P Aeruginosa

Laura Camus

Paul Briaud

Sylvère Bastien

Sylvie Elsen

Anne Doléans- Jordheim

François Vandenesch

Karen Moreau
email: karen.moreau@univ-lyon1.fr

Trophic cooperation promotes bacterial survival of Staphylococcus aureus and Pseudomonas aeruginosa

In the context of infection, Pseudomonas aeruginosa and Staphylococcus aureus are frequently coisolated, particularly in cystic fibrosis (CF) patients. Within lungs, the two pathogens exhibit a range of competitive and coexisting interactions. In the present study, we explored the impact of S. aureus on P. aeruginosa physiology in the context of coexistence. Transcriptomic analyses showed that S. aureus affects significantly and specifically the expression of numerous genes involved in P. aeruginosa carbon and amino acid metabolism. In particular, 65% of the strains presented an important overexpression of the genes involved in the acetoin catabolic (aco) pathway. We demonstrated that acetoin is (i) produced by clinical S. aureus strains, (ii) detected in sputa from CF patients and (iii) involved in P. aeruginosa's aco system induction. Furthermore, acetoin is catabolized by P. aeruginosa, a metabolic way that improves the survival of both pathogens by providing a new carbon source for P. aeruginosa and avoiding toxic accumulation of acetoin on S. aureus. Due to its beneficial effects on both bacteria, acetoin catabolism could testify to the establishment of trophic cooperation between S. aureus and P. aeruginosa in the CF lung environment, promoting their persistence.

Introduction

Infectious sites constitute rich microbial ecosystems shared by a large diversity of microorganisms, including the native microbiota and pathogens. Lungs of Cystic Fibrosis (CF) patients are a well-known example of this microbial richness as they gather more than 60 genera of bacteria (1,2). Such density of microorganisms promotes their interactions, themselves modeling their biological activities and their environment (3,4). However, microbial interactions are dynamic and range from antagonism to cooperation according to species and environmental conditions (5). For instance, the opportunistic pathogen Pseudomonas aeruginosa is well-known for its competitiveness in various ecosystems thanks to many quorum-sensing-mediated factors such as phenazines, rhamnolipids or type 6 secretion system (6). P. aeruginosa thus can alter growth, biofilm formation or respiration of yeasts, fungi, Gram-negative and -positive bacteria (6). Among them, Staphylococcus aureus is particularly sensitive to P. aeruginosa virulence factors and these can directly lyse staphylococci (7).

This competitive interaction between P. aeruginosa and S. aureus is observed for environmental but also clinical strains as both pathogens are frequently co-isolated from wound and CF lung samples (7,8). Until recently, the anti-staphylococcal behavior of P. aeruginosa was the only one observed between the two species and was thus extensively described (7). In the context of CF lung infections, this competitive interaction is highlighted by the decreased S. aureus prevalence as P. aeruginosa colonizes lungs during adolescence (9). However, Baldan et al. first noted that a non-competitive state between P. aeruginosa and S. aureus could establish during the development of CF chronic infections (10), calling into question the antagonistic model between the two pathogens.

The establishment of this particular non-competitive state between P. aeruginosa and S. aureus seems to be linked to P. aeruginosa adaptation to the pulmonary ecosystem. In fact, selective pressures present in CF lung environment, such as host immune system or antibiotic treatments, drive P. aeruginosa isolates towards a low-virulent but high-resistant state (11)(12)(13)(14). Major virulence factors involved in quorum-sensing or motility are often mutated in P. aeruginosa chronic infection isolates, inducing a decrease of anti-staphylococcal factors production and then a non-competitive interaction (15). In addition, a rewiring of metabolism networks and a decrease of its catabolic repertoire also accompany P. aeruginosa adaptation to CF environment. This trophic specialization commonly leads to a slowed growth of chronic isolates and thus a reduced competitive behavior towards shared resources (16). Several independent studies thus observed this coexistence state between S. aureus and P. aeruginosa isolated from chronic infections (10,15,17,18). Briaud et al. recently demonstrated that this interaction pattern appears to be more frequent than expected. Indeed, among the quarter of CF patients co-infected by both pathogens, 65% were infected by a coexisting S. aureus-P. aeruginosa pair (18,19). Recent studies show that coexistence between P. aeruginosa and S. aureus could promote their persistence throughout establishment of cooperative interaction. In these conditions, coexisting bacteria demonstrated an increased tolerance to antibiotics: to tobramycin and tetracycline for S. aureus and to gentamicin for P. aeruginosa; this appeared to be related to the induction of small colony variants (15,17,18,20). However, the effects of coexistence on bacterial general physiology, and not only virulence-associated traits, have not been explored yet. Despite its significance in infectious ecosystem, coexistence between P. aeruginosa and S. aureus remains thus poorly understood.

Using global and targeted transcriptomic approaches, we evaluated the impact of S. aureus presence on P. aeruginosa gene expression on a set of clinical pairs of strains isolated from CF coinfected patients. Coexistence with S. aureus induced the overexpression of many genes involved in utilization of alternative carbon sources in P. aeruginosa, such as amino acids and acetoin. Acetoin was shown to be produced by clinical S. aureus isolates in vitro and in CF sputum, and catabolized by P. aeruginosa. The beneficial effects of acetoin catabolism on both bacteria during their interaction highlight a trophic cooperation between P. aeruginosa and S. aureus in CF lung infections.

Materials and Methods

Bacterial strains

Bacterial strains and plasmids used in this study are listed in Table S1 andS2. CF clinical strains were isolated by the Infectious Agents Institute (IAI) from sputa of patients monitored in the two CF centers of Lyon hospitals (Hospices Civils de Lyon (HCL)). S. aureus and P. aeruginosa strains were isolated from patients co-infected by both bacteria. Each strain pair indicated in Table S1 was recovered from a single sample, obtained from different patients in most cases as indicated in Table S1. All the methods were carried out in accordance with relevant French guidelines and regulations. This study was submitted to the Ethics Committee of the HCL and registered under CNIL No 17-216. All patients were informed of the study and consented to the use of their data.

As schematized in Figure S1A, interaction state was determined for each pair by growth inhibition tests on Tryptic Soy Agar (TSA) and in liquid cultures (18). As previously described, coexistence was characterized by: (i) an absence of inhibition halo on agar tests, and (ii) a similar growth in mono and co-culture during an 8 hours (18).

The knock-out ΔacoR and Δaco mutants were generated in P. aeruginosa PA2600 strain via allelic exchange thanks to suicide plasmids pEXG2ΔacoR and pEXG2Δaco constructed as described previously (21,22). Gentamicin (Euromedex) was used at final concentrations of 50µg/ml. Detailed protocols are given in supplementary data.

Cultures conditions

Strains were grown in monoculture or co-culture in Brain-Heart Infusion (BHI) as described by Briaud et al. (18). Briefly, S. aureus, P. aeruginosa, Burkholderia cenocepacia, Stenotrophomonas maltophilia and Bacillus subtilis overnight precultures were diluted to OD600 of 0.1 in BHI and grown 2h30 at 37°C and 200rpm. Cultures were then diluted to OD600 of 2 in fresh medium and 10ml were mixed with 10ml BHI for monocultures. Co-cultures were performed by mixing 10ml of P. aeruginosa suspension with 10ml of S. aureus, B. cenocepacia, S. maltophilia or B. subtilis suspension. For supernatant exposure, 10ml of S. aureus supernatant from a 4-hours culture were filtered on 0.22µM filter and added to 10ml of P. aeruginosa suspension. Cultures were grown for 8 hours at 200rpm and 37°C for transcriptomic studies. Long-term survival assays were performed by extending incubation time of S. aureus and P. aeruginosa mono-and co-cultures up to five days. Plating at day 0, 3 and 5 were performed on mannitol salt agar (MSA, BBL TM Difco) and cetrimide (Difco TM ) for S. aureus or P. aeruginosa counts, respectively. For growth monitoring in presence of acetoin, minimal medium M63 (76mM (NH4)2SO4, 500mM KH2PO4, 9µM Fe.SO4.7H2O, 1mM MgSO4.7H2O) was inoculated with P. aeruginosa to OD600 of 0.1 and incubated for 25h at 37°C and 200rpm. Every two hours during 10 hours and at t=24h, acetoin was added to obtain a final concentration of 1.5mM in the culture. Plating on TSA (Tryptic Soy Agar) was performed at t=0, one hour after each acetoin addition and at t=24h.

Genome sequencing and annotation

Genome sequencing and annotation of PA2596 and PA2600 strains were performed as previously described (18). In order to compare CDS from PA2596 and PA2600, PAO1 strain (NC_002745.2) was used as a reference. Protein sequences were compared and grouped using a similarity threshold of 95% through Roary (V3.8.2) (23). Gene names and numbers were gathered from PAO1 and used as ID tag for common genes. For non-common genes, CDS from PA2596 and PA2600 were tagged with a specific name (gene number and name recovered from UniprotKB database).

Functional classification was performed using KEGG database and by manual literature check of each gene function. The complete genome sequences for the PA2596 and PA2600 strains have been deposited in GenBank under the accession number GCA_009650455.1 and GCA_009650545.1.

Transcriptomic analysis

Figure S1 schematizes the global methodology used for transcriptomic analysis. RNAseq analysis was performed on four pairs: the patient-specific pairs SA2597/PA2596 (competitive) and SA2599/PA2600 (coexisting), and the crossed pairs SA2599/PA2596 (competitive) and SA2597/PA2600 (coexisting). RNA extraction, cDNA libraries preparation and sequencing and reads treatment were conducted as previously described (18). Gene expression was considered as dysregulated when: (i) the fold change between co-culture and monoculture was at least 4-fold with an adjusted P-value<0.05, (ii) the dysregulation was observed in the two pairs of strains with the same interaction state, (iii) the dysregulation was specific to either coexistence or competition state. RNAseq data that support our findings are available in the SRAdatabase under the BioprojectID: PRJNA562449, PRJNA562453, PRJNA554085, PRJNA552786, PRJNA554237, PRJNA554233.

Confirmation of gene expression was achieved by RT-qPCR as previously described on 14 or 21 coexisting pairs including the SA2599/PA2600 couple used in RNAseq experiment (Fig. S1) (18).

Housekeeping genes gyrB and rpoD were used as endogenous control. Table S3 lists primers used and target genes.

Acetoin and glucose dosages

Acetoin was quantified using modified Voges-Proskauer test (24) optimized in 96-well microplates. To 50µL of culture supernatant, 35µL of creatine (0.5% m/v, Sigma), 50µL of α-naphtol (5% m/v, Sigma) and 50µL of KOH (40% m/v, Sigma) were sequentially added. The mix was incubated 15 minutes at room temperature and optical density at 560nm was read using spectrophometry (Tecan Infinite Pro2000, Tecan-Switzerland). Glucose dosages were performed with glucose (Trinder, GOPOD) assay kit (LIBIOS) in microplates. 185µL of dosage reagent were added to 5µL of culture supernatant and incubated at 37°C for 5 minutes. Optical density at 540nm was measured. Acetoin and glucose standard (Sigma) were performed in water, BHI or M63 according to experiment.

Statistical analysis

Statistical analyses were performed using Prism GraphPad 8.0 software (San Diego, CA).

Differences in gene expression fold change and bacterial survival were studied using one-way ANOVA with Dunnett's or Tukey's post-test comparisons, as specified in corresponding figures. Median acetoin and glucose concentrations were compared through Mann-Whitney test or Kruskall-Wallis test with Dunn's correction when appropriate. Differences were considered significant when P-values were lower or equal to 0.05.

Results

P. aeruginosa transcriptome is affected by S. aureus presence

We studied the genetic expression of P. aeruginosa in absence or presence of S. aureus in two contexts: when P. aeruginosa and S. aureus were in competition or when they were in coexistence. We thus performed RNAseq analyses using a competitive strain pair (SA2597/PA2596) and a coexisting one (SA2599/PA2600). Each pair was recovered from a single sample of a co-infected CF patient (Table S1). As nature of interaction is solely led by P. aeruginosa (18), the pairs were crossed to study gene expression in additional competitive (SA2599/PA2596) and coexisting (SA2597/PA2600) pairs. Transcriptomic effect was therefore evaluated during co-cultures of two competitive and two coexisting strain pairs (Fig. S1). P. aeruginosa gene expression was considered dysregulated when dysregulation was common to both co-cultures in comparison to monoculture. Each dysregulated gene was then associated to a functional class thanks to a KEGG analysis (Fig. 1A, Tables S4 andS5).

Sixty-eight P. aeruginosa genes were dysregulated in co-culture in the context of competition, with a majority of down-regulated genes (79.4%, Fig. 1A). Fifteen genes involved in nitrogen metabolism and 19 genes involved in iron metabolism were down-regulated, making these two functional classes the most affected in competition. Among these genes, the nir and nos systems involved in denitrification but also genes implicated in iron uptake and transport (isc and fec genes) were down-regulated (Table S4). Other functional classes were less affected, as only 4 genes linked to carbon and amino acids metabolism (bauA, ddaR, gntK, arcD) and 3 genes encoding membrane and virulence factors (rfaD, PA2412, cdrA) were dysregulated in presence of S. aureus.

More genes were affected during coexistence interaction, as a dysregulation of 105 genes was observed in P. aeruginosa (Fig. 1A). In spite of a trend of up-regulation (56.4% of genes), we could notice the down-regulation of 11 genes involved in nitrogen metabolism. Among these, 8 were also down-regulated in the context of competition, especially genes from the nir system. We thus can presume that the down-regulation of nir genes is not specific to coexistence or competition interaction states. Conversely, the dysregulations of iron metabolism related genes appeared to be specific to competition strains, as only one gene (fhp) of this functional class was down-regulated in coexistence.

However, coexistence specifically affected numerous genes belonging to functional classes of carbon and amino acids metabolism (18 and 23 genes) and membrane and virulence factors (15 genes).

Concerning this last class, a trend towards lower expression was observed and probably due to the down-regulation of membrane associated factors as the flp-tad system (flp, tad and rcpC genes encoding Flp pilus) and the PA1874-1876 operon (encoding an efflux pump) (Table S5).

The most affected classes in coexistence with S. aureus were related to P. aeruginosa energetic metabolism (Fig. S2). We observed a down-regulation of genes coding for major pentose phosphate pathway enzymes, as the gluconokinase GntK, its regulator GntR and the operon zwf-edaA (PA3183-PA3181) encoding a glucose-6-phosphate 1-dehydrogenase, a 6-phosphogluconolactonase and a 2keto-3-deoxy-6-phosphogluconate aldolase (25). We also noticed the down-regulation of 5 other genes clustered near to this operon and involved in the same pathway (edd and gapA genes) or glucose transport (gltB, gltF and gltK) (25,26).

In contrast, an up-regulation of numerous genes involved in the utilization of alternative carbon sources as butanoate and amino acids was observed. The aco system, comprising the operon PA4148-PA4153 and the gene encoding its transcriptional regulator acoR (PA4147), was thus up-regulated in P. aeruginosa coexisting with S. aureus. This system has been described in P. aeruginosa PAO1 to be responsible for 2,3-butanediol and acetoin catabolism (27). According to KEGG analysis, the upregulated genes acsA (PA0887), PA2555 (acs family) and hdhA (PA4022) are also involved in the butanoate pathway and energy production from 2,3-butanediol and acetoin, as their products catalyse the production of acetyl-coA from acetaldehyde and acetate (Fig. S2). Finally, 23 genes implicated in amino acids metabolism were up-regulated in P. aeruginosa in presence of S. aureus. Most of them were linked to the catabolism of several amino acids (Fig. S2). We can especially notice the liu operon (PA2015-PA2012), the mmsAB operon (PA3569-PA3570) and the hut gene system (PA5097-PA5100), involved in leucine, valine and histidine catabolism, respectively.

In order to confirm these transcriptomic effects, we co-cultivated a set of P. aeruginosa-S. aureus coexistence CF pairs and performed RT-qPCR to evaluate P. aeruginosa gene expression in presence of S. aureus (Fig. 1B). Each pair was isolated from a single sputum. Twenty-six genes were tested, including 19 identified as dysregulated during RNAseq analysis and belonging to the most impacted categories, ie. carbon and amino acids metabolism, and membrane and virulence factors.

Most of the genes were tested in a total of 14 P. aeruginosa-S. aureus pairs; expression of four of these genes was assessed in seven additional pairs to confirm the observed dysregulations. The different P. aeruginosa strains have shown very different transcriptomic patterns during co-cultivation with S. aureus, especially for membrane-associated and virulence factor genes. We noticed an overexpression of rcpC, tadA, tadG and flp from the flp-tad system from 52.4% to 35.7% of the P. aeruginosa strains. We also tested 7 additional genes encoding virulence factors previously described as involved in P. aeruginosa interaction with S. aureus as las, rhl, pch and pvd genes (7). Regarding these last genes, no clear effect of S. aureus co-cultivation was observed.

However, clearer transcriptomic patterns were observed for genes linked to carbon and amino acids metabolism, the two most impacted gene classes during RNAseq experiment (Fig. 1B). We confirmed the up-regulation of liuA gene in 78.6% (11/14) of P. aeruginosa strains co-cultivated with S. aureus. We also confirmed the down-regulation of glucose metabolism genes in a high proportion of strains, ranging from 92.9% (13/14) for zwf, gltF and edd genes to 71.4% (10/14) for gntK gene. Finally, the up-regulation of genes involved in butanoate metabolism was confirmed for acoR (57.2%, 12/21), PA4148 (66.7%, 14/21), acoB (57.1%, 8/14) and PA4153 (64.3%, 9/14), suggesting an impact of coculture on the whole aco system in P. aeruginosa. In view of these results, we focused our study on four genes: liuA and zwf, respectively involved in leucine and glucose catabolism, PA4148, first gene of the aco operon and acoR, both responsible for acetoin catabolism.

P. aeruginosa aco system is induced by S. aureus acetoin

In order to determine if the transcriptomic dysregulations of acoR, PA4148, liuA and zwf in P. aeruginosa PA2600 are specific to interaction with S. aureus, we tested the effect of three other bacterial species: B. cenocepacia and S. maltophilia as they are sometimes associated with P. aeruginosa in CF patients and Bacillus subtilis as it produces high amount of acetoin (28). Dosages in B. cenocepacia and S. maltophilia monocultures confirmed that these bacteria do not produce acetoin (Fig. S3) as previously described (29)(30)(31). We observed a down-regulation of P. aeruginosa zwf gene expression in all co-cultures in comparison to monocultures (Fig. 2A). Regarding aco system genes (acoR and PA4148) and liuA gene, only B. subtilis induced similar levels of overexpression than S. aureus SA2599. We thus hypothesized that acetoin, produced by these two species during our experiment (Fig. S3), may be the inductor signal for these genes during co-culture with S. aureus.

In order to test this hypothesis, we first explored whether an inductor signal was present in the supernatant of S. aureus culture. We indeed observed an overexpression of acoR and PA4148 when P. aeruginosa PA2600 was cultivated in S. aureus SA2599 culture supernatant, as well as the downexpression of zwf but to a lesser extent in comparison to co-culture (Fig. S4). On the contrary, we did not observe overexpression of liuA gene, suggesting that this effect is not due to acetoin and requires the presence of S. aureus cells. Secondly, we cultivated P. aeruginosa PA2600 in presence of S. aureus UAMS-1 WT supernatant or its ΔalsSD derivative defective in acetoin synthesis [START_REF] Tsang | Factors Contributing to the Biofilm-Deficient Phenotype of Staphylococcus aureus sarA Mutants[END_REF]. Supernatant of wild-type UAMS-1 strain induced same transcriptomic patterns on P. aeruginosa as those obtained with CF SA2599 strain (Fig. S4). In presence of UAMS-1 ΔalsSD supernatant, overexpression of aco genes was almost totally abolished (Fig. 2B). However, acetoin addition to this supernatant restored this overexpression in a dose-dependent manner but with threshold effects between 0.375mM and 1mM of acetoin (Fig. 2B). This indicates that induction through acetoin is one of the mechanisms involved in aco system overexpression in P. aeruginosa. According to this experiment, zwf gene down-regulation did not seem to be mediated by acetoin.

Coexisting isolates of S. aureus and P. aeruginosa efficiently metabolize acetoin

As the aco system is involved in acetoin catabolism in P. aeruginosa (27) and S. aureus produces this molecule (27,28), we hypothesized that P. aeruginosa could catabolize S. aureus acetoin.

To explore this hypothesis, we monitored acetoin concentration during mono-and co-cultures of three pairs of strains: SA2599/PA2600 (Fig. 3A), SA146/PA146 and SA153/PA153A (Fig. S5A andB). P. aeruginosa strains did not produce acetoin, but an acetoin accumulation up to 1.3mM was observed in S. aureus monocultures. Interestingly, a reduction of acetoin accumulation of at least 30% was observed when S. aureus was co-cultivated with P. aeruginosa, in comparison to S. aureus monoculture. The same trend could be observed in CF patient sputa, as a higher acetoin concentration was detected in sputa from S. aureus mono-infected patients (n=9) in comparison to sputa from S. aureus-P. aeruginosa co-infected patients (n=11) (Fig. S6). This effect could be due to a downregulation of S. aureus acetoin biosynthesis, or an acetoin catabolism in co-culture. Growth of P. aeruginosa PA2600 in S. aureus SA2599 supernatant containing acetoin actually led to a reduction of acetoin concentration, demonstrating the ability of P. aeruginosa to catabolize acetoin (Fig. 3B). This ability was confirmed for the two other strains PA146 and PA153A when grown in supernatant of SA146 and SA153, respectively (Fig. S5C andD). We also noted that acetoin catabolism started after glucose depletion in the supernatant and could be delayed by glucose addition (Fig. 3B). This suggests that P. aeruginosa uses acetoin as an alternative carbon source in absence of easily available substrates such as glucose. The early glucose depletion observed during co-culture supports this hypothesis (Fig. 3A).

In order to test if this acetoin metabolism was specific to interaction state between S. aureus and P. aeruginosa, we evaluated acetoin production and catabolism for 12 couples of competition and 12 couples of coexistence (Table S1). Cultivated in P. aeruginosa supernatant, S. aureus strains from coexisting pairs were able to produce 4-times more acetoin (230µM) than strains from competitive pairs (60µM) (Fig. 4A). Such distinction was not observed during culture in rich medium (Fig. S7). Regarding P. aeruginosa, we cultivated the sets of competitive and coexisting P. aeruginosa strains in SA2599 supernatant and monitored acetoin catabolism (Fig. 4B). Both competitive and coexisting strains catabolized acetoin since we observed a decrease in acetoin concentration for both groups. However, coexisting strains showed an increased catabolism efficiency. Indeed, this group catabolized 98.6% of acetoin after 4 hours of culture, while competitive strains catabolized only 47% of acetoin. This increased efficiency of acetoin production and catabolism for coexisting strains could not be explained by a difference in glucose utilization between competition and coexistence strains as both groups catabolized glucose with the same efficiency (Fig. S8). Acetoin production by S. aureus and catabolism by P. aeruginosa therefore seem to be more efficient in isolates from coexisting couples.

Acetoin catabolism by P. aeruginosa increases survival rates of both pathogens in co-culture

As P. aeruginosa catabolizes acetoin when medium is glucose-depleted, we tested the effect of acetoin on PA2600 growth in minimal medium M63 (containing no glucose or amino acids) supplemented with 1.5mM acetoin every 2 hours (Fig. 5). P. aeruginosa was able to grow up to 1.6×10 9 CFU/ml after 24h of culture with acetoin as sole carbon source while PA2600 ΔacoR and Δaco mutants grew significantly less, reaching a maximum cell concentration of 1.5×10 8 UFC/ml at 24h (Fig. 5A). In parallel, we quantified acetoin concentration. We observed an accumulation of acetoin all along the experiment in presence of PA2600 ΔacoR and Δaco mutants. For WT strain, the accumulation of acetoin reached its maximum at 5h of culture and afterwards slowly decreased to reach undetectable values at 10h of culture, demonstrating the consumption of acetoin in such conditions (Fig. 5B). A delay of 3h between the start of acetoin catabolism and the growth augmentation of WT strain was noticed, and might be due to metabolism adaptation. Acetoin catabolism nonetheless promoted a 10-fold increased growth of P. aeruginosa during extended culture in glucose depleted medium.

In order to assess the impact of acetoin catabolism on survival of both pathogens, we cocultivated P. aeruginosa PA2600, ΔacoR and Δaco mutants with S. aureus SA2599. As S. aureus was not able to grow in M63 poor medium and acetoin affects its long term survival [START_REF] Chaudhari | The LysR-type transcriptional regulator, CidR, regulates stationary phase cell death in Staphylococcus aureus: Metabolic control of cell death in S. aureus[END_REF][START_REF] Thomas | A Central Role for Carbon-Overflow Pathways in the Modulation of Bacterial Cell Death[END_REF], we performed a long term culture (5 days) in BHI medium. We determined the survival rate of S. aureus co-cultivated with P. aeruginosa in comparison to monoculture (Fig. 6A). Co-culture with the WT strain of P. aeruginosa induced a S. aureus survival rate of 4.7×10 -1 after 3 days of culture and of 5.1×10 -3 after 5 days. S. aureus survival thus appears to be highly affected by long-term co-culture with P. aeruginosa, even if the strains stably coexist during shorter spans of culture (18). Interaction state with S. aureus thus seems to rely on nutritional conditions, a fact already observed elsewhere [START_REF] Miller | Global transcriptome responses including small RNAs during mixed-species interactions with methicillinresistant Staphylococcus aureus and Pseudomonas aeruginosa[END_REF][START_REF] Mashburn | Staphylococcus aureus serves as an iron source for Pseudomonas aeruginosa during in vivo coculture[END_REF]. However, the survival rate of S. aureus was even lower during co-culture with P. aeruginosa ΔacoR and Δaco mutants, reaching only 9.7×10 -2 at 3 days of culture and 5.6×10 -4 at 5 days. S. aureus survival was thus 4 to 10 times lower when P. aeruginosa was not able to catabolize acetoin, in comparison to co-culture with a strain that efficiently used the molecule. These results suggest that accumulation of acetoin may impact S. aureus survival during co-culture with P. aeruginosa. In parallel, we determined the survival rate of P. aeruginosa (Fig. 6B). We noticed that in such conditions, P. aeruginosa WT strain presented a growth advantage in co-culture, with a maximum of 6.6-fold increase of P. aeruginosa population after 5 days in presence of S. aureus in comparison to monoculture (Fig. 6B). The opposite effect was observed for aco mutant strains, as their populations were reduced by 75% for ΔacoR and 32% for Δaco after 3 days of co-culture in comparison to monoculture, confirming the role of acetoin catabolism in favouring P. aeruginosa growth and survival.

In order to figure out if acetoin accumulation was involved in the decrease of S. aureus survival rate, we monitored acetoin concentration in S. aureus monoculture and co-cultures (Fig. 6C). As expected, we did not detect acetoin in co-culture with PA2600 WT strain over the five days but we observed an accumulation of acetoin with PA2600 ΔacoR and Δaco mutants. The proportion of acetoin in co-culture (1300µM to 1700µM/10 6 S. aureus) was more than 500 times higher than in monoculture (2.5µM/10 6 S. aureus) (Fig. 6C). We thus cultivated S. aureus in different acetoin/cells proportions and observed that acetoin had an inhibitory dose-dependent effect on S. aureus growth from 20µM/10 6 S. aureus (Fig. S9). We concluded that acetoin accumulation may be responsible for the decreased S. aureus survival during co-culture with PA2600 ΔacoR and Δaco mutants. P. aeruginosa acetoin catabolism thus allows a greater S. aureus survival during co-culture, in comparison to co-culture with strains unable to catabolize acetoin.

Discussion

Coinfection with S. aureus and P. aeruginosa is a frequent situation especially in lungs of CF patients, where coinfection accounts for 35% to 50% of cases (17,18). In this context of coinfection, two states of interaction between the two pathogens have been described: the well-known competitive interaction where P. aeruginosa is able to inhibit the growth of S. aureus and the coexistence state where growth of both species is not affected by each other. The first state has been extensively studied and the leading bacterial determinants of S. aureus growth inhibition have been described (7). On the contrary, little is known about the impact of coexistence state on bacterial physiology. In the present study, we explored the impact of S. aureus on P. aeruginosa gene expression and physiology.

Comparing competitive and coexistence states, we observed that the down-regulation of genes involved in iron metabolism was specific to competition. Most of these, such as fec genes or PA4467-PA4471 operon, are involved in ferrous iron uptake and down-regulated during iron-replete conditions [START_REF] Visca | An essential transcriptional regulator: the case of Pseudomonas aeruginosa Fur[END_REF][START_REF] Cornelis | Iron uptake regulation in Pseudomonas aeruginosa[END_REF][START_REF] Ochsner | GeneChip expression analysis of the iron starvation response in Pseudomonas aeruginosa: identification of novel pyoverdine biosynthesis genes[END_REF]. These conditions are certainly generated by the lysis of S. aureus that provides an iron source to P. aeruginosa during competitive interaction (7, 36), a situation not observed in coexistence. This hypothesis is supported by the work of Tognon et al. [START_REF] Tognon | Transcriptional profiling of Pseudomonas aeruginosa and Staphylococcus aureus during in vitro co-culture[END_REF] that also identified down-regulation of iron metabolism genes during competitive interaction. Interestingly, they also noted typical responses of amino acid starvation including the down-regulation of genes involved in branched-chain amino acid degradation in competitive P. aeruginosa [START_REF] Tognon | Transcriptional profiling of Pseudomonas aeruginosa and Staphylococcus aureus during in vitro co-culture[END_REF]. While we did not identify such dysregulation in competition, an overexpression of numerous genes involved in amino acid catabolism was noted during coexistence (Table S5), emphasizing that these dysregulations depend on interaction state. More interestingly, we observed that both carbon and amino acids metabolism was specifically affected during coexisting interaction. Many genes involved in glucose catabolism were down-regulated in coexisting isolates during co-culture with S. aureus, especially when the medium was glucosedepleted (Fig. 3). It is worth noting that the zwf gene, down-regulated in almost all P. aeruginosa tested strains, encodes a glucose-6-phosphate dehydrogenase that converts glucose-6-phosphate to 6phosphogluconate; the first enzyme in the Entner-Doudoroff pathway, which is central to carbon metabolism in Pseudomonas sp.

In such condition of glucose depletion, we demonstrated that P. aeruginosa was able to use an alternative carbon source provided by S. aureus: acetoin. Acetoin is a four-carbon molecule produced by the decarboxylation of α-acetolactate. Owing to its neutral nature, production and excretion of acetoin during exponential growth prevents over acidification of the cytoplasm and the surrounding medium.

When other carbon sources are exhausted, it can constitute an external energy source for fermentive bacteria (28).

Acetoin produced by S. aureus was shown to be an inductor of the aco operon and acoR expression in P. aeruginosa (Fig. 2B) (27), allowing acetoin catabolism. This occurred in absence of glucose and was potentially mediated by carbon catabolic repression (Fig. 3), a situation that was already described in other bacteria such as B. subtilis (28). However, threshold effects in acetoinmediated induction and variability in aco system overexpression in P. aeruginosa strains (Fig. 1B and2B) suggest that other regulatory mechanisms may be involved. Our study may also support the relationship between acetoin and branched-chain amino acid pathways. Indeed, the biosynthesis pathways of acetoin and leucine are co-regulated and share the same precursor α-acetolactate in S. aureus (28). In response to co-culture with S. aureus, P. aeruginosa clinical strains showed overexpression of acetoin and leucine catabolism genes (Fig. 1B and2), suggesting the presence of both compounds in our co-culture conditions. All of our analyses were performed in vitro. However, using Voges-Proskauer dosage, we were able to confirm the presence of acetoin in CF patient sputa, and in lower concentrations for P. aeruginosa-positive samples (Fig. S6). No direct correlation between P. aeruginosa presence and acetoin quantity can be established as other microorganisms present in sputa may also have an impact on acetoin concentration. Nevertheless, our data support the work of Španěl et al. [START_REF] Španěl | Do linear logistic model analyses of volatile biomarkers in exhaled breath of cystic fibrosis patients reliably indicate Pseudomonas aeruginosa infection?[END_REF] and suggest that P. aeruginosa may catabolize and use S. aureus acetoin in the lung environment.

More importantly, we observed that catabolism of acetoin by P. aeruginosa and acetoin production by S. aureus were both more efficient for coexisting isolates, in comparison to competitive ones (Fig. 4). This underlines the adapted metabolic regulation in coexisting isolates in comparison to competitive ones. It is well known that the coexistence phenotype between P. aeruginosa and S. aureus is a consequence of an adaptation process. Indeed, P. aeruginosa strains isolated from early infection outcompete S. aureus while strains isolated from chronic infection are less antagonistic and can be co-cultivated with S. aureus (7,10,17). It also has been widely described how both pathogens evolve during colonization to evade the immune response and antibiotic treatment [START_REF] Baishya | Selective pressures during chronic infection drive microbial competition and cooperation[END_REF]. Here, for the first time, we suggest that evolution process leads to an adaptation of interspecies metabolic pathways between P. aeruginosa and S. aureus.

Therefore, we suggest that acetoin produced by S. aureus could contribute to sputum nutritional richness and be used by P. aeruginosa to survive in this nutritionally competitive environment during chronic infection. This hypothesis is supported by the beneficial effect of acetoin catabolism on P. aeruginosa growth and survival, especially during co-culture with S. aureus (Fig. 5 and6B).

S. aureus survival in presence of P. aeruginosa was also shown to be highly affected by nutrient availability induced by co-culture conditions (Fig. 6A). While coexistence is characterized by an absence of S. aureus growth inhibition during 8-hour co-culture ( 18), it appears that nutritional competition can still occur under unfavourable conditions and affect S. aureus survival. Therefore, coexistence between the two pathogens is promoted in nutritionally rich environments, in line with previous observations [START_REF] Miller | Global transcriptome responses including small RNAs during mixed-species interactions with methicillinresistant Staphylococcus aureus and Pseudomonas aeruginosa[END_REF][START_REF] Mashburn | Staphylococcus aureus serves as an iron source for Pseudomonas aeruginosa during in vivo coculture[END_REF]. Under adverse nutritional conditions induced by long-term culture, although its survival rate is affected, acetoin catabolism benefits its producer, S. aureus (Fig. 6A). Although this effect seems to be linked to acetoin accumulation in the medium as demonstrate by P. aeruginosa ΔacoR and Δaco mutants that do not catabolize acetoin anymore (Fig. 5B and6C), the precise mechanism remains unclear. In S. aureus, cell death in stationary phase may be induced by acetate production and ensuing intracellular acidification. Thomas et al. showed that acetoin production counters cytoplasmic acidification by consuming protons and promotes S. aureus survival in late-stationary phase [START_REF] Thomas | A Central Role for Carbon-Overflow Pathways in the Modulation of Bacterial Cell Death[END_REF]. We hypothesize that acetoin accumulation in the medium may induce a negative control of acetoin synthesis, affecting S. aureus survival during co-culture conditions.

Previous studies demonstrated the potential benefits of S. aureus and P. aeruginosa during coinfection. For example, S. aureus facilitates the survival of P. aeruginosa lasR mutants commonly found in CF patients by detoxifying surrounding nitric oxide released by host immune cells [START_REF] Hoffman | Nutrient availability as a mechanism for selection of antibiotic tolerant Pseudomonas aeruginosa within the CF airway[END_REF]. On the other hand, 4-hydroxy-2-heptylquinoline-N-oxide (HQNO) produced by P. aeruginosa cells inhibits respiration in S. aureus but also protects S. aureus cells from aminoglycosides [START_REF] Hoffman | Selection for Staphylococcus aureus small-colony variants due to growth in the presence of Pseudomonas aeruginosa[END_REF]. Additionally, we recently demonstrated that S. aureus antibiotic resistance and internalization into epithelial cells were increased in presence of coexisting P. aeruginosa (18). Here, we show that carbon metabolism is largely affected and that P. aeruginosa uses the acetoin produced by S. aureus as an alternative carbon source. This metabolic dialogue between the two pathogens is selected during bacterial adaptation in CF lungs and promotes their survival. Thereby, we highlight for the first time a trophic cooperation between S. aureus and P. aeruginosa during cooperative interaction. PA2596 competition and PA2600 coexistence strains were cultivated in absence or presence of SA2597 or SA2599 as described in Fig. S1. RNAs were extracted after 4 hours of culture and the RNAseq analysis was performed as described in material and methods. A gene was considered as differentially expressed when the Fold Change (FC) was > |2log2| with an adjusted P-value <0.05. Functional classification was performed thanks to KEGG database and literature.

B. Fold change of 26 P. aeruginosa gene expression induced by co-culture with S. aureus during coexistence interaction.

Twenty-one S. aureus-P. aeruginosa coexisting pairs were isolated from separate CF sputa recovered from 20 different patients. Each P. aeruginosa strain was cultivated in absence or presence of its co-isolated S. aureus strain. RNAs were extracted after 4 hours of culture and gene expression was assayed by RT-qPCR. A gene was considered as differentially expressed when the Fold Change (FC) was > |2|, indicated by dotted lines. Black lines indicate the median. Genes were tested in 14 (regular genes) or 21 (bold genes) strains. List of used strains is shown in Table S1.

Genes annotated with (*) were not identified as dysregulated during the RNAseq experiment.

Trophic cooperation promotes bacterial survival of Staphylococcus aureus and

Pseudomonas aeruginosa.

Laura Camus, Paul Briaud, Sylvère Bastien, Sylvie Elsen, Anne Doléans-Jordheim, François Vandenesch and Karen Moreau.

Supplementary data

Materials and methods: Generation of PA2600 knock-out ΔacoR and Δaco mutants.

Materials and methods

Generation of PA2600 knock-out ΔacoR and Δaco mutants: upstream and downstream flanking regions

of acoR and aco operon (474 bp and 486 bp fragments for acoR ; 654 bp and 708 bp for aco) were PCR amplified (GoTaq polymerase, Promega) and cloned into pEXG2 by Sequence Ligation and Independent Cloning (SLIC) method (1,2). Resulting plasmids pEXG2-acoR and pEXG2-aco were then transferred into PA2600 by triparental mating. A first conjugation was performed between the two E. coli strains carrying either the pRK2013 helper plasmid or the constructed pEXG2 plasmid by spotting 30µL of pre-culture of each strain on LB plates. After two hours at 37°C, 30µL of PA2600 pre-culture were added on the dried spot and the plate was incubated five hours at 37°C. The spot was then re-suspended in LB medium and plated on Cetrimide plates supplemented with gentamycin. Resulting clones were then plated on LB containing 10% sucrose to select for plasmid excision by crossing-over. The resulting strains were checked for gentamicin sensitivity and gene deletion by PCR. Ref.

CF clinical strains CF patient

Strain

PArpoD-R ATCCGGGGCTGTCTCGAATA PAgyrB-F ATCTCGGTGAAGGTACCGGA gyrB PAgyrB-R TGCCTTCGTTGGGATTCTCC OLC8-F GCGAGGATCTCTACTTCCGC acoR OLC8-R CTCACCGAGTTCGATGCGTA OLC9-F GCGGATCGTCAACCTGTCAT PA4148 OLC9-R CGATCACGGCAAACTTCGAG OLC14-F GTTCTTCAGGCTCCAGTCGG pvdS OLC14-R TTGCGGACGATCTGGAACAG OLC16-F CGCGACAAGAGCGAATACCT lasA OLC16-R AGGGTCAGCAACACTTTCGG OLC17-F CTGGACTGAACCAGGCGATG rhlA OLC17-R CAGGTATTTGCCGACGGTCT OLC22-F CGACGGTATCCAGGTCGATG PA1874 OLC22-R GAACTTGACCGTGACCACCT OLC23-F CGGTGTTGCTCGGATACCTC rcpC OLC23-R GCTTGCGTTCGAGCTTTTCC OLC25-F ATCGCCTGCTTCCAGTTGTC pchD OLC25-R AGAGAGTGAAGTTGTGCGCC OLC29-F GAGCGACGAACTGACCTACC rhlB OLC29-R TACTTCTCGTGAGCGATGCG OLC31-F TGCTCACTTCGCTATGGACC acoB OLC31-R AGAAGATCACCGGGTCGTTG OLC33-F CCGACGTGATCGCCTTCATA PA4153 OLC33-R GACGATTTCTTCCAGGCCGA OLC35-F GCCCATCGAGTTCCGTATGT bauD OLC35-R GAGGCAGACGGTGAAGATCG OLC39-F GACGAAGACGGCATGAACCT tadA OLC39-R TCCAGTTCGTAGCGGGAGAT OLC41-F CCACCACGAAACTGCAACTG tadG OLC41-R GCTTCTCCAACCGAAGTCCA OLC54-F TTGCCGTATTGAGTCCCACG flp OLC54-R GACTTTTTCGCCGACTCCGT OLC56-F GGACTGACGCTCAGGCAAT rhlC OLC56-R CCGGAGGAGATCAGGAACGA OLC71-F CAGCCGGACGAAGGTATCTC zwf OLC71-R GCGTGGTAGGTCTCGGAAAA OLC72-F GCTATACCCGCTCAAGGGC dguA OLC72-R TCTTGCGGTCGTAATCGGTG OLC73-F CTTCGCCTACCTGTTCAGCC PA5099 OLC73-R CGGCAGGTAGCGTGAATAGT OLC74-F GCAGTTCGGAGCACATCAAC PA1874 OLC74-R TCGATGCTGACGAAATCGGT OLC75-F TGGTATCCGGCGAACACATC liuA OLC75-R CACATCTTGCTGCCGTTGAG OLC92-F CAGCCAGGACTACGAGAACG lasR OLC92-R TGGTAGATGGACGGTTCCCA OLC93-F GGCATTCCCCTCACCGAC gntK OLC93-R GGGTCAGTTCCAGGTAGACGA OLC94-F TGGAAGTGGCTGCTCAATCC gltF OLC94-R CCAGTCGAAGCGGAAACCTT OLC95-F CACCTGCACCTTCTATGGCA edd OLC95-R GTGTTCGGGTTGACGAAGGA OLC96-F CAACGGCACCTCGATCTTCA mmsA OLC96-R AATCGGGATGTTGATGCCCA Cloning OLC58-F GGTCGACTCTAGAGGATCCCC AGGGCGATGCCCCGGCCGATG acoR downstream OLC58-R CACATGGTCCTTCGAGTGTGC OLC59-F GCACACTCGAAGGACCATGTG CGCCGGCATGGCATCCGCATG acoR upstream OLC59-R ACCGAATTCGAGCTCGAGCCC CTCGATCGCGCGGACGAACCA OLC64-F GGTCGACTCTAGAGGATCCCC TAGTCGGCATCGCGCACCCGT aco operon downstream OLC64-R GGAGAAATCGTCGGACGACGT OLC65-F ACGTCGTCCGACGATTTCTCCA GTTGGTGAACAACAAGGAGC aco operon upstream OLC65-R ACCGAATTCGAGCTCGAGCCC ACAGCCTGACCACTTTCGTGC

Gene (clinical strains)

Table S4: List of P. aeruginosa genes differentially expressed in presence of S. aureus in the context of a competitive interaction. PA2596 competition strain was cultivated in absence or presence of SA2599 or SA2597. RNAs were extracted after 4 hours of culture and RNAseq analysis was performed as described in material and methods. A gene was considered as differentially expressed when the Fold Change (FC) was > |2log2| with an adjusted P-value<0.05 in presence of both SA strains. Genes from the same operon are annotated with an identical letter. Grey cells indicate genes that were also dysregulated in the context of coexistence (Table S5). Functional classification was performed thanks to KEGG database and literature. Table S5: List of P. aeruginosa genes differentially expressed in presence of S. aureus in the context of coexistence. PA2600 coexistence strain was cultivated in the absence or presence of SA2599 or SA2597.

RNAs were extracted after 4 hours of culture and a RNAseq analysis was performed as described in material and methods. A gene was considered as differentially expressed when the Fold Change (FC) was > |2log2| with an adjusted P-value<0.05 in presence of both SA strains. Genes from the same operon are annotated with an identical letter. Grey cells indicate genes that were also dysregulated in competition couples (Table S4). Functional classification was performed thanks to KEGG database and literature. were obtained for a previous study (3).

B. Strain pairs used in transcriptomic analyses. Pairs SA2597/PA2596 and SA2599/PA2600 were isolated from two different patients. Interaction state of crossed pairs was determined as above and confirmed that it is solely led by P. aeruginosa (3). The 21 strain pairs used for qRT-PCR confirmation were both isolated from different patients, except in one case (Table S1).

Figure 1 :

 1 Figure 1: Alteration of P. aeruginosa transcriptome induced by co-culture with S. aureus. A. Number of under-expressed (grey bars) and over-expressed (black bars) genes of P. aeruginosa during co-culture with S. aureus for competitive (left) or coexisting (right) pairs.

Figure 2 :

 2 Figure 2: Fold changes of P. aeruginosa acoR, PA4148, liuA and zwf induced by culture conditions. A. Fold changes induced by co-culture with S. aureus (black bars), B. subtilis (grey bars), B. cenocepacia (hatched white bars) or S. maltophilia (hatched black bars). P. aeruginosa PA2600 strain was cultivated in absence or presence of S. aureus SA2599, B. subtilis, B. cenocepacia or S. maltophilia. RNAs were extracted after 4 hours of culture and gene expression was assayed by RT-qPCR. Bars represent the mean fold change + SEM from three independent experiments. Dotted lines indicate a fold change = |2|. *Padj<0.05, **Padj<0.01, ***Padj<0.001 ANOVA with Dunnett's correction (S. aureus vs. condition).

Figure 3 :

 3 Figure 3: Monitoring of acetoin (black lines) and glucose (grey lines) concentrations in S. aureus and P. aeruginosa monocultures or co-culture (A) or in S. aureus supernatant inoculated with P. aeruginosa (B), during coexisting interaction. A. S. aureus SA2599 and P. aeruginosa PA2600 were cultivated in monoculture or co-culture. Acetoin and glucose were quantified from supernatant each hour. Points represent the mean acetoin or glucose concentration ± SEM from three independent experiments. Similar results of acetoin accumulation are shown in Figure S5 for couples 146 and 153A. B. A 4-hours filtered supernatant of S. aureus SA2599 was inoculated with P. aeruginosa PA2600 culture or sterile medium for controls. Supernatant was used unaltered (dotted lines) or complemented with glucose (solid lines). Acetoin and glucose were quantified from supernatant each hour. Points represent the mean acetoin or glucose concentration ± SEM from three independent experiments. Similar results of acetoin catabolism are shown in Figure S5 for couples 146 and 153A.

Figure 4 :

 4 Figure 4: Ability of acetoin production by S. aureus (A) and catabolism by P. aeruginosa (B) for competitive (grey bars) or coexisting (black bars) strains. A. Acetoin concentration in P. aeruginosa supernatant inoculated with S. aureus strains from competition and coexistence couples. Each S. aureus strain from competition (n=12) and coexistence (n=12) couples was cultivated in P. aeruginosa PA2600 filtered supernatant and acetoin was quantified from supernatant after 6 hours of culture. Bars represent the median acetoin concentration ± 95% CI. ****P<0.0001 Mann-Whitney test.

Figure 5 :

 5 Figure 5: Monitoring of P. aeruginosa growth (A) and acetoin concentration (B) in minimal medium supplemented in acetoin. P. aeruginosa PA2600 WT, ΔacoR and Δaco strains were grown in M63 medium and 1.5mM acetoin was added every 2 hours, indicated by black arrows. A. Cultures were plated on TSA each 2 hours to count bacteria. Points represent the mean bacterial concentration ± SEM from three independent experiments. B. Acetoin was quantified from supernatant each hour. Points represent the mean acetoin concentration ± SEM from three independent experiments.

Figure 6 :

 6 Figure 6: Monitoring of S. aureus survival (A), P. aeruginosa survival (B) and acetoin concentration (C) during long-term co-culture. S. aureus SA2599 was cultivated in presence of P. aeruginosa PA2600 WT, ΔacoR and Δaco during 5 days. Cultures were plated at J0, J3 and J5 on MSA and cetrimide to count S. aureus and P. aeruginosa respectively and acetoin was quantified from supernatant. A, B. Survival rate was estimated by dividing the bacterial concentration in co-culture by bacterial concentration in monoculture for each bacterium. Bars represent the mean survival rate + SEM from five independent experiments. *Padj<0.05, ****Padj<0.0001 one-way ANOVA with Dunnett correction (WT vs. condition). C. Acetoin concentration was normalized to S. aureus counts. Bars represent the median acetoin concentration per 10 6 S. aureus ± 95% CI from five independent experiments. *Padj<0.05, **Padj<0.01, Kruskal-Wallis with Dunn's correction.

Figure S1 :

 S1 Figure S1: Schematic representation of the employed methodology.

Figure S2 :

 S2 Figure S2: P. aeruginosa metabolic pathways and associated genes up-regulated or down-regulated in coexistence with S. aureus.

Figure S3 :

 S3 Figure S3: Acetoin concentration in supernatant of S. aureus, B. subtilis, B. cenocepacia and S. maltophilia monocultures or co-cultures with P. aeruginosa.

Figure S4 :

 S4 Figure S4: Fold change of P. aeruginosa acoR, PA4148, liuA and zwf gene expression induced by culture with S. aureus or its supernatant.

Figure S5 :

 S5 Figure S5: Monitoring of acetoin concentration in S. aureus and P. aeruginosa monocultures or co-culture or in S. aureus supernatant inoculated with P. aeruginosa, for the pairs SA146/PA146 and SA153/PA153A.

Figure S6 :

 S6 Figure S6: Acetoin concentration in CF sputa from patients.

Figure S7 :

 S7 Figure S7: Acetoin concentration in cultures of S. aureus strains from competition and coexistence couples.

Figure S8 :

 S8 Figure S8: Glucose concentrations in cultures of S. aureus and P. aeruginosa strains from competition and coexistence pairs.

Figure S9 :

 S9 Figure S9: Growth kinetic of S. aureus cultivated in absence or presence of acetoin.

Figure S1 :

 S1 Figure S1: Schematic representation of the employed methodology. A. Determination of interaction state within S. aureus-P. aeruginosa co-isolated pairs. Pairs of strains are co-isolated from a single sputum sample. Interaction state is tested during plate and liquid tests, as described in materials and methods and by Briaud et al. (3). Results of competition tests (pictures and kinetics)

Figure S2 :Figure S3 :

 S2S3 Figure S2: P. aeruginosa metabolic pathways and associated genes up-regulated (red) or downregulated (green) in coexistence with S. aureus. PA2600 coexistence strain was cultivated in absence or presence of SA2599 or SA2597. RNAs were extracted after 4 hours of culture and RNAseq analysis was performed. A gene was considered as differentially expressed when the Fold Change (FC) was > |2log2| with an adjusted P-value<0.05. Genes from the same operon are annotated with an identical letter. Genes tested in RT-qPCR and confirmed for PA2600 are underlined. Functional classification and pathway constructions were performed thanks to KEGG database and literature.

Figure S4 :

 S4 Figure S4: Fold change of P. aeruginosa acoR, PA4148, liuA and zwf gene expression induced by culture with S. aureus (grey bars) or its supernatant (hatched and black bars). P. aeruginosa PA2600 strain was cultivated in the absence or presence of S. aureus SA2599 or filtered supernatant of S. aureus SA2599 and UAMS-1 WT. RNAs were extracted after 4 hours of culture and gene expression was assayed by RT-qPCR. Bars represent the mean fold change + SEM from three independent experiments. Dot lines indicate a fold change = |2|. *Padj<0.05, ****Padj<0.0001 ANOVA with Tukey's correction.

Figure S5 :Figure S6 :Figure S7 :Figure S8 :Figure S9 :

 S5S6S7S8S9 Figure S5: Monitoring of acetoin concentration in S. aureus and P. aeruginosa monocultures or coculture (A,B) or in S. aureus supernatant inoculated with P. aeruginosa (B,C), for the pairs SA146/PA146 (A,C) and SA153/PA153A (B,D). A, B. S. aureus and P. aeruginosa were cultivated in monoculture or co-culture. Acetoin was quantified from supernatant each hour. Points represent the mean acetoin concentration ± SEM from two independent experiments per pair. C, D. A 4-hour filtered supernatant of S. aureus was inoculated with P. aeruginosa culture or sterile medium for controls. Acetoin was quantified from supernatant each hour. Points represent the mean acetoin ± SEM from three independent experiments per pair.

Table S1 :

 S1 Clinical CF strains used in this study.

Table S2 :

 S2 Non-CF strains and plasmids used in this study.

Table S3 :

 S3 Primers used in this study.

Table S4 :

 S4 List of P. aeruginosa genes differentially expressed in presence of S. aureus in the context of a competitive interaction.

Table S5 :

 S5 List of P. aeruginosa genes differentially expressed in presence of S. aureus in the context of coexistence.

Table S1 : Clinical CF strains used in this study. Unless

 S1

		PA154A	Coexistence	qRT-PCR screening; Acetoin catabolism screening 3
		PA154B		qRT-PCR screening; Acetoin catabolism screening 3
		SA154		qRT-PCR screening; Acetoin production screening 3
		PA156	Coexistence	qRT-PCR screening; Acetoin catabolism screening 3
		SA156		qRT-PCR screening; Acetoin production screening 3
		PA166A	Coexistence	qRT-PCR screening; Acetoin catabolism screening 3
		SA166		qRT-PCR screening; Acetoin production screening 3
		PA167	Competition	Acetoin catabolism screening	3
		SA167		Acetoin production screening	3
	(■)	PA171A	Coexistence	Acetoin catabolism screening	3
		SA171		Acetoin production screening	3
		PA172	Competition	Acetoin catabolism screening	This study
		SA172		Acetoin production screening	This study
		PA178	Coexistence	Acetoin catabolism screening	3
		SA178		Acetoin production screening	3
		PA179	Competition	Acetoin catabolism screening	3
		SA179		Acetoin production screening	3
		PA181	Competition	Acetoin catabolism screening	3
		SA181		Acetoin production screening	3
	(♦)	PA186	Competition	Acetoin catabolism screening	3
		SA186		Acetoin production screening	3
		PA187	Competition	Acetoin catabolism screening	This study
		PA188A	Competition	Acetoin catabolism screening	This study
		SA188		Acetoin production screening	This study
		PA193A	Competition	Acetoin catabolism screening	This study
		SA193		Acetoin production screening	This study
	(•)	PA194A	Coexistence	Acetoin catabolism screening	This study
		PA194B		Acetoin catabolism screening	This study
		SA194		Acetoin production screening	This study
		PA197	Competition	Acetoin catabolism screening	This study
		SA197		Acetoin production screening	This study
		SA198	Competition	Acetoin production screening	This study
		PA199A	Competition	Acetoin catabolism screening	This study
		PA199C		Acetoin catabolism screening	This study
		PA200	Competition	Acetoin catabolism screening	This study
		SA200		Acetoin production screening	This study
		SA205	Competition	Acetoin production screening	This study
		SA207	Coexistence	Acetoin production screening	This study
	(♦)	SA213	Competition	Acetoin production screening	This study
	B. cenocepacia	LUG2886 Coexistence	qRT-PCR (aco induction)	This study
			(PA2600)
	S. maltophilia	LUG2884 Coexistence	qRT-PCR (aco induction)	This study
			(PA2600)
				indicated, interaction state was tested between
	strains from the same clinical pair (ie. isolated from a single patient). Four strain pairs were recovered from a
	same patient but at different time points and are annotated with identical patient number and symbol (■,•,▲
	or ♦).

Table S2 : Non-CF strains and plasmids used in this study

 S2

	Strains / plasmids P. aeruginosa PA2600 ΔacoR Name PA2600 Δaco S. aureus SA UAMS-1 SA UAMS-1 ΔalsSD UAMS-1489, alsSD deletion Characteristics acoR deletion mutant aco operon deletion mutant Coexistence Interaction state Coexistence (SA2599) (SA2599) WT strain Coexistence (PA2600) mutant Coexistence (PA2600) B. subtilis LUG2953 WT strain Coexistence (PA2600) Plasmids pEXG2 Gm R ; mobilizable, non-replicative vector in P. aeruginosa pEXG2-ΔacoR pEXG2 carrying upstream and downstream sequences of acoR for gene deletion pEXG2-Δaco pEXG2 carrying upstream and downstream sequences of aco for operon deletion pRK2013 Km R , helper plasmid with Name Sequence acoR and aco deletions Use Experiments Culture in minimal medium; 5-day co-cultures Culture in minimal medium; 5-day co-cultures Production of SA supernatant (aco induction) Production of SA supernatant (aco induction) qRT-PCR (aco induction) acoR and aco deletions acoR deletion aco deletion Target Amplicon Size qPCR PArpoD-F GCGCAACAGCAATCTCGTCT rpoD	Reference This study This study 4 4 This study 2 This study This study
	conjugative properties

. P. aeruginosa ΔacoR and Δaco mutants were constructed from the clinical CF isolate PA2600 (Table

S1

). Interaction state was tested with the strain indicated in brackets.

Table S3 : Primers used in this study.

 S3

							SA2599/PA2596	SA2597/PA2596
											LasR
		Gene (PAO1)	UniProt Product	Function	Log 2 fold-change	Adjusted p-value	Log 2 fold-change	Adjusted p-value	regulation
	fecI_2	NA	NA	P23484	Putative RNA polymerase sigma factor FecI	Iron metabolism	-2.67	4.02E-06	-2.51	1.85E-04		6
	group_1318 NA	NA	P40883 Regulatory protein PchR	Iron metabolism	-3.57	3.88E-23	-3.13	6.04E-25		6
	group_1539 NA	NA	NA	Hypothetical protein	Unknown	-2.96	3.51E-11	-3.58	3.20E-13
	bauA_1	PA0132	bauA	Q9I700	Beta-alanine-pyruvate aminotransferase	Aminoacids (ILV) metabolism catabolism, propanoate	3.15	1.00E-06	3.44	6.25E-39 Activation	7
	nirS_1	PA0509	nirN	a Q9I609	Nitrite reductase	Nitrogen metabolism	-2.92	6.77E-10	-2.93	3.30E-09 Repression	8,9
	cysG_2	PA0510	nirE	a G3XD80 Siroheme synthase NirE	Nitrogen, porphyrin and chlorophyll metabolism	-3.00	8.64E-09	-2.56	5.61E-06 Repression	8,9
	group_5012 PA0512	nirH	a P95415 NirH	Nitrogen metabolism	-3.27	8.64E-09	-2.23	4.94E-04 Repression	8,9
	group_3026 PA0513	nirG	a P95414 NirG	Nitrogen metabolism	-2.79	5.29E-06	-2.35	9.60E-04		8
	group_4848 PA0514	nirL	a P95413	Heme d1 biosynthesis protein NirL	Nitrogen metabolism	-3.09	1.71E-08	-3.47	2.61E-08		8
	group_3339 PA0515	nirD	a P95412	Probable transcriptional regulator	Nitrogen metabolism	-2.99	2.04E-07	-2.03	1.30E-03		8
	group_5595 PA0516	nirF	a Q51480	Heme d1 biosynthesis protein NirF	Nitrogen metabolism	-3.34	1.03E-10	-3.47	6.65E-16		8
	nirS_2	PA0519	nirS	a P24474 Nitrite reductase	Nitrogen metabolism	-3.29	3.53E-07	-5.39	6.48E-51		8
	nirQ	PA0520	nirQ	b Q51481	Denitrification regulatory protein NirQ	Nitrogen metabolism	-4.27	3.41E-28	-4.51	3.08E-33		8
	qoxC	PA0521	nirO	b G3XD44 Quinol oxidase subunit 3	Unknown	-4.65	2.60E-22	-4.60	4.38E-15
	group_6044 PA0522	nirP	b Q51483 Hypothetical protein	Unknown	-2.90	1.59E-05	-2.99	7.07E-05
	norB	PA0524	norB	Q59647	Nitric oxide reductase subunit B	Nitrogen metabolism	-5.53	1.99E-23	-8.08	1.91E-79		8
	group_3360 PA0672	hemO	G3XCZ8 Heme oxygenase	Porphyrin and chlorophyll metabolism	-2.38	9.28E-05	-2.53	1.57E-17
					Phthiocerol/phenolphthiocer
	ppsC	PA1137	PA1137	Q9I4J8	ol synthesis polyketide	Unknown	-4.31	1.74E-21	-3.55	1.62E-19
					synthase
	rocR	PA1196	ddaR	Q9I4E2	Arginine utilization regulatory protein RocR	Aminoacids (arginine) metabolism	2.51	3.23E-05	3.22	5.81E-21		10
	fecI_5	PA1300	PA1300 c Q9I444	Putative RNA polymerase sigma factor FecI	Iron metabolism	-3.17	3.51E-11	-2.50	2.25E-11		6
	fecR_1	PA1301	PA1301 c Q9I443	Protein FecR	Iron metabolism	-3.02	1.71E-08	-2.53	1.01E-13		6
	ctpF	PA1429	PA1429	Q9I3R5	Putative cation-transporting ATPase F	Unknown	2.89	8.45E-09	3.63	7.15E-35
	group_3703 PA1673	PA1673	Q9I352	Bacteriohemerythrin	Unknown	2.16	1.57E-04	2.57	1.30E-14
	group_5526 PA1746	PA1746	Q9I2Z1	Hypothetical protein	Unknown	2.42	1.59E-06	2.42	1.38E-09
	group_2540 PA1747	PA1747	Q9I2Z0	Hypothetical protein	Unknown	2.57	8.64E-09	2.46	1.07E-08
	group_269 PA2033	PA2033	Q9I282	Hypothetical protein	Unknown	-2.24	1.65E-03	-2.84	7.11E-23
	ybdM	PA2126	cgrC	Q9I1Y9	CupA gene regulator C, CgrC	Unknown	2.60	3.18E-07	2.46	1.05E-06
	group_6509 PA2321	gntK	G3XD53 Gluconokinase	Carbon metabolism (pentose phosphate)	-2.73	4.03E-06	-2.41	2.68E-05 Repression	9
	group_3203 PA2384	PA2384	Q9I195	Ferric uptake regulation protein	Iron metabolism	-2.44	1.09E-04	-2.56	8.25E-10		6
	mbtH	PA2412	PA2412	Q9I169	Hypothetical protein	Monobactam biosynthesis	-2.12	1.66E-03	-2.27	6.19E-08
	group_3129 PA2468	foxI	Q9I114	Putative RNA polymerase sigma factor FecI	Iron metabolism	-2.32	1.63E-07	-2.03	1.07E-08		6
	hmp	PA2664	fhp	Q9I0H4	Flavohemoprotein	Iron metabolism, NO detoxification	-2.41	1.85E-05	-2.38	1.86E-03		11
	group_3982 PA2691	PA2691	Q9I0F1	NADH dehydrogenase-like protein	Oxidative phosphorylation	-4.38	1.03E-18	-3.45	3.32E-07
	hldD	PA3337	rfaD	Q9HYQ8	ADP-L-glycero-D-manno-heptose-6-epimerase	Lipopolysaccharide biosynthesis	3.40	1.45E-12	4.26	1.62E-48
	yccM	PA3391	nosR	d Q9HYL3 Regulatory protein NosR	Nitrogen metabolism	-3.57	7.09E-14	-4.08	1.98E-30 Repression	8,9
	nosZ	PA3392	nosZ	d Q9HYL2 Nitrous-oxide reductase	Nitrogen metabolism	-3.62	1.57E-10	-5.50	6.62E-51 Repression	8,9
	nosD	PA3393	nosD	d Q9HYL1	Putative ABC transporter binding protein NosD	Nitrogen metabolism	-3.13	1.38E-10	-3.97	3.44E-20 Repression	8,9
	nosY	PA3395	nosY	d Q9HYK9	Putative ABC transporter permease protein NosY	ABC transporters (nitrogen metabolism)	-3.14	1.69E-07	-2.91	1.48E-06 Repression	8,9

Taken together, these results demonstrated that acetoin catabolism promotes P. aeruginosa survival as a nutritional alternative carbon source, and improves S. aureus survival during co-culture since a high concentration of acetoin appears to impair S. aureus growth.

Acknowledgments

This work was supported by the Fondation pour la Recherche Médicale, grant number ECO20170637499 to LC; Finovi foundation to KM; the associations "Vaincre la mucoviscidose" and "Gregory Lemarchal" to KM. We thank Kenneth W. Bayles from University of Nebraska Medical Center (Omaha) for providing S. aureus UAMS-1 WT and mutant strains.

Conflict of interest

All authors declare no competing interests.

Ethical statement

All the strains used in this study were collected as part of the periodic monitoring of patients at the Hospices Civils de Lyon. This study was submitted to the Ethics Committee of the Hospices Civils de Lyon (HCL) and registered under CNIL No 17-216. All patients were informed of the study; however, as the study was non-interventional no written informed consent were required under local regulations.

Supplementary data references


Zhaojun Zhang

Fabien Gatti

Dong H Zhang

Communication: Full dimensional quantum mechanical calculations of the reaction probability of the H+CH 4 reaction based on a mixed Jacobi and Radau description

Paris-Saclay, F-91405 Orsay, France

A full-dimensional time-dependent wavepacket study using mixed polyspherical Jacobi and Radau coordinates for the title reaction has been reported. The non-reactive moiety CH 3 has been described using three Radau vectors whereas two Jacobi vectors have been used for the bond breaking/formation process. A potential-optimized discrete variable representation basis has been employed to describe the vibrational coordinates of the reagent CH 4 . About one hundred billion basis functions have been necessary to achieve converged results. The reaction probabilities for some initial vibrational states are given.

A comparison between the present approach and other methods, including reduced and full dimensional ones, is also presented.

a) E-mail: fabien.gatti@u-psud.fr b) E-mail: zhangdh@dicp.ac.cn such as combustion and interstellar chemistry. Ideally, an accurate understanding at a quantum level of theory is required. However, the computational effort of such calculations increases exponentially with the number of atoms. More relevantly, considering state-to-state reaction probabilities, triatomic and a few tetra-atomic reactive systems could be studied until now ? ? ? ? ? ? ? ? ? ? ? ? ? . Interestingly, several models and methods have been recently proposed to treat reactive systems with more than four atoms.

In this context, the six-atom system H+CH 4 → H 2 +CH 3 has served as a benchmark for both theoretical and experimental studies in quantum reaction scattering studies. Owing to its importance in industry, in the last twenty years different simulation approaches, ranging from 3 to 12 active nuclear degrees of freedoms, have been developed for its study. Takayanagi was the first to report a three dimensional study in which H+CH 4 was considered as a collinear four-atomic system. ? Yu and Nyman added the umbrella mode of nonreacting CH 3 in a four-dimensional model including a rotating bond approximation (RBA). ? Wang and Bowman carried out a sixdimensional (6D) time-dependent wave packet study by treating the three hydrogen atoms in CH 3 as a pseudo-atom. ? Zhang et.al. developed a semi-rigid vibrating rotor target (SVRT) model in which the CH 3 moiety is treated as a semi-rigid vibrating rotor. ? ?

In 2000, Clary and Palma proposed an eight-dimensional (8D) model for the reaction of the type X+YCZ 3 → XY+CZ 3 in which the non-reactive CZ 3 group is restricted to a C 3v symmetry. ? Then Yang et al. carried out seven-dimensional calculations on the H+CH 4 reaction using that model with time-dependent wave packet method (TDWP). ? Subsequently, also using this model, Zhang and Yang carried a number of wave packet dynamics studies like H+CH 4 → H 2 +CH3 ? ? ? ? , H+CD 4 → HD+CD 3 ? , H+CHD that agreed reasonably well with the 7D quantum dynamics calculation. ? Despite these exciting agreements between the low-dimensional models and experience, it is still unknown whether these reduced-dimensional models introduce significant differences with full dimensional simulations.

During the past two decades, possible only the group of Manthe were able to carry out fulldimensional quantum dynamic simulations on the title system. They used the (multi-layer ? ? ? ? ) multi-configurational time-dependent Hartree (ML-MCTDH) approach ? ? ? ? to perform many different types of calculations including the computation of reaction rate constants ? , initial stateselected reaction probabilities, state-to-state reaction probabilities, etc. always within the quantum transition state framework ? ? ? ? ? ? ? ? ? ? ? ? . In these simulations, these authors used a description based on Jacobi and Radau coordinates as we do in the present work ? ? .

In contrast, in our method we use a different definition of the coordinates (purely polyspherical ? ).

This results in a less complicated Kinetic Energy Operator (KEO). Note that the idea to combine Jacobi and Radau coordinates was already introduced in spectroscopy by Bramley and Carrington for CH 2 O in 1993 ? .

In this communication, we present full dimensional quantum calculations on the H+CH 4 → H 2 +CH 3 abstraction reaction using a time-dependent wave packet method. The KEO for the system is straightforwardly derived from the polyspherical formulation ? based on mixed coordinates containing two Jacobi vectors and three Radau vectors. Since they are parameterized in terms of spherical coordinates and there are several vectors, these belong to a particular case of the so-called family of polyspherical coordinates ? . In addition, this approach easily permits the introduction of subsystems. In other words, it is possible to define a body-fixed (BF) frame for specific groups of atoms in the molecular system and to introduce the spherical coordinates inside this body-fixed frame ? ? as in the formulation for van der Waals dimers ? . The mixed coordinates of the system with the structure of X+YCZ 1,2,3 are depicted in the Fig. 1. Here, we have one BF for the whole system, one subsystem for YCZ 1,2,3 , and one subsubsystem for CZ 1,2,3 . This allows us to separate easily the intramolecular motions of the CZ 1,2,3 moiety from the rest. This is a key aspect when considering the dynamics after the reaction. Additionally, the YCZ 1,2,3 moiety is also separated from the colliding X atom, which is very important prior to the reaction. This kind of strategy can be seen as a generalization of the formulation for van der Waals dimers ? combined with polyspherical coordinates. More precisely, the global BF is defined such as its z axis is parallel to R of Fig. 1 and such as the third Euler angle of the BF is the first Euler angle of the BF frame for YCZ 1,2,3 . The BF of the subsystem YCZ 1,2,3 is defined such as its z axis is parallel to r of Fig. 1 and its third Euler angle is the first Euler angle of the BF of the CZ 1,2,3 subsubsystem. The BF of the subsubsystem CZ 1,2,3 is defined such as its z axis is parallel to R 3 of Fig. 1 and its third Euler angle is defined such as R 2 of Fig. 1 lies parallel to the ((x, z); x > 0) half-plan. The definition of the BF frame for CZ 1,2,3 breaks the explicit symmetry of the three C-Z bonds. This has the advantage of keeping the structure of the polyspherical coordinates ? ? ? and its advantages with respect to the use of orthogonal coordinates, where the number of terms is rather well controlled.

In terms of coordinates, we have to add the distance R to the ones necessary for the rotational description of YCZ 1,2,3 (12D including 3 Euler angles). Since we do not consider any overall rotation in the present work, only the last two Euler angles of YCZ 1,2,3 have to be kept. This leads to a problem in 11 dimensions plus R, i.e. 12 dimensions. Recently, this strategy using polyspherical coordinates with subsystems been successfully utilised in the study of the five-atomic scattering process of H+NH 3 ? . In this system, the non-reactive group NH 2 of the reagent NH 3 was described by two Radau vectors while two Jacobi vectors were used for the bond breaking and formation.

At this point, it should be noted that the use of subsystem coordinates, allows a direct product of potential-optimized discrete variable representation ? ? (PODVR) functions for the corresponding degrees of freedom which, in turn, reduces the size of the basis functions. As already shown, the combination of these mixed coordinates and the PODVR method can lead to a high efficiency.

Therefore, such strategy can be extended to some elementary reactions involving six atoms in which the non-reactive moieties keep some symmetry and remain rather rigid. Note also that the flexibility provided by the combination of subsystems and polyspherical coordinates ? is such that extensions to different structures with even more flexibility in the CZ 1,2,3 moeity would be possible without a qualitative change in the strategy. In particular, only new terms, similar to those already implemented in the present code, might be added to the KEO.

As already mentioned, the mixed coordinates of the system with the structure of X+YCZ 1,2,3 are depicted in the Fig. 1. The full dimensional Hamiltonian for such a system, defined in Jacobi and Radau mixed coordinates, can be written as

Ĥ = - 1 2µ R ∂ 2 ∂R 2 + ( J † tot -L † Y CZ 1,2,3 ) • ( J tot -L Y CZ 1,2,3 ) 2µ R R 2 - 1 2µ r ∂ 2 ∂r 2 + ( L † Y CZ 1,2,3 -L † CZ 1,2,3 ) • ( L Y CZ 1,2,3 -L CZ 1,2,3 ) 2µ r r 2 + TCZ 1,2,3 + V (R, β Y , α s , r, β s , γ s , R 1 , R 2 , R 3 , θ 1 , θ 2 , ϕ 1 ) , (1)
where

µ R = m X m Y CZ 1,2,3 m X + m Y + m C + m Z 1 + m Z 2 + m Z 3 , (2)
µ r = m Y m CZ 1,2,3 m Y + m C + m Z 1 + m Z 2 + m Z 3 , (3)
J tot is the total angular momentum operator of the system, L Y CZ 1,2,3 and L CZ 1,2,3 are the rotational angular momentum operator of the YCZ 1,2,3 and CZ 1,2,3 , respectively. V denotes the potential energy surface ? . With respect to the kinetic energy operator TCZ 1,2,3 , its purely vibrational part is given in the appendix of Ref. ? and the additional rotational part is given in Eq. 5 of Ref. ? . The excellent agreement between the rovibrational eigenvalues for different penta-atomic molecules obtained with our code and those from different approaches ? proves that the KEO has been correctly implemented. We additionally define u 1 = cos θ 1 , u 2 = cos θ 2 and u βs = cos β s so that the integral volume element reads:

dV = dR 1 dR 2 dR 3 du 1 du 2 dϕ 1 dα s du βs dγ s dr sin β Y dβ Y dR , (4)
using the convention for the coordinates of Ref. ? .

Concerning the time-dependent wave packet method, we have followed the approach used for the X+YNZ 1,2 system by replacing the nonreactive group NZ 1,2 by the CZ 1,2,3 moiety. The potential energy surface used here was fitted using the permutation invariant polynomial-neural network method by Li et al ? I FIND THAT SOME DESCRIPTION OF THE PIP-NN PARAMETERS

AND CONVERGENCE SHOULD BE GIVEN HERE

The main goal of this communication is to show the efficiency of our method, hence only the abstraction channel H'+CH 4 → H'H+CH 3 will be presented and the exchange channel H'+CH 4 → H+H'CH 3 will not been considered. An L-shaped wave function expansion scheme was used to reduced the size of the basis set. A total of 72 sinus basis functions was used for R range in a range of [2.0,15.0] a.u. whereas 22 grid points were used in the interaction region. For the breaking bond r, a total of 30 vibrational basis functions was used and 5 vibrational basis functions were used in the asymptotic region. For the three Radau radial degree of freedoms R 1 , R 2 and R 3 , three vibrational basis functions were used for each of them. For the three angular degrees of freedoms θ 1 , θ 2 and ϕ 1 in CH 3 , 5, 5 and 15 PODVR functions were used, respectively. For the two angular coordinates β s and γ s , we used 8 PODVR functions. The rotational basis is controlled by L max =24 and k max =3, resulting in a total of 163 functions for J tot = 0, J tot being the quantum number for the total angular momentum. Consequently, the total number of the basis functions reaches 69, 711, 840, 000 in the interaction region and 26, 406, 000, 000 in the asymptotic region. The storage for the wavefunctions necessitates more than 716 GB. We have used combined shared memory parallelization using OpenMP and distributed memory parallelization using message passing interface (MPI). The convergence with respect to the number of DVR points for all the degrees of freedom has been tested very carefully. These tests are presented in the supplementary material.

To carry out the scattering calculations, we first computed vibrational energies of some initial states of CH 4 using the aforementioned parameters. Table I displays the calculated fundamental and excited energy levels for the four vibrational modes of the methane molecular together with their experimental counterparts. In previous papers ? ? , we have calculated the vibrational and rotational energy levels for some isotopic derivatives of methane and CH 3 F and these results have been thoroughly compared to experimental data and to other theoretical methods ? ? ? ? ? . We have shown that the strategy with one Jacobi vectors and three Radau vectors (1+3) along with the PODVR approach leads to very accurate results, proving the reliability of our method, in particular the correct implementation of the complicated KEO to prepare the studies of reactions of the type X+YCZ 1,2,3 .

Fig. 2 depicts the reaction probabilities for J tot =0 and the initial ground state CH 4 as a function of translational energy. obtained with the present full-dimensional, together with reduceddimensional models (7D and 8D) as well as the results of the MCTDH method in full dimensionality (12D), respectively. These MCTDH results have taken from Ref. ? . By visual inspection of Fig. 2, we can notice that the probability increases very fast from around translational energy 0.4 to 0.6 eV. Then the curve goes down slightly. From the energy of 0.66 eV to 1.0 eV, the probability rises very slowly and reaches a maximum of about 0.0036 at 1.0 eV. Overall, the probability for the (0000) initial state is very small for the abstraction reaction and is relatively smooth. As a comparison, the reaction probabilities of the seven-and eight-dimensional method based on the C 3v models are also given. In the 7D model, the non-reactive CH 3 model includes only one vibrational degree of freedom, the so-called umbrella angle, and the stretching motion of three C-H bonds is included in the 8D model. Importantly, the shapes of the probabilities of the reduceddimensional methods are very similar to the present full-dimensional method except in a tiny shift in translational energy. The probabilities for the reduced-dimensional methods also increase very fast in the low energy region whereas in the high energy region the positions of the oscillating structures are almost the same again with a very small shift. The full dimensional probability of the MCTDH method is almost identical to the present 12D results in the low energy region thus

showing that both approaches are in an excellent agreement. However, the MCTDH probability drops down when the energy is larger than about 0.62 eV. Even though the PESs of the MCTDH method is slightly different from our present PES, we firmly believe that such difference cannot be caused by this difference. Indeed, as shown in our previous studies ? ? ? ? , the differences of probabilities among those different PESs for the H+CH 4 → H 2 +CH 3 reactions are very small: the PES ? used for the MCTDH calculations is refitted based on the PES of Ref. ? On the one hand, the transition state for the abstraction channel has a C 3v symmetry and the reaction system always keeps it along the minimal reaction path. On the other hand, we have obtained results with the 7D model, which were in very good agreement with the experimental results. ? ? ? I FIND THAT THE 7D MODEL SHOULD BE RECALLED HERE With those results in mind, we are confident that the results of the present full-dimensional method are reliable, thud confirming that the 7D reduced-dimensional model is sufficient to predict the reaction probability starting from (0000).

Moreover, we believe that the calculations with MCTDH there is probably a lack of convergence in the high-energy region.

In the 7D model, the bond length of the non-reactive CH 3 group is fixed, so that the stretching mode will be localized at the broken bond C-H. In contrast, the three bond lengths of the nonreactive CH 3 group can change simultaneously in the 8D model. As a consequence, there will exist one symmetry stretching mode and one asymmetrical stretching mode. In the full dimensional model, there are four stretching modes including a symmetric one and a triply-degenerate asymmetric one. Similarly, as in the reaction H+NH 3 ? , the four bonds in the reagent CH 4 do not possess explicit permutation symmetry in our 12D model due to the fact that we use one Radau vector to define the z BF axis of the BF of CH 3 . The three asymmetrical stretching modes are thus not perfectly degenerate. For the asymmetrical stretching vibrational state (0010), the reaction probability is obtained by averaging over the three (0010) probabilities. In Fig. 3, the comparison for the present 12D results and 7D and 8D reduced dimensional results is provided. The reaction probabilities of ( 1000) and (0010) states are almost exactly the same and both rise smoothly as translational energy increases. The probabilities for the two stretching states are much larger than those of the ground state and reach about 0.01 at 1.0 eV. In order to further compare the results of our present 12D calculations with the 7D and 8D models, we also give the sums of the probabilities of the stretching vibrational states for both 8D and 12D methods. It is observed that from the threshold energy region to about 0.5 eV, the agreement of the probabilities of the three methods is very good. This indicates that the C 3v model can work very well for low energies and that the reaction happens around the minimal reaction path. However, as the energy increases, the C 3v model fails to describe the reaction: this is one important result of our new calculations. The behavior with increasing energy of the three curves is rather different: the probability in the 12D model is the largest whereas the 7D probability is the smallest.

In Fig 4, we depict the comparison of the probabilities of the present full dimensional method and the calculations with the MCTDH method for the reactant CH 4 (1000) and (0010) initial states. When plotted as a function of total energy, which includes the excitation energy, a very tiny difference between the probabilities of the symmetrical and asymmetrical vibrational states in our simulations can be observed. In the low energy region, our results with the results obtained with MCTDH agree very well. However, the reaction probabilities with MCTDH are higher than our 12D result as the total energy increases.

In summary, a full dimensional time dependent wave packet method for the H+CH 4 reaction system based on a model combining Jacobi and Radau coordinates along with a PODVR approach has been presented. Since the CH 3 moiety does not change dramatically during the whole reaction process, three Radau vectors and PODVR functions can be used to describe very effectively CH 3 thus substantially reducing the number of basis functions needed. This opens up the path to full quantum studies of the title reactions. About one hundred billion functions were needed to converge our results in our energy domain. The reaction probabilities for the ground and stretching excited vibrational states have been calculated. A detailed comparison of the present 12D simulations and reduced-dimensional 7D and 8D models has also been given. This has proven the reliability of the C 3v model in the low energy region. Our results seem to indicate that the convergence of the former MCTDH simulations needs to be further improved in the high energy region.

  FIG.1. The Jacobi and Radau mixed coordinates for the X+YCZ 1,2,3 system. A denotes the "canonical" point of CZ 1,2,3 , G is the center mass of the CZ 1,2,3 . R 1 , R 2 and R 3 are the Radau vectors. R and r are the Jacobi vectors: r from G to Y, R from the center of mass of YCZ 1,2,3 to X.

TABLE I .

 I Vibrational energies (in cm -1 ) of CH 4 for L 0 = 0 (no rotation). Second column: calculated values with the potential energy surface constructed by Li and Chen et al.; third column: experimental values. Our present zero-point energy is equal to 9689.43 cm -1

	State	This work	Expt.
	(0001)F 2	1309.19	1310.76
		1309.83
		1310.33
	(0100)E	1530.40	1533.33
		1530.83
	(1000)A 1	2912.89	2916.48
	(0010)F 2	3014.60	3019.49
		3015.13
		3015.51

Acknowledgments The project was supported by the National Natural Science Foundation of China (Nos. 21590804, 21688102, and 21703243), the Chinese Academy of Sciences(Grant No. XDB17010200). F.G. thanks "French Chinese Network in Theoretical Chemistry" (GDRI 0808) for financial support. FG thanks Daniel Peláez (ISMO) for the careful reading of the manuscript.

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.