Florian Rouzier

Rosanne Sillé

Ophélie Montièqe

Arnaud L'"

Dr A Tessier

Dr Muriel Pipelier

Gilles Í'"

Arnaud ! Dujardin

Martel

Arnaud Nourry
email: arnaud.nourry@univ-lemans.fr

[ Al

Stéphane Guillarme
email: stephane.guillarme@univ-lemans.fr

Or F Rouzier

Dr O Monriège

Prof G Dujordin

Dr A Martel

Dr A Nourry

Dr 5 Guillarme

Synthesis of Constrained C-Glycosyl Amino Acid Derivatives Involving 1,3-Dipolar Cycloaddition of Cyclic Nitrone as Key Step

An efficient two-step strategy for the synthesis of constrained C-glycosyl amino acid derivatives from C-vinylglycosides involving a 1,3-dipolar cycloaddition using L-(-)menthone-derived nitrone as the key step is described. After optimization of 1,3-dipolar cycloaddition conditions, various C-vinylglycosides were tested leading exclusively to one dia-stereoisomer of the corresponding cycloadduct in good to excellent yields. The total facial selectivity observed was also studied by DFT calculations. Original conformationally restricted C-glycosyl amino acid derivatives (8 examples) were isolated after simple cleavage of the chiral auxiliary.

Introduction

Glycoconjugates such as glycoproteins and glycolipids are fundamental for many important biological processes including cell-cell, bacterium-cell, and virus-cell recognition, inflammation, signal transduction, fertilization, immune defense and they are major components of the outer surface of mammalian cells.'!' ln glycoproteins, the carbohydrate part is generally covalently linked to the protein backbone through an oxygen atom (serine, threonine, tyrosine) or a nitrogen atom (asparagine). A glycosyl amino acid known as TN antigen (a-o-GalNAc linked to Ser/Thr) has particularly attracted a great deal of interest since this antigen has been identified as tumor-associated carbohydrate antigens (TACA) which are highly expressed on tumor cellsJ 21 The incorporation of such a structure in an anticancer vaccine in order to stimulate the immune system to fight tumor cells became a therapeutic strategy. However, the main drawback of such carbohydrate-derived molecules is their low metabolic or chemical stability due to the hydrolytic !ability of the glycosidic bond limiting their use as potential drug candidates.

lt is now well established that the replacement of the anomeric oxygen (or nitrogen) atom of the glycosidic bond by a methylene group provide C-glycoside analogs as stable mim-O Suoportinq informotion and ORCID/s) from the outboris) for this article are e available on the WWW under htrps:/ldoi.org/10.1002/ejoc.202001162.

ics.!3 1 ln that context, numerous research groups have focused their attention on the development of new methodologies to prepare C-glycosyl amino acids. These methods have already been reviewed! 4 l and most of them were focused on C-glycosyl serine. The latter can be synthesized involving, as a key step, Smly-promoted C-glycosylation,! 51 nucleophilic addition on carbohydrate derivative,! 61 metathesis reaction.!" Suzuki coupling!BJ and Wittig-Horner! 91 or Rarnberq-Bäcklund!'?' olefination. Construction of the amino acid moiety on a C-glycoside derivative has also been performed.'!" ln the case of C-glycosyl threonine,! 8 • 121 and C-glycosyl tyrosine,! 8 -131 only a few syntheses have been described. ln addition, the recognition of glycoproteins by the biological target is related to the presentation mode of the glycan part. ln order to modulate the glycan presentation, the syntheses of constrained glycosyl amino acids have been reported. For example, Halcomb et al. prepared a conformationally constrained TN antigen by incorporating the side chain into a small ring! 141 or the Ca of the amino acid in a six-membered ring.! 151 Dondoni et al. focused particularly on the synthesis of C-glycosyl amino acids with the amino acid side chains linked to the carbohydrate moiety via linkers such as triazole or isoxazole,! 161 pyridine,! 171 and tetrazole.! 181 Avenoza and Peregrina demonstrated that their conformationally restricted TN antigen analogs were recognized by the SBL lectin (GalNAc specific lectin).! 19 ! ln addition, Nativi and Renaudet reported the first anti-cancer vaccine containing structurally constrained TN antigen analog which presented a robust and longlasting TN-specific antibodies response through a mechanism mediated by B cells leading to improved protection against cancer in mice.r 201 Herein, we describe the synthesis of original constrained C-glycosyl amino acid derivatives in different series involving a 1,3-dipolar cycloaddition between a nitrone! 2 1J and C-vinylglycoside as key step (Scheme 1). This kind of cycloaddition has already been performed between nitrones and carbohydrate-derived alkenes I22 -24I as dipolarophiles but, to the best of our knowledge, the use of carbohydrate-containing a vinyl group in pseudo-anomeric position has not been described. I25I

Results and Discussion

We recently reported an efficient synthesis of C-vinylglycoside in different series from the corresponding alkynes on gram scale.1 261 The reactivity of such dipolarophiles towards the ethyl glyoxylate-derived nitrone I271 2 was first evaluated. The reaction between this nitrone and both a-and ß-anomers of C-vinylgalactoside 1 a and 1 b in toluene at 100 ºC led to the expected adducts 3a and 3b as a mixture of isomers. Separation of isomers by chromatography on silica, although tough, led in both cases to two isolated diastereoisomers identified as a trans and a cis one, in a 3:1 ratio for the cycloadduct 3a (76 % global yield) and in a 2:1 ratio for the cycloadduct 3b (64 % global yield) (Scheme 2). This predominance of the trans adduct was confirmed by NOESY analyses of each isolated diastereoisomer in the two series (see Supporting Information). While trans diastereoisomers are undoubtedly formed via anexo approach (the less congested) to the E nitrone (the more reactive). I211 the cis diastereoisomers can result from either an exo approach to the Z nitrone or an endo approach to the E nitrone (or from both) ln order to control the cis!trans selectivity, 1,3-dipolar cycloaddition was performed with the configurationally stable cyclic nitrone 4. 1281 The latter was prepared in three steps from methyl glycinate in 70 % overall yield (See supporting information). Heating of the cyclic nitrone with ß-C-vinylgalactoside 1 b in toluene at 11 O ºC for 70 hours led to two cycloadducts 5 in 54 % yield in a 2:1 ratio (Scheme 3). The two compounds were clearly identified as the two trans diastereoisomers from the NOESY spectra. The two trans isomers were derived from an exo approach but no facial discrimination was observed, showing that the chirality of the dipolarophile does not bring any selectivity. To improve the facial selectivity, we focused our attention on chiral cyclic nitrones bearing a bulky group in order to mask one face of the dipole. The reactivity of the Katagiri's nitrone 6a1 29 l with the ¡3-C-vinylgalactoside 1 b was first evaluated. Whatever the activation mode (microwave or Lewis acid), the cycloaddition did not occur (Table 1, entries 1-2). Having in mind the reactivity of the chiral menthone-derived nitrone 6b with C-, 0-, and 5-allyl glycosides reported by either Altenbach et al.1 231 or Praly et al., I301 we then performed the 1,3-dipolar cycloaddition with this dipole. The nitrone 6b was prepared in two steps from L-menthone in a 27 % overall yield. As a first attempt, the procedure described by Altenbach et al. I231 i.e. heating of one equivalent of the nitrone 6b with one equivalent of ¡3-C-vinylgalactoside 1 b in toluene at reflux for 72 hours was reproduced, leading to the formation of only one diastereoisomer of cycloadduct 7b in 36 % yield (entry 3). ln our case, the reaction was incomplete after 72 hours. This can be explained by the use of a more hindered olefin compared with those involved by Altenbach. The NOESY analysis of the cycloadduct allowed clearly the identification of a trans diastereoisomer as a result of an exo approach. Unfortunately, all attempts to obtain a crystalline structure of the unprotected cycloadduct,13 1I in order to determine absolute configurations of the two new stereogenic centers, failed.

W hen the reaction was perfo rm ed in p-xylene at 140 ºC fo r 30 hours, incr easing am ounts of degradation products were observed and the sam e diastereoisom er was isolated in lower 27 % yield (entry 4). Reaction times could be reduced by heating the reaction mixture in a sealed tube at 140 ºC or 160 ºC and the yield was significantly improved to 66 % (entries 5-6). The same range of yield was observed when the reaction was performed at 140 ºC under microwave activation but the reaction time was halved (entry 8). Whatever the activation mode, heating at a higher temperature has resulted in a drop in the yields (entries 7 and 9). Increase of the concentration of the reaction mixture (from 0.1 M to 0.5 M) allowed to isolate the cycloadduct in 75 % yield with only 2 hours of reaction time (entry 1 O). lt is noteworthy that traces of nitrone 6b were recovered along with the cycloadduct after purification since the two compounds had the same Rr. Finally, the use of only 0.9 equivalent of nitrone 6b under the' optimal conditions (described in entry 1 O) furnished a pure cycloadduct without any trace of nitrone 6b in 72 % yield.

The optimal conditions were then applied to different C-vinylglycosides. When the reaction was implemented for the ß-anomers in glucose and mannose series, the corresponding cycloadducts 8 and 9 were isolated, after 2 hours of reaction, in excellent yields of 91 and 90 % respectively (Scheme 4). ln the case of a-anomers in galactose, glucose, and mannose series, a longer reaction time (6 hours) was required to complete the reaction and to access the corresponding cycloadducts 10-12 with good yields (Scheme 4). Both anomers of C-vinylgalactosamines were also subjected to the cycloaddition with nitrone 6b leading to the cycloadduct 13 and 14 after 8 hours of reaction in 77 and 63 % yields respectively (Scheme 4).

NOESY analyses of the cycloadducts showed that only one trans diastereoisomer was formed. ln order to study the facial selectivity, OFT calculations were performed using Gaussian 09 132 ! at M06-2X/6-311 +G (d,p) levei.l 33 l The influence of the solvent (toluene) was studied using the SMD rnodel.'!" With the aim of limiting the possible conformations and the calculation time, the study and the cal- Among all cycloadducts, only cycloadduct 9 showed, on the 1 H NMR spectrum, three doublet signals at 0.78, 0.85, and 0.91 ppm as expected for the three corresponding CH 3 of the menthyl moiety. COSY NMR experiment allowed us to identify the two CH 3 of the isopropyl group which were located at 0.78 and 0.85 ppm (Figure 1 ). Furthermore, NOESY NMR spectrum highlighted a cross-peak between one CH 3 of the isopropyl group and H-3', thus indicating an S absolute configuration for the C-3' stereogenic center (Figure 1 ). As already mentioned, due to a trans relationship between H-1' and H-3', S absolute configuration could be assigned for the C-1' stereogenic center. This diastereoisomer could solely be obtained by an exo approach via the Si face of the nitrone. This total facial selectivity could be due to the strong discrimination imposed by the isopropyl group of the chiral auxiliary of the nitrone 6b. The same stereoselectivity outcome was obtained compared to the one observed by Westerman 123 l and Praly 130 l groups with other dipolarophiles suggesting that the stereoselectivity is exclusively dependent on the stereochemistry of this nitrone. At the top of Scheme 5 are depicted the four cycloadducts that could be produced by the reaction of 1 a' and 6b according to exo/endo approaches and Si/Re face of the nitrone. The energy profile calculated for the four diastereoisomers (Scheme SJ describes the Gibbs free energy at 413K (reaction temperature, 140 ºCJ. Five transition states were found during the study and the most favorable approach was the exo one from the Si face of the nitrone (the less hindered). Indeed, the two lowest transition states observed for this approach (see Scheme 5) corresponded to a different orientation of the vinylic bound which benefits from a larger rotation degree than in the other three approaches. lt is noteworthy that the contribution of the hindered face of the nitrone can be considered as the major factor favoring the two approaches from the Si face of this nitrone.

This total facial selectivity is therefore essentially due to the strong discrimination imposed by the isopropyl group of the chiral auxiliary of the nitrone 6b. These theoretical results are therefore in complete agreement with the experimental ones. Thus, taking into account that the stereoselectivity is only driven by the nitrone, we assumed that all the cycloadducts (from all series) have been formed with the same stereoselectivity.

Finally, in order to complete our study, the cleavage of the chiral auxiliary was implemented on all cycloadducts. Treatment of cycloadduct 7b with an aqueous hydrochloric acid solution in presence of acetic acid at 80 ºC provided the constrained C-galactosyl amino acid derivative 15 in 67 % yield. The same procedure was applied to all the cycloadducts leading to the corresponding original constrained C-glycosyl amino acid derivatives 16-22 in moderate to good yields (Scheme 6).

Conclusion

Experimental Section

All experiments were carried out under argon with anhydrous solvents in dried glassware. THF was dried with activated alumina on a dry station purchased from Innovative Technologies. Commercially available materials were used without further purification. Flash chromatography was performed on silica gel (40-63 urn from Macherey-Nagel) using Reveleris X 2 Grace apparatus. Analytical TLCs were carried out on pre-coated silica gel 60 F254 from Macherey-Nagel. Optical rotations were measured using a Jasco P2000 at the sodium D line ( = 589 nm) with a 1-dm path length cell at 25 ºC. Melting points were measured using Büchi B-545 apparatus. NMR spectra were recorded with a Bruker Avance 400. Chemical shifts are reported in ppm from TMS as the internal standard for the 'H NMR spectrum and from the residual peaks of the solvent (CDCl 3 ) for 13 C NMR spectrum. Structural assignments of the isolated compounds were based on 'H, 13 C, COSY, and HSQC NMR experiments (see Supporting Information for numbering of assignment). Highresolution mass spectroscopy was performed with a Bruker micro-TOF QIII mass spectrometer using ESI techniques.

General Procedure for [3+2] Cycloaddition with Nitrone 6b: C-vinylglycoside (1 equiv.) and nitrone (0.9 equiv.) were dissolved in toluene (3 ml, C = 0.5 M). General Procedure for Cleavage of Chiral Auxiliary: A solution of cycloadduct (7b and 8-14) in AcOH (12.5 ml for l mmol) and aqueous 1 M HCI (2.5 ml for 1 mmol) was stirred at 80 ºC for 2 h. The reaction mixture was diluted with EtOAc (30 ml) and a saturated aqueous NaHCO 3 solution (30 ml). Aqueous layer was extracted with EtOAc (30 ml) and organic layers were dried with MgSO., and concentrated under reduced pressure to afford the crude product.

N-

1 .

 1 Scheme 1. General strategy for the synthesis of consrrained C-glycosyl amino acid derivatives.

1 Scheme 2 .

 12 Scheme 2. Reaction between nitrone 2 and C-vinylgalactoside 1 a and 1 b.

Figure 1 .

 1 Figure 1. Main NOESY NMR cross-peaks of cycloaclduct 9.

1 " 5 .

 15 Scheme 5. Different approaches of 1,3-dipolar cycloaddition of nitrone 6b with C-vinylgalactoside 1a' and profiles of óóG, 13 (calculations performed at M06-2X/6-31 l+G(d,p) SMD (toluene) level).

  ln summary, we described a two-step synthesis of original conformationally restricted C-glycosyl amino acid derivatives in different series involving 1,3-dipolar cycloaddition between L-(-)menthone-derived nitrone and C-vinylglycosides as key step.The 1,3-dipolar cycloaddition reaction was totally regio-and stereoselective leading to only one diastereoisomer in good to excellent yields whatever the dipolarophile. Based on both NMR experiments and DFT calculations, we showed that all the cycloadducts could solely be obtained by an exo approach via the Si face of the nitrone with total facial discrimination. The cleavage of the chiral auxiliary allowed to access new constrained C-glycosyl amino acid-derivatives as interesting building blocks.Opening of the isoxazolidine ring and functionalization of the pseudo-anomeric position, offering the possibility to prepare different analogs of C-glycosyl serine, are currently ongoing.

Cycloadduct ( 11 ):

 11 Following the general procedure (4 h), a-C-vinylglucoside (289 mg, 0.52 mmol) afforded cycloadduct 11 (228 mg, 0.28 mmol, 61 %) after purification by column chromatography (cy-clohexanelEtOAc, 95:S to 87:13). Colorless oil. Rr = 0.44(cyclohex- anelEtOAc, 6:4). (aJß 5 + 48.4 (e 1.24, CHCl 3 ). HRMS (ESI+): Calculated for C49H 61 N 2 0 7 [M + HJ+: miz= 789.4473, found 789.4453. 1 H NMR (400 MHz, CDCl 3 ): ó 7.33-7.24 (m, 18H, ArH), 7.16-7.12 (m, 2H, ArH), 4.91 and 4.78 (AB syst, J = 10.8 Hz, 2H, CH 2 Ph). 4.81 and 4.49 (AB syst, J = 10.S Hz, 2H, CH 2 Ph), 4.72 and 4.59 (AB syst, J = 11.6 Hz, 2H, CH 2 Ph), 4.61 and 4.47 (AB syst, J = 12.0 Hz, 2H, CH 2 Ph), 4.19-4.14 (m, 1 H, H-1'), 4.11-4.06 (m, 1 H, H-5), 3.98 (t, J = 9.2 Hz, 1 H, H-3), 3.96-3.88 (m, 2H, H-1, H-3'), 3.83-3.78 (m, 1 H, H-2). 3.67-3.64 (m. 2H, H-6), 3.61 (t, J = 9.2 Hz, lH, H-4), 2.72 (s, 3H, N-CH 3 ), 2.69-2.51 (m, 2H, H-2'), 2.16-2.01 (m, 2H), 1.80-1.67 (m, 2H), 1.59-1.50 (m, 1H).1.43-1.35 (m, lH), 1.33-1.25 (m, lH), 1.15 (t, J = 12.3 Hz, 1H), 0.93-0.72 (m, 10H).

Cycloadduct ( 14 ):

 14 Following the general procedure (8 h), ß-C-vinyl-N-acetylgalactoside (462 mg, 0.921 mmol) afforded cycloadduct 14 (431 mg, 0.58 mmol, 63 %) after purification by column chromatography (cyclohexanelEtOAc, 5:5 to 3:7). Orange solid. M.p. 69.5-71.S ºC. Rr = 0.2 (cyclohexanelEtOAc, 3:7). [aJß 5 +40.1 (e 1.0, CHCl 3 ).HRMS (ES/+): Calculated for C 44 H 58 N 3 0 7 [M + HJ+: miz = 740.4269, found 740.4264. 'H NMR (400 MHz, CDCl 3 ): ó 7.38-7.21 (m, 15H, ArH), 5.21 (d, J = 7.7 Hz, 1 H, NH), 4.87 and 4.57 (AB syst, J = 11.6 Hz, 2H, CH 2 Ph), 4.66 and 4.41 (AB syst, J = 11.8 Hz, 2H, CH 2 Ph), 4.46 and 4.41 (AB syst, J = 11.8 Hz, 2H, CH2 Ph), 4.01-3.97 (m, 1 H, H-4), 3.95-3.84 (m, 3H, H-1 ', H-3', H-3), 3.84-3.75 (m, 1 H, H-2), 3.73-3.67 (m, 1H, H-1), 3.57-3.52 (m, 3H, H-5, H-6), 2.68 (s, 3H, N-CH 3 ), 2.71-2.64 (m, 1 H, H-2'). 2.57-2.48 (m, 1 H, H-2'), 1.98-1.89 (m, 2H). 1.86 (s, 3H, COCH 3 ), 1.82-1.74 (m, 1 H), 1.73-1.60 (m. 1 Hl, 1.59-1.50 (m, 1 H), 1.42-1.33 (rn, 1 H), 1.33-1.25 (m, 1 H), 1.25-1.16 (m. 1 H), 0.90-0.83(m, 1 HJ, 0.90 (d, J = 6.4 Hz, 3H), 0.82 (d, J = 6.8 Hz, 3H), 0.79 (d, J = 6.7 Hz, 3H).

i

  soxazo Ii di ne-3-a mid e (1 S): îhe crude product was purified by column chromatography (cyclohexanelEtOAc, 80:20 to 25:75) to provide compound 1 S (218 mg, 0.

N-Methyl- 5 -

 5 (2,3 ,4,6-tetr a-O-be nzyl-ß-C-o-m an n opy ran os-1 -yl )is oxa zol id in e-3-a mid e (17): The crude product was purified by column chromatography (cyclohexanelEtOAc, 80:20 to 25:75) to provide compound 17 (21 O mg, 0.32 mmol, 59 %). Colorless oil. Rr = 0.25 (cyclohexanelEtOAc, 3:7). [albs + 2.3 (c 1.03, CHCl 3 ). HRMS (ESr-J: Calculated for C 39 H•sN 2 O 7 [M + HJ+: miz= 653.3221, found 653.3232. 1 H NMR (400 MHz, CDCl 3 ): ó 7.37-7.24 (m, 19H, ArH, NH), 7.22-7.18 (m, 2H, ArH), 6.09-5.86 (br s, lH, NH), 4.93 and 4.63 (AB Sys t. J = 11.3 Hz, 2H, CH 2 Phl, 4.84 and 4.56 (AB sys t. J = 10.8 Hz, 2H, CH 2 Ph), 4.75 and 4.70 (AB syst. J = 11.8 Hz, 2H, CH 2 Ph), 4.57 and 4.47 (AB syst. J = 12.0 Hz, 2H, CH 2 Ph), 4.19-4.13 (m, l H, Hl'),

  The crude product was purified by column chromatography(cyclohexanelAcOEt, 80:20 to 25:75) to provide compound 20 (297 mg, 0.45 mmol, 62 %). Colorless oil. Rr = 0.15(cyclohexanelEtOAc, 3:7). [albs + 60.7 (e 1.0, CHCl 3 ). HRMS (ES¡+): Calculated for C 39 H 4 sN 2 O 7 [M + Ht; miz = 653.3221, found 653.3215. 1 H NMR (400 MHz, CDCl 3 ): ó 7.36-7.18 (m, 21H, NH, ArH), 7 6.37 (br s, 1 H, NH), 4.58-4.42 (m, 7H, CH 2 Ph, H-1 '), 4.40 and 4.34 (AB syst. J = 12.2 Hz, 2H, CH 2 Ph), 4.13-4.08(m, l H, H-5), 4.03 (dd, J = 9.7, 2.8 Hz, 1 H, H-3), 3.94-3.90 (m, 1 H, H-3'), 3.82 (t, J = 2.8 Hz, 1 H, H-2), 3.77 (dd, J = 9.7, 0.8 Hz, 1 H, H-4), 3.73 (dd, 1 H, J = 10. l, 8.2 Hz, H-6), 3.55-3.49 {m, 2H, H-1, H-6), 2.84-2.77 (m, 1H, H-2'), 2.80 (d, J = 5.0 Hz, 3H, N-CH 3 ), 2.64-2.56 {m, 1 H, H-2'). 13 C NMR { 100.6 MHz, CDCl 3 ): ó = 172.7 (C=O), 137.9 (2 C), 137.8 (2 C), 128.4 (5 CH), 127.9 (3 CH), 127.8 (CH), 127.7 (2 CH), 127.5 (CH), 77.3 (Cl'), 75.4 (Cl), 74.9 (CS), 74.1 (C3), 73.6 (C2), 73.3 (CH 2 ), 73.0 (C4), 72.8 (CH 2 ), 72.3 (CH 2 ), 71.4 (CH 2 ), 68.3 (C6), 62.7 (C3'), 34.8 (C2'), 25.9 (CH 3 ).

Table l .

 l Optimization of the 1,3-dipolar cycloaddition of nitrone 6 with ß-Cvinylgalactoside 1 b.

	BnÕBn -O BnO Bnü 1b	""'	0i;k 0-N 04 X 6a, X= O O 6b, X= NMe	K Conditions. Bnü ÕBn ~~V' x o . BnO ' o BnO 7a, X= O
				1 eq.	7b, X= NMe
	Entry	Nitrone	Conditions	Yield[%]
	l	6a		CH 3 CN, 140 ºC. µ-waves, 7 h
	2	6a		BF 3 ,0Et 2 , CH 3 CN, 72 h, r.t.
	3	6b		toluene, 11 O ºC, 0.1 M, 72 h	36
	4	6b		p-xylene. 140 ºC. 0.1 M, 30 h	27
	5	6b		toluene, 140 •e, sealed tube, 0.1 M, 20 h	61
	6	6b		toluene, 160 ºC. sealed tube, 0.1 M, 16 h	66
	7	6b		toluene, 180 'C, sealed tube, O. I M, 3 h	38
	8	6b		toluene, 140 ºC, µ-waves, 0.1 M, 7 h	69
	9	6b

toluene, 160 <e, u-waves. 0.1 M, 4 h 35 10 6b toluene, 140 ºC. µ-waves, 0.5 M, 2 11 75

Methyl-5-(2, 3,4,6-tetra-O-benzyl-ß-C-o-g I ucopyranos-1-yl )- isoxazolidine-3-am ide (16): The

	33 mmol, 67 %). Colorless oil. R 1 =
	0.23 (cyclohexanelEtOAc, 3:7). [albs -6.9 (e 0.57, CHCl 3 ). HRMS (ES¡+):
	Calculated for C 39 H 4 sN 2 O 7 [M + HJ+: miz= 653.3221, found
	653.3210. 1 H NMR (400 MHz, CDCl 3 ): ó 7.38-7.23 (m, 21H, ArH, NH),
	6.10-6.08 (m, 1 H, NH), 4.98-4.85 (m, 2H, CH 2 Ph), 4.78-4.62 (m, 2H,
	CH 2 Ph), 4.59-4.35 (m, SH, CH 2 Ph, H-1'), 3.94-3.90 (m, 1 HJ, 3.87-3.81
	(m, 1 H, H-3'), 3.65-3.54 (m, 4H), 3.51-3.40 (m, 2H), 2.79 (d, J = 4.9 Hz,
	3H, NCH 3 ), 2.64-2.56 (m, 1 H, H-2'), 2.42-2.34 (m, 1 H, H-2'). 13 C NMR
	(100.6 MHz, CDCl 3 ): ó = 172.5 (C=O), 138.6 (C), 138.0 (C), 137.6 (2
	C), 128.S (CH), 128.4 (2 CH), 128.2 (2 CH), 128.0 (CH), 127.9 (2 CH),
	127.8 (2 CH), 127.7 (CH), 127.4 (CH), 84.4, 82.3, 78.3, 76.3, 75.2 (CH 2 ),
	75. l, 74.4 (CH 2 ), 73.4 (CH 2 ), 72.2 (CH 2 ), 68.8 (C6), 62.9 (C3'), 32.0
	(C2'), 25.8 (CH 3 ).
	crude product was purified by
	column chromatography (cyclohexanelEtOAc, 80:20 to 25:75) to
	provide compound 16 (94 mg, 0.14 mmol, 61 %). White solid. M.p.
	156.5-158.1 ºC. R 1 = 0.23 (cyclohexanelEtOAc, 3:7). [albs -3.2 (e 0.95,
	CHCl 3 ). HRMS (ESI+): Calculated for C 39 H 4 sN 2 O 7 [M + HJ+: miz =
	653.3221, found 653.3233. 'H NMR (400 MHz, CDCl 3 ): ó 7.36-7.18
	(m, 21 H, NH, ArH), 6.17 (d, J = 5.0, 1 H, NH), 4.91 and 4.87 (AB syst.
	J = 10.9 Hz, 2H, CH 2 Ph), 4.83 and 4.57 (AB syst. J = 11.0 Hz, 2H,
	CH 2 Ph), 4.82 and 4.53 (AB syst. J = 10.8 Hz, 2H, CH 2 Ph), 4.48 and
	4.43 (AB syst. J = 12.1 Hz, 2H, CH 2 Ph), 4.41-4.36 (m, 1 H, H-1 '), 3.85-
	3.79 (m, lH, H-3'), 3.72-3.57 (m, 3H, H-1, H-3, H-6), 3.57-3.45 (m,
	3H, H-4, H-5, H-6), 3.21 (t, J = 9.4 Hz, 1 H, H-2), 2.80 (d, J = 5.0 Hz,
	3H, N-CH 3 ), 2.46-2.54 (m, 1 H, H-2'}, 2.32-2.40 (m, 1 H, H-2'). 13 C NMR
	(100.6 MHz, CDCl 3 ): ó = 172.4 (C=O), 138.2 (C), 137.9 (2 C), 137.3
	(C), 128.6 (CH), 128.5 (3 CH), 128.4 (CH), 128.2 (CH), 127.9 (2 CH),
	127.8 {CH), 127.7 (2 CH), 127.6 (CH), 86.9 (C3), 82.0 (Cl), 78.7 (C2),
	78.3 (C4 or CS), 78.2 (Cl'), 78.0 (C4 or CS), 75.5 (CH 2 ), 75.1 (CH 2 ),
	75.0 (CH

N-2 ), 73.2 (CH 2 ), 69.1 (C6), 62.8 (C3'), 32.0 (C2'), 25.9 (CH 3 ).

  The crude product was purified by column chromatography(cyclohexanelEtOAc, 80:20 to 25:75) to provide compound 18 (809 mg, 1.24 mmol, 62 %). Colorless oil. Rr = 0.13(cyclohexanelEtOAc, 3:7). [albs + 46.7 (c O.SS, CHCl 3 ). HRMS {ESl+J: Calculated for C 39 H 44 N 2 O 7 Na [M + Na}": miz= 675.3041, found 675.3043. 'H NMR (400 MHz, CDCl 3 ): ó 7.36-7.21 (m, 21H, A rH, NH), 4.73-4.46 (m, 8H, CH 2 Ph), 4.39-4.32 (m, 1 H, H-1 '), 4.31-4.25 {m,lH, H-1), 4.02-3.96 (m, lH), 3.91-3.64 (m, SH), 3.61-3.50 {m, l H, H-6), 2.80-2.74 (m, 3H, N-CH 3 ), 2.70-2.60 (m, l H, H-2'), 2.28-2.19 {m, 1 H, H-2'). 13 C NMR (100.6 MHz, CDCl 3 ): ó 17 l.7 (C=O), 138.4 (C), 138.3 (C), 138.2 (Cl, 137.8 (C), 128.4 (3 CH), 128.3 (CH), 128. l (CH), 127.9 (CH), 127.8 (2 CH), 127.7 (CH), 127.6 (2 CH), 127.5 (CH), 78.9 (Cl'), 76.0 (CH), 74.7 (Cl), 74.0 (CH), 73.3 (CH 2 ), 73.2 (3 CH 2 ), 72.9 (CH), 71.3 (CH), 68.0 (C6), 62.2 (C3'), 36.9 (C2'), 25.9 (CH 3 ). The crude product was purified by column chromatography (cyclohexanelEtOAc, 80:20 to 25:75) to provide compound 19 (211 mg, 0.32 rnrnol, 73 %). Colorless oil. Rr = 0.13 (cyclohexanelEtOAc, 3:7). [albs + 34.2 (e 1.04, CHCl 3 ). HRMS (ESl+J: Calculated for C 39 H. 4 N 2 O 7 Na [M + Na]": miz= 675.3041, found 675.3041. 1 H NMR (400 MHz, CDCl 3 ): ó 7.37-7.24(m, 18H, ArH), 7.23-7.18 {m, 2H, ArH), 7.12 (br s, lH, NH), 5.96 (br s, lH, NH), 4.87 and 4.78 (AB syst. J = 10.8 Hz, 2H, CH 2 Ph), 4.78 and 4.74 (AB syst. J = 11.8 Hz, 2H, CH 2 Ph), 4.60 and 4.56 (AB syst. J = 12.0 Hz, 2H, CH 2 Ph), 4,50-4.43 (m, 3H, CH 2 Ph, H-1 ') 4,02-3.85(m, 3H, H-2, H- 4, H-3'), 3.81-3.75 (m, 2H, H-1, H-3), 3.68 (dd, 1H, J = 10.4, 2.3 Hz, H-6), 3.56 (dd, lH, J = 10.4, 5.3 Hz, H-6), 3.55-3.51 (m, lH, H-5), 3.43-3.40 (m, 1 H, H-1 ), 2.80 (d, J = 5.0 Hz, 3H, N-CH 3 ), 2.79-2.70 (m, 1 H, H-2'),2.45-2.35 (m, 1 H, H-2'). 13 C NMR (100.6 MHz, CDCl 3 ): ó 171.3 (C=O), 138.5 (C), 138.1 {C), 138.0 (C), 137.7 (C), 128.5 (CH), 128.4 (CH), 128.3 (2 CH), 128.0 {CH), 127.9 (CH), 127.8 (3 CH), 127.7 (2 CH), 127.6 (CH), 82.4 (C2), 78.8 (Cl), 77.9 (CS), 76.5 (Cl'), 75.1 (CH 2 ), 74.7 (C4), 74.6 (CH 2 ), 73.7 (CHi), 73.5 (CH 2 ), 69.6 (C6), 62.2 (C3'), 36.9 {C2'), 26.0 (CH 3 ).

	3.92-3.90 (m, 1 H, H-2), 3.86-3.81 (m, 2H, H-3', H-4), 3.72-3.67 (m,
	l H, H-6), 3.65-3.56 (m, 2H, H-3, H-6), 3.50-3.45 (m, l H, H-5), 3.43-
	3.40 (m, 1 H, H-1 ), 2.92-2.84 (m, 1 H, H-2'), 2.80 (d, J = 5.0 z, 3H, N-
	CH3), 2.70-2.62 (m, 1 H, H-2'). 13 C NMR (100.6 MHz, CDCl 3 ): ó = 172.2
	(C=O), 138.1 (4 Cl, 128.4 (CH), 128.3 (3 CH), 128.2 (CH), 128.0 (2 CH),
	127.7 (2 CH), 127.6 (CH), 127.5 (CH), 127.4 (CH), 84.S (C3), 80.2 (Cl),
	79.5 (Cl' and CS), 75.2 (CH 2 ), 75.0 (C4), 74.4 (CH 2 ), 74.4 (C2), 73.2
	(CH 2 ), 72.4 (CH 2 ), 69.6 (C6), 62.6 (C3'), 34.8 (C2'), 25.8 (CH 3 ).
	N-Methyl-5-( 2, 3,4,6-tetra-O-benz yl-a-C-o-g alactopy ra nos-1-yl )-

i soxazol id in e-3-a mid e (18): N-Methyl-5-(2,3,4,6-tetra-O-benzyl-a-C-o-g lucopyranos-1-yl)i soxazol idi ne-3-am ide { 19):

Acknowledgments

This work was supported by the Région des Pays de la Loire through the GlycoOuest program and the Ministère de l'Enseignement Supérieur et de la Recherche of France [Ph.D. fellowship (F. R.)]. We also thank Frédéric Legros for technical support, Sullivan Bricaud for the NMR analyses, Patricia Gangnery and Alexandre Bénard for the HRMS analyses.


Khalid Rind

Quentin Rodriguez-Barucg

Delphine Nicolas

Patricia Cucchi

Jehan-Hervé Lignot
email: jehan-herve.lignot@umontpellier.fr

Morphological and physiological traits of Mediterranean sticklebacks living in the Camargue wetland (Rhone river delta)

Keywords: osmoregulation, oxygen consumption, salinity, morphometry

Three-spined sticklebacks (Gasterosteus aculeatus L.) living at the southern limit of the species distribution range could possess specific morphological and physiological traits that enable these fish to live at the threshold of their physiological capacities. Morphological analysis was carried out on samples of sticklebacks living in different saline habitats of the Camargue area (Rhone delta, northern Mediterranean coast) obtained from 1993 to 2017. Salinity acclimation capacities were also investigated using individuals from freshwater-low salinity drainage canals and from mesohaline-euryhaline lagoons. Fish were maintained in laboratory conditions at salinity values close to those of their respective habitats: low salinity (LS, 5‰) or seawater (SW, 30‰). Fish obtained from a mesohaline brackish water lagoon (BW, 15‰) were acclimated to SW or LS. Oxygen consumption rates and branchial Na+/K+-ATPase (NKA) activity (indicator of fish osmoregulatory capacity) were measured in these LS or SW control fish and in individuals subjected to abrupt SW or LS transfers. At all the studied locations, only the low-plated "leiurus" morphotype showed no spatial or temporal variations in their body morphology. Gill rakers were only longer and denser in fish sampled from the LS-freshwater (FW) drainage canals. All fish presented simi-lar physiological capacities. Oxygen consumption rates were not influenced by salin-ity challenge except in SW fish transferred to LS immediately and 1 h after transfer. However, and as expected, gill NKA activity was salinity dependent. Sticklebacks of the Camargue area sampled from habitats with contrasted saline conditions are homogenously euryhaline, have low oxygen consumption rates and do not appear to experience significantly greater metabolic costs when challenged with salinity. How-ever, an observed difference in gill raker length and density is most probably related to the nutritional condition of their habitat, indicating that individuals can rapidly acclimatize to different diets.

INTRODUCTION

Most of the work on rapid evolution in three-spined sticklebacks and adaptation to freshwater has focused on northern populations [START_REF] Defaveri | Global analysis of genes involved in freshwater adaptation in threespine stick-lebacks (Gasterosteus aculeatus)[END_REF][START_REF] Hohenlohe | Population genomics of parallel adaptation in threespine stickleback using sequenced RAD tags[END_REF][START_REF] Mäkinen | Genetic relationships among marine and freshwater populations of the European three-spined stickleback (Gasterosteus aculeatus) revealed by microsatellites[END_REF][START_REF] Taugbøl | Small changes in gene expression of targeted osmoregulatory genes when exposing marine and freshwater threespine stickleback (Gasterosteus aculeatus) to abrupt salinity transfers[END_REF] and very few studies have considered southern populations, notably those of the Mediterranean bioclimatic region which constitutes the southern limit of the species range in the west-ern Palearctic [START_REF] Crivelli | Life history adaptations of Gasterosteus aculeatus in a Mediterranean wetland[END_REF]. Furthermore, some of these southern peripheral populations have steeply declined [START_REF] Clavero | Biology and habitat use of three-spined stickleback (Gasterosteus aculeatus) in intermittent Mediterranean streams[END_REF][START_REF] Foster | The case for conserving threespine stickleback populations: protecting an adaptive radiation[END_REF][START_REF] Kottelat | Handbook of European freshwater fishes[END_REF]. For example, in the Iberian Peninsula, the species is now considered to be endangered following IUCN criteria, after the occurrence of multiple local extinction events from most of its past distribution [START_REF] Araguas | High genetic diversity of the endangered Iberian three-spined stickleback (Gasterosteus aculeatus) at the Mediterranean edge of its range[END_REF][START_REF] Clavero | Biology and habitat use of three-spined stickleback (Gasterosteus aculeatus) in intermittent Mediterranean streams[END_REF][START_REF] Foster | The case for conserving threespine stickleback populations: protecting an adaptive radiation[END_REF][START_REF] Reimchen | Status of unarmoured and spine-deficient populations (Charlotte unarmoured stickleback) of threespine stickle-back, Gasterosteus sp., on the queen Charlotte Islands, British Colum-bia[END_REF][START_REF] Sanz | Glacial refuges for three-spined stickleback in the Iberian Peninsula: mitochondrial DNA phylogeography[END_REF][START_REF] Vila | Phylogeography and conservation genetics of the Ibero-Balearic three-spined stickleback (Gasterosteus aculeatus)[END_REF]. Similarly, this species is listed as threatened or endangered in some Neoarctic locations. For example, the unarmoured three-spined stickleback subspecies Gasterosteus aculeatus williamsoni, located in Southern California, has been on the U.S. Fish and Wildlife Services Endangered Species List since 1970. Other stocks of sticklebacks have also been listed as threatened by states such as Massachusetts and Pennsylvania (Williams et al., 1989). However, along the northern coast of the Mediterranean Sea, stickle-backs living in the Camargue area (Rhone delta) are still abundant [START_REF] Poizat | Life-history variation within a three-spined stickleback population in the Camargue[END_REF][START_REF] Rind | Effects of different salinities on the osmoregula-tory capacity of Mediterranean sticklebacks living in freshwater[END_REF]. The

Camargue is an ecological hotspot of diversity and has been a Biosphere Reserve since 1977. It has an exceptional biological richness and covers 13,000 ha between the northern mesohaline, brackish water Vaccares lagoon and the Mediterranean Sea. It is made up of freshwater ponds and shallow water canals with abundant vegetation, freshwater drainage canals with submerged vegetation, mesohaline (brackish water) and euryha-line (brackish to hypersaline) lagoons flooded throughout the year [START_REF] Crivelli | Life history adaptations of Gasterosteus aculeatus in a Mediterranean wetland[END_REF].

Since the last ice age ended about 10,000 years ago, sticklebacks have repeatedly colonized freshwater habitats because thousands of new streams and lakes formed during glacial retreats [START_REF] Bell | The evolutionary biology of the threespine stickleback[END_REF][START_REF] Schluter | The ecology of adaptive radiation[END_REF]. Therefore, postglacial freshwater stickleback populations share a common suite of adaptation throughout the northern hemisphere such as armour reduction [START_REF] Bell | Interacting evolutionary constraints in pelvic reduction of threespine sticklebacks, Gasterosteus aculeatus (Pisces, Gas-terosteidae)[END_REF][START_REF] Bell | The evolutionary biology of the threespine stickleback[END_REF][START_REF] Colosimo | Widespread parallel evolution in sticklebacks by repeated fixation of ectodysplasin alleles[END_REF]. They also differ significantly in morphology due to divergent selective pressures that they experi-ence in contrasting freshwater habitats [START_REF] Baumgartner | Spatial variation of morphology in a freshwater population of the threespine stickleback, Gasterosteus aculeatus[END_REF][START_REF] Bell | Differentiation of adjacent stream populations of threespine sticklebacks[END_REF][START_REF] Reimchen | Multivariate differ-entiation of parapatric and allopatric populations of threespine stickle-back in the Sangan River watershed, Queen Charlotte Islands[END_REF][START_REF] Spoljaric | 10 000 years later: Evolution of body shape in Haida Gwaii three-spined stickleback[END_REF]. For example, divergent natural selection for the exploitation of benthic vs. limnetic habitats and associated food items is one of the most com-mon diversifying mechanisms affecting resident freshwater stickle-backs [START_REF] Walker | Ecological morphology of lacustrine threespine stick-leback Gasterosteus aculeatus L. (Gasterosteidae) body shape[END_REF][START_REF] Spoljaric | 10 000 years later: Evolution of body shape in Haida Gwaii three-spined stickleback[END_REF]. Sticklebacks also inhabit a large number of coastal brackish water systems throughout the northern hemisphere and present therefore an extremely wide haloniche [START_REF] Bell | The evolutionary biology of the threespine stickleback[END_REF][START_REF] Wootton | Biology of the sticklebacks[END_REF].

Most fish species living in their native freshwater or marine environments are stenohaline and are not able to survive non-native salin-ities.

However, for euryhaline fish such as sticklebacks, the osmoregulatory machinery is adapted to a wide range of salinities.

These fish can sustain salinity variations of their environment and move or migrate to non-native salinities [START_REF] Moyle | Fishes. An introduction to ichthyology[END_REF].

However, osmoregulation must be costly to maintain [START_REF] Perry | Proton pumps in the fish gill and kidney[END_REF]. This cost is expected to be higher in non-native environ-ments compared to native environments due to local acclimation pro-cesses. For instance, the expression of genes related to osmoregulation is considered to be reduced in native environments because of the selection for reduced energy expenditure [START_REF] Aykanat | Rapid evolution of osmoregulatory function by modification of gene transcription in steelhead trout[END_REF]. Although this physiological plasticity facilitates acclima-tion and the colonization of novel environments (through strong eury-haline capacity), the bioenergetic costs (increased lipid, protein and carbohydrate metabolism) and possible associated physiological trade-offs may, however, lead ultimately to adaptive evolution [START_REF] Dalziel | Linking genotypes to phenotypes and fitness: how mechanistic biology can inform molecular ecology[END_REF][START_REF] Komoroske | Sublethal salinity stress contrib-utes to habitat limitation in an endangered estuarine fish[END_REF][START_REF] Schulte | Environmental adaptations as windows on molecular evolution[END_REF][START_REF] Watt | Bioenergetics and evolutionary genetics: opportunities for new synthesis[END_REF].

The physiological mechanisms involved to maintain ion and water homeostasis are coordinated between the gills, the kidney and the gut [START_REF] Eddy | Ecological and environmental physiology of fishes[END_REF]. In fish, the ionocytes, also known as the chloride cells or mitochondria rich cells (MRCs), are crucial cells to facilitate ion transport [START_REF] Laurent | Gill internal morphology[END_REF][START_REF] Jurss | The function of mitochondria-rich cells (chloride cells) in teleost gills[END_REF][START_REF] Rind | Effects of different salinities on the osmoregula-tory capacity of Mediterranean sticklebacks living in freshwater[END_REF]. The internal structure of these cells is rich in mitochon-dria and also possesses a tubulovesicular system composed of basal membrane invaginations containing the sodium pump, Na + /K + -ATPase, or NKA [START_REF] Evans | Osmotic and ionic regulation in fishes[END_REF][START_REF] Dymowska | Structure and func-tion of ionocytes in the freshwater fish gill[END_REF]. This key enzyme involved in salinity tolerance [START_REF] Herrera | Osmoregulatory changes in wedge sole (Dicologoglossa cuneata Moreau, 1881) after acclimation to different environmental salinities[END_REF][START_REF] Sampaio | Salinity effects on osmoregulation and growth of the euryhaline flounder Paralichthys orbignyanus[END_REF][START_REF] Yang | Na+/K+-ATPase expression in gills of the euryhaline sailfin molly, Poecilia latipinna, is altered in response to salinity challenge[END_REF] is responsible for the exclusion of three sodium ions from the cell in exchange for two potassium ions, requiring the hydrolysis of one ATP molecule. Its activity maintains cell membrane potential, facilitates ion transport via channels and transporters that are localized in the apical and bas-olateral membranes, and thus maintains osmotic equilibrium and cell volume. NKA is mostly located in gill ionocytes, the intestinal absorb-ing enterocytes and ionocytes found along the tubules of the kidney [START_REF] Evans | Osmotic and ionic regulation in fishes[END_REF]. NKA activity has already been measured in the gills and kidney of sticklebacks kept at different salinities [START_REF] Divino | Osmoregulatory physiology and rapid evolution of salinity tolerance in threespine stick-leback recently introduced to fresh water[END_REF][START_REF] Judd | Na+/K+-ATPase isoform regulation in three-spine stickleback (Gasterosteus aculeatus) during salinity acclimation (Masters degree the-sis)[END_REF][START_REF] Jurss | Experimental studies on biochemical and physiological differences between the three mor-phs of the 3-spined stickleback, Gasterosteus aculeatus L .1. Gill Na/K-ATPase, muscle alanine aminotransferase and muscle aspartate-aminotransferase activities[END_REF][START_REF] Schaarschmidt | A comparison of transport-related gill enzyme activities and tissue-specific free amino acid concentrations of Baltic Sea (brackish water) and freshwater threespine sticklebacks, Gasterosteus aculeatus, after salinity and tem-perature acclimation[END_REF]. Also, changes in salinity and the coordinated physiologi-cal response are often reflected by different oxygen consumption rates [START_REF] Gracia-Lopez | Effects of salinity on physiological conditions in juvenile common snook Cen-tropomus undecimalis[END_REF][START_REF] Morgan | Physiologi-cal and respiratory responses of the Mozambique tilapia (Oreochromis mossambicus) to salinity acclimation[END_REF]. This measure-ment can be used as an indicator of fish metabolism [START_REF] Cech | Respirometry[END_REF] and to assess the osmoregulatory cost [START_REF] Da Silva Rocha | Metabolic demand and growth of juveniles of Cen-tropomus parallelus as function of salinity[END_REF][START_REF] Morgan | Salinity effects on oxygen consump-tion, gill Na+, K+-ATPase and ion regulation in juvenile coho salmon[END_REF][START_REF] Tsuzuki | Effect of salinity on the oxygen consumption of larvae of the silversides Odontesthes hatcheri and O. bonariensis (Osteichthyes, Atherinopsidae)[END_REF].

This cost can impact growth rate [START_REF] Boeuf | How should salinity influence fish growth?[END_REF][START_REF] Imsland | Gill Na +, K+-ATPase activity, plasma chloride and osmolality in juvenile tur-bot (Scophthalmus maximus) reared at different temperatures and salin-ities[END_REF][START_REF] Woo | Effects of salinity and nutritional status on growth and metabolism of Sparussarba in a closed seawater system[END_REF] with also a minimal osmoregulatory energy demand in an environment that is natural for a particular species, therefore indicat-ing some fitness-related advantages of being adapted to local environ-mental salinities [START_REF] Morgan | Effects of salinity on growth, metab-olism, and ion regulation in juvenile rainbow and steelhead trout (Oncorhynchus mykiss) and fall Chinook salmon (Oncorhynchus tshawytscha)[END_REF].

The aim of this study was to determine whether Mediterranean sticklebacks living in different saline environments (freshwater-low salinity drainage canals and euryhaline-seawater lagoons) of the Camargue area have different morphological and physiological traits. It is hypothesized that this coastal population is morphologically homogenous. However, fish sampled from contrasted saline water bodies could respond differentially when challenged with abrupt salin-ity transfers. It is predicted that oxygen consumption rates, as a mea-sure of metabolic rate, could reflect the key functional osmoregulatory changes that occur with salinity changes, such as NKA activity modulations. To test these hypotheses, we analysed the morphology of fish sampled directly from the different aquatic envi-ronments, Acclimated sticklebacks were challenged with abrupt salin-ity transfers in controlled experimental conditions to evaluate whether some phenotypic traits could be habitat specific at different physiological levels (gill NKA activity and individual oxygen consumption).

MATERIALS AND METHODS

| Fish sampling and experimental design

In the Camargue region, a protected area located within the Rhone river delta in Southern France, subadult three-spined sticklebacks (Gasterosteus aculeatus)

were fished from 1993 to 2017 and from dif-ferent water bodies (Table 1) using fixed hoop nets of decreasing mesh size from 13 to 6 mm at the end of the hoop net ("capéchade"). This sampling was carried out to determine how homogenous the population had been over the last 24 years and to determine whether migration and mixing could occur in this coastal wetland area. Immediately after fishing, some of the collected fish were directly fixed in 10% formalin (salinity ranging from 20 to 50‰). These salinities recorded during fish sampling correspond to the salinities typically measured during that period of the year (winter). However, the highest salinities up to 50‰ were only be recorded during the summer period. These sites are partially interconnected, but their topography could limit migration and mixing among sticklebacks living in these contrasted habitats.

Typically, dams, "salt dams" and the numerous locks along the drainage canals and between lagoons could constrain fish dispersal.

Captured fish were directly transported to the laboratory facility at the University of Montpellier, France in separate large oxygenated containers filled with water from the respective sampling sites. Fish were then kept at room temperature (21 □ C) and under a natural pho-toperiod in separate tanks containing 100 l of recirculated and filtered water (12 fish per tank with an approximate 1:1 sex ratio) for an accli-mation period of 2-3 weeks. Fish were then transferred to 40 l tanks and maintained at different salinities for another 2 weeks. Fish from the BW Vaccares lagoon were acclimated to 30‰ or 5‰, those from the BW/SW Marteau lagoon were kept at 30‰ and those from the FW-LS Versadou canal at 5‰. Fish were fed three times a day with chironomid larvae (EXOMARC, Lormont, France), excluding the last day before experimentation. Salinity and temperature levels were recorded using a YSI 30

Conductivity/Salinity/Temperature instru-ment (Yellow Springs, Ohio).

Fish behaviour was also checked daily. After this acclimation period, fish were directly used for respirometry measurements, with or without salinity transfers from SW to LS or from LS to SW (Figure 1a-c). For gill sampling, fish were sacrificed with an overdose of anaesthetic (2-phenoxyethanol, 500 mg l -1 ), and then dissected on ice. Gills were either directly frozen in liquid nitro-gen or kept at -80 □ C for NKA activity measurements.

Morphometry

For bone and lateral plate staining, fish kept in alcohol were stained overnight with 0.008% Alizarin Red S in 1% potassium hydroxide, destained in water overnight, then lightly cleared in a 0.25% potas-sium hydroxide/50% glycerol solution. The number of lateral plates were counted from 10 fish collected from the different sampling sites.

In addition, head height, body height, dorsal fin length and gill raker length (a)

Fish morphology was analysed using landmark-based geometric morphometrics. Seventeen landmarks were digitized on the right side of the body using TpsDIG [START_REF] Rohlf | Morphometrics at SUNY Stony Brook[END_REF] in order to get the X and Y coordinates (Figure 1d). Digitized landmarks were then transferred to MorphoJ [START_REF] Klingenberg | MorphoJ: an integrated software package for geo-metric morphometrics[END_REF]. Data were analysed through a principal component analysis (PCA) for shape variance, then principal compo-nent coefficient scores were transferred to Excel (2013) to visualize the possible variations between fish sampled from the FW-LS habi-tats and those from the mesohaline-SW lagoons.

Oxygen consumption rate

Respiration measurements were conducted in 73 ml transparent metabolic chambers, equipped with an oxygen optode (OXSP5, sensor code SD7-545-214) (Pyro-Science GmbH, Aachen, Germany) previously glued to its inner wall. Optodes were calibrated to 100% (using airsaturated water) and 0% air saturation (using a freshly made 80 mM Na2SO3 solution). Each metabolic chamber was equipped with a magnetic stirrer (to ensure correct O2 mixing in the water column)

and partially immersed in a 2 l tank. This tank contained a water pump connected to the metabolic chamber through a hole on the lid of the chamber also allowing water overflow and was supplied with an aera-tion system to maintain water fully oxygenated. A structure of 1 mm 2 mesh was installed at the bottom of the chamber above the magnetic stirrer in order to keep the fish away from the stirrer. Fish were intro-duced in each of the chambers containing filtered (0.2 μm Whatman) medium at the salinity values at which the animal was acclimated 24 h before salinity transfer. After this time, the water of each tank and metabolic chamber was quickly siphoned and replaced with water at the desired salinity.

The rates of oxygen consumption were measured at room temperature (21 □ C) and at different salinities (freshwater 0,5‰ and sea-water 30‰). To ensure that fish were consuming O2 differentially at different temperatures, the effects of SW to LS transfers on oxy-gen consumption were analysed at 21 and 23 □ C. Similarly, the rate of oxygen consumption was also assessed with LS to SW transfers monitored at 25 □ C. Change in oxygen concentration over time within each of the chambers was measured at different times before and after water transfer (1 h before, immediately after transfer, 1, 2, 3, 5, 24, 72 h after transfer and up to 3 and 6 weeks after salinity transfer) using 20 min periods during which the water pump and aeration system were shut off. Oxygen concentration was measured using a four-channel fibreoptic oxygen meter (FireSting, Pyro-Science GmbH, Aarhen, Germany) and recorded through Pyro Oxy-gen Logger software (Pyro-Science GmbH, Aarhen, Germany). All measurements started in fully oxygenated water (>98%) and respira-tion was recorded as a function of declining pO2 over time. Parallel measurements were carried out at a time (including a blank) and data were recorded using 5 s. intervals. Animals were then weighed

2.4

Branchial Na + /K + -ATPase activity

From each fish, four gill arches (from the same side of the fish) were dissected and homogenized in pairs in sucrose-EDTA-imidazole (SEI) buffer (150 mM sucrose, 10 mM EDTA, 50 mM imidazole, pH 7.4) using a manual Potter-Elvehjem tissue homogenizer. The specific, Na + -and K + -dependent, ouabain-sensitive ATPase activity was measured in these homogenates using 1.4 mM of ouabain as described in detail by [START_REF] Metz | Regulation of branchial Na+/K+-ATPase in common carp Cyprinus car-pio acclimated to different temperatures[END_REF]. Aliquots (10 μl in triplicate) of homoge-nate (protein content of 1 mg ml -1 ) were incubated in assay medium for 20 min at 25 □ C in microplate wells. Sample protein content was estimated using the protocol originally described by [START_REF] Bradford | A rapid and sensitive method for the quantitation of microgram quantities of protein using the principle of protein dye binding[END_REF]

RESULTS

Fish morphometry

Sticklebacks fished since 1993 from different aquatic habitats of the Camargue area presented on average 4.35 ± 0.88 lateral plates, with a minimum of two and a maximum of six lateral plates observed for some of these fish. No statistical differences in lateral plate number between the different locations and salinities could be identified (Table 1). Also, no statistical differences were observed in terms of body morphology between sticklebacks sampled in 2016-17

(Vaccares and Marteau lagoons, Fumemorte and Versadou canals) and those sampled since 1993 (Malagroy, La Capelière, Fournelet, Baisse Salée and Giraud lagoons) (Tables 1 and2).

Morphogeometric analysis using 17 different landmarks from fish sampled from the FW-LS habitats (Baisse Salée and Giraud lagoons, Fumemorte and Versadou canals) and the mesohaline-SW lagoons (Malagroy and Marteau lagoons) revealed that 32.9% of the variance is explained by the first component while the second component accounts for 16.7% of the variance (Figure 2). The scattered plot for the first and second components indicates limited morphological vari-ations between sticklebacks from the two contrasted habitats. How-ever, a significant difference is observed for the morphology of the gill rakers between sticklebacks sampled from these two habitats (Figure 3). Gill raker length and gill raker density appeared significantly higher in sticklebacks living in the FW-LS drainage canals compared to the fish living in the mesohaline-SW lagoons.

Oxygen consumption rate

different temperatures (21, 23 and 25 □ C) in LS or SW and after salin-ity transfers presented significantly different oxygen consumption rates (P value = 0.0104) (Fig. 4). Oxygen consumption increases with temperature. However, salinity transfer from LS to SW or SW to LS did not induce any change in the rate of oxygen consumption when recorded 24 and 72 h after transfer (P value = 0.283) (Figure 4a,b).

Sticklebacks collected from the BW Vacarres lagoon and kept in SW presented a significant reduction in oxygen consumption rate immediately and up to 1 h after abrupt transfer to LS (Figure 5a).

However, fish collected from the same environment and kept in LS prior to SW transfer did not modify their oxygen consumption rate during this 6 h experiment.

A longer acclimation to SW or LS of up to 3 and 6 weeks did not induce any change in oxygen consumption rate compared to fish kept in LS and SW (Figure 5b).

Branchial Na + /K + -ATPase activity

Following direct transfer from SW to LS, branchial Na + /K + -ATPase activity of sticklebacks sampled from the SW Marteau lagoon signifi-cantly increased by 28% and 40% within 24 and 48 h post transfer, respectively (P value = 0.0009) (Figure 6). However, when sticklebacks sampled from the LS Versadou canal were transferred from LS to SW, gill Na + /K + -ATPase activity was significantly decreased by 36% within 24 h (P value = 0.0127), resulting in a 1.65-fold change in gill Na + /K + -ATPase activity when fish were abruptly transferred to a different salinity. Furthermore, gill Na + /K + -ATPase activity of fish acclimated or transferred to SW or LS appeared to be similar despite the fact that these fish originated from two contrasting habitats. 1963). Lateral plate number is genetically determined, with a high heritability across all the different morphs, although there can be substantial within-morph variation [START_REF] Hansson | Lateral plate number in low-plated threespine stickleback: A study of plasticity and heritability[END_REF]. Usually, marine sticklebacks are predominantly fully plated with more than 30 plates while freshwater fish have fewer than 15 plates, typically between six and 10 [START_REF] Bell | The evolutionary biology of the threespine stickleback[END_REF][START_REF] Hansson | Lateral plate number in low-plated threespine stickleback: A study of plasticity and heritability[END_REF][START_REF] Wiig | Variation in lateral plate quality in threespine stickleback from fresh, brackish and marine water: A micro-computed tomography study[END_REF][START_REF] Østbye | Ongoing niche differentiation under high gene flow in a polymorphic brackishwater threespine stickleback (Gasterosteus aculeatus) population[END_REF]. The three-spined stickleback is well known for having undergone adaptive radiation following the end of the last gla-ciation and is well adapted to the freshwater environment [START_REF] Bell | The evolutionary biology of the threespine stickleback[END_REF]. FW

DISCUSSION

populations are less armoured and smaller than the marine ancestral populations. These typical morphological traits are due to parallel genetic adaptations to a novel environment [START_REF] Schluter | Adaptive radiation along genetic lines of least resis-tance[END_REF][START_REF] Foster | Evolution in parallel: New insights from a classic system[END_REF][START_REF] Colosimo | Widespread parallel evolution in sticklebacks by repeated fixation of ectodysplasin alleles[END_REF]. Many Consequently, fitness advantages could be related to differences in predator regimes or intensity between different habitats [START_REF] Reimchen | Structural relationships between spines and lateral plates in threespine stickleback (Gasterosteus aculeatus)[END_REF][START_REF] Reimchen | Predator handling failures of lateral plate morphs in Gasterosteus aculeatus: functional implications for the ancestral plate condition[END_REF]. A salinity effect on body shape has also been demonstrated [START_REF] Mccairns | Plasticity and heritability of morphological variation within and between parapatric stickleback demes[END_REF]. However, these authors tracked morphological changes exclusively via partial wrap scores but not in terms of physical shape differences, making their results difficult to interpret [START_REF] Mazzarella | Strong and parallel salinity-induced phenotypic plasticity in one generation of threespine stickleback[END_REF]. Also, sticklebacks of the Camargue area have specific life history traits compared to northern populations. They have a shorter life expectancy (1-2 years), a high growth rate, early sexual maturity and a long reproduction period (May to November), reflecting a high metabolism [START_REF] Crivelli | Life history adaptations of Gasterosteus aculeatus in a Mediterranean wetland[END_REF]. A summer pause in somatic growth has also been 0 0 24 72 Time (h) 0 24 72 detected in sticklebacks living in intermittent Mediterranean streams [START_REF] Clavero | Biology and habitat use of three-spined stickleback (Gasterosteus aculeatus) in intermittent Mediterranean streams[END_REF]. This highlights harsh environmental conditions for these Mediterranean fish with an annual life cycle compared to FIGUR E 6 Branchial Na + /K + -ATPase activity for fish collected from the SW Marteau lagoon (FBW 0.54 g ± 0.18) and the FW-LS Versadou canal (FBW 0.57 g ± 0.18) maintained at 21 □ C and transferred for 24 and 72 h from SW to LS and from LS to SW. Results are presented as means ± S.E.M., 10 < n < 12 those living further north.

Although collected from contrasted saline environments, stickle-backs of the Camargue area may still have the possibility to migrate locally between these different coastal habitats, especially between published [START_REF] Jurss | Experimental studies on biochemical and physiological differences between the three mor-phs of the 3-spined stickleback, Gasterosteus aculeatus L .1. Gill Na/K-ATPase, muscle alanine aminotransferase and muscle aspartate-aminotransferase activities[END_REF][START_REF] Judd | Na+/K+-ATPase isoform regulation in three-spine stickleback (Gasterosteus aculeatus) during salinity acclimation (Masters degree the-sis)[END_REF], hypo-osmoregulating fish in SW typically relying on less and smaller ionocytes compared to hyperosmoregulating fish in LS or FW conditions. An increased gill NKA activity has been documented when LS sticklebacks are transferred to SW [START_REF] Schaarschmidt | A comparison of transport-related gill enzyme activities and tissue-specific free amino acid concentrations of Baltic Sea (brackish water) and freshwater threespine sticklebacks, Gasterosteus aculeatus, after salinity and tem-perature acclimation[END_REF]. In their experiment, fish were trans-ferred to a higher salinity level (35‰) compared to the one tested in this study (30‰). As already observed in fish such as the European seabass and the marbled spinefoot, Siganus rivulatus, NKA activity over a large salinity gradient typically presents a U shape curve with maximal activity levels at extreme salinities [START_REF] Lasserre | Increase of (Na+ plus K+)-dependant ATPase activity in gills and kidneys of two euryhaline marine teleosts, Crenimugil labrosus (Risso, 1826) and Dicentrachus labrax (Linnaeus, 1758), during adaptation to fresh water[END_REF][START_REF] Saoud | Influence of salinity on survival, growth, plasma osmolality and gill Na+-K+-ATPase activity in the Experimental[END_REF].

Therefore, the hypersaline condition used in the study from [START_REF] Schaarschmidt | A comparison of transport-related gill enzyme activities and tissue-specific free amino acid concentrations of Baltic Sea (brackish water) and freshwater threespine sticklebacks, Gasterosteus aculeatus, after salinity and tem-perature acclimation[END_REF] could explain the elevated NKA activity they measured.

In conclusion, the low-plated stickleback population sampled from euryhaline, mesohaline and freshwater habitats in the Mediterranean Camargue area are morphologically and physiologically homogenous with efficient osmoregulatory capacities that do not impair their overall energetic balance. However, some habitat-related differences were observed, especially at the gill level. It would be interesting to better characterize the energetic cost of this functional remodelling along the gills and to identify how individual fish can cope with differential, organ-specific energy use and maintain an overall low energy use. Also, it is known that peripheral populations of wide-ranging species have less genetic variation compared to core populations [START_REF] Lesica | When are peripheral populations valu-able for conservation[END_REF]. Isolated populations that inhabit marginal environ-ments tend to be more geneticallydifferentiated from central populations than isolated populations that do not live in extreme environments [START_REF] Bouza | Genetic structure of brown trout, Salmo trutta L., at the southern limit of the distribution range of the anadromous form[END_REF]. Furthermore, local extinction events recently occurred for sticklebacks living at the southern edges of the species distribution [START_REF] Foster | The case for conserving threespine stickleback populations: protecting an adaptive radiation[END_REF] and particularly in freshwater habitats of Mediterranean climate areas in Europe [START_REF] Clavero | Biology and habitat use of three-spined stickleback (Gasterosteus aculeatus) in intermittent Mediterranean streams[END_REF][START_REF] Kottelat | Handbook of European freshwater fishes[END_REF][START_REF] Vila | Phylogeography and conservation genetics of the Ibero-Balearic three-spined stickleback (Gasterosteus aculeatus)[END_REF]. Therefore, there is a strong need for further analysis of the salinity-induced physiological adjustments of these southern peripheral stickleback populations. This could shed light on specific physiological traits and trade-offs limiting the overall energy use despite a highly demanding environment. This knowledge could efficiently contribute to a better protection of these populations and conserve their evolutionary heritage.

  and kept in alcohol until use. For the physiological study, fish [fresh body weight (FBW) 0.56 g ± 0.18] were collected in December 2016 and February 2017 from three different areas. One sampling site corresponds to a freshwater-low salinity (FW-LS) drain-age canal (Versadou canal, salinity values <5‰) running from the Rhône river and loading FW into a brackish (BW)/seawater (SW) lagoon (La Contesse lagoon). The other two sites correspond to the constantly BW Vaccares lagoon (salinity of 20-25‰) and the BW/SW Marteau lagoon

  were measured using the ImageJ image processing program (National Institute of Health, Bethesda, MD, U.S.A.). For gill rakers, only the first gill from the left branchial arch was consid-ered. Gill raker lengths were measured from the base to the tip of the rakers. Gill raker density was measured as the number of gill rakers positioned along the gill arch along a distance of 100 μm. The ratio of these values with the fish length was also calculated. Digital images of fish viewed gill rakers, samples were dehydrated, bathed in 1,1,1,3,3,3-hexamethyldisilazane, air-dried, glued to specimen stubs and coated with palladium for 180 s (~40 mÅ) using an Edwards SputterCoater (BOC Edwards, UK).

  potential selective agents have been proposed to explain the morphological parallel evolutionary changes across stickleback populations[START_REF] Maccoll | Inappropriate analysis does not reveal the ecological causes of evolution of stickleback Armour: a critique of Spence et al[END_REF][START_REF] Smith | The role of calcium and predation on plate morph evolution in the three-spined stickleback (Gasterosteus aculeatus)[END_REF][START_REF] Spence | Ecological causes of morphological evolution in the three-spined stick-leback[END_REF][START_REF] Voje | Adaptation and constraint in a stickleback radiation[END_REF]. It has been suggested, for example, that the nature and intensity of predation(Hagen and Gilbertson 1973et al. 1993), buoyancy[START_REF] Myhre | Body armour and lateral-plate reduction in freshwater three-spinedstickleback Gasterosteus aculeatus: adapta-tions to a different buoyancy regime[END_REF], salinity and calcium availability[START_REF] Giles | The possible role of environmental calcium levels during the evolution of phenotypic diversity in Outer Hebridean populations of the three-spined stickleback, Gasterosteus aculeatus[END_REF][START_REF] Spence | Calcium and salinity as selective factors in plate morph evolu-tion of the three-spined stickleback (Gasterosteus aculeatus)[END_REF][START_REF] Spence | Ecological causes of morphological evolution in the three-spined stick-leback[END_REF] can act as selective factors in plate morph evolution for sticklebacks.

  Switzerland). Only the linear part of the slopes for the optical densities read at 630 nm were considered. The specific activity was calculated by subtracting the K + -independent, ouabain-insensitive ATPase activity from total ATPase activity. ATP hydrolysis was assessed by the amount of inorganic phosphate formed per minute per milligram of protein.

	using a commercially prepared reagent (Sigma-Aldrich, St Louis, U.S.A.), and bovine serum albumin as standard. Initially, two different substrate concentrations were checked (dilution at 1:10 and 1:20) Optical densities were recorded using a spectrophotometer (Tecan Infinite M200, 2.5 Data normality validation was checked using a Shapiro test. Homosce-Statistical analysis dasticity was tested by the Bartlett test, and the residual independence was checked with the Durbin-Watson test allowing parametric tests to be used. Results were evaluated by one-way analysis of variance (ANOVA), followed by Dunn's test or Tukey post hoc test (honestly sig-nificant difference) with a significance level of P < 0.05. t-tests were also performed in order to compare the different ratios. A one-way ANOVA was used to test gill raker data. All statistical analyses were conducted using the R package, IBM SPSS Statistics 23 and Microsoft Excel (2013). All results are presented as means ± S.E.M.

ACKNOWLEDGEMENTS

We are thankful to the Tour du Valat Research Center for continuous support and for providing adult fish from the Camargue region. Legal authorizations for fish sampling were given to the Tour du Valat Research Center from the local French administration (PACA County, Direction Interregionale de la Mer Méditerranée, Service Réglementation et Contrôle no. 892 for 2016 and 703 for 2017). We are also grateful to David McKenzie for valuable help during the oxygen consumption measurements and to Shaheed Benazir Bhutto Univer-sity for providing a PhD scholarship for K. Rind. The authors also sin-cerely thank Munro Language Services for correcting the manuscript.

CONFLICT OF INTEREST

The authors declare that they do not have a conflict of interest.

COMPLIANCE WITH ETHICAL STANDARDS

This study was funded by the Ministère de l'Enseignement Supérieur de la Recherche et de l'Innovation.


François Blanquart

Thomas Berngruber

Marc Choisy

Sylvain Gandon

Evolution of virulence in emerging epidemics: inference from an evolution experiment

Inference using mathematical models of infectious disease dynamics is a powerful tool to analyse epidemiological data and elucidate pathogen life cycles. Key epidemiological parameters can be estimated from demographic time series by computing the likelihood of alternative models of pathogen transmission. Here we use this inference approach to analyze data from an evolution experiment in which we monitored both the epidemiology and the evolution of the temperate bacteriophage 𝜆 during an epidemic. We estimate parameter values for all the life-history traits of two distinct strains of the virus. In particular, we estimate the ability of the two virus strains to modulate plastically the rate of lysogenization with the multiplicity of infection. Our work illustrates how inference from experimental evolution data can feedback on the development of models aiming to predict the epidemiology and evolution of infectious diseases.

Introduction

Evolutionary epidemiology theory is a framework that aims to capture both the short-term and long-term evolutionary dynamics of pathogens [START_REF] Day | A general theory for the evolutionary dynamics of virulence[END_REF][START_REF] Day | Insights from Price's equation into evolutionary[END_REF][START_REF] Gandon | The evolutionary epidemiology of vaccination[END_REF]. It provides a way to bridge the gap between mathematical epidemiology and population genetics and shows how the evolution of pathogen virulence is driven by the change in the density of susceptible hosts. At the onset of an epidemic, when the incidence of the disease is small, evolutionary theory predicts that selection for pathogen transmission is strongest because there are many opportunities to infect new hosts. If there is a positive genetic covariance between the rate of transmission and the virulence of the pathogen, one may expect to see selection for pathogen virulence at the beginning of an epidemic. Later on, the spread of the infection reduces the pool of susceptible hosts and may reverse the selection on virulence [START_REF] Day | A general theory for the evolutionary dynamics of virulence[END_REF][START_REF] Day | Insights from Price's equation into evolutionary[END_REF][START_REF] Gandon | The evolutionary epidemiology of vaccination[END_REF][START_REF] Lenski | The evolution of virulence in parasites and pathogens: reconciliation between two competing hypotheses[END_REF][START_REF] Frank | Models of parasite virulence[END_REF].

We explored the validity of this prediction with an experimental approach where we studied the evolution of bacteriophage 𝜆 throughout the development of an epidemic in continuous cultures of Escherichia coli [START_REF] Berngruber | Evolution of virulence in emerging epidemics[END_REF]. Bacteriophage 𝜆 is a typical temperate virus which integrates into the host genome and transmits vertically to daughter cells at cell division.

Integration of phage 𝜆 into the genome protects the host cell against superinfection of other 𝜆 phage particles and this way provides immunity to superinfection by other 𝜆 phage particles [START_REF] Ptashne | A genetic switch: phage and higher organisms[END_REF]. The reactivation of the integrated phage (the prophage) results in lysis and destruction of the host cell. Lysis of its host prevents vertical transmission but allows the phage to be transmitted horizontally to uninfected susceptible cells. Whereas the non-virulent 𝜆 wildtype transmits mostly vertically by dormant integration into the host genome, the virulent mutant 𝜆cI857 transmits mostly horizontally by host lysis. This difference in virulence and transmission mode is the result of a point mutation in the 𝜆 virulence repressor protein cI which actively controls the decision to lyse the host cell. We monitored the competition of the bacteriophage 𝜆 and its virulent mutant 𝜆cI857 and compared these dynamics with the predictions from a mathematical model that tracks both the epidemiology and the evolution of the virus [START_REF] Berngruber | Evolution of virulence in emerging epidemics[END_REF]. The parameter values used for the model where obtained from independent estimates in previous studies and were used for an experimental validation of the theoretical predictions from our model.

In the present work, we go beyond the qualitative comparison between the theory the frequency of the virulent mutant to fit a dynamical model describing the epidemiology and the evolution of the phage. This approach provides a rigorous way to quantify the phenotypic differences between the two virus strains used in our experiments and in particular quantify key life-history traits like the probabilities of integration and the rates of reactivation. This approach also provides a way to compare the likelihoods of alternative models of virus transmission (with or without phenotypic plasticity).

Methods

An evolutionary epidemiology model

Following Berngruber et al. [START_REF] Berngruber | Evolution of virulence in emerging epidemics[END_REF] we model the dynamics of the bacterial population infected by a polymorphic population of phage 𝜆 in a chemostat. The density of susceptible (uninfected) bacteria is called 𝑆. The two strains of phage, called the "wild type" (WT) and "mutant" (M), have a low and a high probability to cause a lytic (rather than lysogenic infection), respectively. The density of bacteria infected by the strain 𝑖 (𝑖 ∈ {𝑊𝑇, 𝑀}) in a lysogenic state is 𝐿 , , and 𝐿 = ∑ 𝐿 , , is the total density of lysogens. The density of free viral particles of type 𝑖 is 𝑉 , , and 𝑉 = ∑ 𝑉 , , is the total density of free virus. In the absence of infection, bacteria reproduce at a density-dependent rate 𝑟 11 -456 7 [START_REF] Core | R: A Language and Environment for Statistical Computing[END_REF], where 𝐾 is the carrying capacity of the bacteria. Infected (lysogenized) bacteria are assumed to reproduce at the same rate as susceptible bacteria. The outflow of the chemostat removes bacteria and free phages at a rate 𝑚. Infection occurs when free viruses adsorb to a susceptible cell (at a rate 𝑎) and enters the cell (with a probability 𝑏). The rate of infections is thus 𝑎𝑏𝑉. Infection by phage strain 𝑖 gives rise either to a lysogenic bacterium, with probability 𝜙 , , or may immediately lyse the bacterium and release a number B of free phages, with probability 1 -𝜙 , . The parameter 𝜙 , determines the probability of genome integration of the phage. The variable 𝜙 • is the mean probability of integration of free phages defined by:

𝜙 • = 𝑞𝜙 @ + (1 -𝑞)𝜙 D ( 1
)
where 𝑞 is the frequency of mutant phage among free viruses. Consequently, new lysogenic bacteria are created at a rate 𝑎𝑏𝜙 • 𝑉𝑆, while new free phages are created at a rate

𝑎𝑏(1 -𝜙 • )𝑉𝑆𝐵.
The prophage in lysogenic bacteria may switch to a lytic cycle, with rate 𝛼 , . The induction of the lytic cycle kills the lysogenic bacteria and yields B free phages of type 𝑖. The variable 𝛼 ∘ is the mean rate of reactivation of viruses in latently infected bacteria, defined as:

𝛼 ∘ = 𝑝𝛼 @ + (1 -𝑝)𝛼 D ( 2
)
where 𝑝 is the frequency of mutant phage among prophages.

The above life cycle yields the following system of ordinary differential equations describing the epidemiological dynamics (the change in the total densities of different bacteria and the total density of free phages), and the evolutionary dynamics (the change in the frequencies of the mutant phage in the prophage and the free virus compartment):

𝑑𝑆 𝑑𝑡 = 𝑟𝑆 K1 - 𝑆 + 𝐿 𝐾 L -(𝑎𝑏𝑉 + 𝑚)𝑆 𝑑𝐿 𝑑𝑡 = 𝑟𝐿 K1 - 𝑆 + 𝐿 𝐾 L + 𝑎𝑏𝜙 • 𝑉𝑆 -(𝛼 ∘ + 𝑚)𝐿 𝑑𝑉 𝑑𝑡 = 𝑎𝑏(1 -𝜙 • )𝑉𝑆𝐵 + 𝛼 ∘ 𝐵𝐿 -(𝑎(𝑆 + 𝐿) + 𝑚)𝑉 𝑑𝑝 𝑑𝑡 = -𝑝(𝛼 @ -𝛼 ∘ ) + 𝑎𝑏𝑉 𝑆 𝐿 𝑝 K𝜙 @ 𝑞 𝑝 -𝜙 • L 𝑑𝑞 𝑑𝑡 = -𝑎𝑏𝑆𝐵𝑞(𝜙 @ -𝜙 • ) + 𝐵 𝐿 𝑉 𝑞 K 𝑝 𝑞 𝛼 @ -𝛼 ∘ L (3)

Fitting the model to experimental data from a chemostat experiment

We take a maximum likelihood approach to fit the above model to different types of data obtained from the experiment. First, we use the prevalence of the phage infection which refers to the proportion of lysogenic cells:

𝑃 = 𝐿 @ + 𝐿 D 𝐿 @ + 𝐿 D + 𝑆 (4)
where the relative densities of the different types of cells where obtained by flow cytometry.

Second, we used the flow cytometry data to obtain the frequency of mutant phage among lysogenic bacteria:

𝑝 = 𝐿 @ 𝐿 @ + 𝐿 D (5)
Third, we used quantitative PCR to measure the relative densities of wild type and mutant free viruses and to obtain the frequency of free mutant phages 𝑞: 𝑞 = 𝑉 @ 𝑉 @ + 𝑉 D [START_REF] Berngruber | Evolution of virulence in emerging epidemics[END_REF] These three variables (prevalence, frequency of mutant phage in infected cells, frequency of free mutant phages) were measured in four replicate chemostats for a treatment with high initial phage prevalence-the endemic treatment-and four replicate chemostats for a treatment with low initial phage prevalence-the epidemic treatment. The chemostat dynamics were followed approximately every hour for a maximum of 60 hours.

The likelihood of this data is the probability of the data given the dynamical model. As there is no closed-form analytical solution for the model, we integrated it numerically. We assumed that the logit-transformed prevalence and frequencies are measured with a normally distributed error. The likelihood corresponding to the observed prevalence in all treatments, replicates and time is defined as:

ℒ O (𝜽, 𝜎 O ) = R 𝑓Tlogit[𝑃 , ] | logit^𝑃 , _,`( 𝜽)a, 𝜎 O b ,
where 𝑓(𝑥 | 𝜇, 𝜎) is the density of a normal distribution with mean 𝜇 and standard deviation 𝜎, evaluated at 𝑥. The product is over all observations, where the index i scans the two treatments, four replicates for each treatment and up to 60 time points for each replicate. 𝑃 , denotes the ith observation of prevalence. 𝑃 , _,`( 𝜽) is the prevalence corresponding to observation i when integrating the ODE model with parameters 𝜃. We use the logittransformed prevalence: logit(𝑃 , )=log(𝑃 , /(1-𝑃 , )). The parameter 𝜎 O is the standard deviation of the measurement error corresponding to the logit-transformed prevalence. It is assumed to be the same for all treatments, replicates and time points.

Similarly, the likelihoods corresponding to the mutant frequencies among infected bacteria and among free phages are:

ℒ f T𝜽, 𝜎 f b = R 𝑓Tlogit[𝑝 , ] | logit^𝑝 , _,`( 𝜽)a, 𝜎 f b , ℒ g T𝜽, 𝜎 g b = R 𝑓Tlogit[𝑞 , ] | logit^𝑞 , _,`( 𝜽)a, 𝜎 g b ,
These likelihoods also depend on the set of parameters of the ODE model with parameters 𝜽.

The parameters 𝜎 f and 𝜎 g refer to the standard deviation of the measurement error associated with 𝑝 and 𝑞, respectively. Note that for the sake of simplicity, such noise is assumed to be uncorrelated across replicates, and across time points of the same replicate.

We thus neglect the demographic stochasticity that may generate additional variation around the average dynamical process. This is justified by the large population sizes of both the bacteria and the phage in the chemostat. Finally, we defined an overall composite likelihood where the errors on prevalence and frequencies data are assumed to be independent between them, as:

ℒT𝜽, 𝜎 O , 𝜎 f , 𝜎 g b = ℒ O (𝜽, 𝜎 O ) ℒ f T𝜽, 𝜎 f b ℒ g T𝜽, 𝜎 g b
We fitted the model by maximum likelihood methods, maximizing the function ℒT𝜽, 𝜎 O , 𝜎 f , 𝜎 g b with respect to the parameters 𝜽, 𝜎 O , 𝜎 f , 𝜎 g , using the Nelder-Mead algorithm. To ensure convergence to a global optimum, we repeated each optimisation multiple times from random starting points and selected the overall maximum likelihood. We computed 95% confidence intervals for the parameters from MCMC sampling of the likelihood function.

The simpler model without plasticity being nested in a more complex model where the phage additionally exhibits plastic lysogeny, we compare the fit of the two mechanistic models using a likelihood ratio test.

Computations were done with R, using the deSolve package for numerical integration of differential equations [START_REF] Core | R: A Language and Environment for Statistical Computing[END_REF][START_REF] Soetaert | Solving Differential Equations in R: Package deSolve[END_REF].

Results

Maximum likelihood estimation

Of the 13 parameters of the model, 2 were fixed to the values chosen in the experimental design [START_REF] Berngruber | Evolution of virulence in emerging epidemics[END_REF]. Eleven parameters were estimated by maximum likelihood (Table 1), including eight parameters from the model and three error standard deviations. The maximum loglikelihood of this model was 𝐿 h = -1911.96. Many parameters could be estimated with narrow confidence intervals, an exception being the burst size which could be between 44 and 488 phages per cell. In other words, the dynamics of the three variables 𝑃, 𝑝 and 𝑞 contain information on most model parameters. When computing the dynamics with the maximum likelihood parameters, the dynamics of prevalence and frequency of resistance generally closely fitted the data (Figure 1). However, the frequency of bacteria infected by the mutant phage peaked sharply in the epidemic phase in the treatment with low initial prevalence, an observation that the model failed to reproduce.

Extended model including the plasticity of phage 𝝀

The phage 𝜆 is able to modulate the probability of lysogenisation with the multiplicity of infection of the bacteria [START_REF] Kourilsky | Lysogenization by bacteriophage lambda[END_REF][START_REF] Zeng | Decision making at a subcellular level determines the outcome of bacteriophage infection[END_REF]. We examined whether the experimental data was better explained by accounting for plasticity in lysogenisation. We extended the first model to additionally allow the probability of integration to respond plastically to the multiplicity of infection, which depends on the density of free viruses 𝑉 (Supplementary Information)

𝜙 D = 𝜙 D m + (1 -𝜙 D m )(1 -𝑒 op q r ) 𝜙 @ = 𝜙 @ m + (1 -𝜙 @ m )(1 -𝑒 op s r )
The parameter 𝜙 D m is the probability of integration of the wild type strain when a single phage infects a bacteria. The probability of lysogenisation increases with the density of viruses and the parameters 𝛾 D and 𝛾 @ govern the magnitude of this effect for both the wild type and the mutant, respectively.

In the simulations of the best fit model (without plasticity), the density of viruses 𝑉 varies from 0 to 1.4• 10 9 viruses in the endemic conditions, and from 0 to 7• 10 10 viruses in the epidemic conditions. We found that the model with plasticity had a statistically significant better support than the simpler model (𝐿 u = -1898.43, 𝜒 u = 27.06, 𝑝 = 1. 10 o} ). This model finds a strong plastic relationship between the density of virus and the probability of integration in the wild type strain of the virus, and no plasticity in the mutant strain (Figure 2). The model with plasticity yields a better fit to the dynamics of the frequency of the mutant phage during the epidemic in the free virus compartment (Figure S1), which explains its better likelihood.

Discussion

In a previous study we developed a theoretical model to study the evolution of a temperate virus during an epidemic [START_REF] Berngruber | Evolution of virulence in emerging epidemics[END_REF]. This model led to three main qualitative predictions: (i) The virulent mutant initially wins the competition with the wildtype when susceptible hosts are abundant, but the competitive outcome is reversed as soon as the epidemic reaches high prevalence; (ii) The virulent mutant is, at all times, more frequent among free viruses than among proviruses; and (iii) Lower initial prevalence results in a higher increase in frequency of the virulent mutant during the epidemic. In the same study we carried out an experiment with the bacteriophage 𝜆 which successfully tested the validity of these different predictions [START_REF] Berngruber | Evolution of virulence in emerging epidemics[END_REF]. The present work is an attempt to move in the opposite direction, from the experimental data back to the theoretical model. maximise the fit between the data and the simulated dynamics. This inference approach yields precise estimates for 8 different parameters (Table 1). All these estimations are consistent with previous estimates obtained from different studies (see Table S1 in Text S1 in [START_REF] Berngruber | Evolution of virulence in emerging epidemics[END_REF]). This shows that combining data on the prevalence and on the frequency of different strains contains information on the specific values of the life-history traits (transmission, virulence) of different genotypes.

Second, we compared the original version of the model with a more general model that accounts for the observation that the phage can modulate its probability of lysogenisation with the multiplicity of infection determined by the density of free viruses. We explored this effect because we know that phage 𝜆 has the ability to adopt such plastic lifehistory strategies [START_REF] Kourilsky | Lysogenization by bacteriophage lambda[END_REF][START_REF] Zeng | Decision making at a subcellular level determines the outcome of bacteriophage infection[END_REF][START_REF] Gandon | Why be temperate: lessons from bacteriophage λ[END_REF]. The comparison of the two versions of the model reveals that the model with plasticity fits the data better than the original one. We also detect variations in plasticity between the wild type and the mutant phage (Figure 2 We could thus represent the probability of integration as a function of the expected multiplicity of infection (Figure 2). In our model, even in epidemic conditions (V = 6 × 10 10 ), the expected multiplicity of infection is modest (around 2, Table S1) so most cells are theoretically simultaneously exposed to 1 or 2 phages.

The inferred probability of integration is around 0.3 at low multiplicity of infection, which is consistent with the values measured by Zeng et al. However, our inferred relationship approaches 0.9 when the expected multiplicity of infection is 2, which is much higher than that measured experimentally, around 0.5. This difference between our population-based estimate and Zeng et al.'s result could be explained by differences in experimental conditions (e.g. temperature, liquid versus solid medium).

The plasticity of the wild type virus is a very important feature of the bacteriophage life cycle. In contrast, the mutant virus does not seem to exhibit plasticity. This is surprising because the original experiment by Kourilsky who monitored precisely the effect of multiplicity of infection on lysogenisation was performed with the 𝜆𝑐𝐼857 mutant. Note, however, that we carried out our experiments at 35°C while the experiments of Kourilsky were done at 32°C. The higher the temperature, the lower the rate of lysogenisation. The shape of the plasticity function could possibly be flattened by the increase in temperature (because of the destabilisation of the cI857 protein binding to the lambda operator [START_REF] Ptashne | A genetic switch: phage and higher organisms[END_REF]. It would be interesting to explore this hypothesis using the experimental approach of Zeng et al. [START_REF] Zeng | Decision making at a subcellular level determines the outcome of bacteriophage infection[END_REF].

The present work allows to improve the theoretical model that we originally developed to describe the epidemiology and evolution of a temperate virus during an epidemic. This improved model can be used again to generate new predictions. For instance, we can use this epidemiological model of a temperate phage to explore the relationship between the density of free viruses and the density of cells in the environment. Several empirical studies have shown that the density of free viruses saturate when the density of bacteria increase in aquatic communities [START_REF] Knowles | Lytic to temperate switching of viral communities[END_REF][START_REF] Wigington | Reexamination of the relationship between marine virus and microbial cell abundances[END_REF]. What drives the relationship between host and free virus densities has led to some controversy [START_REF] Weitz | Lysis, lysogeny and virus-microbe ratios[END_REF][START_REF] Knowles | Knowles & rohwer reply[END_REF][START_REF] Knowles | Variability and host density independence in inductions-based estimates of environmental lysogeny[END_REF][START_REF] Coutinho | Marine viruses discovered via metagenomics shed light on viral strategies throughout the oceans[END_REF][START_REF] Alrasheed | Caution in inferring viral strategies from abundance correlations in marine metagenomes[END_REF]. Our model can be used to explore the influence of virus plasticity on this relationship (using the two models defined in Table 1). Figure 3 shows this relationship with or without plasticity when we assume a periodic fluctuation in the density of susceptible bacteria in the environment (see Supplementary Information). Phage plasticity increases the probability of integration when the multiplicity of infection increases, which reduces the release of free viruses in the environment. This mechanism, if it is widespread among aquatic viruses, could have a major influence on the functioning of marine ecosystems. Relationship between the ratio of density of free virus and the density of bacterial cells in the environment for the two models described in Table 1: without plasticity (gray) and with plasticity (black).

In conclusion, statistical inference based on mechanistic models of infectious diseases can be a major tool to improve our understanding of the microbial dynamics monitored in evolution experiments. In fact, the back and forth between experiments and dynamical models may help design better experimental protocols were the aim will not only be to test a qualitative prediction but also to generate the data that will allow (1) the estimation of biologically relevant parameters and (2) the comparison of alternative dynamical models. This iterative process between model prediction and experimental validation is yielding a virtuous circle that improves the predictive power of evolutionary epidemiology theory.

Supplementary information

1.

Dynamics of multiple infections

We detail below a modified version of our model to account explicitly for the density 𝐸 , of bacterial cells exposed to 𝑖 viruses. For the sake of simplicity, we only consider the simple case where the virus population is monomorphic (no mutant strain). This yields the following dynamical system:

𝑑𝑆 𝑑𝑡 = 𝑟𝑆
This system of equations is similar to the system defined in equation ( 3). The terms that differ are highlighted in blue. Note that when the rate at which an exposed cell becomes infected is large compared to the rate of exposition, and the rate of dilution (𝜇 ≫ 𝑎𝑏𝑉𝑆and 𝜇 ≫ 𝑚), we recover the original model (equation (3) in the main text). Indeed, in that case, 𝐸 is small and 𝜇𝐸 is approximately 𝑎𝑏𝑉𝑆, and the system becomes:

𝑑𝑆 𝑑𝑡 = 𝑟𝑆 K1 - 𝑆 + 𝐿 𝐾 L -(𝑎𝑏𝑉 + 𝑚)𝑆 𝐸 = 𝑎𝑏𝑉 𝑚 + 𝜇 𝑆 𝑑𝐿 𝑑𝑡 = 𝑟𝐿 K1 - 𝑆 + 𝐿 𝐾 L + 𝑎𝑏𝑉𝑆 † 𝜙 , 𝑓 , , -(𝛼 ∘ + 𝑚)𝐿 (S2b) 𝑑𝑉 𝑑𝑡 = 𝑎𝑏𝑉𝑆𝐵 Š1 - † 𝜙 , 𝑓 , , ‹ + 𝛼 ∘ 𝐵𝐿 -(𝑎(𝑆 + 𝐿) + 𝑚)𝑉
That model is analogous to the system in equation ( 3), except that here for simplicity the virus population is monomorphic. The mean probability of integration in that model is weighted by the frequencies of cells exposed to i virus, 𝑓 , .

This model is particularly useful to estimate what is the expected multiplicity of infection 𝑀 in our dynamical system. The multiplicity of infection depends on the density of free viruses 𝑉. We estimate here the multiplicity of infection at the endemic state and at the epidemic peak, where 𝑉 is estimated to be 10 9 and 6 x 10 10 viruses per mL respectively. We estimate the rate at which an exposed cell becomes infected at 𝜇 = 1.5ℎ oh . Indeed, in an experimental study (Zeng et Table S1: the estimated frequency of cells exposed to 1, 2, 3, 4 viruses, and the estimated expected multiplicity of infection when the system is at endemic state (V = 10 9 ) and the system is at the epidemic peak (V = 6 10 10 ). Figure S1: Difference between the model predictions and the data for the simple model without plasticity and the more complex model with plasticity, with a focus on the logit frequency of the mutant free phage, the variable for which most of the difference between the two models arises. The blue curves represent the endemic conditions (high initial prevalence), and the red curve the epidemic conditions (low initial prevalence). The dashed line is the simple model, the plain line is the model with plasticity that explains better the frequency of mutant free phage during the epidemic peak.

Dynamics of the ratio

  806 -0.906] negative log-likelihood -1911.96 -1898.43

Figure 1 :

 1 Figure1: viral evolution in the chemostat, data (light blue and red lines) and model (dark blue and red thick lines). The blue curves represent the endemic conditions (high initial prevalence), and the red curves the epidemic conditions (low initial prevalence). We show the data for each replicate (light thin lines) as well as the mean across replicates (thick line). Only the predictions of the extended model with plasticity are shown. Top panel: the logit frequency of mutant (virulent) phage in lysogenic state in infected cells. Middle panel: the logit frequency of free mutant phage. Bottom panel: the logit prevalence of infection.

Figure 2 :

 2 Figure 2: inferred relationship between the probability of integration and the expected multiplicity of infection (reflecting the density of free virus,), for the wild type phage λ (blue) and the mutant λcl857 (orange). Left part of the graph (A), the first model without plasticity; Right part of the graph (B), the second model with plasticity, where the probability of integration depends on the density of free viruses. Vertical segments (A) and shaded areas (B) represent 95% confidence intervals.

  the assumption of the original model, we infer the parameter values that

  ). How does the estimated plastic response compare with the experimental measurement of the effect of multiple infections on the probability of lysogenisation by Zeng et al.[START_REF] Zeng | Decision making at a subcellular level determines the outcome of bacteriophage infection[END_REF]? Their measure of plasticity is based on the ability to track with time-lapse microscopy the fate (lysis versus lysogeny) of single bacteria that are exposed to 1, 2, 3, … phages. They found that the probability of lysogenisation increases from about 0.3 to 0.6 when the multiplicity of infection changes from 1 to 5. Our version of the model does not track the fate of individual cells and their multiplicity of infection. However, our model can be derived as an approximation of a more general model that explicitly describes the dynamics of cells exposed to a variable density of viruses (Supplementary Information). This more general model implies that the density of cells exposed to i viruses is geometrically distributed with parameter

Figure 3 :

 3 Figure3: Relationship between the ratio of density of free virus and the density of bacterial cells in the environment for the two models described in Table1: without plasticity (gray) and with plasticity (black).

1 -

 1 𝑉 (𝑆 + 𝐿) ⁄ in temporally variable environments To explore the influence of phage plasticity in a variable environment we use the following model: 𝜙 D )𝑉𝑆𝐵 + 𝛼 D 𝐵𝐿 -(𝑎(𝑆 + 𝐿) + 𝑚)𝑉 function which is meant to induce a periodic fluctuation (seasonal) of the abundance of susceptible cells. These fluctuations result in periodic variations of the densities of free virus and bacterial cells.

Figure 3

 3 in the main text plots the relationship between r 456 and 𝑆 + 𝐿 when the system has reached a periodic equilibrium. Parameter values: 𝜃 m = 10, 𝑇 = 10000ℎ. Other parameter values as in Table1.

  epidemicwith plasticity endemicsimple endemicwith plasticity

Table 1 :

 1 Model parameters. Two parameters (K and m) were fixed in the experiments[START_REF] Berngruber | Evolution of virulence in emerging epidemics[END_REF]. The 13 other parameters were estimated using the model without or with plasticity for the probability of lysogenisation. The table indicates the ML estimation and the 95% confidence interval. The bottom line of the table gives the maximum log-likelihood of the models without or with plasticity.

	Parameter	Definition	ML estimate without plasticity [95% CI]	ML estimate with plasticity [95% CI]
	𝐾	carrying capacity	10 9 cells mL -1
	𝑚	dilution rate	0.8 h -1
	𝑟	growth rate of uninfected cells	2.11 h -1 [1.79-2.97]	1.63 h -1 [1.31-1.82]
	𝐵	burst size	297 [44-488]	120 [51-329]

  is the rate at which a cell exposed to 𝑖 viruses becomes infected (and thus turns into a lysogenic cell, or is lysed and liberates viruses). If we assume that the rates 𝜇 , are relatively large we can use a separation of time scale argument to derive the quasiequilibrium density of the different types of exposed cells:

	We can simplify this system using the additional approximation 𝜇 , ≈ 𝜇∀𝑖, which yields:
							𝐸 ^, = K	𝑎𝑏𝑉 𝑚 + 𝑎𝑏𝑉 + 𝜇	L	,	𝑆
	The frequency of cells exposed to 𝑖 viruses is:
				𝑓 , =	𝐸 ^, ∑ 𝐸 ^, ,	= K	𝑎𝑏𝑉 𝑎𝑏𝑉 + 𝑚 + 𝜇	L	,oh	𝑚 + 𝜇 𝑎𝑏𝑉 + 𝑚 + 𝜇
	and the expected multiplicity of infection is:
	K1 -𝑀 = 𝑆 + 𝐿 𝑚 + 𝑎𝑏𝑉 + 𝜇 𝑚 + 𝜇 𝐾 L -(𝑎𝑏𝑉 + 𝑚)𝑆 = 1 + In other words, the frequency of cells exposed to i viruses follows a geometric distribution 𝑎𝑏𝑉 𝑚 + 𝜇
	with parameter	𝑑𝐸 h 𝑑𝑡 `5• €r5`5~. = 𝑎𝑏𝑉𝑆 -(𝑎𝑏𝑉 + 𝜇 h + 𝑚)𝐸 h
	This yields the following dynamical system:
		𝑑𝐸 u 𝑑𝑡 𝑑𝑆 𝑑𝑡 = 𝑟𝑆 K1 -= 𝑎𝑏𝑉𝐸 h -(𝑎𝑏𝑉 + 𝜇 u + 𝑚)𝐸 u 𝑆 + 𝐿 + 𝐸 𝐾 L -(𝑎𝑏𝑉 + 𝑚)𝑆
			𝑑𝐸 … 𝑑𝑡	= 𝑎𝑏𝑉𝐸 u -(𝑎𝑏𝑉 + 𝜇 … + 𝑚)𝐸 … 𝐸 = 𝑎𝑏𝑉 𝑚 + 𝜇 𝑆	(S1)
	…	𝑑𝐿 𝑑𝑡 𝑑𝐿 𝑑𝑡 = 𝑟𝐿 K1 -= 𝑟𝐿 K1 -𝑆 + 𝐿 + 𝐸 𝑆 + 𝐿 + 𝐸 L 𝜇𝐸 † 𝜙 , 𝑓 , L + † 𝜇 , 𝜙 , 𝐸 , 𝐾 , 𝐾 , 𝑑𝑉 , 𝑑𝑡 = † 𝜇 , (1 -𝜙 , )𝐸 , 𝐵 + 𝛼 ∘ 𝐵𝐿 -(𝑎(𝑆 + 𝐿) + 𝑚)𝑉 -(𝛼 ∘ + 𝑚)𝐿 -(𝛼 + 𝑚)𝐿 𝑑𝑉 𝑑𝑡 = 𝜇𝐸𝐵 Š1 - † 𝜙 , 𝑓 ,
	where 𝜇 , 𝐸 ^h =	𝑎𝑏𝑉 𝑚 + 𝑎𝑏𝑉 + 𝜇 h	𝑆
						𝐸 ^u =	𝑎𝑏𝑉 𝑚 + 𝑎𝑏𝑉 + 𝜇 h	𝑎𝑏𝑉 𝑚 + 𝑎𝑏𝑉 + 𝜇 u	𝑆
			𝐸 ^… =	𝑎𝑏𝑉 𝑚 + 𝑎𝑏𝑉 + 𝜇 h	𝑎𝑏𝑉 𝑚 + 𝑎𝑏𝑉 + 𝜇 u	𝑎𝑏𝑉 𝑚 + 𝑎𝑏𝑉 + 𝜇 …	𝑆
	...

, ‹ + 𝛼 ∘ 𝐵𝐿 -(𝑎(𝑆 + 𝐿) + 𝑚)𝑉

  al), single cells were observed for two hours to determine the outcome of infection (lysis or lysogeny). Assuming that the fate of 95% of exposed cells is decided in two hours gives a mean time to infection of 40 minutes, i.e. 𝜇 = 1.5ℎ oh .

		Endemic state	Epidemic peak
	𝑓 h	0.97	0.35
	𝑓 u	0.029	0.23
	𝑓 …	9 10 -4	0.15
	𝑓 Ž	2.6 10 -7	0.096
	Expected multiplicity of infection 1.03	1.95