Aurélie Piodi

Philippe Chouteau

Hervé Lerat

Christophe Hézode

Prof Jean-Michel Pawlotsky
email: jean-michel.pawlotsky@hmn.aphp.fr

Morphological Changes in Intracellular Lipid Droplets Induced by Different Hepatitis C Virus Genotype Core Sequences and Relationship with Steatosis

Keywords: hepatitis C virus, steatosis, lipid droplets, core protein, colocalization hepatitis C virus, BMI: body mass index, HOMA: Homeostasis Model Assessment, NAFLD: non-alcoholic fatty liver disease, PCR: polymerase chain reaction, FCS: fetal calf serum, mAb: monoclonal antibody, CCF: crosscorrelation function, SEM: standar error fatty acid synthase, SREBP: sterol regulatory element binding protein

    Morphological changes in intracellular lipid droplets induced by different hepatitis C virus genotype core sequences and relationship with steatosis.

 [START_REF] Mccullough | Obesity and its nurturing effect on hepatitis C[END_REF][START_REF] Hourigan | Fibrosis in chronic hepatitis C correlates significantly with body mass index and steatosis[END_REF][START_REF] Adinolfi | Steatosis accelerates the progression of liver damage of chronic hepatitis C patients and correlates with specific HCV genotype and visceral obesity[END_REF][START_REF] Westin | Steatosis accelerates fibrosis development over time in hepatitis C virus genotype 3 infected patients[END_REF][START_REF] Monto | Steatosis in chronic hepatitis C: relative contributions of obesity, diabetes mellitus, and alcohol[END_REF][START_REF] Castera | Worsening of steatosis and fibrosis progression in hepatitis C[END_REF]. Various metabolic parameters are associated with the onset and severity of steatosis regardless of the HCV genotype, including the body mass index (BMI), hyperlipidemia, type 2 diabetes and insulin resistance [START_REF] Hourigan | Fibrosis in chronic hepatitis C correlates significantly with body mass index and steatosis[END_REF][START_REF] Adinolfi | Steatosis accelerates the progression of liver damage of chronic hepatitis C patients and correlates with specific HCV genotype and visceral obesity[END_REF][START_REF] Westin | Steatosis accelerates fibrosis development over time in hepatitis C virus genotype 3 infected patients[END_REF][START_REF] Monto | Steatosis in chronic hepatitis C: relative contributions of obesity, diabetes mellitus, and alcohol[END_REF][START_REF] Asselah | Liver fibrosis is not associated with steatosis but with necroinflammation in French patients with chronic hepatitis C[END_REF][START_REF] Romero-Gomez | Serum leptin levels correlate with hepatic steatosis in chronic hepatitis C[END_REF][START_REF] Rubbia-Brandt | Steatosis affects chronic hepatitis C progression in a genotype specific way[END_REF][START_REF] Poynard | Effect of treatment with peginterferon or interferon alfa-2b and ribavirin on steatosis in patients infected with hepatitis C[END_REF][START_REF] Patton | The impact of steatosis on disease progression and early and sustained treatment response in chronic hepatitis C patients[END_REF][START_REF] Hui | Genotype-specific mechanisms for hepatic steatosis in chronic hepatitis C infection[END_REF][START_REF] Hezode | Impact of moderate alcohol consumption on histological activity and fibrosis in patients with chronic hepatitis C, and specific influence of steatosis: a prospective study[END_REF][START_REF] Castera | Effect of antiviral treatment on evolution of liver steatosis in patients with chronic hepatitis C: indirect evidence of a role of hepatitis C virus genotype 3 in steatosis[END_REF][START_REF] Czaja | Host-and disease-specific factors affecting steatosis in chronic hepatitis C[END_REF][START_REF] Hwang | Hepatic steatosis in chronic hepatitis C virus infection: prevalence and clinical correlation[END_REF][START_REF] Serfaty | Effect of the interaction between steatosis and alcohol intake on liver fibrosis progression in chronic hepatitis C[END_REF][START_REF] Fartoux | Insulin resistance is a cause of steatosis and fibrosis progression in chronic hepatitis C[END_REF][START_REF] Cammà | Insulin resistance is associated with steatosis in nondiabetic patients with genotype 1 chronic hepatitis C[END_REF]. Moreover, HCV genotype 3 is independently associated with hepatocellular steatosis, which can thus be considered as a true cytopathic lesion induced by this HCV genotype (3-13, 17, 20-22). This suggests that one or more viral proteins produced during genotype 3 infection are involved in the steatogenic process, while the same proteins produced during infection by other genotypes are not.

Experimental studies have shown complex interactions between HCV core protein, lipids and lipid metabolism. In particular, HCV core protein can induce intracellular accumulation of lipids, both in cell culture and in transgenic mice [START_REF] Rubbia-Brandt | Hepatocyte steatosis is a cytopathic effect of hepatitis C virus genotype 3[END_REF][START_REF] Barba | Hepatitis C virus core protein shows a cytoplasmic localization and associates to cellular lipid storage droplets[END_REF][START_REF] Fujie | Steatosis and intrahepatic hepatitis C virus in chronic hepatitis[END_REF][START_REF] Shi | Hepatitis C virus NS5A colocalizes with the core protein on lipid droplets and interacts with apolipoproteins[END_REF][START_REF] Abid | An in vitro model of hepatitis C virus genotype 3a-associated triglycerides accumulation[END_REF][START_REF] Moriya | Hepatitis C virus core protein induces hepatic steatosis in transgenic mice[END_REF][START_REF] Moriya | The core protein of hepatitis C virus induces hepatocellular carcinoma in transgenic mice[END_REF][START_REF] Lerat | Steatosis and liver cancer in transgenic mice expressing the structural and nonstructural proteins of hepatitis C virus[END_REF][START_REF] Perlemuter | Alcohol and hepatitis C virus core protein additively increase lipid transgenic mouse model[END_REF]. In cell culture, HCV core protein associates with cytoplasmic lipid droplets, lipid storage organelles rich in cholesterol esters and in di-and triacylglycerol [START_REF] Barba | Hepatitis C virus core protein shows a cytoplasmic localization and associates to cellular lipid storage droplets[END_REF][START_REF] Moradpour | Characterization of cell lines allowing tightly regulated expression of hepatitis C virus core protein[END_REF][START_REF] Hope | The domains required to direct core proteins of hepatitis C virus and GB Virus-B to lipid droplets share common features with plant oleosin proteins[END_REF][START_REF] Murphy | The biogenesis and functions of lipid bodies in animals, plants and microorganisms[END_REF].

This interaction was recently suggested to involve HCV core protein domain D2, that spans amino acids 118-173 and contains two amphipathic -helices that likely associate in-plane at the lipid droplet membrane layer interface [START_REF] Hope | The domains required to direct core proteins of hepatitis C virus and GB Virus-B to lipid droplets share common features with plant oleosin proteins[END_REF][START_REF] Boulant | Structural determinants that target the hepatitis C virus core protein to lipid droplets[END_REF][START_REF] Hope | Sequence motifs required for lipid droplet association and protein stability are unique to the hepatitis C virus core protein[END_REF].

Most experimental studies published to date have focused on sequences derived from HCV genotype 1, which is not associated with steatosis. HCV genotype 3 core protein expression has been reported to induce stronger intracellular lipid accumulation in vitro than genotype 1 core protein expression [START_REF] Abid | An in vitro model of hepatitis C virus genotype 3a-associated triglycerides accumulation[END_REF][START_REF] Hourioux | The genotype 3-specific hepatitis C virus core protein residue phenylalanine 164 increases steatosis in an in vitro cellular model[END_REF], apparently as [START_REF] Hourioux | The genotype 3-specific hepatitis C virus core protein residue phenylalanine 164 increases steatosis in an in vitro cellular model[END_REF]. None of these reports mentioned whether or not the patients from whom the core sequences were isolated had steatosis.

Here we examined in vitro interactions between lipid droplets and full-length core protein isolated from patients with HCV genotype 3a infection, with and without steatosis, and from steatosis-free patients infected by HCV genotype 1b. We also examined morphological changes in the lipid droplets according to the HCV genotype and the presence of steatosis in vivo.

MATERIALS AND METHODS

Materials

The patients were selected from our institutional database of HCV-infected patients, based on the following criteria: (i) chronic HCV infection, confirmed by the presence of serum anti-HCV antibodies (Ortho TM HCV 3.0 Elisa Test System, Ortho-Clinical Diagnostics, Raritan, New Jersey) and HCV RNA (Amplicor HCV 2.0 PCR Test System, Roche Molecular Systems, Pleasanton, California); (ii) HCV genotype 1b or 3a infection, as suggested by a line probe assay (INNO-LiPA HCV II, Innogenetics, Gent, Belgium) and confirmed by sequence determination and phylogenetic analysis of a portion of the NS5B region; (iii) histologically proven chronic hepatitis; (iv) no previous or current antiviral therapy; and (v) no coinfection with hepatitis B virus or human immunodeficiency virus.

All the patients had had a liver biopsy. The specimens were fixed in formalin and paraffin sections were stained with hematoxylin-eosin-safran for analysis by a Steatosis was graded as absent (0 or < 1% of affected hepatocytes, grade 0), mild (1% to 10% of affected hepatocytes, grade 1), moderate (10% to 30% of affected hepatocytes, grade 2) or marked (> 30% of affected hepatocytes, grade 3). Patients were considered to have HCV-induced steatosis only if they had moderate or marked histological steatosis at baseline and a reduction of at least two grades on repeat biopsy after successful antiviral therapy. Steatosis-free patients all had grade 0 steatosis. In order to eliminate patients with metabolic causes of steatosis, we also applied the following selection criteria: (i) mean alcohol intake within the 6 months preceding liver biopsy < 20 g/day; (ii) body mass index (BMI) < 27 kg/m 2 ; (iii) baseline serum glucose level < 6.1 mmol/L; (iv) serum fasting triglycerides < 1.7 mmol/L; (v) cholesterol < 6.1 mmol/L; (vi) Homeostasis Model Assessment (HOMA) index of insulin resistance < 2.4; and (vii) no diabetes or known metabolic risk factors for non-alcoholic fatty liver disease (NAFLD). Eight patients were selected for this study, comprising five patients infected by HCV genotype 3a (of whom three had HCV-induced steatosis), and three steatosisfree patients infected by genotype 1b. Their characteristics are shown in Table 1.

HCV RNA was extracted from their serum and the full-length core protein-coding sequence was amplified by means of reverse transcriptase polymerase chain reaction (PCR). [START_REF] Hope | Efficient cleavage by signal peptide peptidase requires residues within the signal peptide between the core and E1 proteins of hepatitis C virus strain J1[END_REF]. To ensure correct processing, at least the first 100 amino acids of E1 are required for the construction of expression vectors. A sequence spanning the full-length core-coding region and the first 400 nucleotides coding for the E1 envelope glycoprotein (core-E1 sequence) was amplified by means of a nested PCR procedure using genotype-specific primers (Table 2). Restriction sites were included in the second-round primers for the cloning procedure. In order to characterize the quasispecies distribution of HCV proteins, purified PCR products were cloned in the pHM6 vector (Roche Applied Sciences) and 20 clones per sample were generated. Core-E1 quasispecies variant sequences were determined with the ABI PRISM BigDye Terminator Cycle Sequencing Ready Reaction kit on an ABI PRISM 377 DNA Sequencer (Applied Biosystems, Foster City, California). Plasmids containing the most frequent core-E1 quasispecies variant sequence from each of the eight chronically infected patients shown in Table 1 were designated pC E1-1b/1NS, pC E1-1b/2NS, pC E1-1b/3NS, pC E1-3a/1NS, pC E1-3a/2NS, pC E1-F o r P e e r R e v i e w 8 3a/1S, pC E1-3a/2S, pC E1-3a/3S for patients 1b-1NS, 1b-2NS, 1b-3NS, 3a-1NS, 3a-2NS, 3a-1S, 3a-2S, and 3a-3S, respectively.

Methods

HCV

Core-E1 expression in Huh7 cells. Huh7 human hepatoma cells were grown in the presence of 5% CO 2 in Dulbecco's Modified Medium containing 4500 mg/mL glucose (Invitrogen) and supplemented with 10% fetal calf serum (FCS), antibiotics (4.5 mg/L penicillin, 50 mg/L streptomycin), 5 mg/L insulin and 3.5 x 10 -7 M hydrocortisone hemisuccinate. Cells were electroporated (Nucleofection TM , Amaxa, Köln, Germany) with 4 µg of plasmid for 4 million cells. One million cells were cultured on slides (4-well Lab-Tek II chamber slide system, Nalge Nunc Int., Rochester, New York) for core protein immunostaining and lipid droplet analysis, and the remaining 3 million cells were cultured in 6-well plates for western-blot and lipid analyses. Cells were cultured for 24 h in the presence of 5% CO 2 in Dulbecco's Modified Medium containing 1000 mg/mL glucose supplemented with 10% FCS and antibiotics (4.5 mg/L penicillin, 50 mg/L streptomycin).

Assessment of core protein processing by signal peptide peptidase. BHK cells were used to test HCV core protein processing by signal peptide peptidase (SPP). BHK C13 cells were grown in the presence of 5% CO 2 in MEM Eagle with 2 mM Lglutamine (Invitrogen) supplemented with 10% FCS, 100µM Non Essential Amino Acid (Invitrogen) and 10µM sodium pyruvate (Invitrogen). Cells were transfected with the different core protein sequences with Lipofectamine LTX (Invitrogen), according to the manufacter's instructions. When necessary, cells were incubated with 100 µM of the SPP inhibitor (Z-LL) 2 ketone immediately following transfection. After incubation for 16 h, cells were harvested and washed twice in phosphate buffered saline (PBS)

Statistical analysis.

The results are reported as the mean ± standard error of the mean (SEM). Student's t test was used for parametric variables and the Wilcoxon test for nonparametric variables. P values of < 0.05 were considered significant.

RESULTS

Patient selection. The eight selected patients (Table 1) belonged to three groups based on their HCV genotype (3a or 1b) and the presence (S) or absence (NS) of steatosis on liver biopsy prior to any therapy. Three patients (Group A, patients 3a-1S to 3a-3S) were infected by HCV genotype 3a and had marked or severe HCV-induced steatosis, according to the criteria described in Methods; two patients (Group B, patients 3a-1NS and 3a-2NS) were infected by HCV genotype 3a and had no steatosis on liver biopsy; and three patients (Group C, patients 1b-1NS to 1b-3NS) were infected by HCV genotype 1b and had no steatosis on liver biopsy (Table 1). It should be noted that none of the patients had both genotype 1b infection and HCV-induced steatosis. Mean HCV RNA levels did not differ significantly among Relationship between core-E1 sequences (quasispecies analysis), the HCV genotype, and steatosis. In order to ensure correct processing of the experimentally expressed core protein, a sequence spanning the full-length corecoding region from each of the eight patients, plus the first 400 nucleotides coding for the E1 envelope glycoprotein, was PCR-amplified. The PCR products were cloned and 20 clones per sample were sequenced in order to determine the quasispecies distribution of core sequences. As shown in Figure 1A, genotype-specific amino acid differences were observed between the genotype 1b and 3a sequences. Among the patients infected by HCV genotype 3a, only a few single amino acid differences were observed, and these differences were not related to the presence or absence of steatosis in vivo (Figure 1A). The amino acid repertoires deduced by aligning the quasispecies variants from genotype 3a-infected patients did not differ with respect to the presence or absence of steatosis, except, possibly, at position 16, where a difference in amino acid frequencies was observed between the two groups (Figure 1B). Overall, we found no motifs or amino acids specifically associated with the presence or absence of steatosis in the core sequences isolated from patients infected by HCV genotype 3a.

Expression of core-E1 sequences and interaction with lipid droplets.

The most frequent core-E1 variant sequences from each patient's quasispecies were cloned in fusion with an HA tag and a 6xHIS tag at their amino-and carboxytermini, respectively. In order to evaluate potential differences in the processing of different core proteins, we assessed SPP cleavage efficiency by means of (Z-LL) 2 was not significantly different between Huh7 cells transfected with HCV genotype 1b core protein and mock-transfected control cells (487±44 µm 3 vs 603±50 µm 3 neutral lipids/cell, respectively). In contrast, cells expressing genotype 3a core protein contained a significantly larger volume of lipid droplets than control cells and than cells expressing genotype 1b core protein (p<0.0001 and p=0.001, respectively). No difference was seen in genotype 3a core-expressing cells with respect to whether or not the corresponding patients had steatosis (1003±87 µm 3 vs 943±124 µm 3 neutral lipids/cell with genotype 3a core protein derived from patients with and without steatosis, respectively).

The diameters of 9147 individual lipid droplets was also calculated in transfected cells. In control cells the average diameter was 2. Overall, the expression of HCV genotype 1b core protein did not influence the total amount of intracellular neutral lipids associated with lipid droplets. In contrast, the expression of HCV genotype 3a core protein approximately doubled the amount of intracellular neutral lipids associated with lipid droplets. In addition, genotype 3a core protein expression was associated with a significantly higher proportion of large lipid droplets (> 6µm) in the cell cytoplasm as compared to mock-transfected control cells and to cells expressing genotype 1b core protein. Importantly, the larger amount of intracellular neutral lipids and the more frequent presence of very large lipid droplets associated with genotype 3a core expression was independent of steatosis.

Qualitative and quantitative analysis of HCV core protein-lipid droplet colocalization. We used confocal laser scanning microscopy to record single optical slices in each dye-corresponding channel in cells labeled for both HCV core protein and ADRP, a protein associated with the surface of intracellular lipid droplets. The immunofluorescence patterns appeared as intracytoplasmic rings for both HCV core protein and ADRP (Figure 5). Merged images confirmed the tight and exclusive association of HCV genotype 1b and 3a core protein with the surface of lipid droplets (Figure 5). Genotype 3a core protein colocalization was not influenced by the steatotic status of the corresponding patients (Figure 5).

We also studied core protein-ADRP colocalization in lipid droplets of different sizes. As the mean diameter of lipid droplets was 2.3 µm, "large" droplets were defined as having a diameter of 2.3 µm or more, and "small" lipid droplets as having a diameter of less than 2.3 µm. Correlations between the intensities of red (core protein) and green (ADRP) pixels in dual-channel images were studied by using by the deflection of pixel distribution towards the red axis, the scatter plot dots accumulated around the diagonal for large lipid droplets (> 2.3 µm), but were more dispersed for small lipid droplets (< 2.3 µm), suggesting slightly weaker colocalization (Figure 6). Furthermore, the spread of dots was larger with genotype 1b than with genotype 3a core protein, also suggesting weaker colocalization with genotype 1b (Figure 6).

As shown in Figure 6C, which compares mean R-values in large and small lipid droplets for each core protein category, the R-values were always smaller for small lipid droplets than for large lipid droplets. However, the difference was ). Together, these data suggested weaker HCV core protein binding to small than large lipid droplets, a phenomenon that appeared to be more pronounced for HCV genotype 1b sequences. As a difference in pixel intensities in the two fluorescence channels could cause greater spread in the scatter plots, we also calculated Van Steensel's CCF.

This revealed no major differences in pixel intensities (CCF max = 0.915 ± 0.006) and confirmed the correlation of red and green pixels (dx = -0.6 ± 0.1). However, in analyses of small lipid droplets, the presence of peaks at the ends of the bell-shaped curve revealed excluded pixels (Figure 6).

DISCUSSION

We transfected Huh7 cells with HCV core protein sequences from steatosisfree patients infected by HCV genotype 1b, and from genotype 3a-infected patients with and without HCV-induced steatosis. We were thus able to study the relationship between the in vivo steatogenic properties of the viruses and the ability of their core proteins to associate with intracellular lipid droplets and to induce lipid accumulation.

In order to ensure correct processing of the core protein, the full-length core protein sequence was expressed along with the first 400 nucleotides coding for the E1 envelope glycoprotein [START_REF] Hope | Efficient cleavage by signal peptide peptidase requires residues within the signal peptide between the core and E1 proteins of hepatitis C virus strain J1[END_REF]. SPP cleavage of the core protein, which is required for its localization to the surface of lipid droplets, was found to be equally efficient with all of the studied constructs.

We found similar HCV core protein binding to the lipid droplet surface, irrespective of the HCV genotype (1b and 3a) and, in genotype 3a-infected patients, independently of steatosis. Core protein binding was associated with an droplets has previously been reported in cultured transfected cells [START_REF] Barba | Hepatitis C virus core protein shows a cytoplasmic localization and associates to cellular lipid storage droplets[END_REF][START_REF] Abid | An in vitro model of hepatitis C virus genotype 3a-associated triglycerides accumulation[END_REF][START_REF] Moradpour | Characterization of cell lines allowing tightly regulated expression of hepatitis C virus core protein[END_REF][START_REF] Hope | The domains required to direct core proteins of hepatitis C virus and GB Virus-B to lipid droplets share common features with plant oleosin proteins[END_REF][START_REF] Murphy | The biogenesis and functions of lipid bodies in animals, plants and microorganisms[END_REF][START_REF] Hourioux | The genotype 3-specific hepatitis C virus core protein residue phenylalanine 164 increases steatosis in an in vitro cellular model[END_REF] and also recently in the JFH1-based productive HCV culture system, in which mature HCV core protein extensively colocalizes with lipid droplets, as confirmed here [START_REF] Rouille | Subcellular localization of hepatitis C virus structural proteins in a cell culture system that efficiently replicates the virus[END_REF][START_REF] Shavinskaya | The lipid droplet binding domain of hepatitis C virus core protein is a major determinant for efficient virus assembly[END_REF]. Our results indicate that HCV core protein can associate with lipid droplets regardless of the genotype and the in vivo steatogenic potency of the corresponding viral strain. They further suggest that core protein localization at the lipid droplet surface is not the only mechanism underlying HCV-induced steatosis, a complication associated mainly, if not exclusively, with genotype 3a infection.

We also found that, relative to genotype 1b core protein, intracellular expression of HCV genotype 3a core protein was associated with more marked accumulation of neutral lipids contained in lipid droplets and with larger lipid droplets, a result in keeping with a role of core protein-lipid droplet association in the onset of HCV genotype 3a-induced steatosis. Several authors have shown that HCV genotype 3a core protein interacts with lipid metabolism. In particular, it induces fatty acid synthase (FAS), an enzyme required for intracellular triglyceride production [START_REF] Jackel-Cram | Up-regulation of fatty acid synthase promoter by hepatitis C virus core protein: genotype-3a core has a stronger effect than genotype-1b core[END_REF].

Another study has shown that HCV core protein, and other HCV proteins, can induce the cleavage of sterol regulatory element binding proteins (SREBP) and their phosphorylation by triggering oxidative stress (and, thus, fatty acid synthesis), and that this phenomenon is genotype-dependent [START_REF] Waris | Hepatitis C virus induces proteolytic cleavage of sterol regulatory element binding proteins and stimulates their phosphorylation via oxidative stress[END_REF]. These properties, however, could be independent of lipid droplet binding.

The functional differences between genotype 1b and 3a core protein are likely related to amino acid sequence differences. The amino acid sequences of the two genotypes are very similar, likely owing to strong conservatory constraints on the 3D structure of the core protein, which is necessary to form mature nucleocapsids. Single amino acid differences at the protein surface could modulate local folds, their stability and their interactions with other proteins. Core domain D2 has been implicated in lipid droplet association [START_REF] Hope | Sequence motifs required for lipid droplet association and protein stability are unique to the hepatitis C virus core protein[END_REF]. Within this domain, three amino acid positions differ between genotype 1b and genotype 3a, namely L and V at position 144, V and I at position 162 and Y and F at position 164. These amino acid differences are not expected to modify the structure of this region but they could modulate its membrane-binding properties. Indeed, in genotype 1, V144 belongs to the hydrophobic loop that connects the two amphipathic helices interaction in-plane of the membrane interface, whereas L162 and F164 are involved in the last turn of helix II. A recent study has suggested that Y164F mutation of genotype 1a core protein leads to intracellular lipid accumulation [START_REF] Hourioux | The genotype 3-specific hepatitis C virus core protein residue phenylalanine 164 increases steatosis in an in vitro cellular model[END_REF]. This mutation could increase the strength of helix II binding to the lipid droplet surface by eliminating the polar hydroxyl group of the tyrosine residue. In turn, the increased stability of the core-lipid droplet interaction could limit core protein degradation by the proteasome [START_REF] Boulant | Structural determinants that target the hepatitis C virus core protein to lipid droplets[END_REF]. F164 has also been implicated in the stronger FAS activation by genotype 3 core protein than by genotype 1 core protein despite similar localization of the two proteins at the lipid droplet surface [START_REF] Jackel-Cram | Up-regulation of fatty acid synthase promoter by hepatitis C virus core protein: genotype-3a core has a stronger effect than genotype-1b core[END_REF].

Other amino acid differences between these two genotypes are found outside the D2 region. Our sequence analyses indeed revealed the hydrophobic nature of amino acids 4 and 16 in genotype 3a core proteins, while these positions are occupied by a polar residue (asparagine) in genotypes 1, 2, 4 and 5 (in genotype 6, position 4 is occupied by a leucine, a hydrophobic residue). These differences could alter local protein folding and stability, and also other protein interactions mediated by this region. The region located between amino acids 182 and 191 at the C-terminus of the core protein also exhibited numerous differences between genotypes 1b and and signal peptide peptidase cleavage required for core protein maturation. We were not able, however, to identify precisely which amino acid difference(s) between genotypes 1b and 3a is (are) responsible for the observed functional differences.

Another important finding of this study is that the genotype 3a core proteinlipid droplet association is qualitatively and quantitatively independent of HCVinduced steatosis. In addition, alignment of quasispecies variants showed no difference according to steatosis; the only exception was at position 16, but the change was from a hydrophobic to a non-polar side-chain amino acid (valine to isoleucine), which is not expected to influence the protein fold. These results suggest that HCV genotype 3a infection is probably necessary but not sufficient to induce steatosis in patients with chronic HCV infection. They point to a role of other viral proteins, that could either act directly or modulate core protein function, and/or a role of host factors that would determine whether HCV genotype 3a replication in hepatocytes triggers the formation and growth of lipid droplets.

The host factors required for steatosis onset in HCV genotype 3a-infected patients are unknown. It has been shown that HCV core protein reduces the intrahepatic activity of microsomal triglyceride transfer protein (MTP), an enzyme essential for hepatic lipoprotein assembly and secretion [START_REF] Perlemuter | Hepatitis C virus core protein inhibits microsomal triglyceride transfer protein activity and very low density lipoprotein secretion: a model of viralrelated steatosis[END_REF]. Subsequent development of steatosis could vary according to polymorphisms of the apo AII gene [START_REF] Kalopissis | Apolipoprotein A-II: beyond genetic associations with lipid disorders and insulin resistance[END_REF][START_REF] Escola-Gil | Apolipoprotein A-II, genetic variation on chromosome 1q21-q24, and disease susceptibility[END_REF].

In conclusion, we show that the core protein of both HCV genotypes 1b and 3a binds tightly to the surface of intracellular lipid droplets.

F o r P e e r R e v i e w

33 Table 1. Characteristics of the 8 patients selected for this study. The patients are identified by their HCV genotype (3a or 1b), followed by the patient number and the presence (S) or absence (NS) of virus-induced steatosis (example: 3a-1S is patient number 1 among the patients infected by genotype 3a with HCV-induced steatosis). NA: not applicable.

Patients

  triglyceride accumulation in the hepatocyte cytoplasm) is a common histological finding in patients with chronic hepatitis C virus (HCV) infection. Steatosis is a cofactor for fibrosis and disease progression in chronic hepatitis C

  a single amino acid difference in the D2 domain

  and inflammation were graded with the METAVIR system.

  RNA extraction and cDNA synthesis. HCV RNA was extracted from 200 µl of serum with the High Pure viral RNA kit (Roche Applied Science, ), according to the manufacturer's instructions. Viral RNA was recovered in 50 µl of RNase-free water and stored at -80°C until being processed. Five microliters of the extracted viral RNA was reverse-transcribed for 60 min at 50°C using 0.5 mM each dNTP, 10 pmol of random hexamers, 10 mM DTT, 40 U of RNase OUT and 200 U of Superscript III reverse transcriptase (Invitrogen, Carlsbad, California). The samples were heated for 15 min at 70°C to stop the reaction and were frozen until processed. PCR amplification and cloning. It has been shown that expression of the full-length core sequence alone (amino acids 1 to 191) is associated with incomplete cellular translocation

  EDTA, 0.5% NP40 and anti-proteases. A crude total protein extract was obtained by multiple freezing and thawing steps. For western-blot analysis, proteins were separated by SDS-PAGE using 12% Tris-Glycine gels (Bio-Rad, Hercules, California), transferred onto nitrocellulose membranes, and probed with an HRPconjugated rat anti-HA MAb. (3F10, Roche Applied Sciences). The HA-tagged core protein was detected by means of enhanced chemiluminescence. Indirect immunofluorescence and lipid staining experiments were performed in both core protein-transfected Huh7 cells and Huh7 cells infected with JFH1 viral particles (kindly provided by Dr Jean Dubuisson)[START_REF] Lindenbach | Complete replication of hepatitis C virus in cell culture[END_REF][START_REF] Wakita | Production of infectious hepatitis C virus in tissue culture from a cloned viral genome[END_REF][START_REF] Zhong | Robust hepatitis C virus infection in vitro[END_REF]. For the latter experiment, Huh7.5 cells were electroporated with an RNA transcribed from the HCV genotype 2a JFH1 plasmid, grown for two successive passages for approximately 20 days, and their supernatants were applied to naïve Huh7 cells. Cells grown on slides were washed three times with PBS and fixed for 10 min in 4% paraformaldehyde. After two washes with PBS the cells were incubated for 40 min in PBS containing 0.3% bovine serum albumin and 0.1% saponin. The cells were then immunolabeled with either the anti-HCV core monoclonal antibody (mAb) Acap27 (Bio-Rad, Hercules, California) at 1:1000 dilution, or an anti-HA mAb (Roche Applied Sciences) at 1:25 dilution. Anti-HCV core staining was visualized with TRITC-conjugated goat anti-mouse IgG (Sigma-Aldrich, Saint-Louis, Missouri), and lipid droplet association was studied by using the BODIPY 493/503 fluorophore (10 µg/ml, Molecular Probes, Eugene, Oregon). Anti-HA staining was visualized with Alexa 694-conjugated goat anti-rat IgG at 1:400 dilution (Invitrogen and Molecular Probes) and lipid droplet association was studied with an anti-ADRP mAb at 1:2 dilution (Progen, Heidelberg, Germany) and -conjugated goat anti-mouse IgG (Bio-Rad). The slides were washed in PBS and mounted in fluorescent mounting medium containing DAPI (Vectashield, Vector Laboratories, Burlingame, California).Lipid droplet morphometry and colocalization studies. The spatial location of core protein and lipid droplets in Huh7 cells was studied by means of confocal laser scanning microscopy with a Leica DMRE-7/TCS-SP2 device (Leica, Wetzlar, Germany). A 405-nm diode laser, a 488-nm line of an argon-ion laser, a 543-nm line of a helium-neon laser and a 594-nm line of a helium-neon laser were to excite Dapi, Bodipy 493/503 and FITC, TRITC and Alexa 594, respectively. 3D visualization of lipid droplets, with and without core protein, was performed after double-labeling with anti-core mAb and Bodipy 493/503. Z-stacks of serial 0.3-µm-thick confocal sections were acquired separately for each channel to exclude cross-talk between channels due to the partly overlapping emission spectra of the dyes. Image processing and 3D reconstruction were performed with the Imaris software package (Bitplane AG, Zürich, Switzerland). The largest diameter of each reconstructed lipid droplet was exposed by rotating stack and was measured manually in the image graphics plane.To study the colocalization of core protein and ADRP, single optical slices were recorded separately in each dye-corresponding channel in double-labeled cells.Colocalization was assessed by statistical analysis of the correlation of the intensity values of red (core protein) and green (ADRP) pixels in a dual-channel image.JACoP plugging from ImageJ software was used to calculate Pearson's correlation coefficient, to visualize scatter plots, and to perform cross-correlation analysis (Van Steensel's cross-correlation function). Pearson's coefficient-based analysis results in a pixel distribution diagram (scatter plot), where the intensity of a given pixel in the used as the x-coordinate and the intensity of the corresponding pixel in the red image as the y-coordinate. In a colocalization situation, dots on the diagram appear as a cloud centered on a line. The spread of this distribution with respect to the fitted line can be estimated by calculating the correlation coefficient, also called Pearson's coefficient (R). A cross-correlation function (CCF) reveals differences in intensity pixels through the value of the maximum peak of the bellshaped curve and allows partial colocalization events to be discriminated through the deviation from 0 (pixel shift: dx) and/or the presence of peaks aside dx.

  SPP inhibitor. This experiment was performed in BHK cells because (Z-LL) 2 ketone has weaker SPP inhibition activity in Huh7 cells. The cleavage profiles of the different core proteins are shown in Figure2. All constructs were fully processed by SPP. Indeed, in untreated cells, only the processed 21 kD form was present in all instances, whereas in (Z-LL) 2 ketone-treated cells, the uncleaved (23 kD) form of the core protein was also present (Figure2).The tagged Core-E1 sequences were transfected into Huh7 cells and their expression was assessed by immunoblot and densitometric analysis 24 h later. Core-E1 proteins originating from patients infected by HCV genotypes 1b and 3a, with and without steatosis, were equally expressed in transfected Huh7 cells (data not shown). Transfected Huh7 cells were then immuno-labeled for core protein, and lipid droplets were stained with BODIPY 493/503. Core-expressing Huh7 cells were analyzed individually by confocal fluorescence microscopy for core protein-lipid droplet association. Lipid droplets were reconstructed in 3D from optical section stacks. Figure3Ashows representative staining and spatial representations of 3D reconstructions in each group. In core-expressing cells, lipid droplets were surrounded by HCV core protein, regardless of the HCV genotype, and were principally localized in the perinuclear area. Lipid droplets were more evenly distributed in the cytoplasm of mock-transfected cells (data not shown). In order to confirm these observations in the context of an infectious genome, we analyzed the respective core protein and lipid droplet localizations in Huh7 cells infected by JFH1 viral particles produced in cell culture (Figure3A, right panel). Like Huh7 cells transiently transfected with HCV core proteins, JFH1-infected cells showed an exclusive localization of core proteins at the surface of lipid droplets, that formed ringlike structures with a perinuclear localization.

14 Figure

 14 Figure3Bshows a 3D representation of HCV core protein bound to the

  Pearson's coefficient (R) in several isolated lipid droplets obtained from cropped images in each study group. R-values indicated a high level of core-ADRP colocalization (average R-value: 0.885), whatever the genotype of origin of the core protein and the corresponding patients' steatotic status (data not shown). Figures6A and 6Bshow representative results obtained with cells expressing genotype 1b, 3a-NS and 3a-S core protein. Despite slight differences in fluorescence intensity shown

  HCV genotype 1b sequences (p<0.05

  droplets in the perinuclear area. Binding of HCV proteins to lipid

  differences in this area could modulate the kinetics of signal peptidase

Figure 1 .

 1 Figure 1. (A) Alignment of the most frequent core-E1 quasispecies variant

Figure 2 .

 2 Figure 2. Analysis of core-E1 processing by SPP. BHK C13 cells were transfected

Figure 3 .

 3 Figure 3. Analysis of lipid droplet morphology in Huh-7 cells expressing HCV core

Figure 4 .

 4 Figure 4. Lipid droplet morphological changes induced by HCV core protein

Figure 5 .

 5 Figure 5. Colocalization of HCV core protein and ADRP, a protein associated with

Figure 6 .

 6 Figure 6. Qualitative and quantitative analysis of HCV core protein-ADRP

F o r P e e r R e v i e w 34

 34

Table 2 .

 2 Primers and nested PCR conditions used to amplify the core-E1 region.

	1st PCR round

ACKNOWLEDGEMENTS

The data were obtained with the assistance of Daniel Stockholm from the Plateforme Génopôle (Evry, France) and Christo Christov from the Integrated Microscopy Core facility (Créteil, France). We are grateful to Jean-François Delagneau (Bio-Rad, France) for providing us with the Acap27 antibody.

Financial support: This work was supported by grants from Agence Nationale de Recherche sur le SIDA et les Hépatites Virales (ANRS) and Agence Nationale de la Recherche (ANR, Grant ANR-05-PCOD-035-01). A.P. was supported by fellowships from the French Ministry of Research and ANRS.


Junk News Bubbles

Modelling the Rise and Fall of Attention in Online Arenas Maria Castaldo, Tommaso Venturini, Paolo Frasca, Floriana Gargiulo In this paper, we present a type of media disorder which we call "junk news bubbles" and which derives from the effort invested by online platforms and their users to identify and circulate contents with rising popularity. Such emphasis on trending matters, we claim, can have two detrimental effects on public debates: first, it shortens the amount of time available to discuss each matter; second it increases the ephemeral concentration of media attention. We provide a formal description of the dynamic of junk news bubbles, through a mathematical exploration of the famous "public arenas model" developed by [START_REF] Hilgartner | The Rise and Fall of Social Problems: A Public Arenas Model[END_REF] Our objective is to describe the dynamics of the junk news bubbles as precisely as possible to facilitate its further investigation with empirical data. 1

Conceptualizing junk news bubbles

Much has been written in the last years about online media and the threat of "selective exposure" [START_REF] Sears | Selective Exposure to Information: A Critical Review[END_REF], "echo chambers" [START_REF] Garrett | Echo Chambers Online?: Politically Motivated Selective Exposure among Internet News Users[END_REF] and "filter bubbles" (Pariser, 2011). In various ways, all these notions point to the risk that the growing availability of information and the perfecting of filtering and recommendation technologies may create a "situation in which thousands or perhaps millions or even tens of millions of people are mainly listening to louder echoes of their own voices" (Sunstein, 2001, p.16). Reviving a long tradition of homophily and segregation models [START_REF] Schelling | Dynamic Models of Segregation[END_REF], this idea has sparked much interest in computational sociology (cf., among others, [START_REF] Colleoni | Echo Chamber or Public Sphere? Predicting Political Orientation and Measuring Political Homophily in Twitter Using Big Data[END_REF][START_REF] Barberá | Tweeting From Left to Right: Is Online Political Communication More Than an Echo Chamber?[END_REF][START_REF] Quattrociocchi | Echo Chambers on Facebook[END_REF][START_REF] Geschke | The Triple-Filter Bubble: Using Agent-Based Modelling to Test a Meta-Theoretical Framework for the Emergence of Filter Bubbles and Echo Chambers[END_REF] despite evidence that its impacts may be overestimated (cf. [START_REF] Bakshy | Exposure to Ideologically Diverse News and Opinion on Facebook[END_REF][START_REF] Flaxman | Filter Bubbles, Echo Chambers, and Online News Consumption[END_REF][START_REF] Boxell | Is the Internet Causing Political Polarization? Evidence from Demographics[END_REF][START_REF] Dubois | The Echo Chamber Is Overstated: The Moderating Effect of Political Interest and Diverse Media[END_REF].

Less attention and computational efforts have been dedicated to a different type of media bubbles, whose danger comes not from the fragmentation, but from the ephemeral concentration of public attention. In a previous paper [START_REF] Venturini | From Fake to Junk News, the Data Politics of Online Virality[END_REF], we proposed the term "junk news" to expand the notion of "fake news" beyond its excessive focus on deceitfulness (cf., among others, [START_REF] Zuckerman | Stop Saying 'Fake News'. It's Not Helping[END_REF][START_REF] Benkler | Network Propaganda[END_REF][START_REF] Gray | The Infrastructural Uncanny: 'Fake News' and the Fabric of the Web as Matter of Concern[END_REF]. Besides false contents disguised as mainstream news and explicitly directed at deceiving their receivers, media scholars should worry about the avalanche of memes, click-baits, trolling provocations and other forms of ephemeral distractions that prevent online audiences from engaging in a thoughtful public debate. This type of "information disorders" [START_REF] Wardle | Information Disorder: Toward an Interdisciplinary Framework for Research and Policymaking[END_REF]) cannot be defined on the basis of its content or its style (as in manual and automated fact-checking, cf. Graves, 2016 andCiampaglia et al., 2015) nor on the basis of the way in which it polarizes the debate (as in echo chambers and filter bubbles). Instead, ephemeral distractions are distinguished by a feature often neglected when considering online misinformationtheir temporal profile. Like junk food, junk contents tantalize without ever satiating. Like echo chambers, they can be described as bubbles, although not the sense of a secluded informational space, but rather as market bubbles: speculative waves that destroy rather than create richness in public debate.

If the dangers of junk news bubbles are neglected by current media research, it is not because they are lesser than that of fake news and filter bubbles, but because this particular information disorder still lacks the precise conceptualization that supports the research on fact-checking and polarization. To outline such a conceptualization, we propose to define junk news bubbles as an adverse media dynamic in which a large share of public attention is captured by items that are incapable of sustaining it for a long time. Both elements of this definition are crucial. Popular stories and even viral contents are not necessarily junk news, no matter how quickly and largely they spread in online networks (Jenkins et al. 2013). To qualify as junk news bubbles, contents must fade away as quickly as they rose, so that they distract public debate rather than nourishing it. Note that our definition is agnostic about the quality of junk contents. Even a patent piece of misinformation such as the infamous claim that "Brexit will make available 350 million pounds per week for the NHS" plastered onto a red bus during the UK-EU referendum campaign, can end up generating productive discussions if it sticks long enough in the public debate (Marres, 2008). Vice versa, newsworthy stories cannot contribute to democratic conversation if they are too quickly pushed out of the public agenda. In other words, the notion of junk news bubbles applies less to specific pieces of content, than to a general acceleration of online attention cycles.

Central in the '70s and '80s, the question of "attention cycles" [START_REF] Downs | Up and down with Ecology: The 'Issue-Attention Cycle[END_REF] has lost steam in current media research because of the advent of digital technologies and the extension of the media system that they brought with them. Because of this extension, the question of the occupation of public debate has begun to be formulated in spatial rather than in temporal terms (i.e. where something is discussed rather than when). Temporal dynamics, however, remains crucial for, as in the words of McLuhan, "the 'message' of any medium or technology is the change of scale or pace or pattern that it introduces into human affairs... amplif [ying] or accelerate[ing] existing processes" (McLuhan, 1964, p.8). As noted by scholars working on the attention economy (Lanham, 20066;[START_REF] Terranova | Attention, Economy and the Brain[END_REF][START_REF] Crogan | Paying Attention: Toward a Critique of the Attention Economy[END_REF], digital technologies are particularly inclined to amplify "media hypes" [START_REF] Vasterman | Media-Hype: Self-Reinforcing News Waves, Journalistic Standards and the Construction of Social Problems[END_REF] and to concentrate public attention on widespread but ephemeral trends.

Our argument echoes McCombs's plea [START_REF] Mccombs | A Look at Agenda-Setting: Past, Present and Future[END_REF] not to desert the research on "agenda setting" [START_REF] Mccombs | The Agenda-Setting Function of Mass Media[END_REF][START_REF] Mccombs | Opinion, Setting the Agenda: Mass Media and Public[END_REF] on the grounds of online attention being scattered in a myriad of different channels each with its own agenda. Precisely because of this overabundance of sources, digital media have since their inception channeled their flows through increasingly sophisticated "Engines of Order" [START_REF] Rieder | Engines of Order: A Mechanology of Algorithmic Techniques[END_REF] constantly ranking -and updating the rank -of their contents (Cardon, 2005;[START_REF] Cardon | Neurons Spike Back[END_REF]. This is particularly true of social media platforms, whose size could not be sustained without infrastructures to sieve through millions of contents produced every day and whose business model as marketplaces of ideas entails a relentless circulation of new trending topics [START_REF] Webster | The Marketplace of Attention[END_REF]. This unremitting production of trends is an inherent feature of recommendation algorithms, as candidly admitted by YouTube engineers: "in addition to the first-order effect of simply recommending new videos that users want to watch, there is a critical secondary phenomenon of boot-strapping and propagating viral content" (Covington et al., 2016 p.193, see also [START_REF] Zhao | Recommending What Video to Watch next: A Multitask Ranking System[END_REF]. Algorithms, however, are not the only component of online attention infrastructures and not the only actors at play. A similar push for trendiness comes from the interaction between the practices of social media users, which are increasingly driven by micro-celebrity strategies [START_REF] Marwick | To See and Be Seen: Celebrity Practice on Twitter[END_REF][START_REF] Khamis | Self-Branding, 'Micro-Celebrity' and the Rise of Social Media Influencers[END_REF], and the graphic interface of platforms and apps, which are partial to ephemeral visibility and vanity metrics [START_REF] Rogers | Otherwise Engaged: Social Media from Vanity Metrics to Critical Analytics[END_REF].

The term "junk news bubbles", thus, designates less a specific type of content (as in the case of misinformation or "fake news") than a general tendency of media systems to privilege trendy items and thus create an extremely turbulent and superficial public debate. False and low quality stories are the type of content that thrives most directly on the incentives of trendiness, but to some extent all digital conversations are influenced by this acceleration. In the paper where we first proposed the term "junk news" [START_REF] Venturini | From Fake to Junk News, the Data Politics of Online Virality[END_REF], we discuss in more detail the political economy of online acceleration and the way in which it influences the circulation of news. In this paper, our goal is to provide a formal description of these attention dynamics in order to encourage their further empirical study. With a few remarkable exceptions (see in particular [START_REF] Leskovec | Meme-Tracking and the Dynamics of the News Cycle[END_REF][START_REF] Leskovec | Meme-Tracking and the Dynamics of the News Cycle[END_REF][START_REF] Lorenz-Spreen | Accelerating Dynamics of Collective Attention[END_REF], no large-scale research has been devoted to attention cycles, despite the growing availability of traces produced by digital media [START_REF] Lazer | Computational Social Science[END_REF][START_REF] Latour | The Whole Is Always Smaller than Its Parts': A Digital Test of Gabriel Tardes' Monads[END_REF][START_REF] Venturini | Fill in the Gap: A New Alliance for Social and Natural Sciences[END_REF].

To facilitate such research, we propose a mathematical formalization of one of the most influential accounts of attention dynamics: the "public arenas model" introduced in 1988 by Stephen Hilgartner and Charles Bosk. Despite its clarity and insightfulness, H&B's framework has so far found no mathematical formalization for its complexity and lack of formal description. In this paper, we streamline H&B's model focusing on the rise and fall of attention matters (and ignoring the linkages across different arenas and the actors within each arena). Doing so we propose a ready-to-test (prêtà-tester) version of H&B s model hoping that it will encourage further empirical investigation on junk news bubbles. Ours is a case of "toy model" (Reutlinger et al., 2018), whose function is not to be applied or fitted to empirical data nor to offer an accurate description of the phenomenon that it presents, but to help in defining it and setting the conceptual bases for its future study.

Model description (a)

The first ingredient of our model is a population of "matters of attention" (or "social problems" as in H&B original formulation) defined self-referentially as the entities that compete to capture public attention. The non-essential nature of this definition is crucial for H&B, who contend that "social problems are projections of collective sentiments rather than simple mirrors of objective conditions" (H&B p.54). In other words, matters of attention are defined by their visibility and not the other way around ("we define a social problem as a putative condition or situation that is labeled a problem in the arenas of public discourse and action" p.55). Three corollaries descend from this non-essentialist definition:

• First, all attention matters are equal before our model and their rise and fall depend exclusively on the competition between them and not on any substantial features ("social problems exist in relation to other social problems" p.55). • Second, our model focuses on attention dynamics internal to media arenas, deliberately disregarding the influence of exogenous shocks. This does not mean, of course, that these shocks do not exist (clearly the breaking of a war or of an earthquake will command attention in all attention arenas). Yet, their influence is both obvious and insufficient to account for all media dynamics ("if a situation becomes defined as a social problem, it does not necessarily mean that objective conditions have worsened. Similarly, if a problem disappears from public discourse, it does not necessarily imply that the situation has improved" p.58). This is particularly true of the kind of junk news we are interested in, which may occasionally surf the drama of external events, but is more often entirely selfreferential. For these reasons, exogenous shocks are deliberately excluded from our model (but empirical applications should, of course, control for them). • Third and similarly to H&B framework, our model can be applied to different media and at different scales. Attentions matters are broadly defined as recognizable units of content in a particular forum of collective debate (the attention arena). Examples could be different videos in a given YouTube channel or different threads in a given Reddit subreddit. To be sure, we are not promising that our model will fit all media debate but inviting scholars to test it empirically on different phenomena to determine to which it can be fruitfully applied.

(b)

The second ingredient of our model are two competition mechanisms that favor some attention matters over others. The four different "principles of selection" distinguished by H&B find in our model a formalization in two main mechanisms:

• Exogenous influences. Three of the four "principles of selection" distinguished by H&B, "drama" (pp.61-62), "culture and politics" (H&B p.64) and "organizational characteristics" (pp. 65,66) are rendered in a deliberately coarse way in our model. The dramatic value of attention matters as well as the way in which they resonate with the general culture or with the specific organization of the medium are important, but their influence falls outside the self-induced media dynamics that constitute the focus of our model. In our formalization, the influence of these features is thus rendered as a noise which randomly increases or decreases the visibility of each item at each iteration. This solution allows for accounting for this type of influence (and to explore the effect of its variation) under the assumption that its specific nature does not affect the dynamic of junk news bubbles. • Endogenous trending. The last selection principle identified by H&B, "novelty and saturation", is crucial to our model. At each iteration, the model increases or decreases the visibility of each matter, repeating its previous variation, multiplied by a parameter that accelerates or decelerates such variation. The model therefore rewards rising items and penalizes declining ones. This mechanism works as a Matthew effect [START_REF] Merton | The Matthew Effect in Science[END_REF][START_REF] Newman | Clustering and Preferential Attachment in Growing Networks[END_REF], but a dynamic one which rewards not the most visible matters, but the ones that have increased the most since the previous iteration. This boosting of trendiness is consistent with the way in which online platforms "emphasiz[e] novelty and timeliness… [by] identifying unprecedented surges of activity" and "reward[ing] popularity with visibility" (Gillespie, 2016, p.55&60). Such partiality for trendiness is characteristic of both social media and their users, in a sociotechnical loop in which the visibility granted by platform algorithms both depends on and is influenced by the number of views generated by different contents.

(c) The third ingredient of our model are the attention boundaries. At each iteration, after adding (or subtracting) to each attention matter its random variation and its trending acceleration, the model corrects the potential visibility of each item to make sure that it remains within two inflexible boundaries:

• Lower boundary: exclusion of negative visibility. Because it is impossible to conceptualize such a thing as negative attention, when noise or acceleration push the visibility of a matter of attention below zero, the item is removed from the arena and replaced with a new one with null initial visibility. Because a new attention matter can enter the arena only when an old one leaves it, the number of items in the model remains fixed (but some items can have visibility equal to zero). • Upper boundary: saturation of the attention capacity. After having applied noise and acceleration and corrected for negative attention, the model divides the potential visibility of each item by the sum of the potential visibilities of all items. This normalization makes sure that the sum of all computed visibilities remains equal to one. This boundary implements a key ingredient of H&B framework, the idea that each debate arena has a fixed attention capacity (or "carrying capacity", in H&B terms). The fixity of the global "carrying capacity" is crucial to ensure that our model does not converge to a trivial winner-takes-all equilibrium.

While raising attention matters are pushed to an increasing visibility by their trendiness, they all end up reaching a point where they exhausted their potential for growth, begin to slow down and are penalized by competition mechanisms.

The inelasticity of attention capacity also ensures that the visibility gained by one matter of attention is always lost by some other so that "the ascendance of one social problem will… be accompanied by the decline of one or more others" (H&B p.61). While we are, of course, aware that public attention fluctuates with circadian and professional rhythms, we believe that these cyclical fluctuations can be discounted for the sake of simplicity. Following H&B, we think that good reasons for a fixed attention capacity can be found in the limited staging capacity of media ("the prime space and prime time for presenting problems publicly are quite limited" p.59) and, more importantly, in the limited capacity of the public to attend to public ("members of the public are limited not only by the amount of time and money they can devote to social issues, but also by the amount of 'surplus compassion' they can muster for causes beyond the usual immediate concerns" p.59). This second element is crucial to understand why the assumption of a limited carrying capacity remains relevant for online media even if digital technologies removed most of the barriers of conventional news gatekeeping [START_REF] Shoemaker | Gatekeeping Theory[END_REF]. As noted by Ray Maratea in relation to the visibility in the blogosphere:

"Although the Internet may provide an infinite carrying capacity and make the claimsmaking process more efficient, it cannot resolve the problem that audiences have limited amounts of time and attention to focus on various social problems. Furthermore, the blogosphere has developed according to a hierarchical structure, meaning readers and traditional journalists largely concentrate their attention on a relatively small number of well-known blogs. In short, the development of the blogosphere has the potential to dynamically change the claims-making process, but Hilgartner and Bosk's public arenas model remains vital to understanding the rise and fall of social problems in the new media age" (Maratea, 2010, p. 140).

In fact, by eroding the boundaries between news and entertainment (Prior, 2005), digital convergence may have created an even harsher "all-out war for the time of an audience that has more choices than at any point in history" (Klein, 2020, p. 279). While others (see for example, [START_REF] Cinelli | Selective Exposure Shapes the Facebook News Diet[END_REF] takes this competition as a reason for selective exposure and filter bubbles, we believe that they are a crucial ingredient of ephemeral concentration and fake news bubbles. According to the limited capacity model of mediated message processing proposed by Annie [START_REF] Lang | The Limited Capacity Model of Mediated Message Processing[END_REF], media users can deal with an overabundance of media stimuli by switching to an entertainment -rather than understanding -mode, saving their limited cognitive resources by interacting more superficially with the medium ("running on automatic", Lang, 2000, p. 53).

Model formulation and parameters

(a) We call 𝑥 ! each item of our population of matters of attention, with 𝑖 = 1, . . . , 𝑛, where 𝑁is the maximum number of items in the population. We call "visibility" or 𝜋 " ! the share of attention captured by 𝑥 ! at time 𝑡. By a mechanism explained below, at each timestep, the sum of 𝜋 " ! for all 𝑖 is fixed and equal to one. This allows to interpret each 𝜋 " ! as the percentage of the total attention captured by each item 𝑖 at time 𝑡 (b) We model the two competition mechanisms as follows:

• Endogenous trending. At every timestep 𝑡 + 1, the visibility 𝜋 "#$ ! of each item 𝑖 is modified by adding to its current visibility 𝜋 " ! a term which repeats its previous variation (i.e. 𝛥𝜋 = 𝜋 " ! -𝜋 "%$ ! ) multiplied by a positive factor 𝛼, which could be interpreted as a boost of trendiness.

• Exogenous influences. In our formalization, we render all external influences on media dynamics as a noise 𝜀 " ! which increases or decreases the visibility of item 𝑖 randomly at timestep 𝑡. The noise 𝜀 " ! is a realization of a normal distribution 𝑁(0, ! " * $ ! ) with mean = 0 and standard deviation =

$ √'(
where c is a positive parameter. We can therefore write the potential visibility of each item after the iteration 𝑝 "#$ ! as the output of the two above mechanisms as follows:

𝑝 "#$ ! : = 𝜋 " ! + 𝛼(𝜋 " ! -𝜋 "%$ ! ) + 𝜀 " ! (1)
(d) At each iteration 𝑡, the potential visibility 𝑝 "#$ ! is replaced with its corrected version 𝑝 5 "#$ ! to abide by the model's attention boundaries:

• Exclusion of negative visibility. 𝑝 5 "#$ ! equals 𝑝 "#$ ! if 𝑝 "#$ ! is positive. Otherwise it is set to zero. Hence, 𝑝 5 "#$ ! = 𝑚𝑎𝑥(0, 𝑝 "#$ ! ) (2)
• Saturation of the attention capacity. The limited capacity of an arena is represented by the constraint of having a fixed sum of popularities at each timestep. Therefore, each visibility is obtained from the non-negative 𝑝 5 "#$ ! by normalization.

𝜋 "#$ ! = 𝑝 * 𝑡+1 𝑖 ∑ 𝑗 𝑝 * 𝑡+1 𝑗 (3)
Initialization. At the first step of the model, the visibility of every 𝑖 (i.e. 𝜋 $ ! ) is initialized with a random numbers drawn from a uniform distribution between 0 and 1 and normalized to satisfy the constraint ∑ ! 𝜋 $ ! = 1. At the second step, the visibility every 𝑖 (i.e. 𝜋 , ! ) is obtained by adding to 𝜋 $ ! a noise 𝜀 " ! drawn from the normal distribution 𝑁(0, ! " * $ ! ) and normalizing. After the first two steps, the dynamics is self-sustained by evaluating equations ( 1), ( 2) and (3) at each iteration.

Inspecting the equations above, it is easy to observe that our model has only three parameters:

• 𝛼, trendiness boost, which decides whether the visibility variation at the previous iteration is amplified at the next one and by how much, is the key parameter of our model. Conceptually, 𝛼 can be interpreted as the keenness of media algorithms and media users to identify and promote trendy matters of attention. The bigger is 𝛼, the more important is the role played by trendiness in the sociotechnical choices that influence the visibility of media items. High values of trendiness boost thus simulate the attention dynamics occurring in debate arenas prone to junk news bubbles. • The other two parameters are ○ 𝑛, which represent the maximum number of attention matters simultaneously present in the simulation, ○ and 𝑐, which represent the size of noise, that is to say the importance of exogenous influences. Both 𝑛 and 𝑐 are used in the realization of noise and, because they appear in the denominator of the distribution that generates noise, the higher they are, the smaller are the variations due to noise.

Model results and discussion

Despite its simplicity, our model is able to generate patterns comparable with the empirical observations of media systems [START_REF] Leskovec | Meme-Tracking and the Dynamics of the News Cycle[END_REF][START_REF] Lorenz-Spreen | Accelerating Dynamics of Collective Attention[END_REF]. In particular, our formalization supports the H&B intuition that the "shifting waves of social problems" (H&B p.67) typical of media attention cycle can be explained by the interaction between the push of trendiness and the saturation of the carrying capacity: "if we explore these complex linkages, we find a huge number of positive feedback loops, 'engines', that drive the growth of particular problems. Growth is constrained, however, by the negative feedback produced by the finite carrying capacities of the public arenas, by competition among problems for attention, and by the need for continuous novel drama to sustain growth" (H&B p.67).

Previous studies [START_REF] Weng | Competition among Memes in a World with Limited Attention[END_REF][START_REF] Gonçalves | Modeling Users' Activity on Twitter Networks: Validation of Dunbar's Number[END_REF][START_REF] Cattuto | Semiotic Dynamics and Collaborative Tagging[END_REF] considered the role of users' limited attention in media competition assigning users a maximal number of possible interactions (a sort of Dunbar number for individual attention). In most of these models, the fall of popularity is obtained forcing an aging process of media items through an explicit time decay term. This aging process, however, is difficult to justify theoretically and empirically. One of the most original aspects of our model is that it dispenses with this aging process: items' popularity decays naturally through the interplay between the trendiness and the saturation of the overall attention capacity. The comparison between the graphs in fig. 1 suggests that, as the boost of trendiness grows, the rise and fall of attention matters becomes steeper. This relation can be tested by computing the mean steepness of attention curves (the absolute increase or decrease by unit of time) and observing that it increases monotonically with the increase of alpha before reaching a plateau (probably due to the upper and lower constraints on the state and to the impossibility of compressing the width of curve beyond a certain point).

Figure 2. Mean slope of attention curves as function of the trendiness boost (for different values of n and c)

Fig. 2 confirms that the relation between the steepness of attention curve and trendiness boost is not substantially transformed by the other parameters of our model. The number of attention matters and the importance of exogenous influences shift the position of the curve, but do not change its shape. Also, because both 𝑛 and 𝑐 affect the curve in the same way, only 𝑛 will be explored in the next figures.

Considering together fig. 1 and2, it is also interesting to notice that trendiness boost increases riseand-fall steepness by affecting both dimensions of the media cycle: the height of attention curves and their width. This suggests that junk news bubbles can combine features that may appear contradictory.

• Regardless of the number of items or the level of noise, the stronger is trendiness boost the shorter is the lifecycle of individual attention matters (fig. 3a). Remarkably, this is true for all attention matters: even items that reach very high levels of visibility end up falling as quickly as they rose. As a consequence of the shortening of attention weaves, a higher number of matters enter and exit the arena (fig. 3b). This may contribute to making platforms more attractive by increasing the dynamism of their offer of information and entertainment. • On the other hand, higher trendiness boost increases the maximum visibility reached by attention matters (fig. 4a) and, most importantly, amplifies the difference between successful and unsuccessful attention matters, creating a situation in which, at each iteration, most of the available attention is captured by a minority of over-visible items (fig. 4b). "There is a huge 'population' of potential problems-putative situations and conditions that could be conceived of as problems. This population, however, is highly stratified. An extremely small fraction grows into social problems with 'celebrity' status… [while] the vast majority of these putative conditions remain outside or on the extreme edge of public consciousness" (H&B p. 57).

Some empirical examples

Being a toy model, our mathematical formalization is not meant to serve as a simulation of a realworld dynamic or to be fit to empirical data. Still, simplistic as it is, our toy model does capture some features of the current media system as confirmed, for example, by the results of an empirical investigation of Accelerating Dynamics of Collective Attention by [START_REF] Lorenz-Spreen | Accelerating Dynamics of Collective Attention[END_REF].

Comparing different media and over several years, the authors found that "the attention associated with individual topics rises and falls with increasing gradients" and "the shifts of collective attention between topics occur more frequently" (p. 1763) suggesting a general increase of trendiness's importance in the media system. They also find that this tendency is stronger for media such as Twitter, Google and Reddit and less pronounced for Wikipedia and the scientific literature, suggesting that the arenas that are more sensitive to trendiness are also the ones that are most exposed to junk news bubbles.

To find other examples of our model's insights, we explored the dynamics of visibility of the French vlogosphere. While the most obvious (and probably the best) operationalization of H&B model would be to consider the whole French YouTube as an arena for the competition of different thematic issues, this would require a huge data collection and automatic identification of themes which exceed the scope of this paper. We thus decided to exploit the fractal nature of media systems and to consider each YouTube channel as an arena and each video as an attention matter. As the competition between video is likely to take place across channels rather than within them, this operationalization is far from ideal but, as we will see, sufficient to exemplify our argument.

Starting on December 9, 2019, we recorded the number of views collected every hour by each video published by about thousand YouTube channels active in the French public debate (selection was made by iterating expert review and snowball sampling). For this paper, we limit our analysis to the data collected until March 14, 2020 (in order to exclude the Covid19 lockdown period where we observed slightly different attention dynamics, [START_REF] Castaldo | The Rhythms of the Night: Increase in Online Night Activity and Emotional Resilience during the Covid-19 Lockdown[END_REF]. Since we are exploring inchannel competition, we also restrict our analysis to channels having multiple active videos at the same time, thus focussing on the 60 most active channels on our corpus. In this subcorpus the most active channel is "Europe 1" with 4.291 videos published in the three months of collection and the least active is "Charente Libre" with 216 videos. The most popular channel is "France 24" with 731.950 total views and the least popular "L'Opinion" with 1552 total views. For each of these 60 channels, we calculated the same two metrics computed for in our simulation above: the average life cycle of the videos (defined as the average number of hours necessary for a video in the channel to reach the 95% of the total views collected in the first week) and the average Gini index of hourly concentration. The scatter plot in fig. 5 confirms the main insight of our model: the fact that short life cycles and high concentration go hand in hand in the distribution of media attention. The distribution on the diagonal of the scatter plot suggests a sort of continuum that goes from channels that publish few videos with a relatively longer life expectancy and a less skewed distribution of attention (top-left), to channels that publishes videos at a much more rapid pace knowing that most will spike and die very quickly, but hoping that some of them will stick (bottom-right). It is tempting to interpret such continuum as a quality VS click-bait, even though many exceptions are manifest in the diagram (e.g. France24, Europe1 and TV5Monde, are news channels of established quality and yet all find themselves in the bottom right corner because of their practices of publishing multiple videos a day).

The scatterplot also allows us to select three chains (boxed in fig. 5) with a similar number of videos and total views, but with very different life spans and concentrations, which we can use as examples of three different attention regimes: 1. "France Culture" (276 videos, 34.694 views) with long life cycles and low concentration, is a renowned public radio, appreciated for the quality of its contents and the seriousness of its debate. 2. "LCI" or "La Chaîne Info" (738 videos, 54.198 views) with medium life cycles and medium concentration, is an established live-news broadcasting service by French public television channel. 3. "Sputnik France" (466 videos, 32.694 views) with short life cycles and high concentration, is a Russian state-owned news agency, often criticized for spreading misinformation and low quality stories. Beside focussing on individual channels, it would be interesting to investigate if, over a longer period of time, it is possible to observe a general shifting down and to the right of the media system as a whole. Unfortunately the data at our disposal do not yet allow such an inquiry.

Conclusion

Taken alone, none of the consequences of junk news bubbles highlighted by our model is particularly surprising: being an acceleration, trendiness predictably shortens the lifespan of attention matters and, being a positive feedback, it increases their maximum visibility. Their combination, however, is remarkable as it creates a shoaling of attention waves which reduces the width and increases the height of attention curves. Debate arenas characterized by a stronger focus on trendiness may therefore end up displaying a syncopated rhythm of attention that is at the same time increasingly dispersed and increasingly concentrated (as one can easily observe, for example, in YouTube channels or subreddits devoted to buzzing news, memes and viral contents). Junk news bubbles are characterized by the same attention skewness of Boydstun's "media storms" [START_REF] Boydstun | Two Faces of Media Attention: Media Storm Versus Non-Storm Coverage[END_REF], but not by the same persistence in time. As such, they are particularly worrying because they take attention away from other discussions (because of their skewness), without producing the heightened public awareness created by media storm (because of their ephemerality).

While evidence exists that the syncopation described by our model can be found in numerous online platforms [START_REF] Wu | Novelty and Collective Attention[END_REF]Crane & Sornette, 2008;[START_REF] Yang | Patterns of Temporal Variation in Online Media[END_REF][START_REF] Castillo | Characterizing the Life Cycle of Online News Stories Using Social Media Reactions[END_REF][START_REF] Bandari | The Pulse of News in Social Media: Forecasting Popularity[END_REF], little empirical research has been carried out on the consequences of such attention regime. The risks of distraction related to screens and online media have been decried at the individual and cultural level (cf. for instance, [START_REF] Goldhaber | The Attention Economy and the Net[END_REF][START_REF] Hassan | The Age of Distraction: Reading, Writing, and Politics in a High-Speed Networked Economy[END_REF][START_REF] Citton | Pour Une Écologie de l'attention[END_REF][START_REF] Crawford | The World Beyond Your Head: On Becoming an Individual in an Age of Distraction[END_REF], but hardly investigated through the records increasingly made available by digital platforms themselves. This paper hopes to facilitate such line research by providing a formal description of a distracted attention regime: a situation in which attention waves becomes both higher and narrower and in which public debate is trapped in a continual succession of hot button issues.

Such a situation, arguably, is not particularly propitious to quality. While our model defines junk news bubbles independently from their content value, we suspect this attention regime to be associated with misinformation and poor quality. A regime in which visibility is granted and withdrawn with great rapidity unsurprisingly favours click-baity content designed to catch the attention more than to retain it. This observation may explain why, in political discourse, traditional propaganda is increasingly replaced by political trolling aimed at drowning opponents' discourse in noise [START_REF] Jack | What's Propaganda Got To Do With It?[END_REF][START_REF] Flores-Saviaga | Mobilizing the Trump Train: Understanding Collective Action in a Political Trolling Community[END_REF] or simply to monetize political outrage [START_REF] Braun | Fake News, Real Money: Ad Tech Platforms, Profit-Driven Hoaxes, and the Business of Journalism[END_REF].

Being a simplified formalization of a relatively abstract framework, our mathematical model does not allow substantial claims about actual attention dynamics. It allows, however, to advance a precise hypothesis about the junk news bubbles and their detrimental effects on public debate: the fascination with trendiness of digital platforms and their users may create an over-accelerated public debate in which a disproportionate share of media attention is captured by matters which are incapable to sustain it. As the shoaling of sea waves is associated with the entering in shallower waters, so junk news bubbles may be associated with a shallower public debate, a risk that raises concerns and normative implications different from those associated with filter bubbles and fake news. While the latter can be (and has been) addressed by tweaking the recommendation algorithms to favour mainstream sources of information, this solution does not necessarily solve the problem highlighted in this paper.

Describing an attention regime that is increasingly pervasive in online media, junk news bubbles cannot be fought by censoring specific content or specific sources, but demands a deep restructuring of the system of incentives that characterize digital communication. Until social media will obtain the largest share of their profits from selling metrics of shallow and ephemeral engagement (e.g. impressions, views, clicks and shares) and until their users will be rewarded according to the same metrics, little are the chances to avoid dynamics of hyper-acceleration. This does not mean that all content producers will play the game of click bait and junk news -think of the many amazing works produced on YouTube by both mainstream and native creators [START_REF] Snickars | 12 The YouTube Reader[END_REF][START_REF] Burgess | 53 Journal of Chemical Information and Modeling YouTube: Online Video and Participatory Culture[END_REF] -nor that online platforms can only promote superficial forms of engagement -think of how Twitter has been invested by all sorts of political activists [START_REF] Gerbaudo | Tweets and the Streets: Social Media and Contemporary Activism[END_REF]. It does mean, however, that in the old opposition between a distracted public opinion [START_REF] Lippmann | Public Opinion[END_REF][START_REF] Lippmann | The Phantom Public[END_REF] and engaged public inquiry [START_REF] Dewey | The Public and Its Problems[END_REF], accelerated attention regimes stack the odds against the latter.

Figure 1 .

 1 Figure 1. Evolution of our model for trendiness boost = 0, 1, 2, and 3 (with 𝑛 = 20 and 𝑐 = 12). Each color area corresponds to the attention received by an item. Only the first 100 iterations are shown as the shape of the curves does not change in further iterations

Figure 3 .

 3 Figure 3. (a) Mean length of attention matters' life cycle and (b) ratio of new attention matters entering the model in its first 10.000 iterations, at the variation of trendiness boost (for different values of n and with c set to 12)

Figure 4 .

 4 Figure 4. (a) Mean height of the attention curve peaks and (b) Gini index of attention concentration at each iteration of the model, at the variation of trendiness boost (for different values of n and with c set to 12)

Figure 5 .

 5 Figure 5. Scatterplot of the average concentration and average life cycle of the videos of 60 YouTube channels highly active in the French political vlogosphere. The size of the dots corresponds to the total number of views collected by the channel and the color corresponds to the number of published videos (going from dark red for fewer videos, to orange, yellow, green and violet for more videos).

Figure 6 .

 6 Figure 6. Left: Scatterplot of the concentration (share at peak hours) and average life cycle of all the videos published by three selected channels (France Culture, LCI and Sputnik France Play). Right: Average temporal profile of the videos of the three channels. To highlight the difference between the three attention regimes, fig. 6 (left) plots all of their videos for the duration of their lifecycle (the number of hours needed to reach the 95% of the total views collected in the first week) and the share of visibility over the channel that they obtained at their peak hour (the hour in which they collected most of their views). At their peak hour, videos published by France Culture rarely captured over 10% of the total attention for the channel, but many of them remain alive through most of their first week. The videos by Sputnik France often reach shares of 20% or more, but rarely survive after the first two or three days from their publication. The videos from LCI are somewhere in between. The difference is clearer when observing the average trajectory of visibility for the videos of the three channels for the first two days after their publication (fig. 6 right). While the average Sputnik's video makes most of its views in its first hours and then declines extremely quickly, the average France Culture's video has a slower start, but a thicker visibility tail (LCI presents once again an intermediate profile).

1 This work has been partially supported by MIAI@Grenoble Alpes (ANR-19-P3IA-0003) and by CNRS via project 80|PRIME "Disorders of Online Media (DOOM)".