Céline Roose-Amsaleg
email: celine.amsaleg@upmc.fr

Yasmina Fedala
email: yasmina.fedala@gmail.com

Catherine Vénien-Bryan
email: catherine.venien@impmc.upmc.fr

Josette Garnier
email: josette.garnier@upmc.fr

Albert-Claude Boccara
email: claude.boccara@espci.fr

Martine Boccara
email: boccara.martine@gmail.com

Utilization of interferometric light microscopy for the rapid analysis of virus abundance in a river

Keywords: Virus, Membrane vesicle, Interferometric light microscopy, River

Introduction

Water from the Marne River, one of the major tributaries of the Seine River, is used for the production of drinking water for most of the inhabitants of Paris and surroundings.

The Marne River used to be subjected to high levels of nutrients (nitrogen and phosphorus), originating from intensive agriculture and urban impact which entailed uneven and recurrent development of algae. These algal blooms were mostly due to diatoms, and secondarily to Chlorophyceae, cyanobacteria forming only low populations in lotic systems [1][2][3]. Since the 2000s, with the EU Water Framework Directive (2000/60/CE), phosphorus has been considerably reduced [4,5]. Algal blooms have become scarce, except in dry years. These blooms are mainly observed in spring, when the dilution rate by the discharge becomes lower than algal growth rate. These algal blooms constitute a significant inconvenience for the production of drinking water as, in addition to clogging filters, they increase the water pH [2].

Algal dynamics have been extensively studied for 25 years in order to improve their growing prediction by modeling [6], without explicitly considering the ecological effect of viruses.

In any aquatic environment, viruses, about ten times more abundant than bacteria, control the algal and microbial diversity by lysis and may influence biogeochemical cycles.

The abundance of aquatic viruses fluctuates over time, especially with the seasons. A peak of concentration is usually observed during spring-summer periods in surface waters; conversely, a significant decline occurs in autumn-winter [7]. The most common aquatic viruses of phytoplankton are double-stranded DNA-tailed viruses (Caudovirales) such as the following families: Myovirus (head size: 60-145 nm), Podovirus (60-70 nm) and Siphovirus (40-80 nm) which infect prokaryotes while PhycoDNA viruses (large DNA viruses, 100-220 nm) or picorna-like viruses (RNA viruses, 35nm) infect eukaryotic algae [7].

Viral direct counts in any environments remain a critical step requiring a reliable and accurate method [START_REF] Wommack | Counts and sequences, observations that continue to change our understanding of viruses in nature[END_REF]. Transmission electron microscopy (TEM) is one of the best techniques

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since it allows virus morphotypes to be counted and characterized [START_REF] Breitbart | Marine Viruses: Truth or Dare[END_REF], but is highly timeconsuming. Optical methods based on epifluorescence microscopy to detect double-stranded DNA binding fluorophores such as DAPI or SYBR are used extensively. However, these methods are adapted neither for detection of single-stranded DNA, nor RNA viruses [START_REF] Forterre | Fake virus particles generated by fluorescence microscopy[END_REF].

Flow cytometry is also frequently used to enumerate viruses in natural viral assemblages [START_REF] Brussaard | Enumeration of bacteriophages using flow cytometry[END_REF].

Most previous methods need expensive equipment and do not distinguish viruses from extracellular membrane vesicles. Extracellular membrane vesicles are another type of aquatic environmental nanoparticle. Produced by organisms from the three domains of life, they are made of lipids and proteins and sometimes contain genetic material, and could thus be mistaken for viruses [START_REF] Soler | Membrane vesicles in natural environments: a major challenge in viral ecology[END_REF].

We used a new method suitable for all genetic material of viruses and able to differentiate viruses from membrane vesicles. The interferometric light microscope (ILM) combines two measurements for a single nanoparticle (30 to 100nm): its scattered signal and its Brownian motion. The scattered signal is a function of the size and refractive index (related to density) of the particle, while the Brownian motion is a function only of the size of the particle [START_REF] Boccara | Fullfield interferometry for counting and differentiating aquatic biotic nanoparticles: from laboratory to Tara Oceans[END_REF]. ILM was utilized to distinguish virus from other particles and then tested to explore the variations of viral communities in the Marne River in spring 2014, expected to be the algal bloom period. The discharge averaging 180 m 3 s -1 in January-March decreased to 60 m 3 s -1 during the studied period (April-May). The diversity of eukaryotic and bacterial communities was determined simultaneously.

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Material and methods

Sample preparation

Water was collected at Saint Maurice (5 km upstream from Paris, 48°48'58.16" North, 002°25'27.35" East), the outlet of the Marne River, at three dates in 2014: April 1 st and 22 nd and May 14 th . Samples were kept in an ice cooler during transport and filtered as soon as they arrived at the laboratory. Two liters of water were first filtered through 0.22 µm filters (PolyVinyliDene Fluoride, Millipore) to collect eukaryotic and prokaryotic plankton. The filters were replaced every 0.5 L to avoid clogging. Filtrates (nanometric fraction) were then concentrated (10,000x) using a 30 KDa cut off filter (Amicon, Millipore).

Virioplankton characterization and interferometric data processing

We analyzed 5 µL of each filtrate (diluted in PBS to be 50x-concentrated) to collect a stack of 200 images (CMOS camera). The particles were first localized on each image and the average number per frame determined (volume = 10 -8 mL, concentration in particles of the sample). The maximum scattering intensity of each particle and its trajectory was computed [START_REF] Boccara | Fullfield interferometry for counting and differentiating aquatic biotic nanoparticles: from laboratory to Tara Oceans[END_REF]. With these data, we calculated the diameter of each particle from its scattering signal (diameter_ scat ) and from its Brownian diffusion (diameter_ BM ). Viral particles are the particles for which the two diameter measurements are close (refractive index n = 1.5). The nanoparticle populations were resolved using the Mclust package of R software with default parameters. Particles for which the diameter_ BM was over 20% larger than the diameter_ scat were considered as empty capsids or vesicles.

2.3.Transmission electron microscopy

Samples (10 µl, 10,000x-concentrated filtrates using Amicon 30 KDa cut off filters) were applied to electron microscope hydrophilic grids coated with carbon film. The specimen was then negatively stained with 2% uranyl acetate. The preparations were examined using a

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Jeol 2100 electron microscope equipped with an LaB6 filament, with an acceleration voltage of 200 kV and a 2K x 2K Gatan CCD camera. The nominal magnification was 12.5K. Taking into account the position of the camera, this gives a final magnification at the specimen level of 17.8K. Therefore, the pixel size was 0.8 nm. The pictures (>20) were analyzed to count and sort viruses. Viral capsid diameters were measured using ImageJ software (US National Institutes of Health, Bethesda, MD, USA; [START_REF] Abramoff | Image Processing with ImageJ[END_REF]).

Algal biomass

Chlorophyll-a concentrations (Chl-a) used as a proxy of the biomass of all photosynthetic organisms were determined by spectrophotometry according to [START_REF] Lorenzen | Determination of Chlorophyll and Pheopigments -Spectrophotometric equations[END_REF].

M A N U S C R I P T A C C E P T E D

Results and discussion

Virus-like particle direct counting from river water

Using interferometric light microscopy, we counted particles in water samples previously filtered (<0.2 µm) and concentrated (50x). We observed a sixfold increase in the total number of particles between the beginning (5 10 7 mL -1 , April 1 st ) and the end of the sampling (3 10 8 mL -1 , May 14 th ). We then analyzed the samples from a more qualitative point of view, calculating and plotting for each particle diameter_ scat and diameter_ BM. (Fig. 1). Indeed, any particle differing from a virus showed a similar movement, but a lower scattering signal [START_REF] Boccara | Fullfield interferometry for counting and differentiating aquatic biotic nanoparticles: from laboratory to Tara Oceans[END_REF]. We observed other dispersed particles that we predicted to be membrane vesicles [START_REF] Soler | Membrane vesicles in natural environments: a major challenge in viral ecology[END_REF]. Viruses therefore represented between 42% (2.1 10 7 mL -1 , April 1 st ) and 72% (2.1 10 8 mL -1 , May 14 th ) of the particles, in light of the first and last sampling date (Table 1). This analysis revealed that, in the studied river samples, the number of membrane vesicles could represent (by difference) 28-58 % of the detected particles. Estimating the number of membrane vesicles is a novelty which can provide new insight into the dynamics of viruses and their ecological importance.

Viral population composition

After excluding membrane vesicles from the analysis, viral populations were further characterized according to their size. Throughout the study, we observed two major peaks centered at 45 and 60 nm diameters (Fig. 2). We classified the predicted viruses into two groups (Table 1): medium-size diameters (40-59 nm) and larger diameters (≥60 nm). In addition to a general increase in the abundance of 45 nm viruses, the proportion of ≥60 nm viruses increased over time (from 7, 19% to 42%, for April 1 st and 22 nd and May14 th , respectively). The viral population of ≥60 nm in size would correspond to myocyanophages and PhycoDNAviruses [START_REF] King | Virus Taxonomy: Classification and Nomenclature of Viruses: Ninth Report of the International Committee on Taxonomy of Viruses[END_REF]. However, we detected neither small viruses (30 nm range,

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ACCEPTED MANUSCRIPT 8 known to infect diatoms) nor very large viruses (>100nm, infecting freshwater green algae).

In fact, for particles larger than 100 nm, there was no simple proportionality between the scattering signal and the diameter with ILM [START_REF] Boccara | Fullfield interferometry for counting and differentiating aquatic biotic nanoparticles: from laboratory to Tara Oceans[END_REF].

Comparison of interferometric light and transmission electron microscopy

Using TEM, viruses were observed and counted by major family and sized (diameters). Viruses were classified as Myoviruses, Podoviruses, Siphoviruses or PhycoDNAviruses based on their morphology [START_REF] King | Virus Taxonomy: Classification and Nomenclature of Viruses: Ninth Report of the International Committee on Taxonomy of Viruses[END_REF] or spherical particles (the last category corresponds to membrane vesicles, untailed viruses and cellular debris). The percentages of Siphoviruses and Podoviruses were stable between samples, while Myoviruses increased gradually (Fig. S2,S3). We were also able to detect Podoviruses and Myoviruses by DNA amplification (see supplementary information), only in the most virus-concentrated sample from May 14 th (data not shown). However the lack of reproducible amplification for Siphoviruses or PhycoDNAviruses suggested either that the amount of template was too small for proper amplification or that the degenerated primers were not suitable. Overall, while the proportion of prokaryotic viruses (Myoviruses and Siphoviruses and Podoviruses) increased (from 24 to 34%), that of eukaryotic viruses (PhycoDNAviruses) decreased (from 9 to 5%).

To compare the distribution of virus diameters between the TEM measurements with those obtained with ILM, we divided the samples into two groups: above and below 60 nm in diameter (Table 1). Although TEM is not a quantitative method, we observed the same distribution patterns for the two latter samples. However, we noticed a discrepancy for the first sample with a low viral concentration, suggesting that we need a threshold concentration of particles (of about 10 9 particles mL -1 ,corresponding to at least an average number of 10 particles per frame) to reliably analyze samples by ILM.

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Dynamics of photosynthetic populations during spring 2014 at Saint Maurice

We observed a fivefold increase in Chl-a content between April 1 st (0.27 µg L -1 ) and May 14 th (1.35 µg L -1 ), suggesting slight algal growth, but not true algal bloom. Indeed, during a spring algal bloom in the Marne River basin, especially composed of diatoms, the Chl-a concentration at St Maurice tended to reach 100 µg L -1 or more [1]. The last algal bloom was observed in May 2011 and produced 144 µg L -1 of total chlorophyll concentration jerri (Chl-a and Pheopigments). On May 14, 2014, diatoms were responsible for 67% of the total algal biomass, with Cyanobacteria representing less than 0.1%.

DNA fingerprinting methods such as PCR-DGGE enable diversity investigation from natural microbial communities by studying the pattern of operational taxonomic units (OTUs). Concerning the aquatic eukaryotic communities, we noted a similar number of OTU (i. e. an approximation of the species richness) between the beginning (April 1 st , 21±2.8 OTU) and end of sampling (May 14 th , 18±0 OTU) (Fig. S1A). However, community composition showed a net modification, as the patterns of May 14 th showed a weak similarity percentage (43.2%) with those of the other two dates.

In contrast, the species richness of aquatic bacterial communities (Fig. S1B) increased between early April and mid-May (from 13±0.7 to 24±1.4 OTU). Subsequently, the bacterial composition varied between dates: communities from April 1 st and May 14 th shared 43.1% of their OUT, whereas those of April 22 nd shared 33.2% with the other two dates.

Thus, in the studied station of the Marne River, over the short sampling period, prokaryotic viruses proliferated. This suggests that their hosts (whose the number of OTUs increased) would also be numerically dominant in the microbial community. In contrast, eukaryotic phytoplankton viruses became a minor part of the viral population, while their hosts harbored less richness (cf. OUT numbers).

In conclusion, we have presented an analysis of virus abundance and diversity in a lotic freshwater environment, the Marne River, during a growth phase of phytoplankton. To analyze this viral abundance, we used an optical method based on interferometric light microscopy. This method proved its efficacy even at a low algal level. With this method, we observed an increase in virus particles and membrane vesicles which has not been previously described in freshwater.

5

 5

7

 7

Fig. 1 .

 1 New ecological studies on viral dynamics in freshwater are needed to understand how algal and bacterial dynamics are linked to viral communities and to possibly integrate them into existing ecological models. Analysis of particles present at the Saint Maurice station, an outlet of the Marne River. Plot of the diameters of particles computed with their scattered signals (Diameter_scat) and Brownian motion (Diameter_ BM ). Lines indicate refractive indexes of the different particles (viruses and vesicles). The colored bar corresponds to the relative number of characterized particles: the different colors correspond to the Matlab histogram plotted in normalized linear scale. The viruses that possess a refractive index of 1.5 are likely close to this line, while the rest of the particles could be vesicles.

Fig. 2 .

 2 Fig. 2. Analysis of predicted viral particles from the Saint Maurice station.

Fig. S1 .

 S1 Fig. S1. DGGE analysis for eukaryotic (A) and prokaryotic (B) plankton from the Marne

Fig. S2 .

 S2 Fig. S2. Transmission electron microscopy analysis of Saint Maurice water samples.

Fig. S3 .

 S3 Fig. S3. Electron micrograph of concentrated (10,000x) water sample from the Marne River (May 14 th ).

Table 1 : Comparison of analyzed viral particles by interferometric light (ILM) and transmission electron microscopy (TEM).

 1

				Interferometric light microscopy £		Transmission electron microscopy
				ILM				TEM
		Particle	Number	Number of	<60 nm	≥60 nm	Number of	<60 nm	≥60 nm
		concentrations	of	predicted	(%)	(%)	particles⃰	(%)	(%)
		in the water column (mL -1 )	particles #	viruses (% vs. particles)
	April 1	5 10 7	331	141 (42)	93	7	174	74	26
	April 22	8 10 7	830	535 (64)	81	19	172	67	33
	May 14	3 10 8	2243	1625 (72)	58	42	308	74	26

£

The same samples were concentrated 50 or 10,000 times for ILM and TEM, respectively #Number of particles for which we measured the diameter by scattering signal and by Brownian motion.

⃰ Number of particles analyzed from about 20 TEM images.

Table S1 : List of primers used in this study

 S1

	Primer	Sequences (5'-3')	Amplicon	Target	References
	name		size (bp)
	F1427-GC (GC) 20 TCT GTG ATG CCC TTA GA	229	DNA 18S ribosomal	[2]
	R1616	GCG GTG TGT ACA AAG GG
	F357-GC	(GC) 20 CCT AGC GGA GGC AGG AG	201	DNA 16S ribosomal	[3]
	R518	ATT ACC GCG GCT GCT GG
	MZPA1BF GAT ATT TGI GGI GGT CAG CCI ATG A		Major capsid	[4]
	MZPA1BR CGC GGT TGA TTT CCA GCA TGA TTT C	550	protein of Myoviruses
	Pol F	CCA AAY CTY GCM CAR GT		DNA	[5]
	Pol Rb	CTC GTC RTG DAT RAA SGC	650-750	polymerase of Podoviruses
	Mcp F	GGY GGY CAR CGY AAT		Major capsid	[6]
	Mcp R	TGI ARY TGY TCR AYI AGG TA	347-518	protein of PhycoDNAvirus
				es
	lbdintF	TGA TAC TGT GCC GGA TGA AA		Integrase of	[7]
	lbdintR	TTA GGC AGA GAC AGG CGA AT	750	Siphoviruses

Acknowledgments

We would like to thank all the persons who helped us with the experiments: Ellie-Arthur Siéwé-Bobda, Marc Bailly-Bechet, Benjamin Mercier, Fanny Hilaire and Hames Mejri. Dr J-M Guigner is acknowledged for electron microscopy analysis.

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT Supplementary material for on-line submission

PCR-DGGE

Genomic DNA was extracted in duplicate from PVDF filters (Millipore) using the PowerSoil DNA isolation kit (MO BIO Laboratories, Inc). Amplification was performed with specific primers for DGGE (Table S1) to amplify fragments from 16S and 18S ribosomal DNA to study bacterial and eukaryotic diversity, respectively. Denaturing gradient gel electrophoresis (DGGE) was performed using the Phor-U system (Ingeny) as described in [1].

All PCR products were run on a single gel for the 16S and another for the 18S. After development of the DGGE polyacrylamide gel, each image was analyzed to determine similarities between profiles using the software GelCompar II 6.6 (Applied, Math). Each of the two gels was normalized based on an external reference pattern (the 100 bp ladder, Invitrogen) required by the software to compare lanes. Each band of a lane was automatically assigned to a band class, and all band classes were manually checked and eventually overridden to make them consistent between lanes. The Jaccard coefficient was calculated considering only the presence/absence of bands, each representing an operational taxonomic unit (OTU). Aquatic prokaryotic and eukaryotic communities could be compared thanks to their similarity percentages.

PCR amplification of viral fragments

We first established amplification conditions directly with known viruses of Siphovirus, Myovirus, Podoviruses and PhycoDNAvirus. Then, each concentrated filtrate (50x) from water samples was used as a template with the following program: after initial denaturation at 95°C, 1 min annealing at 50°C and 1.5 min of extension at 72°C for 35


Cairedine Kalai

Pr Emilie-Laure L Zins

Mohammad Esmaïl Alikhani
email: esmail.alikhani@upmc.fr

Dr ] C Kalai

A theoretical investigation of water-solute interactions: From facial parallel to guest-host structures

Keywords: noncovalent interactions, exohedral complex, endohedral complex, molecular electrostatic potential (MESP), Quantum Theory of Atoms in Molecules (QTAIM)

Encapsulation of small (bio-)organic molecules within water cages is governed by a subtle equilibrium between water-water and water-solute interactions. The competition between the formation of exohedral and endohedral complexes is investigated. The first step prior to a theoretical characterization of interactions involved in such complexes lies in the judicious choice of a level of theory. The β-propiolactone (BPL), a solute for which the micro-hydration was recently characterized by means of high resolution microwave spectroscopy (Angew. Chem. 2015, 127, 993), was selected for the present study, and a calibration step is carried out. It is shown that the dispersion-corrected density functional theory (DFT-D) suitably reproduce the geometric, energetic and spectroscopic features of the BPL:(H 2 O) 1-5 complexes. The experimentally-deduced structures of the BPL:(H 2 O) 4,5 species are fully understood in terms of the maximization of interactions between complementary sites in the MESPs. DFT-D calculations followed by the topological analysis within the Quantum Theory of Atoms in Molecules framework have shown that the solute could efficiently interact with (H 2 O) 6,10 clusters in a similar manner that the (H 2 O) 4,5 clusters do. The interaction of the solute with two larger water clusters is further investigated. The exohedral and endohedral BPL:(H 2 O) 20 isomers are close in energy with each other, whereas the formation of an inclusion complex is energetically more favored than the facial interaction in the case of the BPL:(H 2 O) 24 cluster. The topological analysis suggests that the substantial energetic stability is due to interactions between the solute and almost all oxygen atoms of the water cage.

Introduction

Due to their ubiquitous implications in almost all chemical fields, the hydration processes of organic molecules have consistently been the topic of experimental and theoretical investigations. Water-water and water-solute interactions compete and efficiently complement each other in important equilibria [1][START_REF] Hobza | Non-covalent interactions: Theory and experiment[END_REF][3][4][5][6][7][8][9].

For instance, hydrated species in which small water clusters are attached to a solute, were characterized for several systems [START_REF] Hobza | Non-covalent interactions: Theory and experiment[END_REF]10,11,12]. In a combined force-field and DFT approach, a clear segregation between the water molecules and the solute in hydrated complexes of 2aminooxazole containing one to twenty water molecules has been reported by Calvo et al. [13] The authors underlined that the solute-solvent hydrogen bonding strength is weaker than the water-water ones, leading to a negligible distortion of the water cluster up to 2aminooxazole:(H 2 O) 15 cluster. For complexes containing more water molecules, the solutesolvent interaction competes with the solvent-solvent interaction. Xantheas et al. recently reinvestigated the Benzene:(H 2 O) 8 complex in a combined DFT and post-Hartree-Fock study [14]. They underlined that unlike to the popular B3LYP functional the dispersion-corrected functional (ωB97-XD) is able to satisfactorily describe the Benzene:(H 2 O) 8 complex interaction. They identified five isomers in which a cubic water octamer is attached to the aromatic ring, with similar energetic stability (Δ E < 4 kJ/mol at the MP2/aVTZ//MP2/aVDZ level of theory). They also showed that each isomer involves a cubic water octamer almost in facial parallel interaction with the aromatic ring.

Furthermore, the formation of inclusion complexes in clathrate hydrates also underline the paramount importance of the complementary water-water and water-solute interaction. For instance it was shown at a molecular level that methane is efficiently encapsulated in a (H 2 O) 20 cage, whereas larger (H 2 O) 24,28 cages lead to more stable complexes when SF 6 is the guest molecule [15]. Smaller guest species such as rare gases, diatomic or triatomic molecules may be efficiently trapped in the (H 2 O) 20 cage with the concomitant formation of multiple water-solute interactions [16], characterized by bond critical points (BCPs) in the Quantum Theory of Atoms in Molecules (QTAIM) approach [START_REF] Bader | Atoms in Molecules. A Quantum Theory[END_REF]. It was found that such small guest molecules do not lead to major distortion of the water cage. Some guest molecules however may dramatically affect water-water interactions, leading to so-called guest-induced Bjerrum defects [18].

A qualitative and quantitative understanding of interactions involved in the formation of endohedral and exohedral complexes at a molecular scale would help in understanding various processes such as hydration of small (bio-)organic molecules, and clathrate formation. Endohedral complexes refer to the formation of inclusion compounds, whereas in exohedral complexes, the solute lies outside the water cluster. The present study is concerned with the mutual competition between endohedral and exohedral complexes.

A simple, powerful and quick method based on a measurable physical property of molecules and clusters was used to identify favorable interactions between two species: the molecular electrostatic potential (MESP) [START_REF] Hobza | Non-covalent interactions: Theory and experiment[END_REF][19][START_REF] Murray | Molecular Electrostatic Potentials: Concepts and Applications[END_REF][21][22][23][24][25][26][27]. When investigating non-covalent interactions, studies based on the MESP analysis are mainly of two types:  explanatory approach: A quantitative analysis of the isolated monomers MESPs may lead to the identification of electron-rich and electron-deficient regions (σ-holes or πholes for instance). The identification of such local features provides a useful tool for interpreting various non-covalent interactions such as tetrel, chalchogen, halogen and hydrogen bondings, as demonstrated by Politzer, Murray et al. [START_REF] Murray | Molecular Electrostatic Potentials: Concepts and Applications[END_REF][21][22];  predictive approach. Among other approaches [28,[START_REF] Stone | The theory of intermolecular forces[END_REF], we can mention the electrostatic potential for intermolecular complexes (EPIC) model of Pundlik et al.[30]. This model allows the study of weakly bond complexes between two species based on the calculation of the electrostatic interaction energy. It relies on the analysis of critical points of the electrostatic potential on isolated monomers, the MESP study of one species and the MESP-driven point-charges of the other species. This model has been applied to the characterization of various complexes. [START_REF] Gadre | Noncovalent forces[END_REF] Herein another predictive approach is proposed:

(i) As a starting point, we investigate the possibility of a simple, qualitative analysis of the MESP for both isolated solute (S) and solvent clusters (W n ) for proposing S:W n guess geometrical structures. Throughout the present work, the MESP analysis was used to unravel so-called "electron-rich" and "electron-deficient" regions. We should mention that such features only refer to surface properties, and not to volumes. The existence of 3D MESP maxima was indeed ruled out by Pathak et al. in the 1990's [32]. Initial geometries of complexes are built up considering the fact that electronrich regions of the solute will be attracted towards an electron-deficient region of water clusters, and conversely. A visual inspection of the MESP of both isolated partners enables us to suggest several possible geometries which maximize the number of complementary MESP regions. Such approach has been already successfully applied to other cases. [11,33]  (ii) In a second step, these structures are fully optimized using ab initio or DFT approaches.  (iii) Finally, water-solute interactions are analyzed by means of the QTAIM topological tool applied on the optimized structures.

For such a study, the judicious choice of a level of theory for a consistent geometric and electronic description of complexes is an obvious and needed prerequisite. It was shown that dispersion-corrected density functionals may suitably describe such complexes provided that a calibration step is carried out, either with respect to the experimental data or to the results coming from high-level theoretical calculations [14,16,34].

Recently Alonso et al. investigated the interaction between the β-propiolactone (BPL) and up to five water molecules [35]. A clear segregation between the water molecules and the solute was experimentally observed for the BPL:(H 2 O) 4,5 complexes. This system was thus chosen for our study.

The paper is structured as follows: First of all, the choice of an exchange-correlation functional able to well reproduce energetic, geometric and electric properties of the water -BPL interaction in the BPL:(H 2 O) n (n=1-4) cluster, is detailed. To further shed some light on the interactions involved in the formation of facial-parallel structures deduced from experimental data for the BPL:(H 2 O) 4,5 clusters, a characterization based on the molecular electrostatic potential (MESP) and the Quantum Theory of Atoms in Molecules (QTAIM) topological tools is presented [START_REF] Bader | Atoms in Molecules. A Quantum Theory[END_REF][START_REF] Koch | Gaussian, Inc[END_REF]. Stable structures involving the formation of similar water-solute interactions for the BPL:(H 2 O) n (n=6,10) clusters are then identified. In the last part, larger clusters involving 20 and 24 water molecules are studied. Two small prototypical 5 12 and 5 12 6 2 water cages constituting elementary assemblies of some water clathrates were investigated. A particular attention is devoted to the transition from a facial parallel structure to the endohedral compound and to their mutual competition, until the completion of the first hydration shell around the BPL molecule.

Method calibration

All the geometry optimizations were carried out using the Gaussian 09 Rev D.01 software [37]. The D2 and D3 versions of the dispersion-corrected density functional theory within the framework of the Becke-Johnson damping function [3,38] further denoted as GD2 and GD3BJ, were employed. The following functionals were selected: B3LYP-GD3BJ, [3,10,39] B2PLYP [40], B2PLYP-GD2, B2PLYP-GD3BJ, ωB97XD and LC-ωPBE-GD3BJ [41,42,43] in combination with the Pople's 6-31++G(d,p), 6-311++G(d,p), 6-311++G(2d,2p), and the Dunning's aug-cc-pVDZ and aug-cc-pVTZ basis sets, further referred to as Pop1, Pop2, Pop3, aVDZ and aVTZ, respectively. The CCSD(T)-F12/aVDZ method was selected as a reference method, and MP2/aVDZ as well as MP2/aVTZ calculations were also carried out. Dipole moments have been calculated with the "Density=Current" instruction for MP2, CCSD/aVDZ//CCSD(T)-F12/aVDZ (single-point with CCSD/ aVDZ at the CCSD(T)-F12/ aVDZ optimized geometry) and B2PLYP calculations. The molecular electrostatic potentials and the Quantum Theory of Atoms In Molecules (QTAIM) analyses were carried out using the AIMAll [44] software, for the identification of hydrogen bonding and non-covalent interactions [START_REF] Bader | Atoms in Molecules. A Quantum Theory[END_REF].

The mono-hydrated BPL:(H 2 O) complex was chosen as a probe to evaluate the accuracy of the exchange-correlation functionals in describing the non-covalent interaction between water and BPL. The most relevant geometrical and energetic characteristics calculated with the 17 selected levels of theory for the BPL:(H 2 O) complex are gathered in the Table 1. The binding energy was calculated as follows:

D e = E comp -(E 1 +E 2 )
, where E comp is the total energy of the H-bonded complex and E 1 and E 2 are the total energies of the optimized free units (BPL molecule and water cluster).

The experimental rotational constants 2 are described with a relative error (RE) less than 5% at all the chosen DFT levels. The experimental values (µ a , µ b and µ tot ) of the dipole moments are accurately reproduced (RE ≤ 5%) only at three levels of theory: B2PLYP-D/Pop3, B2PLYP-GD3BJ/Pop2, and LC-wPBE-GD3BJ/Pop2.

Eight levels of theory accurately reproduce the binding and complexation energies calculated at the CCSD(T) level with a RE ≤ 5%: the B2PLYP-D/Pop2, B2PLYP-D/Pop3, ωB97XD/Pop2, ωB97XD/Pop3, LC-ωPBE-GD3BJ/Pop2, LC-ωPBE-GD3BJ/Pop3, B3LYP-GD3BJ/ Pop2 and B3LYP-GD3BJ/Pop3 levels. Furthermore, the MP2/aVDZ and MP2/aVTZ levels suitably describe the BPL:(H 2 O) interaction, the relative errors on the dipole moments, rotational constants, binding energy and complexation energy being less than 6% (Table 1).

It should be underlined that all the levels of theory selected for the present study satisfactorily reproduce the geometric, energetic and spectroscopic features of the 1:1 complex. Accordingly, dispersion-corrected DFT is able to accurately describe the mono-hydrated complex. This feature is in line with other studies on hydrated species [34,[START_REF] Liu | [END_REF]. The LC-ωPBE-GD3BJ/Pop2, that simultaneously reproduces the selected geometric, energetic and spectroscopic features with errors less than 5%, as well as the MP2/aVDZ levels, were selected for the study of larger hydrated complexes. The calculated rotational constants are in good agreement with the experimental data for the BPL:(H 2 O) 2-4 (Table 2). Consequently, hereafter the LC-ωPBE-GD3BJ/Pop2 method will be used to study all the first order properties of BPL:(H 2 O) n  4 . ) 5 isomers, denoted as 1:4a, 1:4b and 1:5a, respectively. In an attempt to shed some light onto the aggregation pattern of water clusters around the solute, we carried out a MESP analysis. A MESP map of free BPL molecule revealed that both trapezoidal faces of the BPL is characterized by: -two neighboring electron-deficient regions, at two consecutive corners, corresponding to the hydrogen atoms, -two neighboring electron-rich regions, at two consecutive corners, corresponding to the oxygen atoms, -an electron-deficient region in the middle of the face (Figure 1). Electron-rich regions of the solute will be attracted towards an electron-deficient region of water clusters, and conversely. This is the starting point in the entrance channel of any noncovalent interaction. As a matter of fact, two species initially adopt the best spatial configuration to maximize the number of complementary MESP regions. The MESP analysis of water clusters (Figure 2) is indeed in line with the structures earlier reported for the BPL:(H 2 O) 4 and BPL:(H 2 O) 5 isomers:

Distances (Å) Energy (kJ/ mol) Dipole Moment (D) b Rotational Constants (MHz) r OH•••O Δr OH /Δr CO D e (D e CP )/D 0 (D 0 CP) a µ tot (µ a /µ b ) A/B/C
 in the case of the BPL:(H 2 O) 4 complex, it was found that the water tetramer involved in the interaction with the solute is the uudd isomer, thus called with respect to the orientation of free OH groups. Both faces of the MESP of this cyclic water tetramer presents two neighboring electron-deficient regions (corresponding to the hydrogen atoms) followed by two neighboring electron-rich regions (corresponding to the oxygen atoms). As shown in Figure 2, such a MESP can perfectly complement the one of the solute,  in the case of the BPL:(H 2 O) 5 complex, the cyclic ududu water pentamer was found to be distorted by the interaction with the solute. This distortion is in line with the MESP picture of both partners: four of the five water molecules have suitable, complementary MESP features for interaction with the solute, and the fifth one is puckered away from the solute. As underlined by Alonso et al. [35] an inversion in the hydrogen bonding network in the water cluster leads to two similar isomers for the BPL:(H 2 O) 4 complex. Similarly, our calculations also lead to the prediction of two almost isoenergetic isomers for the BPL:(H 2 O) 5 complex, differing from one another by an inversion in the hydrogen bonding network in the water cluster.

It was found that both isomers of the BPL:(H 2 O) 4 and of BPL:(H 2 O) 5 complexes correspond to stable structures at the chosen level of theory. To further characterize the water-solute interaction in the equilibrium structures, the BCPs obtained from the QTAIM analysis were used to identify the interacting atoms, and to quantitatively describe the water-solute interaction by measure of the electron density (r) and Laplacian  2 (r) at BPCs between It is remarkable that the experimentally identified BPL:(H 2 O) 4 and BPL:(H 2 O) 5 isomers involve similar water-solute interactions, as demonstrated by the QTAIM analysis. The above-described structures suggest that the following features of the solvent cluster may favor an efficient facial-parallel interaction with BPL: four almost coplanar water molecules with two consecutive electron-rich regions (oxygen atoms) that may interact with the electrondeficient region of the BPL (hydrogen atoms of the -CH 2 -groups), and two consecutive electron-deficient regions (hydrogen atoms) that may interact with the electron-rich region of the BPL (ester function). We thus selected appropriate isomers of (H 2 O) 6 and (H 2 O) 10 clusters sharing such features, and determined whether they may attach the solute in a similar facial-parallel manner as the water tetramer and pentamer do.

BPL:(H 2 O) 6 complex

Different (H 2 O) 6 isomers were identified for the water hexamer: the tridimensional prism, cage and book are almost isoenergetic, whereas the cyclic isomer is slightly higher in energy [46,47].The MESPs of each of these isomers are presented in Figure 3. One face of the prism isomer presents a similar MESP to the one of the uudd water tetramer, with two consecutive electron-rich regions followed by two consecutive electron-deficient regions. The book isomer also contains four almost coplanar water molecules presenting a complementary MESP feature with respect to the one of the BPL. (Figure 4) The two other isomers do not present two consecutive electron-rich regions followed by two consecutive electron-deficient regions. Thus, the possible interaction of BPL with the cage and cyclic isomers was not further investigated.

BPL:(H 2 O) 10 complex

The most stable isomer for the water decamer is constituted of two stacked dudud pentameric plans [47].The MESP of one of the rectangular face presents two consecutive electron-rich regions followed by two consecutive electron-deficient regions (Table 6), that may efficiently attach the solute.

From the above discussed MESP analysis of the water clusters that may lead to a favorable facial interaction with the solute, it can be anticipated that an alternative water decamer could also favorably attach the BPL. Indeed, the flip of some hydrogen atoms leads to a new isomer constituted of two pentagonal duuud faces. The MESP of the pentagonal face of such an isomer is characterized by two consecutive electron-rich regions followed by three consecutive electron-deficient regions. Thus, the pentagonal face of this isomer is suitable for interaction with the BPL (Table 6). Geometry optimization indeed confirms that a water decamer cluster may attach the solute either by a rectangular face of the dudud isomer or by a pentagonal face of the duuud isomer. In both cases, a facial parallel structure characterized by four BCPs between the water cluster and the solute (H w -O k , H w -O e , O w -H m , and O w -H m ) is obtained (Table 6). Thus, facial parallel structures characterized by four BCPs between the solute and a water cluster, and similar to the ones observed for the BPL:(H 2 O) 4,5 complexes, may exist for the larger BPL:(H 2 O) 6,10 complexes.

In the case of the BPL:(H 2 O) 10 complex, we alternatively considered two isomers in which two water clusters are simultaneously interacting with the BPL (Fig. 5):

-a (H 2 O) 5 :BPL:(H 2 O) 5 isomer in which each water pentamer is interacting with one face of the solute, -a (H 2 O) 4 :BPL:(H 2 O) 6 isomer in which a uudd water tetramer is attached to one face of the BPL whereas a water hexamer in its book shape is interacting with the other face.

The QTAIM analysis on the relaxed 5:1:5 and 6:1:4 structures demonstrates that each water cluster is attached to the solute by means of four interactions: H w -O k , H w -O e , O w -H m , and O w -H m . However, both 5:1:5 and 6:1:4 isomers are significantly higher in energy than the 1:10 isomer by ~40 kJ/mol, thus suggesting that BPL:(H 2 O) n isomers in which a single water cluster is interacting with the solute would be preferentially formed rather than sandwich (H 2 O) m :BPL:(H 2 O) n-m arrangements. The inclusion of BPL inside the 5 12 cage -BPL@(H 2 O) 20 -generates 19 BCPs including two characteristics of the hydrogen bonding between the hydrogen of waters and the ketone oxygen of BPL, which leads to the formation of a solute-induced Bjerrum-like defect, as observed in the encapsulation of several solutes [18]. Nevertheless, the endohedral isomer is found to be slightly less stable than the exohedral form, by ~ 8.3 kJmol -1 .

Contrarily, the endohedral isomer is more stable than the exohedral one by ~21.7 kJmol -1 , for the BPL:(H 2 O) 24 complex. A larger cavity of the 5 12 6 2 structure ( = 4.33 Å vs. 3.95 Å for the 5 12 dodecahedron cluster) [START_REF] Sloan | Clathrate Hydrates of Natural Gases[END_REF] allows the BPL encapsulation without any defect on the water network. The guest molecule is found in sandwich between two hexagonal rings of the 5 12 6 2 structure. According to the QTAIM analysis (Table 8), multiple oxygen-oxygen interactions are formed between the solute and the cage, in addition to the hydrogen bonding involving hydrogen atoms of BPL.

Conclusion

In summary, the dispersion corrected range-separated-hybrid functional LC-wPBE-GD3BJ combined with a moderate size basis set (6-311++G(d,p)) was found to suitably describe the geometric, energetic and spectroscopic (dipole moments and rotational constants) features of micro-hydrated BPL:(H 2 O) n complexes. Facial parallel structures previously reported for the BPL:(H 2 O) 4,5 complexes were rationalized thanks to the MESP analysis of isolated partners.

The QTAIM analysis further demonstrates that attachment of the water cluster on the BPL is similar in these BPL:(H 2 O) 4,5 complexes. It was further shown that two isomers of water hexamer and water decamer could efficiently attach the solute by means of similar watersolute interactions characterized by four BPCs between water molecules and the solute. Larger water clusters may also similarly interact with the solute: the attachment of the 5 12 and 5 12 6 2 water D-and T-cages on the solute leads to a substantial stabilization of the system. Alternatively these water cages can also act as host for the solute. DFT-D calculations confirm that both endohedral and exohedral BPL:(H 2 O) 20,24 complexes are stable with respect to the lowest lying D-and T-cage added to free BPL molecule. Nevertheless, it is interesting to note that these endohedral compounds lie around ten kJmol -1 above the sum of free partners when we take into account the global minimum of water cluster of cuboid structure. In the BPL@(H 2 O) 20 isomer, the BPL simultaneously acts as hydrogen-bond donor and hydrogenbond acceptor to the water cluster, and the formation of solute-induced Bjerrum-like defects results in an opening of the water cage. As a result, the endohedral and exohedral BPL:(H 2 O) 20 isomers are calculated to be close in energy. Such disruption of the water-water interaction is not observed when BPL is inserted inside the larger 5 12 6 2 water cage. The BPL@(H 2 O) 24 isomer is much more stable than the exohedral BPL:(H 2 O) 24 isomer. This can easily be explained from the QTAIM analysis that leads to the identification of 22 BCPs between oxygen atoms of water molecules and the solute in the inclusion complex, whereas only four BCPs are involved in the exohedral interaction.

Supporting Information

Cartesian coordinates of all the studied species are reported in the Supporting Information. This includes the Cartesian coordinates of the cuboidal (H 2 O) 20 and (H 2 O) 24 isomers. Spectrospic features are also gathered for the BPL:(H 2 O) n complexes.

Note: The authors declare no competing financial interest.

  , and rotational constants associated to the experimental data of the 1:1 complex. a) D e is the binding energy, D 0 the binding energy corrected for the vibrational zero-point-energy. D e CP (respectively D 0 CP ) are the D e (respectively D 0 ) corrected for BSSE using the CP method. b)  C = 0 experimentally and theoretically at all levels. c) From Ref 35.

Figure 1 :

 1 Figure 1: Topological study of the BPL molecule: Structure of the β-propiolactone (left), MESP map plotted at the 0.001 a.u. (centre) and 0.04 a.u. (right) isodensity surface. Electronrich regions are depicted in red color, while electron-deficient regions are in blue color.

Figure 2 :

 2 Figure 2: Experimentally-deduced structures for the BPL:(H 2 O) 4 and BPL:(H 2 O) 5 clusters and identification of the complementary interacting sites by the MESP analysis of isolated partners.

  the solute. The interaction between water cluster and the solute for that both isomers of the BPL:(H 2 O) 4 and of BPL:(H 2 O) 5 complexes is characterized by four BCPs denoted as H w -O k , H w -O e , O w -H m , and O w -H m with respect to the atoms involved in these interactions. Their energetic and topological features are reported in Table3. 1:4a_uudd isomer BCP (r)  2 (r) H w -O k 0.013 0.05 H w -O e 0.012 0.04 O w -H m 0.010 0.03 O w -H m 0.009 0.03 E = -572.62750 Hartree ΔE = 0.0 kJ/mol 1:4b_uudd isomer BCP (r)  2 (r) H w -O k 0.012 0.05 H w -O e 0.014 0.05 O w -H m 0.009 0.03 O w -H m 0.009 0.03 E = -572.62701 Hartree ΔE = 1.2 kJ/mol 1:5a_ududu isomer BCP (r)  2 (r) H w -O k 0.015 0.06 H w -O e 0.015 0.05 O w -H m 0.010 0.03 O w -H m 0.010 0.03 E = -649.03643 Hartree ΔE = 0 kJ/mol 1:5b_ududu isomer BCP (r)  2 (r) H w -O k 0.015 0.06 H w -O e 0.015 0.05 O w -H m 0.009 0.03 O w -H m 0.010 0.03 E =-649.035633 Hartree ΔE = 2.1 kJ/mol Table 3: MESP plot and BCPs of 1:4_uudd and 1:4_ududu isomers. See the caption of Figure 1 for more information. The calculated dipole moments and rotational constants for these BPL:(H 2 O) 4 and BPL:(H 2 O) 5 isomers are reported in

Figure 3 :

 3 Figure 3: MESP plot of the water hexamer isomers.

Figure 4 :

 4 Figure 4: The presence of two neighboring electron-deficient regions followed by two neighboring electron-rich regions on the rectangular base of the prism (A) and book (B) structures promote the electrostatic interaction with BPL in a facial parallel arrangement.

Table 6 :

 6 dudud isomer: Te = 0.0 kJ/mol[47] duuud isomer: Te = 17.7 kJ/mol[47] Study of the BPL:(H 2 O) 10 isomer.

6: 1 : 4 E

 14 = -1031.06965 Hartree Δ E = 41 kJ/mol. 5:1:5 E = -1031.06898 Hartree Δ E = 43 kJ/mol.

Table 1 :

 1 Calculated geometries, energetics, dipole moments

	Experimental values c

Table 2 :

 2 Experimental and theoretical dipole moments and rotational constants for the BPL:(H 2 O) 2-4 clusters.

	Dipole Moment (D)	Rotational Constants (MHz)

BPL:(H 2 O) 4 and BPL:(H 2 O) 5 complexes: A MESP picture to rationalize the structures experimentally deduced Facial parallel structures were deduced from spectroscopic features for two BPL:(H 2 O) 4 and one BPL:(H 2 O

Table 4 .

 4

	Dipole Moment (D)	Rotational Constants (MHz)
	µ a /µ b /µ c /µ tot	A/B/C

Table 4 :

 4 Experimental and calculated dipole moments and rotational constants for the BPL:(H 2 O) 4 and BPL:(H 2 O) 5 complexes.

Table 5 :

 5 MESP plot and BCPs of BPL:(H 2 O) 6 .

A B

(H

2 O) 6 Book 1:6-book (H 2 O) 6 Prism 1:6-prism

BPL in or out of water cluster: BPL:(H 2 O) 20 and BPL:(H 2 O) 24 complexes

  The study of larger BPL:(H 2 O) n clusters is particularly relevant in the context of clathrate hydrate formation. Endohedral and exohedral BPL:(H 2 O) 20,24 involving the 5 12 and 5 12 6 2 standard water cages, respectively, were considered (Table7).First of all, we remind the reader that the global minimum reported in the literature for both (H 2 O) 20 and (H 2 O) 24 cluster are cuboidal [19,[48][49][50][51][52][53] in which the insertion sites are too small to accept a guest polyatomic molecule without opening the water network. The (H 2 O) 20 cuboidal structure was confirmed at the MP2 perturbative level of theory[49], while the (H 2 O) 24 cuboidal structure has been identified based on molecular dynamic calculations [Erreur ! Signet non défini.]. However, it is also well known that the unit cell of a host-guest interaction in gas hydrates consists of two hollow 5 12 (H 2 O) 20 (dodecahedron) and six hollow 5 12 6 2 (H 2 O)24 (tetrakaidecahedron) cages. The simplest (H 2 O) 20 dodecahedron structure used in this work corresponds to the lowest lying isomers D-cage containing twelve pentagonal rings which is energetically less stable than the Edge sharing structure (singlet ground electronic state) by ~46 kJmol -1[48]. Concerning the hollow (H 2 O) 24 tetrakaidecahedron structure, Xantheas et al. identified theoretically three family isomers depending on the acceptor/donor characteristic of the bonded O-H bonds and also upon the orientation of dangling O-H bonds (noted as I, II and III) located within a narrow energy windows less than 2.5 kJmol -1[54,55,56,57]. The hollow 5 12 6 2 (H 2 O)24 T-cage considered in this work corresponds to the lowest-lying "family I isomers" of Xantheas. At the present level of theory, the (H 2 O)24 T-cage was found to be 93.8 kJmol -1 above the the global minimum of cuboid (H 2 O) 24 suggested byTakeuchi [53].Furthermore, this T-cage structure has been used to study the stability and reactivity of CH 4 encapsulated in the 5 12 6 2 cage[57]. Concerning the interaction of a BPL molecule with either 5 12 (H 2 O) 20 D-cage or 5 12 6 2 (H 2 O) 24 T-cage, the exohedral structure obeys the same rules as for above studied complexes: the 5 12 or 5 12 6 2 cage interacts with BPL by a pentagonal face offering the most favorable MESP feature, and four S-W BCPs are identified.

	Interaction with	BCP	(r)	 2 (r)
		H w -O k 0.019 0.08	BCP (r)  2 (r)
	W 6	H w -O e 0.013 0.05 O w -H m 0.011 0.04	H w -O k 0.015 0.06 H w -O e 0.015 0.06
		O w -H m 0.010 0.03 H w -O k 0.011 0.04	O w -H m 0.010 0.03 O w -H m 0.010 0.03
	W 4	O w -H m 0.008 0.03 H w -O e 0.013 0.04	Two times symmetrical four BCPs
		O w -H m 0.010 0.03
	Figure 5: Study of alternative BPL:(H 2 O) 10 isomer involving two water clusters in interaction
	with the solute.

Table 7 :

 7 MESP of the 5 12 and 5 12 6

	Remarks

2

water cages are plotted at (r)=0.001 a.u. Optimized geometries for both endo-and exohedral BPL:(H 2 O) 20, 24 complexes. BCP (r)/ 2 (r)

Table 8 :

 8 Electron density (in a.u.) and its Laplacian (in a.u.) at the BCPs between different atoms of BPL and oxygen atoms of the 5 12 6 2 cage. A total of ten BCPs have been found between two oxygen atoms of BPL and those of water molecules. For these O k -O w and O e -O w BCPs, the electron density varies between 0.003 and 0.011 a.u. These values are very close to the ones of the oxygen-oxygen interactions involved in the CO 2 @(H 2 O) 20 endohedral complex ( = [0.004 ˗ 0.008 a.u.][16]). We should underline that the H m -O w interactions are far from being negligible with respect to the O k -O w and O e -O w ones. Consequently, both van-der-Waals O BPL -O w interaction and hydrogen H m -O w bonding contribute to the stability of the BPL@(H 2 O) 24 endohedral complex.

Acknowledgement

We thank the UPMC labex MiChem for providing Ph.D. financial support for M. Kalai. We are grateful to IDRIS for providing computer facilities (Grant No. i2016087615).