (De Neys, 2017a). Since deliberate processing is often assumed to be more time and cognitive resource demanding than intuitive processing, this finding implies that conflict detection occurs without the aid of System 2. Thus, the finding that biased reasoners show logical conflict sensitivity when deliberate processing is experimentally sidelined suggests they are processing the logical principles intuitively.

Two-Response Paradigm

The two-response paradigm was designed to explore the time-course of intuitive and deliberate processing [START_REF] Thompson | Intuition, reason, and metacognition[END_REF]. In this paradigm, participants are asked to give two consecutive responses. First, they are asked to give their initial hunch and to respond as fast as possible with the first intuitive answer that comes to mind. Afterwards, they are allowed to take all the time they want to reflect on the problem and generate a final response. To make sure that the initial response is generated intuitively, it has to be generated under time-pressure and/or cognitive load [START_REF] Bago | Fast logic?: Examining the time course assumption of dual process theory[END_REF][START_REF] Newman | Rule-based reasoning is fast and belief-based reasoning can be slow: Challenging current explanations of belief -bias and base-rate neglect[END_REF]. This procedure again helps to minimize possible deliberation. The critical finding is that many reasoners who give a logic final response (i.e., after deliberation was allowed) already gave this response in the initial response stage in which they had to reason intuitively [START_REF] Bago | Fast logic?: Examining the time course assumption of dual process theory[END_REF], 2019a). Hence, logical responders do not necessarily need to deliberate to override a faulty intuition; often their intuitive response is already logical. This further indicates that logical principles can be processed intuitively in common reasoning tasks.

Instructional Set Paradigm

In traditional reasoning studies, participants are expected to reason in accordance with logical principles. Typically they are explicitly told to disregard their intuitive beliefs. In the instructional set paradigm, these instructions are reversed [START_REF] Handley | Logic, beliefs, and instruction: A test of the default interventionist account of belief bias[END_REF]. People are not asked to indicate which response is logically or probabilistically correct.

Rather, they are asked to follow their intuition and indicate whether or not the conclusion is believable. The key observation is that people are slower to answer (and less confident) in those cases in which the intuitively cued belief-based response conflicts with logicality [START_REF] Pennycook | Base rates: Both neglected and intuitive[END_REF][START_REF] Trippas | When fast logic meets slow belief: Evidence for a parallel-processing model of belief bias[END_REF]. These effects are present even if deliberation is minimized by forcing participants to respond as quickly as possible [START_REF] Thompson | Do smart people have better intuitions?[END_REF]. Hence, although people are not instructed to reason logically, they spontaneously seem to do so and this interferes with their ability to make belief-based judgments.

Logic-Liking Paradigm

In the logic-liking paradigm (Morsanyi & Handley, 2011) participants are presented with classic reasoning problems but are not asked to solve them. They are simply asked to make seemingly trivial judgments such as how much they 'like' the conclusion or even how bright they perceive it to be. The task and instructions explicitly avoid any reference to logic, reasoning or validity. People are told they will see a number of statements and will simply have to indicate how much they like them or how bright they look on the screen. Quite strikingly, results show that people implicitly discriminate valid and invalid conclusions in this task.

Although people are not instructed to reason, they nevertheless indicate that they like valid conclusions more than invalid ones and judge them to be brighter [START_REF] Trippas | Logic Brightens My Day: Evidence for Implicit Sensitivity to Logical Validity[END_REF].

Why do people judge a valid conclusion as more likable or brighter when they are not even expected to reason? The explanation is built on a fluency misattribution account [START_REF] Reber | Effects of perceptual fluency on affective judgments[END_REF]: Specifically, more fluently processed information is known to give rise to positive affect. If logical validity is processed intuitively, more fluently processed valid conclusions can be expected to give rise to positive feelings (Morsanyi & Handley, 2011).

The idea is that this affective fluency signal is subsequently being interpreted as an increase in likability or brightness.

Irrespective of the specific fluency account, just like the instructional set findings, the liking paradigm indicates that people seem to spontaneously take logical validity into account.

This further suggests that they can process elementary logical features intuitively without engaging in a deliberate reasoning process.

TOWARDS A DUAL-PROCESS MODEL 2.0

The intuitive logic findings are hard to account for in the traditional dual-process model.

Various scholars have therefore claimed it is time to move to a revised dual-process model [START_REF] Ball | Conflict and dual process theory: the case of belief bias[END_REF][START_REF] Banks | Heuristic and analytic processes in reasoning: An event-related potential study of belief bias[END_REF][START_REF] De Neys | Bias and conflict a case for logical intuitions[END_REF][START_REF] Handley | Logic, beliefs, and instruction: A test of the default interventionist account of belief bias[END_REF][START_REF] Pennycook | What makes us think? A three-stage dual-process model of analytic engagement[END_REF][START_REF] Reyna | The fuzzy-trace dual process model[END_REF][START_REF] Thompson | Do smart people have better intuitions?[END_REF]. One central aspect of this emerging perspective is that our conception of intuitive ("System 1") processing needs to be upgraded (De Neys, 2017b). Computations that were traditionally considered to require deliberate processing can also be cued intuitively.

Under this view, multiple types of intuitive responses will be cued simultaneously [START_REF] De Neys | Bias and conflict a case for logical intuitions[END_REF][START_REF] Pennycook | What makes us think? A three-stage dual-process model of analytic engagement[END_REF]. For example, when we're faced with a classic reasoning problem one of these will be the traditional "heuristic" intuitive response that is based on prior beliefs and other associations. But a critical second response will be what we can refer to as a "logical" intuitive response which is based on elementary knowledge of basic logical and probabilistic principles.

Crucially, different intuitions can vary in their strength or activation level [START_REF] Bago | Fast logic?: Examining the time course assumption of dual process theory[END_REF][START_REF] Pennycook | What makes us think? A three-stage dual-process model of analytic engagement[END_REF][START_REF] Thompson | Do smart people have better intuitions?[END_REF]. In cases where multiple conflicting intuitive responses are cued, the strength difference will determine whether conflict is registered (the more similar the strength, the higher the likelihood of conflict detection) and whether deliberate processing will be called upon [START_REF] Pennycook | What makes us think? A three-stage dual-process model of analytic engagement[END_REF]. This deliberate processing can then be used to override the dominant intuitive response or to simply rationalize it and look for an explicit justification that supports it [START_REF] Pennycook | What makes us think? A three-stage dual-process model of analytic engagement[END_REF].

Figure 1 sketches three illustrative cases. Obviously, the postulation of logical intuitions does not entail that people will always respond logically or that logical responding cannot be deliberate. Rather, the idea is that people have different types of intuitions-some of which are logical (accurate)-and that these intuitions can differ in strength. In some cases, the logical intuition will dominate the competing heuristic intuition (Figure 1B). Here one can respond in accordance with logic without further deliberation. In other cases, the heuristic intuition will dominate (Figure 1A and 1C), and logical responding will therefore require deliberation.

Crucially, the presence of a competing logical intuition allows people to detect conflict, which then can trigger the deliberative override of the heuristic intuition and result in a classic, "slow" logical response. If the override fails, the reasoner will give the heuristic response. Any deliberate processing will be primarily used here to find an explicit justification for the dominant heuristic intuition (i.e., rationalization). Thus, even with successful conflict detection and resulting deliberation, people may still end up giving a "biased" answer.

Whether or not deliberate override will occur is tied to the likelihood of conflict detection. The more similar the strength of the competing intuitions (Figure 1C), the more conflict will be experienced, and the more likely that deliberation will occur. This, in turn, increases the likelihood that the dominant intuition will be overridden. Results from the tworesponse and conflict detection paradigm indeed indicate that participants who show a more pronounced conflict detection effect (e.g., as reflected in increased doubt about their initial response) are more likely to change their initial heuristic response after deliberation relative to those who are less responsive to conflict [START_REF] Bago | Fast logic?: Examining the time course assumption of dual process theory[END_REF][START_REF] Thompson | Intuition, reason, and metacognition[END_REF].

Experimental manipulations that are aimed to increase or decrease the strength of logical intuitions (e.g., by making probabilities in base-rate neglect problems such as in Table 1 more or less extreme) further support this assumption (Bago & De Neys, 2019a;[START_REF] Pennycook | What makes us think? A three-stage dual-process model of analytic engagement[END_REF].

A key implication of the logical intuition findings and dual-process evolutions is that we need to re-think the traditional view on the nature of biased and logical responding. Biased responding does not necessarily result from a failure to recognize conflict. Although reasoners might not always manage to override their heuristic intuition, they are not necessarily oblivious to its questionable status. At the other end of the spectrum, sound reasoning does not necessarily require a deliberation process. Although deliberate override of an initial dominant heuristic intuition sometimes occurs, the most prolific reasoners do not always need it. This implies that good reasoners do not necessarily deliberate better; often they will simply have better intuitions [START_REF] Bago | Advancing the specification of dual process models of higher cognition: a critical test of the hybrid model view[END_REF][START_REF] Thompson | Do smart people have better intuitions?[END_REF].

OUTSTANDING ISSUES

Boundary conditions and individual differences

The dual-process view "2.0" that is emerging is a work-in-progress. There remain important challenges. For example, the framework does not entail that we have logical intuitions for every possible problem we face in life. Rather, the claims concern the type of elementary principles that are evoked in classic reasoning problems [START_REF] De Neys | Bias and conflict a case for logical intuitions[END_REF]. The idea is that most adult reasoners managed to automatize these principles because they have been extensively exposed to them (e.g., in the school curriculum). Moreover, how complex these principles can be is an active open area of research (Trippas et al., 2016). Studies also point to individual differences: Although the modal biased reasoner might show conflict detection, a subgroup of individuals does not [START_REF] Frey | Individual differences in conflict detection during reasoning[END_REF][START_REF] Pennycook | What makes us think? A three-stage dual-process model of analytic engagement[END_REF]. It is possible that this group has not managed to automatize the application of the necessary logical knowledge [START_REF] Stanovich | Miserliness in human cognition: the interaction of detection, override and mindware[END_REF]. Pinpointing the exact boundary conditions and individual differences remains an important challenge in the coming years.

Origin logical intuition

The concept of a logical intuition does not imply that it is inborn or instinctive. Although infants might show some early logical sensitivity [START_REF] Cesana-Arlotti | Precursors of logical reasoning in preverbal human infants[END_REF], it is assumed that people's intuitive logical knowledge emerges from a learning process in which key principles have been practiced to automaticity [START_REF] De Neys | Bias and conflict a case for logical intuitions[END_REF]. The basic mechanism of a deliberate-tointuitive automatization process (e.g., [START_REF] Shiffrin | Controlled and automatic human information processing: II. Perceptual learning, automatic attending and a general theory[END_REF] has long been recognized in traditional dual-process models. For example, it is long been assumed that experts in various fields are characterized by the automatization of previously deliberate procedures [START_REF] Kahneman | Thinking, Fast and Slow[END_REF]. Hence, the underlying automatization process that is assumed to give rise to logical intuitions is not new. The key insight is that it applies to a much wider range of phenomenaincluding mastery of basic logical principles by laypeople-than previously believed.

Nevertheless, the logical automatization assumption remains to be tested directly.

Role of deliberation?

The case for fast logical intuitions might seem to downplay the role of "System 2" deliberation in dual-process theory. If we can generate logical responses intuitively, why do we even need to engage in effortful deliberation? The answer brings us back to the idea that different types of intuitions will be cued simultaneously. The generation of a logical intuition does not imply that it will dominate. Logical responding to the task will still require a deliberate override when the competing heuristic intuition is stronger. Furthermore, even when people have dominant logical intuitions, the fact that deliberation is not needed to override does not imply it cannot serve a different function. For example, [START_REF] Bago | Advancing the specification of dual process models of higher cognition: a critical test of the hybrid model view[END_REF] observed that after deliberation (in a two-response study) people had little trouble properly justifying their logical responses. Such correct justifications were much less likely for logical responses in the initial response stage. Hence, just like reasoners may use deliberation to look for a justification to support a heuristic intuition, they may need it to come up with a proper, explicit justification for their intuitive logical insight. In theory, such a process can play an important role in communication (e.g., [START_REF] Mercier | The enigma of reason[END_REF], but its precise nature remains to be clarified.

Generalization

We noted that the core ideas that were put forward by the original dual-process model have been applied in various fields. This led to dual-process models of, for example, prosocial cooperation [START_REF] Rand | Spontaneous Giving and Calculated[END_REF] and moral reasoning [START_REF] Greene | The rise of moral cognition[END_REF] that became highly influential in their own right. The research reviewed here indicates that there are good reasons to question core assumptions of the traditional dual-process architecture that inspired these models. In theory, the various paradigms we introduced can be used to test dual-process assumptions beyond logical reasoning tasks. Interestingly, initial findings with the conflict detection and two-response paradigm point to a remarkable similarity between logical and moral reasoning: The moral response that is traditionally believed to result from deliberate processing (i.e., calculating the greater good) often is cued intuitively (e.g., [START_REF] Bago | The intuitive greater good: Testing the corrective dual process model of moral cognition[END_REF]Bialek & De Neys, 2017). Although this lends some credence to the generality of the findings it will be critical to test the applicability of the new architecture in various contexts.

CONCLUSION

Research with new experimental paradigms indicates that logical processing can be done intuitively. We sketched how this is leading to a revision of popular dual-process model assumptions. Although the traditional dual-process model has been highly instrumental, we believe it is time to move to a new conceptualization. We hope that the many students and scholars who are interested in the dual-process perspective will take note of the new developments and integrate them in their work. [START_REF] Kahneman | Thinking, Fast and Slow[END_REF]. Thinking, Fast and Slow. New York, NY: Farrar, Straus and Giroux. Table 1. Illustration of classic reasoning problems. Both standard (a.) and control (b.) versions are shown. The standard versions cue an intuitive response that conflicts with the logical response (i.e., the response consistent with standard logic or probability theory principles, highlighted in bold). In the control versions the cued intuitive response is consistent with the logical response. Rationale: In the standard version intuitive beliefs based on the stereotypical description ("a truck driving southern NFL fan typically drinks beer") conflict with the response that is favoured by the base-rate probabilities (i.e., there are far more wine drinkers in the sample). In the control version the base-rates are switched around so that both the base-rates and description cue the same response. Rationale: Most people readily answer "10 cents" instead of the correct "5 cents" to the standard problem because they intuitively parse the $1.10 in $1 and 10 cents. In the control version this intuitive parsing is also mathematically correct.

RECOMMENDED READING

Accessible

Figure 1.

A key feature of the dual process model 2.0 view is that different types of intuitions will be generated that can differ in activation strength. Three prototypical cases are illustrated. The modal case (A) is the one in which the heuristic intuition dominates. In cases the logical intuition dominates (B) the logical response will be generated without further deliberation. The more similar the activation strength (C), the more likely that the dominant intuition will be overridden via deliberation.

  overview of bias research and the traditional dual-process model account. Evans, J. St. B., & Stanovich, K. E. (2013). Dual-process theories of higher cognition advancing the debate. Perspectives on Psychological Science, 8, 223-241. A detailed overview of the traditional dual-process model, common misconceptions, and critiques. Pennycook, G., Fugelsang, J. A., & Koehler, D. J. (2015). What makes us think? A three-stage dual-process model of analytic engagement. Cognitive Psychology, 80, 34-72. Prototypical example of a dual-process model 2.0. De Neys, W. (Ed.) (2017b). Dual Process Theory 2.0. Oxon, UK: Routledge. Edited volume that gives a detailed overview of the new experimental paradigms, evolutions, and current challenges in dual-process theorizing.

  "Conflict" versionA bat and a ball together cost $1.10. The bat costs $1 more than the ball. How much does the ball cost? ___ (5 cents)b. Control "No Conflict" versionA bat and a ball together cost $1.10. The bat costs $1. How much does the ball cost? ___ (10 cents)

Ryan's favorite drink is beer

  Rationale: The conclusion in the standard version is not logically valid. However, because the conclusion is believable (i.e., it fits with our prior beliefs) many people will nevertheless accept it. In the control version the conclusion is both believable and logically valid. Here our prior beliefs and logic do not conflict. No Conflict" version A psychologist wrote thumbnail descriptions of a sample of 1000 participants consisting of 995 people whose favorite drink is beer and 5 people whose favorite drink is wine. The description below was chosen at random from the 1000 available descriptions.Ryan is 27 and lives in Virginia. He drives to work in his truck and likes to wear shirts of his favorite NFL team. He loves hanging out with his buddies.Which one of the following two statements is most likely? 1. Ryan's favorite drink is wine 2.

	Syllogistic reasoning problem:
	a. Standard "Conflict" version	b. Control "No Conflict" version
	Premises:	All flowers need water	Premises:	All flowers need water
		Roses need water		Roses are flowers
	Conclusion:	Roses are flowers	Conclusion:	Roses need water
	1. The conclusions follows logically	1. The conclusions follows logically
	2. The conclusion does not follow logically	2. The conclusion does not follow logically
	Base-rate neglect problem:
	a. Standard "Conflict" version	b. Control "
	A psychologist wrote thumbnail descriptions of a sample
	of 1000 participants consisting of 995 people whose
	favorite drink is wine and 5 people whose favorite drink is
	beer. The description below was chosen at random from
	the 1000 available descriptions.
	Ryan is 27 and lives in Virginia. He drives to work in his
	truck and likes to wear shirts of his favorite NFL team. He
	loves hanging out with his buddies.
	Which one of the following two statements is most
	likely?
	1. Ryan's favorite drink is wine
	2. Ryan's favorite drink is beer

ACKNOWLEGMENTS

We would like to acknowledge support of the Agence Nationale de la Recherche (ANR-16-CE28-0010-01).