Céline Lavergne
email: celine.lavergne@univ-lr.fr

Laureen Beaugeard

Christine Dupuy

Courties Claude

Lavergne Céline

Beaugeard Laureen

Agogué Hélène

Lavergne Céline Lienss

An efficient and rapid method for the enumeration of heterotrophic prokaryotes in coastal sediments by flow cytometry

Keywords: prokaryotes, cell enumeration, flow cytometry, coastal sediments

come

An efficient and rapid method for the enumeration of heterotrophic prokaryotes in coastal sediments by flow cytometry

Introduction

Microorganisms dominate marine ecosystems [START_REF] Delong | Community genomics among stratified microbial assemblages in the ocean's interior[END_REF] and were often considered as a "Black Box" by scientists [START_REF] Fuhrman | Prokaryotic and viral diversity patterns in marine plankton[END_REF]. To investigate this "Black Box", many studies have focused on new technologies and advances in molecular biology methods, allowing researchers to acquire a huge quantity of phylogenetic and potential physiologic information from oceans and marine coastal ecosystems. But these revolutionary "omics" data need to be completed by single-cell analysis, metabolic studies, and basic determination of prokaryotic abundances. Prokaryotes (Bacteria and Archaea) are key organisms in biogeochemical cycles in all marine environments [START_REF] Azam | Microbial structuring of marine ecosystems[END_REF]Malfatti, 2007, DeLong, 2009) and the first step to study these communities is to estimate their abundance within the microbial assemblage. Estimations of abundance showed that prokaryotes are as abundant as 10 6 cells.mL -1 in ocean water [START_REF] Whitman | Prokaryotes: The unseen majority[END_REF] and more than 10 8 cells.mL - 1 in marine surface sediments [START_REF] Jorgensen | Feast and famine -microbial life in the deep-sea bed[END_REF]. In sediments, prokaryotes play a crucial role in the food web as they remineralize organic matter and lead major cycles such as nitrogen and carbon cycles. Most specifically, heterotrophic prokaryotes are a majority throughout the whole sediment depth and can be present until almost 2 km below the surface [START_REF] Ciobanu | Microorganisms persist at record depths in the subseafloor of the Canterbury Basin[END_REF].

The first advances in heterotrophic prokaryotic enumeration were made using epifluorescence microscopy (EFM) [START_REF] Porter | The use of DAPI for identification and enumeration of bacteria and bluegreen algae[END_REF]. Fluorochromes combined with EFM have been used to develop standardized methods to successfully count bacteria in freshwater and marine water columns [START_REF] Daley | Direct epifluorescence enumeration of native aquatic bacteria: uses, limitations, and comparative accuracy[END_REF]. The most widespread way of staining cells is to target DNA with a fluorescent dye such as DAPI (4', 6-diamidino-2-phenylindole), currently used in microscopy [START_REF] Porter | The use of DAPI for identification and enumeration of bacteria and bluegreen algae[END_REF]. [START_REF] Montagna | Sampling Design and Enumeration Statistics for Bacteria Extracted from Marine Sediments[END_REF] showed under Acridine Orange (AO)-EFM observation that bacteria in muddy sediments occur at levels two orders of magnitude greater than in sandy sediments. Nowadays, EFM is still the most widespread technique for estimating the abundance of prokaryotes (see Supplementary Information Table 1 for references). Nevertheless, [START_REF] Robertson | Characterizing aquatic bacteria according to population, cell size, and apparent DNA content by flow cytometry[END_REF] were the first to use flow cytometry (FCM) to enumerate heterotrophic prokaryotic cells by DAPI-staining in marine and freshwater samples. Even if FCM seemed to be an accurate and rapid method for determining heterotrophic prokaryotic cells, advances were needed in storage conditions or fixative effects on benthic samples. These fixatives were known to permeate cells [START_REF] Troussellier | Flow cytometric analysis of coastal lagoon bacterioplankton and picophytoplankton: fixation and storage effects[END_REF]; consequently, the interactions between dyes and fixatives needed to be taken into account when choosing dyes. During the exponential phase of FCM utilization for environmental marine samples, many dyes have been reported in the literature such as DAPI, Hoechst 33342, TO-PRO-1, SYBRGreen (I or II), SYTO13 etc… (details are reviewed in [START_REF] Gasol | Using flow cytometry for counting natural planktonic bacteria and understanding the structure of planktonic bacterial communities[END_REF]). With technological advances, FCM became more and more useful in marine microbiology and offered new challenges to scientists, such as the prokaryotic enumeration in soils and sediments and the use of specific probes (Fluorescence in situ hybridization -FISH) [START_REF] Llobet-Brossa | Microbial Community Composition of Wadden Sea Sediments as Revealed by Fluorescence In Situ Hybridization[END_REF]. For sediment and soil analysis, the dye mostly used to stain DNA is SYBRGreen I [START_REF] Kallmeyer | New cell extraction procedure applied to deep subsurface sediments[END_REF], and many authors fixed cells with formaldehyde [START_REF] Epstein | Enumeration of sandy sediment bacteria: search for optimal protocol[END_REF] preferentially, but the best temperature for long time storage is still unclear.

FCM is now widely used for water column samples, but sediment samples carry the difficulties of a solid matrix rich in detritus, minerals and exopolymeric substances (EPS). Indeed, sediments are particularly hard to study because dyes (e.g. AO or DAPI) can produce a high fluorescence background with clay and silt-rich sediments containing a high quantity of detritus and EPS [START_REF] Kuwae | Determination of Abundance and Biovolume of Bacteria in Sediments by Dual Staining with 4′,6-Diamidino-2-Phenylindole and Acridine Orange: Relationship to Dispersion Treatment and Sediment Characteristics[END_REF]. Additionally, in such environments, prokaryotic cells are often attached to sediment particles by EPS [START_REF] Decho | Microbial biofilms in intertidal systems: an overview[END_REF], creating a complex with organic and mineral particles [START_REF] Epstein | Enumeration of sandy sediment bacteria: search for optimal protocol[END_REF]Rossel, 1995, Kallmeyer, et al., 2008). The point of divergence between microbiologists remains the separation method to detach cells from the solid matrix. In order to improve counting yield in sediment, chemical dispersion and physical detachment should be applied. Physical detachment can be achieved by isoelectric method [START_REF] Jaspers | Separation of bacterial cells by isoelectric focusing, a new method for analysis of complex microbial communities[END_REF], capillary electrophoresis [START_REF] Schneiderheinze | High efficiency separation of microbial aggregates using capillary electrophoresis[END_REF], sonication bath [START_REF] Duhamel | Flow cytometric analysis of bacteria-and virus-like particles in lake sediments[END_REF][START_REF] Ellery | Comparison of homogenization and ultrasonication as techniques in extracting attached sedimentary bacteria[END_REF][START_REF] Gasol | Benthic flagellates and ciliates in fine freshwater sediments: calibration of a live counting procedure and estimation of their abundances[END_REF], or probes [START_REF] Albright | Attached and Free-Floating Bacterioplankton in Howe Sound, British Columbia, a Coastal Marine Fjord-Embayment[END_REF][START_REF] Epstein | Enumeration of sandy sediment bacteria: search for optimal protocol[END_REF][START_REF] Kallmeyer | New cell extraction procedure applied to deep subsurface sediments[END_REF], vortexing [START_REF] Frischer | Whole-Cell versus Total RNA Extraction for Analysis of Microbial Community Structure with 16S rRNA-Targeted Oligonucleotide Probes in Salt Marsh Sediments[END_REF][START_REF] Whiteley | Analysis of the microbial functional diversity within water-stressed soil communities by flow cytometric analysis and CTC+ cell sorting[END_REF], or by blender homogenization [START_REF] Lindahl | Evaluation of methods for extraction of bacteria from soil[END_REF][START_REF] Maron | Evaluation of quantitative and qualitative recovery of bacterial communities from different soil types by density gradient centrifugation[END_REF][START_REF] Yamamoto | Bacterial abundance in relation to surface area and organic content of marine sediments[END_REF]. The sonication probes appear to be the best way to mechanically detach prokaryotic cells from sediment particles, and applying it with an intensity of 60W for 30 seconds has been shown to be a good compromise between high counting yield and avoiding lysing cells [START_REF] Garet | Transformation bactérienne de la matière organique dans les sédiments côtiers: relation entre les métabolismes respiratoires et les activités exoprotéolytiques bactériennes Ph[END_REF][START_REF] Lei | Impact of Arenicola marina (Polychaeta) on the microbial assemblages and meiobenthos in a marine intertidal flat[END_REF]. Concerning the chemical dispersion solution, the most cited is the sodium pyrophosphate (NaPp), which is often found in detergent solutions in combination with Tween 20 [START_REF] Amalfitano | Flow cytometric analysis of benthic prokaryotes attached to sediment particles[END_REF] or Tween 80 [START_REF] Duhamel | Flow cytometric analysis of bacteria-and virus-like particles in lake sediments[END_REF]Jacquet, 2006, Epstein and[START_REF] Epstein | Enumeration of sandy sediment bacteria: search for optimal protocol[END_REF], the phosphate buffer saline (PBS) solution [START_REF] Barra Caracciolo | In situ analysis of native microbial communities in complex samples with high particulate loads[END_REF], the sodium chloride [START_REF] Fazi | Bacterial communities associated with benthic organic matter in headwater stream microhabitats[END_REF], or methanol [START_REF] Kallmeyer | New cell extraction procedure applied to deep subsurface sediments[END_REF][START_REF] Lunau | An improved method for counting bacteria from sediments and turbid environments by epifluorescence microscopy[END_REF]. Moreover, it is possible to apply a density gradient [START_REF] Kallmeyer | New cell extraction procedure applied to deep subsurface sediments[END_REF][START_REF] Morono | An improved cell separation technique for marine subsurface sediments: Applications for high-throughput analysis using flow cytometry and cell sorting[END_REF] after the chemical separation in order to improve the time and reliability of the counting [START_REF] Fazi | Bacterial communities associated with benthic organic matter in headwater stream microhabitats[END_REF]. However, in the literature, it remains unclear which best dilution and detergent mix need to be applied to sediment samples in order to detach the maximum of aggregates and cells adsorbed on particles.

Nowadays, no simple and standardize method existed to study microorganisms in different type of sediments. On that basis, this study aims at optimizing sediments fixation and storage, cells separation and comparing two analysis methods (EFM and FCM) to count benthic heterotrophic prokaryotes.

Sample collection, fixation and storage

Muddy sediments from the French Atlantic coast were sampled in the Moëze Bay and the Aiguillon Bay from the surface to 10 cm-deep. The sediment samples were collected in 2012 and 2013 at low tide using cores (15 cm diameter). Back in the laboratory (less than one hour), the sediments were homogenized, and sub-samples were put in containers using sterile 50 mL syringes with cutoff tips. Finally, subsamples were fixed with 0.2 µm-filtered formaldehyde solution (vol/vol, 2% final concentration) and kept according two conditions: at +4°C in the dark or frozen in liquid-N 2 directly followed by storage at -80°C. Different storage times were tested on five different muddy samples in duplicates: 1 week, 1 month, 3 months, and 6 months after sampling.

Protocol development

Here, we described the proceedings of the protocol development. Different steps of the procedure were investigated in order to improve the enumeration of prokaryotes in sediment:

1) sample preparation before mechanical extraction; 2) utility of centrifugation to remove sediment particles; 3) repetitive steps of extraction to improve cell counting yield.

Sample preparation before mechanical extraction

First tests were achieved by preparing sediment slurries with a solution of NaPp 0.01M (Pascal et al., 2009, Tso and[START_REF] Tso | Enumeration of Protozoa and Bacteria in Muddy Sediment[END_REF]. Then, in order to disaggregate the attached cells, Tween 80 (0.1% final concentration) was added to the NaPp solution (0.01 M). Indeed, Tween 80 is a non-ionic surfactant known to decrease particle aggregates and to enhance detachment of cells from particles in sediment samples [START_REF] Velji | Microscopic enumeration of attached marine bacteria of seawater, marine sediment, fecal matter, and kelp blade samples following pyrophosphate and ultrasound treatments[END_REF]Albright, 1986, Yoon and[START_REF] Yoon | Improved Method of Enumeration of Attached Bacteria for Study of Fluctuation in the Abundance of Attached and Free-Living Bacteria in Response to Diel Variation in Seawater Turbidity[END_REF]. The influence of Tween 80 addition on the cell recovery efficiency was evaluated on 55 samples. According to preliminary tests, using NaPp solution or NaPp+Tween 80 mixture, slurries were prepared by processing to successive dilutions until 1:2,000 (1:10; 1:100; 1:500; 1:1,000 and 1:2,000) to reduce sediment background [START_REF] Dos Santos Furtado | Different methods for extracting bacteria from freshwater sediment and a simple method to measure bacterial production in sediment samples[END_REF]Casper, 2000, Duhamel and[START_REF] Duhamel | Flow cytometric analysis of bacteria-and virus-like particles in lake sediments[END_REF]. A vortexing step of 5 sec was applied before and after each successive dilution.

According to [START_REF] Epstein | Enumeration of sandy sediment bacteria: search for optimal protocol[END_REF] and [START_REF] Velji | Microscopic enumeration of attached marine bacteria of seawater, marine sediment, fecal matter, and kelp blade samples following pyrophosphate and ultrasound treatments[END_REF] recommendations, 30 minutes of incubation at +4°C was used to detach cells from sediment particles. Then, mechanical extraction consisted of sonicating samples 30 s at 60W in ice with a sonicator probe (Branson, SLPE-150, 1/8" or 3 mm microtip, 40KHz) [START_REF] Lei | Impact of Arenicola marina (Polychaeta) on the microbial assemblages and meiobenthos in a marine intertidal flat[END_REF].

Utility of centrifugation to remove sediment particles

The impact of a centrifugation step was tested by applying or not a low speed centrifugation.

A first part of extracted samples was centrifuged at 1 000 g at +4°C during 1 min, after which supernatant was transferred and then stained for EFM and FCM analysis (see below for staining settings). On the second part of extracted samples, a proportion was mixed, transferred and then stained for EFM and FCM analysis and centrifugation was applied on the remaining proportion to collect sediment and attached cells for a second extraction step.

In any case, after centrifugation step, the remaining supernatant was discarded and the pellet was re-suspended in the detergent mix [0.01 M NaPp and Tween 80 (0.1% final conc.)] with the same volume of supernatant. By this way, the cells remaining attached to the sediment particles in the pellet can be detached and counted in a second step.

Repetitive steps of extraction to improve cell counting

Because cells can be still attached to sediment particles even after the first extraction, we evaluated the number of repetitive extraction steps needed to improve cell counting yield. The second step was processed as the first one, by incubating the samples in the detergent mix [0.01 M NaPp and Tween 80 (0.1% final conc.)] for 30 min at +4°C. Then, sonication was repeated (same settings as above) before the analysis.

Aiming at evaluating how many steps were needed, extraction process was repeated until cells recovery reaches a plateau on 15 different samples. Thus, the total prokaryotic cell abundance corresponded to the sum of all the counting values obtained in each extraction step.

Microscopic count

Extracted samples were stained with 4',6-diamidino-2-phenylindole (DAPI, 250 µg.ml -1 , 15 min, +4°C) and filtered through black polycarbonate membrane (0.2 µm pore size, 25 mm, Nucleopore) [START_REF] Porter | The use of DAPI for identification and enumeration of bacteria and bluegreen algae[END_REF]. Next, filters were mounted on slides using antifading oil type F (Olympus, Japan), and conserved at -20°C until counting. Finally, counts were made with an epifluorescence microscope (Axioskop2, Carl Zeiss Microscopy, LLC, United-States) at 1,000 x magnification under UV excitation (Filter set 01, 397 nm -Zeiss).

For each sample, a minimum of 20 fields (> 600 cells) were counted and averaged [START_REF] Lebaron | Accucary of epifluorescence microscopy counts for direct estimates of bacterial numbers[END_REF]. A cell sorter (FACSAria BF-Biosciences) was used to control extraction yield on prokaryotic population. Then, sorted fraction were observed using EFM (BX300, Olympus) to take pictures.

Flow cytometric and cell sorting analysis

Stained cells were discriminated according to green fluorescence (FL1) from SYBRGreen staining and side scatter properties (SSC). Picophytoplanktonic cells are also discriminated based on their red fluorescence (FL3) and SSC properties and excluded from final prokaryotic counts measured on a gate SSC-FL1 [START_REF] Marie | Enumeration of Phytoplankton, Bacteria, and Viruses in Marine Samples[END_REF].

Accurate cell concentrations were performed using TruCount beads from BD-Biosciences (excitation: red laser 633 nm; emission: FL5 660/20 nm).

Statistical analysis

All statistical analysis was performed using R software (R core Team, 2013). The effect of the addition of Tween 80 was tested with a Paired t-test. The influence of the parameters tested or percentage of sand in samples was evaluated by applying a Kruskal-Wallis rank sum test for one sample and Wilcoxon test for two paired samples on cell abundance values. The relationship between FCM and EFM was shown by fitting a significant linear regression. Effects of storage conditions were tested with a 2-way analysis of variance (ANOVA), residuals were tested for application validation and a TukeyHSD posthoc test was used.

Results

Hereby, we described the results of the protocol development proceedings and then the final protocol that we succeed to establish.

Sample preparation

First, slurries were prepared with NaPp 0.01M alone and cell sorting flow cytometry followed by EFM observations were used to visualize the extracted populations. Two populations were observed: free prokaryotic cells population and attached-prokaryotic cells population. The NaPp alone at 0.01 M was apparently not efficient enough to separate cells from sediment particles, because attached prokaryotic cells were still present in the samples and represented 27.7% of the total abundance. On this basis, the effect of adding Tween 80 was evaluated to minimize cell aggregation [START_REF] Yoon | Improved Method of Enumeration of Attached Bacteria for Study of Fluctuation in the Abundance of Attached and Free-Living Bacteria in Response to Diel Variation in Seawater Turbidity[END_REF]. Both FCM and EFM counting revealed a higher cell counting yield (Fig. 1), with an increase of 130.40 % ± 12.49 SE and 176.79 % ± 14.25 SE respectively, compared to the treatment without Tween 80.

Adding Tween 80 to NaPp in the mixture significantly improve the number of cells counted in FCM (Paired t-test: t = -9.6127, df = 54, p-value <0.001) and EFM (Paired t-test: t = -27.1056, df = 35, p-value <0.001). After two repetitive steps, cell recovery efficiency rose from 43.3 % ± 2.0 SE without Tween to 92.5% ± 2.0 SE with addition of Tween 80.

Moreover, microscopic analysis on sorted populations confirmed that the counted cells were free cells, clearly separated from sediment particles when Tween 80 was added to the mixture.

Consequently, it appears that Tween 80 disaggregated efficiently benthic cells and therefore improved the cell counting results (Fig. 1). The recommended protocol is thus to use sodium pyrophosphate (NaPp) and Tween 80 treatment to prepare sediment samples for heterotrophic prokaryotes enumeration by FCM (Fig. 5). 2-column fitting

Utility of centrifugation

The utility of a centrifugation step before counting analysis was tested by performing an experiment with and without low speed centrifugation (1,000 g, 1 min, +4°C). Experiments showed that centrifugation moderately decreased cell counts (-1.71%) in FCM and EFM because cells that remained attached to the particles were removed (data not shown). Settling velocities of sands have been calculated according to Soulsby (1997), and we evaluated that the settling time of particles is inferior to the standing step applying on cytometer to acquire data before recording. Indeed, particles of 62 µm will take 4.8 seconds to settle in the tube and the cytometer takes 5 seconds to acquire and 10 seconds to record. The particles cannot collapse the flow cell chamber. Thus, we proposed to analyse samples without the centrifugation step and then to centrifuge samples afterward to proceed to a second cells extraction on the pellet.

Repetitive steps of extraction

After the first extraction, 57.04 % ± 2.58 SE of cells were extracted and counted. The cumulative cell recovery increased strongly and reached a plateau after the fourth extraction (Fig. 3), showing that in routine analysis it will not be necessary to do more than four extractions. The coefficient of variation of the first extraction was the highest, reaching 17.52

%. The strongest decrease in CV was observed between the first and the second extraction (Fig. 2) showing that the second extraction allowed counting a higher number of cells (83.67% ± 0.94 SE) with a lower imprecision (CV < 5%). After that, the CV continued to decrease with lower range values. Doing eight extractions can be time consuming and expensive. In our case, with sediment samples, eight extractions were not necessary. Thus, for routine analysis of benthic samples by FCM, we propose a 2-step extraction as a good compromise among 1) cell recovery efficiency (83.67% ± 0.94 SE) and accuracy (CV = 4.34);

and 2) analysis time (4 hours for 30 samples) and cost. single column fitting image

Microscopy versus flow cytometry

Fifty five muddy samples were tested and highly significant correlations were found between EFM and FCM counts (Fig. 3; t-test: R²= 0.615, df =53, p-value <0.001). Moreover, cell abundance estimated by FCM was always higher than cell abundance counted by EFM, by a factor of 1.81. Thus, EFM and FCM results followed the same trends but FCM always allowed detecting more cells than EFM. We prove by this way that the traditional method by EFM need to be re-evaluated and that FCM can be a better method to assess the heterotrophic prokaryotic abundance. single column fitting image

Which type of storage?

The influence of storage conditions on prokaryotic cells was studied. After the first month of storage, a loss of 24.46 % ± 4.5 SE of cells was observed under the two storage conditions (-80°C and +4°C). After that, prokaryotic abundances remained stable until 6 months (-4%; Fig. 4). High standard error bars on Fig. 4 were due to the differences in prokaryotic abundances between sample depths, but the results brought out that prokaryotic abundances in samples stored at -80°C tend to be higher than in those conserved at +4°C. A significant difference was detected between T0 and 12 weeks after sampling (Tukey HSD; p-value<0.05), nevertheless, neither the temperature of storage nor the interaction with time influenced the abundance of prokaryotes counted (2-way ANOVA, p-value > 0.05). After 3 months, the abundances measured with the final protocol were more variable. The recommended protocol is to store fixed sediment samples at -80°C (as for water samples, [START_REF] Marie | Enumeration and cell cycle analysis of natural populations of marine picoplankton by flow cytometry using the nucleic acid stain SYBR Green I[END_REF]) and to analyse samples within 3 months after sampling.

Final protocol

All the assessments above resulted in a final protocol. This final protocol (Fig. 6) detached and homogenized cells in sediment samples thanks to 2 successive extractions ( § 3.3) and allowed to count the prokaryotic cells using FCM.

1) Samples were prepared and extracted using: a dilution (1:1,000 to 1:2,000) in a detergent mix ( § 3.1) [sodium pyrophosphate (0.01 M) + Tween 80 (0.1%)] and a vortexing step and 30 min of incubation at +4°C. After the vortexing step, a sonication separation for 30 sec (60W) in ice with a sonication probe (3 mm) was applied. Without any centrifugation step ( § 3.2), an aliquot of the sample was stained with SYBRGreen I (1:10,000) 15 min in the dark and analyzed by flow cytometry (FCM).

2) the remaining part of the sample was centrifuged at low speed (1 min at 1,000 g at +4°C); the pellet was then resuspended in the detergent mix and step 1 was repeated once more.

Using this two-step protocol, 83.67% ± 3.63 SD ( § 3.3) of total cells can be extracted from a solid matrix and counted by SYBRGreenI-stained FCM.

Application on different types of sample

To validate the protocol, the method for FCM analysis was applied to sandy, sandymud and muddy sediments from different locations with different values of sand contents (from 0 to 90%) following a range of silt/sand content. For each sample, the cell recovery percentages of the first step extraction were high, by mean 61% ranging from 55% to 68% (Fig. 6; Supplementary Information Table 2.). The cell recovery efficiencies of these samples were in the same range and there were no significant effects of the sand content on the cell recovery of the first extraction (Kruskal-Wallis test; ² = 5; df = 5; p-value = 0.4159). These results showed that our developed method is efficient for sandy, sandy-mud and muddy sediments tested whatever the location and sand content or composition.

2-column fitting image 4 Discussion and Conclusions

Flow cytometry (FCM) is now widely used for water column analysis in order to estimate autotrophic diversity and abundance, and to enumerate heterotrophic prokaryotes [START_REF] Legendre | Flow cytometry in oceanography 1989-1999: Environmental challenges and research trends[END_REF]. For sediment analysis, technical advances have been made but not well optimized to get an efficient and rapid method for FCM. The main difficulty remains the necessary step of cell preparation and separation from sediment which need to be adapted for each sediment type [START_REF] Duhamel | Flow cytometric analysis of bacteria-and virus-like particles in lake sediments[END_REF]. Many authors have tried to find the best protocol for separating prokaryotic cells from a solid matrix. One particularly powerful way seems to be the density gradient application on various sediments [START_REF] Aakra | Surface Attachment of Ammonia-Oxidizing Bacteria in Soil[END_REF][START_REF] Amalfitano | Recovery and quantification of bacterial cells associated with streambed sediments[END_REF][START_REF] Kallmeyer | New cell extraction procedure applied to deep subsurface sediments[END_REF][START_REF] Lunau | An improved method for counting bacteria from sediments and turbid environments by epifluorescence microscopy[END_REF][START_REF] Morono | An improved cell separation technique for marine subsurface sediments: Applications for high-throughput analysis using flow cytometry and cell sorting[END_REF][START_REF] Whiteley | Analysis of the microbial functional diversity within water-stressed soil communities by flow cytometric analysis and CTC+ cell sorting[END_REF], but these techniques are relatively time-consuming and expensive. The present study demonstrates a quick and efficient protocol for the enumeration of heterotrophic prokaryotes in coastal sediments.

Since EFM is the classic method of counting heterotrophic prokaryotic cells in sediment, our protocol of extraction followed by FCM analysis needs to be validated by EFM.

We compared the cell abundance obtained by EFM (DAPI-stained cells) and FCM (SYBRGreenI-stained cells). The staining protocol used was different with the two methods (i.e. DAPI preferentially bind on A and T bases). The choice was to compare the traditional protocol (DAPI-stained cells) and the most used protocol in FCM (SYBRGreenI-stained cells). It is known that the two dyes may differ in terms of binding and affinity on DNA and RNA (simple and double-stranded) [START_REF] Marie | Enumeration and cell cycle analysis of natural populations of marine picoplankton by flow cytometry using the nucleic acid stain SYBR Green I[END_REF][START_REF] Troussellier | Flow cytometric discrimination of bacterial populations in seawater based on SYTO 13 staining of nucleic acids[END_REF] and thus can produce different results. Nevertheless, DAPI-stained samples (sorted and non-sorted sediment samples) were counted using FCM equipped with a violet laser (407 nm).

Cytograms were weakly exploitable because DAPI fluorescence yield was not optimal at 407 nm (optimal wave length = 375 nm) resulting in a low signal resolution and thus high fluorescence background of DAPI (data not shown). Moreover, observations of SYBRGreenIstained cells under EFM were not satisfactory.

Finally, FCM appeared to be a consistent method to count benthic prokaryotes as it allows the detection of 1.81 times more cells than EFM with a significant correlation. The explanation could be that EFM is human-dependent and biased by the cell location of the filter (can be hidden by sediment particles). FCM allows assessment of particle count as well as multi-parameters analysis for each cell [START_REF] Bouvier | Using light scatter signal to estimate bacterial biovolume by flow cytometry[END_REF][START_REF] Porter | Go with the flowuse of flow cytometry in environmental microbiology[END_REF]. The use of FCM increases counting efficiency as compared to the classic EFM method, and the estimation of prokaryotic abundance is consistent.

Liquid N 2 storage is the most widely used method of conserving prokaryotic cells in water samples for FCM analysis [START_REF] Vaulot | A simple method to preserve oceanic phytoplankton for flow cytometric analyses[END_REF], but in the case of benthic prokaryotic cells, samples are usually directly counted or stored at +4°C before EFM counting [START_REF] Ellery | Comparison of homogenization and ultrasonication as techniques in extracting attached sedimentary bacteria[END_REF]Schleyer, 1984, Epstein and[START_REF] Epstein | Enumeration of sandy sediment bacteria: search for optimal protocol[END_REF]. We then propose to fix the sediment samples with 2% formaldehyde solution and after liquid-N 2 fixation, store them immediately at -80°C and then count within 3 months after sampling.

Many authors had proposed protocols for FCM analysis including a centrifugation step and/or a filtration through 5 µm because it can limit detritus clogging in the cytometer nozzle [START_REF] Duhamel | Flow cytometric analysis of bacteria-and virus-like particles in lake sediments[END_REF]. The present study brings out that without centrifugation, the sediment particles can settle in the tube and did not accumulate in the flow cytometer nozzle, and FCM analysis was possible. To develop a rapid and easy protocol, we proposed to analyse samples without the centrifugation step and then to centrifuge samples afterward to proceed to the second extraction (on the pellet).

Taking into considerations all these features, the development of the protocol focused on a method of cell separation to define a simple, inexpensive, and rapid method to enumerate prokaryotes in sediment. [START_REF] Kallmeyer | New cell extraction procedure applied to deep subsurface sediments[END_REF] extracted between 65 and 100% of prokaryotic cells in deep subsurface sediments by applying a bilayer density gradient. In soil, Barra Caracciolo, et al.

(2005) also used a bilayer gradient density as well, and were able to extract up to 77% of total prokaryotic cells. More recently, [START_REF] Morono | An improved cell separation technique for marine subsurface sediments: Applications for high-throughput analysis using flow cytometry and cell sorting[END_REF] applied a multilayer density gradient on samples from marine subsurface and obtained from 50 to 80% cell recovery. [START_REF] Lunau | An improved method for counting bacteria from sediments and turbid environments by epifluorescence microscopy[END_REF] worked on muddy and sandy sediments and opted for a low-speed centrifugation method combined with a methanol purification step; by an EFM analysis, they achieved 54 to 114% cell recovery. Even if the cell recovery had been found to be variable among the physico-chemical parameters of a solid matrix [START_REF] Maron | Evaluation of quantitative and qualitative recovery of bacterial communities from different soil types by density gradient centrifugation[END_REF], we confirmed that our method is consistent and quicker, and can be applied to different kind of benthic samples. It allows the extraction of a large quantity of prokaryotic cells (between 10 8 and 10 10 cells.mL -1 ) and the possibility of determining prokaryotic abundances (83.67% mean cell recovery).

Nevertheless, it is clear that some optimization details must be done for each type of samples. We suggest staining cells with more concentrated SYBRGreen I (1:5,000 final concentration) if the prokaryotic population is not easily distinguishable from background noise due to organic and mineral matter. Obviously, during the FCM analysis, threshold and fluorescent parameters must be adapted to population characteristics as well as the dilution of the sample.

Our two-step extraction method is simple to apply, as it allows the estimation of heterotrophic prokaryotic abundance of 30 sediment samples within 4 hours. This method was applied successfully on different types of sediments (muddy and sandy, coastal marine sediments and freshwater sediment) and among the different types of sediments, our method was reproducible. Moreover, these applications showed that our method was suitable not only for coastal sediments but also for freshwater sediment (from the Verdonniere river streambed, France). Aiming at finding a method suitable for a large range of sediments samples, this study prove that our optimized method offers a better efficiency for different marine sediment types even for freshwater sediments. In soils, [START_REF] Williamson | Estimates of viral abundance in soils are strongly influenced by extraction and enumeration methods[END_REF], showed a strong influence of clay content and recommended testing the influence of the extraction mixture prior to analyse the samples. Further analyses remain possible to establish whether our twostep protocol is efficient on clay-containing sediments.

This fast protocol using FCM is a methodological issue but is also crucial for ecological studies by allowing in the end a better understanding of marine benthic ecosystems. Finally, we can confirm that our protocol worked well for turbid water with high organic matter content in a study on prokaryotic community distribution among a salinity gradient in the Charente River (France). For this study, the dilution was adapted because prokaryotic abundance was between two and three orders of magnitude less than in the sediment samples.

In the future, we are convinced that our study can be useful for assessing activity, productivity or diversity analysis in sediments. Although, the abundance of prokaryotes is a central parameter to measure in all ecosystems, the next step to understand the functioning is evaluating the unknown genetic diversity [START_REF] Delong | The microbial ocean from genomes to biomes[END_REF][START_REF] Karl | Microbial oceanography: paradigms, processes and promise[END_REF]. And activity and productivity are powerful indices to characterize the community and are needed to show the key role of prokaryotic community in biogeochemical cycles. The combinations of our protocol and cell sorting [START_REF] Wang | Past, present and future applications of flow cytometry in aquatic microbiology[END_REF] can be a great progress for sediment analysis.

With cell sorting, it will be possible to sort cells according to their average side-anglescattered (SSC) light [START_REF] Bernard | Relationships among Bacterial Cell Size, Productivity, and Genetic Diversity in Aquatic Environments using Cell Sorting and Flow Cytometry[END_REF] (proxy of size-class) for example and then do diverse analysis on different population of the prokaryotic community.

imaging platform that provided organization and service in our lab. We also appreciate the [START_REF] Compton | Distributional overlap rather than habitat differentiation characterizes co-occurrence of bivalves in intertidal soft sediment systems[END_REF]

For

  each extraction step, the flow cytometric analysis consisted of SYBRGreen Istained (1:10,000 final concentration) extracted sample during 15 min in the dark at room temperature. Fluorescent beads (Fluoresbrite Multi fluorescent microsphere 1.0 µm, Polysciences, Germany) were added simultaneously to each sample in order to analyze cell fluorescence and scatter properties of samples. Each sample was analyzed for 30 s at low flow speed with FacsCanto II cytometer (3-laser, 8-color (4-2-2), BD Biosciences) equipped with a 20-mW 488-nm coherent sapphire solid state blue laser. Data were acquired using DIVA software provided by BD-Biosciences.

Fig. 1 .

 1 Fig. 1. Effects of the addition of Tween 80 to sodium pyrophosphate (NaPp) on prokaryotic

Fig. 2 .

 2 Fig. 2. Cumulative percentage of cell recovery using the final extraction protocol (extended to

Fig. 3 .

 3 Fig. 3. Linear regression between prokaryotic cell abundance determined by flow cytometry

Fig. 4 .

 4 Fig. 4. Effects of storage temperature and time on heterotrophic prokaryotic cell abundance

Fig. 5 .

 5 Fig. 5. Final protocol of the improved two-step separation method. FCM = Flow Cytometry ;

Fig. 6 .

 6 Fig. 6. A) Percentage of cells extracted after the first step by applying our two-step extraction

5 FiguresFig. 1 .

 51 Fig. 1. Effects of the addition of Tween 80 to sodium pyrophosphate (NaPp) on prokaryotic

Fig. 2 .

 2 Fig. 2. Cumulative percentage of cell recovery using the final extraction protocol (extended to

Fig. 3 .

 3 Fig. 3. Linear regression between prokaryotic cell abundance determined by flow cytometry

Fig. 4 .

 4 Fig. 4. Effects of storage temperature and time on heterotrophic prokaryotic cell abundance

Fig. 5 .

 5 Fig. 5. Final protocol of the improved two-step separation method. FCM = Flow Cytometry ;

Fig. 6 .

 6 Fig. 6. A) Percentage of cells extracted after the first step by applying our two-step extraction

6 Supplementary information Figure 1.

  Searching for the best protocol for enumeration of heterotrophic prokaryotes in sediments

Table 1 .

 1 Extraction, fixation and staining methods in literature

Table 2 .

 2 Heterotrophic prokaryotes abundance (mean ± SD) in different sediments and cell recovery (% with mean ± SD, min and max) of the first extraction using the two-step extraction protocol analysed by flow cytometry (FCM).

633 Figure 1. Searching for the best protocol for enumeration of heterotrophic prokaryotes in sediments

Table 1 .

 1 Extraction, fixation and staining methods in literature

Table 2 .

 2 Heterotrophic prokaryotic abundance (mean ± SE) in different sediments tested and cell recovery (% with mean ± SE, min and max) of the first extraction using the two-step extraction protocol analysed by flow cytometry (FCM).

		Prokaryotes abundance [cells.mL -1 ] mean +/-SE	% sand	Cell recovery [%] Mean (+/-SE) Min	Max
	Salt Lagoon sediment
	Thau lagoon (n=48), France	1.53.10 9	+/-	4.46.10 7	45 a	67.98 +/-0.49 60.72 75.06
	Intertidal Mudflat sediment
	Moëze Bay (n=45), France	7.31.10 9	+/-	2.92.10 8	10	55.81 +/-0.87 40.77 65.96
	Aiguillon Bay (n=42), France	1.40.10 10	+/-	4.34.10 8	3 b	58.57 +/-1.51 32.31 69.35
	Maroni estuary (n=9), Surinam	3.99.10 9	+/-	3.37.10 8	0	56.70 +/-2.23 38.16 68.72
	Sandy muddy coastal sediment
	Banyuls s/ mer Bay, France
	Proteic enrichment (n=32)	2.81.10 10	+/-	5.52.10 8	40	62.81 +/-1.29 38.14 72.90
	Banyuls s/ mer Bay, France
	Glucidic enrichment (n=60)	1.46.10 10	+/-	3.47.10 8	40	64.03 +/-0.88 41.56 72.75
	Sandy streambed sediment
	Verdonniere River (n=11)	6.75.10 9	+/-	1.41.10 9	90	61.25 +/-2.57 48.86 81.59
					TOT	61.02 +/-1.40

a Ifremer (2008) b

[START_REF] Bocher | Site-and species-specific distribution patterns of molluscs at five intertidal soft-sediment areas in northwest Europe during a single winter[END_REF]

Acknowledgments

This research was supported by a PhD grant from the Charente Maritime Department, by the CPER 2006-2013 (Contrat Projet Etat Région) of Charente Maritime and by EC2CO project (CAPABIOC, CNRS and INSU, 2013-2014). We are grateful to the cytometry and


Antonia Maria Masucci
email: antonia.masucci@orange.com

Alonso Silva
email: alonso.silva@alcatel-lucent.com

An Integer Linear Programming Approach for Coalitional Weighted Manipulation under Scoring Rules

In this work, we are interested to prove that for voting systems which can be expressed as scoring rules, the coalitional weighted manipulation problem which is known to be NP-complete is as difficult as solving an integer linear programming problem. For this integer linear programming problem several software solutions exist, and we have found that with a reasonable number of candidates the solution can be found within seconds.

I. INTRODUCTION

Voting systems, also known as electoral systems, have gained increasing interest in recent years. In particular, the computational aspects of voting have been object of numerous researches. Voting systems establish rules to determine the value of votes and how to aggregate them.

The famous Gibbard-Satterthwaite theorem states that for any voting rule that is not a dictatorship, there are elections in which at least one of the voters would benefit by lying [START_REF] Gibbard | Manipulation of voting schemes: a general result[END_REF], [START_REF] Satterthwaite | Strategy-proofness and Arrow's conditions: Existence and correspondance theorems for voting procedures and social welfare functions[END_REF]. A dictatorship is a voting rule where one of the voters (the dictator) single-handedly decides the outcome of the election.

The Gibbard-Satterthwaite Theorem implies that in theory, voters are able to manipulate elections. In practice, deciding which manipulation to employ may prove to be a hard computational problem. Indeed, there are a superpolynomial number of possibilities of ranking the candidates. Bartholdi et al. [START_REF] Bartholdi | The computational difficulty of manipulating an election[END_REF] showed a voting rule where manipulation is NP-hard. Conitzer et al. [START_REF] Conitzer | When are elections with few candidates hard to manipulate?[END_REF] showed that in a variety of voting rules, coalitional manipulation is NP-hard, even if there are only a constant number of candidates. A shortcoming of the result is that they are worst-case hardness results, and thus provide a poor obstacle against potential manipulators.

In this work, we analyze the computational aspects of manipulation. We propose an integer linear programming appoach and we realize that although the problem is NP-hard, in practice, with a small number of candidates the resolution of the manipulation problem is feasible and rather simple.

II. PRELIMINARIES

An election (V, C) consists of a set V = {v 1 , v 2 , . . . , v N } of voters and a set C = {c 1 , c 2 , . . . , c M } of candidates. Each voter submits a ranking of the candidates (which is a total order over the set C).

The voting setting also includes a voting rule, which is a function from the set of all possible combinations of votes to the set of candidates. We shall discuss the voting rules related to scoring rules. Whenever the voting rule is based on scores, the candidate with the highest score wins.

Examples of voting rules based on scores are [START_REF] Lev | Convergence of Iterative Voting[END_REF]:

• Plurality: Each voter assigns a point to the preferred candidate and the candidate who receives the largest score wins;

• Veto: Each voter "vetoes" a candidate and the candidate that is vetoed by the fewest voters wins;

• Borda: Given m candidates, each voter gives a ranking of all candidates, the j-th ranked candidate score is m -j, and the candidate with largest sum of score wins.

Let the scores x = (x 1 , x 2 , . . . , x M ) be a vector of nonnegative integers such that x 1 ≥ x 2 ≥ . . . ≥ x M . For each voter, a candidate receives x 1 points if it is ranked first by the voter, x 2 if it is ranked second, etc. The score s m of a candidate is the total number of points the candidate receives.

For example, for Plurality scoring rule we have x = (1, 0, . . . , 0), for Veto scoring rule we have x = (1, 1, . . . , 1, 0), for Borda scoring rule we have x = (m -1, m -2, . . . , 0), etc.

In the constructive coalitional weighted manipulation (CCWM) problem [START_REF] Zuckerman | Algorithms for the coalitional manipulation problem[END_REF], we are given a set C of candidates, with a distinguished candidate p ∈ C, a set of weighted voters S that already cast their votes (those are the truthful voters), and weights for a set of voters T that still have not cast their votes (the manipulators). We are asked whether there is a way to cast the votes in T such that p wins the election. The constructive coalitional unweighted manipulation (CCUM) problem is a special case of CCWM problem where all the weights equal 1 [START_REF] Betzler | Unweighted coalitional manipulation under the Borda rule is NP-hard[END_REF].

III. MAIN RESULTS

A. Unweighted manipulation

Consider M candidates and N voters. Every vote can be seen as a permutation of the vector of values

x = (x 1 , . . . , x M ) T
where x m ≥ 0, for all m ∈ {1, . . . , M } where we consider

x 1 ≥ x 2 ≥ . . . ≥ x M
and through translation and scaling without loss of generality we can assume that x 1 = 1 and x M = 0 so that

1 = x 1 ≥ x 2 ≥ . . . ≥ x M = 0.
We consider

σ n (x) = (σ n (x 1 ), σ n (x 2 ), . . . , σ n (x M ))
the permutation of x which gives the vote of voter n, for n ∈ {1, . . . , N }.

The final score for a candidate m ∈ {1, . . . , M }, denoted by s m , can then be written as

s m = N n=1 σ n (x m )
The total final score is denoted as

s = (s 1 , s 2 , . . . , s M ).
Since we are considering the constructive coalitional weighted manipulation (CCWM) problem, we assume that we know S ∈ N ∪ {0} votes and without loss of generality we consider that they are the votes of the first voters, i.e., σ 1 (x), σ 2 (x), . . . , σ S (x). We can then choose the remaining N -S votes σ S+1 (x), . . . , σ N (x).

We denote u the combined votes of the S known votes, i.e.,

u = S i=1 σ i (x m ) m∈{1,2,...,M}
Without loss of generality, we assume that our objective is to elect the first candidate, i.e., the distinguished candidate p corresponds to the first candidate c 1 . Thus, the first coordinate of the votes we can choose are given by

σ i (x 1 ) = 1 ∀S + 1 ≤ i ≤ N.
Since we are dealing with a scoring rule, it is always better to choose the maximum score to the distinguished candidate.

Therefore,

s 1 = u 1 + (N -S).
To see the differential, denoted by x, between the first candidate and all the other candidates of the known votes, we consider

x = u -s 1 ½,
where ½ = (1, 1, . . . , 1) is the m × 1 vector.

We notice that x1 = 0. Our objective is that xk < 0 for all k ∈ {2, . . . , M }. Equivalently, our objective is that there exists ε > 0 such that xk < -ε for all k ∈ {2, . . . , M }.

There are M ! possible permutations of x. If M is a small number, then we can enumerate the possible permutations in a matrix Â. We are thus looking for a vector α = (α 1 , . . . , α M! ) such that Âα ≤ 0 subject to the constraint that α • ½ = N -S.

We assume that we want more than the fact that ε is positive, we want to maximize ε such that Âα < -ε½ in order to maximize the differential with the second closest candidate. or equivalently, by defining A = -Â the constraint becomes Aα > ǫ This is an integer linear programming given by

max ε Aα > ǫ α • ½ = N -S α ∈ AE ∪ {0}.

B. Weighted manipulation

A weight function is a mapping w : V → N. When voters are weighted, the above rules are applied by considering a voter of weight ℓ to be ℓ different voters. The method to convert the weighter manipulation problem to an integer linear programming is similar to the previous method and thus we do not repeat it here.

IV. SIMULATIONS

In this section, we show an example of our integer linear programming approach applied to a voting system, based on Borda voting rules, with four candidates. Then, we generalize generalize the previous approach to any number of candidates and we present the proposed algorithm.

A. Four candidates

Consider that we have 4 candidates, denoted A, B, C and D. The voting rule is Borda, which means that for each vote, the favorite candidate will receive a score of 3, the second favorite candidate will receive a score of 2, the third favorite candidate, a score of 1, and the last favorite candidate will receive a score of 0. Through the transformation of translation and scaling we obtain that it is equivalent to the fact that the scores are given by (1, 2/3, 1/3, 0).

Let us suppose that the total number of votes is 120000 and that the manipulator votes are 25% of those, i.e., 30000 votes.

Consider that we know the remaining 90000 truthful votes:

• 15000 are B > C > A > D • 15000 are B > D > C > A • 30000 are C > D > A > B • 30000 are D > A > B > C
And consider that we want to make the first candidate to win the election, i.e., candidate A. Following the algorithm proposed in the previous section, the first step is to compute the current scores of each candidate.

It is easy to see that the scores are given as follows:

A = 30000 * (2/3) + 45000 * (1/3) = 35000 B = 30000 * (1) + 30000 * (1/3) = 40000 C = 30000 * (1) + 15000 * (2/3) + 15000 * (1/3) = 45000 D = 30000 * (1) + 45000 * (2/3) = 60000.

According to the previous algorithm, the manipulator votes will always start with A, so the final score for A will be

s A = 35000 + 30000 = 65000
The difference between the final score and the current scores of B, C, and D are 25000, 20000, and 5000 respectively.

Since we have imposed that the favorite candidate of the manipulator votes is A, these votes can only be

A > B > C > D A > B > D > C A > C > B > D A > C > D > B A > D > B > C A > D > C > B.
We are looking for the number of votes of each type, that we denote α 1 , α 2 , α 3 , α 4 , α 5 , α 6 respectively.

The system of equations then becomes

α 1    1 2/3 1/3 0    + α 2    1 2/3 0 1/3    + α 3    1 1/3 2/3 0    + α 4    1 1/3 0 2/3    + α 5    1 0 2/3 1/3    + α 6    1 0 1/3 2/3    ≤    30000 25000 20000 5000    .
with equality for the first equation, under the constraints α 1 , α 2 , α 3 , α 4 , α 5 , α 6 ≥ 0 and α 1 , α 2 , α 3 , α 4 , α 5 , α 6 ∈ Z.

This system of equations can be analyzed for a standard mixed integer linear program using as objective function the function 0. We used the software R, in a i7 machine using Ubuntu 12.04 and the time it took to make the computation was 2 ms.

B. Any number of candidates

We can generalize the previous analysis to consider any number of candidates.

The algorithm is as follows:

Under the algorithm described above, we have done a Montecarlo simulation. The simulation consisted on a Borda election with increasing number of candidates (from 4 to 9 candidates) with 100 votes, 20 of which were manipulated and 80 Algorithm 1 ILP CCWM Add the constraint from the column of A and the vector x 9: until we reach the last column of A 10: Set lower bound to be zero 11: Set the solution to be integer 12: Solve the integer linear program 13: Return the list of votes needed (if they exist) truthful votes. We run the simulation 100 times and we present the mean, the minimum and the maximum computational time (in seconds) of the simulations (see Figure 1).

V. CONCLUSIONS

In the present work, we have considered voting systems which can be expressed as scoring rules. In particular, we have analyzed the coalitional weighted manipulation problem and we have provided an integer linear programming approach to solve it. The approach allows us to solve in some milliseconds a problem which is known to be NP-hard.

Fig. 1 .

 1 Fig. 1. Computational time (in seconds) vs No. of candidates.

  1: Compute the combined votes of the S known votes, denoted u 2: Compute the score of the distinguished candidate p 3: Compute the differential between the score of the distinguished candidate and the combined votes of the S known votes, denoted x 4: Compute all the permutations of votes in a matrix A 5: Create a linear program with m! variables 6: Set the objective function to be zero 7: repeat

	8:

ACKNOWLEDGMENT

The work presented in this paper has been partially carried out at LINCS (http://www.lincs.fr).