Dominique Marie

Florence Le Gall

Roseline Edern

Priscillia Gourvil

Daniel Vaulot
email: vaulot@sb-roscoff.fr

Improvement of phytoplankton culture isolation using single cell sorting by flow cytometry

Keywords: Flow cytometry, Single cell sorting, BSA, Picoeukaryotes, Nanoeukaryotes, Antibiotics, Microalgal cultures, Phytoplankton BSA, Bovine Serum Albumin, AMT, Atlantic Meridional Transect, PNS, Penicillin-Neomycin-Streptomycin, RCC, Roscoff Culture Collection, FSC, Forward Scatter, SSC, Side Scatter, DCM, Deep Chlorophyll Maximum, PCR, polymerase chain reaction

Flow cytometry provides a tool to physically sort single algal cells in order to obtain clonal cultures. During sorting, cells are submitted to physical stress factors such as high fluidic pressure, exposure to the laser beam, electrostatic charges, deflection through high voltage fields and collisions with container surfaces. All of these can damage the cells of interest and success rates for initiation of cultures from flow-sorted cells are generally very low. We found that the addition of Bovine Serum Albumin (BSA) in the culture medium into which cells are sorted drastically improved the success of initiation of pico-and nano-eukaryotic phytoplankton strains. Adding a mixture of antibiotics (PNS: Penicillin, Neomycin, Streptomycin) to the medium in order to slow down bacterial growth further improved culture development. This approach was successfully used to isolate taxonomically diverse strains, including novel taxa, from a fresh sample obtained in the English Channel and from enrichment cultures established during an Atlantic Meridional Transect (AMT) cruise. We anticipate that these improvements will be useful to clone or purify existing cultures and to isolate novel cultures from oceanic samples.

Introduction

In the context of the rapid development of metabarcoding and metagenomics approaches to characterize marine microbial communities [START_REF] De Vargas | Eukaryotic plankton diversity in the sunlit ocean[END_REF][START_REF] Sunagawa | Structure and function of the global ocean microbiome[END_REF], ex situ laboratory cultures are absolutely critical to provide reference sequences for marker genes such as 18S or 16S rRNA [START_REF] Guillou | The Protist Ribosomal Reference database (PR2): a catalog of unicellular eukaryote Small SubUnit rRNA sequences with curated taxonomy[END_REF], Decelle et al. 2015) or for genomes or transcriptomes [START_REF] Keeling | The Marine Microbial Eukaryote Transcriptome Sequencing Project (MMETSP): illuminating the functional diversity of eukaryotic life in the oceans through transcriptome sequencing[END_REF], thereby facilitating annotation of the massive datasets obtained. Many phytoplankton taxa are available in culture [START_REF] Del Campo | The others: our biased perspective of eukaryotic genomes[END_REF]), but culture isolation relies mostly on traditional approaches such as serial dilution or single cell pipetting [START_REF] Andersen | Traditional microalgae isolation techniques[END_REF]. Novel methods are necessary to increase the diversity and number of microalgal strains available in culture.

Flow cytometry provides a rapid method for analysis of planktonic cells in both cultures and natural samples. Flow cytometry has been widely used to assess the abundance of autotrophic and heterotrophic oceanic microorganisms for over three decades [START_REF] Olson | Marine phytoplankton distributions measured using shipboard flow cytometry[END_REF][START_REF] Marie | Flow cytometric analysis of phytoplankton, bacteria and viruses[END_REF][START_REF] Zubkov | Flow cytometric enumeration of DNAstained oceanic planktonic protists[END_REF]). Some flow cytometry instruments are equipped with devices that allow sorting of cells based on their physical and biological characteristics. Flow cytometry sorting has been successfully applied to recover natural populations for genetic and genomic characterization [START_REF] Shi | Groups without cultured representatives dominate eukaryotic picophytoplankton in the oligotrophic South East Pacific Ocean[END_REF][START_REF] Woyke | Assembling the marine metagenome, one cell at a time[END_REF][START_REF] Rinke | Insights into the phylogeny and coding potential of microbial dark matter[END_REF], as well as for physiological measurements such as their capacity to fix carbon [START_REF] Jardillier | Significant CO2 fixation by small prymnesiophytes in the subtropical and tropical northeast Atlantic Ocean[END_REF].

However, this technique has relatively rarely been used to bring novel microorganisms into culture [START_REF] Sensen | The production of clonal and axenic cultures of microalgae using fluorescence activated cell sorting[END_REF][START_REF] Sieracki | Automated isolation techniques for microalgae[END_REF][START_REF] Sinigalliano | Viable cell sorting of dinoflagellates by multiparametric flow[END_REF][START_REF] Cho | Novel approach for the development of axenic microalgal cultures from environmental samples[END_REF], one reason for this being the generally low level of recovery of viable cultures after sorting.

Using 14 C-uptake, [START_REF] Rivkin | Effects of flow cytometric analysis and cell sorting on photosynthetic carbon uptake by phytoplankton in cultures and from natural populations[END_REF] showed that the passage of cells through a flow cytometer induces physiological damage to phytoplankton cells that results in a decrease in growth rate during the first days following sorting. These authors associated cell damage to high laser power, but found no effect of sheath fluid, droplet charging or sorting. [START_REF] Haugen | Effects of flow cytometric analysis on morphology and viability of fragile phytoplankton[END_REF] did not find any physical damage or cell lysis due to fluidics or the laser beam, but reported a lag in growth for up to 48 hours after sorting, suggesting physiological damage. [START_REF] Sieracki | Automated isolation techniques for microalgae[END_REF] found higher recoveries when sorting single cells into 24-rather than 96well plates. However, while recovery of sorted Isochrysis, Rhodomonas, Scrippsiella and Thalassiosira varied from 22 to 99%, single-cell sorting failed for the picoplanktonic green microalga Micromonas. [START_REF] Sinigalliano | Viable cell sorting of dinoflagellates by multiparametric flow[END_REF] found that the trauma due to automated cell sorting was not a limiting factor for obtaining unialgal dinoflagellate cultures compared to manual micropipetting. These reports emphasize the large taxon-specific variability in cell recovery after flow cytometry sorting.

The Roscoff Culture Collection (RCC) is one the largest service collections of marine microalgal cultures [START_REF] Vaulot | The Roscoff Culture Collection (RCC): a collection dedicated to marine picoplankton[END_REF]). In the last decade, we have placed considerable focus on using flow cytometry sorting to isolate unialgal cultures from natural samples (e.g. [START_REF] Gall | Picoplankton diversity in the South-East Pacific Ocean from cultures[END_REF][START_REF] Balzano | Diversity of cultured photosynthetic flagellates in the North East Pacific and Arctic Oceans in summer[END_REF]), but cell recovery has always been very low, especially when sorting single cells to obtain clonal cultures. In most cases, therefore, we have used flow cytometry sorting for cell enrichment rather than for single cell isolation. We have tested a range of solutions to try to obtain higher cell recovery such as lowering laser beam intensity, changing sheath pressure or deflection voltage, or adding chemicals such as EDTA that trap bivalent cations or Pluronic F68 that prevents adhesion of cells to the surfaces of plastic culture vessels [START_REF] Marie | An improved protocol for flow cytometry analysis of phytoplankton cultures and natural samples[END_REF]. None of these attempts improved cell recovery in a consistent way (Marie, unpublished data).

In the present study we developed and tested a new protocol for strain isolation based on single cell sorting in culture medium supplemented with Bovine Serum Albumin (BSA) followed by antibiotic addition after a few days. This protocol was developed on cultures from the RCC and then tested on a fresh sample from the English Channel off Roscoff and on enrichment cultures obtained during an Atlantic Meridional Transect (AMT) cruise. In the latter case, we compared flow cytometry sorting with more classical strain isolation approaches (serial dilution and enrichment).

Materials and methods

Cultures.

Five strains from different taxonomic groups were obtained from the Roscoff Culture Collection (RCC, www.roscoff-culture-collection.org): Micromonas pusilla RCC299 (Mamiellophyceae), Florenciella sp. RCC1008 (Dictyochophyceae), Isochrysis sp. RCC90 (Prymnesiophyceae), Rhodomonas baltica RCC350 (Cryptophyceae) and Scrippsiella sp. RCC4108 (Dinophyceae). Cultures were grown in K medium [START_REF] Keller | Media for the culture of oceanic ultraphytoplankton[END_REF]) in 12:12 hour light:dark cycle and were sorted when in exponential growth phase.

Oceanic samples. Surface seawater from the English Channel was sampled in May 2015 at the Estacade Station in Roscoff [START_REF] Guilloux | An annotated checklist of Marine Phytoplankton taxa at the SOMLIT-Astan time series off Roscoff (Western Channel, France): data collected from 2000 to 2010[END_REF]. A larger set of samples was obtained in 2014 during the Atlantic Meridional Transect (AMT, [START_REF] Rees | 20 Years of the Atlantic Meridional Transect-AMT[END_REF] cruise # 24 at two depths (surface and deep chlorophyll maximum, DCM). Twenty-two stations were sampled in the Atlantic Ocean between the United Kingdom and the Falkland Islands (Table 1 and Fig. 1). Precultures were obtained by adding 1 mL of L1 culture medium to 25 mL of seawater sample.

Pre-cultures were maintained on board at 20°C in a L:D cycle and were transported promptly back to Roscoff at the end of the cruise.

Flow cytometry.

A FACS Aria flow cytometer (Becton Dickinson, San Jose CA) equipped with 488 and 633 nm lasers and a standard filter setup was used for cell sorting. In order to minimize the impact of the laser, only the 488 nm laser was employed. Acquisition was triggered on red fluorescence, Forward Scatter (FSC) and Side Scatter (SSC) with the minimum threshold value.

Sorting was performed in "single cell" mode using 20 PSI as sheath pressure. An Accuri C6 (Becton Dickinson, San Jose CA) equipped with a CSampler was used to monitor cell concentration after flow cytometry sorting. Acquisition was triggered on red fluorescence and performed for 1 min at a rate of 65 µL/min.

Microscopy. An inverted microscope (Olympus IX71) equipped with epifluorescence (blue light excitation, red light emission) was used to detect the presence of photosynthetic cells in wells into which 1 cell was sorted. When cells with chlorophyll fluorescence were observed in a well, it was considered as positive for culture growth.

Effect of BSA concentration on cultures. RCC cultures were sorted into 1 mL of K medium either without BSA or with BSA (Ref A7030, Sigma) at concentrations of 0.01, 0.1 or 0.5%.

Typically one 48-well plate (CytoOne, Starlab) was used for each culture: 1000 cells (500 for Scripsiella) were sorted into 3 wells and 1 cell into each of the remaining 45 wells. Using the Accuri C6, cell concentration was monitored over 2 weeks for the wells containing 500 or 1000 cells after sorting. Wells with 1 cell were monitored by epifluorescence microscopy between days 3 and 14 following sorting.

Effect of antibiotic addition. RCC cultures were sorted into 48-well plates (CytoOne, Starlab) containing 1 mL of K medium supplemented with 0.01% BSA. For each culture 500 (Scripsiella) or 1000 (other strains) cells were sorted into 6 wells containing 1 mL of K medium. Three days after sorting, a mixture of Penicillin, Neomycin and Streptomycin (PNS, Ref P4083, Sigma) was added at a final concentration of 0.1% to 3 of the wells. Cell concentration was subsequently monitored by flow cytometry for 2 weeks.

Effect of medium on sorting for a natural sample.

Surface water from the English Channel (see above) was filtered through a 50 µm nylon mesh in order to remove larger cells that can clog the flow cell of the cytometer. Four media supplemented with BSA 0.01% were tested: K (Keller et al. 1987), f/2 (Ref G9903, Sigma, Guillard and[START_REF] Guillard | Studies of marine diatoms. I. Cyclotella nana Husdedt and Detonula confervacea Gran[END_REF], water from the sampling site supplemented with K medium nutrients (SW+Nut) and not supplemented (SW). All media were filter-sterilized through a 0.2 µm filter just before sorting. Two 48-well plates containing 1 mL of medium per well were used per media tested, one for pico-and one for nano-phytoplankton. The first 3 wells were used to sort 1000 cells for the pico-phytoplankton and 500 cells for the nano-phytoplankton, respectively. One cell was sorted in each of the remaining 45 wells. Three days after sorting, PNS 0.1% (final concentration) was added into all wells with 1000 or 500 sorted cells and cell concentration was monitored over 2 weeks by flow cytometry (Fig. 2). Wells with 1 sorted cell were monitored by epifluorescence microscopy every three days for 2 weeks following sorting. When live cells were observed in a well, PNS 0.1% (final concentration) was added. Ten diatom strains isolated during this experiment were kept in culture and incorporated into the RCC.

Oceanic strain isolation. Three different isolation approaches were compared using precultures obtained during the AMT 2014 cruise (see above): flow cytometry sorting, enrichment and serial dilution.

For flow cytometry sorting, 24 AMT pre-cultures were sorted in 1 mL of K medium with 0.01% BSA into 48-well plates (Table 1). Half a plate was used for each population selected: 1000 cells were sorted into the first two wells, 100 into the next two wells as controls and 1 cell into the remaining 20 wells. Plates were incubated in a,12:12 light:dark cycle for 10 days. Wells were then screened by inverted epifluorescence microscopy to detect the presence of photosynthetic cells. When live cells were observed in the wells with 1 sorted cell, they were transferred into a tube containing 5 mL of K medium supplemented with a final concentration of 0.1% PNS.

For enrichment, AMT pre-cultures were screened and counted by flow cytometry. When the pre-culture seemed to contain only one population of cells, the isolation technique used was an enrichment in the appropriate culture medium. This technique was used for 19 pre-cultures from AMT (Table 1). We used K medium for eukaryotes and PCRS11 medium [START_REF] Rippka | Prochlorococcus marinus Chisholm et al. 1992 subsp. pastoris subsp. nov. strain PCC 9511, the first axenic chlorophyll a2/b2-containing cyanobacterium (Oxyphotobacteria)[END_REF] for cyanobacteria.

For dilution, AMT pre-cultures were screened and counted by flow cytometry. Fifteen precultures that contained several cell populations with different sizes and chlorophyll signals were diluted into K medium in 48-well plates. Eight wells were used for each pre-culture with a final target density of 10 cells per well (Table 1). Plates were incubated in a 12:12 light:dark cycle for 3 weeks, after which an inverted epifluorescence microscope was used to check for the presence of cells.

Strain characterization.

Strains were characterized by sequencing partially the 18S rRNA gene. The cells were heated for 5 min at 95°C and cooled to 4°C. The 18S rRNA gene was amplified by polymerase chain reaction (PCR) using the eukaryote specific primers 63F/1818R [START_REF] Lepère | Whole Genome Amplification (WGA) of marine photosynthetic eukaryote populations[END_REF]) and the Phusion Master Mix (Thermo Fisher Scientific, France). For PCR, a 5 minute initial denaturation step at 95°C was followed by 35 cycles including 1 min of denaturation at 95 °C, 90 sec of annealing at 57°C and 90 sec extension at 72°C. The PCR program was finished by a final extension of 10 min at 72°C followed by cooling at 4°C. PCR products were purified using Exosap (USB products, Santa Clara, USA). Partial 18S rRNA gene sequences were determined by using Big Dye Terminator V3.1 (Applied Biosystems, Foster city, CA, USA) and the internal primer Euk 528f [START_REF] Elwood | The small-subunit ribosomal RNA gene sequences from the hypotrichous ciliates Oxytricha nova and Stylonychia pustulata[END_REF]. Sequencing was carried out on an ABI prism 3100 sequencer (Applied Biosystems). Partial 18S rRNA sequences were compared to those available in public databases with NCBI BLAST (blast.ncbi.nlm.nih.gov/Blast.cgi).

All AMT strains and 10 strains isolated from the English Channel have been deposited in the Roscoff Culture Collection (RCC4548 to RCC4579 and RCC4657 to RCC4666, respectively) and their sequences deposited in GenBank under accession numbers KX014627-KX014660.

Results

Effect of BSA addition.

We first tested the effect of adding BSA at different concentrations (0, 0.1, 0.01 and 0.05 %) to the culture medium into which cells were sorted using 5 strains of eukaryotes (Fig. 2 and Table 2).

For the picoplanktonic strain Micromonas pusilla (Mamiellophyceae) RCC299, we observed a rapid decline in cell concentration for the 3 wells with 1000 sorted cells in the absence of BSA and no live cells were detected by flow cytometry after 5 days of incubation (Fig. 2A). After 8 days, cells were detected in 2 of the 3 wells. In presence of BSA, no lag phase or decline in cell numbers were observed. Initial growth rates were identical for the three BSA concentrations tested, but after 5 days of incubation better growth was obtained at the lowest BSA concentration (0.01%). Epifluorescence microscope observations of wells into which 1 cell was sorted (Table 2) revealed the absence of cells in the absence of BSA, 100% recovery with 0.01% BSA, and 50 to 60% recovery with 0.1 and 0.5%, respectively.

In the absence of BSA and at the two lowest BSA concentrations (0.01 and 0.1%), the other picoplanktonic strain Florenciella sp. RCC1008 (Dictyochophyceae) decreased in abundance during the first week and no cells were detected 10 days after sorting (Fig. 2B). Between days 10 and 14, cell abundance recovered slowly. In wells with the highest BSA concentration (0.5%), cell abundance did not decrease significantly and we observed exponential growth after day 7 (Fig. 2B). For single sorted cells of this strain, no recovery was detected at the lowest BSA concentration (0.01%). In the absence of BSA and at 0.1% BSA, 1 and 2 wells, respectively, exhibited growth after 2 weeks. In wells with the highest BSA concentration (0.5%), growth was detected in 7 out of 9 wells at day 14 (Table 2).

BSA did not affect growth of the nanoplanktonic strains Isochrysis sp. RCC90 (Prymnesiophyceae) and Rhodomonas baltica RCC350 (Cryptophyceae) (Fig. 2C andD). For Isochrysis, growth was observed after day 5 in some wells with 1 cell and all wells had growing cultures by the end of the experiment for all BSA concentrations (Table 2). For Rhodomonas, growth was observed in almost all wells at day 3 (Table 2).

For Scrippsiella sp. RCC4108 (Dinophyceae), a small decrease in cell number was observed immediately after sorting of 500 cells in the absence of BSA (Fig. 2E). However, growth rate was very similar in all four conditions. After day 7, cell number was highest with BSA 0.01% and lowest with BSA 0.1%. No effect of BSA was observed for single sorted cells of this strain.

The maximum number of wells with detectable growth was obtained on day 3 in the absence of BSA (5/9) and there was no evolution in the number of positive wells past day 7 (Table 2).

Effect of antibiotic treatment.

For cultures sorted into medium with 0.01% BSA, growth stopped after 4 days for Scrippsiella and 7 days for Micromonas and Rhodomonas in the absence of the antibiotic cocktail (PNS), while cultures continued to grow when PNS was added (Fig. 3). Isochrysis had a higher growth rate in the absence of PNS reaching stationary phase earlier than with PNS, although after 2 weeks cell yield was similar. For Florenciella, addition of PNS resulted in significant cell loss, but cultures recovered one week after sorting to reach a higher final density than in the absence of PNS (Fig. 3).

Recovery and isolation of phytoplankton sorted from a fresh seawater sample

Wells into which 1000 picoeukaryote cells were sorted had similar growth rates irrespective of the medium, but final cell concentration was lower in f/2 and unamended seawater (Fig. 4A).

Single picoeukaryote sorted cells began to grow in some wells after 3 days and the percentage of wells with detectable growth after 2 weeks was highest using f/2 medium, reaching almost 100%, followed by amended SW, SW and K medium for which recovery was only 50% (Table 3). After 9 to 15 days, approximatively 70% of wells containing f/2 or SW with nutrients and only 30% for SW or K medium were dense enough to allow transfer to tubes containing 4 mL of K medium. All strains obtained from single cell sorting (Table 4) were Chlorophyta representing two classes, the Mamiellophyceae (Micromonas, Ostreococcus and Bathycoccus) and the Trebouxiophyceae (Picochlorum). The highest number of different genera was obtained using f/2 medium and the lowest in unamended seawater.

No difference in growth rate was observed after sorting 500 nanoeukaryote cells in different media, but after 6 days, cell numbers were significantly higher in wells with f/2 and SW+Nut (Fig. 4B). Heterogeneity in cell numbers was observed among the 3 wells in all media. As for picoeukaryotes, cells were detected in some single-cell wells after only 3 days (Table 3) and the number of wells with detectable growth did not increase beyond day 9. More than half of the wells yielded growth and this proportion was highest with SW (71%) and lowest with K, as was the case for picoeukaryotes. Strains obtained from single cell sorting were mostly small-(Minidiscus, Minutocellus) or medium-sized (Thalassiosira, Skeletonema, Cylindrotheca) diatoms, or the common prymnesiophyte Phaeocystis (Table 4). The largest variety of genera was obtained using amended SW and the lowest using K, as was the case for picoeukaryotes.

Isolation of phytoplankton strains from oceanic enrichments

During AMT cruise #24, from the UK to the Falkland Islands, two depths (surface and DCM) were sampled at a range of stations in the Atlantic Ocean from temperate to equatorial environments. During the cruise, pre-cultures were obtained by adding L1 medium to natural samples and these pre-cultures were promptly brought back to the laboratory at the end of the cruise. Single-cell flow cytometry sorting was applied to 24 pre-cultures using K medium with 0.01% BSA, yielding a total of 700 wells (Table 1). After 10 days of incubation, phytoplankton growth was observed in 278 (40%) wells. The percentage of wells with growth varied with the pre-culture, ranging from 0% to 100% (Table 1). Positive wells were transferred into tubes containing 5 mL of K medium supplemented with a final concentration of 0.01% PNS.

In parallel, we prepared 120 wells by serial dilution from 15 pre-cultures (8 wells per preculture) with a target concentration of 10 cells per well. After 3 weeks of incubation, 39 (33%) wells showed positive growth (Table 1). As for sorting, the success rate was variable, again ranging from 0 to 100% depending on the pre-culture (Table 1). Cells from positive wells were transferred into tubes using K medium for eukaryotes and PCR-S11 for cyanobacteria. Finally, a simple enrichment approach was performed on nineteen pre-cultures using different media and sixteen cultures were isolated in this manner.

Genetic characterization of the AMT strains using the 18S rRNA gene revealed that many cultures belonged to the same genus. For cultures obtained either by flow cytometry sorting or dilution, all tubes originating from the same pre-culture and obtained with the same technique yielded identical sequences. For example, the 36 positive wells originating from pre-culture 04 (Table 1) were all affiliated to Phaeocystis. When we obtained the same affiliation with the 3 techniques of isolation, we decided to prioritize maintenance of the cultures isolated by flow cytometry sorting because these strains were more likely to be clonal. In total, 31 representative cultures were deposited to the RCC, corresponding to 11 different genera (Table 5). The highest diversity was obtained with cell sorting, but some taxa were only obtained by dilution or enrichment (Table 6). The genera isolated from the largest number (8) of pre-cultures (Table 6) belonged to Pelagophyceae (Pelagomonas) and Cyanophyceae (Synechococcus), although the latter were only isolated by dilution or enrichment since only eukaryotes were targeted by sorting. Strains isolated from more than one pre-culture belonged to the Chlorophyta (Micromonas, prasinophyte clade VII), Prymnesiophyceae (Phaeocystis, Emiliania, Isochrysis) and Pelagophyceae. Finally some strains were only isolated from a single pre-culture. This was in particular the case for RCC4570, the 18S rRNA sequence of which was affiliated to the Heterokontophyta.

Discussion

Isolation of phytoplankton strains from oceanic waters is a difficult task because many taxa have unknown nutritional requirements or are quickly outcompeted by fast growing species.

For small cells (pico-and nano-phytoplankton), the most common approach involves serial dilution (Andersen and Kawachi 2005) using media such as K which have been specifically designed for oceanic strains [START_REF] Keller | Media for the culture of oceanic ultraphytoplankton[END_REF]). However, this strategy is blind and provides random results since no specific group is targeted. For example, during the BIOSOPE cruise in the South East Pacific, serial dilution resulted in isolation of 34 strains of Pelagomonas calceolata (Le [START_REF] Gall | Picoplankton diversity in the South-East Pacific Ocean from cultures[END_REF]), but did not recover any of the dominant taxa in this region that belong to the haptophyte, chrysophyte and prasinophyte clade IX lineages [START_REF] Shi | Groups without cultured representatives dominate eukaryotic picophytoplankton in the oligotrophic South East Pacific Ocean[END_REF]).

The theoretical advantages of flow cytometry include the possibility of targeting specific groups based on their size and chlorophyll content, as well as the capacity to isolate single cells, resulting in clonal cultures. The former factor should allow elimination of fast growing species that tend to be over-represented when using other techniques. However, as outlined above, success rates for culture recovery have been very low for single cell flow cytometric sorting.

While trying different additions to sorting medium, we discovered that BSA had a spectacular impact on cell recovery. The reason for the positive effect of BSA is unclear. Albumin is a major protein from bovine or human serum, with multifunctional properties and is widely used for mammalian cell cultures [START_REF] Francis | Albumin and mammalian cell culture: implications for biotechnology applications[END_REF]. It is well known as a strong antioxidant and has also been proved to avoid attachment of cells onto plastic walls [START_REF] Fletcher | The effects of proteins on bacterial attachment to polystyrene[END_REF]. BSA is also often added when preparing protoplasts from macroalgae (e.g. [START_REF] Bodian | Evaluation of the in vitro methods for micropropagation of Chondracanthus acicularis (Roth) Fredericq (Gigartinales, Rhodophyta): Tissue culture and production of protoplasts[END_REF].

Unfortunately, no detailed study on its effect or role on cell culture has been published. Of the five strains tested in the present study belonging to a range of phylogenetic groups, the nanoplanktonic strains Isochrysis, Rhodomonas and Scrippsiella recovered well after sorting and BSA did not seem to have a significant effect except in the case of Scrippsiella for which the lag phase was reduced with BSA addition (Fig. 2C-E andTable 2). In contrast, the picoplanktonic species Micromonas and Florenciella could not recover after sorting without the addition of BSA (Fig. 2A-B and Table 2), confirming the report of [START_REF] Sieracki | Automated isolation techniques for microalgae[END_REF] who did not obtain any growth of Micromonas when sorting 1 cell per well. With addition of BSA, we obtained 100% regrowth of Micromonas (Table 2). Interestingly, the optimum BSA concentration varied with the species. While concentrations below 0.5% had no effect on Florenciella (Fig. 2 and Table 2), 0.01% was optimum for Micromonas (Fig. 2 andTable 2). This suggests that it will be necessary to test different BSA concentrations when dealing with specific cultures or natural populations. In particular, Florenciella, which apparently requires a high BSA concentration to facilitate regrowth after single cell sorting, has rarely been isolated into culture: there are only 11 strains isolated from 3 cruises available in culture collections (all in the RCC).

When using flow cytometry to sort phytoplankton cells from natural samples, heterotrophic bacteria are also likely to be sorted since they often outnumber phototrophic cells by an order of magnitude. Although flow cytometry has been used to produce axenic cultures [START_REF] Sensen | The production of clonal and axenic cultures of microalgae using fluorescence activated cell sorting[END_REF], it is difficult to completely remove associated bacteria, especially those that adhere to the surface of microalgal cells [START_REF] Surek | CCAC -Culture Collection of Algae at the University of Cologne: A new collection of axenic algae with emphasis on flagellates[END_REF], and antibiotics are often necessary to obtain axenic cultures [START_REF] Cottrell | Production of axenic cultures of Micromonas pusilla (Prasinophyceae) using antibiotic[END_REF]. Even when axenic cultures are not targeted, antibiotic treatment may be critical to reduce competition for nutrients from bacteria. This was apparently the case for Micromonas, Rhodomonas and Scrippsiella which stopped growing after a few days in the absence of antibiotics, while growth continued when PNS was added (Fig. 3A,D,E). The case of Florenciella was paradoxical. Addition of PNS led to an initial decrease of cell concentration which then recovered after day 7, while in the absence of PNS initial growth was continuous but final cell density was ten times lower. This could be explained by Florenciella being mixotrophic, as reported for field populations [START_REF] Frias-Lopez | Use of stable isotopelabelled cells to identify active grazers of picocyanobacteria in ocean surface waters[END_REF]. The initial decrease of the population when antibiotics were added could therefore be due to the decrease in bacterial prey density, followed by a switch to autotrophic nutrition inducing regrowth.

Another factor to take into account during isolation of phytoplankton strains is the composition of the culture medium. Very few studies have assessed the effect of different media on the success of culture isolation or even on culture growth. [START_REF] Harrison | Marine Culture Media[END_REF] quoted McLachlan (1973): "Numerous enriched and synthetic media have been formulated, which together with generally trivial modifications, almost equal the number of investigators". The two most commonly used media for marine microalgae are f/2 [START_REF] Guillard | Studies of marine diatoms. I. Cyclotella nana Husdedt and Detonula confervacea Gran[END_REF] and K [START_REF] Keller | Media for the culture of oceanic ultraphytoplankton[END_REF]. The effect of these two media along with unamended and amended sea water was tested using a fresh sample from the English Channel (Tables 3 and4) . For picoeukaryotes, the use of f/2 resulted in the widest diversity of strains, while for nanoeukaryotes differences were less marked. This could be explained by the fact that f/2 is more appropriate for coastal species [START_REF] Keller | Media for the culture of oceanic ultraphytoplankton[END_REF]. However, some species, such as Ostreococcus, Phaeocystis, Minidiscus and Thalassiosira, were always isolated irrespective of the medium used. Our approach allowed isolation from a single sample of three picoplanktonic genera, Micromonas, Ostreococcus and Bathycoccus, that are dominant in English Channel coastal waters as demonstrated previously both by fluorescent in situ hybridization (FISH) and 18S rRNA clone libraries [START_REF] Not | A single species Micromonas pusilla (Prasinophyceae) dominates the eukaryotic picoplankton in the western English Channel[END_REF][START_REF] Romari | Composition and temporal variability of picoeukaryote communities at a coastal site of the English Channel from 18S rDNA sequences[END_REF][START_REF] Marie | Use of flow cytometric sorting to better assess the diversity of small photosynthetic eukaryotes in the English Channel[END_REF]). The nanoplanktonic species isolated were mostly diatoms reflecting the fact that the sample was taken during the spring diatom bloom [START_REF] Sournia | A daily study of the diatom spring bloom at Roscoff (France) in 1985. I. The spring bloom within the annual cycle[END_REF].

Our protocol proved to be efficient for obtaining clonal strains from pre-cultures established during an Atlantic cruise. In particular, we repeatedly obtained strains of Pelagomonas and prasinophyte clade VII, both of which are typically isolated from oceanic tropical and subtropical waters (Le [START_REF] Gall | Picoplankton diversity in the South-East Pacific Ocean from cultures[END_REF]. We obtained strains of several taxa that, to our knowledge, have not previously been cultured. Within prasinophyte clade VII, we obtained for the first time a representative of clade VIIB3 (Lopes dos Santos et al., submitted). In addition, three Pelagophyceae cultures corresponded to undescribed taxa. The 18S rRNA sequences of two Pelagophyceae strains from the tropical Atlantic (RCC4562 and RCC4563) matched with 100% identity the sequence of RCC1024, previously isolated from the South East Pacific (Le [START_REF] Gall | Picoplankton diversity in the South-East Pacific Ocean from cultures[END_REF]). These strains are also related to the endosymbiont of the tropical dinoflagellate Amphisolenia bidentata [START_REF] Daugbjerg | Using nuclear-encoded LSU and SSU rDNA sequences to identify the eukaryotic endosymbiont in Amphisolenia bidentata (Dinophyceae)[END_REF]. Strain RCC4552, isolated from the temperate North Atlantic, had a sequence only 98.7% similar to any other GenBank sequence and probably corresponds to a novel species. Its sequence was most closely related to RCC2505, isolated from polar waters [START_REF] Balzano | Diversity of cultured photosynthetic flagellates in the North East Pacific and Arctic Oceans in summer[END_REF]. The 18S rRNA sequence of RCC4570, a stramenopile strain obtained by dilution, was related to two strains (RCC853 and RCC862) that had been previously isolated from the South East Pacific (Le [START_REF] Gall | Picoplankton diversity in the South-East Pacific Ocean from cultures[END_REF]), but unfortunately lost since. This group of sequences suggests the existence of a novel algal class, called MOCH-5 by [START_REF] Massana | Exploring the uncultured microeukaryote majority in the oceans: reevaluation of ribogroups within stramenopiles[END_REF]. As evident from Table 1, the success of the three approaches we used (sorting, dilution, enrichment) was highly variable. In several cases only one technique was successful for a given pre-culture: for example, strains were obtained by dilution but not sorting for pre-cultures 26 , 27 and 42, whereas the opposite result was obtained for pre-cultures 54 and 55.

The novel protocol proposed for culture isolation using single-cell flow cytometry sorting has several advantages compared to other techniques for culture isolation. It is much more rapid than serial dilution. A 48-well plate can be sorted in less than 1 minute. Results are obtained in less than 10 days, compared to at least three weeks for serial dilution. More importantly, specific populations can be targeted. For example, many of our AMT serial dilution wells produced untargeted Synechococcus cultures, while sorting targeted only eukaryotes. Flow cytometry sorting is best done on fresh samples since the diversity of the taxa recovered is high and more representative of the initial diversity, as demonstrated for an English Channel sample obtained near our laboratory from which we isolated at least 10 different taxa. However, this requires the availability of a bulky sorting flow cytometer near the sampling site or on the cruise.

An alternative strategy for large scale cruises is to enrich samples to obtain pre-cultures. This can be done many different ways, without or with filtration in order to select specific size classes, without or with tangential flow filtration which allows concentration of samples, or with a range of different media and additives, such as germanium dioxide to prevent diatom growth [START_REF] Vaulot | The Roscoff Culture Collection (RCC): a collection dedicated to marine picoplankton[END_REF][START_REF] Gall | Picoplankton diversity in the South-East Pacific Ocean from cultures[END_REF][START_REF] Balzano | Diversity of cultured photosynthetic flagellates in the North East Pacific and Arctic Oceans in summer[END_REF]). In such cases, since there can be a long delay before the pre-cultures can be sorted, each pre-culture usually becomes dominated by one or two species. Single-cell sorting allows rapid purification and cloning of these pre-cultures as demonstrated for the AMT cruise. Since diversity is typically rather low for a given pre-culture, a relevant strategy to obtain different taxa in culture is to apply sorting to a large number of pre-cultures originating from different stations and depths (Table 5).

Another useful application of this protocol would be to make existing cultures clonal. We recently applied this approach to clone RCC strains of Micromonas, Ostreococcus, Bathycoccus and Triparma (PG, unpublished data). It can also be used to purify mixed cultures, in which case there is no need to perform single cell sorting; sorting of several hundred cells for each target population should provide good results.

Gordon Moore Foundation (MMI EMS grant #4972). The publication reflects the views only of the author, and the European Union cannot be held responsible for any use which may be made of the information contained therein.

Figure 1 :

 1 Figure 1 : Cruise track of Atlantic Meridional Transect # 24 in 2014 with the location of sampled

Figure 2 :

 2 Figure 2: Effect of the concentration of BSA on the recovery of RCC cultures after sorting of

Figure 3 :

 3 Figure 3: Evolution of cell concentration for 1000 cells of Micromonas pusilla RCC299 (A),

Figure 4 :

 4 Figure 4: Concentration of pico-and nano-eukaryotes (A and B, respectively) from a natural

Table 2 :

 2 Evolution over two weeks of the numbers of positive wells (out of a total of 9 wells) 543 observed by epifluorescence on an inverted microscope after single-cell flow cytometry sorting 544 for 5 RCC cultures. Cells were sorted into 1 mL of K medium with BSA at different 545

	546	concentrations.

Table 3 :

 3 Percentage of positive wells (out of 45 wells) obtained from single cell sorting by flow cytometry of picoeukaryotes and nanoeukaryotes into four different media from a natural sample from the English Channel off Roscoff taken in May 2015.

					Day
	Population	Medium	3	6	9	12	15
	Picoeukaryotes	SW	33%	47%	51%	62%	69%
		SW+Nut	33%	56%	71%	78%	80%
		f/2	24%	84%	98%	98%	98%
		K	7%	22%	36%	49%	51%
	Nanoeukaryotes	SW	27%	60%	69%	69%	71%
		SW+Nut	18%	60%	67%	67%	67%
		f/2	20%	51%	60%	60%	60%
		K	16%	33%	47%	49%	49%

Table 4 :

 4 Comparison of the taxonomic identity of cultures isolated by single cell flow cytometry sorting of picoeukaryotes and nanoeukaryotes into four different media of a natural sample from the English Channel off Roscoff taken in May 2015.

					Medium
	Division	Class	Genus	SW	SW+Nut	f/2	K
					Picoeukaryotes
	Chlorophyta	Mamiellophyceae	Ostreococcus X	X	X	x
	Chlorophyta	Mamiellophyceae	Micromonas		X	X	X
	Chlorophyta	Mamiellophyceae	Bathycoccus			X
	Chlorophyta	Trebouxiophyceae	Picochlorum			X
					Nanoeukaryotes
	Heterokontophyta Coscinodiscophyceae Minidiscus	x	x	x	x
	Heterokontophyta Coscinodiscophyceae Thalassiosira x	x	x	x
	Haptophyta	Prymnesiophyceae	Phaeocystis	x	X	x	x
	Heterokontophyta Mediophyceae	Minutocellus	x	x
	Heterokontophyta Mediophyceae	Unk nown		x	x
	Heterokontophyta Bacillariophyceae	Cylindrotheca x			x

Table 5 :

 5 List of cultures isolated from the AMT transect by single-cell flow cytometry sorting, 558

	559	serial dilution and enrichment.

Acknowledgments

We thank Monica Moniz and Dave Scanlan from Warwick University for providing samples from the AMT 2014 cruise #24 as well as Ian Probert for his help improving the English language. Financial support for this work was provided by the European Union's 7th

Framework Programme MaCuMBA project (FP7-KBBE-2012-6-311975) and the Betty and

List of Tables 533

Table 1 : List of pre-cultures obtained during the Atlantic Meridional Transect (AMT) cruise 534 #24 in 2014 with station number, date and depth. Columns indicate whether enrichments were 535 established from pre-cultures (see Material and Methods), the number of single-cell flow 536 cytometry sorted wells and the number of dilution wells. For flow cytometry sorting, the type 537 of population sorted is indicated (P for picoeukaryotes and N for nanoeukaryotes). The number 538 and percentage of positive wells obtained by the two techniques is also indicated. The position 539 of the stations is provided in Fig. 1


Jean Marc

Linareric Anthierens

Jean Michel Sprauel

Synthesis of Tolerancing by Functional Group

Keywords: Functional Tolerancing, Tolerancing Modeling, Tolerancing Analysis, Vectorial Tolerancing, Mechanical Design

This paper presents a systematic tolerancing method based on a new modeling concept called Functional Group. The tolerancing method is composed of two types of tolerancing: (1) "internal tolerancing" limits assembly errors due to the overabundance of contact points between two surface groups and (2) "external tolerancing" places one surface group next to the other. First, several tolerancing methods are presented from the literature. The small displacement screw (SDS) method is also described because it represents a very important investigation tool. Then the concept of the functional group is proposed for the tolerancing of mechanical systems. Finally, this new systematic method is implemented with an actual example in which functional tolerancing is easily carried out.

Introduction

Worldwide industrial competition obliges the mechanical manufacturing industries to be quickly adaptive. The levels in quality, price, and delivery time desired by customers are becoming more and more significant, and the manufacturing process has to be very reactive to ensure reliability, productivity, and flexibility along with cost control. Companies remain competitive when they control their whole industrialization process by taking into account the product and the manufacturing process. This imposes good coherence between the different functions such as design, manufacturing, and so on.

A method is needed to share information and to ensure coordination between several participants with different goals and different reference systems. The design phase is crucial because at this point about 75% of the final cost of the product is decided on. Because it is not possible to manufacture any parts perfectly due to the unavoidable inaccuracy of the manufacturing process, it is necessary to develop a computation method and tolerancing method that are coherent. The tolerancing method should share the errors between the different functions suitably.

State of the Art

Methods of Tolerancing

The geometric data computed by CAD software are considered as surfaces (BRep: boundary representation), and CAD software is based on modeling by features. For the Pro/ENGINEER@ software (Parametric Technology Corp. 1994), the feature data are saved in an assembly neutral file and a part neutral file. Each surface is written with parameters in the local coordinate system (0, el, e2, e3) placed in relation with the general coordinate system. Thus, the principal vector and one point of the surface are known. Each surface that needs an intrinsic attribute for its parametric definition gets further data such as radius and angle. Information on the methodical assembly arrangements of the surfaces is also saved in this file. CAD software usually proposes a specific module to help users with dimensional computation. The method based on technologically and topologically related surfaces (TTRS) [START_REF] Clement | Theory and practice of 3D tolerancing for assembly[END_REF] is used for a module developed by the CATIA software [START_REF] Gaunet | 3D functional tolerancing and annotation: CATIA tools for geometrical specification[END_REF].

The VSA software of Applied Mechanical Solutions is based on a statistical simulation used to calculate the limits of the tolerance zone. The assembly of surfaces is rebuilt to model the behavior of the whole system. The CE/TOL6o software of Raytheon operates on assembly issues and provides solutions for tolerancing. This software is associated with Pro/ENGINEER. Numerous works on these topics can be classified according to three main types of approaches.

Vectorial Tolerancing

This approach is certainly the most widespread today. In this method (Wirtz 199 1,Liu and Wilhelm 200 l), surfaces are represented by one point and oriented by a vector. Two further vectors are usually used to describe the size and the form of the considered surface.

Several research groups have investigated the writing of tolerancing in a kinematics point of view [START_REF] Rivest | Tolarancing a solid model with a kinematic formulation[END_REF][START_REF] Sacks | Parametric kinematic tolerance analysis of planar mechanisms[END_REF]. Each condition is represented by a set of 14 parameters of the kinematics model.

Several methods are based on the small displacement screw (SDS) method. SDS is the result of many investigations in 3-D metrology. The TTRS method provides a vectorial tolerancing [START_REF] Gaunet | Vectorial tolerancing model[END_REF]. UPEL (weighted addition of clearance) is a method used to manage free spaces for 3-D mechanisms [START_REF] Teissandier | Three dimensional functional tolerancing with proportioned assemblies clearance volume: Application to setup planning[END_REF]). Usually, the SDS only transcribes errors of position and orientation. A new concept of the SDS takes into account the variation of the intrinsic parameters of surfaces (radius of a cylinder, angle of a cone). So these variations are included in the vectorial equations [START_REF] Ballot | A computational method for the consequences of geometrical errors in mechanisms[END_REF].

Space of Feasibility

The spaces of feasibility are a graphical representation of inequalities defined in the space of parameters by tolerancing [START_REF] Turner | A feasibility space approach for automated tolerancing[END_REF][START_REF] Bhide | Area1 coordinates: The basis of a mathematical model for geometric tolerances[END_REF]. Other methods based on a graphical resolution by simplex are available to model clearances between two surfaces. The result obtained is a hyperspace called "clearance space." This six-dimension hyperspace is composed of six parameters of the SDS. Each assembled part is considered as rigid with no defects on the surface [START_REF] Giordano | Clearance space in volumic dimensionning[END_REF]). The union and the crossing between these hyperspaces permit the user to solve the assembly problems.

Among numerous investigations on this topic, the computation methods employed in robotics (Jacobian matrix) (Ben&, Pino, Fortin 1999) or computation on polytops with the Minkowski sum (Teissandier, Delos, Couetard .I 999) or the method of noninterference space between two parts [START_REF] Sangho | Verification of assemblability between toleranced parts[END_REF] are certainly the most used.

Tolerancing by Variation Class

A proposition for tolerancing is based on the offset zone [START_REF] Requicha | Toward a theory of geometnc tolerancing[END_REF][START_REF] Wayne | Offset of two dimensional profiles[END_REF][START_REF] Kethara | Curves for profile tolerance zone boundaries[END_REF]. Several works show the difference between this concept and the norm, ANSI Y14.5. In the 1990s other propositions suggested its evolution [START_REF] Farmer | Tolerance technology computer based analysis[END_REF]Galdman 1986, Etesami 1991). Several investigations are close to the American norm, ANSI Y 14.5M [START_REF] Srinivasan | Recent efforts in mathematization of ASME/ANSI Y 14SM standard[END_REF].

This paper presents the results of studies on the functional tolerancing developed to be implemented in CAD software. These advances are based on the concept of the systematic approach, and the mathematical tool used for modeling is the small displacements screw (SDS). This work can be classified in vectorial tolerancing.

Small Displacements Screw (SDS)

A mathematical description of the SDS method is presented below. SDS is used to describe the geometric errors of the surfaces. The displacement ;iM of the point M to the point M' can be defined by the transformation matrix written with homogeneous coordinates in a coordinate system called (0, e,, e,, e3). The three angles and one translation vector make the displacement ( If the three rotations are small enough, the trigonometric functions can be linearized to the first order. Also, the matrix is simplified: A matrix is developed to the first order. In this case, the multiplication of matrices can be replaced by the sum of the translation vector, DO, and the vector obtained_ by the vectorial product between the rotation vector, Q, and the vector of position, 5, as follows:

0 -a3 a2
I ul -ya, + za2 &I= u,+xa,-za, =B,+fir,od ug -xa2 + ya,
The SDS is composed of both vectors (translation, 6, , and rotation, fi): the surface errors (Figure 2). The spatial representation of the surface defects is easily permitted with this concept. The rotation vector represents the orientation error, and the translation vector represents the localization error of the cylinder in the coordinate system (0, el, e2, s>.

Tolerancing Method by Functional Group

Surface errors are considered independent from one another. The errors of the elementary surfaces are computed parameters in the local coordinate system. In a second phase, the surface

Modeling of Internal Behavior of Functional Group Principle

To carry out the tolerancing of a geometric element correctly, it is necessary to take into account only six errors (three rotations and three translations). Several hypotheses are considered:

??
The errors of the surface (flatness...) are negligible in comparison with other geometric errors (1), ??

The parts are rigid. The mathematical tool used to model errors is the SDS [START_REF] Requicha | Toward a theory of geometnc tolerancing[END_REF]) (see Figure 5).

In the example, the two functional groups are composed of a plane and a cylinder. The error number is 7 (4 + 3) whereas the mechanical joint can only accept five errors (see Figure 6). Therefore, several errors should be simultaneously limited (2 errors).

That means there are five parameters of external toler-an&g and two parameters of internal tolerancing in this functional group. This tolerancing is minimal and sufficient. Surfaces of a same functional group can be divided into three classes according to their function in the mechanical joint:

??
Principal su@ke: it guides and imposes the orientation and principal position of the functional groups.

??

Secondary surjhce: it completes the localization and the orientation between the two functional groups.

??

Unspecified sur$zces: they usually contribute to the assembly of the different parts.

Preponderant plane

Preponderant cylinder

Figure 7

Principal Surface

The orientation of the part mounted on this surface group is given by the normal vector of the plane. A circle can also model the cylinder. Nevertheless, the geometric errors of the cylinder must be saved.

In the case where the functional group is composed of a plane and an orthogonal cylinder, two different issues can be considered according to sizes and clearances, as shown in Figure 7.

Translation and rotation parameters have been integrated into a composed translation parameter. Also, cylinder rotation o2 is included in UIcI1, and cylinder rotation o1 is included in U,,,,. When the functional group is toleranced, external tolerancing is limited to only five errors. CQ and o2 are not limited in this tolerancing; they should be limited in the internal tolerancing. Thus, the perpendicularity of cylinder C 11 needs to be imposed in relation with plane P 11. This requirement can be transcribed with the maximum material condition for the cylinder because the diameter of C 11 and its orientation in relation to P 11 have an effect on the interface between both parts. This interface screw represents the behavior of the assembly of both functional groups.

(A) Plane is preponderant (Figure 8). That means:

(B) Preponderant cylinder (Figure 9). That means:

??

Length-to-diameter ratio of the cylinder is ??

Length-to-diameter ratio of the cylinder is very low, very large, ??

Clearances between both parts are high.

??

Clearances between both parts are low. (Figure 20), Frame 3 (Figure 21). This part is placed in both flows F2 and F3. The tolerancing of both functional groups integrated in both flows is identical: NB: tolerancing is the same for the groups of surfaces 31' and 31".

Processing of Flow 1: After computation of F 1 and F2, the external behavior of FG52 composed of FG52' and FG52" is the result of the combination of the external behavior of FG52' and FG52". This is different from the processing of the F2 and F3 flows. The diagram in Figure 22 can also model Flow 1.

Gear (Figure 23): In this phase of study, the pitch cone of the gear should be positioned in relationship with the functional group 52 or 12. Composition rules of both functional groups belonging to the same part are useful to carry out this tolerancing.

It is noted that it is possible to suggest another tolerancing for the gear using the common zone notion of norm IS0 (Figure 24) without changing the functional significance of each surface. The quality of the datum surface FG52 is guaranteed by this tolerancing. This common zone notion permits the tolerancing to be simplified. The constraint between Cy152" and Cy152' in Figure 19 is deleted (Figure 25).

Through the same process as that used for gears, the results in Figure 26 are obtained.

Conclusion

The approach presented is based on a systematic approach. The functional group concept carries out a structured analysis of tolerancing for mechanical systems. This method avoids obtaining a very high number of requirements linked to the same function. The notion of internal hierarchy allows three single composition laws (transformation, integration, and

  Figure I _ Displacement dM

Figure

  Figure 2 uI, II*, q, a, Geometrical Errors of the Cylinder

  Figure 3 Coordinate Systems

  Figure 4 Example

  To explain the tolerancing methodology, refer to the example of Figure4in which the tolerancing of the surface groups (P 11, C 11) and (C 12, P 12) is proposed. The (C 12, P 12) group is the datum. The part and the two surface groups are represented by the graphic format of the functional group. The behavior model of the functional group represents the interface of the surface group, which is in contact with another part.

  Figure 5Plane Small Displacement Screw

  Figure 8Preponderant Plane

um=lJs+u~,+u.g&

Integration changing its effect. A rotation error can be transformed tolerances limit the position errors and the orienas a translation error and vice versa. This operation has tation errors of the surface (Do and fi vectors) no effect on internal tolerancing.

(Figure 12).

(b) S2 error integration (Figure II): Uk = Zt+ Error integration involves from 1 to N-1 internal specifications @I is the number of integrated errors). This operation has an effect on external tolerancing and on the interface model.

(c)

S3 overabundance of errors An overabundant error of a secondary surface (in comparison with a higher level surface) must be limited through internal tolerancing.

Tolerancing of Internal Behavior

The vectorial description is used to model the surface errors. Hypothesis (1) allows writing the tolerancing based on the IS0 norm (IS01 101). Af-ler having calculated the equations of the internal behavior, the geometric parameters can be identified that should specify the tolerances of the surfaces in a qualitative way.

The orientation tolerances limit the angular errors of the surface ( fi vector). The localization overabundance) to be implemented. These operations provide an internal organization of the different surfaces according to their participation in performing the function. This method can also generate equations that characterize the interface between two functional groups.

This method allows the designer to write the tolerance of parts in several ways. Moreover, this method is now being extended to take into account systems with clearances in interfaces.

Authors' Biographies

Dr. Jean Marc Linares studied manufacturing technology at the Ecole Normale Supkrieure de Cachan, earning a PhD in 1996. He works in the EA(MS)' Laboratory at the Universiti de la MtiterranCe in Aix-edrovence.