Charlène Blanchet

Jean Jaubert

Elisabeth Carniel

Corinne Fayolle

Geneviève Milon

Marek Szatanik

Jean-Jacques Panthier

Xavier Montagutelli

Mus spretus SEG/Pas mice resist virulent Yersinia pestis, under multigenic control

Keywords: Plague, mouse, resistance, Yersinia pestis, Mus spretus

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Introduction

Yersinia pestis, a Gram-negative bacterium, is the etiological agent of human bubonic and pneumonic plague. Starting from the bite of a Y. pestis-hosting flea, bubonic plague is characterized by rapid multiplication of the bacteria in the bite site-draining lymph node, and is fatal in at least 50% of untreated cases, due to sepsis and multiple organ failure. Pneumonic plague results from the colonization of the lung by bacteria via infectious respiratory droplets.

It is the most contagious and deadliest manifestation of the disease, with a 100% mortality rate in the absence of effective antibiotherapy [START_REF] Titball | Vaccination against bubonic and pneumonic plague[END_REF] .

Although the current worldwide incidence of plague is low compared to historical records, the steady increase in reported human cases during the past 15 years coupled with its reemergence in areas otherwise declared plague-free for several decades has led to classify plague as a re-emerging disease [START_REF] Schrag | Emerging infectious diseases: what are the relative roles of ecology and evolution?[END_REF] , a threat exacerbated by the recent identification of a antibiotic resistant strain [START_REF] Galimand | Multidrug resistance in Yersinia pestis mediated by a transferable plasmid[END_REF] . Moreover, rapid disease progression with a high mortality rate, the absence of efficient, safe vaccines, and the possibility of aerosol dispersion make Y. pestis a potential major agent for bioterrorism [START_REF] Inglesby | Plague as a biological weapon: medical and public health management. Working Group on Civilian Biodefense[END_REF] .

Historical records of plague pandemics indicate that a fraction of the individuals who developed bubonic plague were able to survive, suggesting that genetic factors of the mammalian host may also influence the outcome of the infection. It is likely that plague, which killed one third of the European population during the 1347-1351 Black Death, has exerted a rapid but strong selective pressure on the human genome. In animals, not all species are equally susceptible to plague. While most rodents, cats, camels and monkeys are susceptible, dogs and cows are usually resistant to Y. pestis [START_REF] Perry | Yersinia pestis--etiologic agent of plague[END_REF] . These differences in susceptibility could help understand how Y. pestis overcomes the human immune system, identify which individuals are at risk, and form a basis for the development of new strategies for therapeutic and vaccine intervention.

Using forward genetic approaches to decipher the genetic control of natural variation in host resistance to viral, parasitic or bacterial infections has already demonstrated its power to unravel the molecular mechanisms engaged in host-microbes interactions [START_REF] Vidal | Forward genetic dissection of immunity to infection in the mouse[END_REF] . The strength of this approach resides in its ability to identify previously unknown mechanisms, and characterize their hierarchy, interactions and individual contributions to the pathogenesis of infectious agents. However, its power remains very limited in humans, in particular because Y. pestis-infected patients undergo antibiotic treatment, thereby masking their intrinsic ability to control bacterial burden, the associated tissue damage and systemic inflammatory processes.

The availability of animal models relevant to human infectious diseases makes possible the identification of susceptibility genes under controlled experimental conditions in which strain, virulence, dose and route of Y. pestis inoculation are standardized. Among rodents, mice are of special interest since they are naturally susceptible to plague [START_REF] Pollitzer | Monograph Series 22[END_REF] , and mouse offers powerful genetics tools to identify susceptibility and resistance genes even when the trait is under complex genetic control. Genetic and phenotypic dissection, which is critical in untangling complex sequences of events with many participating tissues and cell types, can be achieved using congenic strains, in which specific genomic regions harboring a small group of genes are transferred between susceptible and resistant backgrounds.

Differences in susceptibility to Y. pestis have been recently reported between laboratory inbred strains of mice [START_REF] Congleton | Mice naturally resistant to Yersinia pestis Delta pgm strains commonly used in pathogenicity studies[END_REF] , including the mapping of two resistance alleles, close to the interleukin-10 gene (chromosome 1) [START_REF] Turner | Substrains of 129 mice are resistant to Yersinia pestis KIM5: implications for interleukin-10-deficient mice[END_REF] and histocompatibility complex (chromosome 17) [START_REF] Turner | Resistance of BALB/cJ mice to Yersinia pestis maps to the major histocompatibility complex of chromosome 17[END_REF] . These results were obtained upon intravenous injection of the Y. pestis mutant strain KIM5, which lacks the chromosomal pgm locus. Since this strain is highly attenuated, it has to be given intravenously to cause a lethal infection. Although direct penetration of Y. pestis into the blood stream may occur during a flea bite, it is a very uncommon mode of transmission.

Furthermore, the relevance of these results to natural infection in animals and humans is limited, since the same inbred strains of mice are susceptible to virulent Y. pestis strains [START_REF] Congleton | Mice naturally resistant to Yersinia pestis Delta pgm strains commonly used in pathogenicity studies[END_REF] .

All classical laboratory strains (such as C57BL/6 (B6)) are susceptible to subcutaneous (s.c.) injection of fully virulent Y pestis strain C092, an experimental setting designed to mimic many features of natural exposure [START_REF] Doll | Cat-transmitted fatal pneumonic plague in a person who traveled from Colorado to Arizona[END_REF] . In this study, we report that the SEG/Pas (SEG) inbred strain, which was established from Mus spretus progenitors, exhibits a high level of resistance under the same conditions. The genetic analysis of a large backcross cohort between SEG and B6 identified three dominant, additively acting loci that account for most of the difference in susceptibility observed between the two strains.

Results

SEG mice resist virulent Yersinia pestis. Several inbred strains of mice were tested for their ability to survive an infection with the fully virulent Y. pestis strain CO92. Inoculation by s.c. injection of 100 colony-forming units (CFU) in the ventral region was lethal within 4-12 days for almost 100% B6 mice. This dose was used to challenge females of three additional laboratory inbred strains (FVB/N, BALB/cByJ and SJL/J), as well as one Mus musculus castaneus-derived strain (CAST/Ei) and the Mus spretus-derived SEG strain (Figure1). B6 and SEG mice were tested in several experiments and since the results were consistent throughout, the data were pooled. SEG female mice were exceptionally resistant (90% survival; 62/69) compared to 23% (FVB; 5/22) or less in other strains. Only 6.3% (7/111) of B6 mice survived the infection (Figure 1). Interestingly, the few SEG mice that did succumb to the infection did so at the same average timepoint as B6 mice (Figure 2). SEG survivors developed symptoms characterized by a mild hypotonia and reduced activity between days 4 to 6 post-inoculation, before recovering. SEG mice that were susceptible progressed towards marked depression and prostration, and finally died. In B6 mice, death often occurred rapidly after the appearance of the first symptoms.

To further evaluate the level of resistance of SEG mice to the fully virulent CO92 strain, groups of females were inoculated s.c. with ten-fold dilutions ranging from 10 3 to 10 7 CFU of CO92. Remarkably, even the highest doses were unable to cause death in more than 50% of the mice (Supplementary figure 1A). The mortality timepoint of susceptible SEG mice varied across groups, but did not correlate with the number of bacteria inoculated. We therefore concluded that the SEG strain exhibits an exceptional level of resistance to s.c. inoculation with fully virulent Y. pestis. Such a resistance has never been reported for any other mouse strain.

Female SEG mice are more resistant than males. B6 males and females inoculated s.c. with 10 2 CFU of strain CO92 exhibited the same high level of susceptibility (Supplementary figure 1B). By contrast, SEG males were significantly less resistant (68.5% survival; 37/54) than females (89.9% survival; 62/69, p=0.005). Since the difference of susceptibility between SEG and B6 strains was higher in females than in males, further studies, including genetic mapping of QTLs, were carried out with females.

The exceptional resistance of SEG mice to Y. pestis is not CO92 strain specific. In order to assess whether the resistant phenotype of SEG mice was specific to Y. pestis strain CO92, we challenged B6 and SEG female mice with 100 CFU of another wild-type virulent strain, denoted as strain 6/69 [START_REF] Buchrieser | The 102-Kilobase Unstable Region Of Yersinia Pestis Comprises a High-Pathogenicity Island Linked to a Pigmentation Segment Which Undergoes Internal Rearrangement[END_REF] . Survival curves obtained with the two bacterial strains were similar (Supplementary figure 2), demonstrating that SEG mice resistance is not Y. pestis strain specific.

Multigenic control of resistance to Y. pestis in SEG mice. When a group of (B6 × SEG)F1 females (n=16) were challenged by s.c. inoculation of 10 2 CFU of strain CO92, 75% (12/16) of them survived, a resistance level not significantly lower than that of SEG mice (p=0.21). This suggests a dominant mode of inheritance for SEG-derived resistance alleles.

An interspecific backcross was produced to characterize the genetic regions that account for the resistance of SEG mice. F1 females, born from the cross of B6 females and SEG males, were mated with B6 males to yield BSB progeny, out of which 322 females were challenged s.c. with 10 2 CFU of Y. pestis CO92. One hundred and ninety females survived the infection, giving a survival rate of 59%. This proportion was significantly lower than that of SEG mice (p=3.2x10 -7 ), but significantly higher (p=0.0015) than the 50% expected if resistance was inherited as a simple Mendelian trait. From these data, we conclude that resistance of SEG mice to Y. pestis is under the control of multiple genes, likely with SEG alleles acting in a dominant fashion.

The mortality timepoint of susceptible BSB females was similar to that of B6 and SEG mice in both mean value and standard deviation (Figure 2), suggesting that this cross did not segregate genes controlling this trait. In fact, we did not find any significant QTL controlling mortality time. The QTL search therefore focused on survival, analyzed as a binary trait.

SNP genotyping was performed using 721 polymorphic markers covering the entire genome of BSB females. QTL analysis using R/qtl software, revealed the presence of three chromosomal regions significantly associated with survival on mouse chromosomes 3, 4 and 6 (Figure 3). In all cases, the LOD curve reached the 5% genome-wide significance threshold computed by data permutation. These loci were named Yprl1 (Yersinia pestis resistance locus-1), Yprl2 and Yprl3, respectively. Their putative location was taken as the position of the marker with the highest LOD score value. Yprl1, Yprl2 and Yprl3 were positioned at 116, 62 and 95 Mb on chromosomes 3, 4 and 6, respectively. Their 95% confidence intervals were 50, 84 and 81 Mb long, respectively (Table 1).

The individual effects of each QTL were assessed by comparison of survival curves of BSB females depending on their genotype at the peak SNP marker. The SEG allele at the Yprl1 locus was associated with a highly significant increase in resistance (Figure 4A), rising from 48.5% in mice homozygous for the B6 allele, to 68.1% in the B/S heterozygous mice.

The effects of the Yprl2 and Yprl3 loci were similar in direction and magnitude (Figure 4B and C, Table 1).

Interactions between pairs of loci were investigated by comparing survival rates of the four genotype combinations in two-locus effect plots. For example, the difference of survival between Yprl2 B/B and Yprl2 B/S mice was 21.1 % within the group of Yprl1 B/B mice, while it was 18.0% within the Yprl1 B/S mice (Supplementary figure 3). Since these two values were not significantly different (p=0.97), we concluded that the effect of Yprl2 was independent of the genotype of the mice at the Yprl1 locus, and reciprocally. Similar observations were made with Yprl1-Yprl3 and Yprl2-Yprl3 pairs of QTLs, thus suggesting that the three QTLs add up their individual effects without epistasis.

We also searched for additional QTLs which could have remained undetected using the one-QTL search, because of epistatic interactions. The "scantwo" feature of R/qtl did not detect any additional locus significantly associated with survival.

Yprl1, 2 and 3 act additively to confer survival in BSB mice. As the three QTLs appear to act independently of one another, we investigated the level of resistance of BSB mice for each of the eight possible genotype combinations at the three loci (Figure 5). This analysis was made possible by the large size of the cross which resulted in group sizes of at least 33 individuals. Groups were sorted by increasing proportion of SEG alleles at the three QTLs. The distribution of survival rates across groups was compared to that of B6 and SEG.

Mice heterozygous for the SEG allele at the three QTLs show a level of resistance similar to that of SEG (82.7% and 89.9%, respectively). Conversely, mice homozygous for the B6 allele at the three QTLs had the lowest level of resistance (27.0%), but were significantly less susceptible than B6 mice (p=0.0017). The other groups of BSB mice showed intermediate levels of resistance, and groups of mice heterozygous for only one QTL were globally more susceptible than those heterozygous for two QTLs (48.5% and 68.0% survival, respectively; p=0.0043).

We draw four main conclusions from this analysis. First, SEG resistance alleles are dominant over B6 susceptibility allele. Second, the three QTLs act additively and together they account for 67% of the difference in survival to Y. pestis challenge between the two parental strains. Third, these QTLs provide BSB mice with the same level of resistance as parental SEG mice. Fourth, there remain undetected QTLs that contribute to significant resistance even in the absence of the three Yprl loci.

Discussion

Although plague is no longer a major threat to the human population, the recent reemergence of the disease in several countries 2 , the isolation of antibiotic resistant strains [START_REF] Galimand | Multidrug resistance in Yersinia pestis mediated by a transferable plasmid[END_REF] , and the exceptional pathogenicity of Y. pestis fully justify studies aimed at unravelling the mechanisms by which this bacterium is able to induce so efficiently and rapidly a deadly infection of its host. The mouse is a relevant animal model to explore the pathophysiology of plague owing to the fact that it is a natural and susceptible host for Y. pestis. Most previous studies have explored the bubonic form of the disease, although a model for primary pneumonic plague has been recently described and investigated [START_REF] Lathem | Progression of primary pneumonic plague: a mouse model of infection, pathology, and bacterial transcriptional activity[END_REF] .

The majority of in vivo genetic studies previously published on mouse models have focused on the role of genetic determinant in Y. pestis on bacterial load and histological damages in different host tissues [START_REF] Leary | Yersinia outer proteins (YOPS) E, K and N are antigenic but non-protective compared to V antigen, in a murine model of bubonic plague[END_REF][START_REF] Lindler | Yersinia pestis pH-6 Antigen -Genetic, Biochemical, and Virulence Characterization of a Protein Involved in the Pathogenesis of Bubonic Plague[END_REF] . However, two recent reports identified regions of the mouse genome associated with the variable susceptibility of classical inbred mouse strains to Y. pestis. The first study showed that the previously reported resistant phenotype of Il10 knock-out mice was partially due to a closely linked resistance allele inherited from the 129/P2J genetic background of the ES cells used for gene targeting [START_REF] Turner | Substrains of 129 mice are resistant to Yersinia pestis KIM5: implications for interleukin-10-deficient mice[END_REF] . The second study described the resistant phenotype of the BALB/cJ strain, compared to susceptible BALB/c substrains, and C57BL/6J. Using a combination of backcrossing and intercrossing, a QTL was mapped in the H2 region, on proximal chromosome 17 [START_REF] Turner | Resistance of BALB/cJ mice to Yersinia pestis maps to the major histocompatibility complex of chromosome 17[END_REF] . However, both studies were performed using the attenuated Y. pestis strain KIM5 which lacks the pgm locus, an important virulence factor [START_REF] Leal-Balbino | The pgm locus and pigmentation phenotype in Yersinia pestis[END_REF] . This deletion requires that inoculation of Y. pestis be performed intravenously, a route that ensures rapid dissemination of the bacteria, but one that also bypasses several important processes, in particular those deployed in the skin and the draining lymph node.

In this study, we aimed to identify host genetic determinants of resistance to plague, under experimental conditions that more closely resemble natural infection, i.e. using a wildtype, fully virulent Y. pestis strain and a s.c. route of transmission. We took advantage of our collection of wild-derived strains maintained at the Institut Pasteur to explore mouse genetic diversity. This strategy has been previously successful in our hands, with the identification of Oas1b gene as a major determinant of resistance to West Nile virus [START_REF] Mashimo | A nonsense mutation in the gene encoding 2'-5'-oligoadenylate synthetase/L1 isoform is associated with West Nile virus susceptibility in laboratory mice[END_REF] . Indeed, while almost all laboratory inbred strains are highly susceptible to this virus due to a point mutation in the Oas1b gene, all wild-derived strains are highly resistant and carry a functional allele.

In the present study, all tested strains (including Mus m. castaneus CAST/EiJ) were found to be susceptible to plague, with the exception of the Mus spretus derived SEG strain, which exhibited remarkable resistance. Even inoculation of very high bacterial titres did not lead to mortality in more than 50% of the mice. One possible explanation for the high dose resistance of SEG mice could be genetic heterogeneity in the breeding colony, with a mutation conferring complete resistance to high doses segregating in a low dose-resistant inbred genetic background. However, careful analysis of the pedigree of the SEG mice used in this experiment ruled out this possibility. Another explanation might be a dose-dependent stimulation of the SEG innate immune response, with an enhanced, unsaturated capacity to clear the bacteria.

We have identified for the first time a mouse strain that displays high level resistance to inoculation of fully virulent Y. pestis strains, opening a double perspective to better understand the interactions between this highly pathogenic bacterium and its host. First, having both highly resistant and very susceptible mouse strains is an invaluable resource to identify the mechanisms, especially during the early phases following Y. pestis inoculation, which are triggered or disengaged by Y. pestis, and influence the outcome of host-pathogen interactions. Second, genes controlling this difference can be identified by QTL mapping in two generations, although interspecific crosses between Mus spretus and laboratory strains invariably resulted in sterile F1 males, thereby preventing the production of F2 progeny. This forward genetic strategy has already been proven to be successful for the identification of key genes for the control of bacterial, viral or parasitic diseases [START_REF] Vidal | Forward genetic dissection of immunity to infection in the mouse[END_REF] .

An interspecific backcross using SEG and B6 as parental strains was therefore produced. We analyzed more than 300 females since we suspected that SEG resistance was not controlled by a single gene, and that scoring the phenotype as a binary (death or survival) trait, resulting from a complex series of host-bacteria interactions, would result in reduced power of QTL detection. In fact, this large number of animals is required to identify a QTL controlling 20% difference in survival, with a 0.05 genome-wide significance threshold. We identified three significant QTLs, each of which was able, in the context of the segregating background of BSB mice, to confer a 20% increase in survival, from 48 to 68% on average. Moreover, pair-wise analysis of QTL effects revealed an additive mode of action. Subsequently, the survival rate of BSB mice increased as a function of the SEG alleles present at the three QTLs, and mice heterozygous at Yprl1, 2 and 3 displayed the same level of resistance as SEG mice (Figure 5). However, since mice homozygous for the B6 allele at the three QTLs were significantly more resistant than B6 mice, there remain other resistance genes to be identified, which may be too numerous, or may have too weak effects to be detectable in a cross of this size.

Taken together, these data suggest a model for resistance to Y. pestis virulent strains in SEG mice (Figure 6). The B6 strain has a very weak ability to resist Y. pestis, which results most frequently in rapid mortality. One or more yet unidentified loci increase the resistance to a level where approximately 30% of mice eventually survive the infection. The three Yprl loci mapped in our study significantly improve resistance to Y. pestis and together recapitulate the resistance of SEG mice. We cannot predict the contribution the three Yprl loci provide to resistance in the absence of the unidentified loci. It is possible that these unknown loci play a critical role and create a genomic context favourable to the action of the Yprl loci, so that strains congenic for only one of any of the Yprl loci may not show a significant increase in survival rate compared with B6.

The survival curves of the mice that died of the infection showed exactly the same decrease over time, across the B6, SEG and BSB populations (Figure 2). This observation suggests that the disease course in the mice which finally succumb to the Y. pestis challenge is very similar in these three different genetic backgrounds. Thus, the final outcome of infection would depend on events taking place during the first two or three days, before the first mice die.

The Yprl1, 2 and 3 regions overlap several QTLs associated with susceptibility to other bacteria, to viruses or parasites (Supplementary table 1). Regarding bacterial diseases, Tbs1 is involved in control of both body weight loss and survival time following challenge with virulent Mycobacterium tuberculosis, which are rather late phenotypes. Msts2 influences acute inflammatory reaction which correlates with survival following Salmonella typhimurium s.c. injection. This QTL could be relevant to our phenotype and maps close to the Yprl3 peak location. Three other QTLs, associated with susceptibility to Chlamydia trachomatis and Salmonella enteritidis have been mapped at the boundaries of the Yprl confidence intervals and are hence less attractive.

Although the confidence intervals of the Yprl1, 2 and 3 loci encompass large chromosomal segments (between 50 and 84 Mb), it is also possible to consider potential candidate genes in these regions that may, because of their known function in host immune or inflammatory responses, contribute to the observed phenotype. The Yprl1 confidence interval contains the Pglyrp3 and Pglyrp4 genes which are anti-microbial peptides secreted by skin, eyes, oral cavity and gastrointestinal tract in response to pathogen recognition. They play an important role against pathogenic bacteria such as Listeria monocytogenes and Staphylococcus aureus, but seem to be less efficient against Gram-negative bacteria [START_REF] Kapetanovic | Early events in innate immunity in the recognition of microbial pathogens[END_REF] .

Interleukin 6 receptor α chain (Il6ra) also maps to Yprl1. IL-6 is a pleiotropic cytokine expressed by antigen presenting cells (APCs) such as dendritic cells, macrophages and B cells but also by a variety of non-hematopoietic cells [START_REF] Dienz | The effects of IL-6 on CD4 T cell responses[END_REF] . It acts synergistically with a number of growth factors and cytokines to sustain normal proliferation and maturation of macrophages, T and B cells. It has been shown to play a role in resistance to bacteria (such as Listeria monocytogenes [START_REF] Dalrymple | Interleukin-6-deficient mice are highly susceptible to Listeria monocytogenes infection: correlation with inefficient neutrophilia[END_REF] ) or viruses [START_REF] Leblanc | Lack of interleukin-6 (IL-6) enhances susceptibility to infection but does not alter latency or reactivation of herpes simplex virus type 1 in IL-6 knockout mice[END_REF] .

The main candidate in the Yprl2 region is the Toll-like receptor 4 gene (Tlr4), located on the QTL peak. It is involved in the recognition of lipopolysaccharide (LPS), a major component of the outer membrane of Gram-negative bacteria [START_REF] Da | Lipopolysaccharide is in close proximity to each of the proteins in its membrane receptor complex. transfer from CD14 to TLR4 and MD-2[END_REF] . Several mouse strains are hyporesponsive to LPS due to Tlr4 mutations and show increased susceptibility to Gramnegative S. typhimurium, while transgenic mice possessing more than two extra-copies of the gene survived longer and in a greater percentage to Salmonella infection [START_REF] Bihl | LPS-hyporesponsiveness of mnd mice is associated with a mutation in Toll-like receptor 4[END_REF] . Y. pestis also produces LPS, however the Tlr4 stimulating activity of its LPS-lipid A is reduced when the bacteria is at mammalian body temperature [START_REF] Montminy | Virulence factors of Yersinia pestis are overcome by a strong lipopolysaccharide response[END_REF] . It would therefore be interesting to compare the Tlr4 responses of B6 and SEG mice after exposure to Y. pestis LPS. Other genes of interest in the Yprl2 region are 14 genes of the type I interferon and interferon receptor families, although studies have emphasized the role of type II gamma interferon in the control of Y. pestis multiplication in the host [START_REF] Kummer | Antibodies and cytokines independently protect against pneumonic plague[END_REF][START_REF] Nakajima | Association between virulence of Yersinia pestis and suppression of gamma interferon and tumor necrosis factor alpha[END_REF] .

Yprl3 overlaps several potential candidate genes. The nucleotide-binding oligomerization domain containing 1 (Nod1) gene is an intracellular pattern recognition receptor that mediates innate and acquired immunity by recognizing diaminopimelatecontaining muropeptides from Gram-negative bacteria peptidoglycan, which activates the NF-κB pathway [START_REF] Girardin | Nod1 detects a unique muropeptide from gram-negative bacterial peptidoglycan[END_REF] . Nod1 deficiency results in increased susceptibility to various Gram-negative bacteria, including Helicobacter pylori [START_REF] Viala | Nod1 responds to peptidoglycan delivered by the Helicobacter pylori cag pathogenicity island[END_REF] , Pseudomonas aeruginosa [START_REF] Travassos | Nod1 participates in the innate immune response to Pseudomonas aeruginosa[END_REF] and S. typhimurium [START_REF] Bourhis | Role of Nod1 in mucosal dendritic cells during Salmonella pathogenicity island 1independent Salmonella enterica serovar Typhimurium infection[END_REF] .

The interleukin-17 pathway is another interesting lead. There are six IL-17 family members and five receptors. Specifically, IL-17RA and IL-17RC subunits of IL-17 receptor, which map to the Yprl3 interval (Supplementary table 1), interact with IL-17 and IL-17F to induce production of other proinflammatory cytokines, chemokines and growth factors [START_REF] Zhou | Critical role of the interleukin-17/interleukin-17 receptor axis in regulating host susceptibility to respiratory infection with Chlamydia species[END_REF] , leading to an accumulation of neutrophils at the sites of infection and inflammation [START_REF] Kolls | Interleukin-17 family members and inflammation[END_REF] . In fact, several studies have reported that IL-17R deficiency results in significant delay in neutrophil recruitment and impaired host defense against bacteria including L. monocytogenes [START_REF] Sieve | A novel IL-17-dependent mechanism of cross protection: respiratory infection with mycoplasma protects against a secondary listeria infection[END_REF] , Bacillus subtilis [START_REF] Simonian | IL-17A-expressing T cells are essential for bacterial clearance in a murine model of hypersensitivity pneumonitis[END_REF] and Klebsiella pneumoniae [START_REF] Ye | Requirement of interleukin 17 receptor signaling for lung CXC chemokine and granulocyte colony-stimulating factor expression, neutrophil recruitment, and host defense[END_REF] . Finally, Yprl3 also contains IL-23 receptor which has been shown to regulate the function of specific IL-17-producing T-cells [START_REF] Riol-Blanco | IL-23 receptor regulates unconventional IL-17-producing T cells that control bacterial infections[END_REF] . Future work will aim to narrow down the list of candidate genes by reducing the confidence intervals using congenic strains, and by searching for variations in the primary sequence or expression level of specific genes. Whatever the genes involved, it is likely that the SEG resistance alleles are gain-of-function variants, due to their dominant mode of inheritance.

The Mus spretus species diverged from Mus musculus more than 1 million years ago [START_REF] Guénet | Wild mice: an ever-increasing contribution to a popular mammalian model[END_REF] .

The genetic divergence between them at the nucleotide level is estimated to be 1 to 1.5%, the same order of magnitude seen between human and chimpanzee. Our observation of the exceptional resistance of SEG mice to Y. pestis illustrates the usefulness of Mus spretus derived strains as a source of genetic and phenotypic polymorphism [START_REF] Dejager | Thirty years of Mus spretus: a promising future[END_REF] . The fact that the differences in susceptibility to plague between B6 and SEG strains is under the control of multiple genes with additive effects stands in contrast with other infectious diseases in which single gene mutations with major effects were identified. In the case of Oas1b, a nonsense mutation was probably present in the very early founders of laboratory strains and became fixed in the absence of any selective pressure in the vast majority of these strains [START_REF] Mashimo | A nonsense mutation in the gene encoding 2'-5'-oligoadenylate synthetase/L1 isoform is associated with West Nile virus susceptibility in laboratory mice[END_REF] . This mutation has not yet been found in inbred strains derived from progenitors of different Mus musculus subspecies. In the case of plague, the highly resistant phenotype of the SEG strain results from the accumulation of several gain-of-function genetic variations, each of which provides a moderate but significant advantage in the control of Y. pestis proliferation and systemic dissemination. The acquisition of this phenotype may have resulted from selective pressure exerted by endemic exposure to Y. pestis-hosting fleas in wild rodents.

The identification of genes controlling the resistant phenotype of SEG mice will involve the creation and characterization of congenic mouse strains carrying the three genomic regions identified in this study. This will be followed by the genetic dissection of each genomic region to prioritize positional candidates for DNA sequencing and functional evaluation using loss of function alleles at these genes. At the same time, construction and characterization of bi-or tricongenic strains will aim to recapitulate the resistant phenotype observed in the Mus spretus derived SEG strain.

Materials and methods

Mice and crosses. SEG/Pas was first bred as a closed colony by François Bonhomme in Montpellier, France, from Mus spretus progenitors trapped in Spain, near Granada [START_REF] Guénet | Wild mice: an ever-increasing contribution to a popular mammalian model[END_REF] . It was later established as an inbred strain and maintained since 1995 at the Institut Pasteur. C57BL/6 (B6), FVB/NCrl, BALB/cByJ and SJL/JOrlCrl mice were purchased at 6 weeks of age from Charles River Laboratory (L'Arbresle, France). They were maintained for at least three weeks in the Institut Pasteur animal facilities prior to inoculation. CAST/Ei mice were bred at the Institut Pasteur from progenitors purchased from The Jackson Laboratory (Bar Harbor, ME). To produce B6×(SEG×B6)F1 backcross mice (BSB), SEG males were mated with B6 females and the resulting F1 females were mated with B6 males. All animal experiments were approved and conducted in accordance with the Institut Pasteur Biosafety Committee, and in compliance with French and European regulation on protection of animals used for scientific purposes. Mice were kept in isolators after inoculation. They were given food and water ad libitum and were kept at 22±2°C with alternating 12h periods of light and dark.

Culture of Yersinia pestis strains and experimental infections of mice. Experimental infections were performed using the virulent Y. pestis strains CO92 11 and 6/69 [START_REF] Buchrieser | The 102-Kilobase Unstable Region Of Yersinia Pestis Comprises a High-Pathogenicity Island Linked to a Pigmentation Segment Which Undergoes Internal Rearrangement[END_REF] . Cultures were carried out at 28°C for 48h on LB agar medium supplemented with 0.2% (W/v) hemin (LBH). Bacteria were collected and suspended in saline. Bacterial concentration was estimated by spectrometry at 600 nm (1 O.D. ~10 9 CFU/ml) and confirmed by colonyforming units (CFU) counts on LBH agar plates. Mice were injected s.c. between 8 and 12 weeks of age, in the ventral region, with a 100 µl inoculum, and were then monitored daily for 14 days.

Genotyping. Tail biopsies were collected at weaning from BSB mice and high-quality DNA was prepared by standard phenol-chloroform extraction. For BSB genotyping, 1,536 Single Nucleotide Polymorphisms (SNPs) were genotyped at the Centre National de Génotypage (Evry, France) using the Illumina GoldenGate platform. A total of 721 markers covering the entire mouse genome were polymorphic and gave reliable genotypes.

Statistical and QTL analysis. Survival curves were compared by a logrank (Mantel-Cox) test using StatView 5.0 (SAS Institute Inc, Cary NC). Survival rates were compared by Fisher's exact test. QTL analysis was performed by using the R/qtl software version 1.07-12 running under R 2.6.0 [START_REF] Broman | R/qtl: QTL mapping in experimental crosses[END_REF] . The survival rate was analyzed as a binary trait. Significance thresholds of LOD scores were estimated by 1 000 permutations of experimental data, and were 2.77 and 2.43 for 5% and 10% thresholds, respectively. Ninety-five percent confidence intervals were estimated using the bayesint() function of R/qtl. QTL analysis of mortality time in susceptible BC mice was also performed with R/qtl using a non-parametric model.

Survival, over a 14-day period, of various mouse inbred strains following s.c. inoculation with virulent 10 2 CFU of strain CO92 Y. pestis : SEG (N=69), FVB/N (N=22), BALB/cByJ (N=21), CAST/Ei (N=10), B6 (N=111) and SJL/J (N=9) females.

Figure 2

Survival curves of the B6 (N=104), SEG (N=7) and BSB (N=132) female mice that died of the Y. pestis infection. Mortality time did not differ, either in mean, or in variability, across the three groups. [START_REF] Titball | Vaccination against bubonic and pneumonic plague[END_REF] excluding anonymous cDNA sequences and predicted genes

Figure 3

 3 Figure 3QTL mapping of survival to a Y. pestis challenge in 322 BSB females,

Figure 4

 4 Figure 4Survival curves of BSB females showing the effect of the genotype at

Figure 5

 5 Figure 5Survival rate of B6, BSB and SEG females according to their haplotype

Figure 6 A

 6 Figure 6A model illustrating the additive effects of Yprl1, Yprl2 and Yprl3 on

Table 1

 1

		QTL summary
	QTL	Chr Peak position	95% C.I. (Mb)	Effect on	Nb of genes in
			(Mb)		survival	the interval (1)
	Yprl1	3	116	89 -139	20.6 %	469
	Yprl2	4	62	6 -90	20.3 %	371
	Yprl3	6	95	53 -134	20.4 %	644

Acknowledgements

CB is a recipient of a DGA (Délégation Générale pour l'Armement) fellowship. This work was supported by a grant from Aventis Pharma (Sanofi-Aventis group) and Bayer Pharma as part of a multi-organism call for proposal. The Mouse functional Genetics Unit is supported by Merck Serono. We thank Jean-Louis Guénet for his constant interest and challenging discussions. We are grateful to Colin Crist for critical reading and suggestions on the paper, to Isabelle Lanctin for careful breeding of the SEG/Pas colony, and to the CNG (Centre National de Génotypage) for the SNP genotyping of BC mice.

Supplementary information is available at Genes and Immunity's website.

Conflict of interest

The authors declare no conflict of interest.

LEGENDS TO SUPPLEMENTARY FIGURES

Supplementary figure 1 Survival, over a 14-day period, of various mouse inbred strains following s.c. inoculation with virulent Y. pestis strains CO92 or 6/69. (A) Groups of SEG females were inoculated with 10 2 (N=8), 10 3 (N=6), 10 4 (N=11), 10 5 (N=15), 10 6

(N=16) and 10 7 (N=6) CFU of strain CO92. (B) Comparison of susceptibility between male and female in B6 (N=16 and N=111, respectively) and SEG (N=54 and N=69, respectively) mice following inoculation with 10 2 CFU of strain CO92. SEG females were more resistant than males (shown in brackets; 62/69 and 37/54, respectively; p=0.005). Large groups (N>25)

are the result of pooling several experiments.

Supplementary figure 2

Comparison of susceptibility of B6 and SEG females to


C L Bassani

F A A Barbuto

Vinicius R De Almeida

J M Herri

A K Sum
email: asum@mines.edu

A Cameirão
email: cameirao@emse.fr

R E M Morales
email: rmorales@utfpr.edu.br

Coupling of a Growth Kinetic Model of Gas Hydrate Formation With Gas-(Water-in-Oil) Slug Flow

Keywords: gas-oil-water-hydrate flow, heat and mass transfer, flow assurance

This article presents the coupling of a crystallization model of gas hydrate formation to a mechanistic gas-liquid slug flow model. Crystallization of gas hydrates occurs within multiphase flow in oil and gas production operations. Mass transfer (gas absorption and convection up to the growing surface) and heat transfer (since gas hydrate formation is exothermic, thus competitive to the driving force required to hydrates to keep forming) limit crystallization under flow. The model is used to understand these competitive phenomena.

Introduction

Gas hydrates are crystals formed by the imprisonment of gas molecules inside cages made of hydrogen-bonded water molecules [START_REF] Sloan | Clathrate hydrates of natural gases, 3rd ed[END_REF]. Both multiphase flow and gas hydrate formation have been widely studied due to their application in oil and gas production operations, and to this date relevant advances in modeling and experimentation have been made. However, only recently studies coupling gas hydrate formation to multiphase flow have appeared in the literature. The interest is to understand how gas consumption and heat release due to hydrate formation affect mass, momentum and energy balances of the flow [START_REF] Bassani | A three-phase solid-liquid-gas slug flow mechanistic model coupling hydrate dispersion formation with heat and mass transfer[END_REF]; and how the thermodynamic state of the mixture and the flow interfaces influence the mass transfer process in crystal growth kinetics. Furthermore, the existing flow pattern right before gas hydrate onset affects the initial size of the particles, with consequences on the slurry stability. Pipe blockage is imminent whenever the slurry becomes unstable and settles down, what might cause flow stoppage or impairment with consequential revenue losses.

This study couples a new growth model for gas hydrate formation considering the interactions between the hydrate porous structure and the gas mass transfer process in the flow, introducing it into a mechanistic slug flow model [START_REF] Bassani | A three-phase solid-liquid-gas slug flow mechanistic model coupling hydrate dispersion formation with heat and mass transfer[END_REF].

Mathematical model

The liquid is regarded as a water-in-oil emulsion, where the gas-liquid assumes the slug flow pattern, as depicted in Figure 1(a). The droplet size is herein considered as being equal to the experiments, but in the future they can be properly estimated by models such as the Hinze-Brauner criterion [START_REF] Brauner | The prediction of dispersed flows boundaries in liquid-liquid and gas-liquid systems[END_REF]. Crystal nucleation occurs mainly on a droplet's surface, quickly trapping all the available water inside the porous structure of the hydrates, since those latter are hydrophilic [START_REF] Hirata | How liquids wet clathrate hydrates: some macroscopic observations[END_REF].

This porous structure is herein referred to as a 'sponge'. Figure 1(b) shows the path of the gas molecules up to reaching the water inside the capillaries in order to crystallize on the capillary walls. Gas solubilizes in the oil, distributes in the bulk, transfers to the outer surface of the particles and solubilizes in the water at the capillary entrance. At this point, concomitant gas diffusion through the capillary and crystallization on their walls occur. The modeling of these competitive phenomena yields the gas consumption rate per capillary Gas free phase where rc is the capillary radius; Hw and Ho are the Henry constants of gas in water and oil, respectively (given in their solubility form, units of mol/(m 3 Pa); [START_REF] Sander | Compilation of Henry's law constants (version 4.0) for water as solvent[END_REF]; Dw is the gas diffusivity in water; ki is the constant of proportionality of the crystal integration process using a 1 st order law in terms of the fugacity difference at the growing surface (related to the local concentration coming from the mass transfer process) and the three-phase gas-water-hydrate equilibrium condition (feq); kg/o is the absorption coefficient of gas into oil; Ag/o is the gas-oil interfacial surface; o  is the oil volume; Cg/o is the gas concentration at the gas-oil interface, considered as saturated (equilibrium at the interfaces),

/ g o o g C H f 
, where fg is the gas fugacity at the gaseous free phase; np is the number of particles in the system (herein considered constant); and nc is the number of particles per particle (which evolves in time as the capillaries fill up). Parameter  represents the competition of (i) mass transfer between the particle and the bulk against (ii) diffusion and crystallization resistances inside the capillary:

3/2 2 ,/ 2 4 c w c w i m p b o p w n H r D k h H r H   (3)
where ,/ m p b h is the mass transfer coefficient between the particle and the bulk (given by a Sherwood correlation for convection over spheres; [START_REF] Bird | Transport Phenomena[END_REF]; and rp is the particle radius (considered equal to the droplet prior to the onset of hydrate formation). The number of particles and their radius are considered constant over the process. Although 100% conversion of water does not influence the particle size noticeably (which grows at a ratio of 1.09 wh  

for methane hydrates), agglomeration can drastically change the number of particles and their average size as well. Agglomeration is neglected for the sake of simplification, but further coupling with proper population balance models must be done [START_REF] Herri | Methane hydrate crystallization mechanism from in-situ particle sizing[END_REF][START_REF] Sampaio | Non-isothermal population balance model of the formation and dissociation of gas hydrates[END_REF]. The gas mass consumption rate due to hydrate formation comes: , 1

g g i p c g hyd cap dm dn n n M dt dt  ( 4
)
where Mg is the molar mass of the gas. This consumption rate is used to update the superficial velocity of the phases along the pipeline:

                11 1 1 gas consumption term gas expansion/contraction 1 n n n g g n g n gU n n n Z P T dm z jj Z P T A dt L       (5)     1 water consumption term g w w n w n w g U dm M z jj A M dt L      (6)       1 hydrate formation term 1 g h h n h n h g U hyd dm M z jj A M dt L       (7)
where (n) and (n+1) indicate the nodes of the pipeline, Z is the gas compressibility factor, P is the mixture pressure, T is the mixture temperature, Mw and Mh are the molar masses of water and hydrates, respectively, 6

  is the hydration number for methane sI hydrates, and

U zL 
is the ratio between the nodal distance and the slug flow's unit cell length.

The lengths of the slug flow regions and their respective phase fractions are estimated through [START_REF] Taitel | A consistent approach for calculating pressure drop in inclined slug flow[END_REF] model, coupled with correlations for the slug flow frequency [START_REF] Schulkes | Slug frequencies revisited[END_REF], the unit cell translational velocity [START_REF] Bendiksen | An experimental investigation of the motion of long bubbles in inclined tubes[END_REF] and the gas aeration in the slug body [START_REF] Gomez | Prediction of slug liquid holdup: Horizontal to upward vertical flow[END_REF]. Pressure and temperature distributions along the pipeline are estimated as [START_REF] Bassani | A three-phase solid-liquid-gas slug flow mechanistic model coupling hydrate dispersion formation with heat and mass transfer[END_REF][START_REF] Bassani | Evaluation of the gas contribution to the momentum and energy balances for liquid-gas slug flows in high pressure scenarios using a mechanistic approach[END_REF][START_REF] Bassani | Modeling the scooping phenomenon for the heat transfer in liquid-gas horizontal slug flows[END_REF][START_REF] Taitel | A consistent approach for calculating pressure drop in inclined slug flow[END_REF]:

      bubble film G-L interface
friction in the friction in the elongated buble region slug region 2 1 head loss in the elongated bubble r 2

LB LB GB GB i i LS LS S B UU LB T L nn U S S S SL L A L A L UU P P K L                     slug region weight ear elongated bubble region weight cos cos S L LS G GS U B L LB G GB U L R R g z L L R R g L                              (8)     1 exp nn p p n T T z n n m                   (9)
, sensible heat

m P m U T m c AL U   (10)   gas expansivity G GU Gz U G dP n q m m L dz      (11)
 

heat release due to gas hydrate formation film slug elongated bubble gas-liquid interface vi

g W hyd G hyd LS LS S LS LB LB B LB GB GB B GB i i B GB LB dn p qT E M dt S L U S L U S L U S L U U                  scous dissipation (12)   elongated bubble slug film ,,
heat exchange between two consecutive unit cells heat exchange with pipeline wall

GB GB B LB LB B LS LS S Lz P L Gz P G q h S L h S L h S L m c m c           (13) ,, exp exp LB LB B GB GB B LS LS S mB P m mS P m h S L h S L h S L c AJ c AJ                       ( 14
)
where L is the length of the slug flow regions; U is the actual velocity of the phase inside each region, with related wetted surface S, shear stress  and heat transfer coeffi- cient h; TW is the wall temperature; hyd E  is the enthalpy of formation of gas hydrates; UT is the unit cell translational velocity; and J is the mixture superficial velocity. Indexes are 'B' for elongated bubble, 'S' for slug, 'U' for slug flow unit cell, 'G' for gas phase, 'L' for liquid phase (dispersion of water-in-oil or hydrate-in-oil) and 'i' for gas-liquid interface. The liquid properties take the hydrate fraction after hydrate formation onset into account by assuming a homogeneous model. The slurry viscosity is the exception, computed through [START_REF] Krieger | A mechanism for non-newtonian flow in suspensions of rigid spheres[END_REF].

Experiments and model validation

Validation of the slug flow model against experimental data in lab conditions was already published in previous articles [START_REF] Bassani | A three-phase solid-liquid-gas slug flow mechanistic model coupling hydrate dispersion formation with heat and mass transfer[END_REF][START_REF] Bassani | Modeling the scooping phenomenon for the heat transfer in liquid-gas horizontal slug flows[END_REF]. The following maximum percentage deviations were found: (i) ±15% for the temperature gradient; (ii) ±20% for the pressure gradient, for the gas fraction in the elongated bubble and for the lengths of the unit cell and the elongated bubble; (iii) ±35% for the mixture heat transfer coefficient; and (iv) ±60% for the slug length. The kinetic model needs curve fitting of two parameters: the birth-to-death ratio of capillaries ( c  ) and an overall efficiency of the kinetic model ( p  , which multiplies the RHS of Eq. ( 4)). The latter is interpreted as the amount of particles that actually interact with the system on consuming gas for crystallization. Furthermore, p  'corrects' any inconsistency in the order of magnitude of the closure parameters chosen from literature, since exact values of some of the micro-scale closure parameters are not available in literature. As an example, the constant of proportionality of the crystal integration process presents a range of 5 orders of magnitude in literature for methane hydrates   [START_REF] Al-Otaibi | Kinetic studies of gas hydrate formation using in situ particles size analysis and Raman spectroscopy[END_REF][START_REF] Englezos | Kinetics of formation of methane and ethane gas hydrates[END_REF][START_REF] Sharma | Gas hydrate particle size measurements[END_REF]. Furthermore, parameters such as the initial surface porosity and the capillary radius were found only for permafrost hydrates [START_REF] Klapp | Grain size measurements of natural gas hydrates[END_REF].

Table 1 presents the parameters used to fit the model curve against experimental data measured with the flowloop described in [START_REF] Melchuna | Topological modeling of methane hydrate crystallization from low to high water cut emulsion systems[END_REF]. The main modification in the flowloop was the introduction of a sapphire window to estimate the droplet size before the onset of hydrate formation with High Speed Imaging.

Figure 2 presents the comparison of the molar amount of gas consumed in time predicted by the model with the experimental data. The model is capable of predicting the asymptote of gas consumption due to the evolution of the porosity in time, commonly called mass transfer limitation process.

Figure 3 presents photographs of the water-in-oil dispersion flow before hydrate formation and 10 s after that. The hypothesis that all droplets convert almost instantly to hydrates is valid. However, the model needs to be extended to consider agglomeration, since much larger particles then the prior droplets appear. Furthermore, the water-in-oil dispersion flow is dense, thus the bulk existence hypothesis of the model is probably not valid for the whole mixture volume. We are currently working on the experimental data and further curve fitting of the kinetic model shall be presented in literature in a near future.

Results and discussions

The model for gas hydrate formation inside slug flow is used to understand heat and mass transfer limitations on hydrate growth kinetics.

Table 2 presents the input parameters for the model evaluation. The overall efficiency (small in the validation case, but probably higher once a free gaseous phase is introduced), was varied in order to capture different orders of magnitude of mass transfer limitation. Since the kinetic model is not yet fully validated, only trends are analyzed. (I) Heat transfer limited case (magenta line with stars): in this case, the external medium cannot absorb all the heat released due to gas hydrate formation and therefore the mixture reheats towards the equilibrium temperature, achieving a nearly constant subcooling (Figure 4(a)). This reheating causes the supersaturation in the capillaries to decrease (Figure 4(b)) due to: (i) increase in the three-phase hydrate-water-gas equilibrium fugacity related to the system temperature increase; and (ii) decrease in the solubility of gas inside water at higher temperatures (that is, lower solubilization in oil-water interface). With a shorter gas supply, the capillary filling-up rate decreases and the porosity shows a slower decrease (Figure 4(c)), and therefore the growth process lasts longer. The hydrate formation rate is nearly constant in the heat transfer limited system, and therefore the water conversion rate grows linearly (Figure 4(d)). (II) Mass transfer limited cases (red line with crosses and orange line with squares): the heat exchange between the mixture and the outer medium is enough to dissipate all the heat released due to hydrate formation and to continue to cool the mixture down further still (Figure 4(a)). Since the driving force is kept high, a considerable supersaturation is supplied in the capillaries (Figure 4 ). As a rule-of-thumb, one can say that heat transfer would mostly limit the growth process in the beginning of gas hydrate formation, where heat release is higher due to the presence of higher hydrate porosities. With time, the porous structure fills up and the process starts to be mass transfer-limited. This can be seen in the water conversion (Figure 4(d)), which presents a linear trend (heat transfer-limited, from 0.5 to ~ 1 km) that changes to a curved trend (mass transfer-limited, from ~1 to 2 km).

Conclusions

A new kinetic model for gas hydrate formation in water-in-oil dispersion flows was coupled to a slug flow mechanistic model. The kinetic model was compared to preliminary experiments of gas hydrate formation over water-in-oil dispersion flow with dissolved gas, which points to the necessity of further improvements in modeling the agglomeration process, in enhancing the knowledge of micro-scale parameters of the model (crystal integration process and porous structure). By analysis of the model trend behavior, competitive heat extraction from the pipeline and heat release due to the exothermic nature of gas hydrate formation cause a heat transfer limitation process in the crystallization. With heat transfer limitation, the hydrate structure remains 'porous' for a longer time due to lower supersaturations at the growing surface. Therefore, the water tends to have a higher conversion rate for the heat transfer-limited case.

Figure 1 .

 1 Figure 1. (a) Gas-(water-in-oil) slug flow gives rise to hydrate particles with size similar to the water droplets. (b) Gas mass transfer process up to the capillary walls where crystallization occurs.

Figure 2 :

 2 Figure 2: Model trend validation against experimental results for the molar amount of gas consumed over time.

Figure 3 .

 3 Figure 3. High Speed Imaging photos of: (a) the water-oil emulsion flow before the onset of hydrate formation and (b) 10 s after hydrates onset.

Figure 4

 4 Figure 4 presents the sensitivity of the model to different overall efficiencies of the kinetic model. The dimensionless supersaturation at the capillary entrance is defined as the driving force divided by the equilibrium condition,   ,, out w out w w eq w eq C C H f H f  (Figure 4(b)). Also, since an open system was simulated (differently from the closed flowloop system used to validate the kinetic model), we adhere to the analysis of the water conversion instead of the amount of gas consumed (Figure 4(d)). The trends of Figure 4 can be split into:

Figure 4 .

 4 Figure 4. Evaluation for different overall efficiency of the kinetic model showing heat and mass transfer limitations. Distributions along the pipeline of: (a) mixture temperature, (b) surface porosity of the particles, (c) dimensionless supersaturation at capillary entrance, and (d) water conversion.

  (b)) and the porous structure fills up faster(Figure 4(c)). As the porosity drops down, the gas consumption rate decreases and the water conversion presents an asymptote (zoom within Figure4(d)).(III) Competitive heat and mass transfer limitations (green line with diamonds and blue line with triangles): the heat exchange from the mixture to the outer medium dissipates part of the heat released due to hydrate formation, but cannot keep cooling the mixture down (Figure4(a)). The more the mixture reheats, the lower the driving force and the lower the supersaturation in the capillary (Figure4(b)), incurring in a lower decrease in porosity (Figure4(c)). When the porous structure starts to fill up, the amount of hydrate formation decreases, with a consequent decrease in heat release. Therefore, the mixture starts to cool down again (Figure4(a)), thus increasing supersaturation in the capillaries(Figure 4(b)

Table 1 .

 1 Characteristics of the experiments for methane hydrate formation in a flowloop following the method presented in[START_REF] Melchuna | Topological modeling of methane hydrate crystallization from low to high water cut emulsion systems[END_REF].

	Fluids	Dissolved Methane / Kerdane /
		Deionized water
	Pipeline internal diameter	10.2 mm
	Flowloop extensions	30 m -4 o declined section
		(rolled, curves of 60D)
		10 m upward vertical section
		8 m downward vertical section
	Mixture temperature	278 K
	Mixture pressure	80 bar
	Mixture velocity	0.68 m/s
	Water cut	32.25 %
	Volume of mixture inside	10 L
	flowloop
	Droplet diameter before	0.8 -4 mm, average diameter of
	hydrates onset	2 mm (High Speed Imaging)
	Crystal integration con-stant (Al-Otaibi, 2009)	k	i		8 10 	8 	2 mol m sPa
	Absorption coefficient (Herri et al., 1999; Melchuna, 2016)	b // g b g b kA 	1 10 	21 s 
	Kerdane properties (Total, 2015)	H	o	2.7 10 	4 	3 mol	(80 bar,
											m Pa
		5 o C)
		 	3 815 kg m
			o
				3 2 10 Pa.s  	(Newtonian
			o
		behavior, measured in rheome-
		ter at 4 o C, 1 bar)
	Methane hydrate proper-ties (Jung et al., 2010; Sloan and Koh, 2008)	h   E 	3 kg m 53 10 J/mol 917 3  
					hyd
		M	h	17.7 10 	3 kg mol 	;	 	6
	Initial porosity and capil-lary radius (Klapp et al.,		sup, in		15%		;	c r		350	nm
	2010)
	Birth-to-death ratio of	1	6  8 10    
	capillaries (curve fitted)					c
	Overall efficiency of the						2.65 10	3
	model (curve fitted)

p   

Table 2 .

 2 Input parameters for model evaluation.

	Pipeline length / ID / width	2 km / 26 mm / 1 mm
	Pipeline inclination	Horizontal
	Pipeline conductivity	30 W/(m.K)
	Gas superficial velocity	1 m/s
	Liquid superficial velocity	1 m/s
	Water cut	30%
	Fluids	CH4 / H2O / Kerdane
	Pressure at the inlet	100 bar
	Temperature at the inlet	288 K
	External medium temperature	277 K
	External medium heat transfer	100 W/(m 2 K)
	coefficient

Acknowledgements

The authors acknowledge the financial support of Région AURA Auvergne Rhône-Alpes through the project COOPERA FluEnergy, the Institut Mines-Télécom, the Coordination for the Improvement of Higher Education Personnel -Brazil (CAPES) -Finance Code 001, and TE/CENPES/PETROBRAS (5850.0103370.17.9). The authors acknowledge the technical support of M.Sc. Rafael Fabrício Alves with High Speed Imaging.